Summary of previous studies on condensation pressure drop in microchannels and minichannels
1. Introduction
Condensation in microscales has applications in a wide variety of advanced microthermal devices. For instance, condensation in microscales is widely used in small devices like aircooled condensers for the airconditioning and automotive industry, in heat pipes, thermosyphons and other applications for system thermal control. Microchannel condensers are being used to increase heat transfer performance to reduce component size and improve energy efficiency. After 2000s, experimental data became available in open literature in condensation of different refrigerants in small hydraulic diameter microchannels.
This chapter is a continuation of the authors’ previous work about a critical review on condensation heat transfer in microchannels and minichannels [1]. The current chapter consists of four sections: Introduction, Literature Review, Recommendations for Future Studies, Summary and Conclusions. The authors used the same style in writing their recent paper about condensation heat transfer in microchannels and minichannels [1].
In the present chapter, the authors use the microchannels and minichannels classification proposed by Kandlikar [2]. According to his classification, the following can be used: for microchannels,
In macroscale, the gravitational forces are more important than the shear and surface tension forces, and the opposite occurs when the diameter is smaller. Also, Wang and Rose [3] cited another important influence in noncircular microchannel condensation: the viscosity in transverse flow.
Majority of the correlations proposed to predict the frictional pressure gradient during condensation in microscales are based on modifications from the Lockhart and Martinelli [4], Chisholm [5] and Friedel [6] correlations, which were proposed for conventional diameters, and their results show large deviations compared with the experimental data of Dalkilic and Wongwises [7].
2. Literature review
Koyama et al. [8] investigated experimentally the local characteristics of heat transfer and pressure drop for pure refrigerant R134a condensation in two kinds of 865 mm long multiport extruded tubes having eight channels in hydraulic diameter of 1.11 mm and 19 channels in hydraulic diameter of 0.80 mm. The researchers measured the pressure drop through small pressure measuring ports at an interval of 191 mm. They measured the local heat transfer rate in effective cooling length in every subsection of 75 mm using heat flux sensors. They found that the experimental data of frictional pressure drop agreed with the correlation of Mishima and Hibiki [9], while the correlations of Chisholm and Laird [10], Soliman et al. [11], and Haraguchi et al. [12] overpredicted.
Garimella [13] presented an overview of using the flow visualization in micro and minichannel geometries to develop the pressure drop and heat transfer models during condensation of refrigerants. The researcher recorded condensation flow mechanisms for round, rectangular, and square tubes for mass flux (
Garimella et al. [14] presented a multiple flowregime model of refrigerant R134a in horizontal microchannels for pressure drop during condensation. The researchers used five circular channels ranging in hydraulic diameter (
It can be seen that the frictional gradient in the bubble and film region are independently calculated and then related to the total pressure drop by the relative length of the bubble and slug compared to the total unit cell. Also, the pressure drop associated with the acceleration/deceleration of the liquid phase around the fore and aft regions of the vapor bubble is considered. The total number of unit cells per tube length (
Garimella et al. [14] correlated Eq. (2) with pressure drop data from the intermittent and discrete wave flow region [15, 16]. The researchers used data from both flow regimes because as the flow transitions from the intermittent to discrete wavy flow, the vapor bubbles were replaced by stratified welldefined liquid/vapor layers. Therefore, within the discrete wavy flow regime between the pure intermittent and pure annular flow regime, the number of unit cells approached zero. This construct of the intermittent/discrete wavy/annular transition allowed the use of the empirical relation in Eq. (2) in a consistent manner.
For pressure drop in annular flow, Garimella et al. [14] used in their model the following assumptions: (1) steady flow, (2) equal pressure gradients in the liquid and vapor core, (3) uniform liquidfilm thickness, and (4) no liquid entrainment in the vapor core. Therefore, the resulting equation for annular pressure drop could be represented as follows:
Equation (3) could be written in terms of the more convenient tube diameter (
The ratio of this interfacial friction factor (
It should be noted that the liquid phase Reynolds number (
The various correlation constants (
Garimella et al. [14] made many improvements to their preliminary model, even though it was able to successfully predict pressure drop in the annular flow regime for a wide range of circular tubes. Also, the researchers extended the applicability of their model to the mist and disperseflow regions through the use of the surface tension parameter (
Garimella et al. [14] correlated the ratio of the interfacial friction factor to the liquid phase friction factor (
Garimella et al. [14] computed the Fanning friction factors (
They used an interpolation technique for liquid film Reynolds numbers in the transition region (2100 <
Garimella et al. [14] recommended interpolation between the two models for data points determined to be in transition between intermittent/discrete and annular flow. The researchers developed empirical transition criteria from intermittent to other flow regimes from the flow visualization studies of Coleman [24]. These criteria were the model transition criteria for transition from intermittent to other flow regimes. The transition quality from intermittent to other flow regimes was predicted by the following transition criteria, where the mass flux (
The geometrydependent constants
Their combined model accurately predicted condensation pressure drops in the annular, disperse wave, mist, discrete wave, and intermittent flow regimes. They found that their resulting model predicted 82% of the data within ±20%.
