Trailing edge curve
Contents
1. E a Poor quality mesh near concave regions b Quality improvement via edge collapse A c Poor quality mesh near convex regions d Quality improvement via face refinement Figure 11 Topological adaptivity for mesh quality improvement point cloud data but introduces visible slope discontinuities in the surface Additionally this approach 1s not appropriate for data that has not yet been denoised 3 The main deficiency of the pseudo three dimensional surface modeling approach is that unless nu merous spanwise sections are employed potentially significant spanwise variations in the ice accre tion will not be accurately modeled Unfortunately manual filtering of the two dimensional sections is a time consuming process 4 Regardless of the approach used for surface modeling it seems that some type of automated proce dure is necessary to perform filtering The use of image processing techniques for this purpose is promising 5 The mesh generation package SolidMesh was used to generate a mesh for the iced wing configura tion While there was a flaw in the mesh on the left side boundary of the computational domain the mesh appeared to be of generally good quality However SolidMesh which is typical of unstruc tured hybrid mesh generators doesn t provide the intuitive control for point positioning that is needed for the iced wing problem 6 The2. BOO KAAS wa ry 7 K BAN SVAVAVAVAVAVAN DS RAS X SEL AOL i REPRISES EZ ROE SSE VAT AV AN AY My Ls RISEY ROK is BEN ER K NY pY E YA DA ZZO GS oo OS A Dl NS BOY A RI PODNA POR OCA VA AAAAAAAAALRL VG BOOP SOAR DA 222 By YA DAR COTA A 2 X g X S YA OZ N NOE ES PAL SX BAD SSS 22 SADA IVA 2 ADAN PAI AVAVA VAA AAS VZ be D A NINES OOOO Figure 6 Left side boundary of mesh highly stretched near body mesh is extruded from the surface to capture large gradients in the field vari ables Typically the extruded mesh is generated using an advancing layer scheme The remainder of the domain is filled with a tetrahedral mesh If an extruded surface has quadrilaterals some type of transitional element is needed between the extruded mesh and the tetrahedral mesh Typically in a hybrid mesh all the cells are of standard shapes triangular prisms and tetrahedra or hexahedra pyramids and tetrahedra Unfortunately volume meshes generated using advancing layer methods may have poor quality cells near convex and concave regions of the geometry To address this shortcoming of hybrid type meshes several researchers have considered the possibility of using other element types to improve mesh quality The resulting meshe
3. 8 9 10 11 12 13 14 15 Y Choo K D Lee D S Thompson and M Vickerman Geometry Modeling and Grid Generation for Icing Effects and Ice Accretion Simulations on Airfoils P R Eiseman J Hauser B K Soni and J F Thompson editors Proc 7 International Conference on Numerical Grid Generation in Compu tational Field Simulations pages 1061 1070 International Society for Grid Generation Mississippi State MS September 2000 W B Wright User Manual for the NASA Glenn Ice Accretion Code LEWICE 2 0 Technical Report CR 1999 209409 NASA September 1999 J Chung Y Choo A Reehorst D W Sheldon and J Slater Numerical Study of Aircraft Controlla bility under Certain Icing Conditions AZAA Paper 99 0375 AIAA 37 Aerospace Sciences Meeting Reno NV January 1999 NPARC user s guide version 3 0 1996 Y Choo private communication June 2000 T K Dey J Giesen S Goswami J Hudson R Wenger and W Zhao Undersampling and Oversam pling in Sample Based Shape Modeling Proc IEEE Visualization 2001 pages 83 90 2001 D Marcum Unstructured Grid Generation using Automatic Point Insertion and Local Reconnection J F Thompson B K Soni and N Weatherill editors Handbook of Grid Generation CRC Press Boca Raton FL 1998 R E Tomaro W Z Strang and L N Sankar An Implicit Algorithm for Solving Time Dependent Flows on Unstructured Grids AJAA Paper 97 03
4. o ees 12 Cutting planes through the mesh at three spanwise stations lower surface 13 Mesh flaw in left side boundary plane o o 14 Example of simple topological adaptivity in a surface mesh 15 Topological adaptivity for mesh quality improvement 16 Near body volume mesh without topological adaptivity 17 Near body volume mesh with topological adaptivity 18 Navier Stokes solution for iced wing using Cobaltgy M 0 3 Re 2 0x10 a 3deg 19 Basic Strategy Generate six curves to define two surfaces 24 1 Introduction There are two distinct applications related to the aircraft icing problem in which computational fluid dy namics CFD can play a significant role 1 First is the prediction of ice accretion using a code such as LEWICE 2 coupled with a CFD flow solver The second potential application is a detailed flow field analysis to determine the effects of ice accretion on aircraft performance Here we focus exclusively on the second application In general detailed three dimensional simulations of the flow around an iced wing are relatively rare due to the enormous expenditure of resources needed to obtain a quality solution Chung et al 3 demonstrated the potential of CFD by predicting the aerodynamic characteristics of an aircraft involved in an accident attributed to icing The ice shapes were determi
5. 4 Several meshes for iced wing configurations were developed using the existing mesh generation pack age SolidMesh 7 5 A new topologically adaptive surface mesh generation algorithm was applied to the iced wing prob lem 6 A new topologically adaptive volume mesh generation algorithm was applied to the iced wing prob lem 7 A flow solution for an iced wing configuration was generated using the Cobaltgo 8 flow solver 8 Strategies were developed for geometry modeling and mesh generation specific to the iced wing problem The work accomplished to date can best be divided into three categories geometry modeling mesh gen eration and flow solution and the report is organized in this manner A summary of activities relevant to each of these areas performed during Year 1 is described in the sections that follow Also included are a discussion on the implications of the work and a suggested strategy for iced wing CFD 2 Problem Description The problem of generating a computational fluid dynamics solution for the flow about an iced wing is a complex one involving several steps In order to provide motivation for the organization of this report we now provide a problem definition Given a point cloud representation of a wing with an ice accretion 1 Develop a representation of the surface that is suitable for generating a surface mesh 2 Specify the artificial boundaries needed to define the computational domain e g outer
6. Apply to fit the cloud with the curve Change the name to leading_edge_curve Split the point cloud into two surfaces Hide all the data keeping whole point cloud data leading edge curve and trailing edge curve in the viewport Press keyboard button F1 to orient the point cloud This will be helpful in splitting the cloud in to two parts Use Circle Select with option Keep Both the Data checked to split the cloud Click the cursor on the trailing_edge_curve and at the leading_edge_curve and form the loop to break the cloud Change the names of the two resulting point clouds to top and bottom for future reference Create Curves at the Inboard and Outboard Boundaries This section describes the methodology followed to extract the top_zmax_curve The following explains the method followed to generate the cloud corresponding to top_zmax_curve Put all the clouds into invisible mode except top cloud Orient the top cloud to F5 view by pressing keyboard button F5 25 e The point cloud data can be extracted by going to Point Cross section Parallel In the dialog box select the top cloud from the List In the Direction select Z Click on the Start Point and bring the focus to the main screen A plane will be displayed on the screen which may not lie on or touch the cloud Click at the place where the plane passes across the top cloud in order to get the maximum number of boundary points and make sure the plane is not too much inside or o
