Laser differential interferometry for supersonic blunt body receptivity experiments

The numerical simulation of transitional and turbulent e ows in supersonic boundary layers often involves a physical process of a shock ‐disturbance wave interaction in complex multidimensional e owe elds. For such simulations, it is required that there be a high order of accuracy in capturing the shock waves without spurious numerical disturbances. Evaluation of the numerical oscillations generated behind a stationary bow shock by using high-order shock-capturing schemes in computing multidimensional steady supersonic e ow over a circular cylinderiscarriedout.Thenumerical methodsthatarestudied aretheTotalVariation Diminishing schemeand the Essentially Non-Oscillatory scheme. Although the general aerodynamic properties are appropriately captured by the shock-capturing schemes, it is shown that there are numerical oscillations in the gradients of the aerodynamic propertiesin the steady e owe eld behind the bow shock, such asfor vorticity. Thesespurious numerical oscillations in the e owe eld solution may hinder any attempt at tracking the propagation of physical disturbances behind the shock if unsteady simulations are carried out. They can be signie cant enough to pollute a e owe eld containing small physical disturbances. It is shown that the effects of grid ree nement do not reduce the oscillations but rather decreasetheir wavelength. It is also shown that, by roughly aligning the shock with the grid, the amplitude of these spurious oscillations can be reduced but not eliminated.

http://cfdhost.seas.ucla.edu/papers/1999/Lee-T-1999-AIAA-732-595.pdf

Spurious Numerical Oscillations in Simulation of Supersonic Flows Using Shock-Capturing Schemes

Feedback stabilized laser differential interferometry for supersonic blunt body receptivity experiments

AIAA, Fluid Dynamics Conference, 27th, New Orleans, LA, June 17-20, 1996 This paper is concerned with time-stepping numerical methods for computing stiff semi-discrete systems of ordinary differential equations for transient hypersonic flows with thermochemical nonequilibrium. The stiffness of the equations is mainly caused by the viscous flux terms across the boundary layers and by the source terms modeling finite-rate thermochemical processes. Implicit methods are needed to treat the stiff terms, while more efficient explicit methods can still be used for the nonstiff terms in the equations. For additively split autonomous differential equations in the form of u' = f(u) + g(u), three different semi-implicit Runge-Kutta methods have been derived and tested in previous papers, where f is treated by explicit Runge-Kutta methods and g is simultaneously treated by three implicit Runge-Kutta methods. The coefficients of up to third-order accuracy have been derived such that the methods are both high-order accurate and strongly A-stable for the implicit terms. However, these semi-implicit Runge-Kutta methods for the autonomous systems cannot be extended to non-autonomous systems of u' = f(t, u) + g(t, u) because of the coupling between the f and g terms in the split Runge-Kutta methods. In this paper, we derive and test three different semi-implicit Runge-Kutta schemes of up to third-order accuracy for the non-autonomous differential equations using the A-stability and accuracy conditions with four stages. The new schemes have been tested in computations of unsteady reactive flows with explicit time-dependent terms. (Author)

http://cfdhost.seas.ucla.edu/papers/zhong-papers/Shen-J-1996-AIAA-1996-1969-253.pdf

Semi-Implicit Runge-Kutta Schemes for non-autonomous differential equations in reactive flow computations

The interaction of free-stream disturbances and the bow shock wave in hypersonic flow past a blunt leading edge is an important part of hypersonic boundary layer receptivity to free-stream disturbances. It has been shown that, for a perfect gas, the back and forth interaction and reflection of acoustic waves behind the shock greatly amplify the magnitudes of the disturbance waves. The interaction also generates a wide range of wavelengths for entropy and vorticity waves behind the shock due to the nonuniformity of mean flow over the body. For hypersonic flow over a blunt body, real gas effects become important because of high gas temperature behind the shock. In this paper, nonequilibrium real gas effects on the free-stream disturbance/bow shock interaction for hypersonic flow past a cylinder are investigated by numerical simulations and by linear analysis. The freestream disturbances are fixed-frequency planar acoustic wave. It was found that the real gas effects reduce the intensity of the space-time focusing of entropy waves on the wall and introduce new small length scales related to vibrational relaxation to the interaction wave fields.

http://cfdhost.seas.ucla.edu/papers/zhong-papers/Zhong-X-1996-AIAA-1996-1856-949.pdf

Nonequilibrium real-gas effects on disturbance/bow shock interaction in hypersonic flow past a cylinder

Numerical simulation of transient hypersonic flows involving shock-wave-freestream-disturbance interactions is presented using the essentially nonoscillatory (ENO) schemes. The ENO schemes were chosen for transient-flow simulations because they have high-order accuracy at extrema as well as in other parts of smooth solutions. First, the accuracy of the ENO schemes was tested numerically by applying them to the computations of a one-dimensional linear model equation and to an oscillating plate problem using the two-dimensional Navier-Stokes equations. Then, the third-order ENO scheme was used to compute the unsteady interaction of a freestream acoustic wave with a bow shock in hypersonic flow past a cylinder. The numerical results along the stagnation line were compared with linearized analytical solutions. The results show that the disturbance waves generated behind the bow shock are significantly amplified by the back-and-forth interactions and reflections of the acoustic waves. These results on the bow-shock-disturbance interactions will be useful in understanding the effects of the bow shock wave on the receptivity of hypersonic boundary layers to freestream disturbances.

Chein-Erh Chiu

Papers

Numerical simulation of transient hypersonic flow using the essentially nonoscillatory schemes