NUMERICAL STUDY OF COMPRESSIBLE TURBULENT FLOW IN MICROTUBES

Micro- and conventional compressible, turbulent tube flows were solved numerically in this study. The numerical procedure solves the compressible, turbulent boundary-layer equations using an implicit finite-difference scheme. The parabolic character of the boundary-layer equations renders the numerical procedure a very efficient, accurate, and robust tool for studying compressible microtube flows. The Baldwin–Lomax two-layer turbulence model is adopted in the numerical procedure. The numerically calculated friction factors are compared with the Blasius correlation, the Fanno line flow prediction, and the experimental data. The comparison shows that the numerically calculated friction factors for conventional tube flows agree quite well with the Blasius correlation. The numerical friction factors for microtube flows are larger than the Blasius correlation due to the compressibility effects. They also are greater than the Fanno line flow prediction and the experimental data. This is because the Fanno line flow and the experimental data assume that the flow is adiabatic, but in reality, compressible, turbulent microtube flows are neither adiabatic nor isothermal, as demonstrated by the numerical results in this study.     

NUMERICAL SIMULATION OF FLOW PATTERN FORMATION IN A BOTTOM HEATED CYLINDRICAL FLUID LAYER

Abstract

The temporal formation of the buoyancy-driven flow structures in a bottom heated, shallow, cylindrical fluid layer was numerically studied. The unsteady three-dimensional Navier-Stokes and energy equations were discretized by the power law scheme and solved by the fully implicit Marker-and-Cell method. Computations were carried out for the pressurized argon (Pr=0·69) and water (Pr=6·1) layers for various Rayleigh numbers and heating rates of the layer. In the pressurized argon layer at a slightly supercritical Rayleigh number with Ra_f;=1·05Ra_c a steady straight roll pattern was formed when the heating rate was very slow (a=0·001) after a long transient stage. When the heating rate was raised to a=0·01, a very different structure tike U-rolls was formed at steady state. In the water layer with Ra_f=l·05Ra_c, a straight roll pattern was again formed, but at a equals;0·07. At Ra_f;=1·13Ra_c, curved rolls with the three foci at the sidewall were formed for a=0·01. A pattern in the form of U-rolls appears at a=0·01. Regular concentric circular rolls prevail at a=1·0. When the Rayleigh number is further raised to 1·23Ra_c, the resulting steady flow is dominated by incomplete circular rolls with open ends near θ=0°     

NUMERICAL STUDY OF TURBULENT FLOW AND HEAT TRANSFER IN A CONVEX CHANNEL OF A CALORIMETRIC ROCKET CHAMBER

A numerical study on flow and heat transfer in double-wave cross-corrugated passages with different structure parameters was conducted. The three-dimensional governing equations for mass, momentum, and heat transfer were solved using a control volume finite difference method and a validated low-Reynolds number k-? model. The effects of Reynolds number and structure parameters, including pitch ratio (P₁/P₂) and height ratio (H₁/H₂), were studied. It was found that with a decrease in height ratio, the mainstream flow changed from a pattern dominated by L-shaped flow to one dominated by Z-shaped flow, whereas pitch ratio had almost no influence on the flow pattern. The average Nusselt number Nu_av first increased and then decreased gradually with either an increase in the pitch ratio or a decrease in the height ratio. Pressure drop showed the same trend as heat transfer performance. The best performance evaluation criterion number (g) of double-wave passage was nearly 20% higher than that of the corresponding single-wave passage, whereas the worst was nearly 40% lower. On the whole, the double-wave plate with H₁/H₂ = 5 showed better overall performance. The double-wave plate with P₁/P₂ = 1 had better overall performance for Re < 5,000, whereas that with P₁/P₂ = 3 was better for Re > 7,500.     

NUMERICAL STUDY OF TURBULENT NATURAL CONVECTION IN AN INNOVATIVE AIR COOLING SYSTEM

The process of buoyancy-induced turbulent convection in an asymmetrically heated vertical channel is studied numerically to simulate the situation of flow development and heat transfer in an innovative air cooling system. An upgraded two-equation closure model is employed to describe the turbulent motion, and the problem is formulated with proper account of the effects of property variations and surface radiation between the bounding watts. The governing system is solved by an implicit finite-difference method. Variable grid sizes are used in the numerical computation, and the velocity-pressure coupling is treated by a technique involving numerical iteration with underrelaxation. The accuracy of the present computational scheme is demonstrated by comparing the predicted results with available experimental data. Axial variations of watt temperatures and downstream evolution of local velocity and temperature fields are determined as functions of various controlling parameters of the system.     

