M. A. R. Sharif

Mixed convective cooling of a rectangular cavity with inlet and exit openings on differentially heated side walls

A numerical study is conducted to investigate mixed convective cooling of a two-dimensional rectangular cavity with differentially heated side walls. The horizontal walls are assumed to be adiabatic. Cold fluid is blown into the cavity from an inlet in the side wall of the cavity and is exited through an outlet in the opposite side wall. This configuration of mixed convective heat transfer has application in building energy systems, cooling of electronic circuit boards, and solar collectors, among others. The objective of the research is to optimize the relative locations of inlet and outlet in order to have most effective cooling in the core of the cavity by maximizing the heat-removal rate and reducing the overall temperature in the cavity. Various placement configurations of the inlet and outlet are examined for a range of Reynolds number and Richardson number. For a given Reynolds number, the Richardson number is varied from 0, which represents pure forced convection, to 10, which implies a dominant buoyancy effect. Injection of air at the top and bottom of hot and cold walls is compared and the results are presented in the form of isotherms, streamlines, cooling efficiency, average temperature, and local and average Nusselt number at the hot wall. It is observed that maximum cooling effectiveness is achieved if the inlet is kept near the bottom of the cold wall while the outlet is placed near the top of the hot wall.

NUMERICAL STUDY OF LAMINAR NATURAL CONVECTION IN INCLINED RECTANGULAR ENCLOSURES OF VARIOUS ASPECT RATIOS

Numerical investigations are conducted for free convective laminar flow of a fluid with or without internal heat generation in rectangular enclosures of different aspect ratios and at various angles of inclination. Two principal parameters for this problem are the external Rayleigh number, Ra E , which represents the effect due to the differential heating of the side walls, and the internal Rayleigh number, Ra I , which represents the strength of the internal heat generation. Results are obtained for a fixed external Rayleigh number, Ra E =2 2 10 5 , with internal Rayleigh number, Ra I =0 (without internal heat generation), and also with Ra I =2 2 10 5 (with internal heat generation). Flow patterns and isotherms do not show any significant difference between the cases with and without internal heat generation other than slight shift and changes in stream function and isotherm values as long as the internal Rayleigh number Ra I is less than or equal to the external Rayleigh number Ra E . Local heat flux ratios along the hot and the cold walls decrease monotonically in the flow direction for a major downstream portion. At certain inclinations the local heat flux ratios increase initially and then decrease. The variation of average heat flux ratio is similar for cases with and without internal heat generation, but the corresponding amount of heat transfer is higher through the hot wall and lower through the cold wall with internal heat generation. On the other hand, the convection strength increases as the enclosure shape changes from slender through square to shallow at any particular inclination, but varies mildly with inclination at a particular aspect ratio.

Assessment of finite difference approximations for the advection terms in the simulation of practical flow problems

Abstract An assessment of seven discretization schemes for the advection terms of the transport equation to reduce numerical diffusion in practical flow problems has been established. The schemes have been evaluated using three test cases for laminar flow problems. The test cases consist of the transport of a scalar step in a uniform velocity field, two interacting parallel streams, and a slot jet. The performance of the schemes is evaluated for advection-dominated flows in transient and steady-state solutions. The considered schemes include four that have not been evaluated before for practical flow problems. In general, schemes which produced less numerical diffusion suffered from more numerical dispersion or oscillations. Two bounding techniques considered in the study were effective in significantly elliminating numerical dispersion.

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.

Evaluation of the performance of three turbulence closure models in the prediction of confined swirling flows

Abstract The performance of three different turbulence closure models in the prediction of turbulent swirling flows is presented. The models evaluated are: a nonlinear k -ϵ Model (NKEM), the Reynolds Stress Transport Model (RSTM), and the Algebraic Stress Model (ASTM). A decomposition of the Reynolds stresses into the isotropic (eddy viscosity) part and the deviatoric part is applied to avoid numerical instability. A bounded streamwise differencing scheme is used to discretize the convection terms in the governing equations, which substantially reduces the numerical diffusion and eliminates oscillation errors in the solution. Four different swirling flows of varying complexity are simulated. Comparisons of predictions with the experiments show clearly the superiority of the RSTM and the ASTM over the NKEM. The RSTM and ASTM provide good agreement with measured mean velocity profiles. However, the turbulent stresses are over- or underpredicted. The NKEM yields unsatisfactory prediction of the mean velocities and turbulent stresses.

MIXED-CONVECTIVE COOLING OF AN ISOTHERMAL HOT SURFACE BY CONFINED SLOT JET IMPINGEMENT

The flow and heat transfer characteristics in the cooling of a heated surface by impinging slot jets have been investigated numerically. Computations are done for vertically downward-directed two-dimensional slot jets impinging on a hot isothermal surface at the bottom and confined by a parallel adiabatic surface on top. Some computations are also performed where the jet is vertically upward, with an impingement plate at the top. The principal objective of this study is to investigate the associated heat transfer process in the mixed-convective regime. The computed flow patterns and isotherms for various domain aspect ratios (4–10) and for a range of jet exit Reynolds numbers (100–500) and Richardson numbers (0–10) are analyzed to understand the mixed-convection heat transfer phenomena. The local and average Nusselt numbers and skin friction coefficients at the hot surface for various conditions are presented. It is observed that for a given domain aspect ratio and Richardson number, the average Nusselt number at the hot surface increases with increasing jet exit Reynolds number. On the other hand, for a given aspect ratio and Reynolds number, the average Nusselt number does not change significantly with Richardson number, indicating that the buoyancy effects are not very significant in the overall heat transfer process for the range of jet Reynolds number considered in this study. Also, for the same problem configuration, the average Nusselt number does not change significantly when the jet is moving upward or downward.

