Graphical visualization of vortical flows by means of helicity
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Degani, David↗
Engineering topics
Degani, David
Publications and source records attributed to Degani, David.
Analytical study of the origin and behavior of asymmetric vortices
An hypothesis advanced originally to explain computational observations is supported by theoretical considerations: The asymmetric mean flow observed on bodies of revolution at moderate to high angles of attack is the result of a convective instability of an originally symmetric flow to a time-invariant space-fixed disturbance. Additionally, the time-dependent fluctuations characteristic of the flow at higher angles of attack (up to 90 deg) are the result of an absolute instability of an originally steady flow to a small temporal disturbance of finite duration. Within a common domain, the instability mechanisms may coexist. The experimentally confirmed existence of bistable states, wherein the side-force variation with nose roll angle approaches a square-wave distribution, is attributed to the dominant influence of a pair of trailing vortices from the ogival forebody. Their existence is made possible by the appearance of foci of separation in the skin-friction line pattern beyond a critical angle of attack. The extreme sensitivity of the asymmetric flow orientation to nose geometry, demonstrated experimentally, is attributed to the presence of an indeterminate phase in the family of possible solutions for the three-dimensional wave system.
Tobak, Murray↗
Effect of short regions of surface curvature on compressible turbulent boundary layers
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Degani, David↗
Numerical investigation of the origin of vortex asymmetry
The flow about a slender body of revolution placed at incidence to an oncoming stream is numerically investigated for angles of attack ranging from 20 to 80 degrees and a Reynolds number of 200,000, based on freestream conditions and maximum body diameter. Navier-Stokes computations are applied to investigate the phenomena governing the onset of vortex asymmetry. Time-accurate solutions are given for an ogive-cylinder body with and without a space-fixed time-invariant disturbance added near the tip. At a 40-degree angle of attack the flow is found to be steady but becomes highly asymmetric when the disturbance is added. The level of asymmetry is dependent upon the size and location of the disturbance. It is suggested that the origin of the asymmetry is a convective-type instability of the originally symmetric flow. For higher angles of attack (60 and 80 degrees) the flow around the cylindrical part becomes unsteady, and vortex shedding is observed. It is suggested that the origin of flow unsteadiness and vortex shedding in the wake is an absolute-type instability of the originally steady flow.
Degani, David↗
Physical considerations governing computation of turbulent flows over bodies at large incidence
The physical aspects governing accurate numerical simulation of turbulent flows having large regions of crossflow separation are re-examined. Time-accurate, three-dimensional fine-grid Navier-Stokes solutions were obtained for turbulent subsonic and supersonic flows over a slender ogive-cylinder body of revolution at large angles of attack. These flowfields are complex and contain regions of crossflow separation and an organized leeward-side vortex structure. An algebraic eddy-viscosity turbulence model has been modified to correctly account for the effects of the vortices on the underlying viscous layers. The numerical results show that the vortical flow structure of both subsonic and supersonic high incidence flows are similar, and can be accurately treated by the turbulence model. As the angle of attack is increased, the effectiveness of the model increases since the influence of the vortices on the underlying boundary layer decreases.
Degani, David↗
Numerical investigation of the origin of vortex asymmetry of flows over bodies at large angle of attack
The occurrence of the flow about a slender body of revolution placed at incidence to an incoming stream is numerically examined for angles of attack ranging from 20 to 80 degrees and a Reynolds number of 200,000 based on maximum body diameter. Over a certain range of Reynolds numbers, the trend of flowfields around slender bodies at incidence can be roughly divided into three main categories: (1) at alpha = 0-30 deg, the flow is steady and symmetric; (2) at alpha = 30-60 deg, the flow under normal conditions is usually asymmetric, but the level of the asymmetry depends on the amount of disturbances present on the tip of the body; and (3) at alpha 60-90 deg, the flow in the wake of the body acts in a fashion similar to that of the Karman vortex shedding behind a two-dimensional circular cylinder. For each of these categories the range of incidence may change by + or - 10 degrees, depending on the quality of flow, or body finish.
Degani, David↗
Numerical simulation of vortex unsteadiness on slender bodies of revolution at large incidence
Time-accurate, fine-grid Navier-Stokes solutions were obtained for flow over a slender ogive-cylinder body of revolution at angles of attack ranging from 10 deg to 40 deg. The results indicate the progressive growth of crossflow separation and the development of the leeward side vortex pattern with increasing incidence. The computed flows show good agreement with experimental measurements. As the angle of attack was increased, the flows become less damped, and at 40 deg a nonsteady flow exhibiting self-sustained fluctuations was observed. The nonsteadiness was linked to the presence of small-scale three-dimensional vortices moving along the primary surfaces of crossflow separation. The behavior of the fluctuations with incidence parallels the trend observed in experiments.
