Two-equation Turbulence Model Research Articles

Numerical simulation of size effects of gas explosions in spherical vessels

To study the law of sizes on gas explosions, numerical simulations of methane–air mixture explosions in spherical vessels were performed. The law of sizes on gas explosions is studied using FLUENT simulations with the [Formula: see text] two-equation turbulent model, the eddy-dissipation-concept model, thermal dissipation at a wall boundary, the P1 model, and the SIMPLE algorithm. The experimental results suggest that under an adiabatic condition without energy loss, the maximum explosion pressures in different spherical vessels are all 0.82 MPa, and the effect on the explosion intensity in spherical vessels is small. Under the condition of heat dissipation at the wall boundary, the maximum explosion pressure increases with volume of the spherical vessel. However, the explosion intensity in this condition is lower than that in adiabatic condition. Also, the size effect is not obvious. The size effect on the explosion intensity is significant under the combined effects of heat dissipation at the wall boundary and thermal radiation, where the maximum explosion pressure increases with volume of spherical vessels. On the contrary, the maximum pressure rising rate decreases with the volume of the spherical vessels; this rule coincides with the “cube” law. The studies on the size effects of methane–air mixture explosions in a spherical vessel provide an important reference for establishing a model system that can be used to test and design industrial vessels.

Deep Part Load Flow Analysis in a Francis Model turbine by means of two-phase unsteady flow simulations

Hydropower plants are indispensable to stabilize the grid by reacting quickly to changes of the energy demand. However, an extension of the operating range towards high and deep part load conditions without fatigue of the hydraulic components is desirable to increase their flexibility. In this paper a model sized Francis turbine at low discharge operating conditions (Q/QBEP = 0.27) is analyzed by means of computational fluid dynamics (CFD). Unsteady two-phase simulations for two Thoma-number conditions are conducted. Stochastic pressure oscillations, observed on the test rig at low discharge, require sophisticated numerical models together with small time steps, large grid sizes and long simulation times to cope with these fluctuations. In this paper the BSL-EARSM model (Explicit Algebraic Reynolds Stress) was applied as a compromise between scale resolving and two-equation turbulence models with respect to computational effort and accuracy. Simulation results are compared to pressure measurements showing reasonable agreement in resolving the frequency spectra and amplitude. Inner blade vortices were predicted successfully in shape and size. Surface streamlines in blade-to-blade view are presented, giving insights to the formation of the inner blade vortices. The acquired time dependent pressure fields can be used for quasi-static structural analysis (FEA) for fatigue calculations in the future.

Internal Flow Analysis of Seawater Cooling Pump using CFD

This research focuses on simulation and visualization of flow field characteristics inside a centrifugal pump. The 3D numerical analysis was carried out by using a numerical CFD tool, addressing a Reynolds Average Navier-Stock code with a standard k-Ɛ two-equation turbulence model. The simulation accounts for friction head loss due to rough walls at suction, impeller, discharge areas and volumetric head loss at impeller wear ring. A comparison of performance curves between simulation and experimentation is included, and it reveals a same trend of those results with a small difference of maximum 5 %. At best efficiency point, velocity vectors are smooth but it changes significantly under off-design point, a strong recirculation appears at the outlet of impeller passages near tongue area. A relatively uniform preassure distribution was observed around the impeller in despite of the tongue. Within the volute, because of its geometry, spiral vortexes formed, proving that the flow field in this region was relatively turbulent and unsteady.

Numerical second law analysis around a turbine guide vane using a two-equation turbulence model and comparison with experiments

The present investigation considers determination of entropy production from the flow field around a turbine guide vane, and the numerical simulation of this flow field by means of Computational Fluid Dynamics (CFD). These CFD simulations are based upon RANS, the Reynolds Averaged Navier-Stokes equations, and are carried out using ANSYS CFX-14.0 and the Shear Stress Transport (SST) turbulence model. The flows around the vane from an experimental investigation are simulated for three vane Mach number distributions, each of which is characterized by a different vane trailing edge Mach number. To obtain entropy production from the numerical flow field, two approaches based on second law analysis are utilized: a conventional and a differential one. The conventional approach describes global entropy production between two thermodynamic states by calculating it from the total pressure loss inherent to irreversible processes. The differential approach makes use of the entropy transport equation and yields local entropy production rates directly from local flow field variables predicted by CFD. Global entropy production is then determined by integrating local exergy destruction rates along pathlines, with respect to time. Global exergy destruction results for the wake of the guide vane, obtained using the pathline integration approach, are compared with results from the conventional method analysis and from experimental measurements. The comparison of both numerical approaches with the experiments thereby also serves the purpose to validate them. The most important differences between both numerical methods and the experiments are an under-prediction of maximum exergy destruction near the center of the wake, and an under-prediction of the width of the exergy destruction profile by the pathline integration approach. These differences are believed to be because: (1) the numerical model does not correctly account or include all diffusive effects, which are present within the experimental arrangement, and (2) the sensitivity of the pathline-integration approach to the accurate prediction of the course of pathlines through the flow field.