Haui and Koyama [25] investigated experimentally the local characteristics of heat transfer and pressure drop for carbon dioxide (CO_{2}) condensation in a multiport extruded aluminum test section, which had 10 circular channels each with 1.31 mm inner diameter. The researchers performed their measurements for the inlet temperature (
Cavallini et al. [26] reviewed published experimental work focusing on condensation flow regimes, pressure drop, and heat transfer in minichannels. New experimental data were available with low pressure (R236ea), medium (R134a) and high pressure (R410A) refrigerants in minichannels of different cross section geometry and with hydraulic diameters (
Chowdhury et al. [27] presented an ongoing experimental study of condensation pressure drop and heat transfer of refrigerant R134a in a single rectangular microchannel of hydraulic diameter (
Garimella [28] reviewed a large number of the existing studies on mini to microchannel condensation covering the flow pattern, pressure drop, void fraction, and heat transfer prediction methods. The researcher presented the available relevant information on pressure drops in condensing flows through relatively small channels and primarily adiabatic flows through microchannels in tabular form. Also, he compared different techniques for predicting the frictional pressure gradient during condensation of refrigerant R134a flowing through a 1 mm diameter tube, at a mean quality of 0.5, at a mass flux of 300 kg/(m^{2}.s), and a pressure of 1500 kPa. He showed graphically a comparison of the pressure drops predicted by these different techniques. He found that the predicted pressure drops varied considerably, from 4.8 to 32.3 kPa. He attributed this large variation to the considerably various twophase multipliers developed by the different investigators. He recommended choosing a model that was based on the geometry, fluid and operating conditions similar to those of interest for a given application.
Agarwal and Garimella [29] presented a multiple flowregime model for pressure drop during condensation of refrigerant R134a in horizontal microchannels. The researchers considered in their study condensation pressure drops measured in two circular and six noncircular channels with hydraulic diameter (
Cavallini et al. [30] presented a model for calculation of the frictional pressure gradient during condensation or adiabatic liquidgas flow inside minichannels with different surface roughness. The researchers used new experimental frictional pressure gradient data associated to singlephase flow and adiabatic twophase flow of R134a inside a single horizontal mini tube with rough wall in their modelling to account for the effects of surface roughness. It was a Friedel [6] based model and it took into account fluid properties, tube diameter, mass flux, vapor quality, reduced pressure, entrainment ratio and surface roughness. With respect to the flow pattern prediction capability, they built for shear dominated flow regimes inside pipes, thus, annular, annularmist and mist flow were here predicted. However, they extended the suggested procedure to the intermittent flow in minichannels and applied it also with success to horizontal macro tubes. Cavallini et al. [30] suggested the following equations to calculate the frictional pressure gradient during adiabatic flow or during condensation, when the dimensionless gas velocity (
The friction factor from Eq. (15) refers to surfaces with negligible surface roughness.
The entrainment ratio (
where the homogeneous gas core density (
This model, presented above, for the frictional pressure gradient could be extended to lower vapor qualities and mass fluxes when the dimensionless gas velocity (
Cavallini et al. [32] had set up a new test apparatus for heat transfer and fluid flow studies in single minichannels during the condensation and adiabatic flow of R134a and R32 in a single circular section minitube with a much higher surface roughness. The researchers presented new experimental frictional pressure gradient data, relative to singlephase flow and adiabatic twophase flow of R134a and R32 inside a single horizontal minitube, The test tube was a commercial copper tube with an inner diameter of 0.96 mm and a length of 228.5 mm. The uncertainty associated to the diameter was equal to ±0.02 mm. The arithmetical mean deviation of the assessed profile (
The above friction factor (
Park and Hrnjak [33] investigated the carbon dioxide (CO_{2}) flow condensation heat transfer coefficients and pressure drop in multiport microchannels made of aluminum having a hydraulic diameter (
Agarwal and Garimella [38] measured condensation heat transfer coefficients and pressure drops for refrigerant R134a flowing through rectangular microchannels with hydraulic diameters (
Song et al. [39] reported preliminary results from a new research program for making accurate pressure drop and heat transfer measurements during condensation in microchannels. The researchers used a dummy test section with identical channel and header geometry to that to be used in the main test program. While measuring the vapor flow rate and total heat transfer rate based on coolant measurements, they took the opportunity to make accurate pressure drop measurements. They obtained data for steam and FC72. In addition, they presented approximate comparisons with available pressure drop calculation methods.
