Three-Dimensional Simulation of Flow Past a Circular Cylinder by Nonlinear Turbulence Model

Numerical simulation of flow past a circular cylinder at sub-critical Reynolds number Re = 3,900 is performed using three-dimensional, unsteady, Reynolds–Averaged Navier-Stokes (URANS) equations. A nonlinear turbulence model based on the k–ε formulation is used to achieve the turbulent closure. The results obtained by the simulations are compared with experimental and previously reported numerical results. The grid used for the present simulation is reasonable, and the accuracy obtained is good considering the computational cost involved in carrying out large-eddy simulations (LES) for the same test case. The test flow is also simulated using standard k–ε model, and the results obtained by the nonlinear k–ε model are found to be better.     

Numerical Study of Sphere Drag Coefficient in Turbulent Flow at Low Reynolds Number

The drag coefficient of a sphere immersed in turbulent air flow in the Reynolds number (Re = U _∞ d/ν _∞) range up to 250 and turbulence intensity (u _∞′/U _∞) up to 60% is computed numerically. Reynolds-averaged Navier-Stokes equations (RANS) are solved in Cartesian coordinates by using a blocked-off technique. To our knowledge, the present work is the first to employ the blocked-off technique for flow over a sphere. Closure for the turbulence stress term is accomplished by testing four different turbulence closure models. The main findings of the present investigation are that the laminar numerical data compare well with numerical and experimental published work. However, different turbulence closure models produce different trends in the range of Reynolds number up to Re = 100, and this difference is demarcated by the nonagreement between the turbulent predictions and the “standard” drag coefficient results. However, the results obtained using Menter's SST turbulence model show fair agreement with the well-known sphere “standard” drag over the range of test conditions explored here. Thus, the present results confirm recently published findings, which suggest that the free-stream turbulence intensity does not have a significant effect on the sphere mean drag.     

Evaluation of Turbulence Models in the Prediction of Heat Transfer Due to Slot Jet Impingement on Plane and Concave Surfaces

The performance of several turbulence models in the prediction of convective heat transfer due to slot jet impingement onto flat and concave cylindrical surfaces is evaluated against available experimental data. The candidate models for evaluation are (1) the standard k – ε model, (2) the RNG k – ε model, (3) the realizable k – ε model, (4) the SST k – ω model, and (5) the LRR Reynolds stress transport model. Various near-wall treatments such as equilibrium wall function and two-layer enhanced wall treatment are used in combination with these turbulence models. The computations are performed using the commercial computational fluid dynamics (CFD) code Fluent. From the validation exercises, it is found that when the impingement surface is outside the potential core of the jet, most of the turbulence models predict reasonably accurate thermal data (local Nusselt number variation along the impingement surface). When the impingement surface is within the potential core of the jet, the turbulence models grossly overpredict the Nusselt number in the impingement region, but in the wall jet region the Nusselt number prediction is fairly accurate. Overall, the RNG k – ε model with the enhanced wall treatment and the SST k – ω model predict the Nusselt number distribution better than the other models for the flat plate as well as for the concave surface impingement cases. However, the hydrodynamic data such as the mean velocity profiles are not accurately predicted by the SST k – ω model for the concave surface impingement case, whereas the RNG k – ε model predictions of the velocity profiles agree very well with the experiment. The Reynolds stress model does not show any distinctive advantage over the other eddy viscosity models.     

Turbulence Models for Fluid Flow and Heat Transfer Between Cross-Corrugated Plates

Three-dimensional numerical predictions of fluid flow and heat transfer between cross-corrugated plates were obtained for the same geometry and grid using eight turbulence models, i.e., LBKE, SKE, RKE, RNGKE, RSM, KW, SST and LES, for the purpose of model performance evaluation. The average Colburn factor j, friction factor f, and local Nusselt number distribution were presented and compared with available experimental data. The velocity, temperature, and turbulent viscosity ratio distributions were recorded and discussed. It has been found that all models can predict practically satisfactory j and acceptable f within the current Reynolds number range. LBKE and SST provide the best overall agreement with experimental data and thus are highly recommended for application. Taking into account its robustness and economy, SKE with enhanced wall treatment is also recommended for CC channel flow and heat transfer simulation. In addition, near wall treatment approach seems to be significant for the current wall-bounded flow simulation. Since some models predict similar j and f values but very different velocity and temperature distributions, it seems not quite sufficient to only compare the overall heat transfer and pressure drop data between simulation and experiment for comprehensive model evaluations.     

