Near-wall modelling in Eulerian–Eulerian simulations

A computational study for an evaluation of the current turbulence models for the prediction of a thermal striping in a triple jet is performed. The tested turbulence models are the two-layer model, the shear stress transport model, and the elliptic relaxation model. These three turbulence models are applied to the prediction of a thermal striping in a triple jet in which detailed experimental data are available. The predicted time-averaged and root-mean-square values of the temperature are compared with the experimental data, and the capability of predicting the oscillatory behavior of the ensemble-averaged temperature is investigated. From these works, it is shown that only the elliptic relaxation model is capable of predicting the oscillatory behavior of the ensemble-averaged temperature. It is also shown that the elliptic relaxation model predicts best the time-averaged temperature and the root mean square of the temperature fluctuation. However, this model predicts a slower mixing at the far downstream of the jet.

This paper presents the work in numerical computations of turbulent mixed convection based on k-ε and elliptic relaxation model. The 2-dimension mixed convection case demonstrated that significant improvements are obtained in predictions of the flow when compared with conventional models from literature and algebraic model. The new elliptic relaxation model is then applied to the computation of several convection flows in 3-dimension turbulent regime. For all simulated cases, good agreement with available experiment and earlier numerical simulation are obtained. It is proved that the new model provides a rational compromise between physically sounder wall treatment and computational robustness making it possible to use moderately dense computational grids.

The elliptic relaxation model of Durbin [J. Fluid Mech., 249 (1993) 465], which has had remarkable success in predicting wide variety of flows, is applied to prediction of free-surface turbulence for the first time. A set of appropriate free-surface boundary conditions for the elliptic relaxation equations is derived by taking account of the balance of dominant terms in the Reynolds-stress transport equations in the vicinity of a free surface. Test calculations for a fully-developed turbulent open-channel flow is conducted. The flow consists of two kinds of impermeable boundaries, a solid wall and a free surface, and hence is quite suitable to the present benchmark flow. It is demonstrated that the proposed boundary conditions do enable elliptic relaxation models to reproduce the correct surface-induced stress anisotropy and that the model properly describes the differences in feature between wall-bounded flows and free-surface flows by its main quality in reproducing the non-local blocking effect, kind of an elementary process of boundary-turbulence interaction. It is also found that the turbulent-transport term plays a central role in characterizing free-surface turbulence, which is therefore quite suitable for critical evaluation of the model performance.

An analysis of the near-wall behavior of the proper orthogonal decomposition (POD) eigenfunctions (see Lumley 1967) derived from direct numerical simulation (DNS) of channel flow of Dinavahi and Zang (1993) is performed. This work is driven in part by a desire to include structure in turbulence models. Although this particular application is in the near wall region (because of availability of the data base), the ideas discussed here are applicable in free shear flows as well. Consistent with previous studies, a low order multi-mode reconstruction of the kinetic energy and Reynolds shear stress suffices. A similar reconstruction of the isotropic dissipation rate is shown to be insufficient, however. An analysis is performed of the multi-mode composition of the dissipation rate in the near-wall region, and it is shown that a significant number of higher-order modes are required to achieve the correct asymptotic consistency in the near-wall region. In an attempt to avoid this problem, a length scale definition is proposed in terms of an integration of the two-point correlation tensor which factors in the presence of the wall. The wall is accounted for by only integrating out to 2y+and not over the entire domain. Viscous and inviscid estimates for the dissipation rate are used in the near-wall and core regions, respectively, in conjunction with this length scale representation, to obtain an estimate of the dissipation rate throughout the domain. The resulting dissipation rate exhibits the proper behavior near the wall and in the inertial layer. Higher-order POD mode estimates of the length scale are computed and compared to that computed using the full correlation tensor from the DNS results of Dinavahi and Zang (1993).

Chapter 33 - Detailed CFD prediction of flow around a 45° pitched blade turbine

Near-wall LES closure based on one-dimensional turbulence modeling

A stochastic method in simulating particles transport and deposition in wall-bounded turbulent flow

In predicting unsteady turbulent flows around a square cylinder usingκ-e turbulence models, choice of right turbulence models was found to be critical. If a proper care is taken to choose a convection scheme and near-wall resolution, the conventional turbulence models may predict an unsteady turbulent flow at low Reynolds numbers with reasonable accuracy. A systematic computation is carried out to identify the effects of the aspect ratio of a rectangular cylinder and of the flow Reynold number on the spatial resolution requirement. It is found in general that the grid resolution requirement is more stringent for a cylinder with a smaller aspect ratio. By investigating high Reynolds number computations, the grid refinement in terms of viscous wall units is found unimportant in accurately predicting the unsteady aerodynamic forces on the cylinder. Instead, resolution of shear layers formed at the forward separation corners is found to be more critical.

