Two-equation Turbulence Model Research Articles

Experimental and numerical analyses of the combustion characteristics of Mg/PTFE/Viton fuel-rich pyrolants in the atmospheric environment

Magnesium/polytetrafluoroethylene/Viton (MTV) fuel-rich pyrolants use the atmospheric oxygen as a complementary oxidizer to sustain and alter the performance of the combustion reaction. The flame diffusion characteristics of MTV fuel-rich pyrolants in the atmospheric environment are studied by a high-speed camera (HSC). The flame temperature and combustion components are measured by using remote sensing Fourier Transform Infrared Spectrometer (FTIR). In order to obtain the combustion component distribution more accurately, an aerobic combustion model containing the oxidation reaction of the excess reactant Mg and carbonaceous species with O2 is established in this study. Eddy dissipation concept (EDC) model is applied to the numerical simulation of the three dimensional anaerobic and aerobic combustion field coupled with Realizable k-ε two-equation turbulence model. The research results show that flame temperature is mainly contributed by anaerobic combustion reaction. The flame structure obtained by the aerobic combustion model is closer to the experimental results, and the result of component distribution calculated by aerobic combustion is more consistent with characteristic spectrum. Therefore, the aerobic combustion model is more suitable for describing the actual MTV flame, and the combustion field can be divided into an anaerobic core zone and an aerobic diffusion zone.

ENVIRONMENTAL FLOW AND CONTAMINANT TRANSPORT MODELING IN THE AMAZONIAN WATER SYSTEM BY USING Q3DRM1.0 SOFTWARE

This paper reports a fine numerical simulation of environmental flow and contaminant transport in the Amazonian water system near the Anamã City, Brazil, solved by the Q3drm1.0 software, developed by the Authors, which can provide the different closures of three depth-integrated two-equation turbulence models. The purpose of this simulation is to refinedly debug and test the developed software, including the mathematical model, turbulence closure models, adopted algorithms, and the developed general-purpose computational codes as well as graphical user interfaces (GUI). The three turbulence models, provided by the developed software to close non-simplified quasi three-dimensional hydrodynamic fundamental governing equations, include the traditional depth-integrated two-equation turbulence model, the depth-integrated two-equation turbulence model, developed previously by the first Author of the paper, and the depth-integrated two-equation turbulence model, developed recently by the Authors of this paper. The numerical simulation of this paper is to solve the corresponding discretized equations with collocated variable arrangement on the non-orthogonal body-fitted coarse and fine two-levels’ grids. With the help of Q3drm1.0 software, the steady environmental flows and transport behaviours have been numerically investigated carefully; and the processes of contaminant inpouring as well as plume development, caused by the side-discharge from a tributary of the south bank (the right bank of the river), were also simulated and discussed in detail. Although the three turbulent closure models, used in this calculation, are all applicable to the natural rivers with strong mixing, the comparison of the computational results by using the different turbulence closure models shows that the turbulence model with larger turbulence parameter provides the possibility for improving the accuracy of the numerical computations of practical problems.

CFD analysis of cross-ventilation flow in a group of generic buildings: Comparison between steady RANS, LES and wind tunnel experiments

Computational fluid dynamics (CFD) results generated by the steady Reynolds-averaged Navier-Stokes equations (SRANS) model and large eddy simulation (LES) are compared with wind tunnel experiments for investigating a cross-ventilation flow in a group of generic buildings. The mean flow structure and turbulence statistics are compared for SRANS based on different two-equation turbulence models with LES based on the Smagorinsky subgrid-scale turbulence model. The LES results show very close agreement with the experimental results in the prediction of the time-averaged velocity, wind surface pressure around and inside the building, and crossing flow through the openings. In contrast, SRANS fails to predict the most important features of cross-ventilation. LES reproduces well the anisotropic turbulence property around and inside the cross-ventilated building, which is closely related to the transient momentum transfer caused in street canyon flows and has a significant influence on the mean flow structure. In contrast, SRANS could not inherently reproduce such transient fluctuations and anisotropic turbulence property, which results in low accurate predictions for the time-averaged velocity components, wind surface pressure distribution and crossing airflow rate up to 100% error.

