Equation Turbulence Model Research Articles

Aerodynamic Study of Two Opposing Moving Trains in a Tunnel Based on Different Nose Contours

It is well known that the train nose shape has significant influence on the aerodynamic characteristics. This study explores the influence of four kinds of nose shapes (fusiform, flat-broad, bulge-broad, ellipsoidal) on the aerodynamic performance of two opposing high-speed trains passing by each other through a tunnel at 250 km/h. The method of three dimensional, compressible, unsteady Reynolds-averaged Navier-Stokes equations and RNG k-ε double equation turbulence model was carried out to simulate the whole process of two trains passing by each other inside a tunnel. Then the pressure variations on tunnel wall and train surface are compared with previous full-scale test to validate the numerical method adopted in this paper. The assessment characteristics, such as transient pressure and aerodynamic loading, are analyzed to investigate the influence of nose shape on these assessment parameters. It is revealed that aerodynamic performance of trains which have longitudinal nose profile line B (fusiform, flat-broad shape) is relatively better when passing by each other in a tunnel. The results can be used as a guideline for high-speed train nose shape design.

Study of Flow Characteristics of ASP Solution Based on Numerical Simulation in Jet Nozzle Channel

With increasing depth of oilfield development, sublayers are becoming the main object of 0o9alkali-surfactant-polymer (ASP) flooding. Compared with major layers, sublayers differ in permeability, which may cause clogging of low-permeability layers when ASP solution containing polymer of the same molecular weight is injected into these layers. To solve this problem, injection allocators are widely used in oilfields. In this work, the jet nozzle channel was modeled using FLUENT 6.3 software. The ASP solution flowing through the jet nozzle channel in the injection allocator was simulated using a mathematical model based on the Navier-Stokes equation and renormalization group (RNG) turbulence and power-law fluid models. The effect of nozzle diameter on the distribution of differential pressure, velocity, average strain rate, turbulence power, and apparent viscosity of the flow were analyzed. It was found that with an increase in the nozzle diameter the differential pressure and velocity of the flow decrease before and after passing through the nozzle, whereas the average strain rate increases gradually. The simulation results can provide theoretical guidance for optimal design of the nozzle.

Rough Surface Wall Function Treatment With Single Equation Turbulence Models

Most literature in the area of turbulent flow over rough surfaces discusses methods for turbulence models based on two or more transport equations, one of which is that for turbulence kinetic energy which supplies k that is heavily used for the rough wall treatment. However, many aeronautical engineers routinely use single equation turbulence models which solve directly for eddy viscosity and do not involve k. The present work proposes methods by which such one-equation models can predict flow cases which include multiple rough surfaces. The current approach does not impose changes to the wall distance function, should such a function be necessary. Several examples show that the proposed method is able to produce good predictions of both skin friction and heat transfer along rough surfaces. While results are not always as accurate as those predicted by turbulence models which solve for k, especially if detached or wake-like flow regions exist, accompanied by a significant increase in eddy viscosity, the single-equation models are able to provide predictions at least good enough for preliminary studies.

Effect of different turbulence models on combustion and emission characteristics of hydrogen/air flames

This paper aims to present modeling results of hydrogen/air combustion in a micro-cylindrical combustor. Modeling studies were carried out with different turbulence models to evaluate performance of these models in micro combustion simulations by using a commercially available computational fluid dynamics code. Turbulence models implemented in this study are Standard k-ε, Renormalization Group k-ε, Realizable k-ε, and Reynolds Stress Transport. A three-dimensional micro combustor model was built to investigate impact of various turbulence models on combustion and emission behavior of studied hydrogen/air flames. Performance evaluation of these models was executed by examining combustor outer wall temperature distribution; combustor centerline temperature, velocity, pressure, species and NOx profiles. Combustion reaction scheme with 9 species and 19 steps was modeled using Eddy Dissipation Concept model. Results obtained from this study were validated with published experimental data. Numerical results showed that two equation turbulence models give consistent simulation results with published experimental data by means of trend and value. Renormalization Group k-ε model was found to give consistent simulation results with experimental data, whereas Reynolds Stress Model was failed to predict detailed features of combustion process.