ABSTRACTAccurate modelling of near-wall turbulence influenced by roughness is crucial in hydraulic engineering. This study presents modifications on the k-ϵ turbulence model for open-channel flows over rough bed based on reliable particle image velocimetry data. Experiments have been conducted for different roughness heights. Some near-wall turbulence characteristics (e.g. bursting events) are identified and the profiles of mean streamwise velocity, Reynolds shear stress and turbulence intensities are validated with direct numerical simulation data. Experimental results confirm that the coefficient cμ involved in the k-ϵ model varies with roughness Reynolds number in outer region, and with both and y+ (normalized distance from the wall) in near-wall region. A new damping function is reconstructed, and the profile of turbulent kinetic energy close to the wall is analytically obtained. The present modifications accounting for wall roughness effects are further implemented into the k-ϵ model and validation shows that the prediction accuracy for the near-wall flow has been improved.

This thesis is an investigation into computational modelling of the Rotating Cylinder Electrode (RCE) and the Stepped Rotating Cylinder Electrode (SRCE). The Rotating Cylinder Electrode is one of the most widely used methods of producing turbulent flow for the study of corrosion as the flow reaches the turbulent region at quite low rotational speeds. The stepped rotating cylinder was developed at the University of Queensland as a means of investigating erosion-corrosion in disturbed flow [Nesic et al., 2000]. Previous work on the stepped rotating cylinder includes a number of experimental studies and Direct Numerical Simulation (DNS). DNS has also been recently completed for the rotating cylinder electrode. However, DNS is computationally quite expensive for such a complex flow pattern as that produced by the SRCE. Therefore, it becomes necessary to discover an alternate computational method of generating suitably accurate flow data. The majority of turbulence models used today have difficulty simulating the complex flows involved in flow separation and reattachment because of limitations to the accuracy of the wall functions used in the near-wall region. Use of the Reynolds Averaged Navier-Stokes equations (RANS) with various turbulence models will be tested in this thesis with the aim to produce comparable descriptions of the flow, but at much lower computational cost. The thesis will also investigate the near-wall flow around the rotating cylinder electrode using the same models. A number of common turbulence models were selected for investigation. These models were the standard k-e model, the realizable k-e model, the RNG k-e model, the standard k-ω model, the SST k-ω model, and the Reynolds Stress model (RSM). Two-dimensional models of the rotating cylinder geometry and the stepped rotating cylinder geometry were produced using the GAMBIT pre-processor and the computational fluid dynamics (CFD) package FLUENT. The near-wall velocity profile, the wall shear stress and the near-wall turbulent kinetic energy profile were compared to the DNS data for the RCE. For the SRCE simulations, the mean velocity profile, the location of the reattachment point and the near-wall turbulent kinetic energy from the turbulence model simulations are compared with the DNS data provided in Yang et al. [2003] in order to determine the most suitable model for this complex flow pattern. Simulation of the flow for both geometries proved to be difficult to achieve. Meshing of the rotating cylinder electrode was quite simple, but for the stepped rotating cylinder it proved to be difficult to get the mesh to leave the step surface parallel. The flow over the step also had difficulty forming the recirculation pattern expected from the DNS data. For the rotating cylinder electrode flow, the most suitable turbulence model was found to be the standard k-e model. Of the six models, the RNG k-e model proved to be the most suitable for the SRCE geometry. The k-ω turbulence models produced quite poor results for the both rotating cylinder flows. The realizable k-e model also had difficulty modelling the complex recirculation of the SRCE.

Simulation of two-dimensional turbulent forced convection in a plane asymmetric diffuser is performed and the effect of diffuser angle on the flow and heat transfer is reported. This geometry is common in many heat exchanging devices and the convective heat transfer in it has not been examined. The flow field in this geometry, however, has received significant attention already and the results show that the υ2–f turbulence model provides a better comparison with measured velocity distributions than the k–ε turbulence models. This improvement in predictions is due to selecting different turbulent velocity scale and time scale for the eddy viscosity than what is used in conventional two-equation turbulence models. The results show that the diffuser angle influences significantly the flow field (separation and reattachment) and consequently, it must influence significantly the heat transfer. The υ2–f type turbulence models have been shown to provide good heat transfer results for separated flow, and for that reason a k-ε-ζ (or υ2–f type) turbulence model is used in this study. FLUENT 6.2.16 is used as the platform for these simulations and User Defined Functions (UDF) are developed to incorporate this turbulence model (which is not included in the commercial version of the FLUENT code at this time) into this CFD code. The UDF for the k-ε-ζ turbulence model is validated by comparisons with available measured velocity data in an asymmetric diffuser and with available measured heat transfer and velocity data in a backward facing step flow, and with heat transfer data for a normally-impinging jet flow with very good agreement between simulated and measured results.

