Numerical Prediction of Flow over a Prolate Spheroid Undergoing a Pitchup Maneuver
Accurate numerical prediction of truly unsteady, high
excursion, high-Reynolds number separated flows is of great interest in
aeronautics and naval hydrodynamics. The separated flow around a
three-dimensional body almost always gives rise to several adverse phenomena in
aero- and hydrodynamics such as the increase in drag, loss of lift and
amplification of unsteady effects including fluctuations in the pressure field.
It is often possible to avoid separation by placing limitations on the operating
conditions. However, there are times when separated flow cannot be avoided and
must be dealt with.
Prediction of the time-dependent flow around a 6:1 prolate spheroid undergoing a
pitchup maneuver was obtained using Detached-Eddy Simulation (DES). DES is a
hybrid formulation which attempts to capitalize on the often adequate
performance of Reynolds-Averaged Navier-Stokes (RANS) models in predicting
boundary layer growth and separation, and to use Large-Eddy Simulation (LES)
away from solid surfaces to model the typically geometry-dependent and unsteady
scales of motion in separated regions. The DES formulation is based on a
modification to the Spalart-Allmaras RANS model such that the model reduces to
RANS formulation near solid surfaces and to a subgrid scale model away from the
wall. Flowfield predictions are evaluated using experimental measurements and
also contrasted against predictions of the flows at static angles of attack
(a) of 10o, 20o, and 30o.
Flowfield parameters are the same as in the experiments, the Reynolds number
based on freestream velocity and the model length is 4.2x10-6, the
boundary layers on the spheroid surface are tripped at x/L=0.2. The spheroid
pitches about its centroid from 0o to 30o angle of attack
over a period of 0.33 seconds, corresponding to a dimensionless pitch rate of
0.047 (based on the freestream speed and model length). Solutions of the
compressible Navier-Stokes equations are obtained on unstructured grids,
rigid-body motion of the spheroid is accomplished using an Arbitrary
Lagrangian-Eulerian (ALE) formulation. Compared to the solutions at fixed angles
of attack, the flow structure for the pitchup case lags that of static-a
flows. Surface flows for the static- and maneuvering-geometry solutions
show marked differences at the conclusion of the pitchup. At 20o
angle of attack the pitchup solution does not possess a secondary separation as
in the static-a case. Skin friction predictions
exhibit similar variation as the experimental measurements of Wetzel and
Simpson, though are shifted below the measured values. Predictions of the
azimuthal pressure
distribution exhibits good agreement with the measurements of Hoang et al.
Development of the normal force and pitching moment for the maneuvering geometry
also show reasonable agreement with measured values.
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Oil flow patterns and vorticity contours at α = 10o, (a) Static geometry, (b) Pitchup geometry
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Oil flow patterns and vorticity contours at α = 20o, (a) Static geometry, (b) Pitchup geometry
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Oil flow patterns and vorticity contours at α = 30o, (a) Static geometry, (b) Pitchup geometry
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