Buoyancy effects on turbulent swirling flows

A three-parameter model of turbulence applicable to free boundary layers has been developed and applied for the prediction of axisymmetric turbulent swirling flows in uniform and stagnant surroundings under the action of buoyancy forces. The turbulent momentum and heat fluxes appearing in the time-averaged equations for the mean motion have been determined from algebraic expressions, derived by neglecting the convection and diffusion terms in the differential transport equations for these quantities, which relate the turbulent fluxes to the kinetic energy of turbulence, k, the dissipation length scale of turbulence, L, and the temperature covariance, T ′². Differential transport equations have been used to determine these latter quantities. The governing equations have been solved using fully implicit finite difference schemes. The turbulence model is capable of reproducing the gross features of pure jet flows, buoyant flows and swirling flows for weak and moderate swirl. The behaviour of a turbulent buoyant swirling jet has been found to depend solely on exit swirl and Froude numbers. The predicted results indicate that the incorporation of buoyancy can cause significant changes in the behaviour of a swirling jet, particularly when the buoyancy strength is high. The jet exhibits similarity behaviour in the initial region for weak swirl and weak buoyancy strengths only, and the asymptotic case of a swirling jet under the action of buoyancy forces is a pure plume in the far field. The predicted results have been found to be in satisfactory agreement with the available experimental data and in good qualitative agreement with other predicted results.     

Accounting for Buoyancy Effects in the Explicit Algebraic Stress Model: Homogeneous Turbulent Shear Flows

Most explicit algebraic stress models are formulated for turbulent shear flows without accounting for external body force effects, such as the buoyant force. These models yield fairly good predictions of the turbulence field generated by mean shear. As for thermal turbulence generated by the buoyant force, the models fail to give satisfactory results. The reason is that the models do not explicitly account for buoyancy effects, which interact with the mean shear to enhance or suppress turbulent mixing. Since applicable, coupled differential equations have been developed describing these thermal turbulent fields, it is possible to develop corresponding explicit algebraic stress models using tensor representation theory. While the procedure to be followed has been employed previously, unique challenges arise in extending the procedure for developing the algebraic representations to turbulent buoyant flows. In this paper the development of an explicit algebraic stress model (EASM) is confined to the homogeneous buoyant shear flow case to illustrate the methodology needed to develop the proper polynomial representations. The derivation is based on the implicit formulation of the Reynolds stress anisotropy at buoyant equilibrium. A five-term representation is found to be necessary to account properly for the effect of the thermal field. Thus derived, external buoyancy effects are represented in the scalar coefficients of the basis tensors, and structural buoyancy effects are accounted for in additional terms in the stress anisotropy tensor. These terms will not vanish even in the absence of mean shear. The performance of the new EASM, together with a two-equation (2-Eq) model, the non-buoyant EASM of Gatski and Speziale (1993) and a full second-order model, is assessed against direct numerical simulations of homogeneous, buoyant shear flows at two different Richardson numbers representing weak and strong buoyancy effects. The calculations show that this five-term representation yields better results than the 2-Eq model and the EASM of Gatski and Speziale where buoyancy effects are not explicitly accounted for. Received 5 March 2001 and accepted 15 January 2002     

Assessment of the validity of a log-law for wall-bounded turbulent bubbly flows

There has been considerable discussion in recent years concerning whether a log-law exists for wall-bounded, turbulent bubbly flows. Previous studies have argued for the existence of such a log-law, with a modified von Kármán constant, and this is used in various modelling studies. We provide a critique of this idea, and present several theoretical reasons why a log-law need not be expected in general for wall-bounded, turbulent bubbly flows. We then demonstrate using recent data from interface-resolving Direct Numerical Simulations that when the bubbles make a significant contribution to the channel flow dynamics, the mean flow profile of the fluid can deviate significantly from the log-law behaviour that approximately holds for the single-phase case. The departures are not surprising and the basic reason for them is simple, namely that for bubbly flows, the mean flow is affected by a number of additional dynamical parameters, such as the void fraction, that do not play a role for the single-phase case. As a result, the inner/outer asymptotic regimes that form the basis of the derivation of the log-law for single-phase flow do not exist in general for bubbly turbulent flows. Nevertheless, we do find that for some cases, the bubbles do not cause significant departures from the unladen log-law behaviour. Moreover, we show that if departures occur these cannot be understood simply in terms of the averaged void fraction, but that more subtle effects such as the bubble Reynolds number and the competition between the wall-induced turbulence and the bubble-induced turbulence must play a role.     

