Eddy Viscosity Model Research Articles

Dynamics of turbulent natural convection in a cubic cavity with centrally placed partially heated inner obstacle

Natural convection in a cavity with a partially heated obstacle at the center at the Rayleigh number Ra=1.46×109 is investigated using large eddy simulation (LES). The standard and dynamic Smagorinsky models, as well as the wall-adapting local eddy-viscosity model, are used for the subgrid scales, and the flow statistics are compared with recent experiments. The LES results obtained with different meshes show overall good agreement with the experiments as concerns the flow and heat transfer. Simulation with a non-ideal wall at the adiabatic side of the obstacle is also performed to explain the residual discrepancies observed in the unheated channel. Additional simulations performed with periodic conditions in the spanwise direction are very different from the full three-dimensional (3D) simulations, which demonstrate the significance of 3D effects in the cavity. In particular, periodic simulations show Tollmien–Schlichting kind waves in the transitional region, while the 3D cavity shows an early cross-flow transition to turbulence.

Prediction of heat exchanger efficiency using laminar heat transfer in swirling flow of radiated graphene oxide with nano fluid additives using machine learning technique

Nanotechnology has recently led to new possibilities for enhancing heat transfer in heat exchangers. The remarkable thermal characteristics of graphene oxide (GO)-based nanofluids with nanoscale additions have garnered significant attention in particular. When nanofluids and intricate flow patterns are involved, traditional analytical models frequently fail to appropriately forecast the efficiency of heat exchangers. Analyzed the phenomenon of laminar heat transfer in a heat exchanger that has a swirling flow of fluid dynamics, and pressure drop, and predicted the condensation heat transfer coefficient (HTC) of LHT. The functionalized radiated GO was chosen as nanomaterials in the present for the Pre-processing of Data Methods for managing outliers by machine learning (ML) models, like the CLAHE algorithm. The logarithmic mean temperature difference (LMTD) can be used to determine the temperature driving power for heat transfer within a heat exchanger. The Dynamic Smagorinsky Model (DSLM) and Wall-Adapting Local Eddy-viscosity (WALE) Model are turbulence models primarily designed for capturing turbulent behavior in fluid flows. The Kern technique and Hagen–Poiseuille equation are used for the pressure drop and pumping power needed in a shell and tube in laminar flow through a microtube based on Levenberg–Marquardt and Momentum Algorithm to predict Nusselt number and pressure drop in heat exchangers. The prediction sensitivity of the HTC by an LHT-trained ML model is used to evaluate the performance. The ML methods may be effectively used to forecast and maximize heat exchanger performance in the setting of laminar heat transfer in radiated GO nanofluid swirling flows. The accuracy score of 99%, demonstrating its exceptional predictive capabilities and results has great potential to improve energy efficiency, save operating costs, and advance sustainable practices in various industrial applications.

Numerical analyses of water swirls in aquaculture tanks

Water swirls were observed in both model and prototype aquaculture tanks with bottom drains. This phenomenon was seldom replicated in studies of flow fields of water in aquaculture tanks with computational fluid dynamics. A commonality of these studies is that the linear eddy-viscosity turbulence models were employed. This study delves into the water swirls from the aspect of the generation of the turbulence kinetic energy; both the linear and nonlinear eddy-viscosity turbulence models are used, as well as a Reynolds stress turbulence model. A novel identification method is utilized to pinpoint vortex structures. Numerical results affirm the outstanding performance of the Reynolds stress model to estimate the flow fields of water in aquaculture tanks. Both the linear and nonlinear eddy-viscosity models overestimate the kinetic turbulence energy in the stagnation zone of swirls. The overestimation can be restrained by including the effect of the streamline curvature correction (SCC) to the turbulence production term. Even so, the SCC does not help to improve the estimating accuracy between the Reynolds stress tensor and the mean rate-of-strain tensor. While the nonlinear model offers some improvements, the Reynolds stress model provides a more effectvie solution. After that, we calculate the flow fields of water in aquaculture tanks with different inlet–outlet configurations with the Reynolds stress turbulence model. Both the vertical and horizontal scales of water swirls increase with inlet velocities and Froude numbers, where the Froude number is based on the bottom draining velocity and the water depth above the bottom drain. The vertical distributions of the water residence time in aquaculture tanks are shown to improve the design of tanks.

