Types Of Turbulence Models Research Articles

Experimental and CFD investigation on mixing by a jet in a semi-industrial stirred tank

Abstract This paper reports the results of a study on the flow generated and mixing time in a semi-industrial tank equipped with a side entry jet mixer. For this purpose, a three dimensional modeling is carried out using an in-house Computational Fluid Dynamics (CFD) code. In this study, the theoretical mixing curves predicted by the CFD were validated by experiments. The experimental mixing curves were obtained by monitoring of the homogenization progress of the dark blue Nigrosine solution inside the tank. A photometer equipped with an online detector was used for this purpose. The experiments were carried out for 0°, 22.5° and 45° jet angle setups. The results showed that the mixing time in the 45° jet layout is lower than other setups. The CFD code with the ability of simultaneous solving of the continuity, the Reynolds-averaged Navier–Stokes (RANS) equations and employing various types of turbulence models was used. The effect of the mesh size on the predicted results was investigated and the theoretical results obtained from various mesh sizes configuration were compared with the experiments. The results showed that the number of meshes is quite effective on the obtained theoretical results in a way that the predicted results for the largest mesh size were far away from the experiments. In addition, the two equation k – ɛ family models including: standard, RNG and realizable models were introduced to the code and the effect of these models on the predicted results was investigated. The results show that there are considerable differences between the predicted mixing progress using the three versions of the k – ɛ family models. The RNG k – ɛ model shows more convincing results in comparison with the other models.

Assessment of unsteady RANS in predicting swirl flow instability based on LES and experiments

Swirl flows play an important role in many engineering applications such as modern gas turbines, aero propulsion systems etc. While the enhanced mixing and stabilisation of the flame caused by the swirl are desirable features, such flows often exhibit hydrodynamic instabilities called precessing vortex core. For design purposes it is very important to predict such instabilities. Computational fluid dynamics (CFD) using Reynolds-averaged Navier–Stokes (RANS) type turbulence models are state of the art for the prediction of flow properties in engineering practice. The objective of this paper is therefore to evaluate the performance of the unsteady RANS (U-RANS) method in predicting the precessing vortex core phenomenon. To this end, an unconfined swirling flow with precessing vortex core at swirl number 0.75 and Reynolds number ranging from 10 000 to 42 000, investigated by means of both experiments and large eddy simulation, is utilised. The results show that U-RANS is able to capture the precessing vortex core both qualitatively and in parts quantitatively.

A new model on simulating smoke transport with computational fluid dynamics

A new model is proposed for simulating smoke movement induced by a fire. Smoke is taken as a collection of particles with size described by a certain distribution function. Movement of the particles will be studied by dividing the physical problem into two parts: solid phase and air phase. The Lagrangian approach is used for studying motion of the solid phase, with the air flow simulated by computational fluid dynamics (CFD). Interaction between the air phase and the solid phase will be described by the particle-source-in-cell method. k– ε types of turbulence models are used in the simulation of air flow. Some of the results are also compared with the fire dynamics simulator model based on large eddy simulation developed at the Building and Fire Research Laboratory, National Institute of Standards and Technology, USA. Application of the model for designing smoke management system is also illustrated. This model should be useful for designing smoke management system as it describes an intermediate step while using CFD.

A New Low-Reynolds-Number Two-Equation Turbulence Model with Hybrid Time-Scales of Mean Flow and Turbulence for Complex Wall Flows

It is well known that the turbulence energy is overpredicted by the k-e model at the stagnation point. This problem causes inadequate predictions of flow field. In particular, since the wind-power energy is proportional to wind velocity cubed, it is crucial to predict a correct profile of wind in selecting the best site for a wind-power plant. The effects of the ground are often neglected owing to the very large length scale of the real environment. However, the complex terrain affects a profile of wind near the ground. Therefore, we have to consider the ground effects to obtain an exact profile of wind near the ground. In this study, to evaluate the performance of a low-Reynolds-number type turbulence model for flows on a complex terrain, we carried out a simulation of a flow around various complex terrain. From evaluation, we have improved the model introducing the time scale based on the velocity gradient parameter. The proposed model is evaluated in four complex turbulent flows, i.e., forward-facing step, two-dimensional block, two-dimensional hill and three-dimensional block flows. The proposed model indicates good agreement with the experimental data.

