Prediction of convection from a finned cylinder in cross flow using direct simulation,turbulence modeling,and correlation-based methods

Direct numerical simulation (DNS), two shear-stress transport (SST) turbulence models, and three k-ε models are used to predict mixed convection associated with air in cross flow over an isothermal, finned cylinder. The DNS predictions reveal complex time-variation in the flow field. Convection heat transfer coefficients predicted by the SST models are in good agreement with those generated by DNS, whereas the k-ε models do not accurately predict heat fluxes. Correlation-based predictions of heat transfer coefficients are, in general, in poor agreement with the DNS and SST predictions. The impact of various geometrical modifications on convection coefficients is also presented.     

The Effect of Conjugate Heat Transfer on Film Cooling Effectiveness

The film cooling effectiveness of a two-dimensional gas turbine endwall is compared for the cases of conjugate heat transfer and an adiabatic wall condition using five common turbulence models. The turbulence models employed in this study are: the RNG k–ε model, the realizable k–ε model, the standard k–ω model, the SST k–ω model, and the RSM model. The computed flow field and surface temperature profiles along with the film effectiveness for one and two cooling slots at different injection angles are presented. The results show the strong effect of conjugate heat transfer on the film effectiveness compared to the adiabatic case and also compared to the effectiveness values obtained from analytically solvable models.     

Comparison of Turbulence Models for Multiphase-Flow Oscillating Heat Transfer Enhancement

Multiphase-flow oscillating heat transfer is a kind of highly efficient heat transfer method. In this article, two turbulence models are used to simulate the oscillating heat transfer process. Results include qualitative and quantitative comparisons with experimental data. We find that, in both a closed cavity and an open oil cooling gallery, the SST k–ω model performs better in the simulation of oscillating movement, as well as in the heat transfer effect prediction. The error of the heat transfer coefficient begins to increase with at increasing Reynolds number, illustrating that the SST k–ω model has higher accuracy at low Reynolds numbers.     

The Thermoflow Characteristics of an Oscillatory Flow in Offset-Strip Fins

In this work, a numerical study was performed to investigate the characteristics of pressure drop and heat transfer in an oscillatory flow through offset-strip fins. In the laminar regime, the flow does not oscillate, and the Colburn j and friction f factors from a steady simulation are very close to those of an unsteady simulation. The flow begins to oscillate in the transition and turbulence regimes. In these regimes, the error between the f and j values obtained from the unsteady and steady simulations becomes significant. Since an unsteady simulation is too computationally expensive, a steady simulation with a turbulence model was tested. It was found that a steady simulation with the SST(shear stress transport) k-ω turbulence model can accurately predict the Colburn j and friction f factors of an unsteady simulation.     

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.     

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.     

Analysis of exergy loss vs heat transfer rate for Rayleigh–Bénard convection of various fluids in enclosures with curved walls

The investigation of entropy generation is highly desirable for the optimization of the thermal systems to avoid larger energy wastage and ensure higher heat transfer rate. The numerical investigation of natural convection within enclosures with the concave and convex horizontal walls involving the Rayleigh–Bénard heating is performed via entropy generation approach. The spatial distributions of the temperature (θ), fluid flow (ψ), entropy generation due to heat transfer and fluid friction (S_θ and S_ψ) are discussed extensively for various Rayleigh numbers and Prandtl numbers involving various wall curvatures. A number of complex patterns of spatial distributions of fluid flow and temperature for cavities with concave or convex isothermal walls (top and bottom) have been obtained. The zones of high entropy generation for temperature and fluid flow are detected within cavities with concave and convex horizontal walls. The optimal situation involves the high heat transfer rate with moderate or low entropy generation. Overall, case 3 (highly concave) is found to be optimal over cases 1 and 2 (concave) and cases 1–3 (convex) for all Pr and Ra.     

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.     

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.     

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.     

Numerical Simulation of Non-Darcy Forced Convection through a Channel with Nonuniform Heat Flux in an Open Cavity Using Nanofluid

This article aims to numerically investigate forced convection heat transfer phenomena in a two-dimensional horizontal channel having an open cavity with porous medium. A nonuniform heat flux is considered to be located on the bottom surface of the cavity. Three different heating modes are considered at this wall. The rest of the surfaces are taken to be perfectly adiabatic. The physical domain is filled with water based nanofluid containing TiO₂ naparticles. The fluid enters from left and exits from right with initial velocity U _i and temperature T _i . Governing equations are discretized using the penalty finite element method. The simulation is carried out for a range of Prandtl number Pr(=5.2–12.2) and solid volume fraction φ (=0%–15%). Results are presented in the form of streamlines, isothermal lines, local and average Nusselt number, average temperature of the fluid, horizontal and vertical velocities at mid-height of the channel, and mean velocity field for various Pr and φ. It is found that increasing Pr and φ cause the enhancement of the heat transfer rate.     

