Three-equation Turbulence Model Research Articles

A Two-Time-Scale Turbulence Model and Its Application in Free Shear Flows

A novel three-equation turbulence model has been proposed as a potential solution to overcome some of the issues related to the k–ε models of turbulence. A number of turbulence models found in the literature designed for compressed turbulence within internal combustion engine cylinders tend to exhibit limitations when applied to turbulent shear flows, such as those occurring through intake or exhaust valves of the engine. In the event that the flow is out of equilibrium where Pk deviates from ε, the turbulence models require a separate turbulence time-scale determiner along with the dissipation, ε. In the current research, this is accomplished by resolving an additional equation that accounts for turbulence time scale, τ. After presenting the rationale behind the model, its application to three types of free shear flows were given. It has been shown that the three-equation k–ε–τ model outperforms the standard k–ε model as well as a number of two-equation models in these flows. Initially, the k–ε–τ model handles the issue of the plane jet/round jet anomaly in an effective manner. Secondly, it outperforms the two-equation models in predicting the flow behavior in the case of plane wake, one that is distinguished by its weak shear form.

Passive control optimization of condensation flow in steam turbine blades

Due to the decrease in steam temperature in the low-pressure steam turbine, nucleation occurs, and liquid droplets form, reducing thermodynamic efficiency and damaging the blades. A new flow control method and optimization of two-phase flow among stator blades are discussed in this paper. During this flow control, steam is taken from upstream flow and injected into downstream flow through two holes in the turbine's blade. For the current simulation, an in-house code has been developed. This code is density-based, two-dimensional, compressible, and viscous, with a three-equation turbulence model. The main aim of the present study is to increase the thermodynamic performance by reducing the droplet radius and wetness fraction; these features are affected by changing the hole characteristics. Response Surface Optimization Method (RSM) is applied to find the best width and location of the inlets and outlets of the holes (eight independent variables). The optimization method is applied to a two-phase steam turbine flow for the first time. Also, a parametric study of this flow control on the thermodynamic and aerodynamic characteristics has not been done before. Turbine blade changes may result in a loss of aerodynamic performance, such as a reduction in velocity; thus, throughout the optimization process, it's better to consider the impact of holes on this efficiency. The results for the optimum case demonstrated that the average velocity and entropy at the blade output are almost identical to the baseline. However, the droplet radius and wetness fraction are decreased by 5.91 and 16.37 percent, respectively, and these decreases could significantly enhance the thermodynamic efficiency.

Combined Effects of the Turbulence and Interfacial Momentum Transfer on Two-Phase Turbulent Bubbly Flows

Abstract The paper studies one-way and two-way coupling interactions between the liquid turbulence and bubbles' presence in bubbly jets. One-way coupling focuses on jet with low void fraction in which the bubbles have no significant effect on the hydrodynamic liquid fields in comparison to the single-phase jet. It sets out to model the interfacial momentum transfer identifying the turbulent contribution and its effect on the bubbles' dynamics and phase distribution. Two-way coupling considers jets with high void fractions where the liquid turbulence is altered by the bubbles which in turn influence the interfacial momentum transfers. This paper aims to improve the two-fluid model closures by implementing in computational fluid dynamics code a three-equation turbulence model and new interfacial momentum transfer closures. A benchmark of turbulence models combined with different interfacial exchange modeling is achieved to highlight the strong couplings between the interfacial forces, the phase distribution and the hydrodynamic fields of both phases.

On turbulence and interfacial momentum transfer in dispersed gas-liquid flows: Contribution of bubbly flow experiments under microgravity conditions

The major focus of the present work is to develop an adequate closure model for the turbulent contribution of the interfacial momentum transfer term in turbulent bubbly flow. For this purpose, numerical simulations have been conducted on bubbly pipe flows under microgravity conditions. With no buoyancy effect, the average interfacial forces are negligible due to the small interphase relative motion. In these conditions, the distribution and the dynamics of bubbles are mainly controlled by the turbulence effects. Based on a phenomenological approach, a new closure for the turbulent interfacial momentum transfer is developed within Eulerian two-fluid modelling based on the averaging of the added mass force. The turbulent terms thus obtained comprises a non-linear term and a convective acceleration term associated with the drift velocity. The two-fluid model with the proposed interfacial momentum transfer closure and an original three-equation turbulence model for bubbly flows has been implemented in a 3D CFD code and applied to pipe bubbly flow under microgravity conditions. When compared to conventional two-fluid closures, the turbulent contribution of the added mass force proved to be a relevant closure that provides a substantial improvement in predicting the void fraction distribution and the bubbles’ dynamics.

