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A Validation, Comparison and Automation of Different

1. A Validation Comparison and Automation of Different Computational Tools for Propeller Open Water Predictions Master of Science Thesis Olof Klerebrant Klasson Department of Shipping and Marine Technology Division of Sustainable Ship Propulsion CHALMERS UNIVERSITY OF TECHNOLOGY Goteborg Sweden 2011 Report No X 11 264 A THESIS FOR THE DEGREE OF MASTER OF SCIENCE A validation comparison and automation of different computational tools for propeller open water predictions Olof Klerebrant Klasson Department of Shipping and Marine Technology CHALMERS UNIVERSITY OF TECHNOLOGY G teborg Sweden 2011 A Validation Comparison and Automation of Different Computational Tools for Propeller Open Water Predictions Olof Klerebrant Klasson O Olof Klerebrant Klasson 2011 Report No X 11 264 Department of Shipping and Marine Technology Chalmers University of Technology SE 412 96 G teborg Sweden Telephone 46 0 31 772 1000 Printed by Chalmers Reproservice G teborg Sweden 2011 11 A validation comparison and automation of different computational tools for propeller open water predictions OLOF KLEREBRANT KLASSON Department of Shipping and Marine Technology Chalmers University of Technology Abstract Open water
2. 43 Proceedings of the Boundary Element Method 45 Open Water Tests of the Analysed Propellers 45 Cavitation Measurement of the SMP 11 Propeller 46 Automation of the Pre and Post processing 46 5 3 1 The Pre processing 46 5 3 2 The Post processing 47 Proceedings of the Lifting Line Method 49 Proceedings of the Wageningen Series 51 Open Water Prediction of the SMP 11 Propeller 51 Viscous Scale Effects Correction 51 Automation of the Pre and Post processing 51 Automation of Extrapolation to Full Scale 52 Results nn 2020 eneen nnn nnneen en nnne ee enneneee en ncceeesnee 53 Results from the SMP 11 Propeller 53 8 1 1 Case 2 1 The Open Water Test 53 8 1 2 Case 2 2 Velocity Field Measurement
3. 59 8 13 Case 2 2 Cavitation Tests 66 Open Water Results from CPP 1 69 Open Water Results from CPP2 73 The four Methods in Comparison 78 8 5 The Final Performance of the CFD Automation 81 8 6 The Final Performance of the Boundary Element Automation 83 8 7 The Final Performance of the Lift Line Automation 84 8 8 The Final Performance of the Wageningen Automation 84 9 Conclusions and Future Work gt nana 87 10 References amm 89 1 Introduction 1 1 Background In propeller design there are a variety of tools to be used for early predictions of the performance At Berg Propulsion AB Berg there are several alternatives among these tools and it might be difficult to know when to use which tool Some of the tools also have extensive setup times The limitations of the tools are to some extent investigated but no comparison between the tools has been performed at Berg A better understanding of which open water calculation tool that has to be used for a given situation is therefore useful The accuracy of numerical tools such as the boundary
4. 1 The SMP 11 propeller geometry in 3D representation Fig 3 1 1 Case 2 1 Open Water Test The open water test was carried out in a pull configuration The hub was designed to avoid a pressure build up see Fig 3 2 25 Fig 3 2 open water hub with a design that avoids a pressure build up The test was performed in the SVA towing tank The tank had a breadth of 9 m the depth was 4 5 meters and the shaft was submerged with 0 375 m The propeller was placed in the lateral centre of the tank A slide test was performed A principal sketch of the slide with propeller shaft blades and hub is show in Fig 3 3 Fig 3 3 The sled with propeller shaft blades and hub Before the open water test the pressure probes were calibrated using only the rotating hub and the nose cap Hence the results are considered to be solely generated by the propeller blades Table 3 2 shows the operating conditions of the open water test Table 3 2 The operating conditions for the SMP 11 open water test Water density for T 17 5 C kg m 998 67 Kinematic viscosity of water for T 17 5 C m s 1 07E 06 Rate of revolutions 1 5 15 Advance Velocity m s 2 25 5 25 The results for comparison were Kr and Kg at J 0 6 1 4 with an interval of 0 2 20 3 1 2 Case 2 2 Velocity Field Measurements The velocity field measurement was performed in the SVA Pot
5. 26 3 1 3 Case 2 3 Cavitation Tests 28 The Propeller for the Single Screw Vessel CPP 1 29 The Propeller for the Twin Screw Vessel CPP2 29 Computer Resources 30 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 7 1 Haz 71 3 7 4 8 1 8 2 8 3 8 4 Proceedings of CEFD 31 Open Water Test of the SMP 11 Propeller 31 Velocity Field Measurement of the SMP 11 Propeller 35 Post Processing of the SMP 11 Propeller 36 Automation of the Pre processing 37 4 4 1 Geometrical Cleanup and Domain Definition 37 4 4 2 The meshing template 39 4 4 3 Surface Mesh 41 4 4 4 Layers and Volume Mesh 41 Open Water Test of CPP1 42 Open Water Test of CPP2
6. 66 F and PHIW at 0 for case 2 3 1 are shown in Fig 8 27 The same distributions but for case 2 3 2 and 2 3 3 are shown in Fig 8 28 and Fig 8 29 These distributions vouch for converged and reliable results The smooth distribution of Fy implies that the load is evenly distributed over the blade radius with a maximal load at approximately 0 7 lt r R lt 0 85 which is expected since the pitch is highest in this region The smooth distribution of PHIW suggests that the wake panels are correctly distributed and well described Fx for Phi 0 000 vs r R At J 1 025000 Phiw for Phi 0 000 vs r R At J 1 025000 0 190 0 300 0 170 0 270 0 150 0 240 ppo 0 210 Gaai 0 180 0 090 g Ors bas E 0120 0 070 pa 0 050 0 060 0 030 0 030 0 010 0 000 0 300 0 400 0 500 0 600 0 700 0 800 0 900 1 000 0 300 0 400 0 500 0 600 0 700 0 800 0 900 1 000 Radius Fraction r R Radius Fraction r R er E Fig 8 27 F distribution to the left and PHIW to the right at 0 for case 2 3 1 Fx for Phi 0 000 vs r R At J 1 278000 Phiw for Phi 0 000 vs r R At J 1 278000 0 120 0 200 0 110 0 180 0 100 0 160 pta 0 140 0 080 0 070 0 120 x 0 060 0 100 0 050 0080 0 040 0 060 0 030 cn 0 040 0 010 omen 0 000 0 000 0 300 0 400 0 500 0 600 0 700 0 800 0 900 1 000 0 300 0 400 0 500 0 600 0 700 0 800 0 900 1 000 Radius Fraction r R Radius Fraction r R er A E Fig 8 28 F distribution to the left and PHIW to the right
7. Surface roughness um 0 00003 The propellers were meshed in accordance with Lloyd s and PROCAL developer s recommendations see section 2 3 2 The tip spacing was set to 0 3 and the TE spacing to 0 06 times the recommended value This was since experience and previous validation studies have shown to give good results with these settings The velocity was set to match the reasonably high load 0 5 Jy may A steady analysis was performed and the wake panel and axial force radial distribution were studied If the curves showed reasonably smooth distributions and the Kutta condition was converged the solution was considered trustworthy The Kutta condition was set to 0 001 and the jacobian disturbance value was set to 0 0001 for all cases If the solution wasn t trustworthy the trailing edge spacing tip spacing and tip chord fraction were altered Great care was laid on getting the last trailing edge element skew angle to be sufficient This angle should be in the interval 5 lt p lt 30 and preferably as close to 30 as possible This angle is mostly affected by changing the tip chord fraction When the mesh was good enough the open water test could be performed by simply inserting the proper speeds matching the model test i e V4 JnD If the solution was trustworthy for all advance velocities the solution was considered converged Table 5 2 shows the final open water mesh setups for the SMP 11 propeller CPP1 and CPP2
8. Comparison Coarse and Fine CFD mesh CFD_Course CFD Fine 0 T T 1 0 6 0 8 1 2 1 Advance Ratio J Fig 8 3 A comparison between the coarse and the fine mesh for the CFD simulation of the SMP 11 propeller Table 8 1 A comparison between the coarse and the fine mesh for the open water simulation of the SMP 11 propeller Kt coarse Kt fine Kq coarse No coarse 0 624 1 431 0 416 0 504 1 190 0 540 0 392 0 970 0 643 0 287 0 770 0 712 54 The y values at the blades for the coarse and the fine mesh is presented in Table 8 2 They differ more between the fine and the coarse mesh than the forces The prism layers were of the same size in orthogonal direction to the wall for both meshes On the other hand the surface mesh resolution on the blades was higher for the fine mesh y is proportional to the rate of change in normal direction to the wall of the velocity parallel to the wall 1 e m u y dy 25 With more points to measure the gradients at the wall the difference might be explained Table 8 2 The y values at the blades for the coarse and fine mesh at corresponding advance ratios y coarse The axial velocity distribution of the open water test at J 0 6 is visualized in Fig 8 6 J 0 6 was the lowest advance ratio tested for the SMP 11 propeller As can be seen quite an amount of water is sucked in fron
9. 4 6 Open Water Test of CPP2 CPP2 was used to validate the script and standard configuration presented in section 4 4 The script worked very well First the clean blade button was pushed The blade was intersected with the blade foot using the procedure described in Appendix D The pitch was changed in the same way as for CPP1 The blade foot was intersected to the hub in accordance with Appendix D After this the makeSurfaceMesh button was pushed Everything except the surface mesh at leading edge was meshed This was fixed in accordance with the procedure described in Appendix C Finally the layersAndVolumeMesh button was pushed resulting in a complete volume mesh with the proper PID names One problem was that since the propeller was smaller than the propeller used to write the script and the surface mesh resolution was static the number of cells was fewer for this propeller This rises as stated no significant impact on the results Therefore the propeller was tested with the smaller mesh size to save some CPU hours The pitch was checked in accordance with the method in section 4 5 and it matched the model test pitch setting The propeller was tested at J 0 0726 to J 0 9461 with a step size of 0 1452 The resulting mesh can be seen in Table 4 12 Table 4 12 The number of cells for the open water test of CPP2 Element type Cells Surface mesh elements 117000 Prism layer elements 584000 Total elements 4849000 43
10. 19 Since the lift isn t constant over the whole foil the constant lift is divided into discrete piecewise constant vortex segments Summing these vortex segments will form a lifting line of varying vorticity These vortex segments will now be referred to as elements to keep the analogy in accordance with the panel and CFD methods The vortex strengths of the elements are determined at a number of collocation points through which there is no flow There will be one collocation point for each element so that the result is a linear system of equations that can be solved numerically When the vortex strengths are determined the velocities and pressures can be evaluated everywhere For a propeller the blades are represented by one lifting line for each blade The lifting line extends from the hub to the tip and ends with the horseshoe shape by trailing vortices One major concern for the lifting line methods is that it is unclear how the blade should end at the hub It is usual to use the hub less propeller assumption which means that the hub is neglected and that the vortices goes to zero at the tip Usually the lifting line methods result in unrealistic results near the surface of the hub and the blades This is often corrected after the computations in the programs The benefit of the lifting line method is that it is well known and thereby validated to a large extent Its limitations are well known and it takes rotative losses into a
11. 45 Table 5 2 The open water mesh setups in PROCAL for the SMP 11 propeller CPP1 and CPP2 Propeller Panels LE to TE 30 30 Panels Root to Tip 30 30 Spacing at LE 0 003 0 003 0 003 Spacing at TE 0 00126 0 00305 0 00400 Spacing at Root 0 00780 0 00302 0 00299 Spacing at Tip 0 003 0 003 0 005 Tip Chord Fraction 0 6 0 4 0 57 5 2 Cavitation Measurement of the SMP 11 Propeller For the cavitation analysis of the SMP 11 propeller PROCAL was used The cavitation prediction had to be preceded by an unsteady non cavitating prediction to determine the non cavitating Kr which was governing for the design point in accordance with Table 3 4 The mesh setup for the cavitation free analysis was the same as presented in Table 5 2 The analyzed number of revolutions was six and the number of steps between blades was twelve The speeds had to be altered to match the thrust identity This was done in the same way as for the velocity field measurement i e the linear relationship between J and Ky was used The atmospheric pressure was computed from the cavitation number using eq 5 1 18 Pa 0 5p nD oy Py pgH 5 1 Where pq the atmospheric pressure p the fluid density n number of revolutions per second D the propeller diameter o the cavitation number p the vapor pressure g 9 81 m s and H the propeller submergence Finally a cavitation mesh was set up When cavitation should be
12. Kt_Model a QKQ Model EJAo_Model 0 0 2 0 4 0 6 0 8 1 1 2 gt Advance Ratio J PROPULSION Fig 8 47 The open water chart predicted by the boundary element method in model scale compared to the model test results for CPP2 at 8 4 The four Methods in Comparison This section compares the four open water prediction methods between them based on the results presented in section 8 1 to section 8 3 An overlay plot of all the four methods with the prediction of Ky plotted against J for all propellers can be seen in Fig 8 48 As can be seen CFD is closest to the model test results The boundary element method BEM is quite close as well This is valid for all three propellers For the SMP 11 propeller the lifting line method LL is over predicted and the Wageningen Series WS is under predicted For CPP1 and CPP2 both WS and LL are under predicted The under prediction of them is most significant for CPP2 Overlay of Kt for the SMP 11 propeller bd Overlay of Kt for CPP1 0 1 0 3 0 Advance Ratio J A Lifting line BEM CD eS Wageningen a Model test 0 05 0 25 0 45 0 65 0 85 _1 05 Advance Ratio J Fig 8 48 An overlay plot of Kyr for all the four prediction methods An overlay plot of all the four methods with the prediction of 10K plotted against J for all propellers can be seen in Fig
13. These are the parameters that are changed by the user Some have more influence on the results and the convergence than the others Gridding guidelines found by the developers of PROCAL and Lloyd s Registry of Shipping are presented below The number of panels should be set in accordance with the skew angle of the blade Table 2 1 shows how the panel distribution should be Table 2 1 The panelling depending on skew as recommended by Lloyd s Registry of Shipping 28 Panels LE to TE root to tip 20x 20 25x25 30 x 30 35x 35 40 x 40 The leading edge spacing LEs is also determined based on the skew angle of the blade If the skew is larger than 35 LEs should be 0 001 LEs should be 0 004 if the skew is smaller than 25 Otherwise the LEs should be 0 003 Trailing edge spacing TEs is determined based on the skew angle in degrees and leading edge spacing see eq 2 16 TEs Skew LEs 0 15 2 16 The root spacing RS has upper and lower values yielding an interval The interval is determined based on TEs and LEs see eq 2 17 The value should preferably be as close to the minimum value as possible TEs LEs lt RS lt TEs 2 17 The tip spacing TS is determined from LEs propeller diameter D hub ratio E panels root to tip and tip chord fraction TC Again an interval is prescribed see eq 2 18 de Dx HheTC LEs D7 TC STS Sy ___ 2 18 7 panels LE to TE 18 Llo
14. As can be seen the velocity field looks much more intuitive The difference in Kg from the prediction compared to the model test could depend on that the velocity is very low in bollard 75 pull Kg is depending on the viscous forces to a large extent and at low velocities the viscous forces are even more pronounced Since a lot of flow assumptions are made on the viscous part a viscous dominated flow might be incorrectly predicted The results from the boundary element method at full scale compared to the model test results can be seen in Fig 8 44 The results are again very accurate It should be noted that Kg is slightly over predicted all the way Ky is slightly under predicted until J 0 4 and then slightly over predicted The open water characteristics after J ya 18 well predicted me Open Water BEM at Full Scale 7 0 8 0 7 0 6 0 5 0 4 Kt_Procal 10Kg_Procal ETAo_Procal KtModel s 1QKQ Model ETAo_Model Kt 10Kq n 0 0 2 0 4 0 6 0 8 1 1 2 Advance Ratio J PRETEN ADNE Fig 8 44 The open water chart predicted by the boundary element method compared to model test results scaled to full scale for CPP2 The results from the lifting line method compared to the model test results scaled to full scale for CPP2 can be seen in Fig 8 45 The difference is significant This most probably depends on the high skew of CPP2 the skew is 40 which is twice as much a
15. Fig 8 24 The velocity field at x D 0 1 downstream the SMP 11 propeller disc and results of 1 Vx V 65 8 1 3 Case 2 2 Cavitation Tests This section starts by showing the resulting non cavitating and cavitating mesh of the SMP 11 propeller It continues with discussing the validity of the setup and finally the results are shown The non cavitating mesh used for finding the thrust identity is shown in Fig 8 25 As can be seen the mesh is rather orthogonal everywhere which should yield reliable results The trailing edge spacing is reduced to capture the shape of the sharp knuckle at trailing edge Fig 8 25 The non cavitating mesh for the cavitational analysis The cavitation mesh is shown in Fig 8 26 This mesh is the same as the non cavitating mesh but with increased number of panels trailing edge to leading edge and decreased leading edge spacing Fig 8 26 The cavitation mesh for the cavitational analysis Table 8 4 shows the advance ratio needed to fulfill the non cavitating thrust identity for each of the three cavitation cases As can be seen the highest load occurs at case 2 3 1 Case 2 3 3 1s past the efficiency top point in the open water diagram c f Fig 8 5 meaning that pressure side cavitation could be expected Table 8 4 Velocities corresponding J and corresponding Kx to fulfill the thrust identity of the cavitation free condition for the three cavitation cases