Numerical simulation of flow over topographic features by revised k-ϵ models : Lun, Y. F. et al. Journal of Wind Engineering and Industrial Aerodynamics, 2003, 91, (1–2), 231–245

The accurate prediction of the wind energy distribution over terrains is important for making an appropriate selection of a suitable site for installing wind power plant. In this study, two-dimensional numerical simulations of flow over two common types of topographic features, i.e. a cliff and a hill, are presented. Three types of turbulence models, namely standard k-e and its revised linear form (Durbin model) as well as a revised nonlinear form (Shih model) are employed in this work. The performance of these models in predicting flow over these features is investigated. The accuracy of the prediction by using a z 0 type wall function to reproduce the effect of surface roughness on flowfield from these turbulence models is also examined.

208 二方程式乱流モデルを適用した共存対流乱流輸送機構の考察

Recently, the two-equation turbulence models for simulating velocity fields have been improved variously. It becomes possible that the turbulence models accurately estimate turbulent statistic such as Reynolds stress near wall and the wall asymptotic behavior. The two-equation turbulence models have also been developed on temperature fields, and the models are useful for simulating another turbulent statistic such as turbulent heat fluxes near wall. However, the turbulent combined convection strongly affected by buoyancy, there is little research effort in which an appropriate turbulence model is made to reflect the buoyant effect accurately. In general, it is often difficult to measure the turbulent statistic of the combined convection at a good accuracy, because the influence of temperature fluctuation on various sensors is rather large. Analyzing the turbulent transport phenomena strongly affected by the buoyancy has not even been discussed empirically owing to the difficulty of the measurement. In particular, the behavior of the turbulent Prandtl number has not been addressed numerically and empirically for the buoyant dominant flow such as the combined convection. Therefore, in this study, the buoyant components were introduced to the turbulent fluxes such as Reynolds stress and turbulent heat fluxes; the turbulent transport phenomena of the combined convection were modeled by adding several buoyant-induced components to the expressions of the turbulent fluxes. The turbulent transport mechanism of the combined convection was also examined by applying a new damping function being applicable to both the aiding and the opposing flows. The calculation target is the fully-developed turbulent combined convection between vertical smooth parallel plates, where the inertia force acts on parallel or opposite to the buoyant force. The wall is heated uniformly. The numerical computation was performed by combining the two-equation turbulence models of the different type being applicable to both the velocity and the temperature fields. It was revealed from a series of computations that the utilized model simulates the heat transfer and fluid flow of the turbulent combined convection physically. Confirming the applicability of the two-equation turbulence models to the turbulent combined convection is important. Realizing the industrial convenience by using more appropriate and simpler turbulence models with the aid of the empirical knowledge is also necessary.

Numerical simulation of flow over topographic features by revised k– ε models

The accurate prediction of the wind energy distribution over terrains is important for making an appropriate selection of a suitable site for installing wind power plant. In this study, two-dimensional numerical simulations of flow over two common types of topographic features, i.e. a cliff and a hill, are presented. Three types of turbulence models, namely standard k– ε and its revised linear form (Durbin model) as well as a revised nonlinear form (Shih model) are employed in this work. The performance of these models in predicting flow over these features is investigated. The accuracy of the prediction by using a z 0 type wall function to reproduce the effect of surface roughness on flowfield from these turbulence models is also examined.

Reynolds averaged simulation of flow and heat transfer in ribbed ducts

The accuracy of modern eddy-viscosity type turbulence models in predicting turbulent flows and heat transfer in complex passages is investigated. The particular geometries of interest here are those related to turbine blade cooling systems. This paper presents numerical data from the calculation of the turbulent flow field and heat transfer in two-dimensional (2D) cavities and three-dimensional (3D) ribbed ducts. It is found that heat transfer predictions obtained using the v 2– f turbulence model for the 2D cavity are in good agreement with experimental data. However, there is only fair agreement with experimental data for the 3D ribbed duct. On the wall of the duct where ribs exist, predicted heat transfer agrees well with experimental data for all configurations (different streamwise rib spacing and the cavity depth) considered in this paper. But heat transfer predictions on the smooth-side wall do not concur with the experimental data. Evidence is provided that this is mainly due to the presence of strong secondary flow structures which might not be properly simulated with turbulence models based on eddy viscosity.

