Dale B. Taulbee

An improved algebraic Reynolds stress model and corresponding nonlinear stress model

An improved algebraic Reynolds stress model is developed from the modeled dynamic equations for the Reynolds stress. The improved model more closely represents the original Reynolds stress model equation than the standard algebraic Reynolds stress model over the range of time scales for the turbulence and mean flow strain field. Quasi‐non‐local convective effects are also included in the formulation. Explicit solutions to the algebraic Reynolds stress model equation set, in the form of nonlinear stress‐strain models, are presented for two and three dimensions.

Validation of CFD Simulations of Cerebral Aneurysms With Implication of Geometric Variations

BACKGROUND Computational fluid dynamics (CFD) simulations using medical-image-based anatomical vascular geometry are now gaining clinical relevance. This study aimed at validating the CFD methodology for studying cerebral aneurysms by using particle image velocimetry (PIV) measurements, with a focus on the effects of small geometric variations in aneurysm models on the flow dynamics obtained with CFD. METHOD OF APPROACH An experimental phantom was fabricated out of silicone elastomer to best mimic a spherical aneurysm model. PIV measurements were obtained from the phantom and compared with the CFD results from an ideal spherical aneurysm model (S1). These measurements were also compared with CFD results, based on the geometry reconstructed from three-dimensional images of the experimental phantom. We further performed CFD analysis on two geometric variations, S2 and S3, of the phantom to investigate the effects of small geometric variations on the aneurysmal flow field. Results. We found poor agreement between the CFD results from the ideal spherical aneurysm model and the PIV measurements from the phantom, including inconsistent secondary flow patterns. The CFD results based on the actual phantom geometry, however, matched well with the PIV measurements. CFD of models S2 and S3 produced qualitatively similar flow fields to that of the phantom but quantitatively significant changes in key hemodynamic parameters such as vorticity, positive circulation, and wall shear stress. CONCLUSION CFD simulation results can closely match experimental measurements as long as both are performed on the same model geometry. Small geometric variations on the aneurysm model can significantly alter the flow-field and key hemodynamic parameters. Since medical images are subjected to geometric uncertainties, image-based patient-specific CFD results must be carefully scrutinized before providing clinical feedback.

Progress in Favré–Reynolds stress closures for compressible flows

A closure for the compressible portion of the pressure-strain covariance is developed. It is shown that, within the context of a pressure-strain closure assumption linear in the Reynolds stresses, an expression for the pressure-dilatation can be used to construct a representation for the pressure-strain. Additional closures for the unclosed terms in the Favre–Reynolds stress equations involving the mean acceleration are also constructed. The closures accommodate compressibility corrections depending on the magnitude of the turbulent Mach number, the mean density gradient, the mean pressure gradient, the mean dilatation, and, of course, the mean velocity gradients. The effects of the compressibility corrections on the Favre–Reynolds stresses are consistent with current DNS results. Using the compressible pressure-strain and mean acceleration closures in the Favre–Reynolds stress equations an algebraic closure for the Favre–Reynolds stresses is constructed. Noteworthy is the fact that, in the absence of mea...

On the computation of turbulent backstep flow

Abstract This paper discusses the computation of turbulent backstep flow, focusing on the use of Reynolds stress models. A review of existing backstep calculations shows that these calculations generally underpredict reattachment length, and some calculations produce physically unrealistic behavior. Some of these problems are shown to be related to the commonly used pressure-strain coefficients, particularly the linear return-to-isotropy coefficient, C 1 . A new expression for C 1 that is consistent with both homogeneous shear flow experiments and return-to-isotropy experiments produces reasonable results in the present backstep calculations. Some of the present backstep calculations result in unsteady periodic vortex shedding consistent with experimental evidence. This presents a dilemma in the context of Reynolds averaging, which is discussed.