Cooled Vortex Street Generated by Cooling a Cylinder at Low Reynolds Number: Effects of Reynolds Number Difference on Cooled Wake and Cooled Vortex Street

First, the dominant action in the cooled wakes in mercury and water at the Reynolds number Re = 22 and 44 is discussed. Next, the cooled wake at Re = 22 is numerically simulated and is compared with the previous results at Re = 44. Finally, effects of Re on the cooled wake and the cooled vortex street are elucidated, and are found to be extremely powerful as follows.

• 1. The dominant action can be determined at different fluids and different Re. Here, the vorticity and the temperature are relating with each other.

• a. “Table of diffusion intensity order” is invented. By obtaining and using this table, the dominant action can be determined automatically.

• b. The kinds of the dominant action are the advection and the diffusion in the vorticity and the temperature.

• c. In mercury and water at Re = 44 and 22, the dominant action is the vorticity diffusion at the low Re, the vorticity advection at the high Re, the temperature diffusion at the low Peclet number Pe, and the temperature advection at the high Pe.

• d. The dominant action in air at Re = 44 is between the dominant action in mercury and water at Re = 44. The dominant action in air at Re = 22 is the same as the dominant action in mercury at Re = 22.

• e. By using the dominant action, the wake variations and item 2 below, i.e., the characteristics of the cooled wake behavior, can be explained.

• 2. When Re is decreased, the following occurs and its cause is elucidated.

• f. In the cooled wake, the Karman vortex street does not occur, but the cooled vortex street with g below occurs.

• g. The vortex spiral size is not changed in mercury but is increased in water.

• h. The following is decreased in mercury but is increased in water. The range of the absolute Richardson number|Ri|generating the cooled vortex street, the spiral degree in the cooled vortex, the critical|Ri| for the symmetric wake onset, and the reciprocal of the temperature wake area.

     

Numerical simulation and optimization of turbulent fluids in a three-dimensional angled ribbed channel

ABSTRACT

In this study, numerical simulations of turbulent steam forced convection in a three-dimensional angled ribbed channel with constant heat flux are investigated. The elliptical, coupled, steady-state, and three-dimensional governing partial differential equations for turbulent forced convection are solved numerically using the finite volume approach. The standard k?? turbulence model is applied to solve the turbulent governing equations. Numerical results are first validated using reference’s data reported in the literature and the maximum discrepancy between them is 3%. The effects of Reynolds number, angled rib height ratio, angled rib pitch ratio, and rib angle on the friction factor ratio and averaged Nusselt number are investigated. Numerical results show that the increase in heat transfer is accompanied by an increase in the friction factor ratio of the steam, the minimum friction factor ratio occurs at θ = 30^○ and the maximum friction factor ratio is found at θ = 60^○. In addition, after the validation of the numerical results, the numerical optimization of this problem is also presented by using the response surface methodology coupled with computational fluid dynamic method.     

Convective Heat Transfer from a Thick Hemispherical Plate during Free Liquid Jet Impingement

Convective heat transfer during free liquid jet impingement on a hemispherical solid plate of finite thickness has been examined. The model included the entire fluid region (impinging jet and flow spreading out over the hemispherical surface) and solid plate as a conjugate problem. Solution was done for both isothermal and constant heat flux boundary conditions at the inner surface of the hemispherical plate. Computations were done for jet Reynolds number (Re _j ) ranging from 500 to 2,000, dimensionless nozzle-to-target spacing ratio (β) from 0.75 to 3, and for various dimensionless plate thicknesse-to-nozzle diameter ratios (b/d _n ) from 0.08 to 1.5. Results are presented for local Nusselt number using water (H₂O), flouroinert (FC-77), and oil (MIL-7808) as working fluids, and aluminum, Constantan, copper, silicon, and silver as solid materials. It was observed that plate materials with higher thermal conductivity maintained a more uniform temperature distribution at the solid–fluid interface. A higher Reynolds number increased the Nusselt number over the entire solid–fluid interface.     

