Numerical Simulation of Backward Facing Step Flow Using Nonlinear Eddy Viscosity Model

A numerical investigation of accelerated boundary layers (BL) has been performed using linear and non-linear eddy viscosity models (EVM). The acceleration parameters (KS) investigated range between 1.5×10−6 and 3.0×10−6. The one equation (k-l), Spalart Allmaras (SA) and the two-equation Menter SST and Chien models in their standard forms are found to be insensitive to acceleration. Nevertheless, proposed modifications for the SA, Chien and the k-l models significantly improved predictions. The major improvement was achieved by modifying the damping functions in these models and also an analogous source term, E, for the Chien model. Encouraging agreement with measurements is found using the Launder Sharma (LS), Cubic and Explicit Algebraic Stress Models (EASM) in their standard forms. The cubic model best predicted the turbulence quantities. Investigations confirm that it is practical for Reynolds Average Navier-Stokes (RANS) models to capture reversion from the turbulent to laminar state albeit for equilibrium sink type flows.

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. The Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.

This work presents numerical results for heat transfer in turbulent flow past a backward-facing-step channel with a porous insert using linear and non-linear eddy viscosity macroscopic models. The non-linear turbulence models are known to perform better than classical eddy-diffusivity models due to their ability to simulate important characteristics of the flow. Parameters such as porosity, permeability and thickness of the porous insert are varied in order to analyze their effects on the flow pattern, particularly on the damping of the recirculating bubble after the porous insertion. The numerical technique employed for discretizing the governing equations is the control-volume method. The SIMPLE algorithm is used to correct the pressure field. Wall functions for velocity and temperature are used in order to bypass fine computational close to the wall. Comparisons of results simulated with both linear and non-linear turbulence models are presented.

In the present paper, the analysis of concentration and flow fields around a model building was performed using two different approaches in turbulence modeling. In the first approach, the non-linear model of Ehrhard and Moussiopoulos was employed as one of the best cubic non-linear eddy viscosity models, and large eddy simulation was utilized in the second approach. The obtained results suggest that although the non-linear model has the ability to predict the anisotropic normal components of Reynolds stress tensor, due to time-averaged nature of its governing equations, it is incapable of estimating the correct values of Reynolds stress components and turbulent characteristics in the wake region of the model building. So the predicted turbulence kinetic energy values by the non-linear model are 45% smaller than those of large eddy simulation approach in the wake region behind the model building. Also different predictions of the wake region structure by the non-linear model and large eddy simulation approach revealed that elongation of iso-surface for \(\left\langle K \right\rangle\) = 1.5 in non-linear model is 56% more than that of large eddy simulation approach. The large eddy simulation approach shows much consistent behavior to the physics governing the flow compared to the non-linear model. Also good agreement observed between the results obtained through this approach and the experimental data. However, the disadvantage of large eddy simulation approach is the high computational costs.

In rans modelling it is common practice to use classical canonical flow cases such as the isotropic decay, the logarithmic law of the wall or homogeneous shear flows for calibrating the model constants. With the help of Lie group analysis a broad variety of invariant solutions (scaling laws) can be derived comprising the latter classical solutions as well as a broad variety of new solutions which have so far not been used for model calibration or development. The symmetry methods provide therefore a very useful tool for the improvement of existing turbulence models or may be a guideline for the development of new models. In the following we will exemplary investigate linear and nonlinear eddy viscosity models as well as Reynolds stress transport models for their capability to reproduce the scaling laws derived from symmetry methods for the fully developed turbulent rotating pipe flow.

This work examines the performance of linear and nonlinear eddy-viscosity models when used to predict the turbulent flow in periodically sinusoidal-wave channels. Two geometries are investigated, namely a converging-diverging channel and a channel with concave-convex walls. The numerical method employed for the discretization of the equations is the control-volume method in a boundary-fitted nonorthogonal coordinate system. The SIMPLE algorithm is used for correcting the pressure field. The classical wall function and a low Reynolds model are used to describe the flow near the wall. Comparisons between those two approaches using linear and nonlinear turbulence models are done. Here, a new implicit numerical treatment is proposed for the nonlinear diffusion terms of the momentum equations in order to increase the robustness. Results show that by decomposing and treating terms as presented, solutions using nonlinear models and the high Reynolds wall treatment, which combine accuracy and economy, are more stable and easier to be obtained.

