Alan R. Kerstein

Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence

The alignment between vorticity and eigenvectors of the strain‐rate tensor in numerical solutions of Navier–Stokes turbulence is studied. Solutions for isotropic flow and homogeneous shear flow from pseudospectral calculations using 1283 grid points have been examined. The Taylor Reynolds number is 83 or greater. In both flows there is an increased probability for the vorticity to point in the intermediate strain direction and at three‐fourths of the sample points this strain is positive (extensive). This propensity for vorticity alignment with a positive intermediate strain is a consequence of angular momentum conservation, as shown by a restricted Euler model of the coupling between strain and vorticity. Probability distributions for intermediate strain, conditioned on total strain, change from a symmetric triangular form at small strain to an asymmetric one for large strain. The most probable value of the asymmetric distribution gives strains in the ratios of 3:1: −4. The evolution of the distribution ...

A Linear- Eddy Model of Turbulent Scalar Transport and Mixing

Abstract Transport and mixing of diffusive scalars in turbulent flows are simulated computationally based on a novel representation of the temporal evolution along a transverse line moving with the mean fluid velocity. The scalar field along this line evolves by Fickian diffusion, representing molecular processes, and by randomly occurring events called block inversions. Block inversion, representing the effect of turbulent convection, consists of the random selection of an interval (Y0 − 1/2, Y0 + 1/2) of the line, where the interval size l may he either fixed or randomly selected, and replacement of the scalar field θ(y) within that interval by θ(2y0 For fixed l, the model requires a single input parameter, the Peclet number. To demonstrate the performance of the model, this formulation is used to compute the spatial development of diffusive scalar fields downstream of several source configurations in homogeneous turbulence. Generalization to inhomogeneous turbulence is discussed, as well as a formulati...

Linear-eddy modeling of turbulent transport. II: Application to shear layer mixing☆

Abstract The linear-eddy modeling approach involves the representation of a spatially developing flow by a simulation of the time development along a transverse line moving with the mean flow. Scalar quantities evolve by Fickian (molecular) diffusion and by randomly occurring spatial rearrangements, representing turbulent convection. A formulation introduced previously, the block-inversion model, is adapted here for application to turbulent planar shear layer mixing. Predictions of the mixing and chemical reaction rate dependence on Reynolds, Schmidt, and Damkohler numbers, and of the spatially resolved probability density function (pdf) of the concentration field, are consistent with measurements and suggest a simple parameter dependence governing mixing and reaction. The mixed fluid peak of the simulated pdf occurs at a concentration that does not depend on spatial location, as found experimentally. The simulations suggest a simple explanation for the difference between this behavior and observations in the thermal mixing layer in grid turbulence.

Linear-eddy modelling of turbulent transport. Part 6. Microstructure of diffusive scalar mixing fields

The linear-eddy approach for modelling molecular mixing in turbulent flow involves stochastic simulation on a one-dimensional domain with sufficient resolution to include all physically relevant lengthscales. In each realization, molecular diffusion is implemented deterministically, punctuated by a sequence of instantaneous, statistically independent ‘rearrangement events’ (measure-preserving maps) representing turbulent stirring. These events emulate the effect of compressive strain on the scalar field. An inertial-range similarity law is incorporated. The model reproduces key features of scalar power spectra, including dependences of spectra! amplitudes and transition wavenumbers on Reynolds and Schmidt numbers. Computed scaling exponents governing scalar power spectra, higher-order fluctuation statistics such as structure functions, and the spatial distribution of scalar level crossings are close to measured exponents. It is inferred that the characterization of stirring as a sequence of independent events (the model analogue of eddies) leads to a useful representation of mixing-field microstructure.

One-dimensional turbulence : model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows

A stochastic model, implemented as a Monte Carlo simulation, is used to compute statistical properties of velocity and scalar fields in stationary and decaying homogeneous turbulence, shear flow, and various buoyant stratified flows. Turbulent advection is represented by a random sequence of maps applied to a one-dimensional computational domain. Profiles of advected scalars and of one velocity component evolve on this domain. The rate expression governing the mapping sequence reflects turbulence production mechanisms. Viscous effects are implemented concurrently. Various flows of interest are simulated by applying appropriate initial and boundary conditions to the velocity profile. Simulated flow microstructure reproduces the −5/3 power-law scaling of the inertial-range energy spectrum and the dissipation-range spectral collapse based on the Kolmogorov microscale. Diverse behaviours of constant-density shear flows and buoyant stratified flows are reproduced, in some instances suggesting new interpretations of observed phenomena. Collectively, the results demonstrate that a variety of turbulent flow phenomena can be captured in a concise representation of the interplay of advection, molecular transport, and buoyant forcing.