Hybrid LES-RANS using synthesized turbulent fluctuations for forcing in the interface region

The main bottleneck in using Large Eddy Simulations at high Reynolds number is the requirement of very fine meshes near walls. One of the main reasons why hybrid LES-RANS was invented was to eliminate this limitation. In this method unsteady RANS (URANS) is used near walls and LES is used away from walls. The present paper evaluates a method for improving standard LES-RANS. The improvement consists of adding instantaneous turbulent fluctuations (forcing conditions) at the matching plane between the LES and URANS regions in order to trigger the equations to resolve turbulence. The turbulent fluctuations are taken from synthesized homogeneous turbulence assuming a modified von Kármán spectrum. Both isotropic and non-isotropic fluctuations are evaluated. The new approach is applied to fully developed channel flow and it is shown that the imposed fluctuations considerably improve the predictions. It is found that increasing the prescribed turbulent length scale of the synthesized turbulence provides excellent agreement with the classical log-law.     

Implicit unfactored implementation of two-equation turbulence models in compressible Navier–Stokes methods

An implicit unfactored method for the coupled solution of the compressible Navier–Stokes equations with two-equation turbulence models is presented. Both fluid-flow and turbulence transport equations are discretized by a characteristics-based scheme. The implicit unfactored method combines Newton subiterations and point-by-point Gauss–Seidel subrelaxation. Implicit-coupled and -decoupled strategies are compared for their efficiency in the solution of the Navier–Stokes equations in conjunction with low-Re two-equation turbulence models. Computations have been carried out for the flow over an axisymmetric bump using the k–ϵ and k–ω models. Comparisons have been obtained with experimental data and other numerical solutions. The present study reveals that the implicit unfactored implementation of the two-equation turbulence models reduces the computing time and improves the robustness of the CFD code in turbulent compressible flows. © 1998 John Wiley & Sons, Ltd.     

Numerical simulation of an axisymmetric separated and reattached flow over a longitudinal blunt circular cylinder

This article presents a numerical investigation of turbulent flow in an axisymmetric separated and reattached flow over a longitudinal blunt circular cylinder. The governing equations were discretized by the finite-volume method and SIMPLER method was applied to solve the equations on a staggered grid. The turbulent flow was numerically simulated using the standard k–ε, Abe–Kondoh–Nagano (AKN) and Shear Stress Transport (SST) turbulence models. The comparisons made between numerical results and experimental measurements showed that the SST model is superior to other models in the present calculation.Computations were performed for three different Reynolds numbers of 6000, 10 000 and 20 000 based on the cylinder diameter. To our knowledge, this study represents the first numerical investigation of the present flow configuration. The computational results were validated with the available experimental data of reattachment length, mean velocity distribution and wall static pressure coefficient in the turbulent blunt circular cylinder flows. Further, other characteristics of the flow, such as turbulent kinetic energy, pressure, streamlines, and the velocity vectors are discussed.The results show that the main characteristics of the turbulence flow in the separation region, such as reattachment length or velocity profiles, are nearly independent of the Reynolds number. The obtained results showed that a secondary separation bubble may appear in the main separation bubble near the leading edge. Furthermore, it was found that the turbulent kinetic energy has a large effect on the formation of the secondary bubble.     

A computational work on turbulent flow and heat transfer in a channel fitted with inclined baffles

Numerical studies of momentum and heat transfer characteristics have been investigated of a steady incompressible turbulent flow of air through channel. The channel has inclined baffles which are arranged on the walls in a periodically staggered way. The governing equations, namely, continuity, Navier–Stokes and energy, based on k–ω turbulence model to describe the turbulence phenomenon are solved using the finite volume method and the SIMPLE algorithm. Calculations are performed for a Reynolds number between 12,000 and 38,000. The axial velocity profiles, the velocity fields, the local and average coefficient of friction and the Nusselt number distribution were obtained for all the geometry considered and for different sections selected, upstream, downstream and between the two inclined baffles. Simulation results which were obtained by the use of baffles are validated by an experimental study. Good agreement is observed between numerical and experimental results data in the literature.     