NUMERICAL STUDY OF TURBULENT NATURAL CONVECTION IN A SIDE-HEATED SQUARE CAVITYAT VARIOUS ANGLES OF INCLINATION

Turbulent natural convection at a moderately high Rayleigh number (4.9 2 10 10 ) in a two-dimensional side-heated square cavity at various angles of inclination is studied numerically. Initially, the performance of the low Reynolds number k - y model of Wilcox (1994) and the low Reynolds number k m l turbulence model of Lam and Bremhorst (1981), in predicting buoyancy-driven flow in a noninclined enclosure, is evaluated against experimental measurements. The evaluation is focused on the prediction of the flow patterns and convective heat transfer in the boundary layer and corner regions. The performance of the Wilcox k m y model is found to be superior in capturing the flow physics such as the strong streamline curvature in the corner regions. The Lam and Bremhorst k m l model is not capable of predicting these features but provides reasonable predictions away from the corners. None of these models, however, is capable of predicting the boundary-layer transition from laminar to turbulent. In order to study the effect of the inclination of the square cavity on the heat transfer and flow patterns, computations are then performed using the Wilcox k m y model for a range of inclination angles from 0° through 90°, keeping other parameters fixed. The computed flow patterns, isotherms, convection strengths, variation of the local Nusselt numbers along the heated walls, and the average Nusselt number for various inclination angles of the square cavity are reported. It is noticed that the flow fields and heat transfer characteristics become significantly different for inclinations greater than45°. The computational procedure is based on finite-volume collocated mesh. The pressure-velocity coupling in the governing equations is achieved using the well-known SIMPLE method for numerical computation. The linear algebraic system of equations is solved sequentially using the strongly implicit procedure (SIP).

Performance evaluation of vaned pipe bends in turbulent flow of liquid propellants

Abstract Computational fluid dynamics techniques were used to analyze turbulent, incompressible flow in a vaned pipe bend that is being considered for use in the liquid propellant feed lines of the space shuttle main engine. The design is an 80° bend that incorporates two turning vanes. Computations were performed using a finite difference code for solving the Navier-Stokes equations in three dimensions using the method of pseudocompressibility, a flux-splitting upwind differencing scheme, and a Baldwin-Barth one-equation turbulence model. To compare and evaluate the performance of the bend under consideration, two other bend designs—an unvaned 80° bend and a simplified 80° vaned bend—were also analyzed. Evaluation of the bend designs was accomplished by comparing the predicted streamwise and cross-stream velocity distributions at the symmetry plane at several streamwise stations and the predicted mean pressure drops. It was observed that the vaned bend under consideration effectively provides uniform streamwise velocity distributions downstream of the bend, reduces cross-stream velocities, and significantly reduces pressure losses.

Laminar Mixed Convection in a Lid-Driven Square Cavity with Two Isothermally Heated Square Internal Blockages

Laminar mixed convection in a lid-driven square cavity with two isothermally heated square internal blockages is numerically investigated. The top lid of the cavity is moving rightwards with a constant speed. The two blockages are maintained at an isothermal hot temperature, while the walls of the cavity are maintained at a cold temperature. The flow and heat transfer behavior is studied for various placements of the blockages through analyzing the local Nusselt number distribution around the edges of the blockages and the average Nusselt number at the blockage surfaces at various Richardson and Reynolds numbers. Investigations are performed in a range of Reynolds number (100–500), Richardson number (0.1–10), and at a fixed Prandtl number (0.71). Computations are done using the ANSYS FLUENT commercial code based on a finite volume method. It is observed that, the average Nusselt number on the blockage surfaces increases with increasing Reynolds number at any Richardson number. The average Nusselt number changes significantly due to the change of blockage placement locations. The separation distance between the two blockages has large effect on the total average Nusselt number.

An evaluation of the bounded directional transportive upwind differencing scheme for convection-diffusion problems

A bounded version of the directional transportive upwind differencing scheme for discretizing the convection terms in the convection-diffusion transport equations has been proposed and evaluated. The flux-corrected transport algorithm is used for bounding. The evaluation process is based on few one- and two-dimensional benchmark laminar-flow test cases. The predictions are compared with exact or analytic solutions as well as with the predictions by other recent TVD schemes. The study shows that the directional transportive upwind differencing schemes produce less numerical diffusion but introduces unacceptable spatial oscillations in the solution. A simplified theoretical analysis exploring the reason for this behavior is presented. The bounded scheme eliminates the oscillations from the solution without introducing any additional numerical diffusion.