Turbulence kinetic energy budget in bubbly flows in a vertical duct

Understanding turbulence kinetic energy (TKE) budget in gas–liquid two-phase bubbly flows is indispensable to develop and improve turbulence models for the bubbly flows. In this study, a molecular tagging velocimetry based on photobleaching reaction was applied to turbulent bubbly flows with sub-millimeter bubbles in a vertical square duct to examine the applicability of the k–ε models to the bubbly flows. Effects of bubbles on TKE budget are discussed and a priori tests of the standard and low Reynolds number k–ε models are carried out to examine the applicability of these models to the bubbly flows. The conclusions obtained are as follows: (1) The photobleaching molecular tagging velocimetry is of use for validating turbulence models. (2) The bubbles increase the liquid velocity gradient in the near wall region, and therefore, enhance the production and dissipation rates of TKE. (3) The k–ε models can reasonably evaluate the production rate of TKE in the bubbly flows. (4) The modulations of diffusion due to the bubbles have different characteristics from the diffusion enhancement due to shear-induced turbulence. Hence, the k–ε models fail in evaluating the diffusion rate in the near wall region in the bubbly flows. (5) The k–ε models represent the trends of the production, dissipation, and diffusion rates of ε in the bubbly flow, although more accurate experimental data are required for quantitative validation of the ε equation.     

Large-eddy Simulation of Triangular-stabilized Lean Premixed Turbulent Flames: Quality and Error Assessment

In this numerical study, an algebraic flame surface wrinkling (AFSW) reaction submodel based on the progress variable approach is implemented in the large-eddy simulation (LES) context and validated against the triangular stabilized bluff body flame configuration measurements i.e. in VOLVO test rig. The quantitative predictability of the AFSW model is analyzed in comparison with another well validated turbulent flame speed closure (TFC) combustion model in order to help assess the behaviour of the present model and to further help improve the understanding of the flow and flame dynamics. Characterization of non-reacting (or cold) and reacting flows are performed using various subgrid scale models for consistent grid size variation with 300,000 (coarse), 1.2 million (intermediate) and 2.4 million (fine) grid cells. For non-reacting flows at inlet velocity of 17?m/s and inlet temperature 288?K, coarse grid leads to over prediction of turbulence quantities due to low dissipation at the early stage of flow development behind the bluff body that convects downstream eventually polluting the resulting solution. The simulated results with the intermediate (and fine) grid for mean flow and turbulence quantities, and the vortex shedding frequency (f_s) closely match experimental data. For combusting flows for lean propane/air mixtures at 35?m/s and 600?K, the vortex shedding frequency increase threefold compared with cold scenario. The predicted results of mean, rms velocities and reaction progress variable are generally in good agreement with experimental data. For the coarse grid the combustion predictions show a shorter recirculation region due to higher turbulent burning rate. Finally, both cold and reacting LES data are analyzed for uncertainty in the solution using two quality assessment techniques: two-grid estimator by Celik, and model and grid variation by Klein. For both approaches, the resolved turbulent kinetic energy is used to estimate the grid quality and error assessment. The quality assessment reveals that the cold flows are well resolved even on the intermediate mesh, while for the reacting flows even the fine mesh is locally not sufficient in the flamelet region. The Klein approach estimates that depending on the recirculation region in cold scenario both numerical and model errors rise near the bluff-body region, while in combusting flows these errors are significant behind the stabilizing point due to preheating of unburned mixture and reaction heat release. The total error mainly depends on the numerical error and the influence of model error is low for this configuration.     

On the effect of inflow conditions in simulation of a turbulent round jet

This paper investigates the impact of the inflow conditions on simulations of a round jet discharging from a wall into a large space. The fluid dynamic characteristics of a round jet are studied numerically. A numerical method based on the control volume approach with collocated grid arrangement is employed. The k-e{k-\varepsilon} model is utilized to approximate turbulent stresses by considering six different inlet conditions. The velocity field is presented, and the rate of decay at the jet centerline is determined. The results showed that inflow conditions had a strong influence on the jet characteristics. This paper also investigates both sharp-edged and contoured nozzles. The effects of velocity, turbulence intensity, turbulence kinetic energy, and turbulence dissipation rate on flow field characteristics are examined. Results showed that the present simulations in both types of nozzles are in good agreement with experiments when considering the appropriate inflow conditions.     

