Nonlinear Reynolds Stress Research Articles

Prediction of urban airflow fields around isolated high-rise buildings using data-driven non-linear correction models

When it comes to predicting urban airflow, steady Reynolds-averaged Navier-Stokes (SRANS) models that rely on Reynolds stress often face a challenge called the closure problem. This problem involves unresolved structural flaws and uncertainties in the closure coefficients used in the models. Previous attempts to recalibrate coefficients for specific urban flows without breaking the linear constitutive relation have resulted in simulation results constrained by the baseline turbulence model. Therefore, this study aims to enhance the performance of SRANS models by addressing these structural flaws. To achieve this, a novel data-driven framework is proposed. It leverages the deterministic symbolic regression algorithm to discover explicit algebraic expressions for a non-linear Reynolds stress correction model. The robustness of the correction model is ensured by maintaining the linear eddy viscosity model for iterative calculations while keeping the non-linear component frozen. The proposed framework is evaluated using three isolated building cases with varying geometric configurations and inflow boundary conditions. Findings demonstrate that computational fluid dynamics (CFD) predictions incorporating the data-driven non-linear correction model consistently align closer to wind tunnel experimental results compared to both standard and non-linear versions of the k-ε turbulence model. This improvement is reflected in reduced reattachment lengths and more accurate mean velocity distributions in the wake of buildings. However, it should be noted that there is a possibility of overpredicting wind velocity in the windward area. This study introduces valuable insights and additional strategies to enhance the prediction accuracy of SRANS models in urban airflow simulations.

Assessment of nonlinear-low Reynolds number/detached eddy simulation turbulence model for wake flow field simulation of a realistic automotive model

Since the results of wake flow simulation with commonly used turbulence models are unsatisfactory, by introducing a nonlinear Reynolds stress term and combining the DES (Detached Eddy Simulation) model, this paper further validates the nonlinear-LRN (Low Reynolds Number)/DES turbulence model which can predict the flow separation and the reattachment phenomenon more accurately. This model was verified by a wall-mounted hump flow case and was applied to the time-averaged and transient flow field structure analysis of a realistic automotive model with several widely used turbulence models. These simulation results were compared with experimental data, indicating that the nonlinear-LRN/DES model gives better agreement with the experiment and can predict the automobile wake flow structures and aerodynamic characteristics more accurately. Furthermore, the performance of the nonlinear-LRN/DES model in mesh with different refinements is compared, concluding that the new proposed model can obtain high accuracy in the coarse mesh.

High-Order Accurate Numerical Simulation of Supersonic Flow Using RANS and LES Guided by Turbulence Anisotropy

This paper discusses accuracy improvements to Reynolds-Averaged Navier–Stokes (RANS) modeling of supersonic flow by assessing a wide range of factors for physics capture. Numerical simulations reveal complex flow behavior resulting from shock and expansion waves and so, a supersonic jet emanating from rectangular nozzle is considered. PIV based experimental data for the jet is available from literature and is used for validation purposes. Effect of various boundary conditions and turbulence modeling approaches is assessed qualitatively and quantitatively. Of particular interest are the inlet conditions considering the turbulence intensity and the effect of upstream air supply duct, the effect of nozzle wall surface roughness on nozzle internal flow and downstream, wall y+ sensitivity for boundary layer resolution and laminar to turbulent transition modeling. In addition to mesh sensitivity, domain dependency is conducted to evaluate the appropriate domain size to capture the kinetic energy dissipation downstream of the nozzle. To further improve the flow characteristics, accounting for the anisotropy of Reynolds stresses is also one of the focuses. Therefore, non-linear eddy viscosity-based two-equation model and Reynolds stress transport model are also investigated. Additionally, the results of baseline linear (Boussinesq) RANS are compared. Corresponding comparisons with high-fidelity LES are presented. Jet self-similar behavior resulting from all simulation fidelities is assessed and it appears that turbulent flow in LES becomes self-similar, but not in RANS. Finally, various factors such as the nozzle geometry and numerical modeling choices influencing the anisotropy in jet turbulence are discussed.

Validation and Comparisons of Methodologies Implemented in a RANS-VoF Numerical Model for Applications to Coastal Structures

Methodologies to be used in numerical models based on Reynolds-averaged Navier–Stokes (RANS) equations and the volume of fluid (VoF) to deal with waves over coastal structures, which involve wave breaking and overtopping and porous structures, are shown in this manuscript. Two turbulence models, k-ε NLS (non-linear Reynolds stress tensor) and k-ε SCM (stabilized closure model), that are used to avoid the growth of the eddy viscosity, are implemented in the FLUENT® numerical model. Additionally, equations of momentum and turbulence models are adapted to simulate porous media of coastal structures. Comparisons of performance of k-ε NLS, k-ε SCM and standards k-ε and k-ω SST models in several classical cases of regular and random waves on coastal structures are carried out. It was noticed that the standard k-ε turbulence model, and k-ω SST with less intensity, over-predicted eddy viscosity, caused the decay of the free surface elevation and under-estimated wave overtopping discharge. k-ε NLS and k-ε SCM turbulence models have similar performance, with slightly better results of k-ε NLS, showing good agreement with experimental ones.

