High-Order Shock-Capturing Methods for Study of Shock-Induced Turbulent Mixing with Adaptive Mesh Refinement Simulations
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Wong, Man Long↗
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High speed PLIF study of the Richtmyer–Meshkov instability upon re-shock
The Richtmyer–Meshkov instability (RMI) of a twice-shocked gas interface is researched using high-speed planar-laser induced fluorescence (PLIF) in the Wisconsin Shock Tube Laboratory’s vertical shock tube. The initial condition (IC) is a shear layer with broadband diffuse perturbations at the interface between a helium-acetone mixture and argon. This IC is accelerated by a shock of nominal strength M = 1.8, and then accelerated again by the transmitted shock that reflects off the end wall of the tube. An estimate of the light gas mole fraction is extracted from high-speed imaging using an iterative process that accounts for the nonlinear temperature dependence of the acetone’s fluorescence quantum yield (FQY) and absorption cross-section. A vorticity deposition model for the initial growth rate after reshock is compared with the Mikaelian model for re-shock. Previously used in literature, the number of generations is shown to naturally arise from a normalisation of the scalar transport equation. A self-similar analysis is then further performed using the mole fraction data to explore the evolution of the RMI after reshock and the higher order moments of the light gas mole fraction are compared with a proposed model.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Simultaneous measurements of kinetic and scalar energy spectrum time evolution in the Richtmyer–Meshkov instability upon reshock
The Richtmyer–Meshkov instability (Richtmyer, Commun. Pure Appl. Maths , vol. 13, issue 2, 1960, pp. 297–319; Meshkov, Fluid Dyn. , vol. 4, issue 5, 1972, pp. 101–104) of a twice-shocked gas interface is studied using both high spatial resolution single-shot (SS) and lower spatial resolution, time-resolved, high-speed (HS) simultaneous planar laser-induced fluorescence and particle image velocimetry in the Wisconsin Shock Tube Laboratory's vertical shock tube. The initial condition (IC) is a shear layer with broadband diffuse perturbations at the interface between a helium–acetone mixture and argon. This IC is accelerated by a shock of nominal strength Mach number $M = 1.75$ , and then accelerated again by the transmitted shock that reflects off the end wall of the tube. An ensemble of experiments is analysed after reshock while the interface mixing width grows linearly with time. The kinetic and scalar energy spectra and the terms of their evolution equation are calculated and compared between SS and HS experiments. The inertial range scaling of the scalar power spectrum is found to follow Gibson's relation (Gibson, Phys. Fluids , vol. 11, issue 11, 1968, pp. 2316–2327) as a function of Schmidt number when the effective turbulent Schmidt number is used in place of the material Schmidt number that controls equilibrium scaling. Further, the spatially integrated scalar flux follows similar behaviour observed for the kinetic energy in large eddy simulation studies by Zeng et al. ( Phys. Fluids , vol. 30, issue 6, 2018, 064106) while the spatially varying scalar flux exhibits back scatter along the centre of the mixing layer and forward energy transfer in the spike and bubble regions.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Scalar Power Spectra and Scalar Structure Function Evolution in the Richtmyer–Meshkov Instability Upon Reshock
The Richtmyer–Meshkov instability of a twice-shocked gas interface is studied using high-speed planar laser-induced fluorescence in the Wisconsin Shock Tube Laboratory's vertical shock tube. The initial condition is a shear layer with broadband diffuse perturbations at the interface between a helium–acetone mixture and argon. Furthermore, this initial condition is accelerated by a shock of nominal strength M = 1.9, and then accelerated again by the transmitted shock that reflects off the end wall of the tube. Three individual experiments are analyzed, the energy spectrum and the structure functions of the light gas mole fraction field are calculated and compared.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
On turbulence modeling for unsteady transonic flows
A detailed examination of the turbulent field in an unsteady transonic flow undergoing shock-induced separation is conducted. Ensemble-averaged mean and fluctuating velocities, obtained from conditionally sampled laser velocimeter data, are described and analyzed to assess the applicability of modeling concepts usually employed in steady-flow problems. Some comparisons with computations employing the Reynolds averaged Navier-Stokes equations with a mixing length turbulence model are then presented to illustrate the status of current predictive capabilities. The results appear to imply that turbulence models developed for steady flows apply and that the model need not reflect all the fine details of the turbulent structure but rather account in an approximate way for the production and destruction of the turbulence.