16. 0 5103 0 6531 0 7988 0 9461 y OW Mesh 148 146 146 148 150 151 155 The axial velocity field at J 0 5103 is visualized in Fig 8 41 As can be seen it looks symmetrical and the velocity distribution is intuitive The PHIW and E distributions of CPP2 at 0 5 in the PROCAL open water prediction can be seen in Fig 8 39 As can be seen a small knuckle in the F distribution appears This is a result of the high unloading at the uppermost radial sections of CPP2 Experience says that this should have a small impact on the results Fx for J 0 582 vs r R Phiw for J 0 582 vs r R 0 260 0 140 0 240 0 220 0 120 0 200 0 180 0 160 0 140 0 120 0 100 0 080 0 060 0 020 0 040 0 300 0 400 0 500 0 600 0 700 0 800 0 900 1 000 0 300 0 400 0 500 0 600 0 700 0 800 0 900 1 000 Radius Fraction r R Radius Fraction r R F o 8 Phiw 0 040 Fig 8 39 F distribution to the left and PHIW to the right at 0 5 for CPP2 The results from CFD at full scale compared to the model test results can be seen in Fig 8 40 0 4 0 3 0 2 Kt 10Kq n Open Water CFD at Full Scale 0 9 0 8 oF Kt_CFD 0 6 10Kq_CFD 0 5 ETAo_CFD Ki Model QKq Model ETAo_Model 0 0 2 0 4 0 6 0 8 1 Advance Ratio J Fig 8 40 The open water chart predicted by CFD in full scale compared to the model test results scaled to full scale for CPP2 PROPULSION The
17. 8 49 Again it is noted that CFD gives the most accurate results for all propellers BEM slightly over predicts for all cases LL is highly over predicted for SMP 11 quite good for CPP1 and under predicted for CPP2 WS is really good for CPP1 and CPP2 and highly under predicted for SMP 11 78 Overlay of 10Kq for the SMP 11 0 6 0 8 1 Advance ratio J 1 2 Overlay of 10Kq for CPP2 PROPULSION Overlay of 10Kq for CPP1 0 44 0 39 0 34 0 29 D 24 0 19 0 14 0 09 0 04 0 1 0 3 0 5 Advance Ratio J PROPULSION 0 1 0 25 0 45 0 65 Advance Ratio J 0 85 PROPULSION Lifting line BEM ED SS Wageningen E Model test Fig 8 49 An overlay plot of 10Kg for all the four prediction methods An overlay plot of all the four methods with the prediction of 7 plotted against J for all propellers can be seen in Fig 8 50 Here all methods are quite accurate It should be noted that Jy may 18 predicted to appear later in LL for all propellers and a higher maximum efficiency is suggested This is also true in WS for CPP2 79 Overlay of n for the SMP 11 propeller Overlay of n for CPP1 0 7 0 6 0 5 N 0 4 0 3 0 2 0 1 1 2 0 1 0 3 0 5 0 7 Ele I Advance ratio J AdvanceRatio J aus Lifting line BEM
18. This page is intentionally left blank 44 5 Proceedings of the Boundary Element Method This section describes the proceedings of the boundary element method Section 5 1 starts with describing how the open water test was performed for all propellers together since this is the first step that has to be done for all analyses with the boundary element method Section 5 2 continues with a description of how the cavitation test for the SMP 11 was performed which was a part of exploring the functionality of the boundary element method A description of how the open water test was automated considering both pre and post processing is described in section 5 3 5 1 Open Water Tests of the Analysed Propellers The open water test for all the propellers using the boundary element method PROCAL was performed in the same way but of course with different parameters First the geometry file was extracted using a pre calculated Excel sheet with all the parameters given from the blade design workbook A new control file was made in PROCAL The operation conditions were set to full scale defaults in accordance with ITTC 78 for CPP1 and CPP2 see Table 5 1 The SMP 11 propeller was setup in accordance with the operating conditions in Table 3 2 Table 5 1 Default full scale operating conditions in PROCAL Water density kg m3 1025 Kinematic viscosity of water m s 1 14E 06 Atmospheric pressure Pa 102500 Vapour pressure Pa 1700
19. 0 330374721 0 675079783 0 8712 013871995 026912765 0 71469151 087 01093 0 2992 0 5456 08719 0 O omo 0872 0 139964689 0 27590675 0 703388677 0 3438 009874105 020819637 071240124 0 94 0 09908 0 2404 0 619 0 3461 0 or oro 0 9438 0 104148203 0220099314 0 710776724 1064 0 05591625 014292604 0 63286556 102 0 05809 01775 05295 10201 0 Da Divot 10164 0068206009 0163122422 0676384683 os Conver Model Test Topui _Plor Calculate Wageningen Full soa Elo E agerngenFulsoae Modeitestresuts Fulsoale a Pao oe Wageningen Ka Vageioge ETA Wagerirgen y ke WKQ ETA en Water PROCAL Wate aaorasoazoatzese a7vososee 007093890 oras ose3680 oaiesze 00707 os p E _Open Water Wageningen eee eee See ten ee eee eee a oa a 02178 042712543 0694136473 0213298735 0 2178 0475328 0 7044 0 233998 bs en ozas oaooeas2ne osssevones 0282978402 02303 0434813 0654275 0307635 a 0383 0372442969 OSINON 0349679252 03808 008504 OSOETOS 0376808 os os ahea Hes oane OMS OBTEN Osa 04358 035768 05155 0441058 tereien os a asoa oatatssce 0527456422 0477989674 asta O3m2Ds OSHSIN Oso a ewes oa 7 ioih recat o E sew 0279083 0460003 0552171 re prad m nab poca O 0591798737 asa otras osseze 08377 os a bed os 0726 0210918649
20. 58 The generated open water chart after pressing the plot button It should be noted that the mesh performed by the auto generated control files are just good guesses The results still need to be reviewed in PROCAL The radial axial force and wake panel distributions should be studied as well as the Kutta condition 8 7 The Final Performance of the Lift Line Automation The user has completed the propeller design In the open WaterResults sheet the wanted minimum maximum and step of advance ratio J is entered The lift line workbook is opened and the OW calculation button is pressed The Get Lift Line Results button is pressed in the design workbook and the results are loaded to the table in the same way as for the PROCAL results If a plot of the results is wanted the plot button is pressed and an open water chart appears on the screen 8 8 The Final Performance of the Wageningen Automation After insertion of the propeller design in the design workbook Jmax Juin and Jstep 15 inserted in the openWaterResults sheet The button Get Wageningen Results is pressed The model test as predicted by Wageningen appears in the table below the button If the results should be scaled to full scale the ITTC 78 button is pressed A table with the full scale Wageningen prediction is outputted below the button If any of the results should be plotted the plot button besides the table generating buttons should be pressed An open water chart is generate
21. CrD Overlay of n for CPP2 wane Wageningen Sass Model test 0 05 0 25 045 0 65 0 85 papos Advance Ratio J Fig 8 50 An overlay plot of n for all the four prediction methods The CFD method applied in OpenFOAM is very accurate regarding the open water predictions The only points differing from the model test results were in bollard pull and after Inma It Should be noted that OpenFOAM can be used for many other applications than just predicting the open water characteristics as seen in the SMP 11 results section A velocity field could be measured with accurate results as an example It is also always possible to see why the results differ e g the physical explanation of the separation after J In section 8 1 1 and the reason for the dissolved tip vortex at x D 0 2 in section 8 1 2 The largest drawback with CFD is the computational cost An open water chart with eight advance ratio steps takes about a week to analyse and the setup time can be quite extensive as well The boundary element method tool PROCAL is quite accurate It is not as accurate as CFD in predicting open water characteristics but it is rather close One drawback when comparing the open water characteristics predictions is that it was not possible to in a simple way just remove the hub from the results as in the CFD computation in section 8 1 1 This is the major drawback with PROCAL compared to CFD simulations outside t
22. The thick line represents the calculation and the thin fluctuating line represents the model test The velocity field measurement at radius R1 0 in plane x D 0 1 is plotted in Fig 8 20 This time all velocities seem well predicted The fluctuations appear here as well as in Fig 8 18 This should also depend on the convergence 63 PETC smp 11 Workshop Measurements of 5 blades 1 7 7 wr VaV Calculation VIV VAV VgV E Fig 8 20 The velocity field measurement results at R1 0 in plane x D 0 1 for the SMP 11 propeller with non dimensional axial tangential and radial velocities from the prediction plotted against the model test The thick line represents the calculation and the thin fluctuating line represents the model test The velocity field measurement at radius R1 0 in plane x D 0 2 is plotted in Fig 8 21 As for the other measurements at x D 0 2 the tendency is caught but the tip vortex is dissolved PPTC smp 11 Workshop Measurements of 5 blades 1 7 7 Var gt TRE Calculation TE TAs Pa OF SHUG AA A AR UAT PU AAA E LUV VV E 50 AS 40 35 30 25 20 15 10 5 0 5 10 15 20 er Fig 8 21 The velocity field measurement results at R1 0 in plane x D 0 2 for the SMP 11 propeller with non dimensional axial tangential and radial velocities from the prediction p
23. are discussed since they yield more setup sensitive results than the other methods Finally the results of CFD boundary element method lifting line method and Wageningen Series predictions are presented The final coarse and fine mesh for the open water test of the SMP 11 propeller are visualized with a centre plane cut in Fig 8 1 and Fig 8 2 As can be seen the most significant difference is the cell distribution The resolution close to the propeller and in the slip stream is significantly refined for the fine mesh The cells in the domain region are slightly larger for the fine mesh as well The cells close to the domain walls are slightly smaller than the free stream cells for both meshes This depends on the transition from the triads on the domain surface mesh to the hexahedrons in the free stream volume polyhedrons are usually smaller than structured hexahedrons Fig 8 1 The coarse mesh for the open water test 53 Fig 8 2 The fine mesh for the open water test The grid dependence comparison from J 0 6 to J 1 2 is presented in Table 8 1 The results are also plotted in Fig 8 3 The grid dependence is very small the result is almost unchanged between the two meshes The difference should depend on the discretization error and the resolution of the gradients in the slip stream The region around the propeller was also refined more in the fine mesh The gradients in this region should also affect the results to some extent
24. at y 0 for case 2 3 2 Phiw for Phi 0 000 vs r R At J 1 437000 Fx for Phi 0 000 vs r R At J 1 437000 0 160 0 090 0 080 quo 0 070 0 120 0 060 0 100 0 050 3 0 080 0 040 0 060 0 030 0 020 agii 0 010 0 020 0 000 0 000 0 300 0 400 0 500 0 600 0 700 0 800 0 900 1 000 0 300 0 400 0 500 0 600 0 700 0 800 0 900 1 000 Radius Fraction r R Radius Fraction r R Fig 8 29 F distribution to the left and PHIW to the right at y 0 for case 2 3 3 The zero degree position is characteristic for the rest of the radial results which hence would be inadequate to include The cavitation pattern predicted and a sketch of the model test results for case 2 3 1 can be seen in Fig 8 30 The cavitation pattern along the leading edge is over predicted a tendency that has been captured before 30 The blade root cavitation and the free stream cavitation were not captured in the prediction This could depend on the detachment mode of the solver In this calculation detachment was possible from leading edge until 0 8 times the chord length Another approach would be to start searching on the regions of minimum pressure The cavitating Kr was well predicted 67 Berg PROCAL KT 0 3760 Case 2 J 1 0193 Ky 0 3735 10Ky 0 9698 o 2 024 KT 0 3760 Berg PROCAL Fig 8 30 The cavitation pattern on the suction side predicted by PROCAL to the left and model test result to the right for case 2 3 1 The cavitation pattern predicted a
25. axial velocity field at J 0 4 is visualized in Fig 8 32 As can be seen it looks symmetrical and the velocity distribution is intuitive 69 Fig 8 32 Axial velocity field for CPP1 at J 0 4 The PHIW and F distributions of CPP1 at 0 5 may in the PROCAL open water prediction can be seen in Fig 8 33 As can be seen the distribution is smooth and the highest loads occurs at expected radial sections Fx for J 0 300 vs r R Phiw for J 0 300 vs r R 0 230 0 1504 0 2104 0 130 0 190 0 1104 0 1704 0 090 0 150 ES 0100 0 070 a 0 1104 baa 0 0904 0 0304 0 0704 0 010 7 r 1 r 1 0 050 r r r 0 200 0 300 0 400 0 500 0 600 0 700 0 800 0 900 1 000 0 200 0 300 0 400 0 500 0 600 0 700 0 800 0 900 1 000 Radius Fraction r R Radius Fraction r R Fig 8 33 F distribution to the left and PHIW to the right at 0 5 for CPP1 The results from CFD at full scale compared to the model test results can be seen in Fig 8 34 Open Water CFD at Full Scale o 0 8 0 7 0 6 T Kt_CFD oe 10Kg_CFD 204 ETAO_CFD 03 Kt_Model 0Kq_Model 0 2 ETAo_Model 0 1 0 0 0 2 0 4 0 6 0 8 1 BEAG Advance Ratio J 0 PE SHEN Fig 8 34 The open water chart predicted by CFD in full scale compared to the model test results scaled to full scale for CPP1 70 As can be seen the simulation is very accurate Kg differs a little bit in bollard pull which is discuss
26. behaviour of a propeller is an important indication of the propeller performance This Master s Thesis report describes the procedure for computing open water characteristics using four different methods how to measure velocity fields and how to predict cavitation for a propeller in uniform inflow The four methods were Computational Fluid Dynamics CFD boundary element method lifting line method and Wageningen Series Further the report describes how the methods were automated in means of computing open water characteristics and how they compare to model test results The objective with the project was to gain knowledge about when the methods are preferred to use what limitations they have and how to minimize the work effort by means of automation of the tools The benefit of setup automation is not solely the time savings but also the security in standardized setup methods This reduces the risk of setup errors in the results Automatic post processing was developed to some extent for the tools as well For the project three different propeller geometries were used one designed to generate a tip vortex one designed to reduce pressure pulses and one with a more conventional design The propeller designed to generate a tip vortex was part of the SMP 11 Workshop on Cavitation and Propeller Performance The SMP 11 Workshop was intended to give research groups the possibility to validate their computational tools against both model tests and oth
27. boundary element method at model scale compared to the model test results can be seen in Fig 8 38 This validates the automated viscous correction method see section 7 4 The correction seems to follow the built in correction from PROCAL if Fig 8 38 is compared to Fig 8 35 Open Water BEM at Model Scale s 0 7 0 6 Kt_Procal_model m 0 5 Kq_Procal_model 0 4 a ETAo_Procal_model Y 2 0 3 Kt_Model z 0 2 Kq_Model ETAo_Model 0 1 0 0 2 Advfice Ratios 08 1 a Fig 8 38 The open water chart predicted by the boundary element method in model scale compared to the model test results for CPP1 12 8 3 Open Water Results from CPP2 This results section discusses and shows the results of CPP2 First the validity of the boundary element method and CFD setups are discussed After this the predictions from CFD boundary element method lifting line method and Wageningen Series are compared to model test results and discussed Finally results from PROCAL predicted in model scale compared to model test results are shown to validate the viscous correction script The averaged y values at the blades for CPP1 from the open water prediction can be seen in Table 8 7 As can be seen the y values are reasonable and large enough to yield reliable results with wall functions Table 8 7 The averaged y values at the blades for CPP2 from the open water prediction J 0 0726 0 2178 0 3636
28. cavitation patterns were analyzed using high speed camera observations and the cavitating thrust was measured The operating conditions for case 2 3 1 2 3 3 are presented in Table 3 4 22 Table 3 4 The operating conditions for the SMP 11 cavitation test Advanced coefficient 1 019 1 269 1 408 Cavitation number based on n 2 024 1 424 2 000 Thrust coefficient non cavitating 0 387 0 245 0 167 Number of revolutions 1 s 24 987 24 986 25 014 Water density kg m 997 44 997 44 997 37 Kinematic viscosity of water m s 9 34E 07 9 34E 07 9 34E 07 Vapour pressure Pa 2818 2818 2869 Air content 28 53 5 53 5 58 5 3 2 The Propeller for the Single Screw Vessel CPP1 CPP is a large low RPM propeller with moderate pitch It is a four bladed CP propeller The design is very smooth and it is reasonably unloaded at the tip Some propeller characteristics can be seen in Table 3 5 Table 3 5 Some propeller characteristics of CPP1 m rev min Open water tests at two different pitch settings 0 752 and 0 788 for J 0 1 to J 0 8 were available A picture of the propeller can be seen in Fig 3 7 Fig 3 7 The propeller geometry of CPP1 3 3 The Propeller for the Twin Screw Vessel CPP2 CPP2 is a medium sized medium RPM propeller with
29. function was programmed to get the values to be scaled i e Kr and Kg as inputs together with strings containing the places at which the table with the scaled values should be placed The subroutine starts by inserting the input J values in the leftmost column of a table in the openWaterResults sheet The script then loops through the declared number of steps of J The corrections are made The corrected Krs and Kgs are inserted in the columns specified when calling the sub routine 52 8 Results This section discusses and presents all results from the project Section 8 1 reviews the results from the SMP 11 Workshop test cases Section 8 2 and 8 3 reviews the open water characteristics results of CPP1 and CPP2 respectively An overlay discussion of the four methods can be read in section 8 4 Section 8 5 to 8 7 describes what happens when the automation scripts are used 8 1 Results from the SMP 11 Propeller This section is divided into three sub sections each describing the results of one of the three cases of the SMP 11 workshop It should be noted that all analyses of SMP 11 was performed as blind tests 1 e no model test data was available when the tests were performed 8 1 1 Case 2 1 The Open Water Test The first part of this section is describing the resulting CFD grid and the results of the grid dependence study for the SMP 11 open water prediction After this the validity of the CFD and boundary element method setups