On the Numerical Modeling of Impinging Jets Heat Transfer—A Practical Approach

This article compares steady-state and transient simulations in predicting impinging jet heat transfer. The configurations tested are H/D = 2 and 6, Re = 10,000, 20,000, 23,000, and 30,000. The variables considered are: turbulence model (LES, k-?, k-ω, V2F), discretization schemes, mesh density and topology, inlet velocity profile, and turbulence. The V2F model performs best for the steady state simulations. The inlet velocity profile plays an important role. Mesh topology and distribution is also important. The turbulence created in the shear layer plays a stronger role than the inlet turbulence. The LES model reproduces the turbulent structures with a useful degree of accuracy.     

The Effect of Radiation on Flow in a Conical Diffuser

The effect of thermal radiation on the flow in a conical diffuser of half-cone angle 2.5° is studied numerically for constant thermophysical properties. The finite-volume method (FVM) is employed to solve both the Navier-Stokes equation (NSE) and the integro-differential radiative transfer equation (RTE). The effect of radiative parameters, e.g., optical diameter, scattering albedo and wall emissivity at two Reynolds numbers (Re = 500 and 1000) and Pr = 1 has been investigated for constant wall temperature of 1000 K and inlet temperature of 2000 K. The results show that radiation in a transparent or in a purely scattering medium does not affect the flow temperature profile and bulk mean temperature variation, whereas it increases the total Nusselt number; however, radiation in a absorbing-emitting participating medium significantly affects the temperature profile as well as Nusselt number, when compared with the pure convection case.     

Numerical Computation of a New Vortex (A Cooled Vortex Street) and its Generation Mechanism in a Cooled Circular Cylinder Wake at Low Reynolds Number

A strongly cooled, circular cylinder wake with an upward main stream of air at low Reynolds number Re, i.e., 15 ≦ Re ≦ 44, is analyzed numerically, and is elucidated as follows. (1) A new vortex street, i.e., a “cooled vortex street,” is discovered, develops in the range of computed Re, i.e., 15 ≦ Re ≦ 44, has strong asymmetry, and is extremely different from the Karman vortex. (2) The vortex street occurring in the cooled wake is either the Karman vortex street or the cooled vortex street. No vortex street except these vortex streets ever occurs in a wake. (3) The critical Reynolds number Re_c, i.e., the minimum Re occurring in the Karman vortex street by cooling a cylinder, is nearly 24. When the isothermal wake is cooled weakly, the Karman vortex street certainly develops at Re > 24, but never occurs at any cooling rate at Re < 24.

The generation mechanism of the cooled vortex street is elucidated by employing the computed vorticity and temperature distributions as follows. (1) With an extreme increase in the cooling rate, the wake vorticity is generated strongly by the temperature gradient, the absolute value of vorticity in shear layers becomes extremely large, and the shear layers are elongated remarkably. The angle between shear layers and the wake width increase remarkably. (2) As a result, shear layers roll up considerably, and their tips reach the midplane alternately. Extremely large-scale vorticity-concentrated tips are generated, and move to the downstream. Thus a stable wake, i.e., the cooled vortex street, is generated. That is, the stable rolling of shear layers is realized only in the Karman and the cooled vortex streets.     

