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.     

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.     

Measurement and prediction of pressure drop in a two-phase micro-pin-fin heat sink

This study concerns pressure drop in a two-phase heat sink containing an array of staggered square micro-pin-fins having a 200 × 200 μm² pin cross-section by a 670 μm pin height. Three inlet temperatures of 30, 60 and 90 °C, and six maximum mass velocities for each inlet temperature, ranging from 183 to 420 kg/m² s, were tested. Frictional pressure drop in the boiling region is deemed the dominant pressure drop component. The Lockhart–Martinelli correlation for laminar liquid–laminar vapor combination in conjunction with a previous single-phase friction factor correlation can adequately predict the data. Micro-pin-fins offer better flow stability than parallel micro-channels.     

CFD and artificial neural network modeling of two-phase flow pressure drop

A large number of experiments in a 2 cm diameter and 6 m length tube were carried out in order to study the two-phase flow regimes and pressure drops in it. The two-phase flow in the experimental tube was modeled using commercial CFD code, Fluent 6.2. An Artificial Neural Network (ANN) with three inputs including gas and liquid velocities and tube slope was designed and trained to predict average pressure drop across the tube. The comparison between CFD and ANN predictions of pressure drops with experimental measurements shows that the CFD results are more accurate than the ANN evaluations for new conditions.     

Study on the convective heat transfer and pressure drop in the micro-channel heat sink

Experiments have been performed to investigate the heat transfer characteristics and pressure drop in the micro-channel heat sinks under constant heat flux conditions. The experiments are performed for the Reynolds number and heat flux in the ranges of 200–1000 and 1.80–5.40 kW/m², respectively. The micro-channel heat sink with two different channel heights and two different channel widths are accomplished by wire electrical discharge machine. Effects of different geometrical configurations parameters of the micro-channel and heat flux on the heat transfer characteristics and pressure drop are considered. The micro-channel geometry configuration has significant effect on the enhancement heat transfer and pressure drop. The results of this study are expected to lead to guidelines that will allow the design of the micro-channel heat exchangers with improved heat transfer performance of the electronic devices.     

Performance evaluation of flattened tube in boiling heat transfer enhancement and its effect on pressure drop

An experimental investigation has been carried out to study heat transfer and pressure drop characteristics of R-134a flow boiling inside a horizontal plain tube and different flattened tubes. Round copper tubes with an inner diameter of 8.7 mm were flattened into an oblong shape with an internal height of 6.6 mm, 5.5 mm, 3.8 mm, and 2.8 mm. The test apparatus was basically a vapor compression refrigeration system equipped with all necessary measuring instruments. Analysis of the collected data showed that, by flattening the round tube, the heat transfer coefficient and pressure drop increased simultaneously. The performance of these tubes from the point of view of heat transfer enhancement and pressure drop increasing were evaluated. It was concluded that, the tube with an internal height of 5.5 mm has the best performance compared with the other flattened tubes. Finally, based on the present experimental pressure drop data, a correlation was developed to estimate the pressure drop in flattened tubes. This correlation predicts the experimental data of the present study within an error band of ± 20%.     

Effect of porous coating on two-phase pressure drop of water during up-flow boiling in tubes

This paper focuses on the effects of porous coating on two-phase flow pressure drop during up-flow boiling of water in vertical tubes. The experiments were carried out under subcooled fluid–inlet conditions (5–73 K) for different mass fluxes (200–400 kg/m² s) and pressures (0.11–0.69 MPa). The measured pressure drops were compared first with each other, and then with correlations from literature. It was found that the best agreement between predicted and measured values is obtained by the method of Thom [3] for a smooth tube and by Müller-Steinhagen and Heck's method [4] for a porous coated tube respectively.     