Schiff, Lewis B.↗
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 Navier-Stokes computations. The computed results demonstrate the marked asymmetry which has been observed in experiments. To obtain asymmetry, it was found essential to introduce a space-fixed time-invariant perturbation into the computation. 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.
Degani, David↗
Numerical simulation of separated and vortical flows on bodies at large angles of attack
Navier-Stokes computations were carried out for high-angle-of-attack flow about bodies of revolution in supersonic and subsonic flow. Numerical and physical factors affecting flow predictions are discussed. Accurate prediction of the complex three-dimensional separated flow is found to depend on using grids sufficiently fine to resolve the details of both the viscous boundary layer and the off-surface separated flow structures, and, for turbulent flow cases, use of an eddy-viscosity turbulence model which accounts for the leeward vortical flow structures. An example of high-incidence flow computed about a more complex geometry, the F-18 fighter fuselage forebody and leading edge extension, is also presented.
Schiff, Lewis B.↗
Graphical representation of three-dimensional vortical flows by means of helicity density and normalized helicity
The 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 graphical representation of 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 allows locating the singular points in type I primary separations and tracing the vortex-core streamlines that emanate from them. It also allows locating the vortex-core axes in flows of other types.
Seginer, Arnan↗
Computation of asymmetric supersonic flows around cones at large incidence
The Schiff-Steger parabolized Navier-Stokes (PNS) code has been modified to allow computation of conical flowfields around cones at high incidence. The improved algorithm of Degani and Schiff has been incorporated with the PNS code. This algorithm adds the cross derivative and circumferential viscous terms to the original PNS code and modifies the algebraic eddy viscosity turbulence model to take into account regions of so called cross-flow separation. Assuming the flowfield is conical (but not necessarily symmetric) a marching stepback procedure is used: the solution is marched one step downstream using improved PNS code and the flow variables are then scaled to place the solution back to the original station. The process is repeated until no change in the flow variables is observed with further marching. The flow variables are then constant along rays of the flowfield. The experiments obtained by Bannik and Nebbeling were chosen as a test case. In these experiments a cone of 7.5 deg. half angle at Mach number 2.94 and Reynolds number 1.372 x 10(7) was tested up 34 deg. angle of attack. At high angle of attack nonconical asymmetric leeward side vortex patterns were observed. In the first set of computations, using an earlier obtained solution of the above cone for angle of attack of 22.6 deg. and at station x=0.5 as a starting solution, the angle of attack was gradually increased up to 34 deg. During this procedure the grid was carfully adjusted to capture the bow shock. A stable, converged symmetric solution was obtained. Since the numerical code converged to a symmetric solution which is not the physical one, the stability was tested by a random perturbation at each point. The possible effect of surface roughness or non perfect body shape was also investigated. It was concluded that although the assumption of conical viscous flows can be very useful for certain cases, it can not be used for the present case. Thus the second part of the investigation attempted to obtain a marching (in space) solution with the PNS method using the conical solution as initial data. Finally, the solution of the full Navier-Stokes equations was carried out.
Degani, David↗
Comparison Between Navier-Stokes and Thin-Layer Computations for Separated Supersonic Flow
In the numerical simulation of high Reynolds-number flow, one can frequently supply only enough grid points to resolve the viscous terms in a thin layer. As a consequence, a body-or stream-aligned coordinate system is frequently used and viscous terms in this direction are discarded. It is argued that these terms cannot be resolved and computational efficiency is gained by their neglect. Dropping the streamwise viscous terms in this manner has been termed the thin-layer approximation. The thin-layer concept is an old one, and similar viscous terms are dropped, for example, in parabolized Navier-Stokes schemes. However, such schemes also make additional assumptions so that the equations can be marched in space, and such a restriction is not usually imposed on a thin-layer model. The thin-layer approximation can be justified in much the same way as the boundary-layer approximation; it requires, therefore, a body-or stream-aligned coordinate and a high Reynolds number. Unlike the boundary-layer approximation, the same equations are used throughout, so there is no matching problem. Furthermore, the normal momentum equation is not simplified and the convection terms are not one-sided differenced for marching. Consequently, the thin-layer equations are numerically well behaved at separation and require no special treatment there. Nevertheless, the thin-layer approximation receives criticism. It has been suggested that the approximation is invalid at separation and, more recently, that it is inadequate for unsteady transonic flow. Although previous comparisons between the thin-layer and Navier-Stokes equations have been made, these comparisons have not been adequately documented.
Degani, David↗