7. Speed Typically the front speed is a function of a constant term which represents inflation if positive or deflation if negative and a curvature dependent term that provides a surface tension effect F 1 eK 4 where e gt 0 is a user specified constant and K is the local front curvature given by 1 aahh 2010302 buy 3 2 42 43 How to Solve the Level Set Equation The level set equation Eq 3 is a wave type equation What 1s important to note is that like CFD simulations appropriate numerical solutions of the level set equation should satisfy an entropy condition The entropy condition effectively eliminates discontinuities in the front The method suggested by Malladi et al 11 is to use the first order upwind scheme given by 5 AP of At maz Fiy 0 Vt min Fij 0 V where 2 2 V maz D34 0 min Dio 0 5 27 1 2 max D7 0 min 036 0 A I min D34 o maz Dio 0 min Dv o max Dv 0 a 7 where Dy o indicates a forward spatial difference and D O indicates a backward spatial difference of Higher order Essentially Nonoscillatory ENO upwind schemes were also implemented but did not significantly alter the results The initial field is defined using the signed distance function from the initial level set 3 2 2 Curve Surface Extraction Data using Level Set Methods This technique is well developed for pixel based data images The basic idea
8. The surface can be fitted by giving the number of control points as input or accepting the optimal number of control points given by Surfacer The level of accuracy of the description of the NURBS surface can be varied using the smoothness tension and standard deviation parameters One has to be careful in varying the parameters as the sensitivity to the change in these parameters is high In the current approach the values used are 0 75 tension 0 5 smoothness and 0 5 standard deviation Similarly the second surface bottom is fitted to the bottom cloud considering the following curves as the boundaries e Trailing edge curve e Bottom_zmin_curve e Leading edge curve e Bottom_zmax_curve After getting the two surfaces C continuity is verified at the leading and trailing edge If they are not CY continuous they can be forced to be so by matching the two surfaces at the interface Once the two surfaces are matched they are saved in IGES format The Surface Cloud difference plot indicates where the NURBS fit does a poor job matching the point cloud If the maxiumum error is near the horn tips one approach for reducing the error is to create an addi tional curve along the horn tip This can be done by creating a line by picking two points on top_zmin_curve amp top zmax_curve at the turning points After generating the line it can be projected onto the cloud by Points Cross sections Project curve on cloud This will give a set of points
9. configuration long computer execution times are to be expected However any potential savings that can be garnered through judicious mesh generation procedures should be considered From the standpoint of accuracy a mesh should have 1 point clustering in regions of large gradients and 2 high quality elements no highly skewed faces or slivers Obviously points need to be clustered in regions adjacent to no slip boundaries Additionally points need to be clustered in regions where wakes may occur downstream of ice shapes such as horns This might suggest using solution adaptive meshes It should be noted that sufficient resolution must be present in the initial mesh to capture the phenomenon of interest Some control perhaps manual is needed to specify initial point placements From the standpoint of flexibility the mesh generation procedure should be able to treat very complex geometries and still produce high quality meshes In the next section we describe a general procedure used to generate a mesh for the iced wing problem 4 2 Procedure Once the geometry representation has been saved in an IGES file appropriate surface and volume meshes must be generated The general procedure we have defined is outlined below 1 Generate an unstructured triangular mesh on the surface defined in the IGES file 2 Since we anticipate performing viscous computations define a wake surface by inserting a plane downstream of the trailing edge curve
10. level set filtering technique on the point cloud data whereby the chordwise slices could be extracted automatically 3 Continue to identify software that is available as a long term solution to the iced wing mesh generation problem Several candidates are currently being identified 4 Itis our opinion that at some point iced wing specific mesh generation software should be developed What is lacking in current mesh generation software packages is intuitive control of point placement However this effort should be postponed until the utility of computational fluid dynamics simulations is established for iced wing simulations and a clear understanding of the potential benefits of such a system is established 5 Cobaltgg should continue to be used to generate flow field solutions 17 SA SAA SS Se SER SEARS See E LO OS oS DIA eee TSCA XK ERIS SANS A S 5 2 SAS BZ io A Z AN KNN Y va KE X KK YX a YS et l ZA BRS ANS IKA LADRA ADA INR SON DA DADA AKIF a Lower surface of wing b Wing leading edge Figure 13 Near body volume mesh with topological adaptivity 6 Evaluate the effectiveness of computational fluid dynamics techniques for iced wing simulations by comparison of computed results with experimental data 7 Determine by comparison with experimental data if the significant spanwise flow components re ported here are real features rather than computational anomalies If they are real de
11. on the cloud Fit the curve with these points and break the top cloud at the turning point into two clouds Fit the two surfaces with the newly created curve as an interface boundary 27
12. on the extruded surface More work is being performed in the general area of quality improvement The results of these preliminary efforts are presented in the next section 4 4 4 Example Mesh In this section we demonstrate the benefits of topological adaptivity for meshes on iced wings We started from the all triangle surface mesh shown in Figure 5 We then applied our topologically adaptive surface mesh algorithm to combine selected triangles to form quadrilaterals In the final step we used our topolog ically adaptive mesh extrusion algorithm to generate a near body mesh The mesh spacing near the surface was intentionally chosen to be large so that a clear picture of the extruded mesh could be obtained Figure 12 shows a near body volume mesh light color generated by extrusion from a mixed trian gle quadrilateral surface mesh dark color without topological adaptivity A portion of the volume mesh has been cut away to so that the surface mesh is visible In Figure 12 a we note that the mesh quality is poor in the ridge that runs just aft of the horn Similarly in Figure 12 b we see poor quality cells in the center ridge of the ice accretion on the leading edge Figure 13 shows a near body volume mesh light color generated by extrusion from a mixed trian gle quadrilateral surface mesh dark color with topological adaptivity As before a portion of the volume mesh has been cut away In Figure 13 a we note that the mesh quality is impr
13. the need for additional study of the effects of the geometry modeling aspects of the problem It should be noted that no serious attempt has yet been made to establish the validity of the solution However these results indicate that it is possible using existing technology to generate a NS solution for an iced wing configuration Due to an MPI upgrade in our local system we have been unable to obtain a HYBFL3D 22 solution Additionally when we attempted to compute a solution remotely using HYBFL3D the solution diverged after a few hundred iterations We attribute this behavior to the flaw in the mesh shown in Figure 9 6 Assessment of Existing Capabilities Based on efforts to date we have arrived at the following conclusions 1 It is our opinion that Surfacer is a good tool for performing many of the operations needed for basic geometry modeling for wings with complex ice accretions It should be noted however that all filtering needs to be performed manually In our opinion this is Surfacer s primary shortcoming 2 The fully three dimensional surface modeling approach has some difficulties because the procedure used to fit the NURBS surface produces oscillations in the NURBS description that effectively distorts the spanwise shape the three dimensional approach attempts to preserve The modified pro cedure i e adding the splitting curves near the horn tips reduces the position error relative to the 15 LT
