Engineering topics

Lumley, John L.

Publications and source records attributed to Lumley, John L..

12 records

NASA NTRS1997

Modeling of Turbulent Swirling Flows

Aircraft engine combustors generally involve turbulent swirling flows in order to enhance fuel-air mixing and flame stabilization. It has long been recognized that eddy viscosity turbulence models are unable to appropriately model swirling flows. Therefore, it has been suggested that, for the modeling of these flows, a second order closure scheme should be considered because of its ability in the modeling of rotational and curvature effects. However, this scheme will require solution of many complicated second moment transport equations (six Reynolds stresses plus other scalar fluxes and variances), which is a difficult task for any CFD implementations. Also, this scheme will require a large amount of computer resources for a general combustor swirling flow. This report is devoted to the development of a cubic Reynolds stress-strain model for turbulent swirling flows, and was inspired by the work of Launder's group at UMIST. Using this type of model, one only needs to solve two turbulence equations, one for the turbulent kinetic energy k and the other for the dissipation rate epsilon. The cubic model developed in this report is based on a general Reynolds stress-strain relationship. Two flows have been chosen for model evaluation. One is a fully developed rotating pipe flow, and the other is a more complex flow with swirl and recirculation.

Shih, Tsan-Hsing↗

NASA NTRS1995

Applications of direct numerical simulation of turbulence in second order closures

This paper discusses two methods of developing models for the rapid pressure-strain correlation term in the Reynolds stress transport equation using direct numerical simulation (DNS) data. One is a perturbation about isotropic turbulence, the other is a perturbation about two-component turbulence -- an extremely anisotropic turbulence. A model based on the latter method is proposed and is found to be very promising when compared with DNS data and other models.

Shih, Tsan-Hsing↗

NASA NTRS1994

A New Reynolds Stress Algebraic Equation Model

A general turbulent constitutive relation is directly applied to propose a new Reynolds stress algebraic equation model. In the development of this model, the constraints based on rapid distortion theory and realizability (i.e. the positivity of the normal Reynolds stresses and the Schwarz' inequality between turbulent velocity correlations) are imposed. Model coefficients are calibrated using well-studied basic flows such as homogeneous shear flow and the surface flow in the inertial sublayer. The performance of this model is then tested in complex turbulent flows including the separated flow over a backward-facing step and the flow in a confined jet. The calculation results are encouraging and point to the success of the present model in modeling turbulent flows with complex geometries.

Shih, Tsan-Hsing↗

NASA NTRS1994

Modeling of Wall-Bounded Complex Flows and Free Shear Flows

Various wall-bounded flows with complex geometries and free shear flows have been studied with a newly developed realizable Reynolds stress algebraic equation model. The model development is based on the invariant theory in continuum mechanics. This theory enables us to formulate a general constitutive relation for the Reynolds stresses. Pope was the first to introduce this kind of constitutive relation to turbulence modeling. In our study, realizability is imposed on the truncated constitutive relation to determine the coefficients so that, unlike the standard k-E eddy viscosity model, the present model will not produce negative normal stresses in any situations of rapid distortion. The calculations based on the present model have shown an encouraging success in modeling complex turbulent flows.

Shih, Tsan-Hsing↗

NASA NTRS1993

Remarks on turbulent constitutive relations

The paper demonstrates that the concept of turbulent constitutive relations can be used to construct general models for various turbulent correlations. Some of the Generalized Cayley-Hamilton formulas for relating tensor products of higher extension to tensor products of lower extension are introduced. The combination of dimensional analysis and invariant theory can lead to 'turbulent constitutive relations' (or general turbulence models) for, in principle, any turbulent correlations. As examples, the constitutive relations for Reynolds stresses and scalar fluxes are derived. The results are consistent with ones from Renormalization Group (RNG) theory and two-scale Direct-Interaction Approximation (DIA) method, but with a more general form.