Two-equation and multi-fluid turbulence models for Richtmyer–Meshkov mixing

This paper concerns an investigation of two different approaches in modeling the turbulent mixing induced by the Richtmyer–Meshkov instability (RMI): A two-equation K-L multi-component Reynolds-averaged Navier–Stokes model and a two-fluid model. We have improved the accuracy of the K-L model by implementing new modifications, including a realizability condition for the Reynolds stress tensor and a threshold in the production of the turbulence kinetic energy. We examine the models in the one-dimensional (1D) form in the (re)-shocked mixing of a double-planar air and sulfur-hexafluoride (SF6) interface of the Atwood number |At| ≃ 0.6853. Furthermore, we investigated the models’ accuracy to RMI-induced mixing of a (re)-shocked planar-inverse chevron air–SF6 interface. Relevant integral quantities in time, as well as instantaneous profiles and contour plots, are used to assess the models’ accuracy against high-resolution implicit large eddy simulations. The proposed modifications improve the efficiency of the K-L model. The model is designed as a simple model capable of capturing the self-similar growth of Rayleigh–Taylor and Richtmyer–Meshkov flows. The two-fluid model remains more accurate but is also computationally more expensive.

Numerical studies on four-engine rocket exhaust plume impinging on flame deflectors with afterburning

This paper studies the four-engine liquid rocket flow field during the launching phase. Using three-dimensional compressible Navier-Stokes equations and two-equation realizable k-epsilon turbulence model, an impact model is established and flow fields of plume impinging on the two different shapes of flame deflectors, including wedge-shaped flame deflector and cone-shaped flame deflector, are calculated. The finite-rate chemical kinetics is used to track chemical reactions. The simulation results show that afterburning mainly occurs in the mixed layer. And the region of peak pressure occurs directly under the rocket nozzle, which is the result of the direct impact of exhaust plume. Compared with the wedge-shaped flame deflector, the cone-shaped flame deflector has great performance on guiding exhaust gas. The wedge-shaped and cone-shaped flame deflectors guide the supersonic exhaust plume away from the impingement point with two directions and circumferential direction, respectively. The maximum pressure and temperature on the wedge-shaped flame deflector surface are 37.2% and 9.9% higher than those for the cone-shaped flame deflector. The results provide engineering guidance and theoretical significance for design in flame deflector of the launch platforms.

Validation of AIAD Sub-Models for Advanced Numerical Modelling of Horizontal Two-Phase Flows

In this work, the modelling of horizontal two-phase flows within the two-fluid Euler–Euler approach is investigated. A modified formulation of the morphology detection functions within the Algebraic Interfacial Area Density (AIAD) model is presented in combination with different models for the drag force acting on a sheared gas–liquid interface. In the case of free surface flows, those closure laws are often based on experimental correlations whose applicability is limited to certain flow regimes. It is investigated here whether the implementation of the modified blending functions in ANSYS CFX avoids this limitation. The influence of the new functions on the prediction of turbulence parameters in free surface flows is also examined quantitatively for the k-ω and k-ε two-equation turbulence models. Transient simulations of the WENKA counter-current stratified two-phase flow experiment were performed for validation. A prediction of the correct flow pattern as observed in the experiment improved dramatically when a turbulence damping term was included in the standard two-equation models. Using the k-ω and a modified k-ε turbulence model with damping terms close to the interface, better agreement with the experimental data was achieved. The morphology detection mechanism of the unified blending functions within the AIAD is seen as an improvement with respect to the detection of sharp interfaces. Satisfactory quantitative agreement is achieved for the modified free surface drag. Furthermore, it is demonstrated that turbulence dampening has to be accounted for in both turbulence models to qualitatively reproduce the mean flow and turbulence quantities from the experiment.