Marvin, J. G.↗
Numerical simulation of high Reynolds number transonic flows
A code has been developed for simulating high Reynolds number transonic flow fields of arbitrary configuration. An explicit finite-difference method with time splitting is used to solve the time-dependent equations for compressible turbulent flow. A nonorthogonal computational mesh of arbitrary configuration facilitates the description of the flow field. The code is applied to simulate the flow over an 18 percent thick circular-arc biconvex airfoil at zero angle of attack and free-stream Mach number of 0.775. A simple mixing-length model is used to describe the turbulence and chord Reynolds numbers of 1, 2, 4, and 10 million are considered. The solution describes in sufficient detail both the shock-induced and trailing-edge separation regions, and provides the profile and friction drag.
Deiwert, G. S.↗
A numerical method for solving the Navier-Stokes equations with application to shock-boundary layer interactions
A numerical method for solving the compressible form of the unsteady Navier-Stokes equations is described. This method was originally presented in 1970 and has since been modified during the development of computer programs at Ames for implementing models that account for the effects of turbulence in shock-induced separated flows. Although this paper does not describe the turbulence models themselves, a complete description of the basic numerical method is given with emphasis on the choice of a computational mesh for high Reynolds number flows, finite-difference approximations for mixed partial derivatives, extension of the Courant-Friedrichs-Lewy stability condition for viscous flows, mesh boundary conditions, and numerical smoothing for strong shock-wave calculations.
Maccormack, R. W.↗
Study of Forebody Injection and Mixing with Application to Hypervelocity Airbreathing Propulsion
The use of premixed, shock-induced combustion in the context of a hypervelocity, airbreathing vehicle requires effective injection and mixing of hydrogen fuel and air on the vehicle forebody. Three dimensional computational simulations of fuel injection and mixing from flush-wall and modified ramp and strut injectors are reported in this study. A well-established code, VULCAN, is used to conduct nonreacting, viscous, turbulent simulations on a flat plate at conditions relevant to a Mach 12 flight vehicle forebody. In comparing results of various fuel injection strategies, it is found that strut injection provides the greatest balance of performance between mixing efficiency and stream thrust potential.
Axdahl, Erik↗
Geometry and dynamics of passive scalar structures in compressible turbulent mixing
We present a structure-based numerical analysis of passive scalar mixing in decaying homogeneous isotropic turbulence (DHIT) and shock-turbulence interaction canonical configurations. The analysis focuses on the temporal evolution of ensembles of passive scalar structures, initialized as spheres of different sizes relative to the Taylor microscale. An algorithm is introduced to track the evolution of each individual structure and the interactions with other structures in the ensemble, relating changes in the surface geometry and the underlying physical processes (turbulent transport, scalar dissipation, and shock compression). The tracking algorithm is applied to datasets from shock-capturing direct numerical simulations of DHIT, with Taylor microscale Reynolds number Re λ =40 and turbulence Mach number M t =0.2 , and STI cases in which the turbulence is processed by a shock wave at Mach numbers M = 1.5 and 3.0. Temporal surface convolution increases for initially larger structures, resulting in a higher probability of locally hyperbolic geometries where breakup into smaller structures occurs. Shock-induced deformation of the structures amplifies breakup processes, enhancing mixing, particularly for larger structures. Mixing enhancement by the shock is manifested as an amplification of the surface-averaged scalar gradient, which increases for initially larger structures. The alignment between the scalar gradient and the most extensional strain-rate eigendirection on the scalar isosurfaces also increases across the shock. Larger magnitudes of the scalar gradient and its alignment with the most compressive strain-rate eigendirection correlate with flatter surface regions. Shock-induced structure compression increases the area coverage of flat regions, where the amplification of scalar gradient is localized.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Evaluation of turbulence models in the PARC code for transonic diffuser flows
Flows through a transonic diffuser were investigated with the PARC code using five turbulence models to determine the effects of turbulence model selection on flow prediction. Three of the turbulence models were algebraic models: Thomas (the standard algebraic turbulence model in PARC), Baldwin-Lomax, and Modified Mixing Length-Thomas (MMLT). The other two models were the low Reynolds number k-epsilon models of Chien and Speziale. Three diffuser flows, referred to as the no-shock, weak-shock, and strong-shock cases, were calculated with each model to conduct the evaluation. Pressure distributions, velocity profiles, locations of shocks, and maximum Mach numbers in the duct were the flow quantities compared. Overall, the Chien k-epsilon model was the most accurate of the five models when considering results obtained for all three cases. However, the MMLT model provided solutions as accurate as the Chien model for the no-shock and the weak-shock cases, at a substantially lower computational cost (measured in CPU time required to obtain converged solutions). The strong shock flow, which included a region of shock-induced flow separation, was only predicted well by the two k-epsilon models.
Georgiadis, N. J.↗