One major drawback of the eddy viscosity subgrid‐scale stress models used in large‐eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity between the subgrid‐scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid‐scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near‐wall region of a turbulent boundary layer. The results of large‐eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.

A dynamic subgrid‐scale eddy viscosity model

We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.

Lattice boltzmann method for fluid flows

Considerable confusion surrounds the longstanding question of what constitutes a vortex, especially in a turbulent flow. This question, frequently misunderstood as academic, has recently acquired particular significance since coherent structures (CS) in turbulent flows are now commonly regarded as vortices. An objective definition of a vortex should permit the use of vortex dynamics concepts to educe CS, to explain formation and evolutionary dynamics of CS, to explore the role of CS in turbulence phenomena, and to develop viable turbulence models and control strategies for turbulence phenomena. We propose a definition of a vortex in an incompressible flow in terms of the eigenvalues of the symmetric tensor ${\bm {\cal S}}^2 + {\bm \Omega}^2$ are respectively the symmetric and antisymmetric parts of the velocity gradient tensor ${\bm \Delta}{\bm u}$. This definition captures the pressure minimum in a plane perpendicular to the vortex axis at high Reynolds numbers, and also accurately defines vortex cores at low Reynolds numbers, unlike a pressure-minimum criterion. We compare our definition with prior schemes/definitions using exact and numerical solutions of the Euler and Navier–Stokes equations for a variety of laminar and turbulent flows. In contrast to definitions based on the positive second invariant of ${\bm \Delta}{\bm u}$ or the complex eigenvalues of ${\bm \Delta}{\bm u}$, our definition accurately identifies the vortex core in flows where the vortex geometry is intuitively clear.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112095000462

On the identification of a vortex

http://home.eps.hw.ac.uk/~ab226/tmp/implicit/lele_92.pdf

Compact finite difference schemes with spectral-like resolution

/pdf/turbulence-and-the-dynamics-of-coherent-structures-i-1o6o6m60fm.pdf

Turbulence and the dynamics of coherent structures. I. Coherent structures

A Numerical Method to Simulate Radio-Frequency Plasma Discharges

We present direct numerical simulation (DNS) of a stationary turbulent hydraulic jump with inflow Froude number of 2, Weber number of 1820 and density ratio of 831, consistent with ambient water–air systems, all based on the inlet height and inlet velocity A non-dissipative geometric volume of fluid (VOF) method is used to track the detailed interactions between turbulent flow structures and the nonlinear interface dynamics Level set equations are also solved concurrent with VOF in order to calculate the interface curvature and surface tension forces The mesh resolution is set to resolve a wide range of interfacial scales including the Hinze scale Calculations are compared against experimental data of void fraction and interfacial scales indicating, reasonable agreement despite a Reynolds number mismatch Multiple calculations are performed confirming weak sensitivity of low-order statistics and void fraction on the Reynolds number The presented results provide, for the first time, a comprehensive quantitative data for a wide range of phenomena in a turbulent breaking wave using DNS These include mean velocity fields, Reynolds stresses, turbulence production and dissipation, velocity spectra and air entrainment data In addition, we present the energy budget as a function of streamwise location by keeping track of various energy exchange processes in the wake of the jump The kinetic energy is mostly transferred to pressure work, potential energy and dissipation while surface energy plays a less significant role Our results indicate that the rate associated with various energy exchange processes peak at different streamwise locations, with exchange to pressure work flux peaking first, followed by potential energy flux and then dissipation The energy exchange process spans a streamwise length of order jump heights Furthermore, we report statistics associated with bubble transport downstream of the jump The bubble formation is found to have a periodic nature Meaning that the bubbles are generated in patches with a specific frequency associated with the roll-up frequency of the roller at the toe of the jump, with its footprint apparent in the velocity energy spectrum Our study also provides the ensemble-averaged statistics of the flow which we present in this paper These results are useful for the development and validation of reduced-order models such as dissipation models in wave dynamics simulations, Reynolds-averaged Navier–Stokes models and air entrainment models

Direct numerical simulation of a turbulent hydraulic jump: turbulence statistics and air entrainment

