Epsilon Model Research Articles

Numerical Study on Flow Field and Heat Transfer Enhancement in a Cooling Channel With Novel Ribs Based on Battery Thermal Management System

Turbulent flow and heat transfer characteristics in a cooling channel with novel ribs have been numerically studied to improve thermal efficiency inside future electric vehicle batteries. In this study, the essential ratios of channel length, rib height, and rib pitch were all set to 6.67, 0.13, and 8.66, respectively. The realizable turbulent kinetic energy - epsilon model was used for the numerical simulation work under the Reynolds number varied from 10,000 to 50,000. The results showed that the heat transfer enhancement on a surface depended on the secondary flows due to the ribs. The enhancement of the wavy-winglet rib was approximately 9.8%−32% compared to other rib cases. Nevertheless, the improved heat transfer came at the expense of a higher pressure penalty. Above 29.7% of the friction factor for the wavy-winglet rib was obtained, compared to orthogonal ribs. In addition, the wavy-winglet rib gave the best thermal-hydraulic performance of the designs explored.

Parabolic turbulence k-epsilon model with applications in fluid flows through permeable media

In this work, we study a one-equation turbulence \(k\)-epsilon model that governs fluid flows through permeable media. The model problem under consideration here is derived from the incompressible Navier-Stokes equations by the application of a time-averaging operator used in the \(k\)-epsilon modeling and a volume-averaging operator that is characteristic of modeling unsteady porous media flows. For the associated initial- and boundary-value problem, we prove the existence of suitable weak solutions (average velocity field and turbulent kinetic energy) in the space dimensions of physics interest.

A novel three-dimensional numerical model for PV/T water system in hot climate region

Hybrid PV/Thermal systems (PV/T) are proposed to harvest the two renewable forms of solar energy, electrical and thermal. The use of PV/T systems improves electrical efficiency while utilizing the available solar thermal energy for various heating applications. In this work, numerical simulations perform for PV/T system in hot climate conditions. The cooling system consists of eleven channels arranged in parallel to each other on the backside of the PV module. A novel three-dimensional numerical model of the PV/T system was developed to evaluate the thermal efficiency. The standard k – epsilon model was used to simulate the flow. This novel system was based on using symmetric-convection boundary conditions for the right and left sides of the PV/T model and symmetric-symmetric boundary conditions for the middle cooling channels rather than simulating the whole cooling system. Using one channel simulation allows the creation of less number of meshes, hence, reduces the computational time. The thermal efficiency was estimated by the superposition method for all cooling channels of the PV/T system. The thermal efficiency of the PV/T system was 60% at 0.4 (L/min) and 68% at 5.4 (L/min). The obtained results were in good agreement with the results presented in the literature.

Least-squares reverse time migration in TTI media using a pure qP-wave equation

Anisotropy is a common phenomenon in subsurface strata and should be considered in seismic imaging and inversion. Seismic imaging in a vertical transversely isotropic (VTI) medium does not take into account the effects of the tilt angles, which can lead to degraded migrated images in areas with strong anisotropy. To correct such waveform distortion, reduce related image artifacts, and improve migration resolution, a tilted transversely isotropic (TTI) least-squares reverse time migration (LSRTM) method is presented. In the LSRTM, a pure qP-wave equation is used and solved with the finite-difference method. We have analyzed the stability condition for the pure qP-wave equation using the matrix method, which is used to ensure the stability of wave propagation in the TTI medium. Based on this wave equation, we derive a corresponding demigration (Born modeling) and adjoint migration operators to implement TTI LSRTM. Numerical tests on the synthetic data show the advantages of TTI LSRTM over VTI RTM and VTI LSRTM when the recorded data contain strong effects caused by large tilt angles. Our numerical experiments illustrate that the sensitivity of the adopted TTI LSRTM to the migration velocity errors is much higher than that to the anisotropic parameters (including epsilon, delta, and tilted angle parameters), and its sensitivity to the epsilon model and tilt angle is higher than that to the delta model.