Flow boiling heat transfer in two-phase micro-channel heat sinks--I. Experimental investigation and assessment of correlation methods

This paper is the first of a two-part study concerning measurement and prediction of saturated flow boiling heat transfer in a water-cooled micro-channel heat sink. In this paper, new experimental results are discussed which provide new physical insight into the unique nature of flow boiling in narrow rectangular micro-channels. The micro-channel heat sink contained 21 parallel channels having a m cross-section. Tests were performed with deionized water over a mass velocity range of 135-402 kg/m² s, inlet temperatures of 30 and 60 °C, and an outlet pressure of 1.17 bar. Results indicate an abrupt transition to annular flow near the point of zero thermodynamic equilibrium quality, and reveal the dominant heat transfer mechanism is forced convective boiling corresponding to annular flow. Contrary to macro-channel trends, the heat transfer coefficient is shown to decrease with increasing thermodynamic equilibrium quality. This unique trend is attributed to appreciable droplet entrainment at the onset of annular flow regime development, and the increase in mass flow rate of the annular film by droplet deposition downstream. Eleven previous empirical correlations are assessed and deemed unable to predict the correct trend of heat transfer coefficient with quality because of the unique nature of flow boiling in micro-channels, and the operating conditions of water-cooled micro-channel heat sinks falling outside the recommended application range for most correlations. Part II of this study will introduce a new annular flow model as an alternative approach to heat transfer coefficient prediction for micro-channels.     

An empirical correlation for two-phase frictional performance in small diameter tubes

Experimental two-phase pressure drop data in small diameter tubes (D<10 mm) have been collected and updated from the literature which contain eight refrigerant and three air-water datasets. Comparisons between the data and the predictions indicate that the Chisholm correlation fails to predict the data. The Friedel correlation and Souza and Pimenta's correlation give fair predictions for the refrigerant data, but fail to predict the air-water data due to the surface tension effect. The homogeneous model shows a better predictive ability (a mean deviation of 34.7%) than the other empirical correlations. In this regard, an empirical correlation based on the homogeneous model was developed. By introducing the Bond number and Weber number to the modified correlation, the new correlation gives a mean deviation of 19.1% based on 1484 data points.     

Theoretical approach for a pressure drop in two-phase particle-laden flows

The purpose of this research is to develop an analytical model for a pressure drop per unit pipe length due to the turbulence modulations of a carrier phase which results from the presence of a dispersed phase in various types of diluted two-phase flows. The wake behind a particle, a particle size, the loading ratio and the density difference between two phases of a particle-laden flow were considered as significant parameters, which have an influence on the turbulence of a particle-laden flow, and the relative velocity of the laden particles was calculated by using a terminal velocity. The frictional pressure drop was formulated by using the force balance in the control volume by considering the shear stresses due to the presence of particles and an analogy of the shear stresses in the solid surfaces. The numerical results show a good agreement with the available experimental data and the model successfully predicted the mechanism of the pressure drop in the particle-laden flows.     

Transient convective heat transfer of steam-water two-phase flow in a helical tube under pressure drop type oscillations

Experiments for subcooled water flow and for steam-water two-phase flow were conducted to investigate the effects of pulsation upon transient heat transfer characteristics in a closed-circulation helical-coiled tube steam generator. The non-uniform property of local heat transfer with steady flow was examined. The secondary flow and the effect of interaction between the flow oscillation and secondary flow were analyzed on basis of the experimental data. Some new phenomena were observed and explained. Correlations were proposed for average and local heat transfer coefficients both under steady and oscillatory flow conditions. The results showed that there exist considerable variations in local and peripherally time-averaged Nusselt numbers for pulsating flow. Investigations of pressure drop type oscillations and their thresholds for steam-water two-phase flow in a uniformly heated helical tube were also reported.     

Two-phase flow in high-heat-flux micro-channel heat sink for refrigeration cooling applications: Part I--pressure drop characteristics

Two-phase pressure drop was measured across a micro-channel heat sink that served as an evaporator in a refrigeration cycle. The micro-channels were formed by machining 231 μm wide × 713 μm deep grooves into the surface of a copper block. Experiments were performed with refrigerant R134a that spanned the following conditions: inlet pressure of P_in = 1.44-6.60 bar, mass velocity of G = 127-654 kg/m² s, inlet quality of x_e,in = 0.001-0.25, outlet quality of x_e,out = 0.49-superheat, and heat flux of q″ = 31.6-93.8 W/cm². Predictions of the homogeneous equilibrium flow model and prior separated flow models and correlations yielded relatively poor predictions of pressure drop. A new correlation scheme is suggested that incorporates the effect of liquid viscosity and surface tension in the separated flow model’s two-phase pressure drop multiplier. This scheme shows excellent agreement with the R134a data as well as previous micro-channel water data. An important practical finding from this study is that the throttling valve in a refrigeration cycle offers significant stiffening to the system, suppressing the large pressure oscillations common to micro-channel heat sinks.     