14. to determine the importance of the spanwise variation in the ice shape The NURBS representation is output as an IGES file SolidMesh was used to generate a triangular surface mesh from the NURBS representation A mixed prismatic tetrahedral mesh was then generated The mesh appears to be of good quality with the exception of a region on the left side boundary of the computational domain However SolidMesh really does not provide intuitive control of point placement that may be necessary for iced wing flow field calculations We 18 a Upper surface streamlines b Lower surface streamlines Figure 14 Navier Stokes solution for iced wing using Cobaltgy M 0 3 Re 2 0x10 a 3 deg also applied our topologically adaptive surface and volume mesh generation algorithms to the iced wing problem In general we found that while they have much promise these algorithms still require more work before they can be routinely applied to these complex problems A flow field solution was computed using Cobaltgy While there is no experimental data to verify 19 the solution it appears reasonable There is massive flow separation on the upper surface and a significant recirculating region on the lower surface The computed results show a significant spanwise flow component The effects of the geometry model on these spanwise flow components needs to be evaluated 20 References 1 2 3 t 4 5 t 6 a 7
15. topologically adaptive surface and volume meshes appear to have promise However much work still needs to be done to improve the quality of the extruded surface Additionally the problem of 16 DNS VA A N SGN PEZON IS ZAIDA TK TSAI S VAS 7 LT XS A DO AA INDI AEE G TAYAN AS SA O 2 a Lower surface of wing b Wing leading edge Figure 12 Near body volume mesh without topological adaptivity front crossing also needs to be addressed 7 A preliminary flow solution for an iced wing has been obtained using the Cobaltgg flow solver While no validation data is available the results appear plausible However the indicated significant span wise flow components suggest that additional study of the geometry modeling process should be performed to determine the sensitivity of the solution to the geometry 7 Recommendations Based on the assessments outlined above we have developed a plan to accomplish the objective of identify ing a strategy for the iced wing simulation Below are the individual steps of this plan 1 Continue to develop automated surface filtering module using level set theory We believe this ca pability will be useful regardless of the approach used to represent the surface 2 Continue to refine the pseudo three dimensional surface modeling approach In particular develop an automated procedure to generate data slices One possible approach would be to use a three dimensional
16. 20 Topological adaptivity implies using cells that are locally topologically appropriate based on geometric and solution requirements We now discuss how we have implemented topological adaptivity for surface and volume meshes We then conclude with a discussion of integration issues 11 Tar SAA AAAA Ve A 28 A e A DAS SEA LO ZA DORIA DAL ASIA LOK AV LO YAA OEA O A ROO SRA ICIAOS ELLA IIA NTAN ZZ EPIA RIRS MASA 28 PREZIR RSK IRIRI OOOO EK AA CK SRA OSA AN ese PSF SEAXZEERERISERA AS AB OA I OOO AAC TS ESSE TSA POSIT OCR NY EERE AA ERE RISO OSE SB ASSO SA AGO AOE R ae bee TAVAYA STATAVAYAVA N E RX SPE AvANANs E pa PRE A APOLO e a PIO POLOS y ARA ORO OO O ADA S Xf EE ASADO AR PEERS Ae O OOO PEPE SA AI O i van AA OOR AOS PAYA VAYAVAVAVAYAS PAVAVA VAYA Do S De LOOSE A ODO OA AAA SL ll YAA SO APODO DADADLIIA e DOTA ROS DADA AO SI SE SARA G RA AA AZAS AVAATA YATA A YATAYAYAYAVA TAVAYA AS H PRWBAGE RAAB OAL AA lt 7 PS PRES ES PODRAS i POSADAS NA ARE gt DIAS ZOO ZRII A TOO LD IES ALADO BANDO IS DANA NAA AV ar AVAVANAN AVAVA VAN AA Yi a Left side boundary plane b Right side boundary plane Figure 7 Mesh on side boundaries near airfoil 4 4 2 Topologically Adaptive Surface Mesh Generation We developed an algorithm to convert an all triangle surface mesh t
17. 33 AIAA 35 Aerospace Sciences Meeting Reno NV January 1997 Y Choo private communication June 2001 J A Sethian Level Set Methods and Fast Marching Methods Evolving Interfaces in Computational Geometry Fluid Mechanics Computer Vision and Materials Science Cambridge University Press second edition 1999 R Malladi J A Sethian and B C Vemuri Shape Modeling with Front Propagation A Level Set Approach IEEE Trans Pat Anal Mach Int 17 2 158 175 February 1995 R Malladi and J A Sethian A Real Time Algorithm for Medical Shape Recovery Proc International Conference on Computer Vision pages 304 310 January 1998 J A Shaw Hybrid Grids J F Thompson B K Soni and N Weatherill editors Handbook of Grid Generation CRC Press Boca Raton FL 1998 J A Chappell J A Shaw and M Leatham The Generation of Hybrid Grids Incorporating Prismatic Regions for Viscous Flow Calculations M Cross P R Eiseman J Hauser B K Soni and J F Thompson editors Proc 5t International Conference on Numerical Grid Generation in Computa tional Field Simulations pages 537 546 International Society for Grid Generation Mississippi State MS September 1996 Y Kallinderis Hybrid Grids and Their Applications J F Thompson B K Soni and N Weatherill editors Handbook of Grid Generation CRC Press Boca Raton FL 1998 21 16 17 18 19 20 21 22 D S Thompson and B K
18. Geometry Modeling and Mesh Generation Strategies for Complex Three Dimensional Iced Wing Configurations Year 1 Report NAG3 2562 David Thompson Satish Chalasani Sanka Gopalsamy and Bharat Soni Center for Computational Systems Mississippi State University Mississippi State Mississippi February 2002 Abstract The problem of flow field simulation for iced wing configurations is a complex one that severely taxes existing capabilities for geometry modeling mesh generation and flow solvers In this report we focus on activities associated with the first year of a three year program to develop a software package to facilitate the numerical simulation of viscous flows around iced wing configurations We investigated various geometry modeling and mesh generation technologies to evaluate their effectiveness for application to the iced wing problem Based on these evaluations we developed a basic strategy for attacking the problem Further we were able to demonstrate the complete process from geometry to mesh to flow solution for a complex iced wing configuration ii Contents 1 2 3 3 1 3 2 4 4 1 4 2 4 3 4 4 8 A A l A 2 A 3 A 4 A S Introduction Problem Description Geometry Modeling Surface Modeling ci A A a eek had BY a A A o Gr fs 3 1 1 Fully Three Dimensional Surface Modeling o o 3 1 2 Pseudo Three Dimensional Surface Modeling o o Automatic Su
19. Soni Semistructured Grid Generation in Three Dimensions using a Parabolic Marching Scheme AJAA Paper 2000 1004 AIAA 38 Aerospace Sciences Meeting Reno NV January 2000 M Leatham S Stokes J A Shaw J Cooper J Appa and T A Blaylock Automatic Mesh Genera tion For Rapid Response Navier Stokes Calculations AZAA paper 2000 2247 Fluids 2000 Conference and Exhibition Denver CO June 2000 A Cary and T Michal Generalized Prisms for Improved Grid Quality AZAA paper 2001 2552 15 AIAA Computational Fluid Dynamics Conference Anaheim CA June 2001 P R Eiseman J Hauser B K Soni and J F Thompson editors Proc the 7t International Con ference on Numerical Grid Generation in Computational Field Simulations International Society for Grid Generation Mississippi State MS September 2000 S Chalasani D Thompson and B Soni Topological Adaptivity for Mesh Quality Improvement Proc 8 International Conference on Numerical Grid Generation in Computational Field Simulations submitted June 2002 FIELDVIEW User s Guide Version 6 0 1999 R P Koomullil and B K Soni Generalized Grid Techniques in Computational Field Simulation M Cross P R Eiseman J Hauser B K Soni and J F Thompson editors Numerical Grid Gener ation in Computational Fluid Simulations pages 521 531 International Society for Grid Generation Mississippi State MS 1998 22 Appendix A Truly Three Dimensional Surface Mode
