Isotropic Eddy Viscosity Model Research Articles

Unsteady shallow meandering flows in rectangular reservoirs: A modal analysis of URANS modelling

Shallow flows are common in natural and human-made environments. Even for simple rectangular shallow reservoirs, recent laboratory experiments show that the developing flow fields are particularly complex, involving large-scale turbulent structures. For specific combinations of reservoir size and hydraulic conditions, a meandering jet can be observed. While some aspects of this pseudo-2D flow pattern can be reproduced using a 2D numerical model, new 3D simulations, based on the unsteady Reynolds-Averaged Navier-Stokes equations, show consistent advantages as presented herein. A Proper Orthogonal Decomposition was used to characterize the four most energetic modes of the meandering jet at the free surface level, allowing comparison against experimental data and 2D (depth-averaged) numerical results. Three different isotropic eddy viscosity models (RNG k-ε, k-ε, k-ω) were tested. The 3D models accurately predicted the frequency of the modes, whereas the amplitudes of the modes and associated energy were damped for the friction-dominant cases and augmented for non-frictional ones. The performance of the three turbulence models remained essentially similar, with slightly better predictions by RNG k-ε model in the case with the highest Reynolds number. Finally, the Q-criterion was used to identify vortices and study their dynamics, assisting on the identification of the differences between: i) the three-dimensional phenomenon (here reproduced), ii) its two-dimensional footprint in the free surface (experimental observations) and iii) the depth-averaged case (represented by 2D models).

Large eddy simulation of non-Newtonian viscous fluids with low grid dependency using an anisotropy-resolving subgrid-scale model

Large eddy simulation (LES) is expected to be an efficient and accurate numerical method for predicting the behavior of non-Newtonian fluids. However, it has been reported that the LES results obtained using eddy viscosity subgrid-scale (SGS) models have a high dependency on the grid resolution for wall turbulence. In order to resolve this problem, in the present study, a mixed SGS model combining an isotropic eddy-viscosity model and a scale-similarity model, which is proposed by Inagaki and Abe (2017), is applied to non-Newtonian fluids obeying the power law. The model performance is tested in plane channel flows and pipe flows for the power-law index n of 0.5–1.15, using a wide range of grid resolution. The results demonstrate that, whereas conventional eddy viscosity SGS models significantly depend on the grid resolution, the present SGS model successfully prevents such grid dependency and yields accurate results even with relatively coarse grids for both pseudoplastic and dilatant fluids, where the modeled SGS shear stress consistently compensates the damped grid-scale (GS) shear stress. When decreasing the value of n (higher shear-thinning property), it has been recognized that the anisotropy of the turbulence is augmented. Since the present SGS model can express the anisotropy of the turbulence stress, the results from n=1 down to n=0.69 are in fairly good agreement with the DNS data, regardless of the grid resolution used, predicting the reduction of wall-friction drag, quantitatively. Upon further decreasing the value of n to 0.5, most eddy viscosity models do not maintain a turbulent state, whereas the present model maintains turbulence and provides results that are in reasonable agreement with the DNS data. The validity of the present model is also confirmed for high-Reynolds-number flows up to Reτ=750, where the grid independency is retained. These results demonstrate that the present model can remarkably reduce the computational cost of LES for non-Newtonian fluids.

The influence of turbulent transport in reactive processes: A combined numerical and experimental investigation in a Taylor-Couette reactor

Turbulent reactive flows are ubiquitous in industrial processes. Decoupling transport effects from intrinsic chemical reactions requires an in-depth understanding of fluid flow physics; computational fluid dynamics (CFD) methods have been widely used for this purpose. Most CFD simulations of reactive liquid-phase flows, where the Schmidt numbers are large, rely on isotropic eddy viscosity models. However, the assumption of turbulent isotropy in most stirred reactors and wall-bounded flows is fundamentally incorrect and leads to erroneous results. Here, we apply a systematic CFD approach to simulate liquid-phase diffusive and convective transport phenomena that occur in a Taylor-Couette (TC) reactor. We resolve the turbulent flow by extracting statistics from large eddy simulation which is used to tune the anisotropic Reynolds stress model. In addition, we conducted a series of turbulent precipitation and mixing studies in a TC reactor that was designed and fabricated in-house. The numerical model is successfully validated against a published torque correlation and it is found to accurately describe the advection and diffusion of chemical species. The validated model is then used to demonstrate key flow properties in the reactor. We define new local turbulent Peclét numbers to characterize the relative increase in diffusivity from turbulent advection and observe a 29% increase in the turbulent contribution as Reynolds number is doubled. Both reactive simulations and experiments show an increase in overall reaction rates with increased turbulence. The results from reactive simulations provide a deeper understanding of flow-kinetics interactions at turbulent conditions.

