Equation Turbulence Model Research Articles

Machine learning based Reynolds averaged simulation of backward-facing step flows at different Reynolds numbers

To address the closure problem of Reynolds-averaged Navier–Stokes in numerical simulations of turbulence, the method of solving Reynolds-averaged Navier–Stokes equations based on artificial neural network is introduced in this paper. We establish the nonlinear mapping relationship between the average flow field and the steady-state eddy viscosity field. The machine learning (ML) surrogate model for the shear stress transport turbulence model is constructed. The solution process of replacing the original turbulence model equations with the predicted field variables is realized by coupling the ML algorithm with the CFD solver. The classical backward facing step problem is selected in our study to verify the simulation accuracy of the surrogate model. The comparative analysis is carried out on the six backward facing step flows simulations at different Reynolds numbers. The results of simulations show that the testing flows with the Reynolds numbers closest training datasets Reynolds numbers can obtain the best simulation accuracy. Then for the Reynolds number that is lower than the training datasets, the simulation accuracy will decrease as the Reynolds number decreases. On the contrary, the simulation accuracy of the test flow will increase as the Reynolds number increases. These results indicate the feasibility of the ML surrogate model to simulate at higher Reynolds number. It shows the great potential of applying ML algorithms to Reynolds-averaged Navier–Stokes simulation (RANS) turbulence model and also provides a new idea for industrial simulations of turbulent flows.

Numerical Study of Air Flow Induced by Shock Impact on an Array of Perforated Plates.

This study is focused on the propagation behavior and attenuation characteristics of a planar incident shock wave when propagating through an array of perforated plates. Based on a density-based coupled explicit algorithm, combined with a third-order MUSCL scheme and the Roe averaged flux difference splitting method, the Navier–Stokes equations and the realizable k-ε turbulence model equations describing the air flow are numerically solved. The evolution of the dynamic wave and ring vortex systems is effectively captured and analyzed. The influence of incident shock Mach number, perforated-plate porosity, and plate number on the propagation and attenuation of the shock wave was studied by using pressure- and entropy-based attenuation rates. The results indicate that the reflection, diffraction, transmission, and interference behaviors of the leading shock wave and the superimposed effects due to the trailing secondary shock wave are the main reasons that cause the intensity of the leading shock wave to experience a complex process consisting of attenuation, local enhancement, attenuation, enhancement, and attenuation. The reflected shock interactions with transmitted shock induced ring vortices and jets lead to the deformation and local intensification of the shock wave. The formation of nearly steady jets following the array of perforated plates is attributed to the generation of an oscillation chamber for the inside dynamic wave system between two perforated plates. The vorticity diffusion, merging and splitting of vortex cores dissipate the wave energy. Furthermore, the leading transmitted shock wave attenuates more significantly whereas the reflected shock wave from the first plate of the array attenuates less significantly as the shock Mach number increases. The increase in the porosity weakens the suppression effects on the leading shock wave while increases the attenuation rate of the reflected shock wave. The first perforated plate in the array plays a major role in the attenuation of the shock wave.

Detached eddy simulation of the release progress of moving body separating from a cavity

Aiming at the complex unsteady flow during the release progress of moving body separating from a cavity, combined with the overlapping grid technique and Spalart Allmaras equation turbulence model, the three-dimensional unsteady flow solver is presented. On this basis, the validity of the simulation method is verified by M219 cavity example and WPFS example. Then the released moving body is conducted with SA-IDES. The research results show that upward force and pitch down moment of the moving body are affected by the fluctuating flow near the cavity and the SA – DES simulation is good in predicting high frequency flow. In conclusion, the outside shear layer and the inside fluctuating flow of the cavity has a significant impact on the aerodynamic loads and the trajectory of the moving body during the initial separation stage.

An implicit time spectral method using adaptive stablization

An adaptive time spectral viscosity (TSV) approach is proposed to stabilize the time-spectral method (TSM) by dealiasing its solution. Instead of being assigned uniformly in space, the cut-off wave number for TSV is determined locally by spectrum analysis of the flow variables. On each grid cell, the significant low-frequency modes are adaptively separated from the TSV targeted high-frequency ones according to local flow physics. The space-time Lower-Upper Symmetric Gauss-Seidel(ST-LU-SGS) implicit scheme is used to solve the modified time-spectral equations. TSV operator is treated implicitly in the same way as the time spectral operator to facilitate fast convergence. Computational results of inviscid and turbulent flows over a pitching NACA0012 airfoil are presented for validation of the adaptive TSV approach. For the turbulent flow case, the proposed approach is also applied to the Spalart–Allmaras (S-A) turbulence model equation. The accuracy and the convergence rate of the adaptive TSV approach is demonstrated in both test cases.