Wind-buffeting noise characteristics of simple cavity model based on nonlinear LRN/DES turbulence model

In this article, a nonlinear LRN/DES turbulence model is proposed by introducing nonlinear Reynolds stress and scale resolution simulation methods to address the contradiction between computational cost and accuracy of existing turbulence models in wind buffeting noise simulations. After verifying the feasibility of the model by backward-facing step flow, wind buffeting noise simulation is carried out based on the simple cavity model. By comparing with several turbulence models commonly used in wind buffeting noise simulation and experimental results, it is found that the nonlinear LRN/DES model simulates the frequency and sound pressure level of wind buffeting noise of the simple cavity model most accurately, and the capture of the flow field is also closest to the experimental result.

Numerical analysis for wake flow field of Ahmed model based on a nonlinear-LRN/DES turbulence model

PurposeThis paper aims to propose a precise turbulence model for automobile aerodynamics simulation, which can predict flow separation and reattachment phenomena more accurately.Design/methodology/approachAs the results of wake flow simulation with commonly used turbulence models are unsatisfactory, by introducing a nonlinear Reynolds stress term and combining the detached Eddy simulation (DES) model, this paper proposes a nonlinear-low-Reynolds number (LRN)/DES turbulence model. The turbulence model is verified in a backward-facing step case and applied in the flow field analysis of the Ahmed model. Several widely applied turbulence models are compared with the nonlinear-LRN/DES model and the experimental data of the above cases.FindingsCompared with the experimental data and several turbulence models, the nonlinear-LRN/DES model gives better agreement with the experiment and can predict the automobile wake flow structures and aerodynamic characteristics more accurately.Research limitations/implicationsThe nonlinear-LRN/DES model proposed in this paper suffers from separation delays when simulating the separation flows above the rear slant of the Ahmed body. Therefore, more factors need to be considered to further improve the accuracy of the model.Practical implicationsThis paper proposes a turbulence model that can more accurately simulate the wake flow field structure of automobiles, which is valuable for improving the calculation accuracy of the aerodynamic characteristics of automobiles.Originality/valueBased on the nonlinear eddy viscosity method and the scale resolved simulation, a nonlinear-LRN/DES turbulence model including the nonlinear Reynolds stress terms for separation and reattachment prediction, as well as the wake vortex structure prediction is first proposed.

Towards the accurate numerical prediction of thermal hydraulic phenomena in corium pools

The knowledge of heat transfer in corium pools is one of the important issues for corium retention, as it defines the safety margin for vessel integrity. In this regard, in the 90’s the BALI experimental program was performed at the CEA, France. The principal idea was to create a database regarding the heat transfer distribution at corium pool boundaries for in-vessel and ex-vessel configurations at high internal Rayleigh number (1015 to 1017). One of the tasks within the ongoing IVMR project, part of the HORIZON 2020 program, is to assess the up-to-date CFD turbulence models over a wide range of Rayleigh number for the homogenous pool tests of the BALI experiments. In the present study, the assessment of three different turbulence models is performed for two BALI test cases. These turbulence models include a linear k-ε model, a non-linear Reynolds stress model and an advanced turbulent heat flux model known as the AHFM-NRG. After an extensive and careful assessment it has been found that none of the previous models is able to correctly predict the complex heat transfer phenomena appearing in natural convection flow regimes at such high Rayleigh numbers. Hence, a new model is proposed to deal with a wide range of Rayleigh number flow regimes. Accordingly, the results obtained using this new approach are found to be in a very good agreement with the available experimental data.

Excitation of high wavenumber fluctuations by externally-imposed helical fields in edge pedestal plasmas

Two-step mode coupling analyses for nonlinear excitation of the ballooning mode (BM) in pedestal plasma by external helical magnetic field perturbation [Resonant Magnetic Perturbations (RMP)] are presented. This technique allows calculating the effect of higher harmonic sidebands generated by interaction of long scale RMP pump and BM. It is shown that RMP field perturbations can modify the BM growth rate and frequency through nonlinear Reynolds stress and magnetic stress. In particular, it is shown that both stresses can efficiently excite high wavenumber BM fluctuations which, in turn, can enhance the transport in the pedestal. Another notable feature of this analysis is the existence of short scale (high-ky) nonlinear instability at Alfven time scale near the ideal BM threshold boundary.

