Reynolds Stress Transport Research Articles

Measurements and heat-flux transport modelling in a heated cylinder wake

Hot-wire measurements of velocity and temperature fluctuations have been made in the self-preserving turbulent wake region of a heated cylinder. Second order statistics including Reynolds fluxes, , are determined along with relevant triple correlations appearing in the Reynolds stress and Reynolds flux transport equations. The primary aim with these measurements is to study different modelling levels for passive scalar quantities. Models for the pressure scalar-gradient correlation, appearing in the transport equation of the Reynolds fluxes, are compared to measured data. A significant improvement of the simplest model, , is achieved by including a model for the rapid term that is linear in the mean velocity gradients. The mixed timescale, , seems to be an appropriate choice for τ. Also models for the triple correlations, , are compared with the experiments.

98/03972 Experience with combined coal/gas low NO x burners in utility boiler retrofit applications

While recently substantial progress has been achieved in predicting properties of high-NOx (type 2) flames, the task of computing low-NOx flames (type 1) happens to be much more complex. This is due to difficulties in predicting the complex near-burner-zone flow field of type 1 flames which can be characterized by a nonswirling fuel jet penetrating either partially or fully through the swirl-induced reverse flow zone. The objective of this paper is to examine what improvements to the predicted near-burner-zone flow field, chemistry, and subsequent NOx emissions can be made by applying the Reynolds stress (transport) model and the renormalization group theory k-ε model rather than the standard k-ε model. To this end, the 2-MW, flame data collected at the IFRF have been utilized.The flame length and volume, the near-burner-zone temperatures, and oxygen concentrations are directly affected by the jet penetration. Whereas the RSM predictions are in good agreement with the measurements, both k-ε and RNG-k-ε models predict too short and too intensive flames. The physical size of the fuel-rich region and subsequent NOx predictions are strongly dependent on the calculated jet penetration. The failures in predicting properties of the fuel-rich zone while using the k-ε or the RNG-k-ε models results in excessive NO flue concentrations. Thus, contrary to the findings of Lockwood and Shen [12], we see a superiority of the RSM for predicting type I, low-NOx flames.

Flow Through a Curved Duct Using Nonlinear Two-Equation Turbulence Models

Standard isotropic and nonlinear two-equation turbulence closures are employed to calculate the flow through a 90-deg rectangular duct. The models used include the two-layer k-e model, the k-ω model, and two nonlinear variants of the k-ω model based on quadratic and cubic constitutive relations, respectively. Comparisons of the computed results with the measurements show that the cubic nonlinear k-ω closure is the only model that successfully reproduces most of the experimentally observed features of both the mean flow and turbulence fields. This work demonstrates, for the first time, that near-wall, nonisotropic, two-equation models offer a promising alternative to Reynolds-stress transport closures for developing practical computational fluid dynamics methods able to predict complex shear flows of engineering interest.

A consistency condition for non-linear algebraic Reynolds stress models in turbulence

An important consistency condition for non-linear algebraic Reynolds stress models involving their dependence on rotational strains is discussed from a basic theoretical standpoint. A variety of recently proposed models are demonstrated to violate this condition which leads to physically inconsistent results and unrealizable solutions in rotating flows — an undesirable state of affairs that was avoided in the majority of earlier models. It is shown that when non-linear algebraic models are systematically derived from the Reynolds stress transport equation, such inconsistencies are automatically avoided. The implications of these results for turbulence modeling are demonstrated quantitatively by the illustrative example of isotropic turbulence in a rotating frame.

Steady and unsteady computation of a two‐dimensional upwash jet

Computational procedures and results of an upwash jet arising from two opposing plane wall jets based on the Reynolds averaged Navier‐Stokes equations are discussed. For the calculation of the flow, a steady and an unsteady numerical approach were taken. For the steady computation, we adopted various eddy viscosity models(the standard k‐ε model, the RNG k‐ε model and the Bardina’s model) and the Reynolds stress transport model with various diffusion term closures. Results of the steady computation indicated that the jet half‐width was very much underpredicted, and hence the velocity profiles of the upwash jet were in very poor agreement with the experimental data. We found, however, that the velocity profiles nondimensionalized by the jet half width and the maximum velocity appeared to be in good agreement with the experimental data, which could be misleading. When an unsteady approach with an unsteady version of the standard k‐ε eddy viscosity model was taken, a periodic oscillation of the jet was observed. The jet half‐width distribution obtained by taking the time average of the periodic velocity profiles was found to be in much better agreement with the experimental data.

