Z. M. Hu

Downstream flow condition effects on the RR → MR transition of asymmetric shock waves in steady flows

In this paper, the regular reflection (RR) to Mach reflection (MR) transition of asymmetric shock waves is theoretically studied by employing the classical two- and three-shock theories. Computations are conducted to evaluate the effects of expansion fans, which are inherent flow structures in asymmetric reflection of shock waves, on the RR → MR transition. Comparison shows good agreement among the theoretical, numerical and experimental results. Some discrepancies between experiment and theory reported in previous studies are also explained based on the present theoretical analysis. The advanced RR → MR transition triggered by a transverse wave is also discussed for the interaction of a hypersonic flow and a double-wedge-like geometry.

Computational confirmation of an abnormal Mach reflection wave configuration

For the Mach reflection (MR) of symmetric shock waves of opposite families, only the wave configuration of an overall Mach reflection (oMR) consisting of two direct Mach reflections (DiMR+DiMR) is theoretically admissible. For asymmetric shock waves, an oMR composed of a DiMR and an inverse Mach reflection (InMR) is possible if the two slip layers assemble a converging-diverging stream tube, while an oMR including two inverse Mach reflections (InMR+InMR) is absolutely impossible. In this paper, an overall Mach reflection configuration with double inverse MR patterns is computationally confirmed using the computational fluid dynamics technique. The aerodynamic mechanism behind such an abnormal wave pattern is illustrated. Classical two- and three-shock theories are also applied for the theoretical analysis

Geometric criterion for RR↔MR transition in hypersonic double-wedge flows

In a previous research article [Z. M. Hu et al., Phys. Fluids 21, 011701 (2009)], an overall Mach reflection (oMR) configuration with double inverse Mach reflection patterns was computationally confirmed when a double-wedge geometry interacts with a hypersonic flow. Extended computations are conducted in this paper and compared to analytical solutions based on the classical two- and three-shock theories. A geometric criterion is proposed for the transition between regular reflection and Mach reflection occurring inside the parameter space where a type V interaction of shock wave presents in hypersonic double-wedge flows. An oMR solution is allowed by the geometric criterion, while it is theoretically inadmissible. In the vicinity of symmetric condition, regular to Mach reflection transition can also be triggered prior to the theoretical criterion by disturbance generated by a slight increase in the second wedge angle.

Starting Process in a Large-Scale Shock Tunnel

The starting process of the flow in an expansion nozzle (nominal Mach number 6) with an outlet diameter of 1.5 m and 8.9 m length, which is used for a large-scale hypersonic shock tunnel in the Key Laboratory of High-Temperature Gas Dynamics, was simulated and analyzed at incident Mach number M-s = 3.9. The calculating domains include the driven section (the shock-tube end, about 4.8m length), the nozzle with about 8.9 m length, and part of the test section (more than 3 m). The characteristics of unsteady nozzle flow, including the shock wave patterns in the nozzle inlet region and inside the nozzle, were analyzed numerically in the viscous and inviscid flow regimes, respectively. The pressure and Mach number results were presented and discussed by comparing with the experimental findings, where the simulated results of the reflected shock wave in the shock tube and the transmitted shock wave inside the nozzle were found to agree well with the test data. Additionally, the case without a contraction section for the throat configuration was also calculated and compared with the case with a contraction section. The effect of the starting flow in these two cases on the flowfield uniformity is discussed in detail in this paper.

Adaptive space transformation

When developing a new hypersonic vehicle, thousands of wind tunnel tests to study its aerodynamic performance are needed. Due to limitations of experimental facilities and/or cost budget, only a part of flight parameters could be replicated. The point to predict might locate outside the convex hull of sample points. This makes it necessary but difficult to predict its aerodynamic coefficients under flight conditions so as to make the vehicle under control and be optimized. Approximation based methods including regression, nonlinear fit, artificial neural network, and support vector machine could predict well within the convex hull (interpolation). But the prediction performance will degenerate very fast as the new point gets away from the convex hull (extrapolation). In this paper, we suggest regarding the prediction not just a mathematical extrapolation, but a mathematics-assisted physical problem, and propose a supervised self-learning scheme, adaptive space transformation (AST), for the prediction. AST tries to automatically detect an underlying invariant relation with the known data under the supervision of physicists. Once the invariant is detected, it will be used for prediction. The result should be valid provided that the physical condition has not essentially changed. The study indicates that AST can predict the aerodynamic coefficient reliably, and is also a promising method for other extrapolation related predictions.

Numerical study of shock interactions in viscous, hypersonic flows over double-wedge geometries

The characteristics of the boundary layer in a supersonic flow can be drastically altered by a shock wave. The interaction between shock wave and boundary layer plays an important role in the design and operation of high-speed vehicles and propulsion systems. In this paper, the shock/shock interaction and the shock/boundary interaction over a compression ramp and a double-wedge structure in supersonic/hypersonic flows were studied numerically by solving the Favre-averaged Navier-Stokes equations. The numerical simulations show that the viscosity effect results in different interaction transition point, and induce more complex flow patterns, such as the separation shock, shocklets, shear unsteadiness, and complex interactions among them. With the presence of viscous effects the pressure load imposed on the wedge surface can be changed a great deal comparing to the inviscid flow simulations.

A New Flux Splitting Scheme for Euler Equations of Gas Dynamics

A new flux splitting method named K-CUSP scheme is proposed in the paper. The major difference between K-CUSP and two traditional CUSP schemes (H-CUSP and E-CUSP) is that all kinematic quantities and all thermodynamic quantities in total enthalpy will be separately split into convective term and pressure term. The present scheme adopts the cell-face Mach number splitting method of AUSM+ scheme and the interface flux of pressure term is given a new way in the subsonic regime. Numerical solutions demonstrate that the new scheme inherits the simplicity and robustness of FVS schemes, which overcomes the shortcomings of pressure overshoot of shock wave in H-CUSP and E-CUSP schemes, but also retains the high-resolution of FDS schemes, which achieves the high accuracy of contact discontinuity and shock discontinuity.

Relative contribution ratio: A quantitative metrics for multi-parameter analysis

In many applications, the objective function is determined by several parameters simultaneously. Properly assessing the relative contribution of each parameter can give the decision maker a better understanding of the problem. However, widely used assessing methods are qualitative or semi-quantitative. In this paper, a new concept, relative contribution ratio (RCR), is proposed. The concept follows the idea of proof by contradiction, and estimates the impact of absence of each parameter, based on the fact that the absence of a parameter with more contribution will bring more divergence. Based on surrogate models, a statistical method for calculating RCR is also presented. Numerical results indicate that RCR is capable of analyzing multi-parameter problems, regardless of whether they are linear or nonlinear.

Numerical Predictions for the Hypervelocity Test Flow Conditions of JF-16

A hypervelocity test flow is referred to a high-enthalpy flow with speeds above 5 kmps. It is necessary to generate such extreme flows on the ground to simulate the environment of atmosphere reentry. Reflected shock tunnels (RST) and shockexpansion tubes/tunnels (SET) are the major test facilities in gasdynamic laboratories that may satisfy the above request.

Front Structure of Detonation and the Stability of Detonation

The physics of propagation of detonation waves is still a challenging topic in the community. As have been found in experiments and 3D simulations of detonation physics, there are three types of detonation front structures. These are: rectangular mode, oblique mode, and spinning mode [1-6], as shown in Fig.1. For the rectangular modes, there are two further classifications: in phase detonation and out of phase detonation. A logical question raised is: what are the conditions leading to each front structure observed? Is there any relationship among these front structures? These questions provided the motivation for the present investigation.