The computation of three-dimensional systems with various turbulence model variations

The standardk-? equations and other turbulence corrections are evaluated and reported with respect to their applicability in three-dimensional flows. The turbulence models are formulated on the assumption that an isotropic eddy viscosity and the modified Boussinesq hypothesis adequately describe the stress distributions, and that the source of predictive error is a consequence of the modelled terms in thek-? equations. Turbulence model corrections are incorporated to investigate their impact on these errors. Predictions from various turbulence models are compared with experimental data from an isothermal 3-D configuration. The data comparisons delineate the relative advantages and disadvantages of various modifications. Thek-? model performs competitively with other model corrections and in some instances is judged to be superior than the modified treatments. However, given the additional computational time and the marginal superiority of the investigated models, it is recommended that present 3-D computational code calculations retain the standardk-? model.     

Finite element computation of a turbulent flow over a two-dimensional backward-facing step

This paper is devoted to the computation of turbulent flows by a Galerkin finite element method. Effects of turbulence on the mean field are taken into account by means of a k-? turbulence model. The wall region is treated through wall laws and, more specifically, Reichardt's law. An inlet profile for ? is proposed as a numerical treatment for physically meaningless values of k and ?. Results obtained for a recirculating flow in a two-dimensional channel with a sudden expansion in width are presented and compared with experimental values.     

A two‐scale low‐Reynolds number turbulence model

In this study, a two‐scale low‐Reynolds number turbulence model is proposed. The Kolmogorov turbulence time scale, based on fluid kinematic viscosity and the dissipation rate of turbulent kinetic energy (ν, ε), is adopted to address the viscous effects and the rapid increasing of dissipation rate in the near‐wall region. As a wall is approached, the turbulence time scale transits smoothly from a turbulent kinetic energy based (k, ε) scale to a (ν, ε) scale. The damping functions of the low‐Reynolds number models can thus be simplified and the near‐wall turbulence characteristics, such as the ε distribution, are correctly reproduced. The proposed two‐scale low‐Reynolds number turbulence model is first examined in detail by predicting a two‐dimensional channel flow, and then it is applied to predict a backward‐facing step flow. Numerical results are compared with the direct numerical simulation (DNS) budgets, experimental data and the model results of Chien, and Lam and Bremhorst respectively. It is proved that the proposed two‐scale model indeed improves the predictions of the turbulent flows considered. Copyright © 2000 John Wiley & Sons, Ltd.     

Numerical simulation of turbulence suppression: Comparisons of the performance of four k-? turbulence models

The standard k-ε model and three low-Reynolds number k-ε models were used to simulate pipe flow with a ring device installed in the near-wall region. Both developing and fully developed turbulent pipe flows have been investigated. Turbulence suppression for fully developed pipe flows revealed by hot-wire measurements has been predicted with all three low-Reynolds number models, and turbulence enhancement has been predicted by the standard k-ε model. All three low-Reynolds number models have predicted similar distributions of velocities, turbulence kinetic energy, and dissipation rate. For developing pipe flows, the region of turbulence suppression predicted by the three low-Reynolds number models is much more extensive (up to 30 pipe diameters downstream of the device) than for full developed flow; whereas the standard k-ε model has only predicted turbulence enhancement.     

A qualitative assessment of the role of a viscosity depending on the third invariant of the rate-of-deformation tensor upon turbulent non-Newtonian flow

The numerical simulation of some non-Newtonian effects in wall and wall-free turbulent flows, such as drag reduction in pipe flows or the decrease in transverse normal Reynolds stresses, has been attempted in the past with a limited degree of success on the basis of modified wall functions applied to traditional turbulence models (k–ε), rather than through more realistic rheological constitutive equations. In this work, it is qualitatively shown that if the viscosity function of a generalised Newtonian fluid is assumed to depend on the third invariant of the rate of deformation tensor, there is an increase of the viscous diffusion terms, but especially, of the dissipation of turbulence kinetic energy by a factor equal to the Trouton ratio of the fluid, divided by the Trouton ratio of the solvent, thus indicating a possible way to improve rheological–turbulence modelling.     