Effect of Chord Length on the Performance of H-Darrieus Wind Turbine with NACA 4415 Airfoil

The effect of chord length to the performance of an H-Darrieus Vertical Axis Wind Turbine (VAWT) was investigated numerically. The turbine blade made of NACA 4155 airfoil. A set of governing equations has been developed. In order to incorporate the turbulence effect, k – epsilon model was adopted. A Computational Fluid Dynamic code has been used to solve the problem. The non-dimensional chord length of 0.2, 0.3, 0.4, and 0.5 are investigated. The contour velocity in the computational domain was plotted and discussed. By using the average velocity of the wind leaving the turbine, power coefficient is estimated. The results show that the power coefficient for non-dimensional chord length of 0.2, 0.3, 0.4, and 0.5 is 0.51, 0.57, 0.59, and 0.59, respectively. The conclusion here is that non-dimensional chord length strongly affects the power. Increasing the chord length will increase the coefficient power. However, there exists an optimum chord length it is 0.4. Thus, it is suggested to use the non-dimensional chord length of 0.4.

Numerical and Experimental Investigation on Flow Dynamics in a Pipe With an Abrupt Change in Diameter

Flow dynamics in a pipe with an abrupt change in diameter was experimentally and numerically analyzed. Two-dimensional stationary Reynolds-averaged Navier–Stokes (RANS) k–ε epsilon model was used to describe the development of axial and radial velocity and turbulent kinetic energy in two cases. The theoretical results were compared with experimental findings gained in a transparent pipe test rig. Particle image velocimetry (PIV) technique was used to analyze the development of flow in a pipe with complex geometry. The measured and modeled velocities and turbulent kinetic energy were found to be in good agreement. The two-dimensional stationary RANS k–ε model is suitable for the analysis of the flow dynamics in real old rough pipes where the pipe wall build-up leads to changes in the actual diameter of the pipe but the flow can still be considered axially symmetrical.

Modeling the Shear Strength of Reinforced Aerated Concrete Slabs via Support Vector Regression

Autoclaved aerated concrete (AAC) attracts attention as it provides superior material characteristics such as high thermal insulation and environmentally friendly properties. Apart from non-structural applications, AAC is being considered as a structural material due to its characteristics such as lighter weight compared to normal concrete, resulting in lower design cost. This study focuses on the feasibility of support vector regression (SVR) in predicting the shear resistance of reinforced AAC slabs. An experimental dataset with 271 data points extracted from eight sources is used to develop models. Based on random selection, the dataset is divided into two portions, 75% for model development and 25% is for testing the validity of the model. Two SVR model types (epsilon and Nu) and four kernel functions (linear, polynomial, sigmoid and radial basis) are used for model development and the results of each model and kernel type is presented in terms of correlation coefficient (R2) and mean squared error (MSE). Results show that epsilon model type with radial basis function yields the best SVR model.

Investigation of Supersonic Oxygen Jet Potential Core Length at Various Ambient Temperatures

A computational fluid dynamics (CFD) model for a supersonic oxygen jet has been developed with detailed consideration of compressible flow properties and ambient temperature conditions. The model was validated by comparison of the axial velocity of the supersonic jet predicted by the CFD model with experimental measurements under different ambient temperatures. The effects of the turbulence model were studied. A modified standard k–epsilon model was used to consider turbulence mixing due to both compressibility and the temperature gradient. Overall, the predictions of the CFD model showed good agreement with experimental measurements for all temperature conditions. The potential core length of the supersonic oxygen jet was studied and compared with the results of empirical models, indicating good agreement with that used by Sumi et al. Parametric study on the ambient temperature was conducted, revealing that the potential core length of the supersonic oxygen jet increases linearly with the ambient temperature.

Numerical investigation of vapor volume fraction in subcooled flow boiling of a nanofluid

The Mixture model is applied to study the subcooled boiling of Alumina-water nanofluid in both vertical concentric annulus and vertical tube. The turbulence of the fluid is modeled through k–epsilon model. Local flow characteristics of subcooled flow boiling such as axial volume fraction and distribution of temperature are predicted. There is a very good agreement among the numerical and experimental results in the literature. This model is able to predict the distribution of temperature and the axial vapor volume fraction precisely. Variations of vapor volume fraction in conditions of constant velocity and mass flux in inlet are investigated and compared with together in different nanoparticles concentrations.