Theoretical and computational analyses of LNG evaporator

Theoretical and numerical analysis on the fluid flow and heat transfer inside a LNG evaporator is conducted in this work. Methane is used instead of LNG as the operating fluid. This is because; methane constitutes over 80% of natural gas. The analytical calculations are performed using simple mass and energy balance equations. The analytical calculations are made to assess the pressure and temperature variations in the steam tube. Multiphase numerical simulations are performed by solving the governing equations (basic flow equations of continuity, momentum and energy equations) in a portion of the evaporator domain consisting of a single steam pipe. The flow equations are solved along with equations of species transport. Multiphase modeling is incorporated using VOF method. Liquid methane is the primary phase. It vaporizes into the secondary phase gaseous methane. Steam is another secondary phase which flows through the heating coils. Turbulence is modeled by a two equation turbulence model. Both the theoretical and numerical predictions are seen to match well with each other. Further parametric studies are planned based on the current research.

Multiphase injector modelling for automotive SCR systems: A full factorial design of experiment and optimization

Advances in emission control technologies have seen the introduction of Selective Catalyst Reduction (SCR) systems as a method for NOx decontamination in light and heavy duty vehicles. SCR systems make use of a urea–water solution (UWS) injected directly into the exhaust gas stream for the reduction of NOx contaminants to Nitrogen (N2) over a monolith catalyst [2]. The effectiveness of an SCR system depends on many factors including the type of catalysts, the injection and mixing pattern of the UWS, temperature and more [1].Spray analysis involves multi-phase flow phenomena and requires the numerical solution of the conservation and transport equations for the gas and the liquid phase simultaneously. Spray/wall interaction mechanisms such as droplet splash, spread, rebound or stick are complex to model and directly affected by the injection parameters [4]. The accurate modelling of the UWS injector can help in the prediction of phenomena such as wall film formation, droplet evaporation and urea crystallization [7].This study presents a series of multi-phase numerical analyses, computed with the commercial software AVL Fire 2014 v, to measure the impact of injection velocity, spray angle and droplet size, in the overall performance of an SCR system. The analysis consisted of a completely mixed turbulent flow, solved using a two equations turbulence model (k−zeta−f). The interaction of the injected particles was solved with an Euler/Lagrange approach, the liquid phase calculation was based on the statistical Discrete Droplet Method interacting with the numerical solution of the conservation equations of the flow pattern.It was found that the injection parameters had an impact on the final results of the ammonia uniformity index (NH3UI) and wall film formation on the SCR system. The method applied in this work successfully predicted the performance of an SCR system. Moreover, a series of response surfaces were created based on a linear regression model which allowed for further design optimization outside of the initial experimental space.

CFD Studies on Triangular Micro-Vortex Generators in Flow Control

In the present study, the flow characteristics of the commercially used S809 wind turbine airfoil controlled with triangular counter-rotating micro-vortex generators at stall angle of attack of 15 degrees and 10 m/s, 15 m/s and 20 m/s (speed range used in the wind turbine applications) had been computationally investigated. In addition to the controlled airfoil, an uncontrolled airfoil was also studied for the comparison. The modelling and analysis had been carried out using incompressible, Reynolds Averaged Navier Stokes equation using Spalart-Allmaras one equation turbulence model. The numerical computations were performed with SIMPLE algorithm. The velocity profiles at different locations on the suction surface were plotted for both uncontrolled and controlled airfoils. The shear stresses exerted on the upper surface of the airfoil in both the configurations were also compared. It is found that the controlled airfoil, the shear stress distribution was greatly increased near to trailing edge of the airfoil revealing the superiority of vortex generators in increasing the efficiency of wind turbine by delaying boundary layer separation. The qualitative results of flow visualization in the spanwise direction also support the quantitative findings of velocity profiles and shear stress distribution.

Conjugate Heat Transfer Analysis in a Glazed Room Modeled as a Square Cavity

ABSTRACTA numerical study of conjugate heat transfer by turbulent natural convection in a room with three different glazed configurations is presented. The room is modeled as a square closed cavity, where the lower wall is adiabatic, the right wall is semitransparent, and the upper and left walls are opaque conductive surfaces. Governing equations of mass, momentum, and energy were solved by the finite volume method with a two equation turbulence model. The results are presented in terms of streamlines, isotherms, heatlines, turbulent viscosity isolines, and thermal parameters, such as indoor temperatures and heat transfer coefficients. From the three cases considered in this study, the reflective glass window was the optimal configuration from the thermal comfort point of view for both design days. On the contrary, the glass-film configuration showed the worst indoor thermal performance inside the cavity despite of being the configuration that allows lower energy transferred into the room through the glazed surface. A set of useful heat transfer correlations are obtained for building design applications and energy codes in temperate climates.

