Boundary Layer Codes for Students in Java - Paper | MECH 594, Papers of Aerodynamics

Download Boundary Layer Codes for Students in Java - Paper | MECH 594 and more Papers Aerodynamics in PDF only on Docsity! Copyright © 1998 by ASME1 Proceedings of FEDSM’98 1998 ASME Fluids Engineering Division Summer Meeting June 21-25, 1998, Washington,DC FEDSM98-5139 BOUNDARY LAYER CODES FOR STUDENTS IN JAVA W.J. Devenport* and J.A. Schetz** 540-231-4456,540-231-9632(Fax),DEVENPORT@AOE.VT.EDU;540-231-9056,PTIGER@VT.EDU Virginia Polytechnic Inst. and State Univ. Blacksburg, VA ABSTRACT Simple JAVA computer codes for boundary layer problems intended for student use solving the homework problems in a text such as Boundary Layer Analysis by Schetz, 1993 and similar problems on a PC or Work Station have been developed. The notion is to make platform- independent codes conveniently available via the internet. At this point, there are four separate codes for: 1) Thwaites-Walz incompressible, laminar integral method, 2) incompressible, laminar boundary layers by an implicit numerical method, 3) Moses, incompressible turbulent integral method, and 4) incompressible turbulent boundary layers by an implicit numerical method. A brief description of each code precedes the operating instructions. Also, a default input for a typical example and results for that case are presented and discussed. NOTATION Cf skin friction coefficient H  * shape factor M Mach number p pressure r(x) body thickness distribution Re Reynolds number Ro body nose radius s(x) surface distance _____________________________________________ *Associate Professor of Aerospace and Ocean Engineering, Member ASME ** J. Byron Maupin Professor of Aerospace and Ocean Engineering, Fellow ASME T temperature K turbulent kinetic energy u streamwise velocity Ue(x) edge velocity distribution Uinf freestream velocity v transverse velocity x axial and streamwise coordinate y transverse coordinate */ w)dp/dx Clauser pressure gradient parameter boundary layer thickness * displacement thickness momentum thickness 2 )dUe/dx Pohlhausen pressure gradient parameter 2 )dUe/dx Thwaites-Walz pressure gradient parameter viscosity kinematic viscosity density w wall shear INTRODUCTION Here, we present simple JAVA computer codes that are intended for student use solving the homework problems in a text such as Boundary Layer Analysis by Schetz, 1993 and other similar problems on a PC or Work Station. The JAVA language was selected so that such codes could be made conveniently available in a platform-independent form on the internet. These codes are not intended for use by working professionals in the field. The goal has been to keep the Copyright © 1998 by ASME2 formulation, logic and programming as simple as possible so that the student can easily grasp the flow of the calculations. Thus, primitive variables (u,v); (x,y) are employed with no transformations. These codes are meant only to relieve the student of the burden of writing and debugging numerous codes during a course. The hope is to thereby leave sufficient time and energy for the working of actual boundary layer problems of reasonable complexity. The student is not relieved of the burden to think. One should always estimate the answer the computer solution is expected to yield. For example, one could use a simple integral solution to estimate the level of the skin friction to be expected. The student is the analyst, not the computer, and he or she is responsible for producing and interpreting the correct answer. At this point, there are four separate codes for the various methods covered: 1) Thwaites-Walz incompressible, laminar integral method, 2) incompressible, laminar boundary layers by an implicit numerical method, 3) Moses, incompressible turbulent integral method, and 4) incompressible turbulent boundary layers by an implicit numerical method. A brief description of each code precedes the operating instructions. Also, a default input for a typical example and results for that case are presented and discussed. Detailed development of the methods can be found in the referenced text. Earlier FORTRAN versions of these codes are also in that reference. For any boundary layer problem, one must specify the IOXLG WKURXJK GHQVLW\  DQG YLVFRVLW\  RU SHUKDSV MXVW kinematic YLVFRVLW\   ,Q YDULDEOHGHQVLW\ YDULDEOHSURSHUW\ cases, an equation of state and property variation information must also be given. The next information needed would be the freestream velocity Uinf and the inviscid edge velocity distribution, Ue(x). For high-speed flows, Mach numbers, Minf and Me(x), are needed. With heat transfer or compressible flow, the wall temperature, Tw(x), or the wall heat transfer distribution