In this paper, we revisit the eddy viscosity formulation to highlight a number of important issues that have direct implications for the prediction of near-wall turbulence. For steady wall-bounded turbulent flows, we make the equilibrium assumption between rates of production ($P$) and dissipation ($\epsilon $) of turbulent kinetic energy ($k$) in the near-wall region to propose that the eddy viscosity should be given by${\nu }_{t} \approx \epsilon / {S}^{2} $, where$S$is the mean shear rate. We then argue that the appropriate velocity scale is given by$\mathop{(S{T}_{L} )}\nolimits ^{- 1/ 2} {k}^{1/ 2} $where${T}_{L} = k/ \epsilon $is the turbulence (decay) time scale. The difference between this velocity scale and the commonly assumed velocity scale of${k}^{1/ 2} $is subtle but the consequences are significant for near-wall effects. We then extend our discussion to show that the fundamental length and time scales that capture the near-wall behaviour in wall-bounded shear flows are the shear mixing length scale${L}_{S} = \mathop{(\epsilon / {S}^{3} )}\nolimits ^{1/ 2} $and the mean shear time scale$1/ S$, respectively. With these appropriate length and time scales (or equivalently velocity and time scales), the eddy viscosity can be rewritten in the familiar form of the$k$–$\epsilon $model as${\nu }_{t} = \mathop{(1/ S{T}_{L} )}\nolimits ^{2} {k}^{2} / \epsilon $. We use the direct numerical simulation (DNS) data of turbulent channel flow of Hoyas & Jiménez (Phys. Fluids, vol. 18, 2006, 011702) and the turbulent boundary layer flow of Jiménezet al. (J. Fluid Mech.vol. 657, 2010, pp. 335–360) to perform‘a priori’tests to check the validity of the revised eddy viscosity formulation. The comparisons with the exact computations from the DNS data are remarkable and highlight how well the equilibrium assumption holds in the near-wall region. These findings could prove to be useful in near-wall modelling of turbulent flows.

Although engineers are mainly interested in the prediction of mean flow behavior, the turbulence cannot be ignored, because the fluctuations give rise to the extra Reynolds stresses on the mean flow. These extra stresses must be modeled in commercial CFD by selecting convenient turbulence model. The flow inside the control valve is complex and the control valves performance is precisely evaluated by determining the valve coefficient named, flow coefficient. Hence, aim of the present study is to investigate the effect of turbulence model type on the solution accuracy for the valve disk angles 40° and 60° as well as to implement the degree of agreement between experimental and numerical results. The numerical verification has been investigated by FLUENT 6.3 and the valve is meshed by GAMBIT 2. The mesh independent test has been carried out only by standard k-e to evaluate the mesh effectiveness and attain the best accuracy. Among from these several turbulence models which have been studied here are standard k-e, realized k-e, k-ω, and RSM. Butterfly valve, STC model and (DN 50) diameter is chosen to be the test specimen in this research. The results showed that, there is no general turbulent model that can deal successfully with all cases. Numerical and experimental results are in general in good agreement, however are different in details, and showed that, RSM model is the most efficient numerical solver when applied to butterfly valve flow coefficient evaluation. For the future, a significant amount of work still needs to be undertaken in experimental unsteady butterfly valve flow analysis with RSM numerical model.

T HE authors are to be congratulated for providing some light on the significance of the Second Law of Thermodynamics on two-equation turbulence models. The statements made by the Second Law on irreversibility are especially pertinent to turbulence and may in the future allow us a better understanding of the turbulent energy cascade and transition processes. The purpose of this Comment is to point out a few inconsistencies in the turbulence model presented in the above paper, which may help save practitioners of turbulence modeling from pointless programming. First, it is clear with reference to an earlier paper by Busnaina et al. that the value of C used was the usual 0.09, not 0.99. The lack of a low-Reynolds-number damping expression for the turbulent viscosity indicates that the model is not suitable for near-wall or other lowReynolds-number applications. A scrutiny of the proposed dissipation equation indicates that for the equation to balance in the nearwall region, C must equal half of C to insure a quadratic nearwall profile for turbulent kinetic energy, whereas the proposed constants' values were C = C = 1.92. In addition, since the authors were solving for dissipation itself rather than a dissipation variable, the presence of the turbulence kinetic energy k in the denominator of the two leading order terms

A wall-distance-free modification to Wray-Agarwal (WA) one-equation turbulence model is convoked using an elliptic relaxation approach to accurately accounting for non-local characteristics of near-wall turbulence. Model coefficients/functions are parameterized with the elliptic relaxation function to preserve the combined effects of near-wall turbulence and nonequilibrium. The characteristic length scale associated with the elliptic relaxation equation is formulated in terms of viscous and turbulent length scales in conjunction with the invariant of strain-rate tensor. Consequently, non-local effects are explicitly influenced by the mean flow and turbulent variables. A near-wall damping function is introduced to relax the viscous length-scale coefficient adhering to the elliptic relaxation model. Comparisons indicate that the new model improves the accuracy of flow simulations compared to the widely used Spalart-Allmar as model and remains competitive with the SST model.A good correlation is obtained between the current model and DNS/experimental data.