A numerical analysis of passive scalar transport in turbulent shear flows

Abstract

The development of the formation and vortex pairing process in a two‐dimensional shear flow and the associated passive scalar (mass concentration or energy) transport process was numerically simulated by using the Vortex‐in‐Cell (VIC) Method combined with the Upwind Finite Difference Method. The visualized temporal distributions of passive scalars resemble the vortex structures and the turbulent passive scalar fluxes showed a definite connection with the occurrence of entrainment during the formation and pairing interaction of large‐scale vortex structures. The profiles of spatial‐averaged passive scalar ø, turbulent passive scalar fluxes, u'ø’ and v'ø’, turbulent diffusivity of mean‐squared scalar fluctuation, v'ø‘ ², mean‐squared turbulent passive scalar fluctuation, √ø‘ ², skewness, and flatness factor of the probability density function of scalar fluctuation ø’ at three different times are calculated. With the lateral dimension scaled by the momentum thickness and the velocity scaled by the velocity difference across the shear layer, these profiles were shown to be self‐preserved. The probability density function of turbulent scalar fluctuation was found to be asymmetric and double‐peaked.     

Mathematical modelling of turbulent shear flows

A critical review of the current methods of mathematical modelling for quantitative predictions of turbulent shear flows is presented. Emphasis is laid on the basic principles and general strategy rather than on computational or bibliographical details. Three major groups of modelling,viz. the integral methods, the differential methods and the numerical simulations are described in the simplest forms. These methods are compared and their future prospects are discussed.     

Analysis of three-dimensional structures in complex turbulent flows

The basic integral relations used in analyzing various images of flows are given. The differences in the Abel transform for laminar and turbulent flows have been shown. The integral Uberoi–Kovasznay transform used in analyzing direct-shadow images of turbulent flows has been described. The present possibilities of digital laser speckle-photography for analyzing speckle-images of turbulent flows with the use of integral Erbeck–Merzkirch transforms have been analyzed. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 1, pp. 8–17, January–February, 2009.     

On nonlinear models for the pressure-strain rate correlations in turbulent flows

Simple inequalities are obtained that can be used for direct verification of the adequacy of nonlinear models describing a rapid part of the pressure-strain rate correlation tensor. Analysis of a quadratic model shows that such models cannot be accepted in a most part of the physical domain because of violation of the condition of positive definiteness of the spectral matrix of two-point correlations of the pulsation velocity. The boundaries of such “forbidden” zones can be even wider than those for the classical linear models.     

A numerical study of non-equilibrium flows with different vibrational relaxation models

Comparative analysis of a widely used Landau–Teller formula for small deviations from thermal equilibrium and its generalized form, derived from the kinetic theory of gaseous, for an arbitrary deviation from the thermal equilibrium is performed by numerical simulation. Thermally non-equilibrium flows of carbon dioxide near a sharp-edged plate, pure nitrogen flows between two symmetrically located wedges, and the N₂/N mixture flow with vibrational relaxation and dissociation over a cone have been considered. A comparison has been performed with the available experimental data.     

Efficient representation of turbulent flows using data-enriched finite elements

Efficient modal decomposition of high-dimensional turbulent flow data is an important first step for data reduction, analysis, and low-dimensional predictive modeling. The conventional modal decomposition techniques, such as proper orthogonal and dynamic mode decompositions, aim to represent the system response using spatially global basis vectors that span a broad spatial domain. A significant challenge facing approaches based on global domain decomposition is the rapid increase in both the amount of training data and the number of modes that must be retained for an accurate representation of convection dominated turbulent flows. An alternative generalized finite element (GFEM) based approach is explored for efficient representation of high-dimensional fluid flow data. Here, the standard finite element interpolation method is enriched with numerical functions that are learned from a small amount of high-fidelity training data over spatially localized subdomains. The GFEM approach is demonstrated on a 3D flow past a cylinder at Reynolds number of 100 000 and flows inside a 2D lid-driven cavity over a range of Reynolds numbers. Compared with a global proper orthogonal decomposition, the GFEM-based approach increases efficiency in reconstructing the datasets while also substantially reducing the amounts of training data.     

Mathematical modelling of nonisothermal turbulent one- and two-phase swirling flows

A mathematical model is developed and realized numerically for turbulent gasdispersed nonisothermal swirling flows on the basis of Navier-Stokes type equations by using a modified k- turbulence model. Corrections taking account of the influence of particles and the flow swirling on k, are introduced into these latter. A finite-difference method of controlled volume is used to solve the equations. Computations are compared with experimental data on swirling single-phase flows in a cylindrical channel. Data are obtained about the influence of the nonisothermy on the length of the recirculation zone.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 60, No. 2, pp. 191–197, February, 1991.     

Description of some numerical tools for solving incompressible turbulent and free surface flows

During the past ten years various methods have been devised to deal with the solution of the Navier–Stokes equations. In the meantime, different models have been worked out to represent turbulent incompressible flows. At LNH, deep participation in this enthusiastic research is still going on, together with a closely related development of physical modelling and metrology. In this paper, we will give an insight into a set of numerical codes which are now currently in use at our laboratory and some of their main applications to coastal engineering. This will include thermohydraulic internal flows and free surface flows. For each code a short presentation of the algorithm of solution is described.     