Two-phase pressure drop of air–water in minichannels

Results of experimental investigations of pressure drop in two-phase adiabatic flow in tubular minichannels are presented. Air–water mixture was used as a working fluid. Eight tubular minichannels with internal diameter d_w = 1.05 ÷ 2.30 mm and the test section length of 300 mm made from stainless steel were used. The investigations were conducted within the range: mass flow rate of water 0.65 ÷ 59 kg/h, mass flow rate of air 0.011 ÷ 0.72 kg/h, mass fraction of air in the two-phase mixture x = 0.0003 ÷ 0.22, total mass flux (wρ) = 139 ÷ 8582 kg/(m² s). It was found, on the basis of the experimental investigations, that the application of commonly used methods to evaluation of pressure drop in two-phase flow, provided poor results. It is therefore necessary to make some corrections and modifications for the two-phase flow in minichannels correlations.     

Laminar convective heat transfer and pressure drop in the corrugated channels

The results of the heat transfer characteristics and pressure drop in the corrugated channel under constant heat flux are presented in the present study. The test section is the channel with two opposite corrugated plates which all configuration peaks lie in an in-line arrangement. The corrugated plates with three different corrugated tile angles of 20°, 40°, and 60° are tested with the height of the channel of 12.5 mm. The experiments are done for the heat flux and the Reynolds number in the ranges of 0.5–1.2 kW/m² and 500–1400, respectively. Effect of relevant parameters on the heat transfer characteristics and pressure drop are discussed. Due to the presence of recirculation zones, the corrugated surface has significant effect on the enhancement of heat transfer and pressure drop.     

Two-phase pressure drop response during load transients in a PEMFC

Transient behavior of PEM fuel cells can be categorized into electrochemical, thermal and two-phase flows. Overshoot/undershoot behavior has been observed in electrochemical cell voltage during transients, and are attributed to the transition time required for saturation conditions to reestablish. Similar behavior has been reported in two-phase flow pressure drop overshoot/undershoot in a previous work by the authors. In this work, three different temperatures, five ramp rates and four amplitudes of load change were used to investigate the transient two-phase pressure drop behavior. The overshoot/undershoot behavior is observed predominantly at the lower temperature of 40 °C, and is found to decrease at higher cell temperatures. There is a linear increase in the overshoot/undershoot behavior with increase in amplitude of load change. The overshoot/undershoot behavior was found to be independent of the ramp rates used to change the load current. The magnitude of overshoot in pressure drop was always larger than the magnitude of undershoot. The pressure drop required a longer time to return to steady state after an undershoot compared to the time required to return from an overshoot incident.     

Investigations of the pressure drop and flow distribution in a chevron-type plate heat exchanger

In this work the hydrodynamic characteristics and distribution of flow in two cross-corrugated channels of plate heat exchangers have been investigated. A three-dimensional model with the real-size geometry of the two cross-corrugated channels provided by chevron plates and taking into account the inlet and outlet ports has been conducted for the numerical study. The numerical results have been validated with the measurements taken by laboratory experiments. The local flow characteristics around the contact points have been discussed. The velocity, pressure and flow distribution of the fluid among the two channels of the plate heat exchanger have also been presented.     