Differential Equation-Based Specification of Turbulence Integral Length Scales for Cavity Flows

A new modeling approach has been developed that explicitly accounts for expected turbulent eddy length scales in cavity zones. It uses a hybrid approach with Poisson and Hamilton–Jacobi differential equations. These are used to set turbulent length scales to sensible expected values. For complex rim-seal and shroud cavity designs, the method sets an expected length scale based on local cavity width which accurately accounts for the large-scale wakelike flow structures that have been observed in these zones. The method is used to generate length scale fields for three complex rim-seal geometries. Good convergence properties are found, and a smooth transition of length scale between zones is observed. The approach is integrated with the popular Menter shear stress transport (SST) Reynolds-averaged Navier–Stokes (RANS) turbulence model and reduces to the standard Menter model in the mainstream flow. For validation of the model, a transonic deep cavity simulation is performed. Overall, the Poisson–Hamilton–Jacobi model shows significant quantitative and qualitative improvement over the standard Menter and k–ε two-equation turbulence models. In some instances, it is comparable or more accurate than high-fidelity large eddy simulation (LES). In its current development, the approach has been extended through the use of an initial stage of length scale estimation using a Poisson equation. This essentially reduces the need for user objectivity. A key aspect of the approach is that the length scale is automatically set by the model. Notably, the current method is readily implementable in an unstructured, parallel processing computational framework.

Assessment of Simple RANS Turbulence Models for Stall Delay Applications at Low Reynolds Number

This paper assesses the performance of three two-equation turbulence models viz. the SST k-ω, the RNG and realizable k-εfor the simulations of a rotating blade in a wind tunnel experiment where k, ε and ω are turbulent kinetic energy, dissipation rate and specific dissipation respectively. The experiments showed the stall-delay phenomenon at the inboard of the rotating blade at a Reynolds number of 4800. This trend of suction peaks was captured by all three turbulence models albeit not matching the experimental coefficient of pressure accurately. All three models also showed radial flow at the inboard which is consistent with the experiments while the SST predicted the least k at low wall values.

Experimental study and numerical models assessment of turbulent mixed convection heat transfer in a vertical open cavity

Flow and heat transfer in a vertical open cavity with turbulent mixed convection is investigated experimentally and numerically. The internal size of the cavity is 1 m × 1 m × 1.2 m, with liquid nitrogen as the cold source and mica electronic heating plates as the heat source of the experiments. The velocity and temperature fields are obtained by hot-wire anemometry, particle image velocimetry and local temperature sensors for 4.6 × 104 ≤ Re ≤ 5.9 × 104 and Gr ≤ 1.8 × 1013. The secondary upward flow was found to occur near the heated walls. Three two-equation RANS turbulence models, RNG k-ε model, L-B Low Re k-ε model and SST k-ω model, are used in the numerical simulation with the same boundary conditions as experiments. Through comparison with experimental data, Low Re k-ε model performs overall the best in the accuracy in solving mixed convection problems in large-scale vertical cavities with strong buoyancy force.

Numerical study of thermal performance of perforated circular pin fin heat sinks in forced convection

This paper presents a numerical simulation of the heat transfer performance under forced convection for two different types of circular pin fin heat sinks with (Type A) and without (Type B) a hollow in the heated base. COMSOL Multiphysics, which is used for the thermal hydraulic analyses, has proven to be a powerful finite-element-based simulation tool for solving multiple physics-based systems of partial and ordinary differential equations. The standard \( \kappa - \varepsilon \) two-equations turbulence model is employed to describe the turbulent structure and behavior. The numerical results are validated with the experimental results, and are shown to be in good agreement. The effects of the Reynolds number, height of the fin, finning factor and the perforated base plate on the heat-transfer coefficient are investigated and evaluated. The present study strongly recommends the use of a small hollow (\( (D_{h} /D_{b} ) < 0.15 \)) constructed in the base plate of the pin fin heat sink.