Numerical prediction of flow induced vibrations in nuclear reactor applications

Flow induced vibration (FIV) plays an important role in nuclear industry. In nuclear reactors, the FIV are caused by a strong interaction between the fuel rods and the turbulent coolant flow around these rods. Numerical prediction of these strongly coupled fluid structure interaction (FSI) has been a challenge and is the main focus of this work. In this article, three aspects of FSI problems are numerically studied. In this first part, two different coupling schemes namely IQN-ILS and Guess-Seidel are thoroughly assessed for a laminar flow single rod experiment performed by Vattenfall (Lillberg et al. 2015). As a next step, a turbulent flow single rod experiment is selected to assess the capabilities of two different RANS models, i.e. a linear k-ωSST and a non-linear Reynolds Stress Model. Lastly, an application based experiment of Chen and Wambsganns (1972) is selected to validate the combined effect of the selected RANS model along with the coupling method.

The Reynolds stress induced by weakly up-down asymmetric ion temperature gradient mode

A weakly up-down asymmetric ion temperature gradient (ITG) mode (formed in the up-down symmetric equilibrium), localized in the bad curvature region, may contribute dominantly to the nonlinear Reynolds stress because its growth rate is higher than the competing modes: the strongly up-down asymmetric modes, and other modes peaked (poloidally) away from the outboard mid-plane. Based on the fluid ITG model, the parameterized analytic wave function is constructed in the two dimensional (2D) Fourier-ballooning representation, and numerically verified by making use of the finite difference methods. Analytic expressions for the poloidal Reynolds stresses, defined on a rational surface, are given for both the weakly and the strongly up-down asymmetric ITG modes. It is shown that the poloidal stresses of both modes can be interpreted as a superposition of a monopole and a dipole structure. For comparison with the experiment, the stresses are calculated for L-mode discharge parameters on five machines. Analytic expressions for the total parallel Reynolds stresses (contributed from all rational surfaces) are also derived for both modes: they are also exhibited, graphically, using a Gaussian wave intensity model.

Influence of bank vegetation and gravel bed on velocity and Reynolds stress distributions

This paper presents the results of a laboratory flume experimental study on the interaction of bank vegetation and gravel bed on the flow velocity (primarily on the location of the maximum velocity, U max ) and the Reynolds stress distributions. The results reveal that the dip of the maximum velocity below the water surface is up to 35% of flow depth and the difference between U max and the velocity at the water surface is considerable in the presence of vegetation on the walls. The zone of the log-law varies from y/ h=2 up to 15 percent of flow depth and it does not depend on distance from the wall. Deviation of the velocity profile in the outer layer over a gravel bed with vegetation cover on the walls is much larger than the case of flow over a gravel bed without vegetation cover on the walls. The presence of vegetation on the walls changes uniform flow to non-uniform flow. This fact can be explained by considering the nonlinear Reynolds stress distribution and location of maximum velocity in each profile at different distances across the flume. The Reynolds stress distributions at the distance 0.02 m from the wall have negative values and away from the wall, they change the sign taking positive values with specific convex form with apex in higher location. Average of von Karman constant κ for this study is equal to 0.16. Based on κ=0.16, the methods of Clauser and the Reynolds stress are compatible for determination of shear velocity.

Derivation of a Nonlinear Reynolds Stress Model Using Renormalization Group Analysis and Two-Scale Expansion Technique

Adopting Yoshizawa's two-scale expansion technique, the fluctuating field is expanded around the isotropic field. The renormalization group method is applied for calculating the covariance of the fluctuating field at the lower order expansion. A nonlinear Reynolds stress model is derived and the turbulent constants inside are evaluated analytically. Compared with the two-scale direct interaction approximation analysis for turbulent shear flows proposed by Yoshizawa, the calculation is much more simple. The analytical model presented here is close to the Speziale model, which is widely applied in the numerical simulations for the complex turbulent flows.

Nonlinear eddy viscosity modelling for turbulence and heat transfer near wall and shear-free boundaries

Abstract New turbulence and turbulent heat flux models are proposed for capturing flow and thermal fields bounded by walls or free surfaces. The models are constructed using locally definable quantities only, without any recourse to topographical parameters. For the flow field, the proposed model is a cubic nonlinear k–e–A three equation eddy viscosity model. It employs dependence on Lumley's stress flatness parameter A, by solving its modelled transport equation as the third variable. Since A vanishes at two-component turbulence boundaries, introducing its dependency enables a turbulence model to capture the structure of turbulence near shear-free surfaces as well as wall boundaries. To close the modelled A equation, an up-to-date second-moment closure is applied. For the thermal field, an explicit algebraic second-moment closure for turbulent heat flux is proposed. The new aspect of this heat flux model is the use of nonlinear Reynolds stress terms in the eddy diffusivity tensor. This model complies with the linearity and independence principles for passive scalar. The proposed models are tested in fully developed plane channel, open channel and plane Couette–Poiseuille flows at several fluid Prandtl numbers. The results show the very encouraging performance of the present proposals in capturing anisotropic turbulence and thermal fields near both wall and shear-free boundaries in the range of 0.025⩽Pr⩽95.

