Linear Eddy Viscosity Turbulence Models Research Articles

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.

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.

Epistemic uncertainty quantification for Reynolds-averaged Navier-Stokes modeling of separated flows over streamlined surfaces

It is well known that linear eddy-viscosity turbulence models can introduce uncertainty in predictions for complex flow features such as separation and reattachment. The goal of this paper is to advance our understanding of a physics-based approach to quantify this turbulence model form uncertainty in Reynolds-averaged Navier-Stokes simulations of separated flows over streamlined surfaces. The methodology is based on perturbing the modeled Reynolds stresses in the momentum equations; perturbations are defined in terms of a decomposition of the Reynolds stress tensor, i.e., based on the tensor magnitude and the eigenvalues and eigenvectors of the normalized anisotropy tensor. We demonstrate that the accuracy of the predicted Reynolds stress magnitude is strongly influenced by the turbulence production term and subsequently explore the anisotropy tensor eigenvalue and eigenvector perturbations that maximize or minimize turbulence production; these could be expected to provide bounds on the prediction of separation and reattachment locations. The method uses two user-defined parameters to identify the spatial extent of the perturbed region and the magnitude of the eigenvalue perturbations. Results for the flow over a periodic wavy wall and over a three-dimensional hill indicate that the perturbations that increase turbulence production decrease the extent of the separation region, while perturbations that decrease production increase the region of separated flow. The predicted bounds can successfully encompass the reference data, provided the extent of the perturbed region and the eigenvalue perturbation magnitudes are sufficiently large. Importantly, we observed a monotonic behavior of the magnitude of the predicted bounds as a function of the two user-defined parameters.

Using the Reynolds Stress Model to Predict Shock-Induced Separation on Transport Aircraft

Additional results about the wing-body of the NASA Common Research Model at flight conditions derived from those of the AIAA Computational Fluid Dynamics Drag Prediction Workshop are introduced in this Paper. An initial assessment compared the widely used shear stress transport model with the full Reynolds stress model as two possible closures for the Reynolds-averaged Navier–Stokes problem. The study, based on the 6th AIAA Computational Fluid Dynamics Drag Prediction Workshop, confirmed the limitations of linear eddy-viscosity turbulence models in highly anisotropic turbulent flows. A side-of-body separation larger than previous experiments was predicted by the shear stress transport model. By comparison, the study revealed that the Reynolds stress model is capable of simulating higher-incidence transonic flight as the trends observed in the results were in overall good agreement with the experiment. The aim herein was to investigate the high-incidence transonic aerodynamics about the Common Research Model. Using Reynolds-Averaged Navier–Stokes closed with the Reynolds stress model, the aeroelastically deformed Common Research Model was then simulated at incidences outside of the Drag Prediction Workshop remit. The evolution of shock-induced boundary-layer separation was observed. A separation bubble was first predicted at an incidence of 3.5 deg, then developed in the chordwise and spanwise directions, triggering the stall of the aircraft at an incidence of 5.75 deg. Using shear lines helps one understand the three-dimensionality of this phenomenon as large areas of crossflow are present, starting in the wing-kink region and extending toward the wing tip.

The deviation from parallel shear flow as an indicator of linear eddy-viscosity model inaccuracy

A marker function designed to indicate in which regions of a generic flow field the results from linear eddy-viscosity turbulence models are plausibly inaccurate is introduced. The marker is defined to identify regions that deviate from parallel shear flow. For two different flow fields it is shown that these regions largely coincide with regions where the prediction of the Reynolds stress divergence is inaccurate. The marker therefore offers a guideline for interpreting results obtained from Reynolds-averaged Navier-Stokes simulations and provides a basis for the further development of turbulence model-form uncertainty quantification methods.

Nonlinear turbulence models for predicting strong curvature effects

Prediction of the characteristics of turbulent flows with strong streamline curvature, such as flows in turbomachines, curved channel flows, flows around airfoils and buildings, is of great importance in engineering applications and poses a very practical challenge for turbulence modeling. In this paper, we analyze qualitatively the curvature effects on the structure of turbulence and conduct numerical simulations of a turbulent U-duct flow with a number of turbulence models in order to assess their overall performance. The models evaluated in this work are some typical linear eddy viscosity turbulence models, nonlinear eddy viscosity turbulence models (NLEVM) (quadratic and cubic), a quadratic explicit algebraic stress model (EASM) and a Reynolds stress model (RSM) developed based on the second-moment closure. Our numerical results show that a cubic NLEVM that performs considerably well in other benchmark turbulent flows, such as the Craft, Launder and Suga model and the Huang and Ma model, is able to capture the major features of the highly curved turbulent U-duct flow, including the damping of turbulence near the convex wall, the enhancement of turbulence near the concave wall, and the subsequent turbulent flow separation. The predictions of the cubic models are quite close to that of the RSM, in relatively good agreement with the experimental data, which suggests that these models may be employed to simulate the turbulent curved flows in engineering applications.