Modeling a weak turbulent flow in a narrow and wavy channel: case of micro-irrigation

The baffle-fitted labyrinth channel is commonly used in micro-irrigation systems. The flow in this labyrinth channel has a rather low-Reynolds number. In addition, emitter clogging, which is the major drawback of the micro-irrigation technique, is significantly related to flow characteristics. In order to design an anti-clogging emitter with a good performance, the hydrodynamics must be understood and analyzed. As CFD modeling is nowadays the most efficient approach for improving emitter geometry, this paper presents assessment of several k― \\\backslashvarepsilon \epsilon turbulence models for computation of micro-irrigation emitter hydrodynamics. The objective is to determine the simplest and most efficient model to improve emitter conception, in terms of both discharge/pressure loss and limitation of the areas where low velocity is likely to generate emitter clogging. Low-Reynolds number k― \\\backslashvarepsilon \epsilon models are often assumed to be more suitable for the labyrinth-channel flow since these models have no wall functions, they can take into account low turbulence levels and they account for the effect of damped turbulence. The low-Reynolds number k― \\\backslashvarepsilon \epsilon models used in the present study are compared to high-Reynolds number k― \\\backslashvarepsilon \epsilon models. Very different trends are observed between low-Reynolds number k― \\\backslashvarepsilon \epsilon models. Some models reproduce a turbulent behavior, while others reproduce a laminar behavior. The head loss analysis reveals that, contrary to classical smooth pipe flow, the contribution of turbulent dissipation cannot be neglected since its contribution is larger than wall friction ones. This feature explains why different models can induce quite different flow behavior.

Numerical modelling of two-phase oil–water flow patterns in a subsea pipeline

The concurrent flow of oil and water in pipelines is a common occurrence in offshore oil production systems. The internal structure of the oil–water flow, known as the flow pattern, and the distribution of water have a great influence on the design of the pipeline. However, due to the complex nature of oil–water flows, predicting flow patterns under different operating conditions is a challenging task. The present study is an attempt toward using a computational fluid dynamics model for predicting the flow patterns under different working conditions. To this end, an Eulerian–Eulerian model along with appropriate closure laws was employed to model two-phase oil–water flows through a horizontal pipe. The standard k–epsilon model was adopted to account for the turbulence effects. Furthermore, a brief description of the main interfacial forces namely the drag, lift, and turbulent dispersion forces has been presented. The numerical model was used to predict the flow patterns under different operating conditions ranging from low to high velocities and water cuts, respectively. A comparison among the obtained numerical results and published experimental data showed reasonable agreement.

Numerical investigation of flow structures around a cylindrical afterbody under supersonic condition

Large Eddy Simulation (LES) with dynamic Smagorinsky model has been applied to numerically investigate the complicated flow structures that evolve in the near wake of a cylindrical after body aligned with a uniform Mach 2.46 flow. Mean flow field properties obtained from numerical simulations, such as axial velocity, pressure on base surface, have been compared with the experimental measurements as well as with other published results. It has been found that standard k–epsilon model fails to predict the flow properties in the recirculation region where better agreement has been observed between the data obtained from LES and experimental measurements. Flow Statistics like turbulent kinetic energy and primary Reynolds' stress have also been calculated and compared with the results obtained from experiments in order to quantitatively assess the ability of LES technique to predict the turbulence properties of flow field in the highly compressible shear layer region. The data obtained from LES has been further analyzed to understand the evolution of coherent structures in the flow field. Proper Orthogonal Decomposition (POD) of the data obtained from central plane in the wake region has been performed in order to reveal the most energetic structures present in the flow field.

RANS Simulations of Statistically Stationary Premixed Turbulent Combustion Using Flame Speed Closure Model

Turbulent Flame Closure (TFC) and Flame Speed Closure (FSC) models of the influence of turbulence on premixed combustion are applied to RANS simulations of five sets of experiments with (i) highly turbulent, oblique, confined ONERA flames under elevated temperatures, (ii) highly turbulent, conical, confined PSI flames under elevated temperatures and pressures, (iii) open V-shaped flames, and weakly turbulent Bunsen (iv) Erlangen and (v) Orl,ans flames under the room conditions. Besides flame geometry, pressure, and initial temperature, bulk flow velocities, turbulence characteristics, and mixture compositions are different in these five sets of flames, with the equivalence ratio being varied in each set. Turbulence is modeled invoking either the standard or RNG k - epsilon model. The same standard value A = 0.5 of a single constant of the TFC or FSC model is used in all these simulations, but certain input parameters of the turbulence model are tuned by investigating a single reference case for each set of flames. The TFC and FSC combustion models yield similar results when simulating the PSI flames, but the FSC model shows better performance in predicting burning rate for four other sets of flames. All in all, results computed using the FSC model agree reasonably well with the majority of the experimental data utilized to test the model, with a few exceptions discussed in the paper.

