Elliptic Blending Reynolds Stress Model Research Articles

Self-oscillating jets in cooling applications

In the present computational study, an assessment of self-oscillating jets for use in cooling applications is investigated. The jet exits from a square nozzle into a narrow rectangular cavity at a Reynolds number of 54,000 based on nozzle hydraulic diameter and average jet exit velocity. The heated devices, such as electronic chips, are located externally on the surface of the cavity. A three-dimensional numerical simulation of the flow is conducted by solving the unsteady Reynolds-Averaged Navier-Stokes and energy equations to assess the thermal features of the flow field. The unsteady Elliptic Blending Reynolds Stress Model, which consists of transport equations for each of the stress tensor components, was used to model turbulence. The cooling performance of a self-oscillating jet is compared with that of a wall jet and a channel flow for the same flow conditions and the same arrangement of the hot devices. The cooling efficacy of two different arrangements of the heated devices is also evaluated. The self-oscillating jet provides a higher heat transfer for the heated blocks which are located farther from the central region, while the wall jet improves heat transfer around the central region. Self-oscillating jets can improve heat transfer over a larger area when the heated devices are aligned orthogonal to the axis of the nozzle. On a Nusselt number comparative basis, the channel flow provides the least desirable heat transfer performance.

Evaluating the effect of non-Newtonian turbulent blood models within a double-stenosed artery

This article describes the numerical investigation of blood rheology within an artery that includes two narrowing areas via Computational Fluid Dynamics (CFD). Elliptic blending Reynolds stress model and two models of viscosity have been used in this investigation utilizing STAR-CCM+ 2021.2.1. The test model includes two elliptical stenosis with a 2mm distance between them, and the area of stenosis is 75%. Results of normalized axial velocity, turbulent kinetic energy (TKE) and turbulent viscosity ratio (TVR) were evaluated before, through and after the stenosis in order to predict and avoid the real problems that occur from changing the area of the artery. Furthermore, Fractional flow reserve (FFR) was employed to assess the level of risk of stenosis through the artery, which depends on pressure measurements. Corresponding to the author's observation, it was found that the recirculation regions in the area between the stenosis are larger than the area after the stenosis. Moreover, the results of TKE and TVR are almost identical through and downstream of the stenosis, whereas the TKE is slightly higher with the Carreau model than with the Newtonian flow at the upstream and through the first stenosis.

Evaluating the effect of non-Newtonian fluid turbulent flowing for blood within a double-stenosed artery

AbstractThis article describes the numerical investigation of blood rheology within an artery that includes two narrowing areas via Computational Fluid Dynamics (CFD) to offer guidance to the community, especially surgeons, and help them to avoid the risk of stenosis. Elliptic blending Reynolds stress model and two models of viscosity have been used in this investigation utilizing STAR-CCM+ 2021.2.1. The test model includes two elliptical stenosis with a 2mm distance between them, and the area of stenosis is 75%. Results of normalized axial velocity, turbulent kinetic energy (TKE) and turbulent viscosity ratio (TVR) were evaluated before, through and after the stenosis in order to predict and avoid the real problems that occur from changing the area of the artery. Furthermore, Fractional flow reserve (FFR) was employed to assess the level of risk of stenosis through the artery, which depends on pressure measurements. Corresponding to the author's observation, it was found that the recirculation regions in the area between the stenosis are larger than the area after the stenosis. Moreover, the results of TKE and TVR are almost identical through and downstream of the stenosis, whereas the TKE is slightly higher with the Carreau model (arrive to 0.54 J/kg) than with the Newtonian flow (arrive to o.47 J/kg) at the upstream and through the first stenosis.

Numerical study of an impinging jet in cross-flow within and without influence of vortex generator structures on heat transfer

An impinging jet heat transfer in cross-flow within and without influence of a vortex generator pair (VGP) is studied using the unsteady Reynolds averaged Navier-Stokes (URANS) and the large-eddy simulation (LES). The jet Reynolds number is 15,000 and the cross-flow Reynolds number is 30,000. The elliptic-blending Reynolds stress model (EBRSM) is implemented and adapted to capture the effect of the jet close to the wall. A v2 − f model is also implemented to study the ability in predicting such a benchmark. Both models benefit from the elliptic relaxation equation in the entire computational domain. The URANS results are compared with the accurate results of the LES method and also the experimental data. The URANS method successfully presents the flow features of the impinging jet while underpredicts the enhancing heat transfer over the channel bottom wall. The URANS method fails to correctly predict the flow structures forming around the impinging region, because the method is more diffusive than the LES method. When manipulating VGP, a rectangular winglet vortex generator pair is placed in the cross-flow channel and upstream of the jet nozzle to enhance the impinging heat transfer. The VGP increases the Nusselt number at the impingement region. The structures generated by the VGP alter the effects of the cross-flow on the impinging heat transfer. There are Kelvin-Helmholtz instabilities at the shear layer of the jet and the cross-flow in the base flow (the flow without VGP). These instabilities are altered in the flow with VGP. A swirl component is added in the jet to study the effects on the heat transfer. The result shows that for a high or moderate level of swirl, the jet is diffused before the impinging.

