https://www.southampton.ac.uk/~nwb/lectures/GoodPracticeCFD/Articles/Validation_SAND2002-0529.pdf

Verification and Validation in Computational Fluid Dynamics

An analog electronic cochlea has been built in CMOS VLSI technology using micropower techniques. The key point of the model and circuit is that a cascade of simple, nearly linear, second-order filter stages with controllable Q parameters suffices to capture the physics of the fluid-dynamic traveling-wave system in the cochlea, including the effects of adaptation and active gain involving the outer hair cells. Measurements on the test chip suggest that the circuit matches both the theory and observations from real cochleas. >

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An analog electronic cochlea

As an extension of the authors' work on isotropic vortical turbulence interacting with a shock wave (Lee, Lele & Moin 1993), direct numerical simulation and linear analysis are performed for stronger shock waves to investigate the effects of the upstream shock-normal Mach number (M1). A shock-capturing scheme is developed to accurately simulate the unsteady interaction of turbulence with shock waves. Turbulence kinetic energy is amplified across the shock wave, and this amplification tends to saturate beyond M1 = 3.0. An existing controversy between experiments and theoretical predictions on length scale change is thoroughly investigated through the shock-capturing simulation: most turbulence length scales decrease across the shock, while the dissipation length scale (ρq3/e) increases slightly for shock waves with M1<1.65. Fluctuations in thermodynamic variables behind the shock wave are nearly isentropic for M1<1.2, and deviate significantly from isentropy for the stronger shock waves, due to the entropy fluctuation generated through the interaction.

Interaction of isotropic turbulence with shock waves: effect of shock strength

A second-mode stability analysis has been performed for a hypersonic boundary layer on a wall covered by a porous coating with equally spaced cylindrical blind microholes. Massive reduction of the second mode amplification is found to be due to the disturbance energy absorption by the porous layer. This stabilization effect was demonstrated by experiments recently conducted on a sharp cone in the T-5 high-enthalpy wind tunnel of the Graduate Aeronautical Laboratories of the California Institute of Technology. Their experimental confirmation of the theoretical predictions underscores the possibility that ultrasonically absorptive porous coatings may be exploited for passive laminar flow control on hypersonic vehicle surfaces.

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Stabilization of Hypersonic Boundary Layers by Porous Coatings

Experimental and theoretical studies of the effect of an ultrasonically absorptive coating (UAC) on hypersonic boundary-layer stability are described. A thin coating of fibrous absorbent material (felt metal) was selected as a prototype of a practical UAC. Experiments were performed in the Mach 6 wind tunnel on a half-angle sharp cone whose longitudinal half-surface was solid and other half-surface was covered by a porous coating. Hot-wire measurements of ‘natural’ disturbances and artificially excited wave packets were conducted on both solid and porous surfaces. Stability analysis of the UAC effect on two- and three-dimensional disturbances showed that the porous coating strongly stabilizes the second mode and marginally destabilizes the first mode. These results are in qualitative agreement with the experimental data for natural disturbances. The theoretical predictions are in good quantitative agreement with the stability measurements for artificially excited wave packets associated with the second mode. Stability calculations for the cooled wall case showed the feasibility of achieving a dramatic increase of the laminar run using a thin porous coating of random microstructure.

Stabilization of a hypersonic boundary layer using an ultrasonically absorptive coating

