Supersonic Corner Flows Research Articles

Effect of wall temperature in streamwise supersonic corner flow

The interaction between corner flow and heat transfer is very common in the internal and external flow of hypersonic vehicle surface, but it is not clear how the wall thermal boundary condition affects the supersonic corner flow boundary layer. In the present study, the Reynolds stress model is used to solve the Reynolds-averaged Navier–Stokes equations. The results show that when the symmetrical wall temperature Tw is less than or equal to the recovery temperature Taw, the mean velocity profile in the corner zone is similar to the plate zone, and the temperature is higher in the corner zone. At heating wall condition of Tw>Taw, both velocity and temperature profile of outer corner boundary layer are different from that in the plate zone. The near-wall temperature distribution increases relatively, and the temperature profile is no longer similar to the law of the wall when Tw rises. Along the spanwise wall, the deviation of the velocity–temperature quadratic curve and the generalized Reynolds analogy (GRA) relation is within 10%. In the supersonic corner flow, the velocity–temperature relation under non-adiabatic wall condition satisfies the GRA relation. The effect of wall temperature on corner boundary layer velocity and temperature is significant. It is necessary to consider wall thermal boundary condition in the supersonic corner flow boundary layer analysis.

Influence of compressibility on the development of streamwise supersonic corner flow

The effect of compressibility on supersonic corner flow is numerically investigated by the Reynolds-averaged Navier–Stokes equations with a full Reynolds stress model. A grid sensitivity analysis is conducted in this paper to ensure the reliability of our conclusions. Then, a parametric study by changing the Mach number in the range of M∞=0.6−3.0 is carried out to investigate the effect of compressibility. The corner angle is also changed in the range of θ=45°−135° for each M∞ to see the effect of the corner angle. As a result, the Mach number was found to have a negligible effect on the propagation of vortex cores in this study. However, it has a positive effect on both the friction coefficient and the total pressure loss. The geometrical transformation for the position of the vortex center proposed in our recent paper has been proved to be valid in over wide range. Moreover, we further find that a unified formula can describe the distribution of the total pressure loss under different Mach numbers and corner angles. In engineering terms, these laws will play an important role in the initial design and evaluation of the project with streamwise corners.

Influence of corner angle in streamwise supersonic corner flow

We use the Reynolds-averaged Navier–Stokes (RANS) equations with a full Reynolds stress model (RSM) to study the effect of the corner angle in supersonic corner flow. RANS data are compared to reference direct numerical simulation of fully developed a square duct flow, which support predictive capability of secondary flows from Stress-ω RSM. We then carry out a parametric study by changing the corner angle in the range θ=45°–135°, focusing on the effect on the mean streamwise and secondary flow. The maximum strength of the secondary flows of about 0.015u∞ occurs for θ=90°, which is similar to what is found in fully developed square ducts. Secondary eddies have approximately unit aspect ratio, and they maintain their shape for different corner angles by translating in the direction parallel to the closest wall. As a result, the position of the vortex center can be described by a simple geometrical transformation of the wall-parallel coordinate. We find that small corner angles are responsible for locally relaminarization flow at the corner, but otherwise the mean streamwise velocity profiles transformed according to van Driest following the canonical law-of-the-wall.

Investigations of Three-Dimensional Shock/Shock Interactions over Symmetrical Intersecting Wedges

This study explored inviscid supersonic corner flows induced by three-dimensional symmetrical intersecting compression wedges by introducing the spatial dimension reduction theoretical approach to transform the three-dimensional steady shock/shock interaction problem into a two-dimensional pseudosteady problem; this method allows not only wave configurations, which include regular reflection and Mach reflection, to be determined accurately, but also flowfield characteristics, which include density, temperature, pressure, and total pressure recovery coefficient near the regular reflection point (or in the vicinity of the Mach reflection triple point), as well as the location and the strength of the Mach stem. Theoretical results were compared to numerical simulation (performed by solving three-dimensional inviscid Euler equations with an non-oscillatory and non-free-parameters dissipative finite difference scheme) and analyzed thoroughly. The effects of inflow Mach number, sweep angle, and wedge angle on flowfield parameters and wave configurations were also considered. The influence of sweep angle is negligible, but the effects of Mach number and wedge angle are significant.

Parallel three-dimensional direct simulation Monte Carlo method and its applications

The development of a parallel three-dimensional direct simulation Monte Carlo (DSMC) method using unstructured cells is reported. Variable hard sphere molecular model and no time counter method are used for the molecular collision kinetics, while the cell-by-cell ray-tracing technique is implemented for particle movement. Developed serial code has been verified by comparing the results of a supersonic corner flow with those of Bird’s three-dimensional structured DSMC code. In addition, a benchmark test is performed for an orifice expanding flow to verify the parallel implementation of DSMC method by comparing with available experimental data. Static physical domain decomposition is used to distribute the workload among multiple processors by considering the estimated particle weighting distribution. Two-step multi-level graph partitioning technique is used to perform the required domain decomposition. Completed code is then applied to compute a hypersonic flow over a sphere (external flow) and the flow field of a spiral drag pump (internal flow), respectively. Results of the former are in good agreement with previous numerical results using axisymmetric DSMC method and experimental data. Results of the latter also agree well with previous numerical results.

Decomposition of a disturbance in parallel shear flows

While conclusions that may be drawn on the basis of these solutions are strictly valid only for incompressible laminar flow, they can be plausibly assumed to apply to a much larger class of flows. We note that the differences between the various approximations and the full equations decrease with increasing Reynolds number as expected. Since most aerodynamically significant flows are at high Reynolds numbers, the error introduced by the approximation to the governing equations will tend to be small and will certainly be insignificant relative to the errors introduced by the turbulence model. Compressibility effects should not alter the present conclusions insofar as viscous .effects are concerned, and the direct effects of shock waves and normal pressure gradients within the boundary layer as sources of error should be relatively small for moderate Mach numbers. In this regard, the recent comparisons of Navier-Stokes and thinlayer solutions for supersonic corner flow are informative. For any flow, or region of flow, for which viscous-inviscid interaction effects are small, classical boundary-layer equations will provide a satisfactory description of the viscous flow at a fraction of the computational cost of any higher approximation. For flows with significant viscous-inviscid interaction, as long as they are boundary-layer-like, i.e., v/u <1, coupled boundary-layer/inviscid equations will provide an adequate flow description.

Thin-layer approximation for three-dimensional supersonic corner flows

The thin-layer approximation is extended to an axial corner that is formed by the intersection of two perpendicular plates, one of which has an inclination angle with respect to the free stream. A computer code developed by Hung and MacCormack (1978) is modified for the thin-layer approximation, and a case with Mach 5.9 and a wedge angle of 6 deg is computed. In addition, it is shown that it is not necessary to solve the complete Navier-Stokes equations for a three-dimensional high-Reynolds-number corner flow.

Numerical solutions for supersonic corner flow

Analytical solutions for inviscid supersonic corner flows are virtually nonexistent due to the complexity of the interference geometry. In view of this, numerical solutions for swept-compressive and swept-expansive corner flows are obtained. The governing equations are written in strong conservation law form and are solved iteratively in nonorthogonal conical coordinates by use of a second-order, shock-capturing, finite-difference technique. The computed wave structure and surface pressure distributions are compared with high Reynolds number (Re > 3 × 10 6) experimental data and show very good agreement. The results clearly show that supersonic corner flow at reasonably high Reynolds numbers including the effect of sweep is dominated by the inviscid field.