Linear-eddy modelling of turbulent transport. Part 7 : Finite-rate chemistry and multi-stream mixing

The linear-eddy turbulent mixing model, formulated to capture the distinct influences of turbulent convection and molecular transport on turbulent mixing of diffusive scalars, is applied to two mixing configurations in homogeneous flow: a scalar mixing layer and a two-line-source configuration. Finite-rate second-order chemical reactions are considered, as well as the limits of fast reaction and frozen flow. Computed results are compared to measurements in a reacting-scalar mixing layer and in a two-line-source configuration involving passive-scalar mixing

LINEAR-EDDY MODELLING OF TURBULENT TRANSPORT. PART 3. MIXING AND DIFFERENTIAL MOLECULAR DIFFUSION IN ROUND JETS

The linear-eddy model of turbulent mixing represents a spatially developing flow by simulating the time development along a comoving transverse line. Along this line, scalar quantities evolve by molecular diffusion and by randomly occurring spatial rearrangements, representing turbulent convection. The modelling approach, previously applied to homogeneous turbulence and to planar shear layers, is generalized to axisymmetric flows. This formulation captures many features of jet mixing, including differential molecular diffusion effects. A novel experiment involving two unmixed species in the nozzle fluid is proposed and analysed.

One-dimensional turbulence: vector formulation and application to free shear flows

One-dimensional turbulence is a stochastic simulation method representing the time evolution of the velocity profile along a notional line of sight through a turbulent flow. In this paper, the velocity is treated as a three-component vector, in contrast to previous formulations involving a single velocity component. This generalization allows the incorporation of pressure-scrambling effects and provides a framework for further extensions of the model. Computed results based on two alternative physical pictures of pressure scrambling are compared to direct numerical simulations of two time-developing planar free shear flows: a mixing layer and a wake. Scrambling based on equipartition of turbulent kinetic energy on an eddy-by-eddy basis yields less accurate results than a scheme that maximizes the intercomponent energy transfer during each eddy, subject to invariance constraints. The latter formulation captures many features of free shear flow structure, energetics, and fluctuation properties, including the spatial variation of the probability density function of a passive advected scalar. These results demonstrate the efficacy of the proposed representation of vector velocity evolution on a one-dimensional domain.

‘One-dimensional turbulence’ simulation of turbulent jet diffusion flames: model formulation and illustrative applications

Abstract A novel modeling approach to the simulation of turbulent jet diffusion flames based on the One-Dimensional Turbulence (ODT) model is presented. The approach is based on the mechanistic distinction between molecular processes (reaction and diffusion), implemented by the direct solution of unsteady boundary-layer reaction-diffusion equations, and turbulent advection in a time-resolved simulation on a 1D domain. The 1D domain corresponds to a direction transverse to the mean flow of the jet. Temporal simulations of jet diffusion flames are performed to illustrate the model’s predictions of turbulence-chemistry interactions in jet diffusion flames. ODT predictions of flow entrainment, finite-rate chemistry and differential diffusion effects are investigated in hydrogen-air diffusion flames at two Reynolds numbers. Two-dimensional renderings of stirring events from a single realization show that ODT reproduces a number of salient features of simple developing turbulent shear flows that reflect the growth of the boundary layer and the mechanisms of turbulence cascade and spatial intermittency. Multiple realizations of jet simulations are used to compute axial and conditional statistics of streamwise velocity, major species, NO, and temperature. Comparison with experimental measurements indicates that chemical properties of interest can be captured by a model that involves a simplified representation of the flow structure. The results show. strong differential diffusion effects in the near field, with attenuation farther downstream.

Linear-Eddy Modeling of Turbulent Transport. Part 4. Structure of Diffusion Flames

Abstract A simulation model of the axial structure of turbulent jet diffusion flames is formulated for the purpose of interpreting flame-structure measurements. The model, based on the linear-eddy approach, incorporates spatial and temporal variation of the air entrainment rate, reflecting buoyancy effects, and an implementation of turbulent mixing using a novel stochastic representation of convective stirring in conjunction with Ficks law governing molecular diffusion. Simulation results are compared to axial profiles of mixing-cup density measured in propane flames. The comparisons suggest that the measured Froude-number dependences reflect the combined effect of finite-rate mixing and the transition from forced to natural convection. Predictions for hydrogen flames are presented in order to assess the generality of inferences based on the propane results.