Modelling fluid–structure interactions: a survey of methods and experimental verification

It is difficult to study fluid structure interaction (FSI) problems using analytical methods due to flow non-linearity and multiphysics. Therefore, the main emphasis for research is placed on the application and development of numerical methods. Furthermore, for consistent and accurate results, it is essential to run numerical models previously implemented and calibrated with experimental data. This survey paper shows the main concepts and different approaches of the existing numerical models of FSI. Furthermore, the smoothed particle hydrodynamics (SPH) Lagrangian model for numerical simulations of fluid–structure interactions is analysed. In particular, the flow of fluid around a National Advisory Committee for Aeronautics 0024 hydrofoil has been studied using a weakly compressible smoothed particle hydrodynamics scheme, together with a two-equation turbulence model. The high accuracy of the SPH model is confirmed through a comparison with experimental data.

RANS study of very high Reynolds-number plane turbulent Couette flow

The objective of this study is to expound on the deliverables of a steady-state RANS (Reynolds Averaged Navier Stokes) simulation in one of the simplest flows, Couette flow, at a very high Reynolds number. To that end, a process to perform better grid sensitivity testing is introduced. Three two-equation turbulence models ( , , and ) are compared against each other as well as pitted against formal literature on the subject and core flow velocities, slopes, wall-bounded velocities, shear stresses and kinetic energies are analyzed. applied with enhanced wall functions is consistently found to be in better agreement with previous studies. Finally, plane turbulent Couette flow at 51,099, the range at which it has not been studied experimentally, numerically or analytically in former studies, is simulated. The results are found to be consistent with the trends asserted by literature and preliminary computations of this study.

Mathematical modelling of the influence of yield shear stress on blood friction in a turbulent flow

Measurements of blood rheology indicate that human blood has a yield shear stress. Transport of oxygen in the aorta or a vein depends on blood flow rate. Therefore, it is interesting to find out how blood yield shear stress affects blood transportation if flow is turbulent. The majority of mathematical approaches deal with laminar flow of human blood, which is rather simple compared to turbulent flow modelling. This paper presents a mathematical model of fully developed turbulent flow of human blood in the aorta. The physical model assumes that blood is a non-Newtonian liquid that demonstrates yield shear tress. The main objective of the research is to examine the influence of human blood yield shear stress on turbulent properties, like friction factor, in the aorta. Available blood rheology experimental data for various concentrations of haematocrit were used in order to fit the rheological model. The rheological model together with the momentum equation and the two-equation turbulence model constitute a mathematical model of turbulent flow of human blood. Results of simulations are discussed and presented as figures and conclusions.

Turbulence Modeling Insights into Supercritical Nitrogen Mixing Layers

In Liquid Rocket Engines, higher combustion efficiencies come at the cost of the propellants exceeding their critical point conditions and entering the supercritical domain. The term fluid is used because, under these conditions, there is no longer a clear distinction between a liquid and a gas phase. The non-conventional behavior of thermophysical properties makes the modeling of supercritical fluid flows a most challenging task. In the present work, a Reynolds Averaged Navier Stokes (RANS) computational method following an incompressible but variable density approach is devised on which the performance of several turbulence models is compared in conjunction with a high accuracy multi-parameter equation of state. In addition, a suitable methodology to describe transport properties accounting for dense fluid corrections is applied. The results are validated against experimental data, making it clear that there is no trend between turbulence model complexity and the quality of the produced results. For several instances, one- and two-equation turbulence models produce similar results. Finally, considerations about the applicability of the tested turbulence models in supercritical simulations are given based on the results and the structural nature of each model.

