Modeling and Simulation of Turbulent Mixing and Reaction

Low speed shear-driven mixing layers involving fluid streams of different densities due to temperature or compositional variations are described by remarkably similar equations with some differences in the formulations of the molecular transport terms. These differences are related to specifics of the heat conduction and mass diffusion operators, as well as viscosity dependence on mixture molar mass and temperature in the low Mach number limit. Direct numerical simulations are performed in incompressible/low-speed limits to study the differences and similarities in mixing behavior associated with these configurations. The results demonstrate both subtle and significant changes in the mixing behavior for variable composition versus variable temperature mixing. Higher-order statistics related to density field reveal greater differences than are apparent from mean profiles; these differences can be extremely important when the physics is sensitive to mixing, such as in combustion problems. Therefore, conclusions regarding the mixing dynamics drawn from variable temperature mixing are not necessarily applicable to multi-species mixing.

Direct numerical simulations of temporally evolving compressible reacting mixing layers with Schmidt number equal to one are performed to examine the transport of a conserved scalar across the turbulent/non-turbulent interface (TNTI). The budgets of the scalar-gradient transport equation are used to study the effects of compressibility and heat release on the mixing. The simulations include a wide range of convective Mach number (\(M_c\)) from a subsonic and nearly incompressible case (\(M_c = 0.2\)) to a supersonic mixing layer at \(M_c = 1.8\). Furthermore, the highest level of heat release for the reacting simulations is opted to correspond to hydrogen combustion in air. The results suggest that the primary influence of the compressibility and heat release on the mixing of a conserved scalar is felt in a thin interface layer close to the TNTI whose thickness scales with the scalar-Taylor length scale. This interface layer is a juxtaposition of two dynamically different sub-regions referred to as laminar superlayer (LSL) and turbulent sublayer (TSL), whose thicknesses are of order of Kolmogorov and scalar-Taylor length scales, respectively. The transport of scalar is predominately governed by the molecular diffusion inside the LSL, whereas the inertial turbulent production dominates the transport within the TSL. It is shown that as the level of compressibility or heat release increases the rate of scalar mixing decreases. Compressibility affects the scalar mixing via a weakened turbulent production mechanism in the turbulent sublayer part of the interface layer, while the molecular diffusion process remains dynamically unaffected. On the other hand, in reacting cases the molecular diffusion inside the laminar superlayer and the turbulent production across the adjacent turbulent sublayer are subdued, which result in a decreased mixing rate.

Fluid instabilities in the Prandtl model for down-slope flows are studied using linear modal analysis as well as direct numerical simulations. Given Prandtl’s analytical solution for uniformly cooled down-slope flows, we determine the point of instability initiation and the corresponding unstable flow modes. We show that down-slope flows are susceptible to transverse and longitudinal instability modes. The transverse mode consists of stationary longitudinal rolls whose axes are aligned parallel to the base flow direction, whereas the longitudinal mode emerges as transverse waves travelling along the streamwise direction. The emergence of these instabilities are controlled by the Prandtl number, the slope angle, and the stratification perturbation parameter, which is a measure of the strength of the surface buoyancy flux relative to the background stratification. When the other two dimensionless parameters are held constant, the stratification perturbation parameters determines whether the imposed surface buoyancy flux can overcome the stabilizing effect of the background stratification and give rise to dynamically unstable flow. Beyond the linear stability thresholds, these two type of instabilities coexist to form complex flow structures. The absence of strong non-normality of the operator is shown by calculating the pseudospectra for both types of instabilities.

Accurate numerical simulations of shock-turbulence interaction (STI) are conducted by a hybrid monotonicity preserving-compact finite difference scheme for a detailed study of STI in variable density flows. Numerical accuracy of the simulations has been established using a series of grid, particle, and linear interaction approximation (LIA) convergence tests. The results show that for current parameter ranges, turbulence amplification by the normal shock wave is much higher and the reduction in turbulence length scales is more significant when strong density variations exist in STI. The turbulence structure is strongly modified by the shock wave, with a differential distribution of turbulent statistics in regions with different densities. The correlation between rotation and strain is weaker in the multi-fluid case, which is shown to be the result of complex role density plays when the flow passes through the shock wave. Furthermore, a stronger symmetrization of the joint probability density function (PDF) of second and third invariants of the anisotropic velocity gradient tensor (VGT) is observed in the multi-fluid case. Lagrangian dynamics of the VGT and its invariants are studied and the pressure Hessian contributions are shown to be strongly affected by the shock wave and local density, making them important to the flow dynamics and turbulence structure.

