Viscous dissipation effects on the asymptotic behaviour of laminar forced convection for Bingham plastics in circular ducts

The present study concentrates on the effects of viscous dissipation and the yield shear stress on the asymptotic behaviour of the laminar forced convection in a circular duct for a Bingham fluid. It is supposed that the physical properties are constant and the axial conduction is negligible. The asymptotic temperature profile and the asymptotic Nusselt number are determined for various axial distributions of wall heat flux which yield a thermally developed region. It is shown that if the asymptotic value of wall heat flux distribution is vanishes, the asymptotic value of the Nusselt number is zero. The case of the asymptotic wall heat flux distribution non-vanishing giving a value of the Nusselt number dependent on the Brinkman number and on the dimensionless radius of the plug flow region was also analysed. For an infinite asymptotic value of wall heat flux distributions, the asymptotic value of the Nusselt number depends on the dimensionless radius of the plug flow region and on the dimensionless parameter which depends on the asymptotic behaviour of the wall heat flux. The condition of uniform wall temperature and convection with an external isothermal fluid were also considered. The comparison with other existing solutions in the literature in the Newtonian case is analysed.     

Modelling of stratified gas–liquid two-phase flow in horizontal circular pipes

This paper reports numerical and experimental investigation of stratified gas–liquid two-phase flow in horizontal circular pipes. The Reynolds averaged Navier–Stokes equations (RANS) with the k–ω turbulence model for a fully developed stratified gas–liquid two-phase flow are solved by using the finite element method. A smooth interface surface is assumed without considering the effects of the interfacial waves. The continuity of the shear stress across the interface is enforced with the continuity of the velocity being automatically satisfied by the variational formulation. For each given interface position and longitudinal pressure gradient, an inner iteration loop runs to solve the non-linear equations. The Newton–Raphson scheme is used to solve the transcendental equations by an outer iteration to determine the interface position and pressure gradient for a given pair of volumetric flow rates. Favorable comparison of the numerical results with available experimental results indicates that the k–ω model can be applied for the numerical simulation of stratified gas–liquid two-phase flow.     

An inspection of viscosity model for homogeneous two-phase flow pressure drop prediction in a horizontal circular micro-channel

This study analyzes several well-known two-phase viscosity models in order to address the appropriate correlations among them for application to micro-channel. Pressure drop data is obtained from adiabatic two-phase air–water flow experiments. A fused silica channel, 320 mm long, with an inside diameter of 0.53 mm is used as the test section. The measured data is compared with the homogeneous flow predictions calculated using the existing viscosity models and detailed comparisons are discussed.     

An improved numerical scheme to evaluate the pressure gradient on unstructured meshes for two-phase flow analysis

In multi-dimensional two-phase flows, a local pressure is very important because it directly influences the phase change and it may lead to a great change in the flow field. This in turn puts emphasis on the accurate evaluation of local pressure gradient. This paper presents a new numerical scheme to evaluate the pressure gradient at cell centers on unstructured meshes for a three-dimensional thermal-hydraulic code, named CUPID. The results of the new scheme for a simple test function, a gravity-driven cavity, and a wall boiling two-phase flow are compared with those of the previous schemes in the CUPID code.     

Experimental study for the stratified to slug flow regime transition mechanism of gas-oil two-phase flow in horizontal pipe

Theoretical relations that predict the transition from a stratified pattern to a slug pattern, including a onedimensional wave model that contains less empiricism than the commonly used Taitel-Dukler model, and the ideal model for stratified flow for the gas-liquid flow in horizontal pipes are presented. Superficial velocities of each phase, as the onset of slugging occurs, were predicted, and theoretical analysis was conducted on the stratified to slug flow regime transition. The friction, existing between the fluid and pipe wall, and on the interface of two phases, was especially taken into account. A theoretical model was applied to an experiment about air-oil two-phase flow in a 50 mm horizontal pipe. The effect of pipe diameter on the transition was also studied. The results show that this approach gives a reasonable prediction over the whole range of flow rates, and better agreement has been achieved between predicted and measured critical parameters. __________ Translated from Journal of Shanghai Jiaotong University, 2006, 40(10): 1782–1785, 1789 [译自: 上海交通大学学报]     

Investigating the pressure loss associated with two-phase flow in a rectangular microchannel suddenly expanding into a manifold

This study focuses on the experimental investigation of the two-phase pressure loss occurring as air-water flow exits a microchannel to a larger manifold. The microchannel has dimensions of 3.23 mm wide by 0.304 mm high by 164 mm long and expands into an exit manifold of 1.4 cm diameter oriented ${90}^{°}$ relative to the flow direction. The expansion results in an additional 150–400 Pa pressure loss. Visualization of the flow illustrates water accumulation at the channel exit with varying behavior, resulting in the range of the pressure loss. Using the sudden expansion model of Abdelall et al. resulted in a mean absolute percent error of 96%. Treating the pressure loss as a result of the ${90}^{°}$ bend, the model of Paliwoda produced a mean absolute percent error of 81%. The combined influence of the models of Abdelall et al. and Paliwoda predicted the experimental measurement with a mean absolute percent error of 78%.     