The effect of turbulence modelling on the CFD simulation of buoyant diffusion flames

For buoyant diffusion flames, both thermal and mechanical forces affect the turbulence mixing and combustion processes. The computation of individual turbulent heat flux θ′′u i′′ and temperature variance θ″ 2 are necessary and important. This raises questions about the use of traditional two equation k– ε type turbulence models in such applications. The present study is aimed at demonstrating the significant effects of turbulence modelling on the CFD simulation of buoyant diffusion flames. Two different turbulence models are used to compute McCaffrey's flame data. The first model is based on Hanjalic's (Proceedings of the 10th International Heat Transfer Conference, Vol. 1, 1994, p. 1) four-equation turbulence model, which has been modified by the present authors to account for turbulence anisotropy and coupled with an algebraic formulation for Reynolds stresses. The second is the low-Reynolds-number (LRN) k– ε model of Ince and Launder (Int. J. Heat Fluid Flow 10 (1989) 110). The predictions of both models for temperature gradients and buoyancy generation of turbulence are examined. It is found that the generalised gradient diffusion hypothesis formula in the LRN k– ε model severely under-predicts the buoyancy production of turbulent kinetic energy. Considering that the simple gradient diffusion formula in the standard k– ε model with buoyancy modification predicts even lower turbulence production due to buoyancy, fire modellers are cautioned about the use of the two equation k– ε type turbulence models in such applications. Furthermore, it is found that the velocity and temperature predictions by the two turbulence models differ as much as 20% along the centreline. The LRN k– ε model under-predicts the radial spreading rate of the flame, the temperature rise in the persistent flaming region and the lower portion of the intermittent flaming region. For the rest of the intermittent flaming region and the thermal plume, it over-predicts the temperature rise. The modified version of Hanjalic's turbulence model has achieved quantitatively good agreement with the experimental data on the predictions of velocity and temperature distributions. It has also given better predictions for the radial spreading rate of vertical flames and the flame shapes.

Study on Convective Mixing for Thermal Striping Phenomena. Experimental Analyses on Mixing Process in Parallel Triple-Jet and Comparisons between Numerical Methods.

A quantitative evaluation on the thermal striping, in which temperature fluctuation due to convective mixing imposes thermal fatigue on structures, is of importance for reactor safety. As for convective mixing, a water experiment was performed on vertical, parallel triple-jet : a cold jet at the center and hot jets in both sides. Three kinds of calculations based on the finite difference method for the experiment were carried out. Two types of turbulence models were used in the calculations, namely k-e two-equation turbulence model (k-e Model) and low Reynolds number turbulence stress and heat flux equation models (LRSFM). Furthermore, a quasi-direct numerical simulation (DNS) was performed. The DNS could simulate the time-averaged temperature field. The prominent frequency in temperature fluctuation obtained by the LRSFM was in good agreement with that in the experiment. The profile of power spectrum density of temperature fluctuations calculated by the DNS was close to the experimental results.

Fully developed turbulent flow and heat transfer at fiber-flocked surfaces

High-conductivity carbon fibers can be “flocked”, or perpendicularly attached onto surfaces, thus enabling heat transfer enhancement for such fiber-flocked surfaces. An analysis is performed for fully developed turbulent flow and heat transfer in ducts with high-conductivity fibers covering the walls. The fiber volumetric packing density is sparse such that single-cylinder correlations are used for the fiber drag and Nusselt number; this gives rise to body-type terms in the momentum and energy equations for the region near the wall covered with fibers. An eddy-diffusivity type turbulence model is employed, including Laufer core-flow distribution and Van Driest damping, but with a shifted origin. The resulting core- and fiber-region equations are solved by the singular perturbation theory, and matched at the fiber-tip interface, yielding a friction factor function that is fitted to available experimental data with a 32% fiber-length coordinate shift. The results show the variation of the duct Nusselt number with Reynolds number to be similar to that for smooth surfaces, but with an enhancement factor of four for gases. A very strong variation with Prandtl number is predicted for the fiber-flocked surfaces; for liquid metals and gases a moderate enhancement is predicted, whereas for water and viscous liquids an order-of-magnitude enhancement appears possible.