Effect of Inclination on Heat Transfer and Fluid Flow in a Finned Enclosure Filled with a Dielectric Liquid

The problem of two-dimensional natural convection flow of a dielectric fluid in a square inclined enclosure with a fin placed on the hot wall is investigated numerically. The fin thickness and length are 1/10 and 1/2 of the enclosure side, respectively. The Rayleigh number is varied from 10³ to 5 × 10⁵ and the solid to fluid thermal conductivity ratio is fixed at 10³. The enclosure tilt or inclination angle is varied from 0° to 90°. The streamlines and isotherms within the enclosure are produced and the heat transfer is calculated. It is found that for 2.5 × 10⁴ ≤ Ra ≤ 2.5 × 10⁵, the average Nusselt number is maximum when γ = 0° and minimum when γ = 90°. For Ra = 5 × 10⁵, the values of enclosure tilt angle for which the average Nusselt number is maximum or minimum are completely different due to the transition to unsteady state. In this case, the maximum heat transfer is obtained for γ = 60°, while the minimum heat transfer is predicted for γ = 0°. Monomial correlations relating the average Nusselt number with the different values of the Rayleigh number from 10⁴ to 10⁵ are determined for two different angles, γ = 0° and γ = 90°.     

Analytical and Level Set Method-Based Numerical Study for Two-Phase Stratified Flow in a Pipe

A nondimensional analytical study for fully developed and three-dimensional numerical study of developing viscosity stratified flow is presented, at various values of viscosity ratio η, inlet area fraction of the less viscous fluid α _1,in , and Reynolds number. With increasing α _1,in , a change in the trend of axial variation in interface–from inlet to the fully developed region–is found at α _1,in  = α _1,in,c . With increasing η, development length is found to asymptotically decrease for α _1,in  = 0.2 and increase for α _1,in  = 0.5 and 0.8. A physical model for flow development is also presented for single- and two-fluid flow. A favorable operating condition to reduce the cost of transportation of more viscous fluids by pipe is proposed.     

The Effect of a Blockage on Forced Convection Heat Transfer From a Heated Square Cylinder to Power-Law Fluids

Forced convection heat transfer characteristics of a long, heated square cylinder blocking the flow of a power-law fluid in a channel is numerically investigated in this study. In particular, the role of the power-law index n, Reynolds number Re, Prandtl number Pr, and blockage ratio β(=B/H) on the rate of heat transfer from a square cylinder in a channel has been studied over the following ranges of conditions: 0.5 ≤ n ≤ 1.8, 60 ≤ Re ≤ 160, β = 1/4, 1/2, and 0.7 ≤ Pr ≤ 50. A semi-explicit finite-volume method is used on a nonuniform collocated grid arrangement. The third-order QUICK and the second-order central difference schemes are used to discretize the convective and diffusive terms, respectively, in the momentum and energy equations. Irrespective of the type of behavior of fluid (different values of n), the average Nusselt number increases as the blockage ratio increases. Similar to the unconfined flow configuration, the average Nusselt number increases monotonically with Reynolds and Prandtl numbers for both values of the blockage ratio and for all values of power-law index considered here. Further insights into the heat transfer phenomenon are provided by presenting isotherm contours in the vicinity of the cylinder for a range of values of the Reynolds number, Prandtl number, and power-law index for the two values of β considered in this work.     

Transient Analysis on Forced Convection Phenomena in a Fluid Valve Using Nanofluid

A transient numerical study is conducted to investigate the transport mechanism of forced convection in a fluid valve filled with water-CuO nanofluid. The flow enters from one inlet at the left with uniform temperature and velocity T _i and U _i , respectively, but can leave the valve through two outlets at the right. The upper and lower boundaries of the valve are heated with constant temperature T _h , while the remaining walls are perfectly insulated. The numerical approach is based on the finite element technique with Galerkin's weighted residual simulation. Solutions are obtained for fixed Prandtl number (Pr = 1.47), Reynolds number (Re = 100), and solid volume fraction (φ = 5%). The streamlines, isotherm plots, flow rate and the local Nusselt number (Nu _local ) at both heated phases, the average Nusselt number (Nu) for base fluid, and nanofluid with the variation of nondimensional time (τ) are presented and discussed. It is found that the rate of heat transfer in the fluid valve reduces for longer time periods.     