Numerical study of roughness model effect including low-Reynolds number model and wall function method at actual ship scale

A numerical study of roughness effects at an actual ship scale is performed. Low-Reynolds number roughness models based on the two-equation turbulence model are employed, meanwhile, a wall function method is also developed. First, the roughness models are examined for the 2D flat plate case at the Reynolds numbers of $$1.0 \times 10^7$$ , $$1.0 \times 10^8$$ and $$1.0\times 10^9.$$ The resistance coefficient increases with roughness height and uncertainty analysis of the resistance coefficient is performed. Additionally, the distributions of the non-dimensional velocities $$u^+$$ based on the non-dimensional heights $$y^+$$ of the low-Reynolds number models and the wall function method are compared for changing the roughness height. Next, the roughness models and wall function method are applied to the flows around a ship at full scale. The tanker hull form with the flow measurement result from an the actual sea test is selected. The propulsive condition with the free surface effect is achieved by the propeller model. The velocity contours are compared with the measured results of the actual ship. The results of the roughness models show good agreement in comparison with the smooth surface condition. The wall function method leads to reduced grid uncertainty with respect to the resistance coefficient and shows agreement with the measured velocity contours. Consequently, the wall function method is better at full scale.

Computational fluid dynamics modeling of abutment scour under steady current using the level set method

The scour and deposition pattern around an abutment under constant discharge condition is calculated using a three dimensional (3D) Computational Fluid Dynamics (CFD) model. The Reynolds-Averaged Navier Stokes (RANS) equations are solved in three dimensions using a CFD model. The Level Set Method (LSM) is used for calculation of both free surface and bed topography. The two-equation turbulence model (k-ε and k-ω) is used to calculate the eddy viscosity in the RANS equations. The pressure term in the RANS equations on a staggered grid is modeled using the Chorin's projection method. The 5th order Weighted Essentially Non-Oscillatory (WENO) scheme discretizes the convective term of the RANS equations. The Kovacs and Parker and Dey formulations are used for the reduction in bed shear stress on the sloping bed. The model also used the sandslide algorithm which limits bed shear stress reduction during the erosion process. The numerical model solution is validated against experimental results collected at the Politecnico di Milano, Milan, Italy. Further, the numerical model is tested for performance by varying the grid sizes and key parameters like the space and time discretization schemes. The effect of varying bed porosity has been evaluated. Overall, the free surface is well represented in a realistic manner and bed topography is well predicted using the Level Set Method (LSM).

Optimization of pin perforation(s) induced flow dynamic for effective thermal dissipation

This study numerically investigates the 3D perforated pin-fin heat sink forced convection and the induced flow dynamics at Reynolds number ranging between 10 × 103<ReDh < 50 × 103 (Dh represents the hydraulic diameter). The preferences of single perforated pin diameter along pin diameter of Dpin/Dh = 0.188, 0.375 and 0.563, as well as the effect of multiple perforations N on pin of Dpin/Dh = 0.375 and N = 5 are studied. Response surface optimization is incorporated with two-equation turbulence model to explore the correlation between pin perforation diameter and the respective thermal dissipative preferences. Nusselt number maximization serves as the single-objective function to unveil the efficacy of optimized perforated pin-induced flow recirculation. Results show that optimum pin perforation diameter Dpf,opt exists as a function of Dpin and ReDh. Dpf,opt increases with larger Dpin but decreases at higher ReDh, owing to the size of flow recirculation induced leeward from pin. The ratio of Dpf,opt/Dpin is larger for smaller pin to effectively restructure the wider wakes coverage. The optimized flow dynamic in the lee from a perforated pin of Dpf = Dpf,opt is able to strengthen the thermal interaction within the perforation(s), weaken the capability of flow recirculation in trapping thermal energy, as a consequence, provide the most predominant thermal dissipation. Additionally, optimized pins of smaller Dpin and higher N value are more efficient in retrieving back the overheated situation to the targeted low temperature regime in a timely manner.

