A low-numerical dissipation, patch-based adaptive-mesh-refinement method for large-eddy simulation of compressible flows

This paper describes a hybrid finite-difference method for the large-eddy simulation of compressible flows with low-numerical dissipation and structured adaptive mesh refinement (SAMR). A conservative flux-based approach is described with an explicit centered scheme used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. Three-dimensional numerical simulations of a Richtmyer-Meshkov instability are presented

Atwood ratio dependence of Richtmyer-Meshkov flows under reshock conditions using large-eddy simulations

We study the shock-driven turbulent mixing that occurs when a perturbed planar density interface is impacted by a planar shock wave of moderate strength and subsequently reshocked. The present work is a systematic study of the influence of the relative molecular weights of the gases in the form of the initial Atwood ratio A. We investigate the cases A = ± 0.21, ±0.67 and ±0.87 that correspond to the realistic gas combinations air–CO_2, air–SF_6 and H_2–air. A canonical, three-dimensional numerical experiment, using the large-eddy simulation technique with an explicit subgrid model, reproduces the interaction within a shock tube with an endwall where the incident shock Mach number is ~1.5 and the initial interface perturbation has a fixed dominant wavelength and a fixed amplitude-to-wavelength ratio ~0.1. For positive Atwood configurations, the reshock is followed by secondary waves in the form of alternate expansion and compression waves travelling between the endwall and the mixing zone. These reverberations are shown to intensify turbulent kinetic energy and dissipation across the mixing zone. In contrast, negative Atwood number configurations produce multiple secondary reshocks following the primary reshock, and their effect on the mixing region is less pronounced. As the magnitude of A is increased, the mixing zone tends to evolve less symmetrically. The mixing zone growth rate following the primary reshock approaches a linear evolution prior to the secondary wave interactions. When considering the full range of examined Atwood numbers, measurements of this growth rate do not agree well with predictions of existing analytic reshock models such as the model by Mikaelian (Physica D, vol. 36, 1989, p. 343). Accordingly, we propose an empirical formula and also a semi-analytical, impulsive model based on a diffuse-interface approach to describe the A-dependence of the post-reshock growth rate

High-Order Shock-Capturing Methods for Study of Shock-Induced Turbulent Mixing with Adaptive Mesh Refinement Simulations

No abstract availabl

A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state

We present a numerical comparison study of planar Richtmyer-Meshkov instability with the intention of exposing the role of the equation of state. Results for Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state derived from a linear shock-particle speed Hugoniot relationship (Jeanloz, J. Geophys. Res. 94, 5873, 1989; McQueen et al., High Velocity Impact Phenomena (1970), pp. 294–417; Menikoff and Plohr, Rev. Mod. Phys. 61(1), 75 1989) are compared to those from perfect gases under nondimensionally matched initial conditions at room temperature and pressure. The study was performed using Caltech’s Adaptive Mesh Refinement, Object-oriented C++ (AMROC) (Deiterding, Adaptive Mesh Refinement: Theory and Applications (2005), Vol. 41, pp. 361–372; Deiterding, “Parallel adaptive simulation of multi-dimensional detonation structures,” Ph.D. thesis (Brandenburgische Technische Universität Cottbus, September 2003)) framework with a low-dissipation, hybrid, center-difference, limiter patch solver (Ward and Pullin, J. Comput. Phys. 229, 2999 (2010)). Results for single and triple mode planar Richtmyer-Meshkov instability when a reflected shock wave occurs are first examined for mid-ocean ridge basalt (MORB) and molybdenum modeled by Mie-Grüneisen equations of state. The single mode case is examined for incident shock Mach numbers of 1.5 and 2.5. The planar triple mode case is studied using a single incident Mach number of 2.5 with initial corrugation wavenumbers related by k_1 = k_2+k_3. Comparison is then drawn to Richtmyer-Meshkov instability in perfect gases with matched nondimensional pressure jump across the incident shock, post-shock Atwood ratio, post-shock amplitude-to-wavelength ratio, and time nondimensionalized by Richtmyer’s linear growth time constant prediction. Differences in start-up time and growth rate oscillations are observed across equations of state. Growth rate oscillation frequency is seen to correlate directly to the oscillation frequency for the transmitted and reflected shocks. For the single mode cases, further comparison is given for vorticity distribution and corrugation centerline shortly after shock interaction. Additionally, we examine single mode Richtmyer-Meshkov instability when a reflected expansion wave is present for incident Mach numbers of 1.5 and 2.5. Comparison to perfect gas solutions in such cases yields a higher degree of similarity in start-up time and growth rate oscillations. The formation of incipient weak waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected

Numerical simulation of combustion instability: flame thickening and boundary conditions

Combustion-driven instabilities are a significant barrier for progress for many avenues of immense practical relevance in engineering devices, such as next generation gas turbines geared towards minimising pollutant emissions being susceptible to thermoacoustic instabilities. Numerical simulations of such reactive systems must try to balance a dynamic interplay between cost, complexity, and retention of system physics. As such, new computational tools of relevance to Large Eddy Simulation (LES) of compressible, reactive flows are proposed and evaluated. High order flow solvers are susceptible to spurious noise generation at boundaries which can be very detrimental for combustion simulations. Therefore Navier-Stokes Characteristic Boundary conditions are also reviewed and an extension to axisymmetric configurations proposed. Limitations and lingering open questions in the field are highlighted. A modified Artificially Thickened Flame (ATF) model coupled with a novel dynamic formulation is shown to preserve flame-turbulence interaction across a wide range of canonical configurations. The approach does not require efficiency functions which can be difficult to determine, impact accuracy and have limited regimes of validity. The method is supplemented with novel reverse transforms and scaling laws for relevant post-processing from the thickened to unthickened state. This is implemented into a wider Adaptive Mesh Refinement (AMR) context to deliver a unified LES-AMR-ATF framework. The model is validated in a range of test case showing noticeable improvements over conventional LES alternatives. The proposed modifications allow meaningful inferences about flame structure that conventionally may have been restricted to the domain of Direct Numerical Simulation. This allows studying the changes in small-scale flow and scalar topologies during flame-flame interaction. The approach is applied to a dual flame burner setup, where simulations show inclusion of a neighbouring burner increases compressive flow topologies as compared to a lone flame. This may lead to favouring convex scalar structures that are potentially responsible for the increase in counter-normal flame-flame interactions observed in experiments.Open Acces

Hypersonic flows around complex geometries with adaptive mesh refinement and immersed boundary method

This thesis develops and validates a computational fluid dynamics numerical method for hypersonic flows; and uses it to conduct two novel investigations. The numerical method involves a novel combination of structured adaptive mesh refinement, ghost-point immersed boundary and artificial dissipation shock-stable Euler flux discretisation. The method is high-order, low dissipation and stable up to Mach numbers $M \lesssim 30$ with stationary or moving complex geometries; it is shown to be suitable for direct numerical simulations of laminar and turbulent flows. The method's performance is assessed through various test cases. Firstly, heat transfer to proximal cylinders in hypersonic flow is investigated to improve understanding of destructive atmospheric entries of meteors, satellites and spacecraft components. Binary bodies and clusters with five bodies are considered. With binary proximal bodies, the heat load and peak heat transfer are augmented for either or both proximal bodies by $+20\%$ to $-90\%$ of an isolated body. Whereas with five bodies, the cluster-averaged heat load varied between $+20\%$ to $-60\%$ of an isolated body. Generally, clusters which are thin in the direction perpendicular to free-stream velocity and long in the direction parallel to the free-stream velocity have their heat load reduced. In contrast, clusters which are thick and thin in directions perpendicular and parallel to the free-stream velocity feel an increased heat load. Secondly, hypersonic ablation patterns are investigated. Ablation patterns form on spacecraft thermal protection systems and meteor surfaces, where their development and interactions with the boundary layer are poorly understood. Initially, a simple subliming sphere case without solid conduction in hypersonic laminar flow is used to validate the numerical method. Where the surface recession is artificially sped-up via the wall Damk\"{o}hler number without introducing significant errors in the shape change. Then, a case with transitional inflow over a backward facing step with a subliming boundary is devised. Differential ablation is observed to generate surface roughness and add vorticity to the boundary layer. A maximum surface recession of $\sim 0.8\times$ and a maximum surface fluctuation of $\sim 0.2\times$ the inflow boundary layer thickness were generated over two flow times.Open Acces