20. Surface Modeling Choo 9 suggested an alternative approach that is based on lofting two dimensional chordwise slices of the data The primary advantage of this approach is that the needed two dimensional slices can easily be filtered to eliminate noisy data points The disadvantage is that the spanwise resolution is limited by the number of manually generated chordwise slices Once the slices are generated and filtered Surfacer is used to loft a surface between the chordwise slices using the procedure outline below 1 Select several spanwise positions 2 Generate chordwise slices of the point cloud at each spanwise station 3 Manually clean filter the slices to eliminate obviously bad data points 4 Generate a lofted surface between the slices using the two dimensional sections 5 Generate a NURBS description using Surfacer We note that to model a three dimensional surface with significant spanwise variation it will be necessary to employ numerous stations across the span Figure 3 a shows the manually denoised chordwise profiles at different spanwise stations and Figure 3 b shows a wire frame view of the lofted surface a Filtered point cloud b NURBS surface representation Figure 2 Fully three dimensional surface representation 3 2 Automatic Surface Extraction We recently began development of a routine to perform automatic filtering of the point cloud data that has its genesis in image processing In perfor
21. boundary wake etc 3 Generate a mesh and specify boundary conditions on the bounding surfaces of the computational domain 4 Generate a mesh in the interior of the computational domain 5 Generate a flow solution Since our objective is to develop a strategy to solve this problem the problem statement is expressed in terms of an implementation strategy In the sections that follow we will focus on issues relating to geometry modeling and mesh generation We also provide a flow solution to demonstrate existing capabilities 3 Geometry Modeling In this context the objective of geometry modeling is to generate a NURBS representation of the iced wing from the scanned point cloud data This NURBS representation is then output as an IGES file which can be used as input to a mesh generator The primary challenge associated with the geometry modeling is a reconstruction of potentially noisy surface data The software used to generate the geometry description is the SDRC package Imageware Surfacer hereafter referred to simply as Surfacer We acquired Surfacer under the SDRC University Licensing Program S Chalasani and S Gopal took part in a training program on Imageware conducted by SDRC April 16 20 2001 We first describe issues related to surface modeling We then describe two different techniques to gen erate a NURBS representation of the point cloud data Finally we discuss an automated filtering procedure based on techniques f
22. d data called Whole SectCld Change the name to trailing_edge_cloud e Make the whole point cloud data invisible so that you can concentrate only on trailing edge cloud This can be done by Display Point Invisible e Change the trailing edge cloud scatter mode to polyline mode by going to Display Point Display and selecting the polyline mode e Zoom in to one end of the point cloud and start panning to examine the cloud data e If any loops appear in the point cloud then the point cloud data has to cleaned e If so cleanup may include reordering and removing few points and can be accomplished as follows Check how the points are organized by changing the scatter mode to polyline for the trailing edge cloud If the points are not in order reorder the points by going to Points Order By Direction Select Z in the direction box before applying If still there are any loops then remove the points causing the loops by going to Points Modify Pick Delete Points e Fit a curve to the point cloud by using the Curve Create w Clouds Fit Free Form option This will open a small dialog box Choose the cloud from the List Input 50 a the number of control points and 4 as the order Click Apply to fit the cloud with the curve e Change the name of the curve by going to Basic Change name and entering trail edge curve 24 A 2 Create the leading edge curve The following technique is used to extract the leading edge curve A 3 A 4 Make the trail
23. e difficulties associated with filtering three dimensional point cloud data and the surface fitting itself This technique uses Surfacer to fit a NURBS surface to the iced wing data in conjunction with the following strategy 1 Extract trailing edge and leading edge curves 2 Segment the ice wing data into two parts wing top and wing bottom 3 Extract side boundary curves of wing top and wing bottom 4 Fit NURBS surfaces to the wing top and bottom points using the boundary curves and point cloud data This approach is described in detail in the Appendix We note that obtaining the boundary curves was time consuming because of the manual interaction needed to clean up the two dimensional sections Further the three dimensional point cloud needs to be manually filtered A filtered three dimensional point cloud and the surface generated using this approach are shown in Figure 2 There are significant oscillations in the generated surface near the boundary curves Defining curves that pass near the tips of the horns and split the upper and lower surfaces into two surfaces each can reduce these oscillations and reduce the maximum position error by more than 50 However this approach introduces visible slope discontinuities at the surface intersections These artificial slope discontinuities occur at critical regions and could pose potentially serious problems for the flow solver as far as accuracy of the solution 3 1 2 Pseudo Three Dimensional
24. e selected faces are refined and cell connectivity is updated This operation also results in a generalized cell topology Extruded Surface Improvement Edge collapse and face refinement improve the quality along the march ing direction However these operations do not take into account the quality of the mesh in the extruded surface Therefore the quality of the mesh in the extruded surface may be degraded and improvements in 13 VA A Y S EEES AV E RS Ae Se OO o Eb PO z KID uous ee EEE a SOK OLA SAA SS US ODE OOOO PINOS y SN AN BS YA ESE BSCE LOROS Sec oe Boks say LAA LAKE ra eS AL A BAAS a TANET A Sy ORIS PK SZ as EE FL ine SES R AVA A SEE SORA V DOG APRO LODO AD S Y AAA ae ACOA YN AERP OS ROD A VA VAYA Da a Mesh in left side boundary plane b Detail of region near mesh flaw Figure 9 Mesh flaw in left side boundary plane the surface are needed The process is initiated by identifying the minimum angle around each node The following steps are performed to improve the surface mesh quality e Edge collapse This is done to eliminate small angle cells e Local reconnection Poor quality quadrilaterals can be converted into two triangles of better quality and vice versa As the mesh is generated every step is taken to prevent the generation of negative volumes The al gorithm is designed to give yield triangles and quadrilaterals