Keinath and Garimella [40] investigated R404a condensation in channels diameter of 0.53 mm. The researchers obtained quantitative information on flow mechanisms using image analysis techniques on high speed video. They conducted experiments on condensing R404a at vapor qualities (
Fronk and Garimella [41] measured pressure drops and heat transfer coefficients during carbon dioxide (CO_{2}) condensation in small quality increments in microchannels of 100 <
Kuo and Pan [42] investigated experimentally condensation of steam in rectangular microchannels with uniform and converging crosssections and a mean hydraulic diameter (
Goss et al. [44] investigated experimentally the local heat transfer coefficient and pressure drop during the convective condensation of R134a inside eight round (
Keinath and Garimella [46] used the Garimella et al. [14] model on pressure drop data for R404A in circular tubes with diameter ranging from 0.5 mm to 3.0 mm. The researchers found that this model tended to overpredict the data. They observed the poorest agreement for the 3mm tube data. They surmised that at
Bohdal et al. [48] investigated experimentally the twophase pressure drop of the environmentally friendly refrigerant R134a (an R12 substitute) during its condensation in pipe minichannels with internal diameter (
Bohdal et al. [49] presented the results of experimental investigations of heat transfer and pressure drop during R134a and R404A condensation in pipe minichannels with internal diameters (
Bohdal et al. [50] investigated experimentally the pressure drop during R134a, R404a and R407C condensation in pipe minichannels with internal diameter (
The friction coefficients
where the lower index
Alshqirate et al. [51] obtained the experimental results of the pressure drop and convection heat transfer coefficient during condensation and evaporation of CO_{2} at various operating conditions for flow inside micropipes of 0.6, 1.0, and 1.6 mm internal diameter. The Reynolds number (
It should be noted that the mean values of the properties were defined by liquid and gas properties. For example
Alshqirate et al. [51] carried out a comparison between experimental and correlated results. The results showed that for the condensation process, the bias errors were 0.4% and 5.25% for Nusselt number and pressure drops respectively. Consequently, Average Standard Deviation (ASD) values reached 4.62% and 17.94% for both respectively. On the other hand, the Nusselt number error for the evaporation process was 3.8% with an ASD of 4.14%. Their correlations could be used in calculating heat transfer coefficients and pressure drops for phase change flows in mini and micro tubes. Also, their correlations could help to enhance design calculations of evaporators, condensers and heat exchangers.
Kim and Mudawar [52] examined the heat transfer characteristics and pressure drop of annular condensation in rectangular microchannels with threesided cooling walls. The researchers proposed a theoretical controlvolumebased model using the assumptions of smooth interface between the vapor core and annular liquid film, and uniform film thickness around the channel’s circumference. They applied mass and momentum conservation to control volumes encompassing the vapor core and the liquid film separately. They compared their model predictions with experimental heat transfer and pressure drop data for annular condensation of FC72 along 1×1 mm^{2} parallel channels. The data spanned FC72 saturation temperatures (
In their first part of a twopart study, Kim et al. [53] performed experiments to investigate FC72 condensation along parallel, square microchannels with a length (
Rose and Wang [54] investigated the annular laminar flow pressure drop, or more precisely pressure gradient, during condensation in microchannels. The annular laminar flow was the only flow regime permitting wholly theoretical solution without having recourse to experimental data. The researchers obtained solutions and made comparisons with empirical formulae for void fraction (needed to calculate the momentum pressure gradient) when obtaining the friction pressure gradient from experimentally measured or “total” pressure gradient. They restricted to date calculations and comparisons to one fluid (R134a), one channel section and one flow condition. They found that earlier approximate models for estimating void fraction agreed quite well with the theoretical annular flow solutions. However, there was significant difference between momentum pressure gradients obtained from approximate models used in the earlier investigations and that given by the theoretical annular flow solution that was (numerically) higher than all of them. The annular flow solution indicated that the momentum pressure gradient was not small in comparison with the friction pressure gradient. The friction pressure gradient in the annular flow case was appreciably smaller than given by the earlier correlations.