Certain Investigations of Numerical Simulation on Supersonic Combustor of Staged Transverse Injection behind a Backward Facing Step with Cavity

Within the available space and residence time constrain, it is a herculean task to design scramjet combustor. Numerical simulation is carried out to investigate the cavity formation in the scramjet combustor model with staged transverse injection behind the backward facing step (BFS). This paper presents the result of a numerical study that investigates the effect of four different scramjet combustor models on fuel mixing characteristics with Free-stream air at Mach 2, and the fuel injection through both the injectors at Mach 1. In this study, the flow is treated as non-reacting (Cold flow) and the fuel is injected normal to the free-stream direction. Numerical simulation is accomplished by employing the finite volume based code Computational Fluid Dynamics (CFD) ANSYS/Fluent-14 with two equation turbulence models (Shear Stress Transport K-ω). The performance characteristics of the scramjet combustor is assessed by the following parameters such as maximum mole fraction of injectant (fmax), streamwise vorticity (ζ), average stagnation pressure (Poavg) and air fuel mixing efficiency (m). In order to study the performance of the scramjet combustor with cavity formation with staged transverse injection behind the BFS, four different scramjet combustor models are created by introducing a slab between the injectors. The slab shape for the first one is a rectangular, followed by triangular with right side ramp, then triangular with left side ramp and wedge (both side ramp). In all four models, the slab is placed at mid portion of total distance between the staged transverse injector. The study reveals that the air fuel mixing efficiency of the Triangular slab with left side ramp (TLR) placed at a mid portion of the total length between staged injectors comparatively better off than the other cases.

Numerical Investigation of Temporal Variation of Density Flow and Parameters

Experimental investigations and observations indicate that water quality modeling is related to the formation of flows in the dam reservoirs. Correct estimation of dam reservoir flow, plunging point and plunging depth are very important for the dam reservoir sedimentation and water quality problem. Therefore, inflow river-water into a dam is modeled in two dimensions through a reservoir with sloping bottom. The model is developed using nonlinear and unsteady continuity, momentum, energy and k-ε turbulence model equations. The equations of the model are solved based on the initial and boundary conditions of the dam reservoir flow for a range of bottom slopes. In addition to velocity, temperature and turbulence viscosity variation through the dam reservoir, the effects of density flow parameters such as plunging depths, plunging points, mixing rate are determined from the simulation results. The results of the present model are compared to the previous experimental works and the mathematical models.

Numerical Simulation of Combustible Gas Diffusion with Obstacle in Space

The Reynolds averaged Navier-Stokes equation and the turbulence model equation which modified by buoyancy and the species transport equation are used to numerically calculate leakage and diffusion of combustible gas under the influence of obstacle in limited space in order to obtain the influence of obstacle on leakage and diffusion and furthermore get the concentration distribution of different positions of leakage holes. The results show that the obstacle can block diffusion of combustible gas and different positions have different concentration flied. When the leakage hole is at opposite side with outlet, the higher the position of leakage hole, the bigger the burst area. The bigger the height of obstacle, the bigger the burst area of finite space. The simulation results are contribute to safety design of indoor gas pipelines and can supply reference for preventing explosion accidents of indoor combustible gas.

Numerical analysis of solar updraft power plant integrated with external heat source

Many countries started to adopt clean energy sources, where solar energy is the first priority. Solar chimney power plant was selected in this study as a system which converts solar thermal energy to electrical power. In this research, hybrid solar chimney power plant model has been proposed as a day and night functional integrated system using external heat source to enhance the system performance and cover the setback of solar absence at night and cloudy days. With the help of ANSYS Fluent software, three-dimensional steady-state of Navier-Stokes and energy equations have been solved. Realized k–∊ two equation turbulent model equations and discrete ordinates (DO) radiation model equations were solved for the conventional model. The results were validated using experimental measurements. Afterward, the influence of thermal enhancing channels installation on the system performance was predicted and analysed in hybrid mode. The simulation results showed that this system could enhance the plant during the day. Percentage of enhancement was 10% and 14% for velocity and temperature respectively, and the power output percentage enhancement was 18% when the solar intensity was 1000 W/m 2 , and external heat source mass flow rate and the temperature for each channels was 0.015 Kg/s and 100°C respectively, in comparison with the conventional model.

