Daniel C. Haworth

A generalized Langevin model for turbulent flows

A Langevin model appropriate to constant property turbulent flows is developed from the general equation for the fluid particle velocity increment proposed by Pope in an earlier paper [Phys. Fluids 26, 404 (1983)]. This model can be viewed as an analogy between the turbulent velocity of a fluid particle and the velocity of a particle undergoing Brownian motion. It is consistent with Kolmogorov’s inertial range scaling, satisfies realizability, and is consistent with second‐order closure models. The objective of the present work is to determine the form of a second‐order tensor appearing in the general model equation as a function of local mean quantities. While the model is not restricted to homogeneous turbulence, the second‐order tensor is evaluated by considering the evolution of the Reynolds stresses in homogeneous flows. A functional form for the tensor is chosen that is linear in the normalized anisotropy tensor and in the mean velocity gradients. The resulting coefficients are evaluated by matching...

Direct numerical simulation of H 2 /O 2 /N 2 flames with complex chemistry in two-dimensional turbulent flows

Premixed H 2 /O 2 /N 2 flames propagating in two-dimensional turbulence have been studied using direct numerical simulations (DNS: simulations in which all fluid and thermochemical scales are fully resolved). Simulations include realistic chemical kinetics and molecular transport over a range of equivalence ratios Φ (Φ=0.35, 0.5, 0.7, 1.0, 1.3). The validity of the flamelet assumption for premixed turbulent flames is checked by comparing DNS data and results obtained for steady strained premixed flames with the same chemistry (flamelet «library»). This comparison shows that flamelet libraries overestimate the influence of stretch on flame structure. Results are also compared with earlier zero-chemistry (flame sheet) and one-step chemistry simulations

Large Eddy Simulation in Complex Geometric Configurations Using Boundary Body Forces

Anumericalmethodispresentedthatallowslargeeddysimulation (LES)ofturbulente owsincomplexgeometric cone gurations with moving boundaries and that retains the advantages of solving the Navier ‐Stokes equations on e xed orthogonal grids. The boundary conditions are applied independently of the grid by assigning body forces over surfaces that need not coincide with coordinate lines. The use of orthogonal, nondeforming grids simplie es grid generation, facilitates theimplementation of high-order,nondissipativediscretization schemes, andminimizes the spatial and temporal variations in e lter width that complicate unstructured deforming-grid LES. Dynamic subgrid-scaleturbulence models areparticularly appealing in combination with the body-forceprocedure because the dynamic model accounts automatically for the presence of solid walls without requiring damping functions. The method is validated by simulations of the turbulent e ow in a motored axisymmetric piston ‐cylinder assembly for which detailed experimental measurements are available. Computed mean and rms velocity proe les show very good agreement with measured ensemble averages. Thepresent numerical code runs on small, personal computerlike workstations. For a comparable level of accuracy, computational requirements (memory and CPU time ) are at least a factor of 10 lower compared to published simulations for the same cone guration obtained using an unstructured, boundary-e tted deforming-grid approach.

Direct simulation and modeling of flame-wall interaction for premixed turbulent combustion☆

Abstract The interaction between turbulent premixed flames and walls is studied using a two-dimensional full Navier-Stokes solver with simple chemistry. The effects of wall distance on the local and global flame structure are investigated. Quenching distances and maximum wall heat fluxes during quenching are computed in laminar cases and are found to be comparable to experimental and analytical results. For turbulent cases, it is shown that quenching distances and maximum heat fluxes remain of the same order as for laminar flames. Based on simulation results, a “law-of-the-wall” model is derived to describe the interaction between a turbulent premixed flame and a wall. This model is constructed to provide reasonable behavior of flame surface density near a wall under the assumption that flame-wall interaction takes place at scales smaller than the computational mesh. It can be implemented in conjunction with any of several recent flamelet models based on a modeled surface density equation, with no additional constraints on mesh size or time step. Preliminary tests of this model are presented for the case of a spark-ignited piston engine.

Numerical simulation of turbulent propane–air combustion with nonhomogeneous reactants

Abstract High-resolution two-dimensional numerical simulations have been performed for premixed turbulent propane–air flames propagating into regions of nonhomogeneous reactant stoichiometry. Simulations include complex chemical kinetics, realistic molecular transport, and fully resolved hydrodynamics (no turbulence model). Aerothermochemical conditions (pressure, temperature, stoichiometry, and turbulence velocity scale) approach those in an automotive gasoline direct-injection (GDI) engine at a low-speed, part-load operating condition. Salient findings are as follows: (1) There is no leakage of the primary fuel (propane) behind an initial thin premixed heat-release zone. This “primary premixed flame” can be described using a monotonic progress variable and laminar premixed flamelet concepts. (2) For the conditions simulated, differences in global heat release and flame area (length) between homogeneous and nonhomogeneous reactants having the same overall stoichiometry are small. (3) Beyond three-to-four flame thicknesses behind the primary flame, practically all hydrocarbon fuel has broken down into CO and H2. (4) The rate of heat release in the “secondary reaction zone” behind the primary premixed flame is governed by turbulent mixing and the kinetics of CO2 production. Mixture-fraction-conditioned secondary heat release, CO, and CO2 production rates are qualitatively similar to results from a first-order conditional moment closure (CMC) model; CMC gives poor results for H2, H2O, and radical species. Description of the secondary heat release using steady laminar diffusion flamelet concepts is problematic. (5) Of the chemical species considered, HCO mass fraction or the product of CH2O and OH mass fractions correlates best with local heat-release rate [1] . (6) Computational considerations demand modifications to chemical mechanisms involving C3H7 and CH3CO. Specific changes are proposed to strike a satisfactory balance between accuracy and computational efficiency over a broad range of reactant stoichiometry.