Study on the Characteristics of Flow Field and Gas Migration in Gas Tunnels

In order to improve the ventilation efficiency and gas dilution effect in the gas tunnel, the main source and formation mechanism of the gas in the tunnel were analyzed, and the hydrodynamic calculation model is established for the gas tunnel ventilation with the auxiliary vertical shaft. The k-ε two-equation turbulence model was used to simulate the ventilation effect under different wind velocity, the flow field distribution characteristics and gas migration regularity under the auxiliary ventilation conditions were obtained. The results indicate that the internal space of the tunnel can be divided into different zones in the longitudinal direction according to the distribution characteristics of the flow field in the tunnel. The distribution of gas concentration in the tunnel is closely related to the flow field characteristics of each zone. The ventilation of the gas tunnel must meet both the requirements of the gas concentration dilution and the cross section wind velocity. When the cross section wind velocity is greater than 0.5m/s, the airflow reaches full turbulence state in tunnel. There is obvious effect on eliminating accumulation of gas at the top of the tunnel by the cross section wind velocity controlling. Under the condition of cross-section wind velocity is 0.5∼1.0m/s, the methane zone is prone to accumulate at the top of the tunnel, which can be diluted when the cross-section wind velocity is greater than 1.0m/s.

Energy conservation and heat transfer enhancement for mixed convection on the vertical galvanizing furnace

The alloying temperature is an important parameter that affects the properties of galvanized products. The objective of this study is to explore the mechanism of conjugate mixed convection in the vertical galvanizing furnace and propose a novel energy conservation method to improve the soaking zone temperature based on the flow pattern and heat transfer characteristics. Herein, the present study applied the k-? two-equation turbulence model to enclose the Navier-Stokes fluid dynamic and energy conservation equations, and the temperature distributions of the steel plate and air-flow field in the furnace were obtained for six Richardson numbers between 1.91 ? 105 and 6.30 ? 105. In the industrial practice, the side baffles were installed at the lateral opening of the cooling tower to alter the height of vertical flow passage, which affected the Richardson number. The results indicate that the Richardson number of 2.4 ? 105 generated the highest heat absorption and maximal temperature in the steel plate due to the balance between natural and forced convection. Furthermore, the results of the on-line experiments validated the simulation research. The method enhanced the steel plate temperature in the soaking zone without increasing the heat power, thereby characterizing it as energy conservation technology.

Numerical investigation on the generation, mixing and convection of entropic and compositional waves in a flow duct

Recent models and experiments have demonstrated that indirect noise can be generated via acceleration of either entropic or compositional perturbations through a nozzle. These studies found that the acoustic signature depends on the extent of the dispersion effects on the perturbation waves during the convection process. In this work, numerical simulations are undertaken using the URANS formulation to model the mixing of unsteady entropic and compositional waves in an open-ended flow duct in the transitional regime (2500 < Re < 8100). The flow is perturbed by either heat addition or radial injection of an inert gas that is heavier (argon) or lighter (helium) than air. The computed temperature and mass fraction fields are compared to experimental results obtained using both intrusive and non-intrusive techniques. Agreement with the experimental data is good. The signatures of both perturbations are well captured using two-equation turbulence models. However, they lag behind the experimental results at downstream probe locations, suggesting that the centreline velocity is underpredicted. Dispersion effects on the compositional waves are shown to be insignificant for the system studied here. In the heat addition case, heat loss is found to be a key factor in capturing the correct entropic perturbation for long convection lengths.

Analysis of Compressibility Corrections for Turbulence Models in Hypersonic Boundary-Layer Applications

To accurately predict the hypersonic turbulent boundary layer, the compressibility corrections for a two-equation turbulence model are investigated substantially. The two-equation shear-stress-transport model based on the assumption of an eddy-viscous coefficient is adopted. The closure approximations for pressure work, pressure dilatation, and dilatation dissipation are examined by a priori and a posteriori analyses. The direct numerical simulation (DNS) of a hypersonic boundary layer shows that the pressure work term has little influence on the turbulent energy transport, whereas the effect of pressure expansion and pressure diffusion terms can be counteracted. The individual closure assumptions are evaluated by using the DNS data. Furthermore, Reynolds-averaged Navier–Stokes simulations with compressibility corrections are conducted for the hypersonic boundary layers of a flat plate and a cone. Comparisons with the experimental data and engineering correlations show that the original turbulence model overestimates the heat flux, and the pressure dilation and dilation dissipation corrections lead to a decrease in heating transfer rates. The combination of a priori and a posteriori analyses comes to the conclusion that the Zeman correction of the dilation dissipation term is applicable in hypersonic boundary layers.