and Tinf and Te(x) are required. Next is the matter of initial conditions. The integral methods only require initial values of quantities like θ , and Cf at xinit. The differential methods need initial profiles of u and v at xinit. For turbulent cases, one must select the turbulence model, e.g. mixing length model, eddy viscosity model or TKE model with the Prandtl Energy Method. The TKE method requires an initial profile and boundary conditions for K. Finally, the computational region must be selected. With an integral method, this is simply the length of interest. The differential methods require the height and the length of the computational region. The height should grow with streamwise distance to accommodate the growth in thickness of the boundary layer. The programs here are based on the untransformed equations to keep the codes simple, so the user must pick a computational region high enough at the initial station to accommodate the estimated growth of the boundary layer by the downstream end of the computational region. The last matter concerns the choice of the step size(s). The integral methods only need a choice of dx, while the differential methods need dx and dy. This is normally accomplished by picking the number of points across the height and length of the region. For simplicity, most the codes included here have fixed step sized in the x and y directions. For a laminar flow, about 20-25 points across the boundary layer are sufficient. Thus, knowing the thickness of the boundary layer at the initial station permits a reasonable choice for dy. With the boundary layer approximation, we can take dx >> dy, and a value of dx ≈δi/2 is usually adequate. For a turbulent flow a stretched grid in the y direction is much more efficient, but that was not implemented in the interests of simplicity. Therefore, a large number of grid points is necessary, about 1000 points across the boundary layer. PROGRAM WALZ This program is an implementation of the Thwaites- WALZ integral method for incompressible, laminar boundary layer flows. Refer to Sec. 2-3-2 in Schetz (1993) for a description of the technique (and Appendix B in the same reference for the original FORTRAN code). A default input set is included for the following flow problem. This is the same as the original worked example. Example Laminar Integral Method Problem: Consider 2D laminar flow of a fluid with a kinematic viscosity = 2.0x10-4 m2/s at Uinf = 10.0 m/s over a surface that is a flat plate from the leading edge to x = 1.0 m. At that station, a ramp begins that produces an inviscid velocity distribution Ue(x) = 10.5 - x/2, m/s. This is an adverse pressure gradient, since Ue is decreasing so that p increases. Calculate the boundary layer development over this surface up to x = 2.0 m. Does the flow separate? Solution: We must provide input data for the kinematic viscosity as = 2e-4 and the freestream velocity as Uinf = 10.0. Select NMAX = 41 to give dx = 0.05. The body thickness distribution, r(x), can be specified. The code will then calculate the surface distance along the body. The default is r(x) = 0.0. Blunt bodies need input for Ro. Finally, the inviscid velocity distribution is required. Since this case has a bi-linear edge velocity variation, velocities at only a few points including xinit and xfin need to be specified to define the distribution. The window in Fig. 1 shows the input information for the default case. On the left are two panels containing the input data for this case. The input data in the far left panel can be changed by selecting the item to be changed with the menu button, entering the new value in the slot below and pushing SET. The input data in the next panel to the right can be changed in a similar manner. One might wish to change the dimensionless edge velocity distribution, Ue/Uinf and the body shape. All that is required is to enter or modify sets of values for x, r and Ue/Uinf in the panel below and push SET. The code will fit a spline through the points used as input. Then, press the START button and watch the skin friction and the integral quantities develop in the graphs on the right. The Copyright © 1998 by ASME5 Figure 1. Input data for the default case in the WALZ code. Figure 2. Sample output for the default case from the WALZ code. Figure 3. Input data for the default case in the ILBLI code. Copyright © 1998 by ASME6 Figure 4. Sample output for the default case from the ILBLI code. Figure 5. Input data for the default case in the MOSES code. Figure 6. Sample output for the default case from the MOSES code. Copyright © 1998 by ASME7 Figure 7. Input data for the default case in the ITBL code. Figure 8. Sample output for the default case from the ITBL code.