Metal Foam Heat Exchangers for Heat Transfer Augmentation from a Cylinder in Cross-Flow

A numerical study has been conducted to examine the heat transfer from a metal foam-wrapped solid cylinder in cross-flow. Effects of the key parameters including the free stream velocity and characteristics of metal foam such as porosity, permeability, and form drag coefficient on heat and fluid flow are examined. Being a determining factor in pressure drop and heat transfer increment, the porous layer thickness is changed systematically to observe that there is an optimum layer thickness beyond which the heat transfer does not improve while the pressure drop continues to increase. This has been verified by the application of Bejan’s Intersection of Asymptotes method. Results have been compared to those of a finned-tube heat exchanger to observe much higher heat transfer rate with reasonable excess pressure drop leading to a higher area goodness factor for metal foam-wrapped cylinder.     

Numerical characterization of micro heat exchangers using experimentally tested porous aluminum layers

A microporous heat exchanger device is being developed for cooling high-power electronics. The device uses a mechanically compressed aluminum porous layer to improve the heat transfer at the coolant/solid interface and to provide more uniform cooling of the electronics. The hydraulic characteristics (porosity, permeability, and Forchheimer coefficient) of nine distinct compressed layers are obtained experimentally. These layers have porosity from 0.3 to 0.7 and permeability from 1.8 × 10⁻¹⁰ m2 to 1.2 × 10⁻⁹ m2. The inertia coefficient varies from 0.3 to 0.9. These hydraulic characteristics are used in the numerical simulations of a real microporous heat exchanger for cooling phased-array radars in development. Thermal and hydraulic performances are illustrated in terms of total pressure drop across the heat exchanger, maximum temperature difference in the direction transverse to the electronic modules, and maximum temperature within the coolant passage. Results indicate that the proposed design is capable of achieving a maximum transverse temperature difference of 2°C using polyalphaolephin as coolant.     

Effect of mass transfer on flow across a staggered tube bundle

Over a range of Reynolds numbers from 0·6 × 10⁵ to 1·75 × 10⁵ tests were made on a seven rows deep tube bank. These tests were made using a specially instrumented porous cylinder which could be located in any position within the bank. Mass transfer through the porous surface simulating the condensation process in a surface condenser, was applied, and its effect on local parameters investigated. The distribution of static pressure and skin friction was determined around tubes in different rows in the bank. From these measurements, the pressure drag and friction drag were estimated. The total pressure drop across the bank was also measured.

Results showed that, for typical steam condenser loadings, the contribution of the pressure drag to the total drag does not change appreciably with suction. However, the skin friction contribution does change considerably with suction.     

Correlations for the pressure drop for flow through metal foam

Steady-state unidirectional pressure-drop measurements for incompressible airflow through nine open-cell aluminum foam samples, having different porosities and pore densities, were undertaken. The pressure drop increased with increasing Darcian velocity following the quadratic Forchheimer equation. The lower-porosity foam produced significantly higher pressure drop. Both the permeability and the form drag coefficient correlated well with the porosity. The correlations predicted the results of some previous studies reasonably well, especially for the low-pore-density foam.     

Drag difference between steady and shocked gas flows passing through a porous body

Experimental and numerical investigations of gas flows through porous materials have been carried out. We have investigated steady and unsteady processes occurring when the gas flow interacts with porous materials. Densities and porosities of the four open-cell-type polyurethane foams which were investigated are kg/m and , with the foams having different structures. Experiments were conducted to determine the steady drag coefficient of the porous material at low Reynolds numbers, evaluated from the pressure drop. The Forchheimer equation was applied to determine the drag. Values of permeability coefficients () in the Forchheimer equation were estimated by comparing computed and experimental results. Results show that the drag coefficient is largely affected by the internal structure of the foam, and has almost no effect on the stress history, while the value of dominates the stress history variation. Differences of 1000 times exist between the steady flow and unsteady shock tube flow values. Received 15 May 1998/ Accepted 15 March 1999     

The effect of flexible tube vibration on pressure drop and heat transfer in heat exchangers considering viscous dissipation effects

The pressure drop and heat transfer coefficient in tube bundle of shell and tube heat exchangers are investigated considering viscous dissipation effects. The governing equations are solved numerically. Because of temperature-dependent viscosity the equations should be solved simultaneously. The flexible tubes vibration is modeled in a quasi-static method by taking the first tube of the row to be in 20 asymmetric positions with respect to the rest of the tubes which are assumed to be fixed and time averaging the steady state solutions corresponding to each one of these positions .The results show that the eccentricity of the first tube increases pressure drop and heat transfer coefficients significantly comparing to the case of rigid tube bundles, symmetrically placed. In addition, these vibrations not only compensate the effect of viscous dissipations on heat transfer coefficient but also increase heat transfer coefficient. The constant viscosity results obtained from our numerical method have a good agreement with the available experimental data of constant viscosity for flexible tube heat exchangers.     