Numerical analysis of a parallel triple-jet of liquid-sodium in a turbulent forced convection regime

In the present study, we have applied a combined wall-resolving dynamic Large-Eddy Simulation (LES) (for the velocity field) and Direct Numerical Simulation (DNS) (for the temperature field) approach for mixing of parallel triple-jets with different temperatures of liquid sodium in a turbulent forced convection regime. Because of the high thermal conductivity of sodium (a low-Prandtl fluid), we adopted the dynamic Smagorinsky subgrid closure for the unresolved velocity scales, while the thermal scales are fully resolved. Furthermore, the Time-dependent Reynolds-Averaged Navier-Stokes (T-RANS) approach with the high-Reynolds number variant (i.e. with the wall functions as boundary conditions along solid boundaries) of the four-equation eddy viscosity model (k−ε−kθ−εθ) was applied. The fine-mesh LES/DNS provided a close agreement with the experimental data for both velocity and temperature fields (for both first- and second-moments). In contrast, the coarse-mesh LES/DNS overestimated the turbulent kinetic energy profiles at different distances from the inlet plane. The T-RANS results confirmed a good agreement with the mean streamwise velocity and turbulent kinetic energy, as well as the mean temperature profiles. Finally, the analysis of power spectral density distributions of the temperature signal revealed that all simulation techniques captured a dominant flow frequency originating from the induced Kelvin-Helmholtz instabilities between the side and central jets. The presented combined dynamic LES/DNS approach is recommended for future simulations of the turbulent forced convection flows of low Prandtl fluids, especially if thermal fatigue effects need to be predicted correctly.

Numerical study on the performance characteristics of a high-head pump turbine based on the GEKO model

Abstract As the most mature large-scale energy storage facility in the world, the core equipment of pumped storage power stations, the pump-turbine, is currently developing towards high head and large capacity. And the computational fluid dynamics method (CFD) is one of the most important means to research the internal flow mechanism of pump turbines and optimize the hydraulic performance. Turbulence models play an important role in the study of the flow field. Many high-performance RANS turbulence models (such as SST) cleverly combine the advantages of various models to achieve high precision, but they are not universal and their applicability and accuracy for complex flows are still limited. The Generalized k-ω (GEKO) model model may be a good choice among eddy viscosity models as users can adjust the free parameters according to their specific applications. In this study, the internal flow field of pump turbine is numerically simulated by GEKO model with various values of the separation parameter C SEP and the curvature correction parameter C CURV compared with experimental results. The calculation results show that the parameter settings of C SEP and CCURV in GEKO model have a direct impact on the numerical calculation results. The parameter modification of GEKO model has the potential to improve the adaptability and accuracy of turbulence model, and is useful for improving the engineering application of turbulence model.

Modeling of Blockage and Wake Effect: Comparison with Field data

We apply engineering approaches for estimating the induction zone in front of a wind turbine and escalating to the global blockage at wind farm and cluster of farms scale as well accounting for wind farm wake. The methods include the vortex cylinder model and the self-similar model for blockage, and Jensen and Eddy-viscosity models for the wake estimation. To calibrate each model, Reynold Average Navier-Stokes with Actuator disc simulations are employed. Every model’s efficacy is assessed in comparison to the validation data of an operated wind farm in Scotland with more than 100 turbines of 10 MW each. We also examine the widely used process within the wind industry for transferring the application of calibrated wake and blockage models from one wind farm. According to our simulation analysis, blockage causes sideways acceleration and upstream slowdown. This also result in a gradient in the power produced by each turbine on the farm, which, if not properly accounted for, appears to be a wake model constraint. Furthermore, the response of different turbine type in another environment is not effectively predicted by the blockage and wake model, which is based on a particular turbine type and environment.