30. moderate pitch It is a four bladed CP propeller The design is heavily unloaded and has high skew to reduce pressure pulses Some propeller characteristics can be seen in Table 3 6 Table 3 6 Some propeller characteristics of CPP2 m rev min An open water test with the pitch setting 1 088 at J 0 0726 to J 1 0201 were available A picture of the propeller can be seen in Fig 3 8 29 Fig 3 8 The propeller geometry of CPP2 3 4 Computer Resources The CFD simulations were performed on eight cores with a clock frequency of 3 4 GHz each The RAM was 24 GB The boundary element method simulations were performed on two cores with a clock frequency of 2 13 GHz each The RAM was 4 GB 30 4 Proceedings of CFD This section describes how the CFD setups were made how the results were post processed and how the pre processing automation was performed In section 4 1 4 3 the proceedings of SMP 11 are described since these were used to develop the automation method In section 4 4 the proceedings of the automation using CPP1 is described Finally in section 4 5 4 6 the proceedings of the actual open water tests of CPP1 and CPP2 are described since more steps than performed by the automated script were needed to match the model test descriptions for these propellers 4 1 Open Water Test of the SMP 11 Propeller The meshing tool used for the open water test of the SMP 11 propeller was ANSA Th
31. non cavitating propeller The operating condition is presented in Table 3 3 Table 3 3 The operating conditions for the SMP 11 velocity field measurement Water density for tw 24 7 C kg m3 997 1 Kinematic viscosity of water for tw 24 7 C m s 9 03E 07 Number of revolutions 1 5 23 Velocity m s 7 204 Advance coefficient 1 253 Thrust coefficient 0 250 Torque coefficient 0 725 The velocities were positive in the following directions Axial velocities in the flow direction radial velocities for increasing radii and tangential velocities in the direction of rotation The data provided was firstly axial tangential and radial velocities for the angular interval 50 lt lt 22 at 0 25 step size for the two planes in front of the propeller disc at radial positions RO 7 RO 97 and R1 0 The tip vortex at x D 0 1 was also given as velocities in the Cartesian directions at Y in the interval 40 lt lt 0 and r R in the interval 0 4 lt r R lt 1 1 21 3 1 3 Case 2 3 Cavitation Tests The cavitation tests were performed in the same tunnel and at the same position as in the velocity field measurement see section 3 1 2 The test was performed at three different conditions The first and third cases case 2 3 1 and 2 3 3 were off design conditions Case two case 2 3 2 was the design condition For these conditions the
32. solved in a boundary element method the solution is very leading edge sensitive 11 For this reason the number of panels leading edge to trailing edge was increased to 70 panels and the leading edge spacing was reduced to 0 001 The number of panels root to tip was decreased to 20 to save some computation time 5 3 Automation of the Pre and Post processing This section describes how the pre and post processing of PROCAL was automated All scripting were programmed in Visual Basic 26 VBA For a more detailed description example of a PROCAL control file and the VBA code see Appendix E 5 3 1 The Pre processing PROCAL needs a control file and a geometry file to perform an analysis By having those two files preset with the open water proceedings found in section 5 1 and exported to a location where the analysis should be performed the pre processing could be considered automated A grid dependence study needs to be performed before the open water characteristics can be analyzed Therefore one regular control file with one speed and one control file with many ship speeds were programmed separately 46 The geometry file was already pre set in the design workbook when the automation work started Only the lines containing operating conditions and meshing parameters needs to be changed in the control file In PROCAL both files are read in the free format i e spaces are ignored For this reason the generation of the control file was dec
33. solved using different corrections for e g camber induced pitch hub ratio and skew 8 5 The Final Performance of the CFD Automation This section describes what the CFD automation script performs when it is used For a more detailed description of the code see section 4 4 First a script generated blade from solid works on IGS format is provided see Fig 8 51 Fig 8 51 The unclean blade as generated from SW The cleanBladeUntilPitchSetting is pushed The domain MRF zone shaft hub and blades are fixed The blade is ready for pitch setting see Fig 8 52 for the result Fig 8 52 The blade cleaned until pitch setting The pitch is adjusted manually perhaps following the procedure in section 4 5 The blade should be intersected to the blade foot and the blade foot to the hub manually as well As a suggestion the procedure in Appendix D should be used for this Fig 8 53 shows a blade intersected to blade foot and hub 81 Fig 8 53 The pitch adjusted blade intersected with the hub The surfaceMesh button is pushed Everything might be surface meshed The mesh quality could become poor or unmeshed in a few regions Fig 8 54 shows the result Fig 8 54 Surface mesh with unmeshed leading edge macro The obvious meshing problems or unsatisfactory geometrical descriptions should be fixed manually If the problem is at leading edge the recommended procedure in Appendix C might be handy Fig 8 55 shows a finished surfa
34. the PROCAL results table in the open WaterResults sheet When a right curly bracket is found it switches column and continues to print values When three of those signs are found the code stops Every if case has a row counter that defines at which row the new value should be put The rows were set to run from 1 to nj By recording a macro that plots the results sets a Berg Propulsion diagram template and puts the plot in the open WaterResults sheet in Excel a plotting sub routine was made The sub routine was declared as public and can thereby be called for the other result tables i e Wageningen Series lifting line method and CFD Since the open water results predicted by PROCAL are read put in a table and plotted in the design sheet at a button click the post processing can be considered automated 48 6 Proceedings of the Lifting Line Method This section describes how the lifting line method was used It was automated directly so the same procedure was used for all propellers Therefore no sub sections are needed in this section There were not many parameters to change in the lift line code The developers strongly recommended that the parameters shouldn t be changed so it was decided to let the defaults be trustworthy 24 Only geometrical aspects needed to be changed to predict the open water behavior of a propeller The lifting line software was provided as an Excel workbook with macros To call the macros the sheet had t
35. the third and last part of the script layersAndVolumeMesh which makes prism layers on the surface and meshes the volume The script starts by reading a preset quality criterion with fluent skewness of 0 8 and maximum volume element skewness of 0 85 from a predefined file These criterions have proven accurate before and allow ANSA to make a good geometrical description Everything is made visible and the surface meshes for all macros are frozen The setup is merged with another template that is preset with a layers batch mesh scenario The settings of this scenario can be seen in Appendix B Since the mesh was frozen only layers will be generated when the batch mesh scenario is started For the open water setup three volume definitions are needed The first one is the inner volume which is the volume occupied between the top cap fluid layers top cap and the interface The top cap is a surface mesh lying on top of the prism layers The second volume to define is the outer volume which is the volume occupying the space between the domain and the interface These volumes are defined in the script by first making the top cap and the interface being visible and make an auto detection of the volumes The same thing is performed for the outer volume but with only domain and interface visible instead Since all the size boxes and element lengths on the surfaces are set the only thing needed is to apply a volume mesh with a maximum element length large e
36. very accurate until J 1 4 Note again that this prediction was performed as a blind test 55 Open Water CFD at Model Scale Kt_CFD 10Kq_CFD ETAo_CFD Kit Model lt lt 1QKq_ Model ETAo_Model Advance Ratio J E PROPULSION Fig 8 5 The open water chart predicted by CFD compared to model test results for the SMP 11 propeller The pressure distribution on the pressure side of the blades and hub in the open water test at J 0 8 and J 1 4 is visualized in Fig 8 7 and Fig 8 8 respectively As can be seen in Fig 8 8 separation occurs at J 1 4 and not for a speed before J aS in Fig 8 7 The separation after Jy may Might be over predicted due to the fact that wall functions are used and that the flow is assumed steady This is not true for turbulence and especially not in model scale where the turbulent flow isn t fully developed everywhere as the wall functions state The over predicted separation results in lower thrust hence explaining the J may in the last point 56 Fig 8 6 The axial velocity distribution for the open water test at J 0 6 Fig 8 7 Pressure distribution of the pressure side from the open water test at J 0 8 Note the overall high pressure distribution Fig 8 8 Pressure distribution of the pressure side from the open water test at J 1 4 Note the low pressure region at leading edge indicating separation on the pressure side The open water p
37. volume element length in the slip stream was also reduced by a factor two The contingent difference between the coarse and the fine mesh should depend on the discretization error Since a second order accurate scheme was used the error would reduce in the order of x if x is the cell length and the mesh was structured In this case the error would reduce but not necessarily in the exact order of x 7 The mesh settings of the fine mesh can be seen in Table 4 2 The resulting number of cells for the fine and the coarse mesh can be seen in Table 4 3 Table 4 2 The meshing parameters of the fine mesh for the open water test Perimeter length mm Surface mesh type Surface mesh size mm Blades 0 6 CFD 0 6 to 6 Hub 0 6 CFD 0 6 to 6 Shaft 5 CFD 0 6 to 6 Interface 5 CFD 0 6 to 6 Domain 60 CFD 5 to 60 Table 4 3 The resulting number of cells for the coarse and the fine mesh for the open water SMP 11 test OW coarse OW fine Surface mesh elements 100000 150000 Prism layer elements 502920 600000 Total elements 4500000 11000000 As boundary conditions the no slip condition was applied for velocity on the surface The outlet was set as pressure outlet with zero gradients for the remaining quantities The inlet was set up with uniform velocity inlet and the remaining quantities calculated in accordance with
38. 0 This is followed by one proceedings section for each of the methods section 4 7 to avoid nomenclature related confusions After this a combined result and discussion section section 8 follows that compares all the results to find the final recommendations that are presented in the conclusions section section 9 The subsections of section 8 are divided into results of each test case to attain comprehensive comparisons 10 2 Theory To clarify the nomenclature and level of approximation of the compared methods a theory review is introduced in this chapter 2 1 CFD Methods CFD is the analysis of systems with fluid flow heat transfer and similar phenomena using simulation by computer The theory behind steady RANS with a low Reynolds number turbulence model wall functions and multiple reference frames to model rotation will be reviewed in this section 2 1 1 RANS equations The propeller is a hydrodynamic construction Water is an incompressible and a Newtonian fluid hence the incompressible Navier Stokes equations apply see eq 2 1 The continuity equation applies as well see eq 2 2 a oe LaP aU Jy v dx pax 0xj0x au Ox 2 1 2 2 This set of equations requires extreme computer power to solve Since the flow is turbulent it is preferable to decompose the pressure and velocities into a mean and a fluctuating part i e as in eq 2 3 This is known as Reynolds decomposition do 2
39. 0 380004349 0541332378 0 7278 0209824 0 381577 0 636943 Fa 02 zA arses 0175967575 0327298909 0582977798 ayes 0169594 0391913 0880773 ES si 7 sd osma awazzrses 0279088546 0 7123567534 er 0183863 0282164 0658956 5 ossa amuse oztressse 0721618046 Asie 0097332 0239095 0520754 o o i onse aosss0sre 0180799059 0609467509 10201 0055702 0179823 0520851 o 02 oa os os i prue om oza om os om 10 MS o o2 oa os 08 1 ecg g eos E Bea A ES ss Open Water Full Scale ModelTest Open Water Lifting Line gt Ed ES 3 E 0 os as gt boeriesr 05 mu oa series 04 PS Stora 0 sa ies o3 gt rac a2 o2 k y a E a o oa a w a oa o oa a a a oa e De tae Fig 8 59 The complete interface for Wageningen Lift Line PROCAL model test and viscous scaling 85 This page is intentionally left blank 86 9 Conclusions and Future Work Firstly the conclusions of this thesis work are listed method for method in this section If the conclusion only regards the specific method used in the thesis work this is explicitly mentioned after the conclusion Finally recommendations regarding future work are presented The main conclusions that can be drawn about the CFD method are that the CFD method 1s the most accurate among the compared methods regarding open water characteristics predictions but has the very highest computational cost might have long setup times can accurately predict the velocity field down
40. 03 6 Davidsson L Numerical Methods for Turbulent Flow G teborg Sweden Chalmers University of Technology Department of Thermo and Fluid Dynamics January 7 2005 7 Versteeg H K Malalasekera W An Introduction to Computational Fluid Dynamics The Finite Volume Method 2 ed Malaysia 2007 8 OpenFOAM Wikipedia http openfoamwiki net index php See_the_MRF_development 9 Volker Bertram Practical Ship Hydrodynamics Madras 2000 10 Bosschers J PROCAL v2 0 Theory Manual MARIN Report 20834 7 RD Wageningen June 2009 11 Bosschers J PROCAL v2 0 User s Guide MARIN Report 20834 6 RD Wageningen June 2009 12 ANSA v13 1 2 A meshing program for CFD and FEM including CAD tools 13 Andersson B et al Computational Fluid Dynamics for Chemical Engineers 6 ed Goteborg March 2010 14 ANSA v13 1 x Online Reference Manual BETA CAE Systems S A January 2011 15 Hally D Generation of Panels for CRS PROCAL DRDC Atlantic External Client Report Canada October 2004 16 PROCAL discussion forum website http wik1 crships org index php Special Search search idiots go Go 17 Kupier G The Wageningen Propeller Series Netherlands May 1992 18 Dyne G Bark G Ship Propulsion Chalmers University of Technology division of hydromechanics G teborg 2005 19 SMP 11 Workshop case 2 general description http www sva potsdam de assets images smp 1 1 case2_PPTC_geometry pdf 20 SM
41. 100 Domain 1000 1000 40 4 4 3 Surface Mesh This section describes the second part of the script makeSurfaceMesh which performs a surface mesh on blades hub and shaft When this script is started the blade hub and shaft are copy linked 360 to form a full propeller The link option was chosen to guarantee symmetrical and faster meshing Linking means that every change made on the original blade is automatically done on the link blades so if the mesh should be manually improved this only needs to be done at one blade After this an automatic topology to get rid of single cons followed by an automatic geometry cleanup fixing cracks overlaps needle faces collapsed cons and unchecked faces is performed This is since a clean geometry is demanded to make a complete surface mesh The script sets the perimeter length with automatic CFD spacing that should be used prior to CFD meshing This is done making each of the entities hub shaft and blades visible one at a time A call for the batch mesh scenario predefined in the template resulting in a triad surface CFD mesh follows after this The last breakpoint of the code is now reached This gives the user the opportunity to inspect and fix parts of the surface mesh that is found unsatisfactory Usually ANSA has problems with meshing the leading edge A recommended procedure for this is presented in Appendix C 4 4 4 Layers and Volume Mesh This section describes
42. 3 P P p By inserting eq 2 3 into eq 2 1 and 2 2 the Reynolds Averaged Navier Stokes and continuity equation are obtained see eq 2 4 and 2 5 A closure problem appears there are four equations and ten unknown variables 5 AA 10P U uay U0 tu a DA Ox p Ox OxjOx Ox au 0 2 5 Ox 2 1 2 Discretization Schemes When an equation is discretized a continuous differential equation is calculated into an algebraic discrete equation In CFD the domain can be divided into finite volume elements each with known node face and neighbour locations see Fig 2 1 OD 01 e W A a E W e Ag Fig 2 1 A finite volume where capital letters represent nodes small letters represents faces e stands for east w stands for west and p stands for the current cell 6 11 If one finite volume is studied the continuous equation is integrated from face to face in each direction This gives discretized equations telling how the current node is related to the cell faces using the studied differential equation Since the studied quantity was integrated from face to face the quantities are known at the faces The next step is to relate the nodes to the faces This is done using a discretization scheme One example is to assume that the faces are connected by a straight line and linear interpolation can be used to determine the quantity on the node lying between the faces This is known as the central differencing scheme I
