G.3 CBL User's Manual CBLv2 is the Cebeci Boundary Layer
Contents
1. The first set is J grid line index ETA computational normal coordinate Y physical coordinate F transformed streamfunction U U fUe F V U the gradient of the velocity distribution The second set is J grid line index ETA computational normal coordinate Y physical coordinate G H He O G the gradient of the enthalpy distribution B effective viscosity distribution C 1 E B Monday January 27 1997 report typos and errors to W H Mason Appendix G Programs G 17 and then the rest of the parameters of interest are given RX local running length Reynolds number DELS displacement thickness THETA momentum thickness NUSSELTNO Nu 2 gt Ty a T k H shape factor DELS THETA CF 2 skin friction RDELS Reynolds number based on displacement thickness RTHETA Reynolds number based on momentum thickness STANTONNO St dw p Mel H H e At the finish of the calculation the distributions of the computed quantities given above are re peated in two sets in summary form The first set is X RX DELS THETA H CF 2 The second set is X RDELS RTHETA NUSSELT NO STANTON NO It is likely that separation will occur When this happens the programs halts When possible sep aration is flagged in the output and the summary of results up to separation are printed out in the summary Monday January 27 19972. p g w CEP 8 Monday January 27 1997 report typos and errors to W H Mason Appendix G Programs G 15 Example of cblv2 f input cblv2ref inp on the disk upper surf 43 150 0 Re Re HA EO Or OO OvVG O OF O ONO OO Ov O1 Or OO OOO Ou OO OlO W 4O O O O GO Ans 000000 004614 013224 024531 036161 048151 061727 077307 094830 114472 136324 160324 186394 214456 244340 275907 3038993 343418 378998 415537 452835 490691 528899 567257 605569 643650 681338 718408 754647 789814 823666 855952 886487 915043 941433 965482 987046 006006 022249 035669 046187 053742 058293 000 200 Monday January 27 1997 Cps from GA W 1 at M 1 14 0 01 00 1 000 005642 0 000000 936635 0 000000 549866 0 000000 084785 0 000000 708135 0 000000 025962 0 000000 198553 0 000000 272074 0 000000 240493 0 000000 187699 0 000000 137414 0 000000 082872 0 000000 042838 0 000000 010707 0 000000 977603 0 000000 950920 0 000000 927588 0 000000 908177 0 000000 891323 0 000000 873235 0 000000 857548 0 000000 845519 0 000000 831693 0 000000 813231 0 000000 785736 0 000000 732378 0 000000 660691 0 000000 579180 0 000000 493191 0 000000 408020 0 000000 331905 0 000000 257680 0 000000 187632 0 000000 124057 0 000000 067627 0 000000 019300 0 000000 023179 0 000000 062768 0 000000 096355 0 000
3. 000 123776 0 000000 162320 0 000000 228643 0 000000 319797 0 000000 15 and 2 deg AOA 72 0 0 1 0 G 16 Applied Computational Aerodynamics Description of Output The output corresponding to the sample input is in the file cblv2ref out on the disk First the input is echoed P2 1 is given with the distribution of values with X I After the Mach num ber is repeated the computed reference temperature static pressure velocity density total en thalpy and pressure in atmospheres are output The edge velocity distribution converted using the input pressure coefficient distribution is out put together with other computed values in two sets to meet the 80 column output limitation The first set is XD distance along surface in physical units UE edge velocity in meters sec WWI dimensionless temperature or temperature gradient input TEM edge static temperature RHOE I edge density The second output set is X T distance along surface in physical units RMUE edge viscosity P1 edge parameter 1 d h P Aie testo 2 Pelle dx P2 edge parameter ee U dx The computations are then output one station at a time first giving the station number the X value of the station and the convergence history IT is the iteration count and is reset if an extra grid point is added during the calculation After convergence the profiles at each station are given at every third grid point in two sets
4. h solution station to compute the arc length along the surface from the stagnation point which is the surface length X in the boundary layer calculation The utility program POSTp can be used to convert the output file generated by PANELv 2 to a form easily modified to use as input to CBLv2 Reference Tuncer Cebeci and Peter Bradshaw Physical and Computational Aspects of Convective Heat Transfer Springer Verlag Berlin 1984 Note This program is representative of standard programs used in industry Experience by stu dents indicates that successful use of this program requires more patience than some students are willing to use It is very important to put the data in the proper column When the program is near separation the numerical iteration sometimes breaks down and the program stops with an error message This does not necessarily mean that the solution is invalid at previous steps When the pressure is specified the boundary layer equations are singular at separation and any Monday January 27 1997 G 14 Applied Computational Aerodynamics numerical iteration will diverge The program attempts to identify this situation and stop with a message suggesting that separation has been encountered Sometimes the solution blows up be fore the code message is printed One of the most important input parameters is the initial dimen sionaless pressure gradient The values of the pressure gradient should be examined to make sure that t
5. he distribution is smooth The code interpolates the user specified pressures to get the pres sure gradient using a second order polynomial which can poor estimates of the gradient if the input data is not smooth INPUT FORMAT Card 1 A80 Data set title Card 2 213 3F10 5 NXT total number of x stations input 60 max NTR transition location station must be gt 2 P2 1 dimensionless pressure gradient at Ist x station 7 we x e Note for zero pressure gradient case P2 1 is zero for flow that starts at a stagnation point the local stagnation point solution assumes that the velocity increases linearly from zero and the value of this parameter should be one good values of DETA 1 VGP Laminar Turbulent amp Lam Turb DETA 1 hl wall grid spacing 0 2 0 01 VGP K ratio of spacings 1 0 1 14 Card 3 7F10 5 RMI freestream Mach number TO freestream stagnation temperature deg K XLL reference length L RELM _ Reynolds number per unit length in millions PR Prandtl number 72 for air heat transfer control codes values of alphaO alpha1 for specified wall temp heat transfer ALFAO alpha0 1 0 ALFAI alphal 0 1 Card 4 3F10 5 repeat card 4 NXT times X T x L nondimensional distance along surface CPI pressure coefficient WWD dimensionless wall temp 8y OF the heat flux given by the dimensionless wall temperature gradient of p depending on ALFAO and ALFA1 values
6. report typos and errors to W H Mason Appendix G Programs G 13 G 3 CBL User s Manual CBLv2 is the Cebeci Boundary Layer Program The program computes the two dimensional compressible laminar and or turbulent boundary layer This code is described with a listing in the reference Dr Tuncer Cebeci Dept of Aerospace Engineering California State University Long Beach makes it available for 50 The current version has been modified slightly and the output has been redesigned for WATFOR to limit output to 80 columns The code uses the Keller Box Scheme to obtain efficient solutions to the compressible boundary layer equations It uses the Cebeci Smith turbulence model an algebraic eddy viscosity model and can handle heat transfer cases Some compilers will require the use of SAVE statements in each routine The program will prompt you for the name of the input file The output is written to the screen in the version provided This is not an interactive code and the output can be redirected to a file once the input file is defined Note that the boundary layer is computed at each input x station and no others Make sure your input is closely spaced where details are important The boundary layer computation should start at the stagnation point and follow the flow along the upper or lower surface toward the trailing edge This requires identifying the stagnation point in the inviscid solution and using the geometry points x y at eac
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