Passive Control Optimization of Condensation Flow of Steam Turbine Blades by Response Surface Method

A large percentage of the world's electricity is generated by steam power plants. In the low-pressure last stage blade of the steam turbine, due to the decrease in steam temperature, nucleation occurs, and liquid droplets form, which leads to a reduction of thermodynamic efficiency, and damage of the blades. It is essential to study methods to increase steam turbine efficiency. In the present paper, the two-phase flow between the stator blades is simulated. An in-house code is developed; the written code is density-based, two-dimensional, compressible, viscous, and a three-equation turbulence model. Two holes are provided on the turbine’s blade, to passively control the wet steam characteristics of the flow; Also, to optimize and find the best width and location of the inlet and outlet holes (eight independent variables), the Response Surface Method (RSM) has been used. The main aim of the present study is to increase the thermodynamic performances by reducing the droplet radius and wetness fraction. In the optimum case, the droplet radius and wetness fraction were reduced by 16.37 and 5.91 percent, respectively. In addition, the average velocity and entropy at the blade output are almost identical to the baseline.

Optimization design of airfoils under atmospheric icing conditions for UAV

Natural ice accretion on the lifting surface of an aircraft is detrimental to its aerodynamic performance, as it changes the effective streamlined body. The main focus of this work considers the optimization design of airfoils under atmospheric icing conditions for the Unmanned Aerial Vehicle (UAV). The ice formation process is simulated by the Eulerian approach and the three-dimensional Myers model. A three-equation turbulence model is implemented to accurately predict the stall performance of the iced airfoil. In recognition of the real atmospheric variability in the icing parameters, the medium volume diameter of supercooled water droplets is treated as an uncertainty with an assumed probability density function. A technique of polynomial chaos expansion is used to propagate the input uncertainty through the deterministic system. The numerical results show that the multipoint/multiobjective optimization strategy can efficiently improve both the ice tolerance and the cruise performance of an airfoil. The reason for the focus on robust optimization is that the ice angle of the optimized airfoil becomes less critical to the incoming flow. The optimized airfoils are applied to a UAV platform, in which the performance improvement and the relevant key flow feature are both preserved.

Aerodynamic Prediction of Iced Airfoils Based on Modified Three-Equation Turbulence Model

Ice formation on a wing poses a threat to aircraft safety because it changes the effective shape of the wing and considerably deteriorates the aerodynamic performance. The performance prediction of an iced airfoil requires an accurate turbulence model. In this Paper, a three-equation turbulence model for the Reynolds-averaged Navier–Stokes equation is developed to determine the stall behavior of iced airfoils. The model is implemented using a linear eddy viscosity transition model as a baseline and is modified to appropriately simulate complex flow phenomena such as laminar separation, shear layer transition, and turbulent reattachment. The model also takes the nonequilibrium characteristics of turbulence into account. Different airfoils, including clean airfoils and three types of iced airfoils (horn ice, streamwise ice, and spanwise-ridge ice), are numerically tested. The results indicate that the present model demonstrates engineering accuracy in terms of the stall behavior prediction and can be adapted in a wide range of ice shapes. The relative errors of the predicted maximum lift coefficients of the iced airfoils are about 5% of the experimental values.