Numerical analysis of wall shear patterns on the external wall of an API 5L X42 natural gas pipe

Natural gas pipeline is designed and constructed according to stringent international codes and standards, thus it hardly to rupture or leaks. However, erosive water jet from leaked water pipeline is able to erode the pipe surfaces and lead to its failure. Due to complications in understanding the subsurface hydrodynamics of buried pipe condition, Computational Fluid Dynamics (CFD) is commonly used to predict its characteristics to provide multifaceted overview of the erosion phenomenon. In this study, CFD simulation of multiple water leakage surface of 0.05m diameter at 9atm water pipeline pressure was performed with separation distance of 0.05m, using standard k–epsilon model (SKE) of turbulent model. Simulation results were obtained using discrete random walk to determine the instantaneous fluid velocity. It was found that different region of water shear and sand shear on natural gas pipelines was formed due to the strikes of erosive slurry at different angles. The CFD simulation results showed that sand was the primary cause of the natural gas pipe wall shear, causing cutting and deformation region on the surface of gas pipe. The erosion pattern of the three ruptured holes from the incident sites had a similar trend with those from simulated CFD results of water jetting source at angles of 45°, 60°, and 75°.

Accretion and core formation: The effects of sulfur on metal–silicate partition coefficients

The accretion of the Earth was marked by the high-pressure segregation of the core, accompanied by dissolution of about 10% of one or more “light” elements into the metal. Cosmochemical data suggest that, of these 10% “light” elements, the core contains ∼1.7% S (Dreibus and Palme, 1996) and there is evidence that volatile elements such as S accreted to the Earth late in planetary growth, plausibly as a sulfide “matte” (O’Neill, 1991). Given that metallurgical data indicate that dissolution of even small amounts of sulfur in liquid Fe can have profound effects on the activities of some trace components, we have undertaken a study of the affect of S on the metal–silicate partitioning of a number of the most important chalcophile and siderophile elements.We performed experiments at 1.5GPa and 1460–1650°C on metal–silicate partitioning of W, Mo, Ni, Co, Cu, Ag, Mn, Cd, Tl, Cr, Sb, In, Pb, Ga, Ge, V and Zn under conditions where the S content of the metal was varied from 0 to 37wt%. Mn and Ag were found to exhibit the highest ratio of chalcophile to siderophile behaviour while W, Ga and Sb are the most “chalcophobic” of the elements studied. In terms of the 1-parameter epsilon model (Wagner, 1962) we derived values for each element at 1600°C as follows (negative values indicate chalcophile behaviour): εCuS=-2.57;εMnS=-6.41;εAgS=-4.15;εSbS=4.36;εCdS=-3.78;εInS=-0.24;εTlS=-6.21;εGaS=6.54;εPbS=-3.73;εCrS=-3.70;εGeS=7.03;εVS=-3.14;εZnS=-1.68;εMoS=2.27;εWS=6.47;εNiS=2.17;εCoS=2.40.We use these new data in conjunction with published pressure–temperature dependences of metal–silicate partitioning to test the effects of accreted S on the calculated trace element concentrations in bulk silicate Earth. The approach employs a continuous accretion model in which the oxidation state of the Earth and pressure of core segregation both increase during accretion. We find that, without addition of S in the latter stages of accretion, the Mo/W ratio of silicate Earth would be several times larger than that observed. Addition of ∼2% S accompanied by small amounts of carbon in the last 15% of accretion, however, enables us to match the observed concentrations of these elements in silicate Earth. This confirms an earlier conclusion that the Mo/W ratio of silicate Earth requires late sulfide addition to the core (Wade et al., 2012).Further support for late sulfide addition to the core comes from the depletion factors of volatile chalcophile elements Cu, Ga, Sb, Ag, Zn, Pb, Cd, In and Tl in silicate Earth relative to lithophile elements of similar volatility. We find that depletions of these elements are well correlated with their partition coefficients into sulfide (FeS) liquids at 1.5GPa and temperatures of 1460–1650°C. In contrast there is essentially no correlation between their depletion factors and sulfur-free liquid Fe–silicate partition coefficients.

