Approximate factorization algorithm for three-dimensional transonic nacelle/inlet flowfield computations

Vadyak, J.; Atta, E. H.

doi:10.2514/3.22759

Cited by 4 publications

(1 citation statement)

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“…The finite-difference approximation to the full potential equation in £-rj-£ system is given by 3 curate backward-difference operators in the £, 77, and f directions. The quantities p, p, and p are the densities retarded by the use of artificial viscosity; £7, V 9 and W contravariant velocity components along the £, rj, and f directions; and J the Jacobian of transformation.…”

Section: Computation Of Three-dimensional Transonic Inlet Flowfields mentioning

confidence: 99%

Computation of three-dimensional transonic inlet flowfields using an approximate factorization algorithm

Nakamura¹

1988

Journal of Propulsion and Power

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A CCURATE inlet flowfield computation is necessary for inlet contour optimization. Chen and Caughey 1 developed an algorithm for solving the nonconservative full potential equation on a body-fitted curvilinear grid for axisymmetric inlets at incidence. Reyhner 2 developed a threedimensional, nonconservative full potential solution for inlets. In this algorithm, a cylindrical rather than a body-fitted curvilinear grid was used. This eliminates any grid generation problems, but introduces difficulties in accurate imposition of boundary condition at the inlet surface because the grid lines do not coincide with the body contour.Vadyak and Atta 3 developed a method for computing the three-dimensional transonic flowfield about inlet configurations. The solution is obtained by solving the full potential equation in conservative form on a body-fitted curvilinear grid. The difference equations are solved by the AF2 approximate factorization scheme. 4 ' 5 The computational grid is obtained by using two-dimensional grid generation techniques for a series of meridional planes. The inlet centerline represents a singularity in the three-dimensional grid mapping. An extrapolation and averaging technique is used to obtain the flow properties on the centerline.Although the method of Vadyak and Atta is accurate and efficient, the procedure to obtain the flow properties on the centerline is not adequate because the equation is not satisfied there. Therefore, we propose a modification of the method of Vadyak and Atta; the procedure along the centerline is replaced by the solution of a finite-difference equation in the frame of a rectangular coordinate system.The solution is computed on a three-dimensional bodyfitted grid. The grid is generated by the method using conformal mapping. 6 ' 7 Figure 1 shows the topology for an inlet with a centerbody. The computational curvilinear coordinates are denoted by £, 77, and f. The £ coordinate is in the wraparound direction, initiating at the external in-and outflow surfaces and terminating at the compressor face. The 77 coordinate is in the circumferential direction. The f coordinate is in the radial direction, initiating at the centerline (centerbody) and terminating at the inlet surface.The finite-difference approximation to the full potential equation in £-rj-£ system is given by 3 ' 5 U+ M,k -where is the velocity The operators o~^( ), potential and_L the residual operator.( ), and 67 ( ) are first-order accurate backward-difference operators in the £, 77, and f directions. The quantities p, p, and p are the densities retarded by the use of artificial viscosity; £7, V 9 and W contravariant velocity components along the £, rj, and f directions; and J the Jacobian of transformation. The subscripts /, j 9 and k indicate the position in the £, 17, and f finite-difference grid. The implicit approximate factorization (AF) scheme is formulated by considering the two-level iteration procedure (1) where N is an operator and C" the correction ( n+l - n ). The factor L n is the residua...

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Section: Computation Of Three-dimensional Transonic Inlet Flowfields mentioning

confidence: 99%