B110 乱流モデルによる複雑地形上の風況予測(オーガナイズドセッション18 : 環境における乱流熱・物質伝達)

Since the wind-power energy is proportional to wind velocity cubed, it is crucial to predict a correct profile of wind in selecting the best site for a wind-power plant. The effects of the ground are often neglected owing to the very large length scale of the real environment. However, the complex terrain affects a profile of wind near the ground. Therefore, we have to consider the ground effects to obtain an exact profile of wind near the ground. In this study, to evaluate the performance of a low-Reynolds-number type turbulence model in an atmospheric boundary layer, we calculated a stable boundary layer flow with a roughness surface. Also, we proposed a turbulence model including the effects of the roughness and the buoyancy. Moreover, to assess the prediction of the turbulence model on a complex terrain, we carried out a simulation of a forward-facing step flow. In this case, it is well known that the turbulence energy is overpredicted by the k-ε model at the stagnation point; thus, we have improved the model introducing the time scale based on the velocity gradient parameter. The proposed model indicates good agreement with the experimental data.

Computational analysis of the influence of process parameters on the flow field of a plasma jet

A computational analysis has been carried out to simulate the temperature, velocity and air content of a plasma jet by using a computational fluid dynamics (CFD) code. Simplified models based on energy and mass conservation were used to link the velocity and temperature at the nozzle inlet with the operating conditions and this is shown to avoid the need for a complex chemical reaction model. The temperature, velocity and composition of the plasma jet were predicted by computational modelling and the results are in agreement with experimental data in the literature. The model takes into account the type and composition of the plasma gas through the specific values of the gas properties and their variation with temperature. The analysis includes a discussion of the effect of mesh size and the most appropriate type of turbulence model to be applied. To widen the generality of the predicted profiles, the temperature and velocity functions were expressed in a normalized form. It was found that in most cases, the normalized functions were not significantly affected by the process parameters, such as arc power and gas flow rate. As a result, these functions can be used to predict temperature and velocity providing their values at the nozzle exit are known. Further work showed that the accuracy of the predictions using the normalized functions is acceptable. This paper provides master curves and contour diagrams for predicting temperature and velocity profiles of the plasma jet as a function of the operating conditions.

Dissimilarity between heat transfer and momentum transfer in a disturbed turbulent boundary layer with insertion of a rod – modeling and numerical simulation

Abstract Numerical computation was carried out for a turbulent boundary layer disturbed by a square rod based on a concept of decomposing each quantity into its three components, i.e., time mean, periodical and stochastic fluctuations, respectively. The effect of stochastic fluctuation of velocity and temperature on the time mean and periodically changing parts of flow and thermal fields was modeled with a k − e type turbulence model. Numerical results of heat transfer coefficient obtained with a modified LS model agree well with the experimental data. Generation of the dissimilarity between the momentum transfer and heat transfer occurring in the studied boundary layer was successfully predicted. Discussion is developed for the washing action exerted by a spanwise vortex and its role of generating the dissimilarity.

Computation of shock/boundary-layer interactions in bump channels with transport-type turbulence models

In this paper, an explicit time-marching finite-volume scheme has been used together with a number of convergence acceleration techniques such as the multigrid strategy. Two types of turbulence models, a Johnson—King (J—K) model and a two-layer k-ε/k-l model, have been incorporated and modified to model internal compressible flows with multiple walls. Some modifications have been made of the inner layer viscosity formulations of the J—K model in order to improve its predictive capability for flow separation. Partially implicit treatment of the transport-type equations of turbulence in the models is adopted, because the source terms in these equations can cause numerical stiffness when there are flow separation, sharp gradients and high cell-aspect ratio near the solid wall. A two-dimensional arc-bump flow investigated experimentally by Liu and Squire [X. Liu and L.C. Squire, Interaction on curved surface at transonic speed, in: Turbulent Shear/Shock Wave Interactions, IUTAM Symposium Palaiseau 1985 (Springer, Berlin Heidelberg 1985) 93–104.] was calculated using the J—K model with satisfactory agreement with the corresponding measurement. Although efficient and accurate, it is found that the J—K model lacks the theoretical generality to be extended to model three-dimensional (3D) complex internal flows with multiple walls. Therefore, a two-layer k-ε model is employed for 3D flow computation. Various measures are adopted to ensure stable and convergent numerical solution. A three-dimensional transonic channel flow with multiple shock/boundary layer interactions was studied with the aforementioned two-layer model and numerical methods. The results are compared with experimental measurements [J. Cahen, V. Couaillier, J. Delery and T. Pot, Validation of Navier—Stokes code using a k-ε turbulence model applied to a three-dimensional transonic tunnel, AIAA paper AIAA-93-0293, AIAA 1993] and numerical results obtained by using a Low-Reynolds-Number (LRN) k-ε model [VUB/FFA, Turbulence Models in EURANUS and the 3D Delery bump, Technical Report SNWP3.3/01, VUB, Pleinlaan 2, 1050 Brussels, Belgium and FFA, P.O. Box 11021, S-161 11 Bromma, Sweden 1993]. Compared with other (LRN) two-equation models, the two-layer model implemented is promising in modeling very complex 3D internal flows in terms of efficiency, robustness and accuracy. The two-layer model permits uniform distribution of flow properties to be specified as initial condition which makes the simulation easier to be carried out.