Numerical Simulations of Flow and Heat Transfer in a Wall-Bounded Pin Matrix

A detailed computational study was performed for the case of a wall-bounded pin-fin-array in a staggered arrangement, representative of industrial configurations designed to enhance heat transfer. In order to evaluate the level of turbulence modelling necessary to accurately reproduce the flow physics at three (3) different Reynolds numbers (3,000, 10,000 and 30,000), four models were selected: two eddy-viscosity URANS models (k-ω-SST and ϕ-model), an Elliptic Blending Reynolds-stress model (EB-RSM) and Large Eddy Simulation (LES). Global comparisons for the pressure loss coefficients and average Nusselt numbers were performed with available experimental data which are relevant for industrial applications. Further detailed comparisons of the velocity fields, turbulence quantities and local Nusselt numbers revealed that the correct prediction of the characteristics of the flow is closely related to the ability of the turbulence model to reproduce the large-scale unsteadiness in the wake of the pins, which is at the origin of the intense mixing of momentum and heat. Eddy-viscosity-based turbulence models have difficulties to develop such an unsteadiness, in particular around the first few rows of pins, which leads to a severe underestimation of the Nusselt number. In contrast, LES and EB-RSM are able to predict the unsteady motion of the flow and heat transfer in a satisfactory manner.

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.

Influence of multiphase turbulence modelling on interfacial momentum transfer in two-fluid Eulerian-Eulerian CFD models of bubbly flows

Eulerian-Eulerian two-fluid computational fluid dynamic (CFD) models are increasingly used to predict bubbly flows at an industrial scale. In these approaches, interface transfer is modelled with closure models and correlations. Normally, the lateral void fraction distribution is considered to mainly result from a balance between the lift and wall lubrication forces. However, and despite the numerous models available that achieve, at least in pipe flows, a reasonable predictive accuracy, agreement on a broadly applicable and accurate modelling approach has not yet been reached. Additionally, the impact of turbulence modelling on the lateral void fraction distribution has not, in general, been examined in detail. In this work, an elliptic blending Reynolds stress model (EB-RSM), capable of resolving the turbulence field in the near-wall region and improved to account for the contribution of bubble-induced turbulence, is evaluated against best-practice k-ε and high-Reynolds second-moment turbulence closures. Lift and wall lubrication forces are initially deliberately neglected in the EB-RSM. Comparisons for flows in pipes and a square duct show that the EB-RSM reproduces the lateral void fraction distribution, including the peak in the void fraction in the near-wall region, and reaches an accuracy comparable to the other two models noted above. In rod bundles, even if none of the models considered performs with sufficient accuracy, the EB-RSM detects features of the flow that are not predicted by the other two approaches. Overall, the results demonstrate a much more prominent role of the turbulence structure and the induced cross-sectional pressure field on the lateral void fraction distribution than is normally considered. These effects need to be accounted for if more physically-consistent modelling of bubbly flows is to be achieved. The lift force is added to the EB-RSM in the final part of the paper, to provide a two-fluid formulation that can be used as the basis for additional developments aimed at improving the accuracy and general applicability of two-fluid CFD models.

Assessment of RANS models for flow in a loosely spaced bare rod bundle with heat transfer in low Prandtl number fluid

In the present study, a wide range of steady-state and unsteady Reynolds Averaged Navier Stokes (RANS) simulations have been performed to reproduce the turbulent flow and heat transfer in a fuel assembly of the ALFRED reactor. The considered fuel assembly consists of a loosely spaced bare rod bundle with pitch to rod diameter ratio of P/D = 1.32. It is cooled by liquid lead, hence the Prandtl number of the working fluid is very low, i.e. Pr = 0.016. The obtained results are extensively compared with the available Large Eddy Simulation (LES) results. This article is divided in two main parts. In the first part, a thorough assessment of eddy viscosity (i.e. linear and non-linear) and Reynolds stress turbulence models have been performed against the reference LES results. Flow and thermal fields have been qualitatively and quantitatively analysed. In general, RANS results are in a good agreement with the LES, however, most of the models severely overpredict wall shear stress and the corresponding pressure drop in the rod bundle. In the second part, URANS simulations have been performed to reproduce a gap vortex street in the considered loosely spaced bare rod bundle. For this purpose, two turbulence models, that gave the best steady-state RANS predictions, i.e. the k-ε cubic and the elliptic blending Reynolds-stress model, are tested as well. However, the gap vortex street in this particular loosely spaced bare rod bundle turned out to be too weak to be predicted by the URANS approach.