Effect of the bottom material capture and the non-Newtonian rheology on the dynamics of turbulent downslope flows

The paper is devoted to the mathematical modeling of naturally occurring downslope flows, such as snow avalanches, mudflows, and rapid landslides. The medium in motion is modeled as a non- Newtonian fluid, the non-Newtonian fluids of different types corresponding to different-in-nature flows. It is taken into account that the downslope flows capture the slope material and entrain it into the motion. The flow is assumed to be turbulent and the Lushchik–Pavel’ev–Yakubenko three-equation turbulence model is used. It is so generalized that it allows for flow unsteadiness, complicated rheological properties, the presence of a free boundary, and the mass transfer at the lower flow boundary. The effect of the bottom material capture and the nonlinear rheological properties of the medium in motion on the flow dynamics is numerically investigated.

Numerical Investigation of a Ranque–Hilsch Vortex Tube using a Three-Equation Turbulence Model

The thermal separation flow characteristic in a vortex tube using a three-equation turbulence model is discussed in the present research. Flow behavior and energy separation of a vortex tube in different boundary conditions are investigated through a 3D model. The effect of the operating parameters on the turbulent viscosity ratio and the Mach number is also discussed. It was found that strong swirling flows with a high order of tangential velocity in the peripheral flow contributes to the rise in temperature due to viscous heating. Energy separation and cold-end side temperature depend mainly on the ratio of cold and hot-end side mass flow rates and the inlet conditions. Moreover, the effect of back pressure at cold-end side was investigated to determine how it alters the performance of the vortex tube. Finally, the results of the proposed computational fluid dynamics model are validated by the available experimental data.

Turbulent Flow over a Flat Plate Using a Three-equation Model

Aim of this study is to evaluate a three-equation turbulence model based on the Reynolds averaged Navier-Stokes equations. Boussinesq hypothesis is invoked for determining the Reynolds stresses. An average turbulent flat plate flow was simulated. Uncertainty was approximated through validation. Results for the mean axial velocity and friction coefficient were within experimental error.

Simulation of Average Turbulent Pipe Flow: A Three-Equation Model

The aim of this study is to evaluate a three-equation turbulence model applied to pipe flow. Uncertainty is approximated by comparing with published direct numerical simulation results for fully-developed average pipe flow. The model is based on the Reynolds averaged Navier-Stokes equations. Boussinesq hypothesis is invoked for determining the Reynolds stresses. Three local length scales are solved, based on which the eddy viscosity is calculated. There are two parameters in the model; one accounts for surface roughness and the other is possibly attributed to the fluid. Error in the mean axial velocity and Reynolds stress is found to be negligible.

A three-equation turbulence model for high-speed flows

Adding a new equation to the two-equation K-ω turbulence model framework, this paper proposed a three-equation turbulence model to determine the density variance for high-speed aero-optics and high-speed compressible turbulent flows. Simulations were performed with the new model for supersonic and hypersonic flat-plate turbulent boundary layer and hypersonic ramp flows. The results showed that the prediction with the present model agrees well with the experimental data and is significantly better than the Lutz’s model in predicting the density variance for the flat-plate flows. Furthermore, the present model can produce more accurate skin pressure and skin heat flux distributions than the original K-ω model in simulating hypersonic compression ramp flows with separation and reattachment and shock/boundary layer interactions. Without introducing a variety of ad hoc wall damping and wall-reflection terms, the proposed three-equation turbulence model is applicable to high-speed aero-optics and turbulent flows of real vehicles of complex configuration.

Freestream turbulence effect on flow and heat transfer in the flat-plate boundary layer

Flow and heat transfer in the flat-plate boundary layer is numerically investigated using a differential three-equation turbulence model for the initial freestream turbulence intensity ranging from 1.5 to 9%. An increase in the local friction coefficient and the Stanton number obtained in the calculations is in agreement with the most representative experimental data.

Turbulent flow in a circular separationless diffuser at Reynolds numbers smaller than 2000

The results of experimental and numerical investigation of flow in a circular conical diffuser with a small conicity angle ensuring separationless flow are presented. The measurements are carried out in an air flow with the Reynolds number Re2 in the diffuser exit section ranging from 600 to 3000. A considerable effect of the channel expansion on the flow pattern is found to exist. It is shown that, as distinct from a tube, in which only laminar flow can be realized as steady for Re 1000. For Re2 > 1300 this flow is steady, that is, almost independent of the turbulence level at the entry, and is determined by the Reynolds number Re2 in the exit section. For Re2 ≈ 1000 the turbulent flow continuously goes over into a laminar flow. The flow parameters measured at the diffuser exit correspond to calculations in accordance with the threeequation turbulence model.