Prediction of heat transfer coefficients and friction factors for evaporation of R-134a flowing inside corrugated tubes

In this study, experimental and simulation studies of the evaporation heat transfer coefficient and pressure drop of R-134a flowing through corrugated tubes are conducted. The test section is a horizontal counter-flow concentric tube-in-tube heat exchanger 2.0 m in length. A smooth tube and corrugated tubes with inner diameters of 8.7 mm are used as the inner tube. The outer tube is made from a smooth copper tube with an inner diameter of 21.2 mm. The corrugation pitches used in this study are 5.08, 6.35, and 8.46 mm. Similarly, the corrugation depths are 1, 1.25, and 1.5 mm, respectively. The results show that the maximum heat transfer coefficient and pressure drop obtained from the corrugated tube are up to 22 and 19 % higher than those obtained from the smooth tube, respectively. In addition, the average difference of the heat transfer coefficient and pressure drop between the simulation model and experimental data are about 10 and 15 %, respectively.     

A Theoretical Model with Experimental Verification to Predict Hydrodynamics of Foams

An experimentally validated theoretical model, based on hydraulic resistance network and scale analysis at the pore level, is developed to predict the pressure drop for flow through foams. The complex microstructure of the foams is modeled as a matrix of interconnected solid ligaments forming simple cubic arrays of cylinders. New correlations for permeability and form drag (inertia) coefficient are presented as functions of the mean pore and ligament diameter as well as the foam porosity. The present model makes it possible to conduct parametric studies. Results obtained from the proposed model are successfully compared with our experimental data as well those found in the literature to observe good agreement.     

Drag and Separation Flow Past Solid Sphere with Porous Shell at Moderate Reynolds Number

Axisymmetric viscous, two-dimensional steady and incompressible fluid flow past a solid sphere with porous shell at moderate Reynolds numbers is investigated numerically. There are two dimensionless parameters that govern the flow in this study: the Reynolds number based on the free stream fluid velocity and the diameter of the solid core, and the ratio of the porous shell thickness to the square root of its permeability. The flow in the free fluid region outside the shell is governed by the Navier–Stokes equation. The flow within the porous annulus region of the shell is governed by a Darcy model. Using a commercially available computational fluid dynamics (CFD) package, drag coefficient and separation angle have been computed for flow past a solid sphere with a porous shell for Reynolds numbers of 50, 100, and 200, and for porous parameter in the range of 0.025–2.5. In all simulation cases, the ratio of b/a was fixed at 1.5; i.e., the ratio of outer shell radius to the inner core radius. A parametric equation relating the drag coefficient and separation point with the Reynolds number and porosity parameter were obtained by multiple linear regression. In the limit of very high permeability, the computed drag coefficient as well as the separation angle approaches that for a solid sphere of radius a, as expected. In the limit of very low permeability, the computed total drag coefficient approaches that for a solid sphere of radius b, as expected. The simulation results are presented in terms of viscous drag coefficient, separation angles and total drag coefficient. It was found that the total drag coefficient around the solid sphere as well as the separation angle are strongly governed by the porous shell permeability as well as the Reynolds number. The separation point shifts toward the rear stagnation point as the shell permeability is increased. Separation angle and drag coefficient for the special case of a solid sphere of radius r = a was found to be in good agreement with previous experimental results and with the standard drag curve.     

Heat transfer from a vertical tube bundle under natural circulation conditions

A rectangular loop (thermosyphon) was used to measure the average heat transfer coefficients for water at atmospheric pressure under natural circulation conditions. A twenty-one tube bundle with tubes 1.65 m long and 9.55 mm in diameter, and a pitch-to-diameter ratio of 1.33, was used as a test heat exchanger in one of the vertical legs of the loop. A natural circulation flow in the loop developed due to buoyancy differences of the fluid in its two vertical legs. Flow visualization experiments were performed to determine the flow regimes associated with natural circulation flow longitudinal to a tube bundle. Empirical correlations for the average Nusselt number have been developed and are reported. Grid spacers arranged on tube bundles were shown to enhance heat transfer, especially for laminar flow, without any noticeable increase in pressure drop.     