Lateral edge effects on heat/mass transfer on a finite width surface within a turbulent boundary layer

Numerical simulations of the local heat/mass transfer on a finite width surface within a turbulent boundary layer are presented. Different approaches to the RANS modelling of the turbulent heat/mass flux are compared to Large Eddy Simulations (LES). Mass transfer experiments conducted with the naphthalene sublimation technique are used as validation. The isotropic eddy viscosity model, Simple Gradient Diffusion Hypothesis (SGDH), is shown to underestimate the span-wise effects. Its anisotropic extension, Generalized Gradient Diffusion Hypothesis (GGDH), improves the prediction, but still does not account for near-wall contribution in strongly dissimilar velocity and temperature/concentration fields, even in combination with a wall-sensitive second-moment closure model such as the Elliptic Blending Reynolds Stress Model (EB-RSM). A more complete turbulent heat flux model based on the elliptic blending approach, the Elliptic Blending GGDH (EB-GGDH) presents very good agreement with LES and with the experiments, confirming the need for more advanced turbulent heat flux modelling in applications with strong three-dimensional effects.

A novel method for expressing anisotropy of subgrid-scale components for thermal and scalar fields

Some types of mixed subgrid-scale (SGS) models combining an isotropic eddy-viscosity model and a scale-similarity model can be used to effectively increase the accuracy of large eddy simulation (LES). For example, Abe (2013) recently proposed a stabilized mixed model, which can successfully express the anisotropy of the SGS stress, and remarkably improves the predictive performance for wall turbulence at coarse grid resolutions without sacrificing computational stability. In the present work, this approach is extended for thermal and scalar field modeling to express the anisotropy of SGS heat (scalar) flux. A priori tests using direct numerical simulation data demonstrated that the proposed model can accurately predict the anisotropic SGS heat flux in channel flow and its variation with Prandtl number in the range 0.1–2. Its effectiveness is also confirmed by a posteriori tests under flow conditions corresponding to those in the a priori tests.

An improved anisotropy-resolving subgrid-scale model for flows in laminar–turbulent transition region

Some types of mixed subgrid-scale (SGS) models combining an isotropic eddy-viscosity model and a scale-similarity model can be used to effectively improve the accuracy of large eddy simulation (LES) in predicting wall turbulence. Abe (2013) has recently proposed a stabilized mixed model that maintains its computational stability through a unique procedure that prevents the energy transfer between the grid-scale (GS) and SGS components induced by the scale-similarity term. At the same time, since this model can successfully predict the anisotropy of the SGS stress, the predictive performance, particularly at coarse grid resolutions, is remarkably improved in comparison with other mixed models. However, since the stabilized anisotropy-resolving SGS model includes a transport equation of the SGS turbulence energy, kSGS, containing a production term proportional to the square root of kSGS, its applicability to flows with both laminar and turbulent regions is not so high. This is because such a production term causes kSGS to self-reproduce. Consequently, the laminar–turbulent transition region predicted by this model depends on the inflow or initial condition of kSGS. To resolve these issues, in the present study, the mixed-timescale (MTS) SGS model proposed by Inagaki et al. (2005) is introduced into the stabilized mixed model as the isotropic eddy-viscosity part and the production term in the kSGS transport equation. In the MTS model, the SGS turbulence energy, kes, estimated by filtering the instantaneous flow field is used. Since the kes approaches zero by itself in the laminar flow region, the self-reproduction property brought about by using the conventional kSGS transport equation model is eliminated in this modified model. Therefore, this modification is expected to enhance the applicability of the model to flows with both laminar and turbulent regions. The model performance is tested in plane channel flows with different Reynolds numbers and in a backward-facing step flow. The results demonstrate that the proposed model successfully predicts a parabolic velocity profile under laminar flow conditions and reduces the dependence on the grid resolution to the same degree as the unmodified model by Abe (2013) for turbulent flow conditions. Moreover, it is shown that the present model is effective at transitional Reynolds numbers. Furthermore, the present model successfully provides accurate results for the backward-facing step flow with various grid resolutions. Thus, the proposed model is considered to be a refined anisotropy-resolving SGS model applicable to laminar, transitional, and turbulent flows.