Simulations of Twin Turbulent Planar-Like Jets Injected Into a Large Volume Using RANS

The complex behavior of thermal fluids in nuclear reactors require the usage of computational fluid dynamics (CFD) codes for design and analysis. In order to use CFD codes, they require regular benchmark problems to ensure the predictions are reasonable representations of reality. The twin jet water facility (TJWF) designed and built at the University of Tennessee, Knoxville was created for this purpose. The facility features twin planar-like turbulent free shear jets injecting fluid into a transparent tank to study a variety of flow behavior. The experimental work using this facility by Texas A&M University was used for the benchmarking activities. This work was conducted using a steady Reynolds-averaged Navier–Stokes formulation to simulate the flow behavior. It was determined that the standard k–ε and elliptic blending Reynolds stress model (EBRSM) turbulence models can be used to simulate the twin jet behavior with reasonable success for design and analysis activities.

Investigating the impact of non-Newtonian blood models within a heart pump.

A detailed computational fluid dynamics (CFD) study of transient, turbulent blood flow through a positive displacement left ventricular assist device is performed. Two common models for non-Newtonian blood flow are compared to the Newtonian model to investigate their impact on predicted levels of shear rate and wall shear stress. Given that both parameters are directly relevant to the evaluation of risk from thrombus and haemolysis, there is a need to assess the sensitivity to modelling non-Newtonian flow effects within a pulsatile turbulent flow, in order to identify levels of uncertainly in CFD. To capture the effects of turbulence, the elliptic blending Reynolds stress model is used in the present study, on account of superior performance of second moment closure schemes previously identified by the present authors. The CFD configuration includes two cyclically rotating valves and a moving pusher plate to periodically vary the chamber volume. An overset mesh algorithm is used for each instance of mesh motion, and a zero gap technique was employed to ensure full valve closure. The left ventricular assist device was operated at a pumping rate of 86BPM (beats per minute) and a systolic duration of 40% of the pumping cycle, in line with existing experimental data to which comparisons are made. The sensitivity of the variable viscosity models is investigated in terms of mean flow field, levels of turbulence and global shear rate, and a non-dimensional index is used to directly evaluate the impact of non-Newtonian effects. The clinical relevance of the results is reported along with a discussion of modelling uncertainties, observing that the turbulent kinetic energy is generally predicted to be higher in non-Newtonian flow than that observed in Newtonian flow. Copyright © 2016 John Wiley & Sons, Ltd.

Assessment of advanced RANS models against large eddy simulation and experimental data in the investigation of ribbed passages with passive heat transfer

ABSTRACTRough surfaces are widely used to enhance convective heat transfer by the promotion of higher turbulence levels. The present article reports simulations of the flow and heat transfer in a 2-D rib-roughened passage using a number of advanced Reynolds-averaged Navier-Stokes (RANS) turbulence models including eddy-viscosity models (EVM) and a Reynolds stress model (RSM). Large eddy simulation (LES) is also conducted and results are compared against experimental measurements. In addition, the effects of rib thermal boundary condition on heat transfer are also investigated. In the present work, the blockage ratio of the transversely mounted rectangular ribs is 10% and the rib pitch-to-height ratio of 9 is selected. The Reynolds number, based on the channel bulk velocity and hydraulic diameter, is 30,000. The RANS-based turbulence models investigated here are the k-ω-SST, the v2-f, the ϕ-f, and the elliptic blending RSM. All computations are undertaken using the commercial and industrial CFD codes STAR-CD and Code_Saturne, respectively. Of all the models, the LES predictions were found to be in the best agreement with the experimental data, while the k-ω-SST and EB-RSM returned the least accurate results.

Recent progress in the development of the Elliptic Blending Reynolds-stress model

The Elliptic Blending Reynolds Stress Model (EB-RSM), originally proposed by Manceau and Hanjalić (2002) to extend standard, weakly inhomogeneous Reynolds stress models to the near-wall region, has been subject to various modifications by several authors during the last decade, mainly for numerical robustness reasons. The present work revisits all these modifications from the theoretical standpoint and investigates in detail their influence on the reproduction of the physical mechanisms at the origin of the influence of the wall on turbulence. The analysis exploits recent DNS databases for high-Reynolds number channel flows, spanwise rotating channel flows with strong rotation rates, up to complete laminarization, and the separated flow after a sudden expansion without and with system rotation. Theoretical arguments and comparison with DNS results lead to the selection of a recommended formulation for the EB-RSM model. This formulation shows satisfactory predictions for the configurations described above, in particular as regards the modification of the mean flow and turbulent anisotropy on the anticyclonic or pressure side.