An iterative machine-learning framework for RANS turbulence modeling

Machine-learning (ML) techniques provide a new and encouraging perspective for constructing turbulence models for Reynolds-averaged Navier-Stokes (RANS) simulations. In this study, an iterative ML-RANS computational framework is proposed that combines an ML algorithm with transport equations of a conventional turbulence model. This framework maintains a consistent procedure for obtaining the input features of an ML model in both the training and predicting stages, ensuring a built-in reproducibility. The effective form of the closure term is discussed to determine suitable target variables for the ML algorithm, and the multi-valued problem of existing constitutive theory is studied to establish a proper regression system for ML algorithms. The developed ML model is trained under a cross-case strategy with data from turbulent channel flows at three Reynolds numbers, and a posteriori simulations of channel flows show that the framework is able to predict both the mean flow field and turbulent variables accurately. Interpolation tests for the channel flow show the proposed framework can reliably predict flow features that lie between the minimum and maximum Reynolds numbers associated with the training data. A further test of the ML model in a flow over periodic hills also demonstrates improved performance compared with the k-ω SST model, even though the model is only trained with planar channel flow data.

Augmentation of convection heat transfer from a horizontal cylinder in a vented square enclosure with variation of lower opening size

Natural and mixed convection heat transfer from a horizontal cylinder placed in a vented square enclosure has been investigated using numerical method with ANSYS Fluent 16.1 software for laminar and turbulent flow. Navier-Stokes equations and energy equation with standard k-? transport equation turbulence model have been used to simulate both flow and thermal behaviors. The operating conditions covered a range of the Rayleigh number from 103 to 106 and the Richardson number range between 0.1 and 100 at variable sizes of the lower open vent with constant upper opening size. The Nusselt numbers, velocity lines and isotherms are presented to display the flow and thermal behaviors. The results displayed that the average Nusselt number is affected by Rayleigh number, Richardson number, enclosure width, and lower opening size. The Nusselt number is enhanced by controlling the lower opening size. The maximum enhancement range for Nusselt number is between 20-85% depending on the Rayleigh number, Richardson number, enclosure width to cylinder diameter, and lower opening size. The velocity lines and isotherms are directly affected by the Rayleigh number, Richardson number, enclosure width to cylinder diameter, and lower opening size.

The Implication of Injection Locations in an Axisymmetric Cavity-Based Scramjet Combustor

This paper presents the effect of cavity-based injection in an axisymmetric supersonic combustor using numerical investigation. An axisymmetric cavity-based angled and transverse injections in a circular scramjet combustor are studied. A three-dimensional Reynolds-averaged Navier–Stokes (RANS) equation along with the k-ω shear-stress transport (SST) turbulence model and species transport equations are considered for the reacting flow studies. The numerical results of the non-reacting flow studies are validated with the available experimental data and are in good agreement with it. The performance of the injection system is analyzed based on the parameters like wall pressures, combustion efficiency, and total pressure loss of the scramjet combustor. The transverse injection upstream of the cavity and at the bottom wall of the cavity in a supersonic flow field creates a strong shock train in the cavity region that enhances complete combustion of hydrogen-air in the cavity region compared to the cavity fore wall injection schemes. Eventually, the shock train in the flow field enhances the total pressure loss across the combustor. However, a marginal variation in the total pressure loss is observed between the injection schemes.

Modelling of hydrogen-air supersonic mixing and combustion in near-wall region

Abstract Turbulent mixing, ignition, and flame stabilization in the non-premixed supersonic hydrogen-air flow is numerically modelled in a near-wall region. Mixing algorithm based on the turbulence approach SARANS (Reynolds Averaged Navier–Stokes equations closed with Spalart–Allmaras turbulence model) with a diffusion model and a detailed kinetic model for hydrogen-air chemical reactions are employed. The system of governing equations that consists of basic conservation laws and the turbulence model equation is solved in a coupled manner with the LU–SGS–GMRES method. The model is applied to simulate the process of hydrogen injection into a M = 2.44 air flow with their subsequent mixing, ignition, and combustion in the Burrows– Kurkov chamber. The results are compared to available experimental and reference computational data. All calculations are carried out on the ‘MVS-10P’ JSCC RAS supercomputer cluster.