43. Fig 8 36 The open water chart predicted by the lifting line method compared to model test results scaled to full scale for CPP1 71 The results from the Wageningen series compared to the model test results scaled to full scale can be seen in Fig 8 37 The prediction is quite good One large difference is the measurement in bollard pull This could depend on one of the model tests Recall that the Wageningen Series is based on model tests One of the model tests could have been performed in a too small basin resulting in that a too small amount of water could be sucked in the bollard pull condition c f section 8 3 It should be noted that CPP1 is a very Wageningen similar design Note that it is hard to accurately measure bollard pull characteristics in a model test The small difference for the other points probably lies within the larger hub hub ratio of CPP1 is 25 6 and hub ratio of a Wageningen propeller is 18 A larger hub gives lower Kpy but also Kg and in combination results in a slightly lower efficiency 26 os Open Water Wageningen at Full Scale 0 7 0 6 A Kt_Wageningen 20 5 Kq_Wageningen 50 4 ETAo_Wageningen 3 0 3 3 Kt_Model 0 2 1QKQ Model 0 1 ETAo_Model 0 0 0 2 8 5 0 4 0 6 0 1 Advance Ratio J a Fig 8 37 The open water chart predicted by the Wageningen series compared to model test results scaled to full scale for CPP1 The results from the
44. P 11 Workshop case 2 open water test case http www sva potsdam de assets images smp 1 1 case2 1_PPTC_owt pdf 21 SMP 11 Workshop case 2 velocity field measurement case http www sva potsdam de assets images smp 1 1 case2 2_PPTC_vel pdf 22 SMP 11 Workshop case 2 cavitation tests case http www sva potsdam de assets images smp 1 1 case2 3_PPTC_cav pdf 23 FieldView v12 2 A CFD post processing and rendering tool 89 24 Nijland M Lift Line Beta Release User Manual W rtsil Ship Power Technology 2009 25 White F M Fluid Mechanics 5h ed University of Rhode Island New York 2003 26 Klerebrant Klasson O Huuva T The Development of a Correction Formula from Wageningen BSeries Reference Hub Size to Any Other Hub Size Berg Propulsion Technology AB May 2011 27 Visual Basic v6 5 1053 A BASIC based programming language linked with excel 28 Lloyd s Register Procal Task 4 1e Panelling Procedure Department of Consultancy Services Group Technical Investigations Report no 6517 2010 29 Magnus Pettersson Berg Propulsion Technology AB verbally 30 Klerebrant Klasson O Pettersson M Validation study of AMG_STERN and CRS_PIF Berg Propulsion Technology AB September 2010 90
45. _ Model 0 6 10Kq_Model 0 4 ETAo_Model 0 2 0 0 55 0 75 0 95 1 15 1 35 Advance Ratio J PROPULSION Fig 8 10 The open water chart predicted by the lifting line method compared to model test results for the SMP 11 propeller 58 The open water prediction of the SMP 11 propeller by the Wageningen series compared to the model test results can be seen in Fig 8 11 In this prediction the propeller is too light but the efficiency until the design point is well predicted The lightness of the propeller is expected since the pitch wasn t corrected for camber in the Wageningen prediction The camber results in a higher virtual pitch No blade area correction was applied either These corrections could result in more accurate predictions Open Water Wageningen at Model Scale o 1 1 4 1 2 Ki Wageningen pe 3 Kq_Wageningen S 08 ETAo_Wageningen a Kt_Model aw 0 6 x 0Kq_Model 0 4 ETAO_Model 0 2 0 0 55 0 75 0 95 1 15 1 35 3 Advance Ratio J PRAPER SIEN Fig 8 11 The open water chart predicted by the Wageningen series compared to model test results for the SMP 11 propeller 8 1 2 Case 2 2 Velocity Field Measurement This section first describes the resulting fine mesh for the velocity field measurement of the SMP 11 propeller After this the validity of the setup is discussed The last part of the section presents the results of the SMP 11 velocity fi
46. able 4 8 The final number of cells for the coarse and fine mesh of the velocity field SMP 11 measurement Velocity field coarse Velocity field fine Surface mesh elements 290000 200000 Prism layer elements 410000 1000000 Total elements 4600000 13600000 To comply with the thrust identity the speed had to be lowered somewhat Two different speeds were tested and then the linear relationship between J and Ky was used to find the proper velocity yielding the correct thrust 4 3 Post Processing of the SMP 11 Propeller When the CFD computations had reached final convergence they were stopped Final convergence was considered to be achieved when all residuals of velocity and turbulent quantities were below 107 and all residuals of pressure were below 107 The open water diagram was made from the integrated forces along T and moments around Q the x axis Eq 2 20 2 22 were used to compute the open water characteristics The RANS results were post processed in Field View 23 The velocity field was extracted using the sampleDict in OpenFOAM A cloud of points were picked from the input file demands of SMP 11 The input file requested the tangential radial and axial velocity at a given and r R Q is defined as the angle between the dead top centre and the current blade tip position It is positive in clockwise direction Hence it can be described by the relationship 36 in eq 4 5 The giv
47. aviour but good when predicting the free stream To improve the near wall behaviour the k w model could be applied instead The specific dissipation w is an equation derived from the equation It behaves more similar to the exact dissipation term near the wall The k w SST model is a hybrid between the k e and the k w model It is using blending functions to be able to use the k w model near the wall and the k e in the free stream and to get a smooth transition between them The energy and dissipation equation of k w SST can be seen in eq 2 9 and 2 10 7 A pepe past m ax p P Ox ERE Ox a duw y 0 Ow j 2 A A q ae Ox mp po Ox e Ft 2 10 2 1 F o k w i w Ox OX Where u the velocity and v the turbulent viscosity P P o and O are constants 2 1 6 Wall Functions The wall was modelled with wall functions to reduce the need for high mesh resolution near the wall To apply wall functions means that the flow near the wall is assumed to behave as a fully developed turbulent boundary layer The first cells are computed using the wall functions and are then inserted as boundary conditions into the cells computed by the RANS equations The last cell of the wall functions should typically be in the interval 30 lt y lt 100 to get reliable results The dissipation and production term are much larger than the other terms in the log law region Using analytical and empirical equations from the log law an equation for the
48. be compared to each other considering solely open water characteristics of propellers PROCAL s ability to predict open water cavitation and OpenFOAM s ability to predict velocity fields forward the propeller disc will be compared to model test results The automation regards pre processing and post processing for open water characteristics predictions By post processing the generation of open water diagrams is regarded Automatic pre processing is intended as a way to from either a few user questions or by taking data directly from the blade design location get a complete open water setup For the CFD the analysis will be of steady non periodic RANS type without resolving the wall The choice of non periodic boundary condition depended on that the periodic boundary condition was not applicable for ANSA 12 interacting with OpenFoam when the project was performed The model test results are seen as the reality in this project It is known that this might be untrue but it is the best data to use as reference 1 4 Outline and Overall Methodology To complete the objective the methodology of this thesis project could be summarized in seven steps 1 Explore the functionality of the four open water prediction tools 2 Find a standardized method that generate reliable results for each tool 3 Compare the results from each tool between the other tools and to model tests to see if the methodologies are correct 4 Automate each tool for open wa
49. ber of steps of J and in each step it gets the J values from the column defined for the Wageningen table Ky and Kg are calculated from getKt and getKq The open water efficiency is calculated from eq 2 22 Since m which is used in this equation wasn t declared in VBA it was hardcoded as in eq 5 6 m 4 arctan 1 5 6 At each step in the loop the results are inserted in the proper columns of a table in the openWaterResults sheet in the design workbook This script was linked to a button in the openWaterResults sheet The open water characteristics according to the Wageningen Series are hence both calculated and inserted in the design workbook at a button click Consequently the pre and post processing were automated 7 4 Automation of Extrapolation to Full Scale The extrapolation to full scale was automated by first programming a public sub routine containing the equations in section 2 7 First the variables PO75 D c075 and t075 in full scale were needed The values are only given at radial sections RO 7 and RO 8 in the design workbook To get the values at RO 75 a linear interpolation was made where the sum of the properties at each of the above mentioned radial sections were divided by two The diameter and number of blades were also picked from the design sheet kp was set to 30 um To get the chord length at model scale the c075 was divided by the model scale factor The open water efficiency was calculated as in section 7 3 The
50. calculation Therefore it is essential with breakpoints to let the user control the setup The entire pre processing code was programmed in a C like scripting language included in ANSA Below an explanation of what the code performs step by step is described For a more detailed description including records used and the actual code see Appendix B 4 4 1 Geometrical Cleanup and Domain Definition The first part of the script cleanBladeUntilPitchSetting which makes a geometrical cleanup and domain definition starts with cleaning the blade The blade is generated by a script linked with solid works so all blades need to be cleaned in the same way This script will be referred to as Solid Works SW to avoid confusion First there are five excessive faces that need to be removed for the mesh to be generated see Fig 4 8 37 Fig 4 8 The uncleaned blade as extracted from SW If the SW generated blade is studied it is obvious that the smallest area of all the faces occur at the blade The ANSA script script searches for the smallest face makes it and its neighbours visible and saves it in a temporary file and loads the file This makes the five excessive faces in the middle of the blade to disappear After this the solution is compressed which means that parts property identification PID and points that have no use will be erased A finite tip length is applied at the uppermost radial section to close the leading and the trailing ed
51. ccount The largest drawbacks are that it doesn t yield the complete propeller geometry and has problems with high skew 9 2 5 The Wageningen B Series The Wageningen B Series is a large series of model tested propellers with varying blade area ratio pitch number of blades and advance ratio The propellers are based on designs that have been found effective The series consists of about 130 propellers All tests have been performed with a local Reynolds number at 0 75R of 2 million Regression polynomials for Kr and Kg has been derived for the four and five bladed propellers in the series The regression polynomials usually referred to as the Wageningen polynomials are functions of advance ratio pitch blade area ratio and number of blades The B Series is intended to use for predictions of open water characteristics Rake blade contour and thickness distribution has small effect on the performance characteristics It mostly affects the cavitational behaviour Therefore the tests are made as functions of blade area ratio pitch and number of blades which have major importance on the performance characteristics The skew affects the radial loading distribution and thereby the efficiency For this reason the B Series has a small amount of skew To conclude it could be said that the geometries in the Wageningen B Series have reasonable cavitation performance but far from optimized in this respect On the other hand the propellers of the series
52. ce mesh Fig 8 55 The completed surface mesh ready for volume mesh and layers The layersAndVolumeMesh button is pushed The last steps of automatic surface mesh cleanup layer generation and volume meshing is performed The completed mesh can be seen in Fig 8 56 82 Fig 8 56 The completed volume mesh The result could be outputted to e g the OpenFOAM template folder containing the most common boundary conditions If no pitch setting is needed and the user is familiar with the intersect function in ANSA and no big problems occur when surface meshing is performed the estimated working time using the script is 5 10 minutes The whole mesh is completed within 15 25 minutes 8 6 The Final Performance of the Boundary Element Automation The propeller design is finished in the design sheet The user wants to perform a boundary element method analysis In the PROCAL sheet the buttons Export Geometry and Export Control File are clicked PROCAL should be started and file new add existing file should be chosen The User goes to the propeller dialog and hit mesh now and after that output export After this it is only to click procal analysis and wait When the analysis is done the load PROCAL results button has to be clicked from the openWaterResults If a full open water chart is wanted the Jyax gt Juin and Jstep values should be set Then the Export OW Control button should be clicked The exact same procedure as in the paragraph abo
53. d The final interface for Wageningen Lift Line PROCAL model test and viscous scaling can be seen in Fig 8 59 84 Open water diagram specification Altas 303 Model scale factor pas fa Piot vodelts 2500 E A ee _ a e a E mee te Ee r e 00726 040427046 067241289 0 06946927 007 05306 0 854 0 07173 0 0726 a oF oro 0 0728 0473719628 0 763981948 0 071646509 0 1452 039209573 065415126 0 13851623 05 0438 0 8033 0 493 0 456 0 0 oro 052 0451263665 0 732259109 0142415778 02178 037782595 063266445 0 2070124 022 04652 0 7519 0 2145 0 2178 0 o sovio 02178 0426696712 0 697498716 0212058232 02904 03612256 060757782 027478527 023 04321 0 6997 0 2854 0 2309 o o sovo 02904 0400182338 0 659864778 0 280297816 0 363 034256757 057934451 0 34161435 036 0 3986 0 5467 0 3561 0 3636 0 DC 0 363 0371908114 0 619533305 0 346814903 04356 032153414 05474552 040718007 044 03647 0 5927 0 4266 0 4356 0 0 omo 0 4356 0 34205561 0576672306 0411221323 0 5082 029774207 05292 047098626 O51 03297 0543 DAS 05103 o o sova 0 5082 0310806399 0531451789 047302489 0 5808 027135091 047117358 053234981 058 02937 0 4969 0 5464 0 5818 0 o7 evo 05808 0278342049 0484041763 053154829 0 726 02105117 0 37852957 0 64258834 073 ozme 0 4049 0 6216 0 7278 0 O oo 072 0210494218 0 38393322 0 634483694 0 7986 017602219 0 32597625 068632671 080 01789 0354 0 6423 0 7988 0 0 omo 0 7986 0175473878
54. d coarser close to the middle of the surface The mesh is consisting of triads making the geometrical description good but leads inevitable to triads and pyramids before the volume mesh can be hexahedral To mesh a complex geometry such as a propeller a structured grid is hard to apply A structured grid has better numerical properties than an unstructured grid An unstructured grid generally requires less time to apply than a structured grid Unstructured grids are built from polyhedrons in the volume and commonly triads on the surface Close to the wall very large gradients occur In this case the optimal would be to have cells at 90 angles to the wall with equal edge lengths 13 A mesh type that fulfils this criterion is the prism layer A prism layer 15 has a face almost identical to the surface mesh below and grows almost solely in the orthogonal direction to the wall 14 The structured mesh consists of hexahedrons in the volume and quadrilaterals on the surface As said these have imperious numerical properties compared to the unstructured elements and should therefore be used when possible In ANSA there is a volume mesh type called hexa interior It uses as few tetrahedrons and pyramids as possible to quickly evolve into a fully hexahedral mesh This gives a good combination of numerical stability and geometrical representation 14 To fit the geometry the elements need to be squeezed in different ways This might affect the
55. dge on the cutting plane was measured yielding a lateral and an axial distance between the two points In eq 2 30 the axial coordinate x should be measured in Cartesian coordinates but the lateral distance y should be measured in cylindrical coordinates i e the y distance is the arc length described on the cutting cylinder The problem was solved by moving the aft most point of the blade section forward the axial distance measured The angle between the shaft line centre the axially moved aft most point and the foremost point of the blade section was measured see Fig 4 11 ees Uos fetch O er Y Mesure Stings HSE gt ooi Heme Fig 4 11 The angle dp is measured between the two white lines leftmost line goes from the axially moved aft most section point to shaft centre and the rightmost white line goes from the shaft centre to the fore most point This angle was used to compute the arc length Larc as in eq 4 13 42 Larc OY 4 13 Where the measured angle in radians and r is the radius of the cutting cylinder Since y Larc in eq 2 30 eq 2 30 and 2 31 gave the current pitch The pitch before adjustment was 0 774 and the required pitch for the model test was 0 788 Eq 2 31 gave the required pitch angle eq 19 7139 The current angle was computed using eq 2 30 from the measurement It resulted in the current pitch angle fp 20 83 The blade hence had to be rotated 1 1161 around the y axis