Particle dispersion and turbulence modification in a dilute mist non-isothermal turbulent flow downstream of a sudden pipe expansion

Flow, particles dispersion and heat transfer of dilute gas-droplet turbulent flow downstream of a pipe sudden expansion have been numerically investigated for the conditions of heated dry wall. An Euler two-fluid model with additional turbulence transport equations for gas and particulate phases was employed in the study. Gas phase turbulence was modelled using the elliptic blending Reynolds stress model of Fadai-Ghotbi et al. (2008). Two-way coupling is achieved between the dispersed and carrier phases. The partial equations of Reynolds stresses and temperature fluctuations, and the turbulent heat flux equations in dispersed phase by Zaichik (1999) were applied. Fine droplets get readily entrained with the detached flow, spread throughout the whole pipe cross-section. On the contrary, large particles, due to their inertia, do not appear in the recirculation zone and are presented only in the shear layer region. The presence of fine dispersed droplets in the flow attenuates the gas phase turbulence of up 25 %. Heat transfer in the mist flow increased (more than twice in comparison with the single-phase air flow). Intensification of heat transfer is observed both in the recirculation zone and flow development region in the case of fine particles. Large particles enhanced heat transfer only in the reattachment zone. Comparison between simulated results and experimental data of Hishida et al. (1995) for mist turbulent separated flow behind a backward-facing step shows quite good agreement.

A seamless hybrid RANS-LES model based on transport equations for the subgrid stresses and elliptic blending

The aim of the present work is to develop a seamless hybrid Reynolds-averaged Navier–Stokes (RANS) large-eddy simulation (LES) model based on transport equations for the subgrid stresses, using the elliptic-blending method to account for the nonlocal kinematic blocking effect of the wall. It is shown that the elliptic relaxation strategy of Durbin is valid in a RANS (steady) as well as a LES context (unsteady). In order to reproduce the complex production and redistribution mechanisms when the cutoff wavenumber is located in the productive zone of the turbulent energy spectrum, the model is based on transport equations for the subgrid-stress tensor. The partially integrated transport model (PITM) methodology offers a consistent theoretical framework for such a model, enabling to control the cutoff wavenumber κc, and thus the transition from RANS to LES, by making the Cε2 coefficient in the dissipation equation of a RANS model a function of κc. The equivalence between the PITM and the Smagorinsky model is shown when κc is in the inertial range of the energy spectrum. The extension of the underlying RANS model used in the present work, the elliptic-blending Reynolds-stress model, to the hybrid RANS-LES context, brings out some modeling issues. The different modeling possibilities are compared in a channel flow at Reτ=395. Finally, a dynamic procedure is proposed in order to adjust during the computation the dissipation rate necessary to drive the model toward the expected amount of resolved energy. The final model gives very encouraging results in comparison to the direct numerical simulation data. In particular, the turbulence anisotropy in the near-wall region is satisfactorily reproduced. The contribution of the resolved and modeled fields to the Reynolds stresses behaves as expected: the modeled part is dominant in the near-wall zones (RANS mode) and decreases toward the center of the channel, where the relative contribution of the resolved part increases. Moreover, when the mesh is modified, the amount of resolved energy changes but the total Reynolds stresses remain nearly constant.

Revisiting URANS Computations of the Backward-facing Step Flow Using Second Moment Closures. Influence of the Numerics

Previous studies have shown that Unsteady Reynolds-Averaged Navier–Stokes (URANS) computations are able to reproduce the vortex shedding behind a backward-facing step. The aim of the present work is to investigate not only the quantitative predictions of the URANS methodology concerning the characteristic frequencies, but also the amplitude of the energy of the resolved eddies, by using the Elliptic Blending Reynolds Stress Model. This innovative low-Reynolds number second moment closure reproduces the non-viscous, non-local blocking effect of the wall on the Reynolds stresses, and it is compared to the standard k − ε and LRR models using wall-functions. Consistent with previous studies, in the 2D computations shown in the present article, the vortex shedding is captured with the correct Strouhal number, when second moment closures are used. To complete these previous analyses, we particularly focus here on the energy contained in the unsteady, resolved part and its dependency on the numerical method. This energy is less than 5% of the total energy and is strongly dependent on the mesh. Using a refined mesh, surprisingly, a steady solution is obtained. It is shown that this behaviour can be linked to the very small spatial oscillations at the step corner, produced by numerical dispersion, which act as perturbations that are sufficient to excite the natural mode of the shear layer, when the local Peclet number, comparing convection and diffusion effects, is high enough. This result suggests that URANS is not appropriate to quantitatively predict the amplitude of the large-scale structures developing in separated shear-layers, and that URANS results must be interpreted with care in terms of temporal variations of forces, temperatures, etc., in industrial applications using marginally fine meshes.