Global and local POD models for the prediction of compressible flows with DG methods

Proper orthogonal decomposition (POD) allows to compress information by identifying the most energetic modes obtained from a database of snapshots. In this work, POD is used to predict the behavior of compressible flows by means of global and local approaches, which exploit some features of a discontinuous Galerkin spatial discretization. The presented global approach requires the definition of high‐order and low‐order POD bases, which are built from a database of high‐fidelity simulations. Predictions are obtained by performing a cheap low‐order simulation whose solution is projected on the low‐order basis. The projection coefficients are then used for the reconstruction with the high‐order basis. However, the nonlinear behavior related to the advection term of the governing equations makes the use of global POD bases quite problematic. For this reason, a second approach is presented in which an empirical POD basis is defined in each element of the mesh. This local approach is more intrusive with respect to the global approach but it is able to capture better the nonlinearities related to advection. The two approaches are tested and compared on the inviscid compressible flow around a gas‐turbine cascade and on the compressible turbulent flow around a wind turbine airfoil.     

Direct numerical simulation of stably and unstably stratified turbulent open channel flows

Summary Direct numerical simulation of stably and unstably stratified turbulent open channel flow is performed. The three-dimensional Navier-Stokes and energy equations under the Boussinesq approximation are numerically solved using a fractional-step method based on high-order accurate spatial schemes. The objective of this study is to reveal the effects of thermally stable and unstable stratification on the characteristics of turbulent flow and heat transfer and on turbulence structures near the free surface of open channel flow. Here, fully developed weakly stratified turbulent open channel flows are calculated for the Richardson number ranging from 20 (stably stratified flow) to 0 (unstratified flow) and to −10 (unstably stratified flow), the Reynolds number 180 based on the wall friction velocity and the channel depth, and the Prandtl number 1. To elucidate the turbulent flow and heat transfer behaviors, typical quantities including the mean velocity, temperature and their fluctuations, turbulent heat fluxes, and the structures of velocity and temperature fluctuations are analyzed.     

Problems in the study of electrical arcs with turbulent flows

The unique features of a dc electrical arc burning in a long cylindrical channel with an accompanying flow of plasma-forming gas are considered.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 57, No. 1, pp. 48–53, July, 1989.     

Appraisal of energy recovering sub-grid scale models for large-eddy simulation of turbulent dispersed flows

Current capabilities of Large-Eddy Simulation (LES) in Eulerian–Lagrangian studies of dispersed flows are limited by the modeling of the Sub-Grid Scale (SGS) turbulence effects on particle dynamics. These effects should be taken into account in order to reproduce accurately the physics of particle dispersion since the LES cut-off filter removes both energy and flow structures from the turbulent flow field. In this paper, we examine the possibility of including explicitly SGS effects by incorporating ad hoc closure models in the Lagrangian equations of particle motion. Specifically, we consider candidate models based on fractal interpolation and approximate deconvolution techniques. Results show that, even when closure models are able to recover the fraction of SGS turbulent kinetic energy for the fluid velocity field (not resolved in LES), prediction of local segregation and, in turn, of near-wall accumulation may still be inaccurate. This failure indicates that reconstructing the correct amount of fluid and particle velocity fluctuations is not enough to reproduce the effect of SGS turbulence on particle near-wall accumulation.     

Field correlation for flat-topped beam in non-Kolmogorov turbulent medium

Absolute field correlation of flat-topped beam in non-Kolmogorov turbulent medium is examined at the receiver plane. The power law exponent increase affects absolute field correlation inversely. It is found that the absolute field correlation decreases when the propagation distance, deviation from the receiver axis, diagonal transverse distance from the receiver point and turbulence strength increase. Beam flatness order increase yields smaller absolute field correlation. For the employed parameters, the flat-topped beam attains higher absolute field correlation when the wavelength and the source size increase.     

A numerical study of laminar and turbulent flows in a two-dimensional bend with or without a guide vane

A numerical study of the flow in a two-dimensional 90° circular-arc bend is presented. The study is based on the solution of the governing equations using a finite volume technique. Both laminar and turbulent flows are considered. Particular attention is given to the occurrence and size of the separation regions and, in this respect, the effects of Reynolds number and bend radius to height ratio are discussed. The study includes the effect of a guide vane, placed in the bend, on the flow characteristics. It is shown that the emerging velocity distribution is more uniform than that associated with flow in a bend without a guide vane. The presence of a guide vane is shown to suppress the formation of regions of flow separation. Comparisons are made between the effects on the flow of two different designs of guide vane.     

Symmetry of turbulent boundary-layer flows: Investigation of different eddy viscosity models

Summary The symmetrical properties of the turbulent boundary-layer flows and other turbulent flows are studied utilizing the Lie group theory technique. The self-similar forms of the indepedent variables and the solution function for the turbulent boundary layer flows with three different models of the turbulent (eddy) viscosity are obtained. Proceeding from this analysis, a simple numerical method for computation of turbulent flows is developed.     

