The application of panel method code ANTARES to wind tunnel wall interference problems

Abstract

Panel method code ANTARES was developed to solve subsonic wall interference problems in a threedimensional wind tunnel with non-rectangular crosssection. The code uses a singularity representation of the test article. Volume and viscous separation wake blockage effects of the test article are represented by chains of point doublets. Lifting effects are represented by line doublets. The closed wall, open jet, perforated wall, or slotted wall boundary condition may be assigned to each individual wall panel centroid. The code also allows the user to solve wall interference problems with a mixed set of wall boundary conditions. ANTARES may be applied to a fullspan or semispan model test. A typical panel model of the test section consists of up to 8000 panels. A LU decomposition algorithm is used to solve the corresponding large linear system of equations. Therefore, it is critical to compile the code using DOUBLE PRECISION data type in order to obtain sufficiently accurate numerical solutions of the linear system. Available classical solutions of three different wall interference correction problems show excellent agreement with numerical results obtained by using ANTARES. Nomenclature dij — matrix coefficient bi = component of right hand side vector ci» • • • , c4 = boundary condition coefficients F = upwash factor (see Ref. [8], p.29) i = wall panel index j = wall panel index I = slot parameter (see Ref. [3]) M = Mach number n = total number of unknowns N = total number of panels R = restriction parameter * Senior Aerodynamicist; Sverdrup Technology, Inc. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. u = unit round-off error or relative machine precision for floating point operations uw = axial interference velocity UQQ = reference velocity vw = interference velocity, ^-direction ww = interference velocity, ^-direction x = x-coordinate y = t/-coordinate z — z-coordinate Aa = ww/u00; angle of attack correction e = UW/UQQ', blockage factor fj,j = source strength slope p = bound associated with Gaussian elimination 4> = velocity potential of wind tunnel flow field (j)m = velocity potential of test article (f)w = wall interference velocity potential of the wind tunnel flow field in combination with a set of constants ci, • • • , c4. Then, in incompressible flow, we get: n ,^ = 0 (1) where x is the streamwise coordinate, n is the outward normal vector on the test section boundary, and ci,C2,cs,C4 are coefficients that describe the wall boundary conditions. Table 2 lists values of these coefficients for six different types of boundary conditions. The total perturbation velocity potential (/> may be written as the sum of the potential c/>m caused by the test article and the potential (j)w caused by the wind tunnel walls, i.e. the wall interference potential. We get : (/> = 4>m + w (2) Combining Eqs. (1) and (2), we get : + 02 d dx / • N = ci(t)