25. e surface will be required However there is no clear indication at this time what type of preprocessing is needed or to what degree it is needed Additionally within the constraints of accuracy efficiency and flexibility questions remain as to what type of mesh is appropriate for a complex iced wing configuration In this report we focus on activities associated with the first year of a three year program to develop a software package to facilitate the numerical simulation of viscous flows around iced wing configurations To date there have been only limited numerical three dimensional icing effects studies Due to this limited experience the first year emphasis was placed on identifying a sound overall approach to surface mesh gen eration volume mesh generation flow solution rather than developing new technologies The one exception to this is the development of a generalized near body mesh generation module Below is a brief summary of activities accomplished to date 1 An approach to generate a fully three dimensional NURBS representation of the point cloud data was developed using the Imageware Surfacer software package 2 An approach using a pseudo three dimensional lofted geometry representation with the Imageware Surfacer software package was investigated 3 A technique utilizing medical imaging technology was applied to filter chordwise iced wing sections The approach met with mixed although promising results
26. e used in two or three dimensions making it possible to perform curve and surface extractions Additionally in the level set approach it is not necessary to explicitly consider topological changes in the front Topological changes occur implicitly in the level set formulation We now describe how level sets can be applied to image segmentation Level Set Basics Suppose we have a front that moves with speed F t in the direction of the local normal to the curve In general F t may depend on different properties 1 Local properties of the front Properties that are determined by local geometric properties of the front such as curvature 2 Global properties of the front Properties that depend on the shape and position of the front 3 Independent properties Shape independent properties Note that F t is a function that is neither strictly positive nor strictly negative We now want to embed the front position as the zero level set of a higher dimensional function and link the propagation of the front to the evolution of the function 6 We start with the zero level set o x t t 0 1 Differentiating using the chain rule we obtain be Vo x t t x t 0 2 Note that the normal to a curve of constant is given by n V V so that Eq 2 can be written as di FIVE 0 6 where F is the velocity component of the front normal to the curve This is the basic level set equation given by Sethian 10 The Front
27. ing _edge_cloud invisible This can be done using Display Points Display and selecting the trailing_edge_cloud in the List with the visible button off Now put the whole point cloud data with the trailing_edge_curve in Fl view by pressing keyboard button F1 The point cloud data at the leading edge has to be extracted to define the leading edge curve This can be done by going to Points Cross sections Parallel A dialog box opens up In the dialog box select the whole cloud and set the Number of Sections equal to one Select the Y button in the Direction box There will be white plane appearing below the wing where the default start point exists To change the start point click on the Start Point in the dialog box and bring the focus to the main screen Place the cursor near the stagnation point of the leading edge and click The plane will move to that point Click on the Apply button This will generate point cloud data which will have some points near the trailing edge region These points are deleted by Circle Select option Put the whole cloud in invisible mode to concentrate on the leading edge cloud Change the name of the cloud to leading_edge_cloud Check the point ordering by changing the scatter mode to polyline for the leading_edge _cloud Per form cleanup if required Choose Fit Free Form from the Curve Curve w Clouds to fit the curve for the leading edge cloud Input 50 as the Number of Control Points and 4 as the Order Click
28. ion This ratio is used to identify the converging cells near non convex regions e Marching aspect ratio This ratio is used to force the faces in the marching direction to become more isotropic The selected edges are given priorities according to the marching aspect ratio and are sorted according to the assigned priorities Edge collapse is performed by collapsing the selected edge to a point typically the midpoint of the edge If one of the nodes is a boundary node then this node is kept to maintain boundary integrity The edge collapse process is initiated at the first edge in the list To avoid performing an operation that results in an invalid mesh all of the edges sharing either of the two nodes of the edge under consideration are marked as non collapsible edges After processing the list the cell connectivity is updated Edge collapse results in a generalized cell topology Face Refinement Face refinement is performed to improve the mesh quality near convex regions and to force the mesh to become more isotropic Faces are refined according to the number of edges marked for refinement The edges are marked for refinement using one of the following criteria e Divergence angle This angle quantifies the degree of divergence of mesh faces near convex regions e Marching aspect ratio This ratio is used to force the faces in the marching direction toward isotropy The selected edges are given priority according to their divergence angles Th
29. is to use the level set method with one modification the front velocity is driven to zero as it approaches an edge in the image Here we define an edge to be a significant pixel gradient Therefore a straightforward approach is to employ the modified level set equation bt g1 x y F VO 0 8 7 b Level sets darkest contour is extracted airfoil surface Figure 4 Airfoil surface extraction using level sets where gr x y is a speed function that approaches zero as the zero level set approaches an edge Possible choices for the speed function include 1 gi x y 1 V Go 1 a y and G E EAE A 10 where Go is a Gaussian smoothing function Although we are interested only in the zero level set we are performing calculations for all of the level sets Therefore we need to stop the other level sets when the zero level set has stopped The approach used here is the extension velocity approach 10 For a given point x y the speed function is given by the speed function for the point on the zero level set closest to x y For point based data the technique is not well developed The basic problem is that for point data there is no edge to detect so that the stopping criteria are difficult to define We have tried several functions to date most based on proximity to a point and none have proved wholly successful These difficulties can be illustrated using a simple two dimen
30. l domain the additional lines are part of a frame around the plot The first thing to notice is that there is no concentration of points in the wake of the wing The wake was not included in this demonstration mesh The mesh extends approximately 15 chords from the wing in the chordwise and vertical directions Detailed images of the 9 PISOS ESA LR aan a wae AS RO SS QS A SS BOERS x KY My SEN BOY SS x ORRE eo SSL POS PERL RS LL A a4 TERN SANS 5 SOS SY SORE x X N Ka ay 3 Y N is Ny ANY oe a All triangle surface mesh b Detail image near ice accretion N Figure 5 Triangular surface mesh wing lower surface mesh in the left boundary plane and right boundary plane are shown in Figures 7 a and b respectively Notice the boundary layer mesh clustered near the no slip boundaries Figure 8 shows cutting planes through the mesh on the lower surface of the wing at three spanwise stations Note that because these are cutting planes the connectivity shown in the images does not represent the actual connectivity of the mesh Of particular interest in the figure is the boundary layer mesh near the surface Finally in Figure 9 we show a flaw that we located in the mesh in the left side boundary plane Notice the widely varying cell sizes and the apparent collapse of the cells near the boundary At this time we are unsure of the precise cause of the problem One po