An immersed boundary/wall modeling method for RANS simulation of compressible turbulent flows

In this paper, an immersed boundary (IB) method is developed to simulate compressible turbulent flows governed by the Reynolds‐averaged Navier‐Stokes equations. The flow variables at the IB nodes (interior nodes in the immediate vicinity of the solid wall) are evaluated via linear interpolation in the normal direction to close the discrete form of the governing equations. An adaptive wall function and a 2‐layer wall model are introduced to reduce the near‐wall mesh density required by the high resolution of the turbulent boundary layers. The wall shear stress modified by the wall modeling technique and the no‐penetration condition are enforced to evaluate the velocity at an IB node. The pressure and temperature at an IB node are obtained via the local simplified momentum equation and the Crocco‐Busemann relation, respectively. The SST k ? ω and S‐A turbulence models are adopted in the framework of the present IB approach. For the Shear‐Stress Transport (SST) k ? ω model, analytical solutions in near‐wall region are utilized to enforce the boundary conditions of the turbulence equations and evaluate the turbulence variables at an IB node. For the S‐A model, the turbulence variable at an IB node is calculated by using the near‐wall profile of the eddy viscosity. In order to validate the present IB approach, numerical experiments for compressible turbulent flows over stationary and moving bodies have been performed. The predictions show good agreements with the referenced experimental data and numerical results.     

Two‐dimensional prediction of time dependent,turbulent flow around a square cylinder confined in a channel

This paper presents two‐dimensional and unsteady RANS computations of time dependent, periodic, turbulent flow around a square block. Two turbulence models are used: the Launder–Sharma low‐Reynolds number k–ε model and a non‐linear extension sensitive to the anisotropy of turbulence. The Reynolds number based on the free stream velocity and obstacle side is Re=2.2×10⁴. The present numerical results have been obtained using a finite volume code that solves the governing equations in a vertical plane, located at the lateral mid‐point of the channel. The pressure field is obtained with the SIMPLE algorithm. A bounded version of the third‐order QUICK scheme is used for the convective terms. Comparisons of the numerical results with the experimental data indicate that a preliminary steady solution of the governing equations using the linear k–ε does not lead to correct flow field predictions in the wake region downstream of the square cylinder. Consequently, the time derivatives of dependent variables are included in the transport equations and are discretized using the second‐order Crank–Nicolson scheme. The unsteady computations using the linear and non‐linear k–ε models significantly improve the velocity field predictions. However, the linear k–ε shows a number of predictive deficiencies, even in unsteady flow computations, especially in the prediction of the turbulence field. The introduction of a non‐linear k–ε model brings the two‐dimensional unsteady predictions of the time‐averaged velocity and turbulence fields and also the predicted values of the global parameters such as the Strouhal number and the drag coefficient to close agreement with the data. Copyright © 2009 John Wiley & Sons, Ltd.     

Computation of Compressible Flows using a Two-equation Turbulence Model on Unstructured Grids

This paper presents a numerical method for solving compressible turbulent flows using a k - l turbulence model on unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multi-stage Runge-Kutta time stepping scheme, while the turbulence equations are advanced using a multi-stage point-implicit scheme. The positivity of turbulence variables is achieved using a simple change of dependent variables. The developed method is used to compute a variety of turbulent flow problems. The results obtained are in good agreement with theoretical and experimental data, indicating that the present method provides a viable and robust algorithm for computing turbulent flows on unstructured meshes.     

MULTIGRID CONVERGENCE ACCELERATION FOR TURBULENT SUPERSONIC FLOWS

A multigrid convergence acceleration technique has been developed for solving both the Navier–Stokes and turbulence transport equations. For turbulence closure a low-Reynolds-number q–ω turbulence model is employed. To enable convergence, the stiff non-linear turbulent source terms have to be treated in a special way. Further modifications to standard multigrid methods are necessary for the resolution of shock waves in supersonic flows. An implicit LU algorithm is used for numerical time integration. Several ramped duct test cases are presented to demonstrate the improvements in performance of the numerical scheme. Cases with strong shock waves and separation are included. It is shown to be very effective to treat fluid and turbulence equations with the multigrid method. A comparison with experimental data demonstrates the accuracy of the q–ω turbulence closure for the simulation of supersonic flows. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 1019–1035, 1997.     

