David Degani

Computation of turbulent supersonic flows around pointed bodies having crossflow separation

Abstract A recently reported thin-layer parabolized Navier-Stokes method has been used to compute turbulent supersonic flows around pointed bodies at large incidence. These flow fields are complex and contain extensive regions of crossflow separation. Extensive investigations were carried out to assess the effects of grid resolution in the viscous region and inviscid region of the leeward side vortices, and the effects of the algebraic eddy-viscosity turbulence model. Comparisons between computed and experimentally measured flow fields of several pointed bodies show significant improvement in the computed flow fields obtained using a properly modified turbulence model in the crossflow separation region and adequate spatial grid resolution. The effect of adding the circumferential and cross viscous terms was found to be insignificant for the present cases.

Graphical Visualization of Vortical Flows by Means of Helicity

Helicity density and normalized helicity are introduced as important tools for the graphical representation of three-dimensional flowfields that contain concentrated vortices. The use of these two quantities filters out the flowfield regions of low vorticity, as well as regions of high vorticity but low speed where the angle between the velocity and vorticity vectors is large (such as in the boundary layer). Their use permits the researcher to identify and accentuate the concentrated vortices, differentiate between primary and secondary vortices, and mark their separation and reattachment lines. The method also allows locating singular points in the flowfield and tracing the vortex-core streamlines that emanate from them. Nomenclature H = helicity Hd = helicity density Hn — normalized helicity MOO = freestream Mach number ReD = Reynolds number V = velocity a = angle of attack co = vorticity

Asymmetric vortices on a slender body of revolution

The symmetric and asymmetric leeward-side flow fields on an inclined ogive-cylinder have been investigated using a number of experimental techniques. Naturally occurring and perturbed flow fields were studied at a moderate Reynolds number and at many incidence angles. By close examination of the steady side force behavior at different roll orientations of the tip, it has been established that micro-variations in the tip geometry of the model have a large influence on the downstream development of the flow field. Under certain conditions, a bistable flow field was observed.

Numerical simulation of the effect of spatial disturbances on vortex asymmetry

The steady asymmetric vortex pattern observed on slender bodies of revolution at large angle of attack was investigated using fine-grid, thin-layer Navier-Stokes computation. The results demonstrate the marked asymmetry that has been observed in experiments. To obtain asymmetry, it was essential to introduce a space-fixed, time-invariant perturbation into the computation. If the perturbation was removed, the asymmetric flow returned toward symmetry. The perturbations were found to be more effective when located close to the nose. Taken together with the experimental observations, the computational results suggest that vortex asymmetry is forced by amplification of small disturbances, such as those due to surface roughness, occurring within the body viscous boundary layer.

Stability and existence of multiple solutions for viscous flow in suddenly enlarged channels

Abstract Instability of two-dimensional symmetric flows through channels with a symmetrical expansion about their centerline was studied. A numerical solution of viscous flow in two-dimensional channels with symmetric changes in width is presented. The channel semi-angles range from 10° to 90°, with width ratios up to 3, and Reynolds number based on the small width of up to 400. Two types of calculations for the flowfield were made, one for a full channel and the second for a half channel assuming symmetry. Using linear stability analysis the stability limit for the half-domain calculation is then shown to be the minimum Reynolds number for which an asymmetric full-flowfield solution can be obtained. For example, for a 1 : 3 expansion ratio the critical Reynolds number for stability changes from 82 for the 90° semi-angle to 147 for the 10° semi angle. A linear disturbance was applied and a time-dependent finite element solver was used to isolate the least stable mode and the corresponding eigenvalue. The eigenvalues corresponding to the least stable modes for all cases were real, indicating that the instability was local. The least stable mode was found to have a shape which indicates that this disturbance is due to the Coanda effect. This causes the change from symmetric to asymmetric flow pattern for Re > Re cr . The disturbance eigenfunction is antisymmetric for the linear regime of disturbances studied here.

Systematic study of the correlation between geometrical disturbances and flow asymmetries

Recently, large efforts were directed to numerical simulations of high-incidence flows around slender bodies of revolution to gain more insight into the problem of flow asymmetry. One of the significant advantages in using numerical simulation to investigate these flows is the ability to obtain a disturbance-free base solution. This base solution can then be perturbed for parametric studies of controlled disturbances. The experimentally observed asymmetric flow is numerically simulated by the introduction of a simulated disturbance (bump) placed near the body apex. A series of asymmetric flows over an ogive cylinder at a high angle of attack is computed by systematically varying the bump size. The results reproduce the experimentally observed effect of nose imperfections on flow asymmetry and are used to demonstrate the role of the sectional side force variation along the body. Analysis of the numerical results and the correlation between the disturbances and the asymmetric flow point to a convective instability mechanism as the origin of flow asymmetry.

Effect of Geometrical Disturbance on Vortex Asymmetry

The phenomena of the flow about a slender body of revolution placed at incidence to an oncoming stream were numerically investigated for angles of attack of 20 and 40 deg and a Reynolds number of 2×10 5 based on maximum body diameter. At angle of attack of 20 deg, the flow was steady and symmetric, and the presence of a perturbation, which was placed near the tip of the body, made only a small change.

Asymmetric turbulent vortical flows over slender bodies

Time-accurate numerical solutions have been obtained of equations modeling turbulent subsonic flows over a slender ogive-cylinder body of revolution in the high-angle-of-attack regime where a large asymmetry in the mean flow has been observed experimentally. A modified algebraic eddy-viscosity turbulence model was utilized to correctly compute the effects of the asymmetric vortices on the underlying viscous layers. In order to reproduce any one of the experimentally observed asymmetric flow-fields, it was found necessary to add a small geometrical disturbance near the body apex. By determining an appropriate size of the disturbance, it was possible to obtain excellent agreement between numerical results and experimental data for angles of attack of 30 and 40 deg, Reynolds numbers of 3.0 x 10 to the 6th and = 4.0 x 10 to the 6th, and several roll angles. When the disturbance was removed, the flow field returned to its original symmetric shape. These results are similar in behavior to solutions obtained previously for laminar flows. Just as in the laminar case, results suggest that the origin of the asymmetry is a convective-type instability of an originally symmetric flow.

Experimental study of controlled tip disturbance effect on flow asymmetry

The effect on the asymmetric mean flow observed on pointed bodies of revolution at incidence of changing the size and location of a controlled disturbance as well as changes in angle of attack and flow conditions are evaluated experimentally. Flow visualization and side‐force measurements are carried out for a generic ogive‐cylinder body inclined at high angle of attack in a low‐speed wind tunnel. For all angles of attack tested (30°–60°), minute changes in the size or location of the controlled disturbance result in finite changes in the asymmetric flow field, even to the extent of reversing the sign of the side force or becoming almost symmetric. The process is reversible; returning the wire to an original position likewise restores the corresponding flow field and mean side force. The variation of side force with continuous variation of a perturbation’s size or location remains continuous and single valued, even in the incidence range of 50° to 60°, where ‘‘bistable’’ behavior of the asymmetric flow fi...

Instabilities of flows over bodies at large incidence

The phenomena of the flow about an ogive-cylinder placed at incidence to an oncoming stream were numerically investigated for angles of attack of 60 and 80 deg.The flow around the cylindrical part of the body became unsteady, and vortex shedding was observed. For the 80-deg case, the corresponding Strouhal frequency was about 0.2. For both angles of attack, a small temporal disturbance of finite duration was sufficient to trigger the unsteadiness, which evolved to a finite amplitude fluctuation in the wake