Navier-Stokes solutions for vortical flows over a tangent-ogive cylinder
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Hartwich, PETER-M.↗
Engineering topics
Hartwich, PETER-M.
Publications and source records attributed to Hartwich, PETER-M..
Fresh look at floating shock fitting
A fast implicit upwind procedure for the two-dimensional Euler equations is described that allows accurate computations of shocked flows on nonadapted meshes. Away from shocks, the second-order accurate upwinding is based on the split-coefficient-matrix (SCM) method. In the presence of shocks, the difference stencils are modified using a floating shock fitting technique. Rapid convergence to steady-state solutions is attained with a diagonalized approximate factorization (AF) algorithm. Results are presented for Riemann's problem, for a regular shock reflection at an inviscid wall, for supersonic flow past a cylinder, and for a transonic airfoil. All computed shocks are ideally sharp and in excellent agreement with other numerical results or 'exact' solutions. Most importantly, this has been accomplished on unusually crude meshes without any attempt to align grid lines with shock fronts or to cluster grid lines around shocks.
Hartwich, PETER-M.↗
Navier-Stokes computations of vortex asymmetries controlled by small surface imperfections
Navier-Stokes analyses are employed to explore the driving mechanisms controlling asymmetric vortical flows with Re(D) = 0.8 million (Reynolds number based on maximum diameter) over a 3.5 caliber tangent-ogive cylinder at large angles of attack (alpha = 20, 30, and 40 degrees). All flowfield results are steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in the thin-layer approximation. The numerical results are temporally and spatially fully converged, and are in good agreement with experimental data. The major findings are: (1) for alpha not less than 30 degrees, the vortex flows are genuinely asymmetric yet recurrent; (2) asymmetric vortex patterns are highly sensitive toward such parameters as machine accuracy, grid topology, etc., unless triggered by a slight deformation (similar to an out-of-round nose tip) in the neighborhood of the apex; and (3) for alpha = 20 degrees, the flow is symmetric for both circular and elliptic cross-sectional shapes of the nose tip.
Hartwich, PETER-M.↗
Navier-Stokes solutions for vortical flows over a tangent-ogive cylinder
Reynolds number (Re) effects on low-speed vortical flows over a 3.5 caliber tangent-ogive cylinders at two angles of attack (alpha = 20 and alpha = 30 degrees) are computationally assessed for Re(D) = 0.2 -3.0 million (D: maximum diameter). The flow field results are steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in their thin-layer approximation. Using a properly modified algebraic turbulence model, the numerical results are in good to excellent agreement with experiments.
Hartwich, PETER-M.↗
Total Variation Diminishing (TVD) schemes of uniform accuracy
Explicit second-order accurate finite-difference schemes for the approximation of hyperbolic conservation laws are presented. These schemes are nonlinear even for the constant coefficient case. They are based on first-order upwind schemes. Their accuracy is enhanced by locally replacing the first-order one-sided differences with either second-order one-sided differences or central differences or a blend thereof. The appropriate local difference stencils are selected such that they give TVD schemes of uniform second-order accuracy in the scalar, or linear systems, case. Like conventional TVD schemes, the new schemes avoid a Gibbs phenomenon at discontinuities of the solution, but they do not switch back to first-order accuracy, in the sense of truncation error, at extrema of the solution. The performance of the new schemes is demonstrated in several numerical tests.
Hartwich, PETER-M.↗
Numerical study of the vortex burst phenomenon for delta wings
A flux-difference splitting scheme is employed to compute low-speed flows over a delta wing for angles of attack from 0 to 40 deg as steady-state solutions to the three-dimensional, Reynolds-averaged Navier-Stokes equations in their thin-layer approximation. The finite-difference scheme is made spatially second-order accurate by applying a total variation diminishing-like discretization to the inviscid fluxes and central differencing to the viscous shear fluxes. Using first-order accurate Euler backward-time differencing, an efficient implicit algorithm is constructed, which combines approximate factorization in cross planes with a symmetric planar Gauss-Seidel relaxation in the remaining third spatial direction. The geometry of the thin (maximum thickness is 0.021), slender (aspect ratio is unity), sharp-edged delta wing is taken from Hummel's (1967, 1978) wind tunnel model. Over the entire angle-of-attack range, the computed values of lift and pitching moment are in good agreement with the experimental data. Also details of the flow-fieldlike spanwise surface pressure distributions compare well with the experiment. Computed flow-field results with a bubble-type vortex burst are analyzed in detail.
Hartwich, PETER-M.↗
High resolution upwind schemes for the three-dimensional incompressible Navier-Stokes equations
Based on flux-difference splitting, implicit high resolution schemes are constructed for efficient computations of steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. These schemes use first-order accurate Euler backward-time differencing and second-order central differencing for the viscous shear fluxes. Up to third-order accurate upwind differencing is achieved through a reconstruction of the solution from its cell averages. The reconstruction is accomplished by linear interpolation, where the node stencils are selected such that in regions of smooth solution the flow is highly resolved while spurious oscillations in regions of rapid changes in gradient are still suppressed. Fairly rapid convergence to steady-state solutions is attained with a completely vectorizable hybrid time-marching method. Flows around a sharp-edged delta wing are computed with the maximum accuracy of the upwind-differencing restricted to first-, second-, and third-order, to illustrate the effect of accuracy on the global and on the local vortical flow fields. The results are validated with experimental data.
Hartwich, PETER-M.↗