Effects of Reynolds Number on the Wake Characteristics of a Notchback Ahmed Body

Abstract This paper investigates the effects of Reynolds number on the wake characteristics of a notchback Ahmed body with effective backlight angle, βe=17.8 deg. The Reynolds number based on the body height was varied from 5×103 to 5×104. Prior to the Reynolds number investigation, a Reynolds-averaged Navier–Stokes (RANS) model assessment was performed using nine turbulence models consisting of one- and two-equation eddy-viscosity models and second moment closure models. The standard Spalart–Allmaras model was the only model that accurately predicted the asymmetric time-averaged wake topology, as reported in previous studies, for the βe=17.8 deg notchback Ahmed body at Re=5×104. The drag coefficient decreased with increasing Reynolds number, while the lift coefficient remained constant for Re≥1×104. The wake structure exhibited three regimes: symmetric (Re≤1×104), transitionally asymmetric (1×104<Re≤3.5×104), and fully asymmetric (Re>3.5×104) states. The wake asymmetry was attributed to an imbalance in entrainment from the sides and asymmetric separation from the roof and the C-pillars of the body. The tilting and stretching terms in the vorticity transport equation were used to provide insight into the source of asymmetry in the vorticity field around the body.

Evaluation of flow and flame characteristics of turbulent bluff-body CH4-H2 flame using LES-FPV approach

ABSTRACT This study investigated the flow and flame structure of a bluff-body stabilised CH4-H2 flame using the large eddy simulation (LES) and the flamelet progress variable (FPV) model. The performance of three subgrid-scale (SGS) LES models, i.e. the standard Smagorinsky model (SSM), the wall-adapting local eddy viscosity (WALE) model, and the dynamic Smagorinsky model (DSM) in predicting turbulent and reactive flow characteristics was assessed. Parameters, namely y+ , Pope index (M), vorticity field, and resolved turbulent kinetic energy (kt ), were analysed to determine the predictive capability of the three models. The results demonstrated that DSM and WALE successfully resolved 80% of kt for chosen grid configurations, whereas SSM exhibited discrepancies. The overall trends captured by all three models matched well with the experimental trend with DSM and WALE outperforming SSM in predicting reacting flow fields in the recirculation zone, while SSM produced better predictions in the regions away from the recirculating zone.

Integrating NSGA-II and CFD for enhanced urban airflow prediction: Recalibration of closure coefficients for a nonlinear eddy viscosity model

Accurately predicting urban environmental airflows using the Reynolds-averaged Navier‒Stokes (RANS) approach presents significant challenges due to unsolved closure issues. Previous attempts to address these limitations through coefficient adjustments were constrained by isotropic assumptions, resulting in limited generalizability and reliability, especially for complex building configurations. In this study, we proposed a recalibration approach within a multi-objective optimization framework. Nondominant sorting genetic algorithm-II (NSGA-II) and computational fluid dynamics (CFD) numerical computations were utilized to optimize the closure coefficients of a nonlinear eddy viscosity (NLEV) model, with a focus on improving the accuracy of the mean velocity, turbulent kinetic energy, and airflow characteristic predictions. To ensure the robustness of the model, appropriate objective functions were carefully defined. The proposed approach was evaluated using three-dimensional (3D) building cases related to urban prototypes, and the results demonstrated the necessity of multi-objective optimization. Our findings indicated that the trade-off solution on the Pareto front consistently outperformed the baseline and single-objective optimal versions across different types of urban airflow, demonstrating superior generalizability. The simulation results of this solution exhibited closer agreement with the wind tunnel experimental data and provided more accurate distributions of the time-averaged values and airflow characteristics. The normalized root mean square errors are reduced by about 33 %, 52 %, 35 % and 9 % in velocity, and 31 %, 25 %, 24 % and 11 % in turbulent kinetic energy, respectively. These results underscore the effectiveness of the multi-objective optimization framework in addressing closure issues and improving the prediction accuracy of complex urban environmental airflows.