Modeling fluid and heat transport in the reactive, porous bed of downdraft (biomass) gasifier

A fluid flow and heat transfer model has been developed for the reactive, porous bed of the biomass gasifier to simulate pressure drop, temperature profile in the bed and flow rates. The conservation equations, momentum equation and energy equation are used to describe fluid and heat transport in porous gasifier bed. The model accounted for drag at wall, and the effect of radial as well as axial variation in bed porosity to predict pressure drop in bed. Heat transfer has been modeled using effective thermal conductivity approach. Model predictions are validated against the experiments, while effective thermal conductivity values are tested qualitatively using models available in literature. Parametric analysis has been carried out to investigate the effect of various parameters on bed temperature profile and pressure drop through the gasifier. The temperature profile is found to be very sensitive to gas flow rate, and heat generation in oxidation zone, while high bed temperature, gas flow rate and the reduction in feedstock particle size are found to cause a marked increase in pressure drop through the gasifier. The temperatures of the down stream zones are more sensitive to any change in heat generation in the bed as compared to upstream zone. Author recommends that the size of preheating zone may be extended up to pyrolysis zone in order to enhance preheating of input air, while thermal insulation should not be less than 15 cm.     

Local Thermal Non-Equilibrium and Heterogeneity Effects on the Onset of Convection in a Layered Porous Medium

The effect of local thermal non-equilibrium on the onset of convection in a porous medium consisting of two horizontal layers is studied analytically. Linear stability theory is applied. Variations of permeability, fluid conductivity, solid conductivity, interphase heat transfer coefficient and porosity are considered. It is found that heterogeneity of permeability and fluid conductivity have a major effect, heterogeneity of interphase heat transfer coefficient and porosity have a lesser effect, while heterogeneity of solid conductivity is relatively unimportant.     

Filtration model of longitudinal flow in a finned cylindrical channel

The problem of laminar flow of a viscous incompressible fluid in a finned circular tube is considered. A solution is obtained in the form of series in eigenfunctions of the Laplace operator; the coefficients in the series are found numerically. For the same problem, a simpler filtration approximation is proposed in which the system of fins is modeled by a radially inhomogeneous porous layer, and fluid flow in it is described by the Brinkman equation. A formula for the effective permeability of the porous medium is obtained by varying the number and height of fins. The formula provides an accurate evaluation of the mean flow velocity and viscous drag coefficient in finned channels.     

Heat transfer and two-phase flow characteristics of refrigerants flowing under varied heat flux in a double-pipe evaporator

A mathematical model based on the annular flow pattern is developed to simulate the evaporation of refrigerants flowing under varied heat flux in a double tube evaporator. The finite difference form of governing equations of this present model is derived from the conservation of mass, energy and momentum. The experimental set-up is designed and constructed to provide the experimental data for verifying the simulation results. The test section is a 2.5 m long counterflow double tube heat exchanger with a refrigerant flowing in the inner tube and heating water flowing in the annulus. The inner tube is made from smooth horizontal copper tubing of 9.53 mm outer diameter and 7.1 mm inner diameter. The agreement of the model with the experimental data is satisfactory. The present model can be used to investigate the axial distributions of the temperature, heat transfer coefficient and pressure drop of various refrigerants. Moreover, the evaporation rate or the other relevant parameters that is difficult to measure in the experiment are predicted and presented here. The results from the present mathematical model show that the saturation pressure and temperature of refrigerant decrease along the tube due to the tube wall friction and the flow acceleration of refrigerant. The liquid heat transfer coefficient increases with the axial length due to reducing the thickness of the liquid refrigerant film. Due to increase of the liquid heat transfer coefficient, increasing wall heat flux is obtained.Finally, the evaporation rate of refrigerant increases with increasing wall heat flux.     

Modelluntersuchungen des Wärmeaustausches und Strömungswiderstandes an den Heizflächen mit Diagonalflossen

This paper presents the results of an experimental study on the heat transfer and pressure drop in diagonally finned tube banks. The investigations have been carried out using the napthalene analogy. The performance of a heat exchanger with fins arranged a certain angle to the flow direction with the plain tube heat exchanger have been compared.     