Compound Open-Channel Flow Modeling with Nonlinear Low-Reynolds k -ε Models

Turbulent flow in compound open channels is studied numerically with nonlinear k-ε turbulence models of low-Reynolds type. Emphasis is given to the flow characteristics and the performance of the models for conditions of low relative depths (up to 0.2547) for which the interaction between main channel and flood plain flow is significant. Experiments and computations indicate that the velocities follow the law of the wall in the interaction region even for such low relative depths. Secondary currents are predicted by a modified version of a previous model; however, the predicted currents are not as strong as the experimental ones. Turbulent shear stresses and especially -uw¯, which is significant for low relative depths, are predicted reasonably by the model, except in the interaction region in the main channel. The turbulent intensities v′ and w′ are captured by the model while u′ is underestimated. A depth-averaged analysis identifies two basic mechanisms that influence the variation of the bed shear stress and suggests a means of assessing the contribution of each mechanism to the deviation of the bed shear stress from its respective two-dimensional value.

Predicting noninertial effects with linear and nonlinear eddy-viscosity, and algebraic stress models

Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coroiolis-modified eddy-viscosity model, a realizable nonlinear eddy-viscosity model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the validation of the turbulence models. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.

RNG Modeling of Turbulent Heat Flux and Its Application to Wall Shear Flows.

In a previous paper[Phys.Fluids 9(1997)], we proposed an improved renormalization group(RNG)theory based on conditional iterative-averaging for turbulent flow with mean shear to derive an eddy-viscosity type turbulence model. In the present paper, we have applied this iterative-averaging RNG theory to the governing equation for a thermal field, and derived a thermal eddy diffusivity representation relevant to the turbulent heat flux. Furthermore, we have also obtained the RNG-based equation for the turbulent Prandtl number Prt, with a hogh Reynolds-number limit as Prt=0.79. The present RNG-based model is applied to the calculations of wall turbulent heat transfer. Agreement with the experiment and the direct simulation data is generally very satisfactory.

Renormalization group theory for turbulence: Eddy-viscosity type model based on an iterative averaging method

The renormalization group (RNG) theory of turbulence is often used for the forced Navier–Stokes equation in order to investigate turbulence models in Fourier space. The strong point of this kind of theory is the ability to construct turbulence models with the aid of the Kolmogorov −5/3 power law for the energy spectrum. In this paper, we have made use of an iterative averaging method proposed by McComb (1990), which does not have the misleading ε-expansion technique developed by Yakhot and Orszag (1986), then applied this method to the derivation of an eddy-viscosity type turbulence model. Using the exact Navier–Stokes equation excluding artificial external forces, we have obtained the eddy-viscosity type turbulence model which is equivalent to the Boussinesq postulate, and its model constant Cμ is determined from only a Kolmogorov constant α.

A model for adiabatic supersonic turbulent boundary layers

An asymptotic analysis of the equations describing supersonic turbulent flow over an adiabatic wall is carried out for high Reynolds numbers, Re, and mainstream Mach numbers, Me=O(1). A general expression for the adiabatic-wall temperature is derived. The asymptotic theory constrains the types of turbulence models that are suitable to represent the effects of viscous dissipation. A simple algebraic turbulence model is proposed and comparisons with measured total enthalpy profile data show good agreement, capturing the overshoot observed in total enthalpy near the boundarylayer edge.