Numerical Simulation of Vortex Pyrolysis Reactors for Condensable Tar Production from Biomass

A numerical study is performed in order to evaluate the performance and optimal operating conditions of vortex pyrolysis reactors used for condensable tar production from biomass. A detailed mathematical model of porous biomass particle pyrolysis is coupled with a compressible Reynolds stress transport model for the turbulent reactor swirling flow. An initial evaluation of particle dimensionality effects is made through comparisons of single- (1D) and multi-dimensional particle simulations and reveals that the 1D particle model results in conservative estimates for total pyrolysis conversion times and tar collection. The observed deviations are due predominantly to geometry effects while directional effects from thermal conductivity and permeability variations are relatively small. Rapid ablative particle heating rates are attributed to a mechanical fragmentation of the biomass particles that is modeled using a critical porosity for matrix breakup. Optimal thermal conditions for tar production are observed for 900 K. Effects of biomass identity, particle size distribution, and reactor geometry and scale are discussed.

Particle Deposition with Thermophoresis in Laminar and Turbulent Duct Flows

ABSTRACT A numerical simulation procedure for studying deposition of aerosol particles in duct flows including the effect of thermal force under laminar and turbulent flow conditions is developed. An improved model for thermophoretic force acting on small particles is presented. Perturbation based analytical expressions for velocity and temperature profiles are used in the analysis for the laminar duct flow. The Reynolds stress transport model (RSM) of the FLUENT code is used to evaluate the mean flow and temperature fields for the turbulent duct flow case. The instantaneous fluctuation velocity field is generated by the continuous filtered white noise model. Effects of Brownian diffusion, thermophoresis, lift force, and gravity are included in the computation. Ensembles of particle trajectories are generated and statistically analyzed. Particle dispersion from a point source in the presence of a temperature gradient field in laminar and turbulent duct flows is studied. For an initially uniform concentrat...

Application of Turbulence Models to Bypass Transition

The present study considers the use of low-Reynolds number, single-point closures for transition prediction at high levels of free-stream turbulence. The work is focused on two differential Reynolds Stress Transport models, which are compared with the k – ε model of Launder and Sharma. Calculations are carried out for attached boundary layer flow on a flat plate equipped with a sharp leading edge at zero-pressure gradient and for various free-stream turbulence levels. Comparisons with results from a large eddy simulation reveal significant shortcomings in the modeling of the dissipation, with a large overprediction in the pretransitional boundary layer. The present results are in some cases in conflict with other results reported in the literature, and it is shown that the discrepancies can be ascribed to the implementation of the free-stream boundary conditions.

Reynolds-stress modelling of turbulent rotating flows

The present analysis shows that the EVM can not reflect the turbulence physics in non-inertial frame. The effects of Coriolis force on turbulence is embodied naturally in the Reynolds-stress transport equation. It is observed that the existing second-moment closure model with appropriate near-wall treatment can adequately predict flows in rotating channel and in axially rotating pipe for moderate rotation rate.

Calculation of Fully-Developed Turbulent Flow in Rectangular Ducts With Nonuniform Wall Roughness

The predictive capabilities of four transport-type turbulence models are analyzed by comparing predictions with experimental data for fully-developed flow in (1) a rectangular duct with a step change in roughness on one wall (Case 1), and (2) a square duct with one rib-roughened wall (Case 2). The models include the Demuren-Rodi (DR) k-ε model, the Sugiyama et al. (S) k-ε model, the Launder-Li (LL) Reynolds stress transport equation model, and the differential stress (DS) model proposed recently by the authors. For the first flow situation (Case 1), the results show that the DS model yields improved agreement between predicted and measured primary and secondary mean velocity distributions in comparison to the DR and LL models. For the second flow situation (Case 2), the DS model is superior to the DR and S models for predicting experimentally observed mean velocity, turbulence kinetic energy, and Reynolds stress anisotropy behavior, especially in the vicinity of a corner formed by the juncture of adjacent smooth and rough walls. The results are analyzed in order to explain why the DR model leads to the formation of a spurious secondary flow cell near this corner that is not present in the experimental flow.

Numerical prediction of laminar, transitional and turbulent flows in shrouded rotor-stator systems

The paper deals with numerical prediction of laminar, transitional and turbulent regimes in confined flow between rotating and stationary discs. For the laminar and transitional flows, a spectral tau-Chebyshev method associated with a multistep time scheme is used. This approach allows accurate prediction of the two laminar regimes mentioned by Daily and Nece (1960) in their experimental studies. For the geometry under consideration (1/11 aspect ratio), the transition to unsteady motion occurs abruptly without any oscillatory behavior. Thus, the instabilities develop in a region localized near the external shroud, primarily along the stator side, according with experimental findings. For calculating turbulent flow regimes, one point second-order transport modeling has been implemented in a finite volume code. The superiority of advanced Reynolds stress transport models over the classical k−ε model is decisive for predicting such a complex flow. This is particularly important in order to get a precise delineation of the adjacent turbulent and relaminarized regions within the cavity. This level of closure was crucial to produce numerical results in good agreement with experimental data.