Simulation study on Air Outlet of Data Center

How to reduce the amount of wasted cooling in corridors and gaps is a problem in data center air conditioning design. Modeling the data center airflow data and simulating the temperature distribution are the prerequisites and key points to solve this problem. This paper uses the optimal idea to establish a mathematical model to simulate the location of the air conditioning vent. Determine the layout of the computer cabinet based on the analysis of the internal and external environment of the computer cabinet. The external environment analysis is mainly the analysis of several directions: According to the CFD simulation and simulation, the wind speed and tuyere arrangement of the air supply port are compared and the optimal wind speed of the air supply port is obtained. For the problem of the ceiling height and the spacing of the upper air outlet, discuss the method of determining the air supply spacing on the air duct so that the upper air supply can cover all the air inlets of the cabinet to achieve the most reasonable air supply flow. For the numerical simulation and optimization of the airflow organization in the equipment room, it is easy to know that the farther away from the air conditioner, the higher the temperature is relative to the air conditioner, and the wind speed far from the air conditioner is relatively large, so the temperature in the distance is higher. Also, because the hot aisle has no ventilation slots, its temperature must be higher than the cold aisle. Therefore, the temperature in the hot aisle is higher than the ground and the air conditioner is far away. According to the airflow dynamic equation and the K-ε turbulence model equation, the Fluent software is used, and combined with the data given in the data center room, the airflow data is simulated. Finally, the best solution for setting the position of the air conditioning air outlet is given.

Leading Edge Shape Optimization of Whitcomb IL Airfoil in Transonic Flow Using a Multi-Objective Genetic Algorithm (MOGA)

Leading edge shape optimization of transonic airfoils requires creating an airfoil surface that reduces the drag divergence due to transonic shocks by either delaying them or reducing their strength at a given transonic cruise speed while maintaining the lift. Aircrafts like Boeing 757, Airbus A300, Boeing 777 and McDonnell Douglas AV-8B Harrier II use Whitcomb IL supercritical airfoil for efficient aerodynamic performance in transonic conditions. This study employs a multi-objective genetic algorithm for shape optimization of leading edge of the Whitcomb IL airfoil to achieve three objectives, namely dilation of shock, reduction in leading edge radius and increment of lift at a given transonic Mach number and at the given AoA. The commercially available software ICEM CFD and Fluent are employed for calculation of the flow field using the RANS (Reynolds-averaged Navier-Stokes equations) in conjunction with a two equation turbulence model. It is shown that the (MOGA) Multi-objective genetic algorithm can generate superior airfoil compared with Whitcomb IL airfoil by achieving three objectives. The optimized airfoil configuration is validated by wind tunnel testing facility.

Testing a one-closure equation turbulence model in neutral boundary layers

We aim to test the performances of an incompressible turbulence Reynolds-Averaged Navier–Stokes one-closure equation model in a boundary layer (NSTKE model). We model a new boundary condition for the turbulent kinetic energy k (TKE), and we achieve the mathematical analysis of the resulting NSTKE model. A series of direct numerical simulation are performed, with flat and non trivial topographies, to obtain by interpolation a generic formula for the Prandtl mixing length ℓ=ℓ(Re⋆,z), Re⋆ being the frictional Reynolds number, and z the distance to the wall. This allows us to carry out numerical simulations at high Reynolds numbers with this turbulence model, in order to discuss its ability to properly reproduce the standard profiles observed in neutral boundary layers, and to assess its advantages, its disadvantages and its limits.

Computational fluid dynamics and experimental study of the effect of inclination angle on turbulent natural convection in an upward open cubic cavity

The effect of inclination angle on heat transfer by turbulent natural convection in an inclined open cubic cavity with side length of 1[Formula: see text]m is experimentally and numerically studied. The wall opposite to the aperture is subjected to uniform heat flux condition with a value of 110[Formula: see text]W/m2, whereas the remaining walls were kept thermally insulated. Six most used two equations turbulence models were tested, with Computational Fluid Dynamics (CFD) software ANSYS FLUENT. The results were obtained for four inclination angle values: 0∘, 15∘, 30∘ and 45∘. The spatial distribution for temperature, flow pattern and magnitude of velocity are determined and analyzed. An experimental prototype was built to obtain experimental temperature profiles and heat transfer coefficients. The experimental average Nusselt number increases as the inclination angle increases, having a minimum of 203 for 0∘ case and a maximum of 225 for 45∘ case. The comparison between experimental and numerical average Nusselt numbers indicates that the minimum average difference is with the realizable [Formula: see text] turbulence model, therefore, this turbulence model is recommended to model this type of systems.