As part of the Accelerated Strategic Computing Initiative (ASCI) program, an accurate and robust simulation tool is being developed to perform high-fidelity LES studies of multiphase, multiscale turbulent reacting flows in aircraft gas turbine combustor configurations using hybrid unstructured grids. In the combustor, pressurized gas from the upstream compressor is reacted with atomized liquid fuel to produce the combustion products that drive the downstream turbine. The Large Eddy Simulation (LES) approach is used to simulate the combustor because of its demonstrated superiority over RANS in predicting turbulent mixing, which is central to combustion. This paper summarizes the accomplishments of the combustor group over the past year, concentrating mainly on the two major milestones achieved this year: 1) Large scale simulation: A major rewrite and redesign of the flagship unstructured LES code has allowed the group to perform large eddy simulations of the complete combustor geometry (all 18 injectors) with over 100 million control volumes; 2) Multi-physics simulation in complex geometry: The first multi-physics simulations including fuel spray breakup, coalescence, evaporation, and combustion are now being performed in a single periodic sector (1/18th) of an actual Pratt & Whitney combustor geometry.

/pdf/unstructured-les-of-reacting-multiphase-flows-in-realistic-4ao584vkb3.pdf

Unstructured LES of Reacting Multiphase Flows in Realistic Gas Turbine Combustors

It has been observed in experiments that significant levels of sound may be produced when a curved flame propagates downwards along a tube in a gravity field In this paper, we present a mathematical description of this acoustic amplification process, which represents a simple form of combustion instability First, based on the large-activation-energy and small-Mach-number assumptions, a general asymptotic formulation is derived, in which the nature of flame-sound coupling is brought out explicitly This framework is then employed to study the weakly nonlinear coupling between a Darrieus-Landau (D-L) instability mode of the flame and an acoustic mode of the tube, which is the main mechanism for sound generation in the experiments In order to provide a somewhat unified description, the linear coupling via the direct pressure effect has also been included in our analysis A set of coupled equations which govern the evolution of the acoustic and D-L modes was derived The solutions show that the nonlinear coupling leads to very rapid amplification of sound After reaching an appreciable level, the sound inhibits the flame, causing the latter to flatten The sound then saturates at an almost constant level, or continues to grow at a smaller rate owing to the pressure effect The above theoretical predictions are in good qualitative agreement with experiments The present study also considered the influence of weak vortical disturbances in the oncoming flow It is shown that certain components in these perturbations may form resonant triads with the acoustic and D-L modes, thereby providing an additional coupling mechanism

/pdf/combustion-instability-due-to-the-nonlinear-interaction-30ci0gr1dl.pdf

Combustion instability due to the nonlinear interaction between sound and flame

We present a computational aeroacoustics method to evaluate sound generated by low Mach number flows in complex configurations in which turbulence interacts with arbitrarily shaped solid objects. This hybrid approach is based on Lighthill’s acoustic analogy in conjunction with sound source information from an incompressible calculation. In this method, Lighthill’s equation is solved using a boundary element method that allows the effect of scattered sound from arbitrarily shaped solid objects to be incorporated. We present validation studies for sound generated by laminar and turbulent flows over a circular cylinder at Re 100 and 10,000, respectively. Our hybrid approach is validated against directly computed sound using a high-order compressible flow solver as well as the solution of the Ffowcs Williams and Hawkings equation in conjunction with compressible sound sources. We demonstrate that the sound predicted by a second-order hybrid approach is as accurate as sound directly computed byasixth-ordercompressible flowsolverinthefrequencyrangeinwhichlow-ordernumericscanaccuratelyresolve the flow structures. As an example of an engineering problem, we calculated the sound generated by flow over an automobile side-view mirror and compared it to experimental measurements. Nomenclature CD, CL = drag and lift coefficients, respectively c = speed of sound d = dimension of the problem eij = viscous stress tensor f = frequency G = Green’s function of the Helmholtz operator k = wave number L, Lc = width of the mirror, recirculation length M, Mi = freestream Mach number, freestream vector Mach

Parviz Moin

Papers

A Numerical Method to Simulate Radio-Frequency Plasma Discharges

Direct numerical simulation of a turbulent hydraulic jump: turbulence statistics and air entrainment

Unstructured LES of Reacting Multiphase Flows in Realistic Gas Turbine Combustors

Combustion instability due to the nonlinear interaction between sound and flame

Prediction of Sound Generated by Complex Flows at Low Mach Numbers