56. died in this thesis should be used are that e the Wageningen Series should be used for predictions at a very early design stage and to check whether the other predictions are within reasonable values e the boundary element method should be used when the propeller design is finished and more reliable open water predictions are needed e the CFD method should be used when more odd designs should be tested or when exact guarantees of open water performance should be leaved There are some aspects that should be performed as future work after this thesis The volume mesh close to the propeller disc in the velocity field measurement should be improved This could solve the convergence issue at x D 0 1 and resolve the vortex at x D 0 2 To get better results in bollard pull and after J yay the wall could be entirely resolved It would also be interesting to perform an analysis with a fully hexahedral mesh to improve the results A comparison between the MRF results and results with a sliding mesh would also give better understanding in the level of approximation The script should be rewritten to handle the periodic boundary condition as soon as the bug in ANSA is fixed This allows as many more times higher cell resolution as the number of blades of the propeller It is a qualified approximation as well the analysis is steady and hence the results won t be affected by the symmetry assumption The cavitation analysis should be tested with a minimum pres
57. e original geometry of the SMP 11 propeller had some deficiencies from the beginning Firstly there was a small play between the blade and the hub see Fig 4 1 F ig 4 1 The small play between the blade and the hub The intention was to use prism layers Since they would grow into each other in the play it was filled by projecting the blade downwards and intersect the blade with the hub fillet see Fig 4 2 This should make negligible difference since almost no work is performed near the blade root see pitch distribution in Appendix A Fig 4 2 The small play between the blade and the hub removed The same prism layer related problem would occur for the play in the intersection between shaft and hub see Fig 4 3 31 Fig 4 3 The gap between the shaft and the hub The geometry was simplified by removing this gap see Fig 4 4 Fig 4 4 The gap between shaft and hub removed Lines with no connections was pasted together and the tip length at r R 1 0 was smoothened by a small cut yielding better geometrical representation see Fig 4 5 Fig 4 5 The modification of the tip where the sharp line shows the new representation and the thinner one the old representation To make the blade meshing more efficient and above all symmetrical only one blade was meshed and then the completed mesh was copied to the remaining four blades The blade hub and shaft were surface meshed with triads The triads were smaller at
58. eally are the same in model as full scale The difference is the viscous scale effects which are dealt with in the ITTC recommendations in the Hague 1978 see section 2 7 18 2 7 Viscous Scale Effects The values of Ky Kg and No obtained at the model test or from the Wageningen series are in model scale These values would be identical in full scale if the lift and drag coefficient Cp and C would be the same at model scale This is approximately true for C but not for Cp Cp is decreasing with increasing Reynolds number This results in higher Ky lower Kg and studying eq 2 22 thereby higher 7 According to the ITTC 78 recommendations the scale effects should be taken into account as described below First the local Reynolds number at model scale is defined as in eq 2 23 VaCo 75 2 23 Raco v Where Co 75 the model scale chord length at 0 75R and v is the viscosity at the model test Cp in model and full scale are defined as in eq 2 24 and 2 25 respectively 18 ty 0 044 5 Com 2 1 2 gt 2 24 R co Roa 21 t Cps 2 1 2 199 E 2 5 p Where t the full scale thickness at RO 75 c the full scale chord length at RO 75 and k the full scale propeller surface roughness standard value 30 1076m 17 2 25 The difference in profile resistance between the model and ship propeller ACp is computed using eq 2 26 ACp Com Cos 2 26 Finally the coefficients in full scale K
59. ed further in section 8 3 This also happens after Jy may Which is discussed further in section 8 1 1 The results from the boundary element method compared to the model test results scaled to full scale can be seen in Fig 8 35 As can be seen the approximation is very good Both Kr and Kg are slightly over predicted until the design point resulting in a slightly higher efficiency Note that this is for CPP1 which is a very smooth propeller aa Open Water BEM at Full Scale e 0 7 OF a Kt_Procal 0 5 10Kg_Procal c z 0 4 ETAo_Procal ie 0 3 Kt_Model 10Kq_Model 0 2 ETAo_Model 0 1 0 0 0 2 0 4 0 6 0 8 1 x Advance Ratio J tints Fig 8 35 The open water chart predicted by the boundary element method compared to model test results scaled to full scale for CPP1 The results from the lifting line method compared to the model test results scaled to full scale can be seen in Fig 8 36 These results are significantly better than the results from the SMP 11 propeller The prediction tends to over predict the efficiency somewhere around the design point This is a result of a under predicted Kg The skew of CPP1 is 34 which should result in problems for the lifting line method Open Water Lifting Line at Full Scale o Kt_LiftLine spas QKQ_LiftLine ETAo_LiftLine Kt_Model 2 1QKQ Model ETAo_Model PROPULSION
60. el scale the results needed to be scaled to full scale to be compared to the CFD and the lifting line method results This was performed using the equations described in section 2 7 where the full scale values were taken from the propeller to be analyzed and the model values from the model test reports This had to be done for CPP1 and CPP2 7 3 Automation of the Pre and Post processing This section describes how the pre and post processing of the Wageningen series was automated The VBA code that was made is presented in Appendix G The Wageningen method consists as mentioned of a lot of charts from which results can be withdrawn as a function of pitch blade area ratio number of blades and advance ratio Since the Wageningen Propeller Series Program uses the polynomials the easiest way to automate would be to program the polynomials directly into VBA The polynomials are divided in two one for Kr and one for Kg These polynomials were already at hand at Berg Propulsion so they were programmed into separate VBA functions The polynomials were programmed so that pitch blade area ratio and number of blades were picked in the design sheet The remains were Ky and Kg as function of advance ratio These functions were called getKt and getKq in the code The advance ratios were computed using 51 eq 5 5 They were programmed to be inserted in order in the leftmost column of the Wageningen table The VBA script loops through the given num
61. eld measurement and compares them to the CFD predictions The fine mesh used in the velocity field measurement is shown in Fig 8 12 As can be seen the mesh is very refined in the slip stream region This is for the velocity gradients close to the propeller disc to be resolved and thereby preserving the tip vortex Fig 8 12 The fine mesh used for the velocity field measurement 59 The velocity corresponding Ky and corresponding y for the fine mesh are tabulated in Table 8 3 y tend to be higher than compared to the open water results c f Table 8 2 This depends on that the inflow condition was changed to a push configuration with higher RPS and inlet velocity than for the open water test Table 8 3 Velocities and corresponding J Ky and y for the fine mesh of the velocity field measurement Va 7 1867 was chosen as working point since it was closest to the thrust identity Kr 0 250 In Fig 8 13 an iso surface with helicity of 150 m s is shown to visualize the generated tip vortex Helicity is the tendency of a particle to perform cork screw motions which is exactly what happens to the particles in a tip vortex The tip vortex is evident from this figure If the cell resolution would be higher further downstream the vortex would probably continue a bit further 60 Fig 8 13 Tip vortex with helicity of 150 m s at the working point For a better understanding of the results the axial velocit
62. element method and Reynolds Averaged Navier Stokes RANS methods are not solely dependent on the tools capabilities itself but also on how they are set up by the user There are an abundance of tools that performs the same calculations with only slight differences in layout and user friendliness The SMP 11 Workshop was intended to give research groups the possibility to validate their computational tools against both model tests and other software setup by different users This 1s a very valuable reference when studying the accuracy of the computational tools The setup time for different tools might be very long One example is CFD which might have several days and even weeks as setup time The result from a computational tool might also as stated depend on the user A procedure that not only reduces the setup time significantly but also standardizes the methods and rules out setup errors is for this reason desirable 1 2 Objective with the Investigation The objective of the thesis is to investigate and validate the computational tools for open water propeller predictions at hand at Berg and make a user environment that speed up pre and post processing for the tools 1 3 Limitations The tools to automate and compare are only the Wageningen Propeller Series Program 1 the boundary element method PROCAL 2 the lifting line method LiftLine 3 and the open source Computational Fluid Dynamics CFD toolbox OpenFOAM 4 The tools will
63. en radial section can be described in terms of Cartesian coordinates as in eq 4 6 This is since the equation will yield a cylinder cutting through the given radial section tan p z 4 5 TZ s 4 6 R 5 5 Pa Where r the radial coordinate and R the propeller radius Rewriting gives the Cartesian coordinates as in eq 4 7 and 4 8 y tan d z 4 7 eo J tan 2 1 4 8 By sampling the requested points results of velocity in x y and z direction were attained To convert y and z direction into radial and tangential velocities the relationship described by eq 4 9 and 4 10 were used V cos p V sin V 4 9 V cos p Vy sin p Vz 4 10 Where V the radial velocity V the tangential velocity V the velocity in z direction and V is the velocity in y direction 4 4 Automation of the Pre processing CPP1 was used to make the script for automatic CFD pre processing In short terms it could be said that the methodology found to be efficient when analysing the open water characteristics of the SMP 11 propeller see section 4 1 was automated The script was made in three parts one geometrical cleanup and domain defining part one surface meshing part and one volume meshing part This was since the meshing needs two natural breakpoints Firstly the pitch needs to be controlled and set and secondly the surface mesh needs to be checked These two points naturally determines the quality and accuracy of the
64. ency turbulent kinetic energy Full scale propeller surface roughness Dimensionless torque Dimensionless thrust Revolutions per second Pressure Torque Radial coordinate Propeller radius Local Reynolds number based on chord length Thrust blade thickness Instantaneous velocity Averaged velocity Fluctuating velocity Effective wake fraction Advance velocity Reference velocity Distance Dimensionless wall distance Number of blades Contents 1 1 1 1 2 1 3 1 4 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 3 1 3 2 3 3 3 4 Introduction 7 7 4 244 41M 9 Background 9 Objective with the Investigation 9 Limitations 9 Outline and Overall Methodology 10 Theory n ee 11 CFD Methods 11 2 1 1 RANS equations 11 2 1 2 Discretization Schemes 11 2 1 3 Pressure Velocity Coupling 12 2 1 4 Multiple Refe
65. eq 4 1 4 4 and set as Dirichlet conditions 5 34 Table 4 4 and Table 4 5 summarizes the boundary conditions for the surface and the outer domain respectively 3 2 k gt VA 4 1 Where k the turbulent kinetic energy V the advance velocity and I the turbulent intensity E _ 0 09pk He u u 4 2 Where u the turbulent viscosity u the fluid viscosity the turbulent dissipation and p the density of the fluid Where w the specific dissipation m 10 4 3 4 4 Table 4 4 The boundary conditions for the surface boundaries Boundary Velocity Blades no slip Hub no slip Shaft no slip Turbulent kinetic energy Wall function Wall function Wall function Specific dissipation Wall function Wall function Wall function Pressure Homogenous Neumann Homogenous Neumann Homogenous Neumann Table 4 5 The boundary conditions for the outer boundaries Boundary Velocity Domain slip Dirichlet Outlet Homogenous Neumann Turbulent kinetic energy Wall function Dirichlet Wall function Specific dissipation Wall function Dirichlet Wall function Pressure Homogenous Neumann Homogenous Neumann Homogenous Dirichlet For the domain wall functions were used and the pressure was of zero gradient type here The CFD package used for the simulations was OpenFOAM
66. er software set up by different users The workshop provided model test results of open water characteristics velocity field measurements and cavitation patterns These test results were predicted in this project and will also be included in the workshop The other two propellers were used to automate the four methods and validate them against model test results The CFD analyses were performed with the open source CFD toolbox OpenFOAM Steady Reynolds Averaged Navier Stokes RANS simulations with k w SST turbulence model and wall functions in combination with Multiple Reference Frames MRF were used for the CFD simulations The grids and automatic CFD pre processing were performed with the commercial meshing software ANSA The boundary element method predictions and grid generation were performed in the CRS developed tool PROCAL The lifting line method predictions were performed in an Excel workbook with macros The Wageningen Series predictions came directly from the Wageningen polynomials The three latter methods were automated using visual basic and Excel One important conclusion is that CFD gives the most accurate predictions but requires many CPU hours When results are needed quickly the boundary element method is useful and accurate enough The lifting line method generates less accurate results than the other methods The Wageningen Series is useful to give an indication of the predicted results validity The automated codes save ho
67. etup template can be seen in Table 8 5 As can be seen the difference between a MRF zone that is 1 5 times larger and a regular one gives negligible difference The difference between the short shaft and the long shaft is larger This should of course depend on that the boundary layer developed over the long shaft is larger increasing the load at the blade root This statement is strengthened by the comparison between the long shaft with and without spherical end cap When the end cap is present the load at the root gets lower since the boundary layer gets smaller The long shaft gave the results closest to the model test suggesting that the development of a proper boundary layer is important for the results Therefore the pull arrangement yielding the best results was introduced Table 8 5 A comparison of the results when the open water setups were changed J 0 499 y blades Spherical end cap 121 Spherical end cap MRF 1 5 times larger 121 Long shaft 121 Long shaft spherical end cap 121 Pull arrangement 121 The averaged y values at the blades for CPP1 from the open water prediction can be seen in Table 8 6 As can be seen the y values are reasonable and large enough to yield reliable results with wall functions Table 8 6 The averaged y values at the blades for CPP1 from the open water test J 0 1 02 03 04 05 0 6 0 7 0 8 y OW mesh 133 133 134 135 136 136 137 139 The
68. ew Angle describing the asymmetry of the blade face Thickness distribution The thickness of the blade at different radial sections Thrust identity Load condition in model test stating equal Kt rather than velocity Abbreviations BEM Boundary Element Method CFD Computational Fluid Dynamics CP Controllable Pitch CPP1 Berg propeller for a single screw vessel CPP2 Berg propeller for a twin screw vessel EAR Blade area ratio ITTC International Towing Tank Conferrence LDV Laser Doppler Velocimetry LE Leading Edge foremost part of the blade LEs Leading Edge spacing LLM Lifting Line Method MRF Multiple Reference Frames OW Open Water P D Non dimensional Pitch P0 7 D Non dimensional pitch at RO 7 PHIW Wake panel distribution PID Property Identification r R non dimensional propeller radius RO 7 Propeller radial section at 0 7 propeller radius RANS Reynolds Averaged Navier Stokes RPM Revolutions Per Minute RS Root spacing SMP 11 Workshop for propellers held in Potsdam SW Solid Works TC TE TEs VBA WS Tip chord fraction Trailing Edge aftmost part of the blade Trailing Edge spacing Visual Basic Wageningen Series Roman letters e C0 75 Cp 5 Q o qr AD A A US aecq Chord length Chord length at RO 75 Drag coefficient Lift coefficient Propeller diameter Radial axial force Turbulence intensity Advance ratio Advance ratio at maximum effici
69. f the discretized equation is Taylor expanded and compared to the continuous differential equation it can be shown that terms of order x will remain This is known as second order accuracy Since x is the cell length this means that the error will be reduced by a factor 4 if the cell length is halved There are some problems with the central differencing scheme it is neither bounded nor transportive If a scheme is conservative it is meant that the flux leaving the cell should be the same as the flux entering the neighbouring cell This is fulfilled by the central differencing scheme A bounded scheme fulfils the requirement that the value at a face cannot be larger or smaller than the cell values used to compute the face value With a transportive scheme it is meant that the information is transported in the correct way Velocity e g is transported from upstream to downstream This means that the current cell should depend more on the cells upstream than the cells downstream to be transportive The first order upwind scheme takes the value from the node closest to west if the velocity in direction west to east is larger than zero If the velocity is in the other direction it takes the value from its eastern node This scheme fulfils all the criterions it is conservative bounded and transportive The drawback is that it is inaccurate due to the fact that it is only first order accurate Since it is bounded it is a very stable scheme To sol