31. ling This appendix describes the five steps needed to generate a fully three dimensional NURBS representation of iced wing point cloud data The main objective is to create two distinct surfaces i e the top and bottom surfaces These two surfaces have common boundaries at the trailing edge and at an artificial leading edge The basic approach is to create a set of curves that will assist Surfacer in the NURBS definition These curves will also be helpful in maintaining C continuity at the common surface boundaries In the following report a bold font is used to identify Surfacer buttons and an italic font is used to identify as the entities created in Surfacer The top surface is created by designating the following curves as boundaries of the point cloud e Trailing edge curve e Top_zmin_curve e Leading edge curve e Top_zmax_curve The bottom surface is created by designating the following curves as boundaries of the point cloud e Trailing edge curve e Bottom_zmin_curve e Leading edge curve e Bottom_zmax_curve The two surfaces match at common curves at the trailing edge and the leading edge with C continuity Fig ure 15 illustrates the notation employed here The NURBS representation is output in the IGES format so that it can be imported into most mesh generation software The unstructured mesh is generated after com bining the two surfaces with the mesh generation package The following steps explains the methodology for creati
32. ming manual filtering of two dimensional chordwise slices NASA personnel select only the innermost points to be the surface 9 This approach is based on the assumption that data points that must be filtered are not located below the actual surface We have been investigating the use of level sets to generate this innermost contour In this approach the velocity function used in the level set formulation is defined to drive the velocity of a specific level set to zero at the surface of the airfoil We have implemented a preliminary version of this approach and have applied to images of iced wing sections generated in Surfacer We now provide some background information on level set theory as well as implementation details for this approach 3 2 1 Introduction to Level Sets In the context of curve surface extraction we basically want to segment a region by locating bounding curves i e an edge detection However we also want to extract a set of points on this bounding curve surface Much work has been performed in the field of medical image processing to accomplish this task 10 12 a Denoised chordwise slices b Wireframe view of lofted surface Figure 3 Pseudo three dimensional surface representation The basic idea behind any level set methods is to perform front tracking a task normally performed using a Lagrangian formulation using an Eulerian formulation The main advantage is that the level set approach can b
33. ned from tests in the NASA GRC Icing Research Tunnel Once a representative two dimensional chordwise sections was discretized a three dimensional geometry was generated by extruding the two dimensional ice shape in the spanwise direction and fairing the shape at the tip A two block structured grid was generated with noncontiguous overlapping interfaces The flow field solution was computed using the general purpose code NPARC 4 Recent advances in scanning technology have made it possible to generate descriptions of complex shapes in the form of point clouds This technology has been exploited to generate three dimensional point cloud data for iced wing configurations 5 Although scanners typically employ a preset scan pattern the resulting data can perhaps be best characterized as unorganized because the only connectivity informa tion is in terms of the scan line Further the data obtained from a scan may be noisy Existing techniques depend solely on geometric characteristics to reconstruct a surface and may have difficulty reconstructing a nonsmooth surface from noisy data 6 The ability of geometry mesh generation tools to adequately address the unique needs of an iced wing flow simulation is also much in question Obviously there are significant issues related to representation of the iced wing surface There are also questions regarding the quality of the NURBS representation of the surface It is obvious that some preprocessing of th
34. ng the six curves A 1 Create the trailing edge curve The following methodology is employed to create the trailing edge curve e Import the whole point cloud into the current viewport Change the point cloud display to scatter mode if it is not in the scatter mode by going to Display Point and selecting the scatter button e Change the name of the point cloud to whole by going to Basic Change Name e Orient the view of whole point cloud by using keyboard button F5 e Extract the cross section of the point cloud at the trailing edge using Point Cross section Parallel e This will bring up a small dialog box Click the List button This will show the all point cloud data currently visible i e the whole cloud Select the whole point cloud e Select the X direction in the dialog box 23 Top_zmin_curve Trailing Edge Curve Leading Edge Curve A Top_zmax_curve Bottom_zmax_ curve Figure 15 Basic Strategy Generate six curves to define two surfaces e Click on the Start Point button and to return your focus to the main screen You will see a white line with a point on it Decide where the trailing edge is Place the cursor in this location and click The white line moves to that location This white line is a cross sectional plane It will pass through the whole point cloud and create new point cloud at that cross section e Use only one section Click on the Apply button e This will create a new point clou
35. o mixed triangle quadrilateral surface mesh The advantage in performing such a transformation is that the expense of performing a flow solution strongly depends on the number of faces in a mesh Therefore if the number of faces can be reduced without adversely affecting mesh quality the cost of a solution can be reduced The particular algorithm we employ here combines two triangles if the directions of the surface normals for each triangle differ by less than a prescribed amount Figure 10 shows a comparison of the all triangular mesh generated by SolidMesh with a mixed element mesh generated by appropriately combining adjacent triangles The resulting 37 savings in cells faces is significant We have not applied any surface mesh smoothing at this time 4 4 3 Topologically Adaptive Volume Mesh Generation The quality of a mesh generated using extrusion methods may be poor near convex and concave regions of the geometry Figure 11 a shows an example of poor quality cells near a concave region As this mesh is extruded poor aspect ratio cells will develop which will result in slivers being generated in the tetrahedral mesh One solution to this problem is to employ a change in the topology of the mesh Edge collapse as shown in the Figure 11 b will stop the generation of poor quality cells and thereby provide the opportunity to extrude further into the domain and increase the percentage of nontetrahedral elements Figure 11 c shows poor qualit
36. of the wing Then generate an unstructured triangular mesh on the wake surface Finally merge the wake surface mesh with the airfoil mesh 3 Define side and outer boundaries Also define flow solver boundary conditions on these surfaces 4 Generate unstructured triangular mesh on all surfaces 5 Generate a near body volume mesh from the surface meshes 6 Generate a tetrahedral volume mesh in the interior of the domain defined above Note that in some mesh generators the extrusion and void filling steps are seamlessly combined into a single step We now consider a sample mesh generated using the SolidMesh 7 software package 4 3 Example Mesh To illustrate existing mesh generation software we have used SolidMesh 7 to generate a mixed ele ment prismatic tetrahedral mesh starting from an all triangle surface mesh SolidMesh was developed by D Marcum and A Gaither at the Mississippi State University Engineering Research Center The mesh has approximately 1 million nodes 6 7 million faces and 3 million cells This mesh was used to obtain a Navier Stokes solution with the Cobalt flow solver The results of flow solution are discussed in a later section Figure 5 shows the mesh on the surface near ice accretion Notice the nearly isotropic nature of the mesh and the potentially inefficient point distribution on the surface The mesh appears to be of high quality however Figure 6 shows the mesh in the left side boundary of the computationa