Extended Eddy-Viscosity Model to Rayleigh-Benard Convection in Cavity

This paper presents a study of developing a numerical turbulent model in a cavity heated from below using eddy viscosity combined with elliptic relaxation approach. The model uses a set of differential equations that consist of kinetic energy, its dissipation, variance of temperature, velocity scale and elliptic relaxation parameter, which are solved using a finite-volume and Navier-Stokes solver. The unresolved stress tensors and heat flux vectors are modelled with an algebraic formula. The discretization method is carried out by CDS, or second-order differencing scheme, and LUDS, or second-order linear upwind scheme. The model is applied to the natural convection heated from below, known as Rayleigh-Benard convection, in a two-dimensional cavity with a height-to-length aspect ratio of 1:1.5, 1:4, and 1:8. The model has been validated using numerical data from DNS (direct numerical simulation) and experiments. The model produced similar results with both DNS and experiments. It was also shown that the model can visualize the main feature of turbulent convective flow in the enclosure for various aspect ratio.

Large-eddy simulation of wind pressures on elevated low-rise buildings

Residential buildings in coastal communities are often elevated to mitigate flooding and wave-surge impacts. However, the elevations change the local wind field characteristics and may increase the aerodynamic pressure on buildings. Post-event reconnaissance showed that elevated buildings experienced severe structural damage to the roofs, walls, and floors during major hurricanes. Currently, our understanding of aerodynamic pressure on elevated houses is limited. In this paper, a large eddy simulation (LES)-based method is developed to better understand the wind effects on elevated buildings. The inflow generation method, discretizing and synthesizing random flow generation, is adopted to generate inflow boundary conditions satisfying the target spectrum. Two sub-grid scale models, the Smagorinsky and wall-adapted local eddy-viscosity models, are employed to represent the unresolved small-scale eddies. It is found that the eddy structure sizes can strongly affect the pressure fluctuations at the eddy separation zones. The present study advances the understanding of aerodynamics on elevated buildings and provides a reference for future LES-based research on wind effect modeling.

Autonomous large-eddy simulations of turbulence using eddy viscosity derived from the subgrid-scale similarity stress tensor

A previously developed method for large-eddy simulations (LES), based on spectral eddy-viscosity models, is generalised to the physical space representation. The method estimates the subgrid-scale (SGS) energy transfer using a similarity-type model expression for the SGS tensor obtained using Gaussian filtering of velocity fields advanced in the simulations. Following steps for the spectral space representation, the SGS transfer in the physical space is used to obtain a spatially varying eddy viscosity at each time step in LES. The computed eddy viscosity is employed to model the SGS stress tensor in the familiar Boussinesq form for use in LES. The method is tested in LES of isotropic turbulence at high Reynolds numbers where the inertial range dynamics is expected and for lower Reynolds number decaying turbulence under conditions of the classical Comte-Bellot and Corrsin experiments. In both cases the agreement with reference data is very good and the SGS transfer computed for the proposed eddy-viscosity model is highly correlated with the transfer computed for the similarity-type stress tensor.

A tensor basis neural network-based turbulence model for transonic axial compressor flows

Traditional turbulence models encounter limitations when simulating intricate flows within transonic axial compressors. In contrast, recent advancements in machine learning turbulence models have demonstrated enhanced potential in refining the precision of turbulence modeling. Notably, the tensor basis neural network (TBNN) methodology has successfully developed non-linear eddy viscosity turbulence models. These models possess the capability to capture the anisotropic characteristic of Reynolds stress. However, applying machine learning non-linear eddy viscosity models to aircraft turbomachinery remains relatively infrequent. Current research mainly focuses on linear eddy viscosity turbulence models based on the Boussinesq hypothesis that presupposes isotropy in Reynolds stress. In this work, we introduce a non-linear eddy viscosity turbulence model, denoted as the k-ω-SST-TBNN model based on the TBNN framework. This model has been employed to simulate the transonic axial compressor NASA Rotor 37. The TBNN is trained using large eddy simulation (LES) results datasets. The importance of input scalar features is analyzed using the random forest method, from which significant and low-degree variables are selected as inputs for the TBNN. Furthermore, this study proposes including the turbulent Mach number as one of the extra features, representing fluid compressibility, thereby extending the computational mass flow rate range of compressor. Additionally, this paper proposes a method involving the weighted average of Reynolds stress, combining the high-precision but less robust TBNN predictions with results based on the Boussinesq assumption to enhance the turbulence model's robustness. The trained k-ω-SST-TBNN model undergoes validation on Rotor 37, where it exhibits a marked improvement in the prediction of overall performance, tip-gap vortex, and radial distribution of flow parameters. The model also displays a commendable capacity for generalization.