70. fter this it is combined with the discretized Navier Stokes equation so that a direct relation between a velocity correction and a pressure correction is achieved When the continuity error in the continuity equation vanishes the pressure correction is converged 6 There are other ways to couple pressure and velocity such as PISO PISO is similar to SIMPLE but has one further corrector step 7 2 1 4 Multiple Reference Frames Multiple reference frames can be used to model rotating boundaries in a flow such as a propeller To derive the equations used for solving with multiple frames of reference in OpenFOAM the steady Navier Stokes equations for incompressible flow are used First the acceleration term of the rotating frame Q is studied It is related to the position vector r Note that cylindrical coordinates are used After this the incompressible Navier Stokes equations of the inertial frame is introduced To get the relative velocity the acceleration term 1s taken into account for the incompressible Navier Stokes equations The equation for absolute velocity in the rotating frame comes from coupling the rotating frame with the inertial frame so that the convected velocity in the rotating frame is the velocity in the inertial frame For the full derivation see 8 The incompressible Navier Stokes equations with multiple frames of reference can be written as eq 2 6 2 8 The inertial frame of reference s absolute velocity is described b
71. ge in SW This hole needs to be filled By searching for holes smaller than the sum of 10mm and 3 of the propeller diameter and fill them the script gets rid of this hole The resulting cleaned blade can be seen in Fig 4 9 Fig 4 9 The cleaned blade as a result of the cleanup algorithm The best way to get a proper computational domain definition is to use a template From the methodology used when analysing the SMP 11 propeller see section 4 1 a good setup could be made The methodology of how the template was made can be seen in section 4 4 2 The template contains among more things a domain a MRF zone a shaft a hub different size boxes and an empty PID named blades all made to fit a propeller with a diameter of 2760 mm and a hub with diameter 690 mm In the script this template file is merged to the cleaned blade The blade is put in the PID blades Two input dialogs asking for the hub and propeller diameter shows up When the inputs are typed in they are recomputed into scale factors which are based on the template 38 hub and propeller diameter The two scale factors pyp and Aprop are given by eq 4 11 and 4 12 _ inputorop prop 3760 4 11 inputpyp hub 690 4 12 The shaft and the hub are scaled with amp pup and the rest of the parts except for the blades are scaled with amp prop The code has now reached its first breakpoint the domain is defined the geometry is clean and all the parts have pro
72. have very good open water performance All the propellers have a hub ratio of 18 17 2 6 The Open Water Test The open water test is performed with the model scale propeller working in a uniform inflow This could be done in a towing tank or in a cavitation tunnel The test is usually performed altering the advance velocity V for a fix number of revolutions per second n The propeller thrust T and the propeller torque Q is measured during the test The fix RPM is altered to get the open water test at different Reynolds Numbers The RPM must be sufficiently high to overcome the viscous effects when scaling To get the same 20 conditions in full scale as in model scale the relationship between V and the velocity in tangential direction yielding an indication of the angle of attack for the blade profiles must be the same This relationship is known as the advance ratio J and is defined as in eq 2 19 V J 2 19 Where D the propeller diameter The non dimensional quantities Kr Kg and nyare defined as in eq 2 20 2 22 T AO Gaps 2 20 ie Ko TDs 2 21 JKr No 2 22 20K Where Kr dimensionless thrust Kg dimensionless torque p the fluid density and y the open water efficiency Kr Kg and 7 are the values usually measured in the open water test and are known as open water characteristics Plotting them against J gives the open water chart These characteristics are of interest since they id
73. he box are not possible The largest benefit of PROCAL is the low computational cost an open water chart with eight advance ratio steps takes about two minutes to get The setup time can be rather extensive sometimes but not in the near field of CFD The reason for that the CFD and BEM methods used in this thesis project was so accurate depends on that the flow was pressure driven The exact potential flow problem for propellers modelled in PROCAL accurately predicts the pressure forces since it is derived directly from the Navier Stokes equations only neglecting viscosity The pressure was also well modelled in the CFD method The major difference between the methods is how viscosity is handled In 80 PROCAL it is analytically corrected In OpenFOAM turbulence models were used The turbulence models could be seen as a more accurate viscous correction The lifting line method program used in this project was not very accurate For two out of three cases the differences between the model test results were significant There was no way to logically explain the difference in the results either The setup time for the lifting line method was very short and the computational cost was extremely low on the other hand When using the Wageningen method the computational cost and setup time was extremely low The results were rather accurate when the propeller was similar to a Wageningen design but less accurate otherwise This deficiency could be
74. he velocity field measurement results at RO 7 in plane x D 0 1 for the SMP 11 propeller with non dimensional axial tangential and radial velocities from the prediction plotted against the model test The thick line represents the calculation and the thin fluctuating line represents the model test The velocity field measurement at radius RO 7 in plane x D 0 2 is plotted in Fig 8 17 The tendency is captured but it should be noted that the tip vortex in the interval 50 lt 0 lt 45 is not captured at all 0 8 sa PPTC smp 11 Workshop 0 7 Y ij Measurements of 5 blades 7 06 LTT Vr Y 0 5 t Py V 04 E 0 3 N F ye Va V 4 sis idi im w A ai Me 0 1 E T 0 0 qa A AF PAPIT t 01 4 Trak 0 2 Eee S eee nn na a A S ar 03 di i l i dadau a a 04 0 5 0 6 0 7 0 8 1 LV VAY VRV j id 50 45 40 35 30 25 20 15 10 5 0 5 10 15 20 er Fig 8 17 The velocity field measurement results at RO 7 in plane x D 0 2 for the SMP 11 propeller with non dimensional axial tangential and radial velocities from the prediction plotted against the model test The thick line represents the calculation and the thin fluctuating line represents the model test The velocity field measurement at radius RO 97 in plane x D 0 1 is plotted in Fig 8 18 The tip vortex is well captured The axial field seems to be a litt
75. high curvature and larger near mid surface sections This is since the large gradients from the flow occur at the sharp edges For the coarse mesh the smallest element length on the surface was 1 mm and the largest 10 mm see Fig 4 6 PERO OX TANAPA O Fig 4 6 The triad surface mesh on one blade As turbulence model the K omega SST model was applied To model the boundary layer wall functions were needed Five prism layers with 1 2 as growth ratio and a starting length of 0 5 mm were applied to get the gradients close to the wall resolved The rotation was modeled with MRF To make use of MRF a volume surrounding the rotating parts was needed This volume was made cylindrical with a radius 59 mm larger than the propeller radius The length of the volume was 69 mm upstream and 2442 mm downstream Within this volume all parts were set to rotate The propeller inside this volume is shown in Fig 4 7 The motive for the distances was based on experience and assumptions A slip stream of approximately ten diameters length is appropriate The diameter of the cylinder was based on experiments increasing this parameter by a factor 1 5 made no difference on the results see section 8 2 Fig 4 7 The propeller inside the MRF zone As domain a larger cylinder was used This cylinder was made with 1261 mm upstream 3000 mm downstream and 1261 mm diameter These distances were based on experience five propeller diameters as upstream leng
76. ided to take place in Excel By simply copying a control file from PROCAL put it in an Excel sheet and letting commas be separators for new cells the lines in the control file could be manipulated The recommendations in section 2 3 2 were applied for the meshing parameters The operating conditions in the regular control file were set to be in accordance with the operating conditions specified in the blade design sheet V RPM and reference velocity V f were set in accordance with eq 5 2 5 4 i Lew 5 2 RPM 5 3 ET 5 3 Vrep n D 5 4 Where V the ship speed and w the effective wake fraction A new sheet for combined pre and post processing was made in the design workbook the openWaterResults sheet This sheet was given the three input cells Jmin Jmax and Jstep The names are quite self explanatory the minimum and maximum value of the advance ratio and the step size to be analyzed between these points should be given From this the number of advance ratio steps is calculated by eq 5 5 Imax Jmin nj e ed A 0 5 5 A code developed to generate the open water control file reads these four inputs calculates the ship speeds and puts them in order in the control file in accordance with the demanded PROCAL format To continue the analysis with the defined geometry and control file some kind of export from Excel to text files was needed A script was made that reads the cells in the Excel sheets and saves
77. ise direction The trailing edge spacing is the same but for the first panel at trailing edge see Fig 2 4 I A Li Z II Fig 2 4 The trailing edge spacing to the left and the leading edge spacing to the right exaggerated to visualize the effect The tip spacing determines the first element length at the tip in radial direction see Fig 2 5 The root spacing is the same but for the first panel at the root see Fig 2 6 MAA A CTN Y Fig 2 5 PROCAL tip spacing exaggerated to visualize the effect E e Py ETE a a SAR lt A EAT a gt AA PAR gt Ss QS SS gt Fig 2 6 PROCAL root spacing exaggerated to visualize the effect The two additional options to get good convergence and smooth reliable pressure distributions are the tip chord fraction and the hub smoothening The tip chord fraction uses the fact that the tip length at the last radial section is finite This allows the user to increase the chord fraction as a percentage of the length of the radial section before the tip section The effect of changing the tip chord fraction is to reduce the skewness of the last element at trailing edge 17 see Fig 2 7 The hub smoothening should be performed to avoid overlapping panels near leading and trailing edges This is performed preferably using Thomas Middlecoff control functions 15 Fig 2 7 Last trailing edge element placed in the top right corner
78. le under predicted The fluctuating behavior of the prediction should depend on that the solution wasn t entirely converged in this region To achieve convergence there is hard 62 PPTC smp 11 Workshop Measurements of 5 blades a A de MIA do a gh Nis aa UY VV VV J ty 50 45 40 35 30 25 20 15 10 5 0 5 10 15 20 er Fig 8 18 The velocity field measurement results at RO 97 in plane x D 0 1 for the SMP 11 propeller with non dimensional axial tangential and radial velocities from the prediction plotted against the model test The thick line represents the calculation and the thin fluctuating line represents the model test The velocity field measurement at radius RO 97 in plane x D 0 2 is plotted in Fig 8 19 Here it is more evident that the tip vortex is dissolved at plane x D 0 2 The tendency of the velocities is captured until the vortex The reason for the unresolved tip vortex will be explained later in this section PPTC smp 11 Workshop Measurements of 5 blades 1 V4V IR Calculation 50 45 40 35 30 25 20 15 10 5 0 5 10 15 20 ar Fig 8 19 The velocity field measurement results at RO 97 in plane x D 0 2 for the SMP 11 propeller with non dimensional axial tangential and radial velocities from the prediction plotted against the model test
79. lotted against the model test The thick line represents the calculation and the thin fluctuating line represents the model test The axial velocity field downstream the propeller disc with the mesh visible is visualized at x D 0 1 in Fig 8 22 As can be seen the mesh resolution is high near the blades The convergence could have been disturbed by the large cells occurring between the blades This issue could have been solved by using a stricter setting for the size box Unfortunately this problem was not noted when the results were submitted to the SMP 11 workshop 64 Fig 8 22 The velocity field at x D 0 1 downstream the SMP 11 propeller disc with the mesh visible and results of 1 Vx V The velocity field downstream the propeller disc with the mesh visible is visualized at x D 0 2 in Fig 8 23 It is evident that the mesh is coarser in this region being the reason for the dissolved the tip vortex Again a size box with stricter mesh settings should be used to avoid this Fig 8 23 The velocity field at x D 0 2 downstream the SMP 11 propeller disc with the mesh visible and results of 1 Vx V The velocity field at x D 0 1 downstream with smoothed shading can be seen in Fig 8 24 to visualize the velocity field with resolved tip vortex From this picture it can be seen that the results from Fig 8 16 Fig 8 18 and Fig 8 20 are reasonable and that the gradients seem to be dissolved near the large cells in Fig 8 22
80. nd a sketch of the model test results for case 2 3 2 can be seen in Fig 8 31 This is the design point which occurs at a rather low load Again neither the blade root cavitation nor the free stream cavitation was captured The cavitating Kr was not well predicted Berg PROCAL KT 0 2425 Case J 1 2686 Ky 0 2064 10K 0 6312 o 1 424 Fig 8 31 The cavitation pattern on the suction side predicted by PROCAL to the left and model test result to the right for case 2 3 2 It should be noted that Fig 8 30 and Fig 8 31 shows only suction side cavitation since pressure side cavitation didn t occur in the predictions Case 2 3 3 on the other hand has a lot of pressure side cavitation PROCAL recognizes when pressure side cavitation occurs but cannot calculate it Therefore case 2 3 3 did not as expected show any cavitation at all 68 8 2 Open Water Results from CPP1 This section starts by discussing the results of the template setup comparison mentioned in section 4 4 2 After this the validity of the CFD and boundary element method setups are discussed Further the predictions from CFD boundary element method lifting line method and Wageningen Series are compared to model test results and discussed Finally results from PROCAL predicted in model scale compared to model test results are shown to validate the viscous correction script The comparison between the different setup methods for the CFD script open water s
81. ningen Propeller Series Program was used on the SMP 11 propeller since this was the first step in the exploration of the program functionality Section 7 2 describes how the results of the predictions were scaled to full scale since this was necessary for the predictions of CPP1 and CPP2 The final sections section 7 3 and section 7 4 describe how the automation of the Wageningen Series and the full scale extrapolation was performed 7 1 Open Water Prediction of the SMP 11 Propeller The Wageningen series program Wageningen Propeller Series Program was used for the SMP 11 propeller The propeller has a PO7 D of 1 635 and a blade area ratio of 0 77896 Four open water characteristics tables were extracted since neither the blade area ratio nor the P07 D could be calculated directly in the program The contains of the generated tables is summarized in Table 7 1 Table 7 1 A summary of the tables used for the Wageningen interpolations Tabe 1i 2 3 4 EAR 0 75 0 9 0 75 0 9 P07 D 1 55 1 55 1 6 1 6 One table was interpolated between table 1 and table 2 yielding results at the proper blade area ratio but at too low pitch Table 3 and 4 was also interpolated to yield another table with the proper blade area ratio but at another too low pitch These two new tables with the too low pitches were extrapolated into one table with the correct pitch 7 2 Viscous Scale Effects Correction Since the Wageningen results are given in mod
82. nough to give stable volume meshing A maximum size of twice the domain element length has proven sufficiently large to give a stable meshing session The defined volumes are set up with the hexa interior mesh set to a maximum fluent skewness of 0 85 and a growth ratio of 1 2 The defined volumes are meshed with these settings 41 The file is merged with a template only containing the PID names innerVolume and outerVolume The fluid layers and the inner volume are put in PID innerVolume and the outer volume is put in outerVolume The solution is compressed to remove excessive parts and PIDs Finally the mesh quality is improved by allowing a node movement of maximum 0 2 times the local element length 4 5 Open Water Test of CPP1 As stated CPP1 was used to make the CFD ANSA script see section 4 4 The resulting mesh after using the script can be seen in Table 4 11 Table 4 11 The number of cells for the open water test of CPP1 Element type Cells Surface mesh elements 270000 Prism layer elements 1350000 Total elements 8125000 The propeller was analysed in a pull configuration for the points J 0 1 to J 0 8 with the standard configuration presented in section 4 1 but with viscosity and density matching the ITTC 78 defaults in PROCAL see Table 5 1 The pitch was adjusted to yield accordance with the model test A cylinder with radius 1806 mm computed using eq 2 29 was made The distance from trailing to leading e
83. o be open and propeller geometry inputs had to be put at certain cells in the workbook The solution was to link the blade design workbook to the lifting line workbook Pitch rake skew etc were called as functions from the values presented in the blade design sheet With the proper values inserted in the lift line workbook and the Jmax Jmin and Jstep Values from the open WaterResults sheet inserted as well the user only has to open the lift line workbook and press the OW calculation button The results from the lift line workbook are put in a Results sheet A VBA code was made that reads the values from the known starting row and column and ends at the known end column and end row of the lift line results sheet A staggered for loop running through first columns and then rows was used to extract data at a specified row and column in the lift line workbook and put at a specified row and column in the openWaterResults sheet The code for data extraction can be seen in Appendix F The result extracting code was linked to a button in the openWaterResults Consequently only two buttons need to be pushed to perform an open water analysis with the lifting line method and the code could thereby be considered automated 49 This page is intentionally left blank 50 7 Proceedings of the Wageningen Series This section describes how the Wageningen Series was used for open water predictions and how it was automated Section 7 1 describes how the Wage