A Simplified Model with a Hybrid Analytical-Numerical Solution for Predicting the Unsteady Conjugate Heat Transfer Process in Pipelines

This work presents a new, simplified and yet efficient model for studying the transient conjugate heat transfer process in pipelines. The simplified model consists of assuming the thermal transport by fluid flow in bulk form and the pipe–wall heat conduction as two-dimensional. The scale analysis of the dimensionless equations resulting from the simplified model allows for the identification of two predicting parameters useful in determining when axial diffusion in the pipe wall is important, ψ = Pe Γ/ξ < 1 and λ = 4 Nu E ²/ξ < 1, and when radial diffusion is important, ψ > 1 and λ > 1. When these criteria are satisfied, in which case the existing analytical solution becomes invalid, the simplified model proposed here becomes an efficient alternative to the full-scale numerical simulations required for solving the problem. The scale analysis predictions and the hybrid analytical-numerical solutions of the simplified model, involving the Laplace transform and the finite-volume method, are validated first by comparison against the existing analytical solution, and then by comparison against experimental results of turbulent flow, showing excellent agreement in both cases.     

NATURAL-CONVECTIVE HEAT TRANSFER IN A SQUARE CAVITY WITH TIME-VARYING SIDE-WALL TEMPERATURE

ABSTRACT

The natural-convective heat transfer in an inclined square enclosure is studied numerically. The top and bottom horizontal walls are adiabatic, and the right side wall is maintained at a constant temperature T ₀. The temperature of the opposing vertical wall varies by sine law with time about a mean value T ₀. The system of Navier–Stokes Equations in Boussinesq approximation is solved numerically by the control-volume method with SIMPLER algorithm. The enclosure is filled with air (Pr = 1) and results are obtained in the range of inclination angle 0° ≤ α ≤ 90° for two values of Grashof number (2 × 10⁵ and 3 × 10⁵). It can be noted that there is a nonzero time-averaged heat flux through the enclosure at α ≠ 0°. The dependencies of time-averaged heat flux on oscillation frequency and inclination angle are depicted. It is found that the maximal heat transfer corresponds to the values of inclination angle α = 54^○ and dimensionless frequency f = 20π for both Grashof numbers studied (2 × 10⁵ and 3 × 10⁵).     

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°.     

NUMERICAL INVESTIGATION OF JET IMPINGEMENT WITH CROSS FLOW—COMPARISON OF YANG-SHIH AND STANDARD k–ϵ TURBULENCE MODELS

ABSTRACT

Computational fluid dynamics models are used to predict the heat transfer distribution on a smooth surface under an array of angled impinging jets. The three-dimensional numerical models simulate impingement with cross flow in one direction. Jet angle is varied between 30°, 60°, and 90° as measured from the smooth flat impingement surface. Conjugate conduction in the heated boundary is included in the analysis. Two turbulence models are examined, the standard k–? model and the Yang-Shih model. Local and average heat transfer coefficients are compared with test data for 30 test cases. The Yang-Shih model was able to predict average Nusselt number within 2–30%. The standard k–? model predicts average Nusselt number with 0 to nearly 60% error.     

Application of Variational Iteration and Homotopy-Perturbation Methods to Nonlinear Heat Transfer Equations with Variable Coefficients

Since analytical perturbation methods depend on a small parameter and finding this small parameter is difficult, two powerful analytical methods are introduced to be applied to solve nonlinear heat transfer problems in this article. One is He's variational iteration method ( VIM ) and the other is the homotopy-perturbation method ( HPM ). The VIM is used to construct correction functionals using general Lagrange multipliers identified optimally via the variational theory. The HPM converts a difficult problem into a simple problem which can be easily solved. In this article, the VIM is used to solve some nonlinear heat transfer equations with variable heat transfer coefficient. The results are then compared with those obtained by the HPM and the exact solution.     

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.     

Role of Entropy Generation On Thermal Management During Natural Convection in a Tilted Square Cavity with Isothermal and Non-Isothermal Hot Walls

Entropy generation during natural convection within tilted square cavity inclined with different angles (? = 30°and 75°) for various thermal boundary conditions (case 1: isothermal heating and case 2: non-isothermal heating) has been studied. Simulations are carried out over a range of parameters: Rayleigh number (10³ ≤ Ra ≤ 10⁵) and Prandtl numbers (Pr = 0.025 and 998.24). The numerical results are presented in terms of isotherms (θ), streamlines (ψ), entropy generation due to heat transfer (S _θ ) and fluid friction (S _ψ ). Heating strategy is energy efficient for case 2 (non-isothermal heating) due to its less total entropy generation with reasonable heat transfer rate, irrespective of Pr.