Coupling of Eddy-Viscosity-Scale Reynolds-Stress Model with an Algebraic Transition Model

Attempts to extend a Reynolds-stress model (RSM) for transition flow simulations have begun to cause concern in recent years based on the fact that the RSM has more potential than an eddy viscosity model when applied to complex three-dimensional flowfields. In terms of the RSM, however, coupling more transport equations will further increase its complexity (may worsen robustness and convergence rate). In this paper, a γ-based algebraic transition model originating from the SA-BC model is coupled with an νt-scale RSM (EV-RSM) to form a new transition/turbulence model, called tEV-RSM. Some numerical tests are conducted with a fifth-order scheme, WCNS, including the well-known T3 flat plate series, a two-dimensional airfoil (S809), a two-dimensional three-element airfoil (30P-30N), a three-dimensional prolate-spheroid, and a three-dimensional circular cylinder. The proposed model is compared with the SA-BC and γ-Reθt SST models, which indicates that it can predict the flows primarily governed by Tollmien–Schlichting transition or bypass transition well and has an advantage in predicting the flows with detached separation. Meanwhile, the iteration convergence rate of the tEV-RSM is fast enough considering it as a seven-equation model.

A turbulence model: Model, analysis, and algorithm

The standard eddy viscosity model is commonly used to simulate turbulence, but there exist difficulties in simulating the backscatter of the non-statistical equilibrium turbulence. In this work, we construct a novel modified eddy viscosity model based on a simplified Cebeci–Smith equation, which is applied to the non-equilibrium turbulence. Moreover, we analyze some properties of the model and propose a fully discrete scheme, which is proven to be stable and convergent. Finally, some numerical examples are presented to test the theoretical prediction of the proposed scheme, and intermittent backscatter is captured and observed by simulating the established model.

Large eddy simulations of turbulent pipe flows at moderate Reynolds numbers

Wall-bounded turbulence is relevant for many engineering and natural science applications, yet there are still aspects of its underlying physics that are not fully understood, particularly at high Reynolds numbers. In this study, we investigate fully developed turbulent pipe flows at moderate-to-high friction velocity Reynolds numbers (361≤Reτ≤2000), corresponding to bulk velocity-based Reynolds numbers of 11 700≤Reb≤82 500, using wall-modeled large eddy simulations (LES) in OpenFOAM. A grid convergence study is performed for Reτ=361, followed by an investigation of the accuracy of various subgrid-scale stress models for the same Reynolds number. Results show that the wall-adapting local eddy (WALE) model performs well compared to experiments and direct numerical simulations, while one-equation eddy-viscosity model and Smagorinsky are too dissipative. LES utilizing WALE is then performed for four different Reynolds numbers with gradually refined grids, revealing excellent agreement with DNS data in the outer region. However, a significant deviation from DNS data is observed in the sub-viscous layer region, indicating the need for further mesh refinement in the wall-normal direction to accurately capture the smallest-scale motions' behavior. Additional mesh sensitivity analysis uncovered that, as the Reτ value rises, it becomes crucial for a grid to adhere to the condition of Δx+≤20−25 and Δz+≤10 in order to precisely capture substantial large and small-scale fluctuations. Overall, the WALE model enables accurate numerical simulations of high-Reynolds number, wall-bounded flows at a fraction of the computational cost required for temporal and spatial resolution of the inner layer.