Application of three-equation turbulence model in numerical simulation of vehicle external flow field

There are many kinds of turbulence models for automobile external flow field simulation. It is a very important significance to find a kind of turbulence model with high calculation efficiency and precision from the turbulence models for vehicle external flow field simulation. Three equation k- e-v2 turbulent model is used to simulate automobile external flow field, because the effect of turbulence spatial scale and turbulence time scale to turbulence transportation is involved in the calculation of eddy viscidity coeffi- cient μ tand more physical mechanism of turbulence transportation is described in the model, therefore, k-e-v2 turbulent model has higher calculation precision than shear stress transport (SST) and k-eturbulent model. So, three-equation model is a compara- tively ideal numerical simulation model of vehicle external flow field. The presented simulation example of car external flow field with the eddy viscosity type three equation k-e-v2, SST model and k-eturbulent model, through comparison of calculated drag coefficients of car with experimental date, validate the advantages of k-e-v2 turbulent model. In additional, the curve of pressure coefficient of car longitudinal symmetry face calculated by three models and wind tunnel pressure coefficient experimental data is compared. Turbulent kinetic energy distribution, velocity vector, exterior streamline graph at the position of 0.1 m away from the car rear simulated by k-e-v2 turbulent model, are also shown.

Navier-Stokes Prediction of Internal Flows with a Three-Equation Turbulence Model

Navier-Stokes Prediction of Internal Flows with a Three-Equation Turbulence Model

Navier-Stokes prediction of internal flows with a three-equation turbulence model

Navier-Stokes prediction of internal flows with a three-equation turbulence model

Three-equation turbulence model for prediction of the mean square temperature variance in grid-generated flows and round jets

This paper presents a three-equation turbulence model for the determination of turbulent quantities, such as the mean square temperature variance, turbulence kinetic energy and its dissipation rate. The conservation equations are discretized by the finite volume method SOLA [Hirt et al., Los Alamos Laboratory, Report LA-5852 (1975)]. The model is tested for a grid-generated flow and for a fairly hot axisymmetrical turbulent air jet. The results of the present calculations are compared with the experimental data of other authors. The comparison shows that the good agreement, for the thermal field, depends fundamentally on the value of the turbulent Prandtl number and the ratio of time scales of turbulent temperature and velocity field.

Three-Equation Turbulence Model with Coherent Structures Incorporated through the Helicity. Application to a Swirling Flow in a Straight Pipe.

Helicity, which is defined by the inner product of the velocity and vorticity, is an important indicator for large-scale vortical structures in turbulent flows. In order to incorporate these structures into a turbulence model, the effect of helicity on the Reynolds stress is taken into account and a three-equation model is proposed, whereby a model transport eqation for the turbulent helicity is added to the k-ε model. This model is applied to a swirling flow in a straight pipe. As a result, this model can recover some important properties of a swirling flow such as the slow-down of the axial velocity near the center and the decay rate of the strength of swirling.

Three-equation modeling of inhomogeneous compressible turbulence based on a two-scale direct-interaction approximation

Mathematical functional forms of important correlation functions in inhomogeneous compressible turbulence are investigated, with the focus on the turbulence modeling based on bulk turbulence quantities. A two-scale direct-interaction approximation (TSDIA) is applied using three fundamental variables, that is, the density, momentum, and internal energy per unit volume. This choice of variables under the ensemble-mean procedure retains the simplicity of the mean-field equations under the Favre-mean procedure. Using these theoretical results, a three-equation turbulence model is constructed, where the turbulence equations consist of the equations for the intensity of momentum fluctuation, its viscous dissipation rate, and the intensity of density fluctuation. Direct effects of compressibility on the Reynolds stress and other important correlation functions are related to the intensity of density fluctuation. These results give a clue for explaining the virtual decrease of the eddy-viscosity effect near a shock wave.