The computation of flow development through stationary and rotating U-ducts of strong curvature

This article presents comparisons between predictions, obtained during the course of this investigation, and recently produced measurements of the flow development through a square cross-sectioned U-bend of strong curvature, Rc/D=0.65, that is either stationary or in orthogonal rotation. For the stationary case, four turbulence models have been tested; a high-Re κ-ε model interfaced with the low-Re 1-equation model in the near-wall regions, a high-Re algebraic second-moment (ASM) closure with the low-Re 1-equation model in the near-wall regions, and two versions of a low-Re ASM model. The two low-Re ASM models return noticeably better predictions of the flow development. There is, however further scope for improvement, especially in the downstream section. Two rotating flow cases have been computed both with the axis of rotation parallel to the axis of bend curvature; one at a positive rotation number R_o≡ΩD/W_b of 0.2 and one at R_o≡-0.2. In the case of positive rotation, where the Coriolis and curvature forces reinforce each other, the flow predictions of the low-Re ASM are in very close agreement with the data. When the U-bend rotates negatively, the complex flow field generated in the downstream section is not well reproduced by the low-Re ASM model. More refined turbulence models are thus necessary when the curvature and Coriolis forces oppose each other.     

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 Launder¹ and followers^2,3,4,5. 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 characterised by Kolmogorov microscales. According t o 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 a n example, the concept is incorporated in the standard κ - εmodel which is then applied t o channel and boundary layer flows. Using appropriate boundary conditions (based on Kolmogorov behaviour of near-wall turbulence), there is no need for any wall-modification to the κ - ε equations (including model constants). Results compare very well with the DNS and experimental data.     

Effect of wall distance on the prediction of variable property flow with two-equation turbulence models

This paper investigates the effect of wall distance coordinate on predicting variable property flows with two-equation turbulence models. Three of five different definitions of wall distance coordinate are employed: the wall-property definition, the integral-property definition and the local-property definition. Three different two-equation turbulence models that involve the wall distance coordinate are tested against the varying property flow: Superheated gas flow. The definition of wall distance coordinate affects the size of the viscous region. The wall-property based unit makes the wall distance to be the smallest and contributes to widen the viscous damping region, so that the skin friction factor and the Nusselt number is lowered. All the predictions with three different wall distance coordinates lie within less than 20% in the calculated Nusselt number.     

Wall-modeled large eddy simulation of turbulent channel flow at high Reynolds number using the von Karman length scale

The von Karman length scale is able to reflect the size of the local turbulence structure. However, it is not suitable for the near wall region of wall-bounded flows, for its value is almost infinite there. In the present study, a simple and novel length scale combining the wall distance and the von Karman length scale is proposed by introducing a structural function. The new length scale becomes the von Karman length scale once local unsteady structures are detected. The proposed method is adopted in a series of turbulent channel flows at different Reynolds numbers. The results show that the proposed length scale with the structural function can precisely simulate turbulence at high Reynolds numbers, even with a coarse grid resolution.     

基于涡粘性模型的翼型湍流流场熵产率计算

利用有限体积法实现了基于非正交同位网格的SIMPLE算法。基于熵分析方法,采用涡粘性模型求解湍流熵产方程,系统研究了湍流模型对二维翼型绕流流场熵产率的影响。通过计算NACA0012翼型在来流雷诺数为2.88×10⁶时,0°攻角~16.5°攻角范围内的翼型表面压力系数分布和升阻力特性,验证了算法及程序的正确性。结果表明,选择不同湍流模型时,翼型流场熵产的计算结果存在差异,湍流耗散是引起流场熵产的主要原因;翼型流场的熵产主要发生在翼型前缘区、壁面边界层和翼型尾流区域,流场熵产率与翼型阻力系数线性相关;当产生分离涡时,粘性耗散引起的熵产下降。     

A Dissipation Rate Equation for Low-Reynolds-Number and Near-Wall Turbulence

Two-equation turbulence models are usually formulated for specific flow types and are seldom validated against a variety of flows to account for near-wall and low-Reynolds-number effects simultaneously. In addition to low-Reynolds-number effects, near-wall flows also experience wall blocking, which is absent in free flows. Consequently, near-wall modifications to two-equation models could be quite different from low-Reynolds-number corrections. Besides, it is known that existing two-equation models perform poorly when used to calculate plane wall jets and two-dimensional backstep flows. These problems could be traced to the modeling of the dissipation rate equation. In this paper an attempt is made to improve the modeling of the dissipation rate equation so that it could successfully predict both free and wall-bounded shear flows including plane wall jets and backstep flows. The predictions are compared with experimental and direct numerical simulation data whenever available. Most of the data used are obtained at low Reynolds numbers. Good correlation with data is obtained. Therefore, for the first time, a model capable of correctly predicting free and wall-bounded shear flows, backstep flows, and plane wall jets is available. Received: 12 December 1995 and accepted 12 November 1996     

