Optimisation Studies Validation Document

Transcription

1 Vortex Lattice Method ode for Optimisation Studies Validation Document K. Sudhakar ASDE Report : TR entre for Aerospace Systems Design & Engineering Department of Aerospace Engineering Indian Institute of Technology Bombay, Mumbai January 2002

2 Vortex Lattice ode for Optimisation Studies Validation Document This VLM code is written to for use in design optimisation studies. Theoretical background on VLM can be found in the book by Plotkins & Katz [1]. ode is in 4 files, 1. main.f - Main program that calls vlm subroutine 2. vlm.f - Input is wing geomtery, output is cl, cd, cm 3. vortex.f - provides support for AI calculation 4. mesh_vlm.f - generates a parametric mesh Main program sets up wing geometry details and mesh size. VLM subroutine when called returns cl, cd, cm. The reference area is computed inside as the plan-form area. Reference chord used is the root chord and moment reference point is the wing apex. User should modify only the main.f and supply a subroutine deform that will returns the angles of attack at each collocation point. Files vlm.f, vortex.f & mesh_vlm.f are not to be modified. Some of the important routines are explained below. main.f EXTERNAL deform define values for all the following. They are inputs amach : Mach number for applying compressibility corrections cr : Wing root chord ct : Wing tip chord bby2 : Semi-span of wing sweep : Leading Edge Sweep in Radians isym : 0 - no symmetry, 1 - symmetry about x-z plane ni_gr : No of mesh points chordwise nj_gr : No of mesh points spanwise deform: Name of user supplied subroutine for local alpha All the above need to be assigned values. Following are outputs cl : Lift coefficient cd : drag coefficient cm : pitching moment coefficient ALL vlm(amach, cr, ct, bby2, sweep, isym, ni_gr, nj_gr, cl, cd, cm, deform) STOP

3 SAMPLE deform SUBROUTINE for rigid, planar wing SUBROUTINE deform (r_p, beta, alpha, np) DIMENSION r_p(3,np), alpha(np) r_p : coordinates of collocation point all panels where alpha is to be defined. beta = SQRT(1. - m^2) alpha : angles of attack at panel collocation points np : no of panels DO i_p=1, np r_p(1,i_p) = r_p(1,i_p) * beta de-stretching d_alp = FUNTION of (r_p(1,i,j), r_p(2,i,j) & r_p(3,i,j)) For rigid planar wing. d_alp = 0. alpha(i_p) = 1. + d_alp full wing is at 1 rad. d_alp is the additional alpha due to deformation. r_p(1,i_p) = r_p(1,i_p) / beta re-stretching DO RETURN SUBROUTINE vlm(amach, cr, ct, bby2, sweep, isym, 1 ni_gr, nj_gr, cl, cd, cm, setalp) PARAMETER (ni_gr_max=25, nj_gr_max=25) PARAMETER (np_max =(ni_gr_max-1)*(nj_gr_max-1) ) EXTERNAL setalp.... RETURN Verification of the code is done as follows, onsider constant chord wings of aspect ratios 2, 4 & 6 with sweep 0, 30, 45 and 60 degrees. Half wing is discretised with 11 x 11 mesh (ie 10 x 10 panels) and symmetry is invoked. Results from the code are given in Table below. Note the results are for Mach = 0. These results may be compared with Figure (pp 398) in Katz & Plotkin (reproduced here for easy reference.)

4 Aspect Ratio Leading edge sweep dl/dα Limited comparison with Desktop Aeronautics web calculator. Wing geometry: cr=1, ct=0.5 (taper = 0.5), sweep = 25, AR=10. horwise panel = 1 (Desktop Aero code is Wiesinger method) Span-wise panels used in desktop Aero not known. Results for present code generated using 21 panels span-wise. Present code DTAero L d M

5 More detailed comparison of VLM results: IIT-B and University of Sydney. Mach no. = 0; L_a and m_a are per radian. There are 2 rows of results for each wing. First rows of results are from Univertsity of Sydney ode; Second row is IITB ode NPc - No. of panels chordwise; NPs - No. of panels spanwise b r t Sweep NPc x NPs AR L_a m_a K 1. e = (K π AR) x x x x x Examine the last planform of aspect ratio 8.21, which shows different values of m_a. This is due to difference in reference chord used. Univ. Sydney uses average = as refernce chord IIT-B uses root = as refernce chord If Univ. Sydeney m is refered to 5.526, we have, m_a = * 3.37 /5.526 = The above code has been put through ADIFOR for derivative code for alpha, Mach and span, but one at a time. Results of derivative code were verified using values obtained by finite differencing. Derivative code for Mach no. was correctly computing derivatives during first call. But subsequent calls during the same execution generated erroneous results. Inspection revealed that g_xyz was used without initialisation. During the first invocation g_xyz was set to 0 which was correct. Second call had non-zero values for g_xyz that resulted in errors. A forced initialisation of g_xyz in the derivative code solved the problem. Reference "Low Speed Aerodynamics - From Wing Theory to Panel Methods", Joseph Katz & Allen Plotkin. McGraw-Hill, Inc