Shih, Tsan-Hsing↗

NASA NTRS1993

Critical comparison of second-order closures with direct numerical simulations of homogeneous turbulence

Recently, several models have been proposed for closing the second-moment equations, in which the velocity-pressure gradient tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so-called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behaviors in different flows have not been fully examined because they are unmeasurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the possibility to do this kind of study. With direct numerical simulation, we may use the solution to calculate exactly the values of these correlation terms and then directly compare them with the values from their modeled formulations. In this paper, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of 45 homogeneous flows, which were done by Rogers et al. (1986) and Lee and Reynolds (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones that give the best performance. The paper also describes the modeling procedure, model constraints, and the various evaluated models. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.

Shih, Tsan-Hsing↗

NASA NTRS1993

A Realizable Reynolds Stress Algebraic Equation Model

The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

Shih, Tsan-Hsing↗

NASA NTRS1992

Kolmogorov Behavior of Near-Wall Turbulence and Its Application in Turbulence Modeling

The near-wall behavior of turbulence is re-examined in a way different from that proposed by Hanjalic and Launder and followers. It is shown that at a certain distance from the wall, all energetic large eddies will reduce to Kolmogorov eddies (the smallest eddies in turbulence). All the important wall parameters, such as friction velocity, viscous length scale, and mean strain rate at the wall, are characterized by Kolmogorov microscales. According to this Kolmogorov behavior of near-wall turbulence, the turbulence quantities, such as turbulent kinetic energy, dissipation rate, etc. at the location where the large eddies become Kolmogorov eddies, can be estimated by using both direct numerical simulation (DNS) data and asymptotic analysis of near-wall turbulence. This information will provide useful boundary conditions for the turbulent transport equations. As an example, the concept is incorporated in the standard k-epsilon model which is then applied to channel and boundary flows. Using appropriate boundary conditions (based on Kolmogorov behavior of near-wall turbulence), there is no need for any wall-modification to the k-epsilon equations (including model constants). Results compare very well with the DNS and experimental data.

Shih, Tsan-Hsing↗

NASA NTRS1991

A critical comparison of second order closures with direct numerical simulation of homogeneous turbulence

Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.

Shih, Tsan-Hsing↗

NASA NTRS1991

Advances in modeling the pressure correlation terms in the second moment equations

In developing turbulence models, various model constraints were proposed in an attempt to make the model equations more general (or universal). The most recent of these are the realizability principle, the linearity principle, the rapid distortion theory, and the material indifference principle. Several issues are discussed concerning these principles and special attention is payed to the realizability principle. Realizability (defined as the requirement of non-negative energy and Schwarz' inequality between any fluctuating quantities) is the basic physical and mathematical principle that any modeled equation should obey. Hence, it is the most universal, important and also the minimal requirement for a model equation to prevent it from producing unphysical results. The principle of realizability is described in detail, the realizability conditions are derived for various turbulence models, and the model forms are proposed for the pressure correlation terms in the second moment equations. Detailed comparisons of various turbulence models with experiments and direct numerical simulations are presented. As a special case of turbulence, the two dimensional two-component turbulence modeling is also discussed.

Shih, Tsan-Hsing↗

NASA NTRS1991

Collaborative testing of turbulence models

A review is given of an ongoing international project, in which data from experiments on, and simulations of, turbulent flows are distributed to developers of (time-averaged) engineering turbulence models. The predictions of each model are sent to the organizers and redistributed to all the modelers, plus some experimentalists and other experts (total approx. 120), for comment. The 'reaction time' of modelers has proved to be much longer than anticipated, partly because the comparisons with data have prompted many modelers to improve their models or numerics.

Bradshaw, Peter↗

NASA NTRS1989

Low dimensional models of the wall region of a turbulent boundary layer, and the possibility of control

A method of identification of coherent structures in a random turbulent flow is outlined with emphasis on the structure best correlated with a random energy-integrable field and application of the proper orthogonal decomposition to the shear flow of the wall region. The wall region of a pipe flow with almost pure glycerine is investigated experimentally, dynamic equations are obtained, and an energy-transfer model is employed. Numerical solutions are obtained, implications for the flow in the wall region are discussed with focus placed on the sets of solutions exhibiting intermittency. The most significant finding of the study is considered to be the suggestion of the etiology of the bursting phenomenon; presuming that abrupt transitions from one fixed point to the other can be identified with a burst, these bursts appear to be produced autonomously by the wall region, but be triggered by pressure signals from the outer layer.

Lumley, John L.↗