Numerical investigation of a HPT with different rotor tip configurations in terms of pressure ratio and efficiency

The choice of the most appropriate rotor tip configuration is important, because it helps to avoid high blade tip losses due to the leakage flow that are responsible for efficiency and pressure ratio drops, mainly in High Pressure Turbine (HPT). This subject has been investigated to improve the axial turbines performance. The HPT used in this work is the turbine designed during the Energy Efficient Engine Program (E3 Program). This HPT was evaluated with different rotor tip geometry configurations: without tip clearance (hypothetical condition), with standard tip clearance geometry (flat-tip), with squealer, with winglet and squealer with winglet. Results were obtained based on the three-dimensional turbulent flow calculations making the use of a commercial CFD RANS equation-based solver with the addition of a two-equation turbulence model, in which the numerical solutions were compared with data available in the open literature for a HPT design-point operation. It was determined that for the HPT studied in this work, the machine efficiency can be improved using the rotor tip geometry equipped with winglet tip configuration. However, the rotor tip geometry equipped with squealer–winglet tip configuration presented a better pressure ratio compromise.

Comparison of Five Two-Equation Turbulence Models for Calculation of Flow in 90° Curved Rectangular Ducts

This paper presents a comparative study of five most widely used two-equation turbulence models in predicting the developing flows in two 90° curved rectangular ducts. These include the standard k-ε model, the shear stress transport k-ω model, and three low-Reynolds number k-ε models by Jones and Launder, Launder and Sharma, and Nagano and Hishida, respectively. The computational time for convergent solutions, streamwise and secondary velocities, pressure distributions as well as the Reynolds-averaged turbulence quantities resolved by these models are compared and validated against available experimental data. The purpose of this paper are to provide a detailed comparative verification for applying the five most widely used two-equation turbulence models to predicting curved rectangular duct flows, which are a kind of proto type flows in fluids engineering, and to provide a reference for the selection of turbulence models in predicting such flows in industrial applications.

Numerical investigations on fully-developed mixed turbulent convection in dimpled parabolic trough receiver tubes

The fully-developed mixed turbulent convective heat transfer characteristics in dimpled tubes of parabolic trough receiver are numerically studied at a certain Reynolds number of 2×104 and different Grashof numbers ranged from 0 to 3.2×1010 to produce substantial surface heat transfer augmentations with relatively small pressure drop penalties. The Boussinesq approximation is applied, in which variations in fluid properties other than density are ignored. The Realizable k-ε two-equation turbulence model with enhancement wall treatment is adopted. The influences of outer wall heat flux distributions and dimple depth on flow resistance and heat transfer rate are illustrated and analyzed. The results indicate that the average friction factor and Nusselt number in dimpled receiver tubes under non-uniform heat flux (NUHF) are larger than those under uniform heat flux (UHF). In most cases, the comprehensive performance of dimpled receiver tube under NUHF is also better than that under UHF. The deep dimples (d/Di=0.875) are far superior to the shallow dimples (d/Di=0.125) at a same Grashof number.

Numerical study of a turbulent impinging jet for different jet-to-plate distances using two-equation turbulence models

▪ Numerical results of a turbulent impinging jet on a flat plate are compared with experimental reference data from ERCOFTAC. Four different jet-to-plate distances from H/D=2 to 14 have been considered at a jet Reynolds number of 23,000. Local flow and heat transfer characteristics are analyzed using the SST turbulence model by Menter and an additional turbulence production limiter by Kato and Launder. For the smaller jet-to-plate distances of H/D=2 and 6, the Kato–Launder turbulence production limiter reproduces the heat transfer in the stagnation region very well. At the higher values H/D=10 and 14, the modification underpredicts the reference data.The near-wall grid resolution at the target plate has been varied for a jet-to-plate distance of H/D=6. The results show the influence of the dimensionless distance of the first node near the wall on flow and heat transfer characteristics. A comparison of a hybrid and a block-structured grid assesses the influence on the mesh topology.

Simulation of Reynolds number influence on heat exchange in turbulent flow of medium slurry