Large-eddy simulation on unstructured deforming meshes : towards reciprocating IC engines

A variable explicit/implicit characteristics-based advection scheme that is second-order accurate in space and time has been developed recently for unstructured deforming meshes (O’Rourke PJ, Sahota MS. A variable explicit/implicit numerical method for calculating advection on unstructured meshes. J Comput Phys 1998;142:312–45). To explore the suitability of this methodology for large-eddy simulation (LES) in reciprocating internal combustion engines, three subgrid-scale turbulence models have been implemented: a constant-coefficient Smagorinsky model, a dynamic Smagorinsky model for flows having one or more directions of statistical homogeneity, and a Lagrangian dynamic Smagorinsky model for flows having no spatial or temporal homogeneity (Meneveau C, Lund TS, Cabot WH. A Lagrangian dynamic subgrid-scale model of turbulence. J Fluid Mech 1996;319:353–85). Quantitative results are presented for three canonical flows (decaying homogeneous isotropic turbulence, non-solenoidal linear strains of homogeneous turbulence, planar channel flow) and for a simplified piston-cylinder assembly with moving piston and fixed central valve. Computations are compared to experimental measurements, to direct-numerical simulation data, and to rapid-distortion theory where appropriate. Generally satisfactory evolution of first, second, and some higher order moments is found. Computed mean and rms velocity profiles for the piston-cylinder configuration show better agreement with measurements than Reynolds-averaged turbulence models. These results demonstrate the suitability of this methodology for engineering LES, and the feasibility of LES for computing IC engine flows.

Effects of oxygenated additives on aromatic species in fuel-rich, premixed ethane combustion: a modeling study

Abstract The motivation for the work described in this paper was conflicting results from diesel engine research on the question of whether the structure of an oxygenated compound blended into diesel fuel can affect the level of reduction of particulate emissions. A constant-pressure reactor model (SENKIN) was used to investigate the effect of oxygenated additives on aromatic species, which are known to be soot precursors, in fuel-rich ethane combustion. 5% oxygen by mass of the fuel was added to ethane using dimethyl ether (DME-CH3OCH3) and ethanol (C2H5OH). A significant reduction in aromatic species relative to pure ethane was observed with the addition of both DME and ethanol, but DME was more effective in reducing aromatic species than ethanol. One reason for the greater effectiveness of DME was found to be its higher enthalpy of formation, compared to ethanol, which led to a higher final temperature. However, with initial temperatures adjusted to achieve the same final temperature for all fuels, DME was still more effective than ethanol in reducing aromatic species compared to the base case of pure ethane. A reaction flux analysis was conducted to determine the mechanism of aromatic species reduction by the oxygenated compounds and the cause of the greater effectiveness of DME.

Application of the proper orthogonal decomposition to datasets of internal combustion engine flows

The proper orthogonal decomposition (POD) is applied to both computational fluid dynamics and particle imaging velocimetry data of simplified motored engine flows using two different methods. The first method is to apply the POD to ensembles of velocity fields obtained by considering the flow field taken at fixed crank-angle positions over a number of cycles. As a result, sets of POD modes are found, each of which describe the structure of the flow at a given piston position. These sets give some indication of the instability mechanism involved in tumble breakdown. The second method we use represents a novel approach of applying the POD to flows within a time-varying domain. The velocity fields are stretched to a fixed domain and normalized so that all phases of the flow are equally weighted. In this way, ‘phase-invariant POD modes’ are created. The phase-invariant modes show desirable properties for forming a suitable basis for future low-dimensional models which should describe the breakdown process mor...

A pdf modeling study of self‐similar turbulent free shear flows

A modeled transport equation for the joint probability density function (pdf) of the velocities and a scalar has been solved numerically for four self‐similar turbulent free shear flows: the plane mixing layer, the plane wake, the plane jet, and the axisymmetric jet. In the pdf equation, convection is treated exactly but the effects of viscosity, molecular diffusion, and the fluctuating pressure gradient have to be modeled. Five different models are evaluated; four of these are based on the Langevin equation for the fluid particle velocities, and the fifth is a particle pair interaction model. In each case, a stochastic mixing model represents the effects of molecular diffusion, and conditional modeling is included to account for intermittency. The resulting modeled pdf equation is solved by a Monte Carlo method. Calculated spreading rates and profiles of the mean velocity and Reynolds stresses show generally good agreement with experimental data for three of the five velocity models. However, discrepanci...

Numerical simulation and modeling for lean stratified propane-air flames

Direct numerical simulations (DNS) of combustion in globally lean non-homogeneous propane-air mixtures have been performed for several initial distributions of non-homogeneities. Results show the strong influence of the PDF and length scales of this distribution on both the combustion efficiency and thermal NO production, in qualitative accordance with experimental results. The simulations have been used to quantitatively assess flamelet models for heat release in partially premixed combustion and NO production modeling assumptions; good agreement is found for the models tested. A qualitative estimation of flamelet models for the secondary reaction zone has shown a limited range of application for those models, as only some of the intervening reactions were found to present a stationary structure in mixture fraction space. A conditional moment closure (CMC) model for the secondary reaction zone appears to be more satisfactory.