Eddy-viscosity-improved resolvent analysis of compressible turbulent boundary layers

An improved resolvent analysis is proposed in the regime of compressible turbulent boundary layers. To better model nonlinear processes in the input, the resolvent framework is augmented by adding eddy viscosity. To this end, we propose two eddy-viscosity models: a modified Cess eddy-viscosity model coupling the compressibility transformation and outer-layer correction, and a new eddy-viscosity model based on an empirical relationship and mixing-length theory. Both are incorporated into the resolvent operator to examine the performance of the eddy-viscosity-improved resolvent-based reduced-order modelling. Results of the augmented resolvent analysis are compared qualitatively and quantitatively with the first leading mode of spectral proper orthogonal decomposition, by checking the profiles and cross-spectral densities of velocities, density and temperature in two hypersonic turbulent boundary layers under different wall conditions. Higher accuracy of the turbulence prediction is achieved by adding the proposed eddy-viscosity models, particularly for the energetic cycle in the outer-layer region where strong nonlinear energy transfer exists.

Revisiting Tensor Basis Neural Network for Reynolds stress modeling: Application to plane channel and square duct flows

Recent advances in computing power devoted to Computational Fluid Dynamics (CFD) have opened up a new avenue for addressing the turbulence closure problem through Machine Learning (ML). Several Tensor Basis Neural Network (TBNN) frameworks aimed at enhancing turbulence Reynolds-Averaged Navier–Stokes (RANS) modeling have recently been proposed in the literature as data-driven constitutive models for systems with known invariance properties. However, persistent ambiguities remain regarding the physical adequacy of applying the General Eddy Viscosity Model (GEVM) within these frameworks. This work aims at investigating this aspect in an a priori stage for better predictions of the Reynolds stress anisotropy tensor, while preserving the Galilean and rotational invariances. In particular, we propose a general framework providing optimal tensor basis models for two types of canonical flows with increasing complexity: Plane Channel Flow (PCF) and Square Duct Flow (SDF). Subsequently, deep neural networks based on these optimal models are trained using state-of-the-art strategies to achieve a balanced and physically sound prediction of the full anisotropy tensor. A priori results obtained by the proposed framework are in very good agreement with the reference Direct Numerical Simulations (DNS) data. Notably, our shallow network with three layers excels in providing accurate predictions of the anisotropy tensor for PCF at unobserved friction Reynolds numbers, both in interpolation and extrapolation scenarios. The learning of the SDF case is more challenging because of its physical nature but also due to a lack of training data at various regimes. We propose a numerical strategy to alleviate this problem based on Transfer Learning (TL). In order to more efficiently generalize to an unseen intermediate Reτ regime, we take advantage of our prior knowledge acquired from a training with a larger and wider dataset. Our results indicate the potential of the developed network model, and demonstrate the feasibility and efficiency of the TL process in terms of training data size and training time. Based on these results, we believe there is a promising future by integrating these neural networks into an adapted in-house RANS solver.

Vortex model of plane turbulent air flows in channels

We present a theoretical model of plane turbulent flows based on the previously proposed equations, which take into account both the longitudinal motion and the vortex tube rotation. Using the simple model of eddy viscosity, we obtain the analytical expressions for the mean velocity profiles of stationary turbulent flows. In particular, we consider the near-wall flow over a flat plate in a wind tunnel as well as Couette and Poiseuille flows in rectangular channels. In all these cases, the calculated velocity profiles are in good agreement with experimental data and results of direct numerical simulations.

Vertical structure of flows on a shallow reef flat: A coral reef surf zone

We present a 1D model of the vertical structure of wave-driven flows on a shallow coral reef and compare that model to observations made on the reef flat on Ofu, American Samoa. This model is based on longstanding approaches to modeling flow structure in beach surf zones including the averaged effects of breaking and broken surface waves. Waves enter the model through an imbalance between the radiation stress and barotropic pressure gradients that exists below the troughs of the waves, which is offset by turbulent shear stress gradients. Assuming that the depth varying eddy viscosity takes the form found in open channel flows, i.e., a parabola, the horizontal momentum equation can be integrated twice with respect to height to derive the distribution with height of the velocity. The resulting theory is compared to observations made on a reef flat located on Ofu, American Samoa. Using a velocity scale in the eddy viscosity model that is proportional to the rms wave velocity, modeled profiles match observations reasonably well (average skill= 0.66), although there is some ambiguity introduced because matching observations and theory requires the addition of a correction that is found to depend on the square of the rms wave height.