Three flow problems are discussed whose solutions suggest flow control schemes. These are 1) unsteady hypersonic flow over bodies in the Newtonian approximation, 2) a mechanism of hypersonic flow stabilization over acoustically semi-transparent walls and 3) store separation from cavities. Simplified systematic approximations based on asymptotic frameworks lead to compact computational models that elucidate the flow structure and opportunities for control. Besides generalizing the steady model of Cole, the Newtonian approximation in the unsteady context shows that unsteady body perturbations can lead to inflectional velocity profiles that can produce instabilities and boundary layer transition to enhance mixing in combustors and inlets. The absorbing wall illustrates a mechanism that can be exploited to damp 2 mode hypersonic instabilities. Simplified flow modeling based on systematic asymptotics for store separation from cavities shows the influence of the cavity shear layer on apparent mass effects that are important to damping in pitch and clearance from the parent body. Comparisons with free drop experiments are used for initial validations of the analytical models. * Senior Scientist, Fellow, AIAA f Principal Researcher, Member, AIAA * Margaret Damn Distinguished Professor, Mathematical Sciences, Fellow, AIAA § Professor ** Professor, Associate Fellow Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc. 1. Unsteady Newtonian thin shock layers and hypersonic flow stability 1.11ntroduction Although the stability of high speed flows has received much attention in the recent literature, major complicating aspects have not been treated in a unified way. These features include the combined effects of the finite shock displacement on the boundary layer, the nonparallelism of the flow and the vorticity introduced by the shock curvature. The relevant structure of the shock and boundary layers has been treated in [1][9]. In [6] and [7], the aforementioned stability issues were discussed within the Hypersonic Small Disturbance approximation for the inviscid deck strongly interacting with the hypersonic boundary layer. Equations of motion for the mean and fluctuating small amplitude flows were analyzed. Because of nonparallelism in this framework, the spatial part of the waves cannot be treated by the usual Fourier decomposition and an initial value rather than eigenproblem for spatial stability is obtained. The initial value problem leads to partial rather than ordinary differential equations that require a numerical marching method for their solution. Results indicate that the specific heat ratio 7 plays a major role in the stability of flow since it controls the reflection of waves from the shock and the radiation of energy in the shock layer whose thickness scales with 7 -1. Early experiments such as those described in [2] showed that for a practically interesting class of flows, the shock layer becomes very thin compared to the boundary layer near the nose of hypersonic flat plates. This feature and the desire to further understand the shock and boundary layer structure encourage the use of the Newtonian approximation 7 —> 1. The connection with flow stability motivates the study of this approximation in an unsteady context. In this chapter, limit process expansions will be discussed relevant to unsteady viscous interactions as a prelude to the analysis of hypersonic stability and transition. The application of these limits is an unsteady extension of the steady state analysis of [3]. Although the focus here is the treatment of viscous interaction, boundary layer stability, receptivity and transition, the results derived are useful in inviscid hypersonic unsteady aerodynamic methodology and load prediction as well. 1.2 Analysis Figure 1 schematically indicates strong interaction flow near the leading edge of a hypersonic body. The viscous boundary layer which is usually thin, occupies an appreciable fraction of the distance between the shock and body that will be considered without undue loss of generality a flat plate in what follows. Accordingly F(x,f} = Q, in the notation of Fig. 1. The results in this chapter will be expressed in terms of the boundary layer thickness function A(3c,r) = 0, which in the interpretation mentioned in the Introduction could be the body shape in an inviscid context. Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc. The unsteady form of the Hypersonic Small Disturbance Theory (HSDT) equations [9] are applicable and are obtained as in [7] from limit process expansions of hatted variables defined as quantities normalized by their freestream counterparts, with p,T,u,v,fJL the density, temperature, horizontal, vertical components of the velocity vector, and viscosity respectively. If the freestream density, pressure and velocity are denoted as U,p^ and p^ respectively, then a pressure coefficient used in these expansions is defined as p = (P-PJ/P-U. Fig. 1 Schematic of hypersonic strong interaction flow. With these definitions and the coordinate system in Fig. 1 as well the normalization of the Cartesian dimensional coordinates x and y to the unit reference length L and the reference time scale L/U for the time t, unbarred dimensionless normalized counterparts of these independent variables are defined. If M^ and R^ are respectively the freestream Mach and Reynolds numbers, and 5 is a characteristic flow deflection angle, then the expansions are p=a(x,y,t;H,y)+--(1.1) T=T+— p = 8p+M = l+v =• §v+• • (1.2) (1.3) (1.4) (1.5) (1.6) where y = y/(L8}. These expansions are valid in the HSDT limit x, y, t, H = M o are fixed as 8 — > 0 ,

Problems in high speed flow prediction relevant to control

A three‐dimensional hydroelastic model of the cochlea is analyzed, in which the fluid is viscous and the basilar membrane is an inhomogeneous orthotropic elastic plate. After the solution is obtained using a multiple‐scale approximation, comparison is made with experiment for the human cochlea.

Cochlear mechanics: Analysis for a pure tone

Shock wave location on a slender transonic body of revolution

Pseudo-resonance in the cochlea

A new transonic small-disturbance model to analyze the interactions of freestream disturbances with a weak shock has been developed. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. An alternative approach shows that the pressure field may be described by an equation that has an extended form of the classic nonlinear acoustic equation that describes the propagation of sound beams with a narrow angular spectrum. The model shows that diffraction effects, nonlinear steepening effects, focusing effects, and induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite difference algorithm to solve the mixed-type elliptic/hyperbolic flows around the shock wave has also been developed. Numerical calculations of shock wave interactions with various deterministic vorticity and temperature disturbances result in complicated shock wave structures and describe peaked as well as rounded pressure signatures across the shock front, as were recorded in experiments of sonic booms running through atmospheric turbulence.

Julian D. Cole

Papers

Problems in high speed flow prediction relevant to control

Cochlear mechanics: Analysis for a pure tone

Shock wave location on a slender transonic body of revolution

Pseudo-resonance in the cochlea

Interaction of a weak shock with freestream disturbances