고속열차의 지하정거장 통과 시 발생하는 공기역학적 영향에 대한 전산유체해석 연구

Dong-tan Station, shared by high-speed railway and urban express railway, is a very complicated underground station having 6 tracks together with barrier and shafts between them, therefore it seems very hard to investigate the aerodynamic effects including the pressure variation and train gust in the station when a high-speed train runs through it. In this study, the aerodynamic effects on the structures and platform passengers when a high-speed train runs through an underground station have been studied using Computational Fluid Dynamics. STAR-CCM+ has been employed for numerical simulation based on Navier-Stokes equation and 2-equation turbulence model and moving mesh scheme supported by STAR-CCM+ has also been used to represent the relative motion between a train and station. Based on the simulation results, the unsteady flow fields in the underground station induced by the high-speed train have been analyzed and the pressures on the PSDs and pressure variation at the platform have quantitatively assessed.

RANS simulation of high-Re turbulent flows using an immersed boundary method in conjunction with wall modeling

Abstract In this paper, an immersed boundary method, called the domain-free discretization (DFD) method, is developed to simulate the turbulent flows at high Reynolds numbers governed by the RANS equations. The strategy of DFD is that the discrete form of partial differential equations at an interior mesh node may involve some nodes outside the solution domain. Wall-modeling techniques, such as the adaptive wall function and the two-layer wall model, are adopted to alleviate the requirement on the near-wall mesh size. In the two-layer wall model, the effect of streamwise pressure gradient can be taken into account. The no-penetration condition and the wall shear stress prescribed by wall modeling, instead of the no-slip condition, are enforced at the immersed boundary. The normal and tangential velocity components at an exterior dependent node are evaluated via the linear extrapolation in the normal direction in conjunction with the no-penetration condition and the prescribed shear stress, respectively. The pressure at an exterior dependent node is obtained by solving the simplified momentum equation, and the temperature is calculated via the Crocoo-Busemann relation. By using analytical solutions, appropriate boundary conditions for the SST k − ω turbulence model equations are specified and then the turbulence variables at an exterior dependent node are determined. Various subsonic and transonic high-Re turbulent flows over stationary and moving bodies have been simulated to validate the present developed DFD method.

Modeling of wind turbine wakes under thermally-stratified atmospheric boundary layer

In the present work, the wake behavior of wind turbines, operating under thermally-stratified atmospheric boundary layer (ABL), is numerically investigated. The steady state three dimensional Reynolds-Averaged Navier–Stokes (RANS) equations, combined with the actuator disk approach, are used in the simulation. The standard k-ε turbulence model as well as a modified one namely El Kasmi model are adopted. Two different methods are used and compared, for representing the atmospheric stratification flow conditions: In the first one (direct method), the energy equation is considered along with mass, momentum, and turbulence model equations. In the second one (indirect method), stratification is modeled by means of additional buoyancy production and dissipation terms. Such terms are added to the turbulent kinetic energy and dissipation rate equations, instead of solving the energy equation. The results obtained from both methods show a reasonable agreement with the experimental data available from the literature. Moreover, it is concluded that, there is no significant difference between the predicted results from both methods. Further, the effect of the atmospheric stability class on the wake deficit and the available wind power in the wake region has been also investigated using the indirect method. It has been found that, there is a significant influence of the different atmospheric conditions on the wake behavior. In particular, the wake region becomes smaller with the decreasing of atmospheric stability, and hence a higher wind power in the wake region is observed for unstable conditions.

Numerical analysis of hydrogen fuel scramjet combustor with turbulence development inserts and with different turbulence models

In this paper an attempt has been made to find out the better mixing of fuel and air in the supersonic ramjet engines (SCRAMJET). For this the modified and innovated computational models were created by considering the DLR scramjet model as a standard and reference model for the validation of results. The mixing of fuel and air in the combustion chamber is greatly affected by the turbulence, shock waves and vortices. Hence the basic and standard DLR scramjet model has been remodelled by considering the triangular and circular bumps attached to the sides of combustion chamber walls. The numerical analysis has been carried out by using ANSYS-FLUENT. Different turbulence models like two equation turbulence models (k–ω and k–ε) and the most significant and efficient turbulence model for combustion analysis is large eddy simulation model is also considered for better understanding of turbulence effect on the mixing of fuel and air and also to find out the best suitable turbulence model for the scramjet combustion type numerically simulated problems. From the numerical analysis of various turbulence models, it is observed that the numerical results of k–ω model are in a good agreement qualitatively and quantitatively with experimental results. From the comparison of different computational domain numerical results, it is identified that the formation of oblique shock and effect of this shock on fuel jet is more for the case of scramjet model with circular inserts and also it increases the combustion efficiency.