Two-phase air-water flow in micro-channels: An investigation of the viscosity models for pressure drop prediction

Adiabatic two-phase air-water flow is experimentally studied in this work. Two channels, made of fused silica, with different diameters of 0.53 and 0.15 mm are used as test sections. The void fraction data for both tubes are obtained by image analysis. For the larger channel, the void fraction is found to be a linear relationship with the volumetric quality. In the case of the smaller one, however, the non-linear void fraction is obtained. The measured frictional pressure drop data are compared with the predictions regarding the homogeneous flow assumption. Several well-known two-phase viscosity models are subsequently evaluated for applicability to micro-channels.     

Gas–liquid two-phase flow patterns in parallel channels for fuel cells

Two-phase flow in horizontal parallel channels has been experimentally investigated under fuel cell related operating conditions. Pronounced hysteresis is observed in the pressure drop versus flow characteristic curve when starting from either flooded or dry conditions. When gas is introduced into channels initially filled with water (flooded initial condition), both gas and liquid tend to flow predominantly in one channel at low gas or liquid flow velocities. As the gas flow velocity increases, even distribution of gas and liquid flow in both channels is observed, accompanied with a sudden decrease in the pressure drop. On the other hand, even gas and liquid flow distribution between both channels is found at comparatively lower gas flow velocities when starting with dry-gas flow conditions with liquid introduced into channels filled with gas (stratified flow regime). The flow regimes of this system are visualized in plots of the pressure drop against gas and liquid flow velocities. However, this phenomenon tends to vanish at high gas and liquid flow velocities, suggesting that high gas and liquid flow velocities are required to ensure even flow distribution in parallel channels. The hysteresis points appear at the same level of the pressure drop, reflecting intrinsic characteristics of the parallel channels used in this study. These results have important implications for PEM fuel cell operational strategies. In order to avoid reactant mal-distribution in parallel flow channels in the flow field in the two-phase flow regime, fuel cells should be operated at sufficiently high gas flow velocities.     

A two-phase flow and transport model for the cathode of PEM fuel cells

A unified two-phase flow mixture model has been developed to describe the flow and transport in the cathode for PEM fuel cells. The boundary condition at the gas diffuser/catalyst layer interface couples the flow, transport, electrical potential and current density in the anode, cathode catalyst layer and membrane. Fuel cell performance predicted by this model is compared with experimental results and reasonable agreements are achieved. Typical two-phase flow distributions in the cathode gas diffuser and gas channel are presented. The main parameters influencing water transport across the membrane are also discussed. By studying the influences of water and thermal management on two-phase flow, it is found that two-phase flow characteristics in the cathode depend on the current density, operating temperature, and cathode and anode humidification temperatures.     

A two-phase flow pattern map for annular channels under a DC applied voltage and the application to electrohydrodynamic convective boiling analysis

An experimental study of tube side boiling heat transfer of HFC-134a has been conducted in a single-pass, counter-current flow heat exchanger under an electric field. By applying 0–8 kV to a concentric inner electrode, the mechanics of EHD induced flow and heat transfer augmentation/suppression have been investigated for flow conditions with inlet qualities of 0% to 60%, mass fluxes from 100 kg/m² s to 500 kg/m² s, and heat flux levels between 10 kW/m² and 20 kW/m². A theoretical Steiner type two-phase flow pattern map for flow boiling in the annular channel under applied DC high voltage is also developed. The flow regimes encountered in the convective boiling process have been reconstructed experimentally and compared with the proposed EHD flow regime map. The results show that when the proposed dimensionless criterion M_d Re² is satisfied, EHD interfacial forces have a strong influence on the flow pattern which is considered to be the primary mechanism affecting the increase in pressure drop and the augmentation or even suppression of heat transfer.     

Computer-aided numerical solution for the flow of compressible fluid through a series of identical annular orifices

The paper represents a general semi-empirical model for the calculation of the pressure distribution and the mass flow rate of a compressible fluid flowing through a set of concentric annular orifices in series. The flow through a single orifice is discussed taking into consideration the variation of the discharge coefficient and the effect of kinetic energy being carried from one throttling to the next one. The study is extended to a set of orifices resulting in the general model. A computer program based on this model is described which is applicable for different geometries and overall pressure ratios. Comparison with available experimental results shows that the model gives fairly accurate results.     