Turbulent jet ignition (TJI) is a novel ignition enhancement method which facilitates the combustion of lean and ultra-lean mixtures in propulsion systems including internal combustion engines. An overview of numerical study of TJI-assisted combustion in different systems is presented in this chapter. The numerical simulations are conducted by direct numerical simulation (DNS) and hybrid Eulerian-Lagrangian large eddy simulation (LES)-filtered mass density function (FMDF) methods. DNS of TJI-assisted combustion of lean hydrogen-air mixture in a planar jet for various thermo-chemical conditions reveals fundamental features of TJI systems such as localized flame extinction and re-ignition processes. LES-FMDF of TJI-assisted combustion in a rapid compression machine (RCM) reveals three main phases: (1) cold fuel jet, (2) turbulent hot product jet, and (3) reverse fuel-air/product jet. The simulated results are in good agreement with the experimental data.

Flamelet models have proven useful in enabling fast and accurate simulations of subsonic turbulent combustion. However, in supersonic combustion, these models face many challenges. The current work presents an a priori analysis of the steady flamelet model using the HIFiRE Direct Connect Rig (HDCR) dual-mode scramjet combustor. The analysis uses Reynolds-averaged simulation (RAS) data obtained with a finite-rate reaction mechanism to assess some of the flamelet model assumptions. Two flight conditions are numerically simulated: Mach 5.84 and Mach 8. These conditions cover a range of combustion phenomena that could be expected to occur in a scramjet engine during flight. The analysis reveals that both nonpremixed and premixed combustion occur in the HDCR combustor. In addition, under some conditions, strong finite-rate effects are also present. These physical aspects could be readily modeled with existing flamelet techniques, however, the effects of variable pressure, wall heat transfer, and flamelet equation boundary conditions are more challenging to address. The latter three elements present the key barriers to utilizing flamelets for supersonic combustion simulations. Although techniques to address these additional challenges are limited, a few perspectives are provided highlighting physics-based requirements in the context of flamelet modeling.

An overview of the current state of progress in the large eddy simulation of turbulent combustion using the filtered density function (FDF) coupled with a discontinuous spectral element method is presented. It is assumed that the reader has some prior knowledge of the FDF method and its implementation in other codes. The unique challenges presented by the discontinuous spectral element method are outlined, and their solutions are described in the context of variable-density flows. Specifically, we discuss approaches for interpolating Eulerian quantities to particle locations, searching for particles on an unstructured grid, and constructing filtered quantities on collocation points. Sample results are presented to demonstrate the algorithm’s efficacy and a discussion follows describing the future of the method.

An overview is presented of recent developments in filtered density function (FDF) methodology as utilized for large eddy simulation (LES) of turbulent flows. The review is focused on computational and physical modeling of the FDF, along with a survey of some of the most recent results via LES-FDF.

Many important engineering and biological flows involve solid boundaries moving within a fluid at high Reynolds numbers, e.g., pumps, fish swimming, wind/hydrokinetic turbines. Simulating such flows requires dealing with moving boundaries and turbulence, which are two of the main challenges facing numerical methods today in computational fluid dynamics (CFD). In this chapter, the numerical methods that deal with moving boundaries in turbulent flows are reviewed and the recent advances are summarized. Some of the state-of-the-art simulations, their results, and the insights gained about the flow physics are discussed. Finally, some of the future developments, such as developing wall models over moving boundaries, required to advance large eddy simulations (LES) with moving boundaries are discussed.

Interfacial multiphase flows are challenging to simulate because they involve many spatio-temporal scales and discontinuous fluid properties. This chapter describes a new framework for simulating interfacial flows (with an emphasis on sprays) that is consistent and conservative. The framework is based on the coupling of point mass particles (PMPs) with an Eulerian grid. Three different simulation methods are derived by enforcing different levels of coupling between the PMPs and the Eulerian grid. We first develop an expression that relates the PMP velocity to the fluid velocity, and use this expression to define a methodology for tracking an arbitrary number of phases and scalars. Performance of this approach is demonstrated in the context of heated air blast atomization. Next, we derive a governing equation for the fluid velocity in the context of the PMP, and present a consistent and conservative framework for solving the multiphase Navier-Stokes equations. The chapter concludes with the development of a formulation for consistent and conservative large eddy simulation, with particular attention paid to the importance of closure models.

Effect of swirl on turbulent surface fluctuations in swirl nozzle atomizers is investigated based on a model of fluid elements moving in Lagrangian frame. The model indicates turbulence can be suppressed by swirl. The model is verified by performing a set of experiments on swirl nozzles, which keeps the internal turbulence level relatively constant and changes only the level of swirl. This is achieved by using nozzles with different swirl inserts to change the tangential inlet velocities and keep the jet velocity at the nozzle exit constant. It is shown that increasing the swirl suppresses surface fluctuations.