Natural Convection Coupled with Radiation Heat Transfer in Slanted Square and Shallow Enclosures Containing an Isotropic Scattering Medium

A finite-volume method (FVM) is used to address combined heat transfer, natural convection, and volumetric radiation with an isotropic scattering medium, in a tilted shallow enclosure. Numerical simulations are performed in the in-house fluid flow software GTEA. All the results obtained by the present FVM agree very well with the numerical solutions in the references. The effects of various influencing parameters such as the Planck number (0.0001 ≤ Pl ≤ 10), the scattering albedo (0 ≤ ω ≤ 1), the inclination angle (?60° ≤ α ≤ 90°), and aspect ratio (1 ≤ AR ≤ 5) on flow and heat transfer have been numerically studied. For a constant Pl number, flow is slightly intensified at the midplane as the Ra number increases from 10⁶ to 5 × 10⁶. As the scattering albedo increases, the effect of radiation heat transfer decreases on both slanted and horizontal enclosures. In positive tilt angles, the influence of α on heat transfer is quite remarkable. The highest Nu_rad appears at α = 30° (ω = 1)and 0° (ω = 0, 0.5), whereas Nu_rad is maximum at α = ? 15° (ω = 1) and ?45° (ω = 0, 0.5). At α = ?15°, the maximum and minimum values of Nu_rad are presented for ω = 0, AR = 1 and ω = 1, AR = 5.     

Numerical investigation on heat transfer of supercritical water in a roughened tube

ABSTRACT

The turbulent mixed convection heat transfer of supercritical water flowing in a vertical tube roughened by V-shaped grooves has been numerically investigated in this paper. The turbulent supercritical water flow characteristics within different grooves are obtained using a validated low-Reynolds number κ-ε turbulence model. The effects of groove angle, groove depth, groove pitch-to-depth ratio, and thermophysical properties on turbulent flow and heat transfer of supercritical water are discussed. The results show that a groove angle γ = 120° presents the best heat transfer performance among the three groove angles. The lower groove depth and higher groove pitch-to-depth ratio suppress the enhancement of heat transfer. Heat transfer performance is significantly decreased due to the strong buoyancy force at T_b = 650.6 K, and heat transfer deterioration occurs in the roughened tube with γ = 120°, e = 0.5 mm, and p/e = 8 in the present simulation. The results also show that the rapid variation in the supercritical water property in the region near the pseudo-critical temperature results in a significant enhancement of heat transfer performance.     

Numerical Investigation of Confined Multiple-Jet Impingement Cooling Over A Flat Plate at Different Crossflow Orientaions

This study investigates the fluid flow and heat transfer characteristics of round jet arrays impinging orthogonally on a flat-plate with confined walls at different crossflow orientations. A computational fluid dynamic technique based on a control volume method is used to compute the detailed Nusselt number distributions on the flat plate. This is achieved by solving the steady-state three-dimensional incompressible Reynolds-averaged Navier-Stoke's equations. The Reynolds stress turbulence quantities are determined by a realizable κ-ε turbulence model with an enhancement near-wall treatment. Numerical computations are performed for two types of arrangements in round jet arrays, both inline and staggered, and three different crossflow directions, parallel, hybrid, and counter. The jet Reynolds numbers ranging from 2,440 to 14,640 and three different jet-to-plate spacing ratios (Zn/d_j) of 1, 3, and 6 are investigated in this study. Results show that the flow exit crossflow direction would significantly affect the developing jet flow fields and Nusselt number distributions on the target flat-plate. Area-averaged Nusselt number increases with an increase of jet Reynolds number. Of all the cases tested, the highest average Nusselt numbers were obtained for the case with inline jets and hybrid crossflow orientation. The thermal performance of impingement multiple jets is enhanced when the value of Zn/d_j decreases from 6 to 3. Results show that further reducing the value of Zn/d_j to 1 creates a significant nonuniform distribution in local Nusselt number over the target plate regardless of the crossflow orientations. This study also provides a correlation of the area-averaged Nusselt number with the jet Reynolds number for both inline and staggered jet arrays.     

