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Flow Over a Missile Forebody:
OVERFLOW and PMARC Solutions

The NASA-Ames developed Navier-Stokes solver OVERFLOW and the panel code PMARC are applied to the computation of the subsonic flow over a typical missile forebody. The flowfields at low angles of attack from 0 to 14 degree incidences are investigated.

In the OVERFLOW computations, the computational domain is discretized with six structured, sub-grids with a total number of 850,000 grid points. The PEGSUS code is used to determine the overset and overlapping sub-grid boundaries with grid blanking and to obtain the inter-grid interpolation data. At 45 degree roll angle, the flowfield is assumed to be symmetric across the mid-span plane. The flowfield is assumed to be turbulent and the Baldwin-Lomax algebraic turbulence model is employed. The present steady-state flowfields were computed at a free stream Mach Number of 0.3, and a Reynolds Number of 2 million which is based on the diameter of the missile body. A typical run for a converged solution takes approximately 4000-6000 time steps and 40-60 CPU hours on a CRAY Y-MP.

In the PMARC computations, the full missile body is modeled with approximately 5000 surface panels. The Kutta condition is applied at the trailing edges without introducing source and doublet singularities in the wake. A typical PMARC run takes approximately 20 minutes on a CRAY Y-MP.

The flowfields computed by OVERFLOW are given in terms of particle traces originating from the mid-body section and the leading edges of the canards, the surface pressure contours and the surface streamlines at 0 , 2 , 6 , 10 and 14 degree incidences. Up to 6 degree incidence, the flow stays attached over the forebody. At 6 degree incidence, development of a vortex over the leading edge of the canards is observed. Yet, the flow stays mostly attached over the canards as well. At 10 and 14 degree incidences, the flow separates over the aft-body and the canard vortices become stronger. Flow separation and re-attachment lines over the upper canard surfaces are clearly observed at 10 and 14 degree incidences. Similarly, the flow separation line over the aft-body is seen in the top view of the surface streamlines. The flowfield between the canards also becomes highly complex starting from 6 degree incidence with the development of corner flows around the canard-body junctions and the leading edge vortices. The flow above the canard leading edges is first strongly deflected away from the canards and then sucked in under the influence of the canard vortex. In general, it is observed that starting from 10 degree incidence, the viscous effects begin to dominate the flowfield with strong canard vortices, corner flows and flow separation over the aft-body.

The surface pressure distributions computed by OVERFLOW and PMARC are compared along the missile body past the trailing edges of the canards at the top, bottom and mid sections at 0 , 2 , 6 , 10 and 14 degree incidences. As seen, the overall agreement is remarkably good except at the suction peak. It is likely that this discrepancy is caused by coarse panel distribution near the suction peak in the present PMARC solution. Past the trailing edge of the canards, the increase in pressure also appears to be overstated in the PMARC prediction, which may be attributed to the absence of wakes. Starting from 10 degree incidence, the OVERFLOW solution predicts higher suction on the top surface past the canard leading edge, which is attributed to the suction induced by the canard vortex. On the bottom surface where the flow stays attached and the effect of the canard vortices is minimum, the agreement is quite good up to 14 degree incidence. Although the flowfield between the canards is predicted to be highly vortical by the OVERFLOW solution, the computed pressure fields agree remarkably well. At 14 degree, the suction predicted by the OVERFLOW solution past the trailing edge may again be attributed to the wake effects.

The computational efficiency of PMARC suggests to extend the calculations to higher angles attack than explored in the present work. We believe that this can be done by including the unsteady wakes shed from the canards and from properly chosen separation lines on the body of revolution. The range of applicability of this approach will then be assessed by comparison with OVERFLOW Navier-Stokes solutions.

We thank Mr. David Siegel, Office of Naval Research, Dr. Craig Porter and Mr. Clint Housh, Naval Air Warface Center, Weapons Division, China Lake, for their support of this project.

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Updated on Monday, 03-Aug-1998 21:30:08 EEST