A typical high-speed compressor cascade flow is simulated using an eddy viscosity model and a Reynolds stress model. Based on comparisons with experimental results, the simulation accuracies of the two turbulence models are evaluated, and some recommendations are provided for further research. Inside the cascade flow passage, the simulation accuracies of both turbulence models decrease because of the corner effect. Downstream of the blade, the wake mixing influence, and thus the flow loss, is under-predicted by both turbulence models. Compared with the linear eddy viscosity model, the modification of the simulation accuracy with regard to endwall flow prediction using the Reynolds stress model is limited, which only occurs at a highly positive incidence angle. The corner separation strength and wake mixing influence predicted by the eddy viscosity model are surpassed by those of the Reynolds stress model. At a negative incidence angle, the simulation result of the Reynolds stress model is proved to be physically unreasonable according to the flow loss prediction.

The numerical simulation of a flow through a duct requires an externally specified forcing that makes the fluid flow against viscous friction. To this end, it is customary to enforce a constant value for either the flow rate (CFR) or the pressure gradient (CPG). When comparing a laminar duct flow before and after a geometrical modification that induces a change of the viscous drag, both approaches lead to a change of the power input across the comparison. Similarly, when carrying out direct numerical simulation or large-eddy simulation of unsteady turbulent flows, the power input is not constant over time. Carrying out a simulation at constant power input (CPI) is thus a further physically sound option, that becomes particularly appealing in the context of flow control, where a comparison between control-on and control-off conditions has to be made. We describe how to carry out a CPI simulation, and start with defining a new power-related Reynolds number, whose velocity scale is the bulk flow that can be attained with a given pumping power in the laminar regime. Under the CPI condition, we derive a relation that is equivalent to the Fukagata–Iwamoto–Kasagi relation valid for CFR (and to its extension valid for CPG), that presents the additional advantage of naturally including the required control power. The implementation of the CPI approach is then exemplified in the standard case of a plane turbulent channel flow, and then further applied to a flow control case, where a spanwise-oscillating wall is used for skin-friction drag reduction. For this low-Reynolds-number flow, using 90 % of the available power for the pumping system and the remaining 10 % for the control system is found to be the optimum share that yields the largest increase of the flow rate above the reference case where 100 % of the power goes to the pump.

A computational study of the near-field generation and decay of wingtip vortices

A brief introduction of the time-filtered Navier–Stokes (TFNS) equations for very large eddy simulation (VLES) and its distinct features is presented. A set of nonlinear subscale models and their advantages over the linear subscale eddy viscosity models are described. A guideline for conducting a TFNS/VLES simulation is also provided. In this paper, we present simulations for three turbulent flows. The first one is the turbulent pipe flow at both low and high Reynolds numbers to illustrate the basic features of TFNS/VLES; the second one is the swirling turbulent flow in an LM6000 single injector to further demonstrate the differences between the results from nonlinear models versus linear viscosity models; the third one is a more complex turbulent flow generated in a single-element lean direct injection combustor, which demonstrates that the current TFNS/VLES approach is capable of predicting dynamically important, unsteady turbulent structures even with a relatively coarse mesh grid.

Quadratic and cubic non-linear eddy-viscosity turbulence Models (NLEVM) with low Reynolds number correction were employed to provide better treatment about the anisotropic turbulence stresses in cavitating flows, in which large density ratio and swirling structures consist. These models were carried out through a self-developed computer code, and were validated by the case of the cavity over disk cavitator. It was proven that, the nonlinear models could effectively eliminate the non-physical numerical oscillation of the cavity profile which was usually caused by linear models. It had also been experimentally proved that the computed cavity shapes and pressure inside the cavity were accurately captured by these nonlinear models. One of such nonlinear models was further applied on the simulation of the cavitating flows around submerged vehicles. The numerical results were compared with experiment data to investigate the influence of the vehicle’s head and the after-body on the characteristics of the cavity. Ultimately, the cavitating flows around an especially designed complex underwater vehicle were predicted using the cubic k–ε turbulence model. The corresponding cavitation behaviors were studied to provide a beneficial experience for the research in future.