37. oved in the ridge aft of the horn in comparison with Figure 12 a Similarly the mesh quality in the ridge running down the front face 14 a All triangle surface mesh b Mixed triangle quad mesh Figure 10 Example of simple topological adaptivity in a surface mesh of the horns is likewise improved as shown in Figure 13 b It should be noted that we did have some difficulty extruding much beyond several layers due to mesh crossing in a concave region We are currently working to address the problem of mesh crossing using topological adaptivity 5 Flow Solution We have generated a Navier Stokes solution on the mesh shown in Figures 5 9 using Cobaltgg 8 The flight conditions were M 0 3 Re 2 0x10 and a 3deg The solution required more than 30 hours of wall clock time on a 96 processor SGI Power Challenge 3 We have investigated the flow field using the visualization package FIELDVIEW 21 Not surprisingly the flow is largely separated over the upper surface There is also a significant recirculating region on the lower surface Stream ribbon traces in the region above the surface aft of the horn are shown in Figure 14 a A similar image for the region below the surface is shown in Figure 14 b Of particular interest in these images is the three dimensional nature of the flow separation Even though the selected ice shape is mostly two dimensional there are significant spanwise flow components further re enforcing
38. rface Extracti0On 3 2 1 Introduction to Level Sets e e 3 2 2 Curve Surface Extraction Data using Level Set Methods Mesh Generation Example Mesh i sissi ON dee He tal a A Bette Non B wh Poles he de tee The IGEWING System oda Gala e tae iD NP o a Geek le de tue de ALAT Rationale liinda ra ee dee ah ety Bed 4 4 2 Topologically Adaptive Surface Mesh Generation o o 4 4 3 Topologically Adaptive Volume Mesh Generation 4 4 4 Example Mesh 2 2 as 42 i 25 2 aa San Pee SAS aR EE Sal aks Flow Solution Assessment of Existing Capabilities Recommendations Summary Truly Three Dimensional Surface Modeling Create the trailing edge curve o oo ee Create the leading edge Curve o Split the point cloud into two surfaces 2 o e Create Curves at the Inboard and Outboard Boundaries Creation of Surfaces scor pa ee iii 15 15 17 18 List of Figures VNOo0 Duo Rh a bh Un kr O Noisy point cloud data e 3 Fully three dimensional surface representation 00 4 5 Pseudo three dimensional surface representation aoaaa aaa 6 Airfoil surface extraction using level sets 0 o o eee 8 Triangular surface mesh wing lower surface ahaaa aaa a 10 Left side boundary of mesh a 11 Mesh on side boundaries near airfoil o
39. rom medical image processing 3 1 Surface Modeling Advances in scanning technology have provided impetus for cataloging and characterizing three dimensional ice accretions on aircraft wings Shown in Figure 1 is a side view of a typical noisy point cloud In addi tion to obvious outliers there are points relatively near the surface that are clearly not part of the surface It should be noted that the points near the leading edge that appear to be inside the airfoil are actually in 2 Figure 1 Noisy point cloud data front of and behind the model in this view Clearly the data must be filtered before any kind of sur face reconstruction can be performed Manual denoising is relatively easy to perform for two dimensional slices but is more difficult for three dimensional data One approach is to generate chordwise slices of the three dimensional data at different spanwise positions manually denoise the slices by deleting the outlying points and generate a three dimensional surface by lofting between the slices Unfortunately this approach may adversely affect the fidelity of the surface unless many chordwise slices are employed Once the data are denoised it is necessary to generate a surface representation that is homeomorphic to and lies in close geometric proximity to the original surface This is a significant topic in current CAD computer graphics computer vision and mathematical modeling re
40. s which may contain arbitrary polyhedra i e no restrictions are placed on the number of edges a face can have or the number of faces a cell can have have been dubbed generalized meshes 16 In 17 edge collapse and refinement are used near concave and convex regions of the geometry respectively to improve the mesh quality In 18 the concept of the generalized prism is introduced to improve mesh quality by controlling the resolution of the mesh near convex corners In addition to these operations the transition between the near body mesh and tetrahedral mesh should also be considered Improved mesh quality in the transition region can be obtained by having isotropic cells at the extruded mesh tetrahedral mesh interface Edge collapse and face refinement may give the required isotropy in the marching direction but can spoil the quality in the extruded surface Therefore surface cleanup may be required to improve the quality of the extruded surface The added flexibility and potential for higher accuracy in viscous regions make generalized hybrid meshes attractive for the iced wing problem The current interest in hybrid meshes can be ascertained by a review of the proceedings of the 7th International Conference on Numerical Grid Generation in Com putational Field Simulations 19 where there were no fewer than twelve papers on the topic of generalized and hybrid mesh generation We have recently introduced the concept of topological adaptivity
41. search In these applications a mesh is often generated using only the scanned data points 6 In our application we want to generate a surface upon which a mesh with a controllable point distribution can be generated Simply interpolating a NURBS surface may not be a good approach due to the potentially oscillatory nature of the reconstruction Further there may be issues related to undersampled data i e insufficient resolution in regions of high curvature It seems that many fine scale features such as roughness and small feathers are likely to be undersampled by the scanner Therefore an additional scale dependent filtering of the data might also be appropriate We are not currently addressing this issue In the two approaches discussed below we consider NURBS representations of the surface We do this only because most mesh generation software is based on NURBS representations of the underlying geometry definition We now outline two general strategies to generate a NURBS representation from the point cloud data a fully three dimensional approach and a pseudo three dimensional approach 3 1 1 Fully Three Dimensional Surface Modeling In the fully three dimensional approach we developed as part of this effort Surfacer was used to fit a NURBS representation to the actual point cloud data The main advantage of this approach is that the three dimensional nature of the ice accretion can be retained The primary disadvantages are th