Stress relation for three‐dimensional turbulent flows

In this Brief Communication, the nonlinear stress–strain model for three‐dimensional turbulent flows, as given by Taulbee [Phys. Fluids A 4, 11 (1992)], is expanded upon. That relation represents a closed form solution to the algebraic Reynolds stress model equation set which is obtained from the modeled transport equation for the Reynolds stress. The parameter values, which appear in the linear pressure–strain closure, that were suggested by Taulbee to obtain a simplified stress relation for three dimensions, are justified in this Brief Communication. A stress solution is also presented for a wider range of pressure–strain model parameter values.

Simultaneous diffusion and sedimentation of aerosols in channel flows

Abstract The problem of particle loss to the wall of a narrow rectangular channel through which an aerosol is passing is studied with simultaneous consideration of diffusion and sedimentation. Both slug flow and Poiseuille flow are considered. It is found that the relative importance of diffusion and sedimentation on the fractional penetration depends upon a parameter σ = hvg/D, where h is the half height of the channel, vg is the settling velocity of a particle and D is the Brownian diffusion coefficient. For σ 200, the loss is due to settling. The loss due to the combined mechanism in the range 0·1

Simultaneous diffusion and sedimentation of aerosol particles from Poiseuille flow in a circular tube

Abstract The deposition of aerosol particles from simultaneous diffusion and sedimentation in Poiseuille flow in a horizontal circular tube is studied. The relative importance of settling as compared to diffusion is determined by a parameter σ = v g R/D where v g is the settling velocity. R is the tube radius and D is the Brownian diffusion coefficient. A series solution is found for the concentration distribution near the tube entrance and the results of a numerical solution are presented for the concentration distribution over the penetration distance for various values of σ.

Simultaneous diffusion and sedimentation of aerosols in a horizontal cylinder

Abstract The problem of particle loss to the wall of an infinitely long horizontal cylinder filled with an aerosol of uniform concentration initially is studied. The particle movements due to the mechanisms of Brownian diffusion and gravitational settling are considered simultaneously. A series solution for the particle distribution is obtained, from which the deposition loss to the wall is calculated. However, for small time, this series solution does not converge rapidly enough for practical computation, thus, an asymptotic expression is developed for this case. The relative importance of diffusion and sedimentation on the deposition efficiency depends upon the parameter σ = v g a /2 D , where v g is the settling velocity, D the Brownian diffusion coefficient and a the radius of the cylinder. For σ

Statistics in particle-laden plane strain turbulence by direct numerical simulation

Abstract Direct numerical simulation is utilized to generate statistics in particle-laden homogeneous plane strain turbulent flows. Assuming that the two-phase flow is dilute (one-way coupling), a variety of cases are considered to investigate the effects of the particle time constant. The carrier phase is incompressible and is treated in the Eulerian frame whereas the particles are tracked individually in a Lagrangian frame. For small particle Reynolds numbers, an analytical expression for the particle mean velocity is found, which is different from the fluid one, and the dispersed phase is shown to be homogeneous. This is not the case for particles with large Reynolds numbers and no statistics involving particle fluctuating velocity is presented for large particles. The results show that the root mean square (r.m.s.) of the particle velocity in the squeezed direction exceeds that of the fluid in the same direction and increases with the particle time constant. The mean velocity gradient component in the elongated direction has the opposite effect, that is the r.m.s. of the particle velocity is decreased below that of the fluid in this direction. Further, the dispersed phase exhibits a larger anisotropy than the fluid phase, and its anisotropy increases with the particle inertia. Dispersion is shown to depend strongly on the injection location and quantified dispersion results show that increasing the injection location coordinates in the strained directions increases the dispersion.

Application of a nonlinear stress-strain model to axisymmetric turbulent swirling flows

Abstract A nonlinear stress-strain relation (NLSM) for the turbulence stresses is applied to axisymmetric free shear flows with and without swirl. This relation is an explicit solution to an algebraic Reynolds stress model (ARSIVI). The stress relation is a finite sum of tensor groups depicting various interactions between the mean strain and vorticity fields. Implementation is in the context of a k −e type model. Comparisons are made between flow field predictions obtained with the full Reynolds stress model, the NLSM corresponding to improved and standard ARSMs, the k −e model and experimental data.