On the Computation of Compressible Turbulent Flows on Unstructured Grids

An accurate, fast, matrix-free implicit method has been developed to solve compressible turbulent How problems using the Spalart and Allmaras one equation turbulence model on unstructured meshes. The mean-flow and turbulence-model equations are decoupled in the time integration in order to facilitate the incorporation of different turbulence models and reduce memory requirements. Both mean flow and turbulent equations are integrated in time using a linearized implicit scheme. A recently developed, fast, matrix-free implicit method, GMRES+LU-SGS, is then applied to solve the resultant system of linear equations. The spatial discretization is carried out using a hybrid finite volume and finite element method, where the finite volume approximation based on a containment dual control volume rather than the more popular median-dual control volume is used to discretize the inviscid fluxes, and the finite element approximation is used to evaluate the viscous flux terms. The developed method is used to compute a variety of turbulent flow problems in both 2D and 3D. The results obtained are in good agreement with theoretical and experimental data and indicate that the present method provides an accurate, fast, and robust algorithm for computing compressible turbulent flows on unstructured meshes.     

Statistical models for predicting the effect of bidisperse particle collisions on particle velocities and stresses in homogeneous anisotropic turbulent flows

The purpose of this paper is to present and compare two statistical models for predicting the effect of collisions on particle velocities and stresses in bidisperse turbulent flows. These models start from a kinetic equation for the probability density function (PDF) of the particle velocity distribution in a homogeneous anisotropic turbulent flow. The kinetic equation describes simultaneously particle–turbulence and particle–particle interactions. The paper is focused on deriving the collision terms in the governing equations of the PDF moments. One of the collision models is based on a Grad-like expansion for the PDF of the velocity distributions of two particles. The other model stems from a Grad-like expansion for the joint fluid–particle PDF. The validity of these models is explored by comparing with Lagrangian simulations of particle tracking in uniformly sheared and isotropic turbulent flows generated by LES. Notwithstanding the fact that the fluid turbulence may be isotropic, the particle velocity fluctuations are anisotropic due to the impact of gravitational settling. Comparisons of the model predictions and the numerical simulations show encouraging agreement.     

Study on anisotropic buoyant turbulence model

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Interaction of a submerged turbulent jet with a solid wall

The turbulent layer of a wall jet has been analyzed in many theoretical and experimental studies [1–10]. Most theoretical investigations are based on the simultaneous solution of the equations of the turbulent jet and the boundary layer that forms at the wall. The differences lie in the methods used to correlate the velocity and temperature distributions, as well as in the friction and heat-transfer laws employed. In this article we present a method based on the further development of the idea of conservation of the laws governing wall turbulence with respect to change in boundary conditions.     

Investigation of three dimensional air flow characteristic and effect of heated obstruction within room

This study reports the results of a numerical investigation of three-dimensional turbulent buoyant recirculating flow within rooms with heated obstruction. The study involves the solution of partial differential equations for the conservation of mass, momentum, energy, concentration, turbulent energy and its dissipation rate. These equations were solved together with algebraic expressions for the turbulent viscosity and heat diffusivity using k-ε turbulence model by performing simulations on FLUENT 6.3. The CFD method was validated via comparing with the available experimental data. A comparison with experimental results shows good agreement. This means that the present computer code has a good capability to simulate 3D airflow and effect of obstruction within room. The present study demonstrates the flow behavior, thermal distribution and CO₂ concentration inside the room in the presence of heat flux obstruction. Two different configurations of ventilation system have been studied. Mixing and Displacement ventilation system have been used in two geometries depending on location of opening inlet. The ventilation effectiveness for heat removal (E_T) is used to evaluate the indoor climate and average temperature is an important parameter in designs the ventilation systems. Two notable points are presented; first, mixing ventilation is depending on throw of jet. CO₂ concentration and temperature distribution have been effected in upper zone more than occupied zone with presence the obstruction. Second notable points are presented; in displacement ventilation buoyancy effect is considerable. Vertical temperature gradient above the obstruction implies that both fresh air and CO₂ concentration.     