Implicit Time-Spectral Method for Unsteady Reynolds-Averaged Navier–Stokes Computations of Turbulent Flows

An efficient implicit Fourier time-spectral method is developed for the unsteady Reynolds-averaged Navier–Stokes (URANS) computations of turbulent flows. In addition to the time-spectral URANS equations, the time-spectral Spalart–Allmaras turbulence model equation is also solved by the space–time lower-upper symmetric Gauss–Seidel (LU-SGS) implicit scheme. The efficient LU-SGS sweeps are directly extended to the time domain without introducing additional approximation error, delayed implicit temporal coupling, and additional algorithmic steps. The ability of the algorithm is verified through the test cases of the pitching NACA0012 airfoil and pitching ONERA M6 wing. Dominant Fourier modes of the drag coefficient and its components are identified. Special attention is paid to the nonlinear behavior of the surface pressure and skin friction coefficients in the shock-free area, especially the region downstream the shock where the influence of turbulence is significant. For the test case of a pitching ONERA M6 wing, difference in local flow unsteadiness for the two branches of the -type shock is observed. The phenomenon is further discussed through study of the shock motion range and the upstream Mach number for each shock branch.

Analysis of the interaction of a supersonic gas flow with a solid low melting polymer as a ramjet engine propellant

The performance of ramjet engines with a supersonic combustion is one of the main directions of hypersonic aircraft development research is studied. Researchers around the world create special experimental facilities for testing engine models, investigate fuels for ramjet engines and classify new scientific data. Since the ambient temperature and the oxidizer flow temperature in engine air duct are low at the flight altitude of a hypersonic aircraft, low melting materials can be used as a fuel agent in a solid propellant. The main purpose of this work is analysis of heat and mass exchange processes associated with the motion of a supersonic gas flow in an axisymmetric duct described as a combustion chamber of a ramjet engine with a solid polymer. The mathematical model of the problem consists of the unsteady Reynolds-averaged Navier-Stokes equations and the equations of a semiempirical turbulence model. The stated problem was solved by the finite volume method. Initial and boundary conditions are identical to experimental conditions and this makes it possible to verify the results of the numerical solution directly during aerodynamic tests. Gas dynamic parameters for the gas flow in an air duct of a ramjet engine are described, pressure profiles at the gas-solid interface are plotted, and a transient pressure behavior is considered. The results of the solution of a coupled heat transfer problem allow analyzing a dynamic heat exchange pattern in a solid polymeric material (caprolone, polyethylene and polyoxymethylene). It has been found that the effect of a supersonic flow on the surface of a low melting material within one second leads to temperature changes in a solid to a depth of 20% of its total thickness.

Vorticity Confinement Applied to Accurate Prediction of Convection of Wing Tip Vortices and Induced Drag

The vorticity confinement (VC) method was applied to tip vortices shed by edges of wings in order to predict induced drag using far-field integration. The optimal VC parameter was determined by its application to tip vortices shed by 3-D stationary and rotating wings. The VC was used with a total variation diminishing (TVD) approach to reduce the needed confinement. The TVD minmod and differentiable flux limiters were tested to evaluate their effect on the VC parameter. The 3-D inviscid simulations were post-processed using the wake-integral technique to determine lift-induced drag force. Dependence of the VC parameter on the flight Mach number and the angle of attack was evaluated. Grid convergence studies were conducted for induced drag generated by 3-D wing. The VC approach was combined with the Reynolds stress equation turbulence model, and the results were compared to experimental data of tip vortex evolution.

Computational study of the effect of cavity geometry on the supersonic mixing and combustion of ethylene

In this numerical study, the supersonic combustion of ethylene in three model combustor configurations namely, baseline (no cavity), square cavity and inclined cavity are investigated. To this end, 3D, compressible, turbulent, non-reacting (with fuel injection) and reacting flow calculations using single step and 10-step chemical kinetics in conjunction with a one equation turbulence model have been carried out. In the mixing study, predictions of the flow features with fuel injection, fuel trajectories, contours of total pressure loss along the combustor are compared between the combustor models. In the combustion study, contours of heat release are compared across the combustor models. Overall performance metrics such as mixing efficiency, total pressure loss and combustion efficiency are also compared between the combustor models. The comparison of combustor top wall static pressure and exit total pressure predictions with experimental data reported in the literature are also presented and discussed. The results clearly show that the model combustor with a shallow and inclined aft wall cavity has the highest residence time and maximum heat release. In addition, the role of a smaller L/D ratio cavity is shown to be minimal on the predictions of residence time and the heat release.