An assessment of turbulence models for linear hydrodynamic stability analysis of strongly swirling jets

Linear stability analysis has proven to be a useful tool in the analysis of dominant coherent structures, such as the von Kármán vortex street and the global spiral mode associated with the vortex breakdown of swirling jets. In recent years, linear stability analysis has been applied successfully to turbulent time-mean flows, instead of laminar base-flows, which requires turbulent models that account for the interaction of the turbulent field with the coherent structures. To retain the stability equations of laminar flows, the Boussinesq approximation with a spatially nonuniform but isotropic eddy viscosity is typically employed. In this work we assess the applicability of this concept to turbulent strongly swirling jets, a class of flows that is particularly unsuited for isotropic eddy viscosity models. Indeed we find that unsteady RANS simulations only match with experiments with a Reynolds stress model that accounts for an anisotropic eddy viscosity. However, linear stability analysis of the mean flow is shown to accurately predict the global mode growth rate and frequency if the employed isotropic eddy viscosity represents a least-squares approximation of the anisotropic eddy viscosity. Viscosities derived from the k−ϵ model did not achieve a good prediction of the mean flow nor did they allow for accurate stability calculations. We conclude from this study that linear stability analysis can be accurate for flows with strongly anisotropic turbulent viscosity and the capability of the Boussinesq approximation in terms of URANS-based mean flow prediction is not a prerequisite.

Corotating Disk Assembly with Turbulent Through Flow

Turbulent flow in a paired corotating disk assembly with through flow is studied numerically. A RANS equation with near wall turbulence model is used in conjunction with an isotropic eddy viscosity model to disclose the mean and turbulent flow properties. The velocities and the mean shear vectors change directions continuously as they move away from wall. The lag angle between them is up to 31° within the log layer and precludes the use of log laws to bridge the near wall flow. A wake less wall law represents the resultant velocity profile in terms of wall coordinates. The disks' moment coefficient is lower than the one found for free-disk flows but it follows the same tendency. The turbulent flow properties are in qualitative agreement with recent experimental measurements and DNS on disk flows.

Large Eddy Simulation of High-Reynolds-Number Free and Wall-Bounded Flows

The ability to simulate complex unsteady flows is limited by the current state of the art of subgrid-scale (SGS) modeling, which invariably relies on the use of Smagorinsky-type isotropic eddy-viscosity models. Turbulent flows of practical importance involve inherently three-dimensional unsteady features, often subjected to strong inhomogeneous effects and rapid deformation, which cannot be captured by isotropic models. Although some available improved SGS models can outperform the isotropic eddy-viscosity models, their practical use is typically limited because of their complexity. Development of more-sophisticated SGS models is actively pursued, and it is desirable to also investigate alternative nonconventional approaches. In ordinary large eddy simulation (LES) approaches models are introduced for closure of the low-pass filtered Navier–Stokes equations (NSE). A promising LES approach is the monotonically integrated LES (MILES), which involves solving the unfiltered NSE using high-resolution monotone algorithms; in this approach, implicit SGS models, provided by intrinsic nonlinear high-frequency filters built into the convection discretization, are coupled naturally to the resolvable scales of the flow. Formal properties of the effective SGS modeling using MILES are documented using databases of simulated free and wall-bounded inhomogeneous flows, including isotropic decaying turbulence, transitional jets, and channel flows. Mathematical and physical aspects of (implicit) SGS modeling through the use of nonlinear flux limiters are addressed using a formalism based on the modified LES equations.

Computation of Flow and Heat Transfer in Two-Pass Channels With 60 deg Ribs

Numerical predictions of three-dimensional flow and heat transfer are presented for a two-pass square channel with and without 60 deg angled parallel ribs. Square sectioned ribs were employed along one side surface. The rib height-to-hydraulic diameter ratio e/Dh is 0.125 and the rib pitch-to-height ratio (P/e) is 10. The computation results were compared with the experimental data of Ekkad and Han [1] at a Reynolds number (Re) of 30,000. A multi-block numerical method was used with a chimera domain decomposition technique. The finite analytic method solved the Reynolds-Averaged Navier Stokes equation in conjunction with a near-wall second-order Reynolds stress (second-moment) closure model, and a two-layer k-ε isotropic eddy viscosity model. Comparing the second-moment and two-layer calculations with the experimental data clearly demonstrated that the angled rib turbulators and the 180 deg sharp turn of the channel produced strong non-isotropic turbulence and heat fluxes, which significantly affected the flow fields and heat transfer coefficients. The near-wall second-moment closure model provides an improved heat transfer prediction in comparison with the k-ε model.