Lattice Boltzmann Simulation of Natural Convection in an Inclined Square Cavity with Spatial Temperature Variation

In this paper, natural convection heat transfer in an inclined square cavity filled with pure air (Pr = 0.71) was numerically analyzed with the lattice Boltzmann method. The heat source element is symmetrically embedded over the center of the bottom wall, and its temperature varies sinusoidally along the length. The top and the rest part of the bottom wall are adiabatic while the sidewalls are fixed at a low temperature. The influences of heat source length, inclination angle, and Rayleigh number (Ra) on flow and heat transfer were investigated. The Nusselt number (Nu) distributions on the heat source surface, the streamlines, and the isotherms were presented. The results show that the inclination angle and heat source length have a significant impact on the flow and temperature fields and the heat transfer performance at high Rayleigh numbers. In addition, the average Nu firstly increases with γ and reaches a local maximum at around γ = 45°, then decreases with increasing γ and reaches minimum at γ = 180° in the cavity with ? = 0.4. Similar behaviors are observed for ? = 0.2 at Ra = 10⁴. Moreover, nonuniform heating produces a significant different type of average Nu and two local minimum average Nu values are observed at around γ = 45° and γ = 180° for Ra = 10⁵ in the cavity with ? = 0.2.     

Improvement of a Turbulence Model for Conjugate Heat Transfer Simulation

For the conjugate heat transfer simulation, two-equation turbulence models will predict an anomalously large growth of turbulent kinetic energy in high strain rate flows, and then the flow and heat transfer will be unreasonable. The current study improved the low Reynolds number Chien k-? two-equation model using the “realizability” based C _μ limiter and the production term P _k limiter. This study was conducted based on a developed preconditioned density-based conjugate heat transfer algorithm. Calculations are presented for the flat plate turbulence flow and the conjugate heat transfer of the MarkII cooling turbine blade using the improved model. The results were analyzed and compared with semi-empirical formula and experimental data. Significant improvement in the turbulent kinetic energy anomaly was obtained using both limiters. The prediction accuracy of the Chien k-? model for the flow and heat transfer in the conjugate heat transfer simulation was significantly enhanced. The changes in the model are guaranteed to not have unfavorable influence on the simulation of low strain rate flows.     

Momentum and Heat Transfer Phenomena for Power–Law Liquids in Assemblages of Solid Spheres of Moderate to Large Void Fractions

This work extends our previously reported results for the flow of and heat transfer from expanded beds of solid spheres to power–law fluids by using a modified and more accurate numerical solution procedure. Extensive results have been obtained to elucidate the effects of the Reynolds number (Re), the Prandtl number (Pr), the power–law index (n), and the bed voidage (ε) on the flow and heat transfer behavior of assemblages of solid spheres in the range of parameters: 1 ≤ Re ≤ 200, 1 ≤ Pr ≤ 1000, 0.6 ≤n ≤ 1.6, and 0.7 ≤ε ≤ 0.999999. The large values of bed voidage are included here to examine the behavior in the limit of an isolated sphere. As compared to Newtonian fluids, for fixed values of the Reynolds number and the voidage, the total drag coefficient decreases and the average Nusselt number increases for shear thinning fluids (n < 1); whereas, for shear thickening fluids (n > 1), the opposite behavior is observed. The drag results corresponding to bed voidage, ε = 0.99999, are very close to that of a single sphere; whereas, the heat transfer results approach this limit at ε = 0.999. Based on the present numerical results, simple correlations for drag coefficient and average Nusselt number are proposed which can be used to calculate the pressure drop for the flow of a power–law fluid through a bed of particles, or rate of sedimentation in hindered settling and the rate of heat transfer in assemblages of solid spheres in a new application. Broadly speaking, all else being equal, shear-thinning behavior promotes heat transfer, whereas shear-thickening behavior impedes it.