A Moving Grid Capability for NPARC

Abstract Version 3.1 of the NPARC computational fluiddynamics flow solver introduces a capability to solveunsteady flow on moving multi-block, structuredgrids with nominally second-order time accuracy.The grid motion is due to segments of the boundarygrid that translate and rotate in a rigid-body manneror deform. The grid is regenerated at each time stepto accommodate the boundary grid motion. Theflow equations and computational models sense themoving grid through the grid velocities, which arecomputed from a time-difference of the grids at twoconsecutive time levels. For three-dimensional flowdomains, it is assumed that the grid retains a pla-nar character with respect to one coordinate. Theapplication and accuracy of NPARC v3.1 is demon-strated for flow about a flying wedge, rotating flap, acollapsing bump in a duct, and the unstart / restartflow in a variable-geometry inlet. The results com-pare well with analytic and experimental results. Introduction Version 3.11 of the NPARC 2'3 computationalfluid dynamics (CFD) flow solver was released in Oc-tober 1997 with modifications that enhance the ca-pability to solve unsteady flows and introduce a ca-pability to simulate flows with moving, multi-block,structured grids. This paper discusses those modifi-cations, explains the approach for defining the mov-ing grid problem, and presents several test casesthat demonstrate the application and accuracy ofNPARC v3.1 for moving grids.Moving grids in CFD arise when there is motionof a region of the flow domain relative to the restof the flow domain. An example is a flow domainabout a high-speed, variable-geometry, axisymmet-ric inlet. The centerbody of the inlet may translate*Aerospace Engineer, Inlet Branch, AIAA Senior Memberand collapse as part of the restart operation for theinlet once it has unstarted. The grid block contain-ing the centerbody may deform to accommodate thecenterbody motion. Such grid motion is consideredmoderate in that the magnitude of the motion isless than the scale of the block dimensions and thetopology of the block remains intact.NPARC v3.1 assumes that there are moderatelevels of grid motion associated with the motion ofsegments of the boundary grid relative to the rest ofthe grid of the block. This motion may be a rigid-body translation and / or rotation about a point ora deformation of the segment according to a codedrelation. The remainder of the grid of the block de-forms to accommodate the boundary motion. Thisrequires that some regions of the grid be regeneratedat each time step. Efficiency in the grid regenera-tion process is obtained by limiting the regenerationto only those regions in which there is grid motion.Thus, the grid becomes a computed function of time.The flow equations and boundary conditions are ex-pressed in terms of an absolute frame of referencewith the grid motion accounted for through the gridvelocities. The velocity of each grid point can becalculated from a time difference of the grids at twoconsecutive time levels. For three-dimensional flowdomains, the grid is assumed to be "quasi-2d" or ax-isymmetric in which the grid consists of planar gridswith respect to the 'T'-coordinate.The flow equations and physical models are firstpresented in integral form for a deforming controlvolume to show the influence of the velocities of thecontrol surface. The finite-difference approximationsare then discussed to show how the grid velocities in-fluence the computational methods. The approachfor defining the moving grid problem within NPARCv3.1 is then discussed. Several test cases involvingmoving grids are presented to demonstrate the appli-cation and accuracy of the moving grid capability. Afew simple test cases involving supersonic flow overa stationary wedge, a flying wedge, and a rotatingflap on a fiat plate allow comparison with steady-state oblique shock theory. A test case involvingthe collapse of an axisymmetric bump in an annu-1American h, stitute of Aeronautics and Astronautics