The paper deals with the numerical simulation of mass and heat exchange in turbulent flow of solid-liquid mixture in the range of averaged solid particle diameter from 0.10mm to 0.80mm, named further as the medium slurry. Physical model assumes that dispersed phase is fully suspended and a turbulent flow is hydro-dynamically, and thermally developed in a straight horizontal pipeline. Taking into account the aforementioned assumptions the slurry is treated as a single-phase flow with increased density, while viscosity is equals to a carrier liquid viscosity. The mathematical model constitutes time averaged momentum equation in which the turbulent stress tensor was designated using a two-equation turbulence model, which makes use of the Boussinesq eddy-viscosity hypothesis. Turbulence damping function in the turbulence model was especially designed for the medium slurry. In addition, an energy equation has been used in which a convective term was determined from the energy balance acting on a unit pipe length, assuming linear changes of temperature in main flow direction. Finally, the mathematical model of non-isothermal medium slurry flow comprises four partial differential equations, namely momentum and energy equations, equations of kinetic energy of turbulence and its dissipation rate. Four partial differential equations were solved by a finite difference scheme using own computer code. The objective of the paper is to examine the influence of Reynolds number on temperature profiles and Nusselt number in turbulent flow of medium slurry in the range of solids concentration from 0% to 30% by volume. The effect of influential factors on heat transfer between the pipe and slurry is analysed. The paper demonstrates substantial impact of Reynolds number and solids volume fraction on the Nusselt number. The results of numerical simulation are reviewed.

A gas-kinetic scheme coupled with SST model for turbulent flows

In order to simulate the compressible and incompressible turbulent flows, a gas-kinetic scheme (GKS) based on the Bhatnagar–Gross–Krook (BGK) model coupled with the shear stress transport (SST) two-equation turbulence model is developed. The SST model is a two-equation eddy-viscosity model based on the k−ω and k−ε models, which is one of the most common turbulence models and widely used in Reynolds averaged Navier–Stokes (RANS) modeling for turbulent flows. In this study, we implement GKS–SST coupling model by (a) solving the GKS and SST models in vertex-based finite volume method on hybrid grids; (b) incorporating the SST model into the GKS based on the eddy viscosity hypothesis and using the eddy viscosity to modify the collision time in gas-kinetic scheme; (c) using a modified Venkatakrishnan limiter for hybrid and highly stretched grids during the initial reconstruction stage; (d) applying the boundary conditions adopted from vertex-based solvers for Navier–Stokes equations in present GKS solver. The original gas-kinetic scheme has been proved to be an accurate and effective approach for incompressible and compressible laminar flows, and the SST turbulence model is incorporated here for the turbulent flow. The eddy viscosity at the cell centers is obtained by solving SST model, and then the eddy viscosity on the cell interface can be interpolated from cell centers around. Numerical experiments performed on high Reynolds number turbulent flows around the 2D zero pressure gradient flat plate and a RAE2822 airfoil demonstrate the applicability of the GKS–SST model presented in this study for simulations of high Reynolds number turbulent flows.

Study to identify computational fluid dynamics models for use in determining HVAC duct fitting loss coefficients

This article presents results from a systematic study to establish whether computational fluid dynamics techniques are capable of predicting pressure drop in close-coupled five-gore elbows having nominal diameters of 203 mm (8 in.) and turning radii r/D = 1.5. The close-coupled elbow combinations comprised either a Z-shape or a U-shape. In every instance the duct length separating the center-points of the elbows was systematically varied. An experimental program was likewise conducted to verify the computational fluid dynamics predictions, and data from the measurements are included. Zero-length pressure loss coefficients were predicted using five two-equations Eddy Viscosity Models including the standard k-ϵ, the Realizable k-ϵ, RNG k-ϵ, standard k-ω, and SST k-ω models, as well as the Reynolds Stress Model, and compared to the experimental data. The two-equation turbulence models predicted incorrect trends when applied to flow in U- and Z-configuration ducts. However, the Reynolds Stress Models with enhanced wall treatment was generally able to correctly predict elbow loss coefficients with less than 15% of error.

Numerical Simulation of Supersonic Oxygen Jets at High Ambient Temperature

In this paper, the behavior of cold supersonic oxygen jets entering into high-temperature environment is predicted with four two-equation turbulence models and they are the standard k–ϵ model, the realizable k–ϵ model, the standard k–ω model, and the SST k–ω model. The comparison with experimental results in the literature shows that the standard k–ω turbulence model is superior to the other models when simulating the supersonic jet at high temperature. On this basis, the characteristics of supersonic oxygen jets at high temperature especially at steelmaking temperature are studied. The simulation results indicate that the attenuation of axial velocity of jets slows down and the length of jet potential core extends when increasing the ambient temperature. Meanwhile, the dynamic pressure of multiple jets near the lance centerline increases as the ambient temperature rises. In addition, the effects of ambient temperature on the dynamic pressure of the jet core and the coalescence of multiple jets are also discussed.