Modelling of three-dimensional jet array impingement and heat transfer on a concave surface

We describe and demonstrate both our newest projection method (fully implicit) for the incompressible Navier-Stokes equations via the finite element method and our newest turbulence model - a somewhat sophisticated nonlinear (cubic) eddy viscosity model that does not employ wall functions or normal distances to walls - the combination providing a method and a model that is each applicable in arbitrary geometry. We demonstrate both via a flow simulation past an automobile-like body at a Reynolds number of 4.3 million.

Many hydroelectric power plants use a Francis turbine, known for its versatility and efficiency in converting hydraulic energy into mechanical energy.Two integral components of this hydroturbine are the spiral case and the guide vane, which play a key role in controlling the flow of water through the hydroturbine system, ensuring optimal performance and energy production. The process of developing new flow space of hydroturbines consists ofseveral consecutive stages, in particular: selection of design parameters of the hydroturbine for given conditions of the hydroelectric power plant anddesign of flow space elements (as a rule, several options are considered, differing in calculation methods, geometric, kinematic and other parameters); computational study of flow characteristics, power and torques, energy losses in flow space elements and determination of the best options; experimental study of model hydroturbine units on energy cavitation stands, and the dimensions of the model, test conditions and stand parameters must meet the requirements of the international IEC standard. Based on the results of experimental and computational studies of the model, the characteristics are calculated and guarantees for the operation of a full-scale hydroturbine are issued. The article presents some results of a computational study of the spatial turbulent flow of a viscous fluid in the flow space of a high-head turbine Fr500, performed using the CFXTASCflow application software package. To improve the energy characteristics at the stage of preliminary turbine design, numerical simulation of the flow should be carried out. Such a CFD approach reduces costs and time compared to the experimental approach and makes it possible to improve and analyze the characteristics of the hydroturbine and its design before manufacturing the model. The computational complex of programs provides an opportunity to see the pressure distribution pattern, the velocity vector field and the motion of fluid particles for substantiation and analysis of the results. Numerical simulation of the spatial flow in the flow section of the hydroturbine was carried out to determine changes in energy characteristics, therefore, the k-ε turbulence model was chosen. As a result of the calculation, the distribution of speeds and pressures in various elements of the hydroturbine was determined for different profiles of the guide vane. An analysis of energy losses in the flow part of the high-head hydroturbine was carried out: a spiral case, a stator with flat rings, a guide vane, an runner and a suction pipe for the optimal operation mode of the hydroturbine, and an analysis of the influence of opening the guide vane on the change in energy losses in various elements of the flow space was also carried out. The issue of increasing the energy efficiency of the flow space of the high-head hydroturbine was also considered.

The high head Pelton turbines operate with extreme conditions. In case to need a sudden stop of operation, one of the important parts is jet deflector, which can be in push-out, or cut-of options. The paper presents the optimisation procedure of Pelton Turbine push-out jet deflector shape using numerical simulation of three-dimensional turbulent flow in order to minimize the forces, stresses, deformations and torque of jet deflector servomotor. The calculations are performed using the CFD package Ansys CFX. The steps for flow modelling, 3-D geometry definition, mesh generation, pre-processing and post-processing, as well as the optimised results obtained from the numerical simulation of the flow in the jet-deflector are presented. The work corresponds with the actual approach of methods development for flow simulation and calculations of Pelton Turbines. The kinematic and dynamic flow parameters are calculated based on CFD simulations. The results of the calculations represents reliable tool in the procedure of development and construction of Pelton Turbines parts.