42. sional example Figure 4 a shows an image of a chordwise section of the clean wing generated in Surfacer including noise Figure 4 b shows the extracted level sets with the surface of the airfoil indicated by the darker contour As is clearly visible in the figure the velocity function does not stop at the front in the regions where the pixels are spaced relatively far apart i e where the pixels do not form an edge Also note the difficulty identifying the sharp trailing edge This can be attributed to the relative coarseness of the mesh A finer mesh upon which the level set equation is solved would provide a better representation of the trailing edge 4 Mesh Generation Mesh generation for an iced wing geometry is a challenging problem In the sections that follow we first discuss some of the issues related to mesh generation We then outline a procedure to generate a mesh Next we provide images of an example mesh generated using an existing software package Finally we conclude with a discussion of the preliminary efforts related to developing the ICEWING software package 8 4 1 Issues From a mesh generation standpoint there are three driving issues From the standpoint of efficiency a mesh should have 1 as few cells faces as possible 2 anisotropic mesh refinement and 3 some degree of automation Since we are attempting to compute the solution for a high Reynolds number viscous flow for a complex three dimensional
43. ssibility is the fact that the ice accretion seems to have a severe slope with its normal directed toward the boundary plane It should be noted that SolidMesh may not represent a long term solution since it is not public domain software We are currently investigating alternative software packages for generating unstructured meshes However we have demonstrated that a mesh of generally high quality can be generated for the iced wing using existing technology 4 4 The ICEWING System One of the specified first year objectives was to begin development of a mesh generation system for iced wing configurations In the sections that follow we present the rationale we developed and discuss our progress to date 4 4 1 Rationale It appears highly unlikely that a high quality multiblock structured mesh can be generated for the iced wing problem without a prohibitive expenditure of manpower Therefore some type of unstructured mesh is a ne cessity The problems associated with an unstructured purely tetrahedral mesh for viscous flow calculations namely the accuracy of the highly stretched tetrahedra in the boundary layer and the inefficiency of a purely tetrahedral mesh are well documented 13 14 These deficiencies suggest employing a hybrid mesh 13 15 Hybrid meshes have the advantages of both structured and unstructured meshes In a hybrid mesh a 10 WAVAVAVAVAVAVA TAAN ENA THS J gt TS A SO
44. termine the sensitivity of the spanwise flow components on the resolution of surface model 8 Summary The problem of flow field simulation for iced wing configurations is a complex one that severely taxes existing capabilities for geometry modeling mesh generation and flow solution In the first year of a three year effort we investigated various geometry modeling and mesh generation technologies to evaluate their effectiveness for application to the iced wing problem Based on these evaluations we developed a basic strategy for attacking the problem and were able to demonstrate the complete process from geometry to mesh to flow solution for a complex iced wing configuration Surfacer was used for all geometry modeling activities Starting from a point cloud representation of the iced wing surface we developed a technique to generate a fully three dimensional NURBS representation of the point cloud However this approach can only be applied to relatively clean data and manual denoising of the three dimensional point cloud can be challenging We also investigated a geometry modeling technique based on lofting two dimensional chordwise sections This approach facilitates manual clean up of the two dimensional section However if significant variation of the ice shape occurs in the spanwise direction many sections are needed to accurately model the surface Given these limitations both techniques perform adequately Further study is needed
45. urve Create 3D from Surface Surface boundary curve Click on the sides of the two surface boundaries This will create the curves Convert the boundary curves to 50 sample points Perform cleanup operations if required to both the clouds Now add the two small clouds to one and then add this one with top_zmax_cloud_temp to form one cloud Change the name of this to top_zmax_cloud Before adding the two clouds check the starting and ending point of the clouds which will be helpful later while creating the curve If the ending point of top_zmax_cloud_temp and starting point of newly created sample points are not consecutive then change the order of the point cloud by Points Order Set Start Point e Check top_zmax _cloud with polyline mode and do necessary clean up if there are any loops e Create the curve with Curve Fit w Cloud Fit Free Form Give Number of Control Points to 100 and Order as 4 This will create a new curve e The curve may not extend all through and hit the leading edge but it will be very close to it e Change the name of the curve to top_zmax_curve The remaining 3 curves Top_zmin_curve Bottom_zmin_curve and Bottom_zmax_curve are extracted using the procedure described above 26 A 5 Creation of Surfaces After generating all 6 curves the first surface top is fitted to the top cloud using following curves as the boundaries e Trailing edge curve e Top_zmin_curve e Leading edge curve e Top_zmax_curve
46. utside the cloud e Select one section and click on Apply This will create a new point cloud data Change the name to top_zmax_cloud_temp One can notice the top_zmax_cloud_temp will not touch the lead ing edge curve near the far and leading edge intersection e Now put the top_zmax_cloud_temp into polyline mode and check if there are any loops If there are any loops clean the cloud to remove the loops In the polyline mode cleanup the top_zmax_cloud_temp by removing the points which are causing this if the top_zmax_cloud_temp is not entirely following the cloud e After cleaning up the top_zmax_cloud_temp select a small region of top cloud near the intersection of leading edge and top_zmax_cloud_temp with Circle Select option Put the top cloud into invisible mode e This will create a new cloud Break the surface into two parts at the turning point by putting the cloud in F1 keyboard button view by using Circle Select with keeping both option e Fita surface to both of the new clouds This can be done by going to Surface Create w Cloud Fit Free Form In the dialog box select the new cloud created Set the Order to be 4 and the Number of Control Points to be 10 in both directions The Fitting Direction as Best Fit Plane Keep all the other data as default e After obtaining the two surfaces extract the boundary curve of the surfaces which will help in con necting the leading edge to top_zmax_cloud_temp This can be done by going to C
47. y cells near convex regions of the geometry Face refinement as shown in Figure 11 d can improve the quality of the mesh by eliminating highly divergent cells Edge collapse and face refinement can also be used to force the mesh to become more isotropic which in turn smoothes the transition to the tetrahedral mesh However these operations may lead to poor quality on the top surface of each layer Therefore quality improvement operations should be performed on the extruded surface as well The various operations are discussed in the following sections The terms listed below are used in the discussion of the quality improvements e Aspect ratio is defined as the ratio of the largest edge to the smallest edge in a face This is defined for each face in the top and base surface of each layer 12 a b Figure 8 Cutting planes through the mesh at three spanwise stations lower surface e Marching aspect ratio is defined by edge length in the marching direction to the minimum edge length on the base surface e Divergence angle is defined for each edge and is defined as the maximum of the in surface angles Edge Collapse The edge collapse operation is performed to improve the quality of the mesh near concave regions and to force the mesh to become more isotropic The edges to be collapsed are selected using the following criteria e Change in aspect ratio of the faces of the surface mesh before and after extrus
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