Numerical simulation of SGT-600 gas turbine combustor, flow characteristics analysis, and sensitivity measurement with respect to the main fuel holes diameter

In this article, the combustion chamber of SGT600 gas turbine with 18 Alstom EV burners is numerically simulated to investigate the flow field and combustion properties and analyze the sensitivity of this combustor to diameter of main fuel holes. The three-dimensional simulation is carried out based on the turbulent flame closure model for the two-equation turbulence model, k-ɛ, using OpenFOAM code for SGT600 industrial gas turbine burner. An accurate grid combined of structured and unstructured mesh scheme is employed, which is sufficiently fined in areas of high gradients. Grid independency is investigated and validation of the code established comparing the outlet temperature and flame shape with experimental results. Excellent agreement between numerical analyses and experimental data was observed, so that the difference between calculated and measured outlet temperature was 0.1%. On the basis of reasonable matching of the predicted and experimental results for the combustor, the computational fluid dynamics model enables the prediction of the heat shield and combustor’s wall temperature and critical points of operation. In this article, flow-field and operation condition of this combustor and sensitivity analysis with respect to the main fuel holes diameter are numerically investigated.

Forced convective heat transfer on a horizontal circular cylinder due to multiple impinging circular jets

A computational study is undertaken to investigate convective heat transfer on a horizontal cylinder due to a bank of vertically oriented circular jets. The importance of this study stems from the real-world application of convective cooling of rotary cement kilns by the use of large axial fans. A computational model is developed which considers one spatially-periodic section of the domain, and solutions of the conservation equations combined with an appropriate two-equation turbulence model are obtained using the commercial software Fluent™. The computational model is validated by a comparison to previous studies of a single circular jet impinging on a cylinder. A parametric study is presented which considers the impact on average heat transfer due to: jet-to-cylinder spacing (y/d), axial jet spacing (z/d), jet-to-cylinder diameter ratio (d/D), jet offset from the axial centerline (x/d), and jet Reynolds number. Results of the parametric study show that for jet-to-cylinder ratios of d/D⩾0.23, that movement away from the cylinder axis, increased axial spacing and lateral offset all lead to degradation of heat transfer from the cylinder. For d/D=0.15, similar degradation occurs, but in part of the parametric space studied, increased distance from the cylinder and lateral offset leads to enhancements of the heat transfer. The complete set of results is presented as a correlation wherein the influence of all parameters studied are included as power-law corrections to the average Nusselt number.

Flow characteristics prediction in pump mode of a pump turbine using large eddy simulation

To obtain more accurate flow characteristics of pump turbines, the method of large eddy simulation with wall-adapting local eddy viscosity model is applied in simulating several operating points in the pump mode. Firstly, based on the experimental validation, the method of large eddy simulation could better predict the external performance and internal flow characteristics in a pump turbine in the pump mode compared with the method of Reynolds-averaged Navier–Stokes with two-equation turbulence model shear stress transport k–ω. Then, flow characteristics under 1.00 QBEP (best efficiency point), 0.91 QBEP, 0.88 QBEP, and 0.85 QBEP operating points are investigated to find out the causes of the head drop in the energy-discharge curve through large eddy simulation. The detailed analysis reveals that the head drop at the point 0.85 QBEP is related to the recirculation flow at the runner inlet. Finally, unsteady studies confirm that vortex movement at the runner inlet lead to the variation of the amplitudes and directions of the velocity, which generates the rotation of the separation vortices in the runner and stay vane channels.

Quasi-three dimensional hydraulic design and performance calculation of high specific speed mixed-flow pump

According to the basic parameters of 211-80 high specific speed mixed-flow pump, based on the quasi-three dimensional flow theory, the hydraulic design of impeller and its matching spaced guide vanes for high specific speed mixed flow pump was completed, in which the iterative calculation of S1, S2 stream surfaces was employed to obtain meridional flow fields and the point-by-point integration method was employed to draw blade camber lines. Blades are thickened as well as blade leading edges are smoothed in the conformal mapping surface. Subsequently the internal fields of the whole flow passage of the designed pump were simulated by using RANS equations with RNG k-ε two-equation turbulent model. The results show that, compared with the 211-80 model, the hydraulic efficiency of the designed pump at the optimal flow rate increases 9.1%. The hydraulic efficiency of designed pump in low flow rate condition (78% designed flow rate) increases 6.46%. The hydraulic efficiency in high flow rate areas increases obviously and there is no bad phenomenon of suddenly decrease of hydraulic efficiency in model pump. From the distributions of velocity and pressure fields, it can be seen that the flow in impeller is uniform and the increase of pressure is gentle. There are no obvious impact phenomenon on impeller inlet and obvious wake shedding vortex phenomenon from impeller outlet to guide vanes inlet.