Scalar turbulence model investigation with variable turbulent Prandtl number in heated jets and diffusion flames

Traditional turbulence models using constant turbulent Prandtl number fail to predict the experimentally observed anisotropies in the thermal eddy diffusivity and thermal turbulent intensity fields. Accurate predictions depend strongly on the turbulence model employed. Consequently, the objective of this paper is to assess the performance of turbulence model with variable turbulent Prandtl number in predicting of thermal and scalar fields quantities. The model is applied to axisymmetric turbulent round jet with variable density and in turbulent hydrogen diffusion flames using the flamelet concept. The k − ɛ turbulence model is used in conjunction with thermal field; the model involves solving supplemental scalar equations for the temperature variance and its dissipation rate. The model predictions are compared with available experimental data for the purpose of validating model. In reacting cases, velocity and scalar (including temperature and mass fractions) predictions agree relatively well in the near field of the investigated diluted hydrogen flames.     

Study of Density Effects in Turbulent Buoyant Jets Using Large-Eddy Simulation

Large-Eddy simulations (LES) of spatially evolving turbulent buoyant round jets have been carried out with two different density ratios. The numerical method used is based on a low-Mach-number version of the Navier–Stokes equations for weakly compressible flow using a second-order centre-difference scheme for spatial discretization in Cartesian coordinates and an Adams–Bashforth scheme for temporal discretization. The simulations reproduce the typical temporal and spatial development of turbulent buoyant jets. The near-field dynamic phenomenon of puffing associated with the formation of large vortex structures near the plume base with a varicose mode of instability and the far-field random motions of small-scale eddies are well captured. The pulsation frequencies of the buoyant plumes compare reasonably well with the experimental results of Cetegen (1997) under different density ratios, and the underlying mechanism of the pulsation instability is analysed by examining the vorticity transport equation where it is found that the baroclinic torque, buoyancy force and volumetric expansion are the dominant terms. The roll-up of the vortices is broken down by a secondary instability mechanism which leads to strong turbulent mixing and a subsequent jet spreading. The transition from laminar to turbulence occurs at around four diameters when random disturbances with a 5% level of forcing are imposed to a top-hat velocity profile at the inflow plane and the transition from jet-like to plume-like behaviour occurs further downstream. The energy-spectrum for the temperature fluctuations show both −5/3 and −3 power laws, characteristic of buoyancy-dominated flows. Comparisons are conducted between LES results and experimental measurements, and good agreement has been achieved for the mean and turbulence quantities. The decay of the centreline mean velocity is proportional to x ^−1/3 in the plume-like region consistent with the experimental observation, but is different from the x ⁻¹ law for a non-buoyant jet, where x is the streamwise location. The distributions of the mean velocity, temperature and their fluctuations in the near-field strongly depend upon the ratio of the ambient density to plume density ρ_a/ρ₀. The increase of ρ_a/ρ₀ under buoyancy forcing causes an increase in the self-similar turbulent intensities and turbulent fluxes and an increase in the spatial growth rate. Budgets of the mean momentum, energy, temperature variance and turbulent kinetic energy are analysed and it is found that the production of turbulence kinetic energy by buoyancy relative to the production by shear is increased with the increase of ρ_a/ρ₀. Received 16 June 2000 and accepted 26 June 2001     

Large eddy simulation of free surface shallow‐water flow

Shallow‐water flow with free surface frequently occurs in ambient water bodies, in which the horizontal scale of motion is generally two orders of magnitude greater than the water depth. To accurately predict this flow phenomenon in more detail, a three‐dimensional numerical model incorporating the method of large eddy simulation (LES) has been developed and assessed. The governing equations are split into three parts in the finite difference solution: advection, dispersion and propagation. The advection part is solved by the QUICKEST scheme. The dispersion part is solved by the central difference method and the propagation part is solved implicitly using the Gauss–Seidel iteration method. The model has been applied to free surface channel flow for which ample experimental data are available for verification. The inflow boundary condition for turbulence is generated by a spectral line processor. The computed results compare favourably with the experimental data and those results obtained by using a periodic boundary condition. The performance of the model is also assessed for the case in which anisotropic grids and filters with horizontal grid size of the order of the water depth are used for computational efficiency. The coarse horizontal grid was found to cause a significant reduction in the large‐scale turbulent motion generated by the bottom turbulence, and the turbulent motion is predominately described by the sub‐grid scale (SGS) terms. The use of the Smagorinsky model for SGS turbulence in this situation is found inappropriate. A parabolic mixing length model, which accounts for the filtered turbulence, is then proposed. The new model can reproduce more accurately the flow quantities. Copyright © 2000 John Wiley & Sons, Ltd.