84. ole strength and V the undisturbed velocity Blades hub and part of the wake for each blade are represented by dipole panels The Kutta condition makes the pressure difference between the face and the back go to zero This condition couples the wake to the propeller The condition is non linear and therefore requires an iterative solution A Jacobian disturbance value is used as a relaxation factor for the Kutta iterations 9 The boundary is divided into structured quadrilateral panels The sources and potentials are assumed to be constant over each panel The Bernoulli equation is used to compute the pressure over each panel as in eq 2 15 10 11 Doo 0 5p Ua w x x V ee P Poo PUU TW XX P at 2 15 pgh 2 3 Mesh Types The boundary element method and the CFD method need to be meshed in proper ways to get reliable and converged results Some grid generation theory is described below 2 3 1 CFD Method CFD is a very grid dependent technique The largest errors occur where the largest gradients are For this reason the resolution should be increased in such regions Only a restricted amount of cells can be used due to restrictions in computational power Therefore it is beneficial to have a denser grid where e g the curvature of the surface is high and having larger cells closer to the middle of the surface In ANSA there is a surface mesh type called CFD This mesh becomes dense at high curvature and boundaries an
85. per PIDs The next step is for the user to set up the pitch which can be done in many ways A recommended procedure for this is the procedure presented in section 4 5 4 4 2 The meshing template The template mentioned in section 4 4 1 is described in this section From the methodology used when analysing the SMP 11 propeller see section 4 1 a good setup could be made The only difference between the SMP 11 procedure and this template was that the domain was surface meshed with a uniform surface mesh in the template This was because a size varying mesh is unnecessary so far from the propeller and the large cylinder is not a complex geometry The template was made as a regular ANSA file One of the Berg Propulsion s standard hubs with a diameter of 690 mm was used Based on this hub a propeller diameter D four times the hub diameter 1 e 25 hub ratio and thereby D 2760 mm was assumed Based on this diameter and the proceedings of the SMP 11 propeller the template could be set up with properties as in Table 4 9 and Table 4 10 Note that the volume mesh and surface mesh parameters in the template will scale in accordance with the scale factors mentioned in section 4 4 1 The standard hub was cleaned and made to an intact surface for simple intersection with the blade foot A shaft was connected to the hub Fig 4 10 shows the computational domain in the template Fig 4 10 The domain template where the shaft is the small structu
86. re in the middle the thick lines are the size boxes and the thinner lines are the interface and the domain 39 To conclude the most accurate open water setup template a study of some different possible open water setup techniques was performed The first decision to make was whether the shaft should be long or short to yield accurate results The propeller was set in a push configuration The shaft was altered from 1 D to 2 D length and the results of Kr and Kg was compared to the model test results Further a comparison between the results when using a spherical and a straight end cap was performed This was tested with a long shaft The difference when increasing the size of the MRF zone by a factor 1 5 was tested This was only performed for the short shaft with a spherical end cap The difference between the setups pointed toward one conclusion the most accurate ones generated a high load near the blade root Therefore the setup was switched into a pull configuration which yielded the most accurate results This was expected since the open water tests usually are carried out in this way The spherical end cap did not affect the results at all but made the convergence faster As a consequence a pull configuration using a long shaft with spherical end cap in a MRF Zone with slightly larger diameter than the propeller diameter was used for the open water configuration template All parts were named after representation to make the OpenFOAM set
87. rediction of the SMP 11 propeller by PROCAL compared to the model test results can be seen in Fig 8 9 The prediction is quite accurate Kg is slightly higher in the prediction resulting in a little lower efficiency This is reasonable since the hub is present in the PROCAL computation 57 Open Water BEM at Model Scale 6 K Procal 10Kq_Procal ETAo_Procal Kt_Model 1QKQ Model ETAo_Model Kt 10Kq n 0 55 0 75 0 95 1 15 1 35 Advance Ratio J PROPULSION Fig 8 9 The open water chart predicted by the boundary element method compared to model test results for the SMP 11 propeller The open water prediction of the SMP 11 propeller by the lifting line method compared to the model test results can be seen in Fig 8 10 The propeller predicted by the lifting line method seems to be too heavy It should be noted that the effect from the hub is excluded in the model test force measurement This should of course result in higher Ky than if the hub was present since the hub would work in the counter direction of the thrust The lifting line results on the other hand points in the opposite direction The skew of the propeller is below 20 which should benefit the lifting line calculation Open Water Lifting Line at Model Scale o 1 8 1 6 1 4 Kt_Liftline 1 2 10Kq_LiftLine e 1 S ETAo_LiftLine a 0 8 Kt
88. reducing the risk of setup errors This conclusion only regards the method applied in this thesis The main conclusions that can be drawn from the lifting line method applied in this thesis are that the lifting line method was not very reliable regarding open water characteristics predictions has a very short setup time has inaccuracies that do not solely depend on the amount of skew has no relationship in whether the method will predict a too light or too heavy propeller tends to predict a later J and a higher Nmax could be automated both in regard to pre and post processing which saves some time Note that all the above conclusions regarding the lifting line method might only be true for the method used in this thesis 87 The main conclusions that can be drawn from the Wageningen Series are that the Wageningen Series e is accurate for Wageningen similar propeller designs e should be corrected if the propeller designs are dissimilar from Wageningen designs e has an extremely low setup time e does not need a complete geometry only pitch blade area ratio number of blades and advance ratio are needed to make a prediction e is very useful at an early design stage due to the low number of inputs e is useful to get an indication of whether the PROCAL CFD results are correct e could be automated both in regard to pre and post processing which saves some time The final recommendations of how the tools and specific methods stu
89. rence Frames 13 2 1 5 Turbulence Models 13 2 1 6 Wall Functions 14 Boundary Element Method 14 Mesh Types 15 2 3 1 CFD Method 15 2 3 2 Boundary Element Method 16 Lifting line Theory 19 The Wageningen B Series 20 The Open Water Test 20 Viscous Scale Effects 21 Pitch Setting 22 Propeller Geometries Test Setups and Resources 25 The SMP 11 Propeller and Test Setups 25 3 1 1 Case 2 1 Open Water Test 25 3 1 2 Case 2 2 Velocity Field Measurements
90. results High skewness of the cells might lead to instabilities and lower accuracy In Fig 2 2 the fluent definition of skew is shown Skewness 0 for isotria FLUENT EquiArea Skewness Fig 2 2 The definition of skewness used for quality checking 14 The numerical error will increase and convergence will be harder to achieve if adjacent cells are very different in size or if the ratio between cell height and cell area is high This is known as aspect ratio 13 There are an abundance of quality criterions for the mesh but these two mentioned problems are the ones that have been considered extra carefully in this thesis work 2 3 2 Boundary Element Method For the boundary element method a structured quadrilateral mesh is needed The parameters for the user to change are usually on the surface mesh of the blade in PROCAL The hub mesh may be changed as well but this has small effect on the results The panels leading edge to trailing edge determine how many panels that should be placed in chord wise direction on each of the suction and pressure side of the blade The panels root to tip determines the same but in radial direction instead see Fig 2 3 16 ad EE Ld aaa Poff A AZ Rave So E SSS ANS hd Fig 2 3 The panelling leading edge to trailing edge and root to tip in PROCAL The leading edge spacing determines the element length of the first panel at leading edge in chord w
91. results are very good except for in bollard pull as noted for CPP1 and the last point after Inma 45 noted for both the SMP 11 propeller and CPP1 The problem in bollard pull originates in the domain size When the domain size was the same as for the other measuring points i e J 0 21278 to J 0 9461 the solution wouldn t converge The final axial velocity field after several thousand iterations look as in Fig 8 42 74 Fig 8 41 Axial velocity field for CPP2 at J 0 5103 Fig 8 42 The axial velocity field of an unconverged bollard pull solution of CPP2 Note the unsymmetrical shape and the unrealistic velocities The velocity field is unsymmetrical and the velocities indicate a swirling motion in the flow The velocity on negative x coordinates has opposite sign to the velocity on positive x coordinates Note that x is in a lateral direction and z is in the axial direction This is exactly the problem to operate in bollard pull the propeller needs a large amount of water to suck in Since the domain is too small to provide enough water upstream the propeller it tries to suck water from the rest of the domain and hence the swirling motion The remedy was as mentioned to significantly increase the size of the domain This resulted in a more realistic velocity field see Fig 8 43 Fig 8 43 The axial velocity field of a bollard pull solution with increased domain size Note the large region of water sucked into the propeller
92. s the lifting line method should be able to handle Open Water Lifting Line at Full Scale Kt_LiftLine Kt_LiftLine Kt_LiftLine 0 0 2 0 4 0 6 0 8 1 1 2 Advance Ratio J PROPULSION Fig 8 45 The open water chart predicted by the lifting line method compared to model test results scaled to full scale for CPP2 76 The results from the Wageningen series compared to the model test results scaled to full scale can be seen in Fig 8 46 These results suffer from the same problem in bollard pull as for CPP1 The efficiency is over predicted after the design point as an effect of an under predicted Kg It should be noted that CPP2 is very different from a Wageningen propeller design Open Water Wageningen at Full Scale O 0 9 0 8 0 7 06 Kt_Wageningen E Kq_Wageningen 05 g ETAo_Wageningen g 04 Kt_Model Z 0 3 10Kq_Model 0 2 ETAo_ Model 0 1 0 0 0 2 0 4 0 6 0 8 1 1 2 gt Advance Ratio J PRARHESIAN Fig 8 46 The open water chart predicted by the Wageningen series compared to model test results scaled to full scale for CPP2 The results from the boundary element method at model scale compared to the model test results can be seen in Fig 8 47 These results do again confirm the validity in the automated viscous correction method in the same way as for CPP1 c f Fig 8 44 Open Water BEM at Model Scale K Procal 10Kq_Procal ETAo_Procal
93. sdam cavitation tunnel K15A The tunnel had a cross section of 600 600 mm and a length of 2600 mm The propeller was positioned in the vertical and lateral centre of the tunnel The longitudinal position was 570 mm from the beginning of the test section see Fig 3 4 The test setup was a push 26 configuration Another type of hub was used for the test to match the push configuration better see Fig 3 5 Fig 3 4 The lateral and longitudinal propeller position for cavitation tests and velocity field measurement Fig 3 5 The hub used in the cavitation tests and the velocity field measurement The velocity field was measured using Laser Doppler Velocimetry LDV The inflow was homogenous and the LDV measurements were performed in the planes 0 1D and 0 2 D in front of the propeller disc see Fig 3 6 0 2D 0 094D 0 2D Fig 3 6 The measuring planes for the velocity field measurement 21 The measurements were angular based with the zero degree position defined as the 12 o clock position The velocities in all directions were measured at every 0 25 step The 27 measurements were performed along a constant line at angular position P 225 and then related to the zero degree position The blade position was recorded at every time step making the velocity field relating to the zero degree position possible The test was performed with a
94. stream the propeller disc if the mesh resolution is high enough is good for out of the box predictions such as predicting the characteristics from an odd design or removing the hub from the force results gives the possibility to visualize problem areas such as separation zones has problems with predicting bollard pull and efficiency after J ma assuming that the model test measurements are correct and that the viscous corrections apply in bollard pull which might be an incorrect assumption This conclusion only regards the method applied in this thesis could be automated regarding pre processing for open water predictions leaving only two manual moments intersect the blade to the blade foot and hub and check the surface mesh saving at least five hours of manual work and guaranteeing consequent setups This conclusion only regards the method applied in this thesis The main conclusions that can be drawn from the boundary element method are that the boundary element method is almost as accurate as CFD regarding open water characteristics predictions and has significantly lower computational cost has much shorter setup time than CFD tends to over predict sheet cavitation at the leading edge at a high load This conclusion only regards the method applied in this thesis is a good tool for early propeller performance predictions could be automated both in regard to pre and post processing saving some time and more importantly
95. sure detachment mode in PROCAL This could solve the issue with the missed blade root and sheet cavitation on the trailing edge It would also be valuable if a two phase modeling of the cavitation computation was performed in CFD to get a comparison between the methods in that respect The lifting line method should be tested with another software and a deeper investigation should be performed to understand why the results are so unreliable The Wageningen Series should also be tested with corrections applied for the propellers to get a better insight in the capabilities of the tool 88 10 References 1 Wageningen propeller series program v2003_1 A program containing the Wageningen charts 2 PROCAL v 2 0 2 0 A boundary element method tool with GUI post processor grid generator and solver for the direct formulation of the potential flow problem for propeller It can also solve for cavitation using the Morino formulation 3 LiftLine 0 412ges A lifting line method tool made as an Excel sheet with macros containing the lift line code 4 OpenFOAM v1 6 An open source CFD toolbox It can solve anything from complex fluid flows involving chemical reactions turbulence and heat transfer to solid dynamics and electromagnetics quoted http www openfoam com 5 Davidsson L an Introduction to Turbulence Models G teborg Sweden Chalmers University of Technology Department of Thermo and Fluid Dynamics November 20
96. t of the propeller The velocity field looks reasonable the velocity is accelerated in the direction of the inflow velocity A separation zone is developed behind the shaft This could be avoided if the slide in Fig 3 3 was modeled It affects the velocity field behind the propeller disc and thereby the forces on the propeller which to some extent might affect the results The separation could be reduced by replacing the flat end of the shaft with a sphere On the other hand the forces were computed over the blades only so the impact of the separation zone should be of small significance The radial wake strength PHIW and radial axial force F distributions of the SMP 11 propeller at 0 5Jy may in the PROCAL open water prediction can be seen in Fig 8 4 As can be seen they are smooth and the maximum load appears at the sections were most work should be performed vouching for reliable results Fx for J 0 600 vs r R Phiw for J 0 600 vs r R 0 460 0 270 0 420 0 240 0 380 0 210 0 340 0 300 0 180 0 260 E 0 150 0 220 0 120 0 180 0 090 0 140 0 100 0 060 0 060 0 030 0 020 0 300 0 400 0 500 0 600 0 700 0 800 0 900 1 000 0 300 0 400 0 500 0 600 0 700 0 800 0 900 1 000 Radius Fraction r R Radius Fraction r R Phiw Fig 8 4 F distribution to the left and PHIW to the right at 0 5 ma for CPP1 The results from the CFD simulations compared to the model test results can be seen in Fig 8 5 As can be seen the prediction is