Shear-free turbulence near a wall

The mean shear has a major influence on near-wall turbulence but there are also other important physical processes at work in the turbulence/wall interaction. In order to isolate these, a shear-free boundary layer was studied experimentally. The desired flow conditions were realized by generating decaying grid turbulence with a uniform mean velocity and passing it over a wall moving with the stream speed. It is shown that the initial response of the turbulence field can be well described by the theory of Hunt & Graham (1978). Later, where this theory ceases to give an accurate description, terms of the Reynolds stress transport (RST) equations were measured or estimated by balancing the equations. An important finding is that two different length scales are associated with the near-wall damping of the Reynolds stresses. The wall-normal velocity component is damped over a region extending roughly one macroscale out from the wall. The pressure–strain redistribution that normally would result from the Reynolds stress anisotropy in this region was found to be completely inhibited by the near-wall influence. In a thin region close to the wall the pressure–reflection effects were found to give a pressure–strain that has an effect opposite to the normally expected isotropization. This behaviour is not captured by current models.

Modeling of the Reynolds Stress Transport Equation

An empirical strategy for improving modeling of the energy dissipation rate e ij and the velocity-pressure gradient Π ij terms in the transport equations for the Reynolds stresses is proposed on the basis of available direct numerical simulations of the turbulent boundary layer and fully developed turbulent channel flow. The dissipation-rate model takes into account the anisotropy of the dissipation rate not only near the wall but elsewhere in the flow as well. When modeling the velocity-pressure gradient term, the usual split between pressure-transport and redistributive terms is avoided. One consequence of this strategy is the elimination of wall reflection or near-wall correction terms. Wall-topography parameters, such as the distance to the wall and wall-normal vectors, are also absent. Calculations of a turbulent boundary layer over a smooth wall confirm the potential improvements that can be achieved with this approach.

Toward consistent formulation of Reynolds stress and scalar flux closures

Langevin stochastic differential equations provide a consistent basis for Reynolds stress, scalar transport and p.d.f. models. However, the stochastic equations must be capable of representing existing closures, like the General Linear Model, or the Rotta and Monin return to isotropy formulations. A consistent approach to derive both Reynolds stress and scalar flux transport equations, starting from a stochastic differential equation for velocity fluctuations, is presented here. A set of algebraic relations for the dispersion tensor is derived for homogeneous shear flow and for the log-layer.

Some developments in computational modeling of turbulent flows

In this paper, some recent developments of two turbulence closure schemes at ICOMP, NASA Lewis will be discussed. One is the Reynolds-stress algebraic equation model and the other is the Reynolds-stress transport equation model. Various model constraints required by the rapid distortion theory, the invariant theory and the realizability principle, etc. will be described in the model development. The models discussed are for high-turbulent Reynolds number flows, so that the near-wall turbulence and the low-Reynolds-number turbulence are not discussed here.

Reynolds Stress Transport Equations in a Momentumless Wake: Experiments and Models

The determination of the transfer terms in the Reynolds stress transport equations is an important issue in the improvement of closure models in turbulence. A part of these efforts is to provide accurate experimental information on each term of these equations and, particularly, on the pressure-strain term. The self-similar region of the momentumless wake of an axisymmetric, propeller-driven body is studied to enable the required balances of the Reynolds stress transport equations. The axial and azimuthal balances show that the flow is mainly dominated by convection. For the shear equations, there is a quasiequilibrium between production and pressure strain, except in the center of the wake. Comparisons are made between the experimentally determined distributions of pressure-strain terms and the corresponding distributions predicted by second-order closure models.

Modeling of the Reynolds stress transport equation

Modeling of the Reynolds stress transport equation

The prediction of turbulent transport in an axially rotating pipe

Two Reynolds stress transport closures are adopted for modelling flow and heat transfer in fully-developed, axially-rotating pipe flow. Modelled transport equations are solved for the turbulent stresses and heat fluxes, and the turbulence-energy dissipation rate. Numerical calculations are performed with and without rotation, and the results show that both models simulate the strong attenuation of turbulent transport due to rotation. The model solutions are in reasonable agreement with published data and large eddy simulations.

Reynolds stress transport equations in a momentumless wake - Experiments and models

Reynolds stress transport equations in a momentumless wake - Experiments and models

Computation of dispersed turbulent liquid-particle flows impinging a centerbody using an improved lagrangian stochastic model

A computational study is carried out for a dilute turbulent liquid-particle flow impinging a centerbody through a sudden-expansion pipe. An improved Lagrangian stochastic particle-dispersion model and a second-moment Reynolds-stress transport model are used for the dispersed and continuous phases, respectively. Complete initial conditions obtained from the experimental measurements are used to specify the two-phase flow conditions at the inlet. Detailed experimental measurements of both the liquid- and particle-phases at several downstream stations are employed to validate numerical predictions by comparing the predicted and measured radial profiles of such two-phase flow properties as mean and fluctuating velocities, mass fluxes, and mean diameters. In addition, the problem of correcting artificial accumulation is also addressed. It is found that numerical predictions obtained with the improved particle-dispersion model are in reasonable agreement with experimental measurements.