Development of the Isotropic Eddy Viscosity Type SGS Models for the Dynamic Procedure Using Finite Difference Method and its Assessment on a Plane Turbulent Channel Flow

Recent researches on the dynamic Smagorinsky’s model of Germano et al. in the context of using finite difference method (FDM) on a turbulent channel flow have revealed the serious overestimation of mean velocity and streamwise turbulent intensity. The objective of our research here is to develop an isotropic eddy viscosity model that mitigates this problem, as an alternative to Smagorinsky’s model. The procedure proposed by Yoshizawa et al. was utilized and a more consistent eddy viscosity model for the dynamic procedure was obtained. The proposed model was tested in plane turbulent channel flows at Reτ=180 and 590 normalized by the friction velocity and the channel half-width, and predicted better statistics than Smagorinsky’s model. The new model was also found to be less sensitive to a discrete filtering operation than Smagorinsky’s. The organized structures near the wall were also investigated and it was found that the overestimation of the eddy structures reproduced by Smagorinsky’s model is clearly improved by the proposed model.

Numerical Prediction of Flow and Heat Transferin a Two‐pass Square Channel with 90° Ribs

Numerical predictions of three‐dimensional flow and heat transfer are presented for a two‐pass square channel with ° parallel ribs. Square sectioned ribs were employed along the one side surface. The rib height‐to‐hydraulic diameter ratio (e/Dh) is 0.125 and the rib pitch‐to‐height ratio (P/e) is 10. The computation results were compared with the experimental data of Ekkad and Han (1997) at a Reynolds number (Re) of 30,000.A multi‐block numerical method was used with a chimera domain decomposition technique. The finite analytic method solved the Reynolds‐Averaged Navier‐Stokes equation in conjunction with a near‐wall second‐order Reynolds stress (secondmoment) closure model, and a two‐layer k − ε isotropic eddy viscosity model. Comparing the second‐moment and two‐layer calculations with the experimental data clearly demonstrated that the rib turbulators and the 180° sharp turn of the channel produced strong non‐isotropic turbulence and heat fluxes, which significantly affected the flow fields and heat transfer coefficients. The near‐wall second‐moment closure model provides an improved heat transfer prediction in comparison with the k − ε model.

Near-Wall Second-Moment Closure for Rotating Multiple-Pass Cooling Channels

A multiblock numerical method has been employed together with chimera domain decomposition technique to calculate three-dimensional flow and heat transfer in rotating two-pass square channels with smooth walls. The method solves Reynolds-averaged Navier-Stokes equations in conjunction with a near-wall second-order Reynolds stress (second-moment) closure model and a two-layer k-e isotropic eddy viscosity model. The second-moment solutions show that the Coriolis and centrifugal buoyancy forces produced strong nonisotropic turbulent stresses and heat fluxes that significantly affected the friction factors and heat-transfer coefficients in the rotating two-pass square channel, particularly in the 180-deg bend region. The near-wall second-moment closure model provides an improved heat-transfer prediction in comparison with the k-e model

Computation of heat transfer in rotating two-pass square channels by a second-moment closure model

A multiblock numerical method has been employed for the calculation of three-dimensional flow and heat transfer in rotating two-pass square channels with smooth walls. The finite-analytic method solves Reynolds-averaged Navier–Stokes equations in conjunction with a near-wall second-order Reynolds stress (second-moment) closure model and a two-layer k–ε isotropic eddy viscosity model. Comparison of second-moment and two-layer calculations with experimental data clearly demonstrate that the secondary flows in rotating two-pass channels have been strongly influenced by the Reynolds stress anisotropy resulting from the Coriolis and centrifugal buoyancy forces as well as the 180° wall curvatures. The near-wall second-moment closure model provides accurate heat transfer predictions which agree well with measured data.

Analysis of Turbulent Mixing in Rod Bundles with an Anisotropic Turbulent Diffusion Model Based on the Flow Pulsation Phenomenon

A thermal-hydraulic field analysis code using the finite element method is developed to analyze the effects of anisotropic turbulent diffusion and secondary flow on turbulent mixing, which is essential to the nuclear fuel performance analysis.In this study a new model of anisotropic eddy viscosity is developed. The representative value of the anisotropic factor is determined from the scale relation that is derived on the basis of the flow pulsation phenomenon. The spatial distribution is deduced qualitatively from well-known experiments. The flow fields calculated by this code are compared with experimental data and show good agreements, and the predicted turbulent mixing rates are successfully compared with the scale relation derived in the authors’ previous work.The results show that the isotropic eddy viscosity model underestimates the mixing rate and gives the reverse trend as the gap size reduces, and the secondary flow has a minor effect compared with the anisotropic eddy viscosity in the turbulent mixing process. Although the mixing phenomenon of the flow pulsation is a convective process, it can be simulated only by the anisotropic model.