NUMERICAL INVESTIGATION OF FLOW AND HEAT TRANSFER IN TWISTED CIRCULAR-SECTOR DUCTS

Flow and heat transfer in a twisted circular-sector duct are analyzed numerically for steady, fully developed, and incompressible laminar flow with a uniform-wall-temperature boundary condition. A rotating coordinate system is employed to account for the duct twist. The friction factors and Nusselt numbers are predicted for duct sector angles ranging from 15° to 90°, Reynolds numbers ranging from 1 to 1,000, and Prandtl numbers ranging from 1 to 100. Results show significant influence of duct twist on both friction factors and Nusselt numbers, particularly at large values of Reynolds and Prandtl numbers. Accurate correlations are developed to predict the friction factors and Nusselt numbers for the entire range of geometric and operating conditions studied.     

COMPUTATIONAL ANALYSIS OF TURBULENT FLUID FLOW AND HEAT TRANSFER OVER AN ARRAY OF HEATED MODULES USING TURBULENCE MODELS

A computational analysis is carried out using the standard k - l model and two low Reynolds number turbulence models as applied to developing turbulent fluid flow and heat transfer in a channel with surface-mounted heat-generating modules. The channel is assumed to be formed between two adjacent circuit boards with surface-mounted heat-generating modules mounted on a single side of each board. A detailed discussion of the computational model and the solution algorithm is given. Numerical experimentation is carried out with respect to mesh size and other mesh parameters. Calculation is performed for a Reynolds number range 2,000-7,000, and a Prandtl number of 0.7. The predictions of both pressure drop and heat transfer coefficient over the modules are compared with selected experimental data. The comparison showed that the low Reynolds number model based on Jones and Launder gives good predictions in a Reynolds number range of 2,000-5,000. At higher Reynolds numbers such as at Re=7,000, the standard k - l results in better predictions.     

NUMERICAL EVALUATION OF WEAKLY TURBULENT FLOW PATTERNS OF NATURAL CONVECTION IN A SQUARE ENCLOSURE WITH DIFFERENTIALLY HEATED SIDE WALLS

This article presents the results of numerical evaluation of weakly turbulent natural convection of air in a rectangular enclosure with differentially heated side walls and adiabatic horizontal walls. The turbulence in the natural convection was described by k–ε equations, which were solved by Strang splitting, while average thermal and fluid flow fields were described by statistically averaged equations, which were solved by the projection method PmIII. The combined application of projection method and the Strang splitting characterizes the numerical method in this study. Numerical results for Rayleigh number 1.58 × 10⁹ have revealed reasonable agreement with the existing experimental ones, with some discrepancy attributable to the adiabatic boundary conditions on the horizontal walls. The results are also in good agreement with some published numerical results, particularly at higher Rayleigh numbers. However, comparison with the latest experimental data reveals that the turbulent heat flux model is not quite capable of giving satisfactory temperature distribution.     

NUMERICAL INVESTIGATION OF HEAT TRANSFER UNDER CONFINED IMPINGING TURBULENT SLOT JETS

This work numerically in vestigates confined impinging turbulent slot jets. Eight turbulence models, including one standard and seven low-Reynolds-number k-epsilon models, are employed and tested to predict the heat transfer performance of multiple impinging jets. Validation results indicate that the prediction by each turbulence model depends on grid distribution and numerical scheme used in spatial discretization. In addition, spent fluid exits are set between impinging jets to reduce the cross-flow effect in degradation of the heat transfer of downstream impinging jets. The overall heat transfer performance can be enhanced by proper spent fluid removal.     

NUMERICAL STUDY ON TURBULENT FLOW AND HEAT TRANSFER IN CIRCULAR COUETTE FLOWS

Abstract

A numerical study is performed to investigate heat transfer and fluid flow in the entrance and fully developed regions of an annulus, consisting of a rotating, insulated inner cylinder and a stationary, heated outer cylinder. Several different k-ε turbulence models are employed to determine the turbulent kinetic energy, its dissipation rate, and the heat transfer performance. The governing boundary layer equations are discretized by means of a control volume finite difference technique and numerically solved using the marching procedure. In the entrance region the axial rotation of the inner cylinder induces a thermal development and causes an increase in both the Nusselt number and the turbulent kinetic energy in the inner cylinder wall region. In the fully developed region, an increase in the Taylor number causes an amplification of the turbulent kinetic energy over the whole cross section, resulting in a substantial enhancement in the Nusselt number. These transport phenomena are also affected by the radius ratio and Reynolds number.     