Effects of miter bend on pressure drop and flow structure in micro-fluidic channels

The characteristics of a pressure-driven water flow including flow micro-structures and pressure drops are investigated in serpentine micro-channels with miter bends. The micro-channels have rectangular cross-sections with hydraulic diameters of 0.209 mm, 0.412 mm and 0.622 mm, respectively. To segregate the bends and entrance effects individually from the total pressure drop, for each size three types of micro-channels: straight short, straight long and long serpentine, were fabricated to get the reliable pressure data without entrance effect. A micron-resolution particle image velocimetry system (micro-PIV) was develop and used to obtain the detailed velocity vector field. The experimental results show that the vortices around the outer and inner walls of the bend do not form when Re < 100. Those vortices appear and continue to develop with increasing Re number when Re is larger than a value around 100, and the shape and size of the vortices almost remain constant when the Re is larger than a value around 1000. The experimentally observed additional pressure drop due to the bend is commensurate with the strength of the calculated vortices. The bend loss coefficient K_b was observed to be related only with the Re number when Re < 100, but with the Re number and channel size when Re > 100. It almost keeps constant and changes in the range of ±10% when the Re is larger than a threshold value somewhere in 1000–1500.     

Consolidated method to predicting pressure drop and heat transfer coefficient for both subcooled and saturated flow boiling in micro-channel heat sinks

Published studies concerning transport phenomena in micro-channel heat sinks can be divided into those concerning saturated boiling versus those focused on subcooled boiling, with the vast majority related to the former. What has been lacking is a single generalized method to tackle both boiling regimes. The primary objective of the present paper is to construct a consolidated method to predicting transport behavior of micro-channel heat sinks incurring all possible heat transfer regimes. First, a new correlation is developed for subcooled flow boiling pressure drop that accounts for inlet subcooling, micro-channel aspect ratio, and length-to-diameter ratio. This correlation shows excellent predictive capability against subcooled HFE 7100 pressure drop data corresponding to four different micro-channel geometries. Next, a consolidated method is developed for pressure drop that is capable of tackling inlet single-phase liquid, subcooled boiling, saturated boiling, and single-phase vapor regimes as well as inlet contraction and outlet expansion. A similar consolidated method is developed to predict the heat transfer coefficient that is capable of tackling all possible combinations of heat transfer regimes. The new consolidated method is shown to be highly effective at reproducing both data and trends for HFE 7100, water and R134a.     

Numerical investigation of heat transfer and pressure drop in enhanced tubes

This study investigates passive heat transfer enhancement techniques to determine the distribution of temperature and static pressure in test tubes, the friction factor, the heat flux, the temperature difference between the inlet and outlet fluid temperatures, the pressure drop penalty and the numerical convective heat transfer coefficient, and then compares the results to the experimental data of Zdaniuk et al. It predicts the single-phase friction factors for the smooth and enhanced tubes by means of the empirical correlations of Blasius and Zdaniuk et al. This study performed calculations on a smooth tube and two helically finned tubes with different geometric parameters also used in the analyses of Zdaniuk et al. It also performed calculations on two corrugated tubes in the simulation study. In Zdaniuk et al.'s experimental setup, the horizontal test section was a 2.74 m long countercurrent flow double tube heat exchanger with the fluid of water flowing in the inner copper tube (15.57–15.64 mm i.d.) and cooling water flowing in the annulus (31.75 mm i.d.). Their test runs were performed at a temperature around 20 °C for cold water flowing in the annulus while Reynolds numbers ranged from 12,000 to 57,000 for the water flowing in the inner tube. A single-phase numerical model having three-dimensional equations is employed with either constant or temperature dependent properties to study the hydrodynamics and thermal behaviors of the flow. The temperature contours are presented for inlet, outlet and fully developed regions of the tube. The variations of the fluid temperature and static pressure along tube length are shown in the paper. The results obtained from a numerical analysis for the helically tubes were validated by various friction factor correlations, such as those found by Blasius and Zdaniuk et al. Then, numerical results were obtained for the two corrugated tubes as a simulation study. The present study found that the average deviation is less than 5% for the friction factors obtained by the Fluent CFD program while Blasius's correlation has the average deviation of less than 10%. The corrugated tubes have a higher heat transfer coefficient than smooth tubes but a lower coefficient than helically finned tubes. The paper also investigates the pressure drop penalty for the heat transfer enhancement.