Effect of pressure on entrainment flow rate in vertical upwards gas—liquid annular two-phase flow. Part I: Experimental results for system pressures from 0.3 MPa to 20 MPa

The purpose of this study is to investigate the pressure effects on the entrainment flow rates in vertical gas—liquid annular two-phase flow. The cross-sectional entrainment flow rates were measured using an isokinetic probe method. It was found that the behavior of cross-sectional entrainment flow rate profiles is divided into low- and high-pressure regions. Also, the entrainment flow rates amount to 90 percent of the total liquid flow rate under high-pressure conditions. In this study, system pressure in the closed-loop system was changed substantially from 0.3 MPa to 20 MPa at a constant fluid temperature in vertical upward flow. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 25(5): 267–280, 1996     

Improved velocity and temperature profiles for integral solution in the laminar boundary layer flow on a semi‐infinite flat plate

One of the most important problems in Mechanical Engineering is the determination of laminar boundary layer thickness over a flat plate. Integral solution and similarity solutions are two well‐known methods for calculation of boundary layer thickness. However, integral solution method is a computational cost‐effective method rather than the similarity solution method. Velocity and temperature profiles must be determined for the integral solution method. Velocity boundary layer thickness can be determined by the velocity profile whereas for determination of thermal boundary layer thickness both velocity and temperature profiles must be used. Available velocity profiles do not give an exact value for velocity boundary layer thickness, while the Nusselt number is affected by these profiles. In this study, a new velocity profile is proposed which gives an exact value for laminar boundary layer thickness on a flat plate. In addition, two temperature profiles are proposed that give the exact values of the Nusselt number over a flat plate for uniform temperature and uniform heat flux boundary conditions. The calculated constants in the velocity boundary layer thickness equation and the Nusselt relations are validated with the results of the similarity solution method. Excellent agreement between the results of the two methods is observed.     

Experimental analysis for the determination of the convective heat transfer coefficient by measuring pressure drop directly during annular condensation flow of R134a in a vertical smooth tube

This study investigated the direct relationship between the measured condensation pressure drop and convective heat transfer coefficient of R134a flowing downward inside a vertical smooth copper tube having an inner diameter of 8.1 mm and a length of 500 mm during annular flow. R134a and water were used as working fluids on the tube side and annular side of a double tube heat exchanger, respectively. Condensation experiments were performed at mass fluxes of 260, 300, 340, 400, 456 and 515 kg m⁻² s⁻¹ in the high mass flux region of R134a. The condensing temperatures were around 40 and 50 °C; the heat fluxes were between 10.16 and 66.61 kW m⁻². Paliwoda’s analysis, which focused mainly on the determination of the two-phase flow factor and two-phase length of evaporators and condensers, was adapted to the in-tube condensation phenomena in the test section to determine the condensation heat transfer coefficient, heat flux, two-phase length and pressure drop experimentally by means of a large number of data points obtained under various experimental conditions.     

The experimental study on the flow characteristics for a swirling gas–liquid spray atomizer

A new spray atomizer, that is, swirling gas–liquid spray atomizer, is presented in this paper based on the analysis of various air-assist atomizers and their atomization mechanism. The air-to-liquid mass flow rate ratio (ALR) of the atomizer during the hot-state tests is 4–6% (by compressed air for emulsified heavy oil). And it is of excellent atomization. The discharge coefficient and the spray cone angle of the atomizer are studied systematically. The influence factors considered are as follows: the structure parameters, ALR and the viscosity of the liquid. Through the experiments, the formula of discharge coefficient and the spray cone angle of the atomizer are given in the paper. And it can give good direction on the atomizer design. The atomizer can be employed in the industrial furnaces and other equipments where the liquid must be atomized.     

Integrating a new flow separation model and the effects of the vortex shedding for improved dynamic stall predictions using the Beddoes–Leishman method

This paper aims at improving dynamic stall predictions on the S809 aerofoil under 2D flow conditions. The method is based on the well‐known Beddoes–Leishman model; however, a new flow separation model and a noise generator are integrated to improve the predictions in the load fluctuations, including those induced by vortex shedding on the aerofoil upper surface. The flow separation model was derived from a unique approach based on the combined use of unsteady aerodynamic loads measurements, the Beddoes–Leishman model and a trial‐and‐error technique. The new flow separation model and random noise generator were integrated in the Beddoes–Leishman model through a new solution algorithm. The numerical predictions of the unsteady lift and drag coefficients were then compared with the Ohio State University measurements for the oscillating S809 aerofoil at several reduced frequencies and angles of attack. The results using the proposed models showed improved correlation with the experimental data. Hysteresis loops for the aerodynamic coefficients are in good agreement with measurements. Copyright © 2016 John Wiley & Sons, Ltd.