Development of projection and artificial compressibility methodologies using the approximate factorization technique

Predictions for two-dimensional, steady, incompressible flows under both laminar and turbulent conditions are presented. The standard k-? turbulence model is used for the turbulent flows. The computational method is based on the approximate factorization technique. The coupled approach is used to link the equations of motion and the turbulence model equations. Mass conservation is enforced by either the pseudocompressibility method or the pressure correction method. Comparison of the two methods shows a superiority of the pressure correction method. Second- and fourth-order artifical dissipation terms are used in order to achieve good convergence and to handle the turbulence model equations efficiently. Several internal and external test cases are investigated, including attached and separated flows.     

Introduction of turbulent model in a mixed finite volume/finite element method

The aim of this work is to present a new numerical method to compute turbulent flows in complex configurations. With this in view, a k-? model with wall functions has been introduced in a mixed finite volume/finite element method. The numerical method has been developed to deal with compressible flows but is also able to compute nearly incompressible flows. The physical model and the numerical method are first described, then validation results for an incompressible flow over a backward-facing step and for a supersonic flow over a compression ramp are presented. Comparisons are performed with experimental data and with other numerical results. These simulations show the ability of the present method to predict turbulent flows, and this method will be applied to simulate complex industrial flows (flow inside the combustion chamber of gas turbine engines). The main goal of this paper is not to test turbulence models, but to show that this numerical method is a solid base to introduce more sophisticated turbulence model.     

Finite element computation of a turbulent flow over a two-dimensional backward-facing step

The present paper is devoted to the computation of turbulent flows by a Galerkin finite element method. Effects of turbulence on the mean field are taken into account by means of a (k-ε) turbulence model. The wall region is treated through wall laws and, more specifically, Reichardt's law. An inlet profile for ε is proposed as a numerical treatment for physically meaningless values of k and ε. Results obtained for a recirculating flow in a two-dimensional channel with a sudden expansion in width are presented and compared with experimental values.     

An Attempt to Combine Large Eddy Simulation with the k-ε Model in a Channel-Flow Calculation

Large eddy simulation (LES) is combined with the Reynolds-averaged Navier–Stokes (RANS) equation in a turbulent channel-flow calculation. A one-equation subgrid-scale model is solved in a three-dimensional grid in the near-wall region whereas the standard k–ε model is solved in a one-dimensional grid in the outer region away from the wall. The two grid systems are overlapped to connect the two models smoothly. A turbulent channel flow is calculated at Reynolds numbers higher than typical LES and several statistical quantities are examined. The mean velocity profile is in good agreement with the logarithmic law. The profile of the turbulent kinetic energy in the near-wall region is smoothly connected with that of the turbulent energy for the k–ε model in the outer region. Turbulence statistics show that the solution in the near-wall region is as accurate as a usual LES. The present approach is different from wall modeling in LES that uses a RANS model near the wall. The former is not as efficient as the latter for calculating high-Reynolds-number flows. Nevertheless, the present method of combining the two models is expected to pave the way for constructing a unified turbulence model that is useful for many purposes including wall modeling. Received 11 June 1999 and accepted 15 December 2000     

EXPERIMENTAL STUDY OF MEASUREMENT FOR DISSIPATION RATE SCALING EXPONENT IN HEATED WALL TURBULENCE

Experimental investigations have been devoted to the study of scaling law of coarse-grained dissipation rate structure function for velocity and temperature fluctuation of non-isotropic and inhomogeneous turbulent flows at moderate Reynolds number. Much attention has been paid to the case of turbulent boundary layer, which is typically the non-istropic and inhomogeneous trubulence because of the dynamically important existence of organized coherent structure burst process in the near wall region . Longitudinal velocity and temperature have been measured at different vertical positions in turbulent boundary layer over a heated and unheated flat plate in a wind tunnel using hot wire anemometer. The influence of non-isotropy and inhomogeneity and heating the wall on the scaling law of the dissipation rate structure function is studied because of the existence of organized coherent structure burst process in the near wall region . The scaling law of coarse-grained dissipation rate structure function is foun