A numerical study of breaking waves in the surf zone

This paper describes the development of a numerical model for studying the evolution of a wave train, shoaling and breaking in the surf zone. The model solves the Reynolds equations for the mean (ensemble average) flow field and the k–ε equations for the turbulent kinetic energy, k, and the turbulence dissipation rate, ε. A nonlinear Reynolds stress model (Shih, Zhu & Lumley 1996) is employed to relate the Reynolds stresses and the strain rates of the mean flow. To track free-surface movements, the volume of fluid (VOF) method is employed. To ensure the accuracy of each component of the numerical model, several steps have been taken to verify numerical solutions with either analytical solutions or experimental data. For non-breaking waves, very accurate results are obtained for a solitary wave propagating over a long distance in a constant depth. Good agreement between numerical results and experimental data has also been observed for shoaling and breaking cnoidal waves on a sloping beach in terms of free-surface profiles, mean velocities, and turbulent kinetic energy. Based on the numerical results, turbulence transport mechanisms under breaking waves are discussed.

A nonlinear low-Reynolds-number κ-ε model for turbulent separated and reattaching flows—I. Flow field computations

An improved version of nonlinear low-Reynolds-number κ-ε model is developed. In this model, the limiting near-wall behavior and nonlinear Reynolds stress representations are incorporated. Emphasis is placed on the adoption of R y (κ 1 2 y v ) instead of γ + ( ≡ τ y v ) in the low-Reynolds-number model for predicting turbulent separated and reattaching flows. The non-equilibrium effect is examined to describe recirculating flows away from the wall. The present model is validated by doing the benchmark problem of turbulent flow behind a backward-facing step. The predictions of the present model are cross-checked with the existing measurements and DNS data. The model performance is shown to be generally satisfactory.

Nonlinear Reynolds stress models and the renormalization group

The renormalization group is applied to derive a nonlinear algebraic Reynolds stress model of anisotropic turbulence in which the Reynolds stresses are quadratic functions of the mean velocity gradients. The model results from a perturbation expansion that is truncated systematically at second order with subsequent terms contributing no further information. The resulting turbulence model applies to both low and high Reynolds number flows without requiring wall functions or ad hoc modifications of the equations. All constants are derived from the renormalization group procedure; no adjustable constants arise. The model permits inequality of the Reynolds normal stresses, a necessary condition for calculating turbulence-driven secondary flows in noncircular ducts.

The steady streaming generated by a vibrating plate parallel to a fixed plate in a dusty fluid

A viscous dusty fluid between two parallel plates, when the top plate is performing both normal and lateral small translatory oscillations, is considered. The unsteady Navier-Stokes equations are solved using the perturbation method. It is observed that nonlinear Reynolds stress introduces a secondary steady streaming. Normal oscillations induce a steady lift while the interaction between normal and lateral oscillations causes a directional net flux. The system thus is seen to be operating as a valveness pump with rigid walls. The presence of dust particles has accelerated the rate of increase of the lift forces. Net pumping is computed for both the fluid and the dust, and certain significant conclusions are drawn for the case Re = 1.

The steady streaming generated by a vibrating plate parallel to a fixed plate

A viscous fluid is sandwiched between two parallel plates. The top plate performs both normal and lateral small translatory oscillations. The unsteady Navier-Stokes equations are solved using perturbations. The nonlinear Reynolds stress causes a secondary steady streaming. It is found that the normal oscillations induce a steady lift while the interaction between normal and lateral oscillations causes a directional net flux. The system thus operates as a valveless pump with rigid walls.

Rotation of a cylinder about an eccentric parallel axis in a viscous fluid

A circular cylinder in an infinite fluid rotates rigidly about a fixed axis which is parallel to, but does not coincide with, its geometric axis. It is found that, depending on the relative magnitude of the Reynolds number R and eccentricity ε, the flow may have two, one or no boundary layers. General solutions for R [Lt ] are obtained. It is found that owing to eccentricity there exist both a flow periodic in the circumferential direction and a non-periodic flow which is a function only of the radial distance from the centre of the cylinder. The non-periodic flow is caused by the nonlinear Reynolds stress and contributes to the torque experienced by the cylinder. The high Reynolds number case, \[ 1 \Lt R \Lt\epsilon^{-\frac{3}{2}}, \] is solved by matched asymptotic expansions. The stream function can be represented by Hankel functions of order 1/3 and a slight decrease in torque is found. In the low Reynolds number case, R [Lt ] 1, the torque is increased owing to eccentricity when R < 0·145 and decreased when R > 0·145. A physical explanation is presented.