Predicting S-Duct Flow Using a Composite Algebraic Stress Model

An incompressible composite algebraic stress model is presented that accounts for dissipation rate anisotropies and that is validated against S-duct flow. The component algebraic stress and algebraic, anisotropic dissipation rate models have been developed previously, and tested against homogeneous flow. The composite model is developed for integration to the wall and is calibrated against high-Reynolds number plane channel flow data to ensure the correct log-law behavior. The model is validated and analyzed against turbulent flow in an S duct. Both predicted mean flow quantities and turbulence statistics are compared with experimental data, as well as with an isotropic eddy viscosity model and an algebraic stress model with an isotropic dissipation rate. The experimentally observed lag between the shear stress vector direction and the mean velocity-gradient vector direction is qualitatively predicted. The effects of anisotropic dissipation rate on the production of the dissipation term in the dissipation rate equation and on the scalar functions that multiply the linear and nonlinear terms in the tensor expansion are examined relative to the algebraic stress formulation with an isotropic eddy viscosity.

Prediction of complex flow fields using higher-order turbulent closures

The tool of choice in computing turbulent flows of engineering interest is the Reynolds averaged Navier-Stokes equations for the mean motion, coupled with a closure scheme for the unknown higher-order turbulent correlations. The focus of this paper is to discuss some recent advances in turbulent closure schemes and their application to a weakly compressible flow. Specifically highlighted are the development and utilization of formulations for obtaining explicit algebraic stress and dissipation rate models. Results are presented for the flow over a two-dimensional single element airfoil as well as the downstream wake flow using the explicit algebraic stress model with a comparison to both experiment and a standard isotropic eddy viscosity model.

Assessment of a Reynolds Stress Closure Model for Appendage-Hull Junction Flows

A multiblock numerical method, for the solution of the Reynolds-Averaged Navier-Stokes equations, has been used in conjunction with a near-wall Reynolds stress closure and a two-layer isotropic eddy viscosity model for the study of turbulent flow around a simple appendage-hull junction. Comparisons of calculations with experimental data clearly demonstrate the superior performance of the present second-order Reynolds stress (second-moment) closure over simpler isotropic eddy viscosity models. The second-moment solutions are shown to capture the most important features of appendage-hull juncture flows, including the formation and evolution of the primary and secondary horseshoe vortices, the complex three-dimensional separations, and interaction among the hull boundary layer, the appendage wake and the root vortex system.

Submarine Flows Studied by Second-Moment Closure

A multiblock numerical method has been employed for the calculations of viscous flow around two appended submarine configurations used in the DARPA SUBOFF experiments. The method solves Reynolds-averaged Navier-Stokes equations in conjunction with a near-wall second-order Reynolds stress (second-moment) closure model and a two-layer isotropic eddy viscosity model. Comparison of second-moment and two-layer calculations with experimental data clearly demonstrated the significant influence of Reynolds stress anisotropy in the vortex-induced spatial nonuniformity of the propulsor inflow. The second-moment solutions are shown to capture the most important features of submarine flows including the formation and evolution of the appendage root and tip vortices, the development of thick stern boundary layer, and the complex interaction among the horseshoe vortex system and appendage wakes.

PREDICTION OF EVAPORATING SPRAY IN ANISOTROPICALLY TURBULENT GAS FLOW

Numerical investigation was conducted for a confined evaporating isopropyl alcohol spray issuing into a coflowing, heated turbulent air stream. The Eulerian-Lagrangian stochastic model was used for the spray calculations. The gas phase turbulence was modeled using either the isotropic eddy viscosity model or the second-moment transport model for both Reynolds stresses and heat fluxes. Two droplet dispersion models were studied for the Lagrangian trajectory calculations; the conventional particle-eddy encounter model and the time-correlated dispersion model. In the time-correlated model, gas phase turbulent velocity fluctuations were correlated temporally and directionally between two successive time steps in modeling the droplet dispersion. The droplet evaporation was accounted for by the infinite-conduction evaporation model, where the gas-film variable properties were considered using the one-third rule. Detailed numerical results of the liquid droplet phase, i.e., the droplet mean diameters, mass fluxe...