Numerical simulation and performance optimization of the centrifugal fan in a vacuum cleaner

This paper focuses on the efficiency improvement of a centrifugal fan used in a vacuum cleaner. In order to check the performance of the centrifugal fan system, computational fluid dynamics (CFD) analysis is used. The numerical simulation with CFD tool is carried out with RNG [Formula: see text] two-equation turbulence model based on Reynolds-averaged Navier–Stokes equations. To perform the coupling between rotating impeller and stationary area, the multiple reference frame (MRF) model is used. The numerical results of the fan are validated against with experimental results and are found to be highly reliable. The design and optimization of diffuser and impeller of a centrifugal fan are realized by using numerical investigations. For reducing the kinetic energy loss inside the fan, a guide baffle is added to optimize diffuser. The optimization results show that overall efficiency of the fan is improved by 5.27% and considering the lower efficiency of impeller caused by blockage at the blade inlet, etc., the design of impeller with long-short blades is proposed. Several cases of affecting factors under different operating conditions are simulated. Relative length (denoted as [Formula: see text]) and circumferential position of short blades are chosen as design variables. It is found that the efficiency of a fan with a relative length of 0.7 can be increased by 9.34%, and the best circumferential position of short blades is between two adjacent long blades.

Investigation of flow-field around a single generic planar fin using CFD

The purpose of this paper is to initiate a 3-D non-spinning semi-circular missile model with a single generic planar fin and perform a computational analysis on it to understand the flow pattern around the fin. A freestream computational fluid dynamics analysis was done in the subsonic and supersonic Mach range, in which, the fluid behaviour was investigated using a two-equation turbulence model. A structured mesh was adopted to visualize the flow pattern around the fin. The aerodynamic coefficients were calculated for the model, and the predicted values were compared with the previous experimental results as well as the numerical results. This paper attempts to present all the possible flow visualizations which might help in better understanding of flow around missiles having planar fins. This work also attempts to establish a turbulent computational model for a single planar fin missile model for subsonic to supersonic range.

CFD code-to-code benchmarking on simulation of fire and smoke propagation for nuclear applications

Abstract The nuclear industry has seen an increased use of Computational Fluid Dynamics (CFD) technology as a high-fidelity tool for design-basis and beyond design-basis accident simulations. For fire hazards, detailed experimental investigation in a realistic environment is often impractical. Therefore, the use of an advanced 3D CFD modeling approach to predict smoke and fire propagation has risen, especially for nuclear power plant fire modeling applications. CFD simulations can include major contributing and mitigating mechanisms regarding the fire propagation and its consequences, in fine detail and under realistic geometry conditions. In addition, accurate simulations of unsteady 3D fire and smoke spread, in conjunction with evacuation analyses, can be used to establish effective emergency evacuation strategies. In the present study, the fire and smoke propagation in a main control room was modelled using Reynolds-Averaged Navier-Stokes Equation based twoequation turbulence models and a Large Eddy Simulation model implemented in a commercial CFD code, Siemens STAR-CCM+. The predictions from STAR-CCM+ were compared with those obtained in a previous study using the NIST Fire Dynamic Simulator (FDS) code. Although higher temperature was predicted at the fire source by STAR-CCM+, the current study predicted trends similar to the FDS results with some minor differences at the operator location. A follow-up study is currently underway to investigate the factors affecting the differences, including further assessment of codes against available benchmark experiments.