DIRECT NUMERICAL SIMULATION OF LAYER MERGING IN A SALT-STRATIFIED SYSTEM

Time-dependent double-diffusive convection was studied numerically to clarify the mechanism of layer merging in a salt-stratified system. Using the Chebyshev collocation method, a typical example of stably stratified salt fluid subject to a lateral temperature difference in a rectangular enclosure (Ar = 1.25) is considered for realistic values of parameters (Ra_T = 2.7 X 10⁷, N_i = 0.882, Pr = 7.15, and Sc = 685). Two cases that differ by the initial salt concentration profile, i.e., linear and steplike profiles, are examined. Although globally, in both cases, the layer merging process is characterized by the mass transfer across the interface separating two convection layers, the two instances are quite different with respect to the interface structure. For the linear profile, vertical motion due to salt fingers is dominant, whereas for the steplike profile horizontal motion due to strong shear flows prevails. In particular, in the latter case, unlike for the linear profile case, traveling plumes perpendicular to shear flows that lead to the time variations in temperature and concentration are periodically generated within the interface. Predictions obtained with the simulations are in good agreement with experimental data.     

A NUMERICAL INVESTIGATION OF THE CONVECTIVE HEAT TRANSFER IN UNSTEADY LAMINAR FLOW PAST A SINGLE AND TANDEM PAIR OF SQUARE CYLINDERS IN A CHANNEL

The unsteady laminar flow and heat transfer characteristics from square cylinders located in a channel with a fully developed inlet velocity profile were studied numerically. The time-averaged Nusselt number for each face and the time-averaged cylinder Nusselt number (Nu) were determined, as well as aerodynamic characteristics such as cylinder lift, drag, and eddy-shedding Strouhal number (St) . The results show that the cylinder Nu decreases for both the single and the tandem pair of cylinders as they approach the channel wall. The upstream eddy-promoting cylinder significantly reduces the drag of the downstream cylinder as compared with that of the single cylinder. The St decreases as the wall is approached and is larger for the tandem pair than for the single cylinder for all positions.     

SIMULATION OF TURBULENT FLOW IN IRREGULAR GEOMETRIES USING A CONTROL-VOLUME FINITE-ELEMENT METHOD

A modified error indicator and a locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh are developed to study the supersonic turbulent flow over a backward-facing step. In the Cartesian coordinate system, the unsteady Favre-averaged Navier-Stokes equations with a low-Reynolds-number k –ε turbulence model are solved. The modified error indicator, in which the unified magnitude of substantial derivative of pressure and unified magnitude of substantial derivative of vorticity magnitude are incorporated, is applied to treat the new node spacing of mesh remeshing. To assess the present approach, the transsonic turbulent flow around an NACA 0012 airfoil is performed. According to the high-resolution result on the adaptive mesh, the structure of the back-step corner vortex, expansion wave, and oblique shock wave are distinctly captured.     

NUMERICAL INVESTIGATION OF TWO-DIMENSIONAL LAMINAR FLOW AND SOLUTE TRANSPORT IN A CHANNEL WITH SOME SYMMETRIC EXPANSIONS AND CONTRACTIONS

Numerical investigation of two-dimensional (2D) laminar flow and solute transport in a channel with some sudden symmetric expansions and contractions has been performed using the fictitious regions method. This method allows us, instead of solving Navier-Stokes equations in a complex domain, to solve equations with suitably continued coefficients in a rectangle. Stream function-vorticity variables are used in the present paper. Dependence of the flow and solute transport from the dimensions of the channel expansions and contractions is numerically investigated for different values of Reynolds and Péclet numbers using a finite differences method on a relatively fine grid.     

NUMERICAL INVESTIGATION OF CONVECTION HEAT TRANSFER IN A HEATED ROOM

We describe numerical investigation of airflow and temperature field in a room with a convective heat source. The simulation involves using computational fluid dynamics (CFD) to validate different turbulence models, i.e., the standard k- k model and the low Reynolds number k- k model. The comparisons between computations and experiments show good and acceptable agreement. It can be concluded that the CFD simulations can capture the main flow features and provide satisfactory results. It can be seen that the thermal wall jet created by the heat source greatly influences airflow pattern and temperature field in the room. It can also be seen that the advanced turbulence model may produce better results than the standard one under a suitable mesh scheme.     

NUMERICAL SIMULATION OF HEAT TRANSFER IN MIST FLOW

A numerical simulation of heat transfer over a row of tubes, in the presence of mist flow, is described. Computations include the solution of the flow field around the tubes, the prediction of the motion of water droplets, and the evaluation of the cooling effect of the water film on the tube surface. The entire analysis is carried out using FENSAP-ICE (Finite Element Navier-Stokes Analysis Package for In-flight icing), a simulation system developed by Newmerical Technologies for icing applications. The numerical model is described, including the Navier-Stokes solution, the water thin film computation, the droplet impingement prediction, and the conjugate heat transfer procedure. The predictions are verified against experimental data for different droplet mass flow rates, showing satisfactory agreement and allowing a useful insight in the physical characteristics of the problem.     