Numerical investigation of grid spacer effect on heat transfer of supercritical water flows in a tight rod bundle

The numerical investigation was carried out for the effect of grid spacer on the local heat transfer performance of supercritical water flows within the inner sub-channel of a tight, hexagon rod bundle using commercial CFD code STAR CCM+ 6.04. The standard two layer k–epsilon model by Wolfstein with two layer all y+ wall treatment was used as turbulence model. The main objective has focused on the special thermal hydraulic characteristics caused by the standard grid spacer and the grid spacer with split-vanes. The circumferential heterogeneity of heat transfer performance and corresponding mechanism, as well as the effect of heat conduction within the stainless steel cladding, were analyzed in detail. It was found that the local heat transfer within the grid strap is greatly enhanced due to the reduced flow area. In the downstream region of the standard grid spacer, the enlarged circumferential temperature difference and decreased heat transfer near the narrow gap are caused by the aggravated flow choking effect. In the downstream region of the grid spacer with split-vanes, the circumferential distribution of heat transfer performance is greatly changed. The local heat transfer is enhanced just downstream of the grid spacer. However, big circumferential temperature difference and a decreased heat transfer region are also caused by the swirling flow, indicating that the swirling flow has adversely affected the local heat transfer. The improved heat transfer performance downstream of the grid spacer with split vanes is more pronounced for the higher Reynolds number case. The circumferential distribution of cladding temperature is more uniform and the enhanced heat transfer caused by split-vanes is more pronounced when the heat conduction is considered.

The Experimental and Simulations Effect of Air Swirler on Pollutants from Biodiesel Combustion

In the present study the effect of air swirl on the combustion characteristics and pollutant emission of biodiesel B5, B10 and gasoil combustion is studied. The experiments are carried out on an axisymmetric cylindrical combustion chamber. Numerical investigation is conducted using fluent computer code. The RNG, k-&epsilon model is used for the modelling of the turbulence phenomena in the combustion chamber. The eddy dissipation model is used for the simulation of transport combustion. The experimental and numerical result show that the exhaust gas temperature, the levels of NO_x and CO₂ emission increase with increase of swirl number and then decrease. The CO emission declines with increase of swirl number. The numerical and experimental results are in good agreement.

Numerical studies for performance evaluation of a permeable ceiling panel for regulation of indoor humidity

A novel panel which is capable of responding to both sensible and latent load is being developed at the University of Saskatchewan (UoS), Canada. The purpose of this work is to see the performance of this panel known as heat and moisture transfer panel (HAMP) while placed in a room using CFD simulations. A computational fluid dynamics (CFD) model using a commercial software FLUENT is developed for the numerical simulation of fluid flow, heat and mass transfer inside a 3-D room. The transport of water vapour through the membrane is considered to be only by diffusion. Standard k–epsilon model is used for modelling of turbulence. The predictions of fluid flow, temperature and humidity distributions are compared with and without a HAMP for different cases: Dehumidification, Humidification, Cooling–Dehumidification, Cooling–Humidification and Heating–Humidification. The effectiveness of the panel is found to be about 50% for most of the cases considered. A panel of size of 0.75m×0.75m is seen to be optimum for a room of 2m×2m×2m size.

Impinging Diffusion Flame and NO Production

This paper reports a numerical investigation of an impinging diffusion flame on the pollutant emission for tree hydrocarbon fuels characteristics. The effects of the wall plate, the nozzle diameter, the Reynolds number on both thermal and prompt NO production. This work based on the Pre PDF simulation and K Epsilon models for study the reactive turbulent flow spreading on the lateral wall. We found that when the temperature increases the production of thermal NO increase, the NO production is more influenced by the hydrocarbon fuels.

Tracking of Bubble Trajectories in Vertical Pipes in Bubbly Flow Regime by Coupling Lagrangian, Eulerian and 3D Random Walks Models: Validation with Experimental Data

A set of air-water experiments has been performed under isothermal upward concurrent flow conditions, in a vertical column. The interfacial velocity, the bubble interfacial area and the void fraction distributions have been measured. Numerical simulation of these experiments were performed by coupling a Lagrangian code which tracks the 3D motion of the individual bubbles, with an Eulerian one. In the Eulerian solver the velocity and turbulence fields of the liquid phase were computed by solving the time dependent conservation equations in its Reynolds Averaged Transport Equation form (RANS). The turbulent kinetic energy k, and the dissipation rate transport equations were simultaneously solved by using the k, epsilon model in a (r,z) grid by the finite volume method and the SIMPLER algorithm. Both Lagrangian and Eulerian calculations were performed in parallel and an iterative self-consistent method was developed. The turbulence induced by the bubbles is an important issue considered in this paper, in order to obtain good predictions of the void fraction distribution and the interfacial velocity at different gas and liquid flow conditions. The Eulerian Code was upgraded from an axisymmetric 2D code to a 3D code in order to improve the turbulence solution. The results of the 3D CFD code have been tested and show a good agreement with the experimental results. In this paper special attention is given to the coupling between the different models.