Prediction of acceleration length in turbulent gas–solid flows

CFD investigation for gas–solid flows in a horizontal pipe was performed using Euler–Euler approach or two-fluid model and accounting for four-way coupling. Calibration of the numerical model is obtained by confirming the numerical predictions with published experimental data. Based upon the axial profiles of the pressure gradient, the authors investigated the acceleration length for different particle properties and loadings. It is found that acceleration length increases generally with increasing particulate loading and/or decreasing gas phase mean flow velocity. However, the variations of acceleration length with particle diameter are quite different under different operating conditions. Finally, an empirical correlation for acceleration length (L_a) is proposed, which contains two terms: the first-term matches with the entrance length for gas only flow; whereas the second term is regarded as the enhancement due to addition of solids to gas flow. The accuracy of the correlation is approximately ±11%.     

Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: Computational issues

This paper presents essential numerical procedures in the context of the coupled lattice Boltzmann (LB) and discrete element (DE) solution strategy for the simulation of particle transport in turbulent fluid flows. Key computational issues involved are (1) the standard LB formulation for the solution of incompressible fluid flows, (2) the incorporation of large eddy simulation (LES)‐based turbulence models in the LB equations for turbulent flows, (3) the computation of hydrodynamic interaction forces of the fluid and moving particles; and (4) the DE modelling of the interaction between solid particles. A complete list is provided for the conversion of relevant physical variables to lattice units to facilitate the understanding and implementation of the coupled methodology. Additional contributions made in this work include the application of the Smagorinsky turbulence model to moving particles and the proposal of a subcycling time integration scheme for the DE modelling to ensure an overall stable solution. A particle transport problem comprising 70 large particles and high Reynolds number (around 56 000) is provided to demonstrate the capability of the presented coupling strategy. Copyright © 2007 John Wiley & Sons, Ltd.     

A note on the turbulent energy as a parameter of turbulent flow

The art of modeling turbulence is a needed tool in the construction of computer codes for turbulent flows. The state to which this art has been developed is inadequate, and quotations from authoritative sources support this point of view. The energy contained in the turbulent fluctuations, i.e., the turbulent energy, is often used as a parameter in the modeling process. The present article attempts to examine this quantity as it is being created, transported, and dissipated. For this purpose experimental evidence from the author's own experiments (free jets), as well as theoretical conclusions from the elementary deductions of the basic equations, the concept of turbulent potential flow, and a general solution to the Navier-Stokes-Reynolds equations, is drawn to attention. Recirculating flow is given special attention. The paper concludes with recommendations for principles that must be satisfied if improved modeling is to be achieved. These principles are necessary; whether they are also sufficient is open to question.Nomenclature A ₀ Constant - b _1/2 Jet's half-width - b ₁ ^2/(0) Jet's half-width at z=z(in0) - E _z Kinetic energy contained in the jet's axial velocity at a given profile - E _r Kinetic energy contained in the jet's radial velocity at a given profile - f() Dimensionless velocity profile [f(0)=1] - F(), H() Defined functions - L _char Jet's characteristic length - m, n Exponents - p Pressure - q Kinetic energy in the turbulent fluctuations - Heat flux - q ² - r, , z Cylindrical coordinates - t Time - û Internal energy - u, v, w Velocity components - Mean velocity components - Mean velocity components - U ₀ Constant - U _plate Plate's velocity - Uskc/(0) Centerline velocity at z=z₀ - X, Y, Z Components of body force - W Total work done by surface stresses - W ₁ Recoverable work done by surface stresses - W ₂ Dissipated work - z ₀ Downstream distance from the nozzle beyond which self-similar velocity profiles occur - Fluid's kinematic viscosity - Fluid's density - Normal stresses - Shear stresses - Normal stresses with the pressure removed - Dimensionless Crossflow coordinate - ₀ Constant - Stress functions - Stress potential Paper dedicated to Professor Joseph Kestin.Definitions of symbols are given under Nomenclature.     

Simulation of a premixed turbulent flame with the discrete vortex method

The behaviour of a premixed turbulent flame is numerically studied in this paper. The numerical model is based on solving turbulent flow field by the discrete vortex method. The flame is considered to be of zero thickness boundary which separates burnt and unburnt regions with different constant density and propagates into the fresh mixture at a local curvature‐dependent flame speed. The flame front is located by means of level‐set algorithm. The flow turbulence is simulated through the unsteady vortex‐shedding mechanism. The computed velocity fields, turbulence scalar statistics as well as flame brush thickness for the turbulent V‐flame are well comparable to experimental results. The computed Reynolds stresses in the flame brush region based on unconditioned velocities are substantial, but the two conditioned Reynolds stresses are negligible. These results show that the intermittency effect is a major influence on turbulent statistics in premixed flame and should require careful consideration in numerical models. Copyright © 2000 John Wiley & Sons, Ltd.