Coanda Wall Jet Calculations Using One- and Two-Equation Turbulence Models

The wall jet over a convex surface, the Coanda wall jet, has many potential technical applications, such as circulation control of airfoils. Reynolds-averaged Navier-Stokes is a potentially very powerful tool for Coanda wall jet calculations. A number of common linear eddy-viscosity turbulence models were used for Reynolds-averaged Navier-Stokes calculations of a turbulent Coanda wall jet experiment. Calculations were also carried out with an explicit algebraic stress model. The differences in the computed results were shown to be large depending on what turbulence model was employed. The k-w model was then employed for three-dimensional Reynolds-averaged Navier-Stokes calculations where the downstream evolution of streamwise vortices in the turbulent wall jet was studied for various spanwise wavelengths and forcing amplitudes. It was found that a centrifugal instability of the turbulent mean flow may lead to the streamwise growth of longitudinal vortices. Beyond a certain disturbance amplitude threshold the relative phase of the vortices had a noticeable impact on the amplification rates and the mean flow characteristics were affected by the added wall normal momentum exchange.

A New Model for Boundary Layer Transition Using a Single-Point RANS Approach

This paper presents the development and implementation of a new model for bypass and natural transition prediction using Reynolds-averaged Navier-Stokes computational fluid dynamics (CFD), based on modification of two-equation, linear eddy-viscosity turbulence models. The new model is developed herein based on considerations of the universal character of transitional boundary layers that have recently been documented in the open literature, and implemented into a popular commercial CFD code (FLUENT) in order to assess its performance. Two transitional test cases are presented: (1) a boundary layer developing on a flat heated wall, with free-stream turbulence intensity Tu∞ ranging from 0.2 to 6%; and (2) flow over a turbine stator vane, with chord Reynolds number 2.3×105, and Tu∞ from 0.6 to 20%. Results are presented in terms of Stanton number, and compared to experimental data for both cases. Results show good agreement with the test cases and suggest that the new approach has potential as a predictive tool.

Transition on a flat plate with a semi-circular leading edge under uniform and positive shear free-stream flow

The effect of the free-stream velocity profile on the transition from laminar to turbulent flow on a flat plate was studied experimentally and numerically and it is presented in this paper. The flows investigated are based on the T3L test case of the ERCOFTAC Special Investigation Group for transition. According to this test case, the boundary layer development on a flat plate with a semi-circular leading edge is examined by means of transition due to separation, under various free-stream conditions concerning the turbulence intensity and velocity magnitude. In the present work, two free-stream velocity distributions were studied. The first was a uniform velocity one and the second, with a mean shear velocity profile with positive gradient, ∂ U/ ∂y=27.7 s −1. Measurements using hot-wire anemometry were taken in two primary regions: far upstream of the flat plate to observe the velocity and turbulence distributions and near the flat plate to capture the boundary layer development and the transition phenomenon. The effect of the two free-stream velocity distributions was studied and it was shown that for both velocity distributions a recirculation region of the flow occurred near the flat plate wall that led to transition dominated by the boundary layer separation. For the positive velocity gradient the separation region was smaller compared to the case of uniform free-stream profile. Both cases were also studied computationally. Two widely used linear eddy-viscosity turbulence models, the k– ε and the k– ω with specific low Reynolds formulations were applied and in addition, a non-linear eddy-viscosity based on the k– ε model has been implemented. In general, all the k– ε models gave satisfactory predictions for both flow cases regarding the predicted velocity distributions, while the k– ω model gave poor results. Concerning the longitudinal Reynolds stress distributions in the near-wall region, the non-linear k– ε model gave the best predictions inside the separation zone but it over predicted the corresponding values beyond the reattachment point while beyond the separation the linear models predicted the longitudinal stresses in a more satisfactory way.

Prediction of High-Lift Flows Using Turbulent Closure Models

The flow over two different multi-element airfoil configurations is computed using linear eddy viscosity turbulence models and a nonlinear explicit algebraic stress model. A subset of recently-measured transition locations using hot film on a McDonnell Douglas configuration is presented, and the effect of transition location on the computed solutions is explored. Deficiencies in wake profile computations are found to be attributable in large part to poor boundary layer prediction on the generating element, and not necessarily inadequate turbulence modeling in the wake. Using measured transition locations for the main element improves the prediction of its boundary layer thickness, skin friction, and wake profile shape. However, using measured transition locations on the slat still yields poor slat wake predictions. The computation of the slat flow field represents a key roadblock to successful predictions of multi-element flows. In general, the nonlinear explicit algebraic stress turbulence model gives very similar results to the linear eddy viscosity models.