Smooth Local Correlation-Based Transition Model for the Spalart–Allmaras Turbulence Model

A smooth version of the local correlation-based transition model (LM2015) for the Spalart–Allmaras (SA) turbulence model is presented. The LM2015 model with helicity-based crossflow correlations is modified and coupled to the SA turbulence model, designated SA-LM2015. The LM2015 and SA-LM2015 transition models include source terms that contain stiff and nonsmooth functions. Approximations to these functions are introduced to eliminate discontinuities and improve the numerical behavior of the model, with the smooth model designated SA-sLM2015. Deep convergence is achieved using a fully coupled, implicit Newton–Krylov algorithm globalized using an efficient pseudotransient continuation strategy. Modifications to the Newton–Krylov algorithm are introduced, including a source-term time stepping strategy, to address the large sources introduced by the turbulence and transition model equations. Two- and three-dimensional transition test cases demonstrate that both models, SA-LM2015 and SA-sLM2015, are able to predict transition due to a variety of mechanisms accurately, with the smooth variant displaying significantly improved numerical behavior. Several of the strategies presented, including the smoothing techniques and source-term time stepping, could be useful in the context of other transition models as well.

Numerical simulation of wave overtopping above perforated caisson breakwaters

A two-dimensional numerical model was used to study the wave overtopping performance above perforated caisson breakwaters under regular waves. The turbulent flow was simulated by solving the Reynolds Averaged Navier–Stokes (RANS) equations and the k–ε turbulence model equations. In the numerical wave flume, the free surface was tracked by the Volume of Fluid (VOF) method, and a relaxation zone was added to avoid the unwanted re-reflection from the inflow boundary. Based on the ideal gas equation at a constant temperature, the pressure change caused by the compressed air inside the wave chamber was incorporated into the numerical model for accurately simulating the wave motion inside the wave chamber. The numerical results of the free surface elevations inside and outside the wave chamber, the wave overtopping discharges and the reflection coefficients of perforated caisson breakwaters were in good agreement with the experimental data. This means that the numerical model is valid in estimating wave action and overtopping on complicated coastal structures with perforated thin walls. The distributions of flow velocity and turbulence kinetic energy (TKE) around the perforated caissons were clarified, which gave a better understanding of the wave overtopping mechanism above the perforated caisson breakwaters. Numerical results showed that the wave energy transferred by the overtopping flows is much smaller than that dissipated by the perforated caisson breakwater. When the relative freeboard (the ratio of the crest freeboard to the incident wave height) of the perforated caisson breakwater was larger than 0.58, the existence of the overtopping flow has no significant influence on the reflection coefficient. Besides, avoiding the air compression inside the wave chamber can effectively reduce the overtopping discharge. Increasing the caisson porosity or the wave chamber width can also reduce the overtopping discharge above the perforated caisson breakwaters.

Simulating of Microbial Growth Scale Up in a Stirred Tank Bioreactor for Aerobic Processes using Computational Fluid Dynamics

In this paper, the effects of some empirical scale up criteria (Reynold's number and Impeller power per bioreactor volume) on gas-liquid mass transfer and microbial growth rates are analyzed using computational fluid dynamics simulations in a stirred tank bioreactor. The effects of turbulence, fluid flow and bubbles dynamics were simulated by using a two equation turbulence model, a multiple reference frame and a population balance, respectively. The impeller power per bioreactor volume scale up criterion showed better microbial growth rates than Reynold's number scale up criterion. However, high cellular damage due to turbulence in animal cell culturing are still challenges in large scale up bioreactor prototyping.

Viscosity effect on an underwater vehicle-free surface hydrodynamic interaction

The present paper aims to explore and gain more knowledge about the viscosity effect on a shallowly submerged UV hydrodynamics. For this purpose, the hydrodynamic drift tests are performed on the generic SUBOFF UV geometry using URANS equations with a Reynolds stress turbulence model and Euler equations available in the commercial code STARCCM+. The simulations are conducted for drift angles ranging from β=0 to β=18.11∘ at a Froude number equal to Fn=0.512 in two different scenarios: with and without the presence of the free surface. The simulations with the presence of the free surface are performed using both URANS and Euler equations at a submergence depth h=1.1D (D: UV maximum diameter), while the simulations without the presence of the free surface are carried out using only the URANS equations. Although the Euler simulations appear to predict reasonably well the free surface contribution to the axial and lateral forces acting on the UV, further analysis of the results reveals that, generally, the viscosity has a non-negligible influence on the UV hydrodynamics and, consequently, on the loads acting on the UV. This is true even at zero incidence with respect to the incoming flow, where the Euler simulations are expected to provide satisfactory results due to the absence of large flow separation over the UV.