Effect of Confining Wall on Properties of Gas Flow Through Metal Foam: An Experimental Study

While the Darcy and Forchheimer relations are widely applied to determine the permeability and the form drag coefficient of open-cell metal foam, they both assume that the porous medium is infinite in all directions, i.e., large enough so that the effect of any confining walls is negligible. Many researchers, however, pay little or no attention to the size of metal foam samples in pressure-drop studies. The size of a foam sample perpendicular to the flow direction may be small enough such that wall effects are significant. This article experimentally investigates the wall effect on the permeability and form drag coefficient for two types of open-cell aluminum foam subjected to airflow entering the foam in the Forchheimer regime. The Forchheimer equation was recast in two different manners, which resulted in new non-dimensional numbers that correlated very well with the diameter of the foam samples measured in cells. The correlations are valid for a confining-tube-diameter-based Reynolds number ranging from approximately 13,000 to 105,000, and for diameters ranging from 12 to 36 cells and 24 to 60 cells for 10- and 20-pore per inch foam, respectively. The obtained correlations allow for determining pressure drop given only the velocity and the diameter of an aluminum foam sample.     

Stress-Dependent Porosity and Permeability of Porous Rocks Represented by a Mechanistic Elastic Cylindrical Pore-Shell Model

The stress dependency of the porosity and permeability of porous rocks is described theoretically by representing the preferential flow paths in heterogeneous porous rocks by a bundle of tortuous cylindrical elastic tubes. A Lamé-type equation is applied to relate the radial displacement of the internal wall of the cylindrical elastic tubes and the porosity to the variation of the pore fluid pressure. The variation of the permeability of porous rocks by effective stress is determined by incorporating the radial displacement of the internal wall of the cylindrical elastic tubes into the Kozeny–Carman relationship. The fully analytical solutions of the mechanistic elastic pore-shell model developed by combining the Lamé and Kozeny–Carman equations are shown to lead to very accurate correlations of the stress dependency of both the porosity and the permeability of porous rocks.

     

Fluid flow simulation in a random elliptical porous medium by using the lattice Boltzmann method

A fluid flow through an isotropic porous medium with randomly arranged elliptical particles is simulated by the lattice Boltzmann method. The dimensionless pressure drop and the dimensionless permeability are evaluated as functions of the Reynolds number. The effect of the aspect ratio of the major to minor semi-axis of the ellipse on the dimensionless permeability is considered for different values of porosity. The pressure drop is thoroughly investigated as a function of fluid viscosity for different values of the aspect ratio and porosity. The influence of various parameters of the problem on the mean tortuosity of the medium is considered.     

Calculation of relative permeability in reservoir engineering using an interacting triangular tube bundle model

Analytical expressions of relative permeability are derived for an interacting cylindrical tube bundle model. Equations for determining relative permeability curves from both the interacting uniform and interacting serial types of triangular tube bundle models are presented. Model parameters affecting the trend of relative permeability curves are discussed. Interacting triangular tube bundle models are used to history-match laboratory displacement experiments to determine the relative permeability curves of actual core samples. By adjusting model parameters to match the history of oil production and pressure drop, the estimated relative permeability curves provide a connection between the macroscopic flow behavior and the pore-scale characteristics of core samples.     

The influence of tube bundle geometry on cross-flow boiling heat transfer and pressure drop

An experimental investigation was performed to compare the boiling heat transfer coefficients and two-phase pressure drops from a square inline and a staggered tube bundle having the same tube pitch-to-diameter ratio (P/D = 1.30) and from two square inline tube bundles having different pitch-to-diameter ratios (P/D = 1.30 and 1.70). Except at the highest heat fluxes the heat transfer coefficients generally were higher in the staggered tube bundle than in the inline tube bundle and higher in the larger P/D tube bundle than in the smaller. As the heat flux increased, the differences decreased. The differences were attributed to the tradeoff between nucleation and convection. The staggered tube bundle had higher pressure drops than the inline bundle except at low mass velocities; the larger pressure drop in the staggered bundle was attributed to the combination of a larger void fraction and a larger friction multiplier, with the frictional component dominating at higher mass velocities. Comparing the inline tube bundle pressure drops, it was concluded that the larger P/D bundle had a larger void fraction than the smaller P/D tube bundle; no conclusions could be drawn regarding the relative magnitude of the two-phase fraction multiplier.