Simulation of exchange flow between open water and floating vegetation using a modified RNG k-ε turbulence model

The paper focuses on the numerical simulation of the exchange flow between open water and floating vegetation, which plays an important role in maintaining the ecological balance by transporting nutrient matter. The simulation was conducted using a new solver developed upon OpenFOAM. A modified RNG k-e turbulence model, which is expected to model both the high- and low-Reynolds number flows correctly, was used to determine the eddy viscosity. Several particular terms were added into the momentum equations and turbulence model equations to model the effects of vegetation and buoyancy. Among these terms, the term for the effect of vegetation in the e-equation was re-modelled. The model was validated by properly predicting the profiles of mean velocity and turbulent kinetic energy for flows through suspended canopies. The density flow between open and vegetated water was simulated with the same conditions as those of the experiment conducted by Zhang and Nepf. The predicted results agreed well with the experimental data and provided more detailed information of such exchange flow. The convection between the root layer and the layer beneath the roots, which was not observed in the experiment, was observed in the numerical simulation.

Turbulence: Does Energy Cascade Exist?

To answer the question whether a cascade of energy exists or not in turbulence, we propose a set of correlation functions able to test if there is an irreversible transfert of energy, step by step, from large to small structures. These tests are applied to real Eulerian data of a turbulent velocity flow, taken in the wind grid tunnel of Modane, and also to a prototype model equation for wave turbulence. First we demonstrate the irreversible character of the flow by using multi-time correlation function at a given point of space. Moreover the unexpected behavior of the test function leads us to connect irreversibility and finite time singularities (intermittency). Secondly we show that turbulent cascade exists, and is a dynamical process, by using a test function depending on time and frequency. The cascade shows up only in the inertial domain where the kinetic energy is transferred more rapidly (on average) from the wavenumber $k_{1}$ to $k_{2}$ than from $k_{1}$ to $k'_{2}$ larger than $k_{2}$.

Installation position determination of wind speed sensors on steel pole along a high-speed railway

In order to consider the influence of steel pole on the measurement of wind speed sensors and determinate the installation position of wind speed sensors, the flow field around wind speed sensors was investigated. Based on the three-dimensional steady Reynolds-averaged Navier-Stokes equations and k-e double equations turbulent model, the field flow around the wind speed sensor and the steel pole along a high-speed railway was simulated on an unstructured grid. The grid-independent validation was conducted and the accuracy of the present numerical simulation method was validated by experiments and simulations carried out by previous researchers. Results show that the steel pole has a significant influence on the measurement results of wind speed sensors. As the distance between two wind speed sensors is varied from 0.3 to 1.0 m, the impact angles are less than ±20°, it is proposed that the distance between two wind speed sensors is 0.8 m at least, and the interval between wind speed sensors and the steel pole is more than 1.0 m with the sensors located on the upstream side.

Numerical analysis of entropy production on a LNG cryogenic submerged pump

LNG cryogenic submerged pumps are the core component of LNG terminals and filling stations for mass transmission. A deep understanding of hydraulic behavior in LNG cryogenic submerged pumps is helpful to improve their performance. However, traditional analysis of hydraulic losses lacks intuitiveness. In this study, the irreversible energy loss was investigated based on entropy production theory, focusing on the magnitude and position of hydraulic loss of a two-stage LNG cryogenic submerged pump. Subsequently, a 3D steady flow field with a Reynolds stress turbulence model and energy equation model was conducted, and a UDF was used to calculate the entropy production. The results indicated that entropy production theory had advantages for evaluating the energy characteristics of the LNG pump. Turbulent dissipation and wall friction were considered to be the primary sources of generating irreversible hydraulic loss. Turbulent entropy production and wall entropy production accounted for approximately 73.25%–77.48% and 22.49%–26.72% of the entire production, respectively. At a 1.0Qd flow condition, STD and SW were 73.51% and 26.46%, respectively. The impeller at the second stage and guide vanes at the two stages (greater than 40 W/K) were the hydraulic loss domains, and the volumetric entropy production rate in impeller of the second stage was extremely high (average 10 000 W/m3K). The separation flow, shock phenomenon and vortex were considered to be hydrodynamic factors for the formation of entropy production. This research indicated that the entropy production theory can help to quantify irreversible energy loss and locate where and how it occurs, and even further to optimize pump performance.