97. ter characteristics predictions 5 Validate the automation 6 Compare all the open water results gained from the predictions to model tests for a complete benchmark of the tools 7 Develop recommendations based on the results from step 6 To understand how to use the tools and how to perform the setups a literature study had to be performed This study was partly from program theory manuals and partly from relevant theory literature Three propeller geometries were provided one propeller for the SMP 11 Workshop SMP 11 one propeller for a single screw vessel CPP1 and one propeller for a twin screw vessel CPP2 The SMP 11 propeller was used to complete step 1 3 above This was since SMP 11 provided test cases for predictions of open water characteristics open water velocity field measurements and open water cavitation measurements These test cases were enough to cover the exploration of the program functionality CPP1 was used to develop the open water characteristics automation scripts constantly applying the methods that were found reliable when analyzing the SMP 11 test cases CPP2 was used to validate the scripts The outline of this thesis is based on the working order described above It is started with a theory section section 2 to describe the theory behind the computational tools and the setup methodologies After this a summary of the used propeller geometries is presented in the geometries and setup section section
98. th and as domain diameter and twelve propeller diameters as downstream length has proven accurate and giving a reasonable amount of cells before 29 The inner volume is except for being the MRF zone representing the slipstream The settings of the final coarse mesh can be seen in Table 4 1 It should be noted that the maximum computational power at hand allowed about thirteen million cells This was the reason for the cell length choice the aim was to have high resolution near the propeller a maximum growth ratio of 1 2 and not cells of a size that completely dissolves the gradients 33 Table 4 1 The meshing parameters of the coarse mesh for the open water test Perimeter length mm Surface mesh type Surface mesh size mm Blades CFD 1 to 10 Hub CFD 2 to 10 Shaft CFD 3 to 10 Interface CFD 1to 10 Domain CFD 10 to 50 As interpolation schemes first order accurate schemes were used for the turbulent quantities kinetic energy inverse turbulent time scale and the turbulent viscosity The computation was started with a first order upwind scheme for the velocity When the computation was stabilized a second order upwind scheme was applied instead To indicate grid independence for the results the mesh was refined at regions with large gradients The mesh was made larger around shaft and hub but refined with a factor of two at blade corners and blade tip The maximum
99. them in a text file in a specified location with a format supported by PROCAL Three sub routines one for exporting the geometry one for exporting the regular control file and one for exporting the open water control file was made These subroutines were linked to one button each in the geometry file sheet in the design workbook see Fig 8 59 The pre processing could now be considered automated since only opening PROCAL hit the mesh and the perform analysis button needs to be pressed to get a completed analysis This is either for the design speed or for the complete open water diagram 5 3 2 The Post processing With the pre processing automated it was time to make automatic post processing The PROCAL result files always have the same file names The location of the files is known since the control and geometry file are put there from the automatic pre processing A script for reading the results was made First it opens the results file It loads it into Excel and cleans it to get the values free from text and number separators It searches for the cell in the beginning and the end of the open water results section in the file and gets the cell s addresses An interval between these addresses is specified Every line of open water data i e Kr Kg and no ends with a right curly bracket in the result file If cases determine whether 47 the cell in the interval is a value or not If it is a value the value is outputted in
100. tionally left blank 24 3 Propeller Geometries Test Setups and Resources Three different propellers and five different setups were used for the validation and automation of the computational tools The first propeller and three first setups were from the SMP 11 case 2 which provided a CP propeller with different hub caps for push and pull configuration Further a CP propeller for a single screw vessel CPP1 and a CP propeller for a twin screw vessel CPP2 were provided from Berg Propulsion In order to protect the commercial value of the two last mentioned propellers the exact data of them cannot be provided in this report 3 1 The SMP 11 Propeller and Test Setups The SMP 11 case 2 contained three setups one open water characteristics measurement one velocity field measurement and one cavitation test setup These setups where performed at different test points and for different inflow conditions The propeller was a five bladed CP propeller One of the design criterions for the propeller was to generate a tip vortex The propeller design was provided with different hub caps for push and pull arrangement 19 Some propeller characteristics can be seen in Table 3 1 A picture of the propeller can be seen in Fig 3 1 The propeller drawing and detailed propeller characteristics can be seen in Appendix A Table 3 1 Some propeller characteristics of the SMP 11 propeller m 0 25 rev min 900 1 635 5 0 77896
101. turbulent viscosity can be written see eq 2 11 5 UNK V t In En je Where n the normal distance to the wall u the friction velocity E constant and k the turbulent wave number 2 11 2 2 Boundary Element Method The panel method or boundary element method is using the exact formulation of the potential flow problem on propellers The direct formulation is used in PROCAL and will be described in this section The direct formulation solves directly for the potential and then determines the velocities The Morino formulation which is a direct formulation is used in PROCAL Assuming irrotational and incompressible flow the velocity can be expressed as a potential see eq 2 12 V Vo 2 12 The potential can be written as the sum of the potential of the undisturbed flow and the disturbance potential to be solved q By applying Green s second theorem the 3D 14 computational domain will be reduced to the unknowns at the boundaries only The potential at the boundaries can be written as in eq 2 13 1 1 0 1 z lea z 5 Bd jas 2 13 2T Js ANg Roq ONg Rp q Where n the normal to the surface R the vector connecting a point on the surface and the point p and p the collocation point Here the potential interior of the surface S has the value zero On the surface the zero penetration boundary condition gives the source strengths see eq 2 14 3p Og ine Vong 2 14 Where o the monop
102. up understandable The PID names were set to blades hub shaft domain inlet outlet and interface where interface is representing the MRF zone To simplify the meshing function in the script a batch mesh scenario was added to the template A batch mesh scenario is a tool where one adds a filter finding a PID with a certain name e g blades and then meshes this blades PID automatically in accordance with the quality criterion mesh size requirements and geometrical representation requirements The size boxes were set behind the propeller disc to have a good resolution in the slip stream This was both for the computational accuracy and for the visualization it is beneficial to have high resolution when e g rendering including a velocity field is performed The size boxes were set with a maximum volume element length of 100 mm and 200 mm for the box closest to and the one more downstream respectively Table 4 9 The dimensions of the template file Domain diameter 5D MRF zone length 7D Domain length upstream 5D Size boxes length each 5D Domain length downstream 10D Size boxes diameter each D 0 25D MRF zone diameter D 0 25D Propeller diameter D 2760 mm Table 4 10 The mesh settings from the batch mesh scenario in the template file Perimeter length mm Surface mesh type Surface mesh size mm Blades 5 to 50 CFD 5 to 50 Hub 5 to 50 CFD 5 to 50 Shaft 50 to 200 CFD 50 to 200 Interface 100 CFD 5 to
103. urs of work and results in consequent setups Keywords Open water characteristics CFD Boundary element method Lifting line method Wageningen Series SMP 11 Workshop Validation Setup automation Automatic post processing Preface This thesis is a part of the requirements for the master s degree at Chalmers University of Technology G teborg and has been carried out at Berg Propulsion Technology AB H n I would like to acknowledge and thank my examiner Associate Professor Rickard Bensow at the Department of Shipping and Marine Technology and my supervisor Ph D Tobias Huuva at Berg Propulsion Technology AB for all help and support throughout the project I would also like to show my gratitude to Magnus Pettersson at Berg Propulsion Technology AB for all help concerning both support in the use of the software and valuable theory discussions Finally I would like to thank Lars L bke at SVA for the support with the SMP 11 test cases and Johan Bosschers at MARIN for all the PROCAL support Goteborg June 2011 Olof Klerebrant Klasson Nomenclature Glossary Bollard pull Low speed condition where the ship is towing Dead top centre The twelve O clock position of the propeller disc Design workbook Excel workbook at Berg Propulsion containing the blade design Angle that blades slant forward aftward compared to a line perpendicular to Rake the shaft line Size box Box drawn in ANSA used to locally refine the mesh Sk
104. ve should be repeated after this The complete open water table is tabulated below the Get PROCAL Results button when pressed see Fig 8 57 Get PROCAL Resuts Plot PROCAL J Kt_Procal 10Kq_Procal ETAo_Procal 0 07 0 5306 0 854 0 07179 0 15 0 498 0 8033 0 1433 0 22 0 4652 0 7519 0 2145 0 29 0 4321 0 6997 0 2854 0 36 0 3986 0 6467 0 3561 0 44 0 3647 0 5927 0 4266 0 51 0 3297 0 543 0 4911 0 58 0 2937 0 4969 0 5464 0 65 0 2562 0 4522 0 5892 0 73 0 2178 0 4049 0 6216 0 80 0 1789 0 354 0 6423 0 87 0 1393 0 2992 0 6456 0 94 0 09908 0 2404 0 619 1 02 0 05809 0 1775 0 5295 Fig 8 57 The generated table after pushing the Get PROCAL Results button If the user wants to plot it the button plot should be hit An open water chart is generated see Fig 8 58 83 Get PROCAL Results Plot PROCAL Input for CFD J Kt_Procal 10Kq Procal ETAo_Procal Tpres N Tvisc IN a 0 07 0 5306 0 854 0 07179 ji 0 15 0 498 0 8033 0 1433 0 22 0 4652 0 7519 0 2145 0 29 0 4321 0 6997 0 2854 0 36 0 3986 0 6467 0 3561 0 44 0 3647 0 5927 0 4266 0 51 0 3297 0 543 0 4911 058 0 2937 0 4969 0 5464 i 0 65 0 2562 0 4522 0 5892 120464 1612 13 0 73 0 2178 0 4049 0 6216 0 80 0 1789 0 354 0 6423 0 87 0 1393 0 2992 0 6456 0 94 0 09908 0 2404 0 619 1 02 0 05809 0 1775 0 5295 Open Water PROCAL____ TS I Procal z Fig 8
105. ve the problem with the inaccuracy of the first order upwind scheme a second order upwind scheme could be used It uses two nodes upstream and assumes that the gradient between them is the same as the gradient between the current face and the upstream neighbouring node The scheme is transportive and conservative but it is not bounded making it less stable than the first order upwind scheme On the other hand it is second order accurate 6 2 1 3 Pressure Velocity Coupling If the pressure gradient in the Navier Stokes equations is discretized over a control volume the discretized equation will be computed without respect to the pressure in the current node This results in a so called checker board pressure field It means that the equation is solved but the result is a highly oscillating pressure field This can be solved using Rhie Chow interpolation and a correction algorithm such as SIMPLE The procedure of the SIMPLE algorithm is to 1 Guess the pressure 2 Solve the Navier Stokes equations using the old pressure 3 Solve the pressure correction equation 4 Correct the velocities and the pressures based on the computed pressure correction 5 Repeat point 2 4 until convergence is reached 12 The pressure correction equation comes from discretizing the continuity equation and rewriting it so it contains one old velocity term and one correction term for each velocity direction and a term representing the continuity error A
106. with the solver MRFSimpleFoam The simulation was of steady RANS type The forces and moments were computed on the blades only 4 2 Velocity Field Measurement of the SMP 11 Propeller The velocity field computation of the SMP 11 propeller was performed in the same way as for the open water test and for the same propeller but with a different hubcap see section 4 1 The domain and inner volume were rotated and elongated to fit the new arrangement and the longer shaft The final fine and coarse mesh settings and number of cells can be seen in Table 4 6 and Table 4 7 The final number of cells for the coarse and fine mesh can be seen in Table 35 4 8 A square size box was used due to a bug in ANSA making the preferred cylindrical size box unusable Table 4 6 The settings of the coarse mesh for the velocity field measurement Perimeter length mm Surface mesh type Surface mesh size mm Blades 1 CFD 1to 10 Hub 1 CFD 1to 10 Shaft 5 CFD 1to 10 Interface 10 CFD 1to 10 Domain 50 CFD 10 to 50 Table 4 7 The settings of the fine mesh for the velocity field measurement Perimeter length mm Surface mesh type Surface mesh size mm Blades 0 3 CFD 0 3 to 5 Hub 1to5 CFD 1to 10 Shaft 5 CFD 0 3 to 10 Interface 5 25 CFD 0 3 to 5 25 Domain 100 CFD 5 25 to 100 T
107. y eq 2 6 The relative and absolute velocities of the rotating frame of reference are described by eq 2 7 and 2 8 respectively Since the indexes might be confusing using tensor notation the equations are written on vector notation Se cy p 5 V U x Uy vc vV V U e vV U 0 gt gt p V Ugx Up 20xUp 2x0 v v v U Up x Up 20x Up 0x0xF a ee 2 7 V Un 0 Ed el at p ES V UrxU 0xU V C vV V U ee V U 0 Where notation I Inertial notation R rotating and U is the velocity vector in Cartesian coordinates 8 2 1 5 Turbulence Models With the RANS equations there is still a closure problem This is solved using a turbulence model Turbulence is irregular diffusive three dimensional and dissipative The better the turbulence model can represent these statements about turbulence the more accurate it is A common way to make a turbulence model is to divide the turbulence into one turbulent kinetic energy k and one dissipative part If eq 2 4 is subtracted from eq 2 1 and the result is multiplied by u and time averaged the exact k equation is attained An exact equation for can also be derived from the Navier Stokes equations The number of unknown terms in both the exact k and model are large Therefore the equations are modelled using physical reasoning The result from this is the so called k 13 model 5 This model is unsatisfactory when predicting near wall beh
108. y field is shown in Fig 8 14 and the pressure distribution of the propeller suction side is visualized in Fig 8 15 As can be seen no odd separation occurs at the blades and the velocity field looks stable The boundary layer on the shaft looks stable too The low pressure zone on the shaft indicates separation which could have been avoided by setting the inlet at the beginning of the shaft This small separation zone should not affect the results though since it is sufficiently far upstream as can be seen on the boundary layer in Fig 8 14 Fig 8 15 Pressure distribution of the suction side at the working point for the velocity field measurement 61 The velocity field measurement at radius RO 7 in plane x D 0 1 downstream the propeller disc is plotted in Fig 8 16 The calculation is smooth which is an effect of the averaged simulation RANS The prediction is quite good as can be seen The fluctuations in the model test depends on that the measured turbulence is real and turbulence is fluctuating The tendency of the velocity field is definitely caught by the calculations 0 8 7 PETC smp 11 Workshop oY Measurements of 5 blades 1 727 0 6 ae 0 5 VIV 0 4 0 3 19 0 1 0 0 S01 02 03 04 0 5 0 6 0 7 0 8 Calculation I IV VAV VaV E gt S0 45 40 35 30 25 20 15 10 5 0 5 10 15 20 911 Fig 8 16 T
109. yds Registry recommends tip spacing in the interval 0 1 lt TS lt 0 2 but this interval might be too narrow The goal when meshing is to get the mesh as orthogonal as possible Following these recommendations gives a good starting estimation of an orthogonal mesh 16 2 4 Lifting line Theory The lifting line methods are common in propeller design as a first design step They are then used to find an optimum geometric radial distribution of the propeller with respect to efficiency Lifting line methods are based on lifting line theory which will be explained below Assume that a foil has a line of vortices see Fig 2 8 Fig 2 8 A foil with a line of vortices from an inflow 9 These vortices create a lifting force perpendicular to the inflow velocity Adapting Helmholtz s first and second law i e 1 The strength of a vortex line is constant along its length 2 A Vortex line must be closed it cannot end in the fluid leads to the bending of the vortex line at the end of the foil The vortex lines are closed again far downstream in this context at infinity resulting in an infinitely long horseshoe vortex line In Fig 2 9 one can see the vortex line following the foil called bound vortex Together with this bound vortex there are vortex lines known as trailing vortices which shapes the imaginary infinite horse shoe Bound _ _ LMM vorticity Fig 2 9 The bound and trailing vorticity for a foil 9
110. ys and Kgs can be calculated using eq 2 27 and 2 28 P cz Krs Kru ACp 0 3 2 27 TS TM D D x D cZ Where D the propeller diameter at full scale P the full scale pitch at R0 75 and Z the number of blades 18 2 8 Pitch Setting In the CFD setups for Controllable Pitch CP propellers it is commonly necessary to adjust the pitch This might be to match e g a model test or to change from free running to bollard pull The pitch is usually changed with the pitch at RO 7 as reference The pitch is defined as the axial distance every blade section screws itself during one rotation see Fig 2 10 Cylinder cut at radius 7 Fig 2 10 The definition of pitch for a propeller 18 Since the blade section at RO 7 is of interest a cylindrical cut must be performed The reason for this is to present the radial coordinates in a Cartesian plane The radius of such a cut can be described by eq 2 29 D Tout 0 7 3 2 29 22 The distance between the intersection of the cutting plane and the leading and trailing edge respectively describes a distance in the lateral y and axial x direction The pitch angle see Fig 2 10 can then be described by the relationship in eq 2 30 arctan C 2 30 From Fig 2 10 it is evident that the pitch P can be described by eq 2 31 18 P x tan d x a at RO 7 T2R z P0 7 P0 7 AL 2 31 ED D sD 2 31 2n 0 7 2 m 0 7 23 This page is inten

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