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).     

NUMERICAL SIMULATION OF TURBULENT CONVECTIVE HEAT TRANSFER IN SQUARE RIBBED DUCTS

This article reports on an investigation on numerical prediction of thermal characteristics of a certain type of duct. The ducts considered have rib turbulators to enhance the heat transfer rate. The calculation method consists of a low Re number turbulence model and two methods for determining the turbulent Reynolds stresses, namely, a simple eddy viscosity model (EVM) [1] and an explicit algebraic stress model (EASM) [2]. The model development is carried out to make the original EASM consistent with the low Re number k- epsilon turbulence model applied. A certain method is developed to deal with the decoupling of the velocity and Reynolds stress fields inthe collocated grid arrangement that is chosen in this study. The SIMPLEC algorithm handles the pressure-velocity coupling. The computations are performed with the assumption of fully developed periodic conditions. These models are used to predict the convective turbulent forced convection in different test cases and the results are compared with experiments. A ribbed duct with two ribs on opposite walls is chosen and the obtained results including the mean thermal characteristics of the considered duct are compared with an experimental correlation. Two further duct configurations, identical to an experimental setup, are then computed. These experimental cases are chosen because detailed thermal-hydraulic information is available and then local comparisons between the two prediction models and experimental results are possible. The calculated mean and local thermal-hydraulic values are compared with corresponding experimental data and the prediction capabilities of the two turbulence models (EVM and EASM) are discussed. Theresults show that the EASM has some superiority over the EVM in the prediction of the velocity field structure, but the mean thermal predictions are not very different. There are also some important features of the flow field, whichare not revealed by theEVM calculations. However, the required CPU times are considerably higher for the EASM case.     

NUMERICAL STUDY OF CONVECTION HEAT TRANSFER DURING THE MELTING OF ICE IN A POROUS LAYER

A numerical study is made of the melting of ice in a rectangular porous cavity heated from above. The Landau transformation is used to immobilize the ice-water interface, and the Darcy-Boussinesq equations are solved by a finite-difference technique. Results are analyzed in terms of the heating temperature and the aspect ratio of the cavity. A comparison is made with the case of melting from below. It was found that melting from above is more effective than melting from below when the heating temperature is between 0 and 8°C: convection arises earlier, the melting process is faster, and the total melt at steady state is thicker. The critical time for onset of convection is minimum when the upper boundary is heated at 6°C. At this heating temperature, one also obtains a maximum heat transfer rate (Nusselt number).     

NUMERICAL PREDICTIONS OF FLOW AND THERMAL FIELDS IN A RECIPROCATING PISTON-CYLINDER ASSEMBLY

An efficient solution method for predicting unsteady, compressible flow and thermal fields in a reciprocating piston-cylinder assembly is developed in this study. The solution method, based on a two-stage pressure correction scheme, is applied for simultaneously determining the absolute pressure, density, temperature, and velocity components of the fluid inside the cylinder at any instant during the start-up and the periodically stable periods. Discretization equations are derived from the integral mass, momentum, and energy equations on a moving grid, which is deforming to accommodate the movement of the piston. A test problem is solved by means of the proposed method to illustrate the validity of the numerical procedure. Results show that the two-stage pressure correction scheme can be readily incorporated into existing numerical techniques to yield reasonably accurate results. Effects of the influential factors, including gravity (g) and rotation speed of the crank shaft (f), thus can be evaluated.     

NUMERICAL PREDICTION OF TURBULENT PLANE BUOYANT JETS DISCHARGING IN A STRATIFIED STAGNANT OR FLOWING OCEAN

The discharge of sewage effluent from ports in a long diffuser pipe on the ocean bottom produces a flow pattern that may be idealized as a buoyant jet from a line source. To minimize the impact of emission of pollutants, the dispersion of wastewater should be predictable, and the prediction of the maximum height of rise is important in determining whether or not the jet will remain submerged. A buoyancy-extended K-ε model of turbulence has been developed for calculating the dynamical and thermal fields in forced plane plumes vertically discharged into a stably stratified environment. The predicted maximum height of rise for the linearly stratified quiescent ambient case is compared with available experimental data. An idealized two-layer situation is then considered in such a way as to simulate a thermocline in the upper part of the ocean. Numerical results are presented for a uniform horizontal cross-stream situation.