Fronk and Garimella [55] investigated experimentally pressure drop and heat transfer during Ammonia condensation in a single circular tube of
Charun [56] investigated experimentally the heat transfer and pressure drop during the R404A condensation in 1.43.30 mm stainless steel pipe minichannels. The researcher provided a review of the present state of knowledge concerning the R404A condensation in conventional channels and in smalldiameter channels. He found that there were few prior publications concerning this issue. The test setup is described as well as the results of the experimental tests. He discussed the dependence of the heat transfer coefficient and the pressure drop of the R404A on the minichannel diameter (
Previous correlations and models for the pressure drop prediction in adiabatic and condensing mini/microchannel flows had been validated for only a few working fluids and relatively narrow ranges of relevant parameters. Therefore, Kim and Mudawar [57] developed a universal approach for the prediction of pressure drop in adiabatic and condensing mini/microchannel flows that was capable of tackling many fluids with drastically various thermophysical properties and very broad ranges of all geometrical and flow parameters of practical interest. The researchers amassed a new consolidated database of 7115 frictional pressure gradient data points for both adiabatic and condensing mini/microchannel flows from 36 sources to achieve this goal. The database consisted of 17 working fluids (air/CO_{2}/N_{2}water mixtures, N_{2}–ethanol mixture, R12, R22, R134a, R236ea, R245fa, R404A, R410A, R407C, propane, methane, ammonia, CO_{2}, and water), hydraulic diameters (
For laminar flow forced convection in rectangular ducts, the Shah and London relation [58] can be used. This relation can be written as a function of the aspect ratio (
where subscript
In Eq. (46),
The different correlations for
For turbulent liquidturbulent vapor flow (
For turbulent liquidturbulent vapor flow (
For laminar liquidturbulent vapor flow (
For laminar liquidlaminar vapor flow (
In the equations of the parameter (
Kim and Mudawar [57] showed their new twophase frictional pressure drop correlation predicted the entire 7115 experimental mini/microchannel database quite accurately, with Mean Absolute Error (MAE) values of 26.3%, 22.4%, 26.8%, and 21.1% for the laminarlaminar (vv), laminarturbulent (vt), turbulentlaminar (tv), turbulentturbulent (tt) flow regimes, respectively. These low values of MAE could be attributed to the large database (7115 data points) upon which it was based. Also, their approach was capable of tackling single and multiple channels as well as situations involving significant flow deceleration due to condensation.
Zhang et al. [59] investigated experimentally condensation pressure drop and heat transfer of R22, R410A and R407C in two single round stainless steel tubes with
Mikielewicz et al. [60] presented a general method for calculation of twophase flow pressure drop in flow boiling and flow condensation because flow boiling and flow condensation were often regarded as two opposite or symmetrical phenomena, however their description with a single correlation had yet to be suggested. This task was a little easier in the case of flow boiling/flow condensation in minichannels in comparison to the case of flow boiling/flow condensation in conventional size tubes (diameters greater than 3 mm). This was because they were dealing with two major structures of twophase flow, namely bubbly flow and annular flow in conventional size tubes while they were dealing with the annular flow structure only in minichannels where the bubble generation/collapse was not present. The difficulty in devising a general method for pressure drop calculations, applicable to both flow condensation and flow boiling, lay in the fact that the nonadiabatic effects were excluded into the present in literature models. In case of bubbly flow the applied heat flux effect was not encountered, similarly the heat flux effect in annular flow was excluded.
The key feature of their method was the approach to model the modification of interface shear stresses in flow boiling and flow condensation due to mass flux and heat flux on interface. In case of annular flow structure incorporation of the so called “blowing parameter” that differentiated these two modes of heat transfer, was considered. The researchers devoted that effect to a correct mass flux modeling on interface. The differences in shear stress between vapor phase and liquid phase was generally a function of nonadiabatic effect. Correct modeling of that heat flux enabled to predict a thinner liquid film thickness in boiling and thicker in condensations at otherwise exactly the same flow conditions. That was a major reason why that up to date approaches, considering the issue of flow boiling and flow condensation as symmetric, were failing in successful predictions. In case of bubbly flow structure the applied heat flux effect was considered. Therefore, a modified form of the twophase flow multiplier was obtained, in which the nonadiabatic effect was clearly pronounced. They made comparisons with some well established experimental data from literature for many fluids. These data would be carefully scrutinized to extract the applied heat flux effect. Preliminary calculations showed a satisfactory consistency of their model with experimental data. Also, they made comparisons with well established empirical correlations for calculations of heat transfer coefficient. Their calculations showed that their method presented above was universal and could be used to predict heat transfer in flow boiling and flow condensation for various halogeneous refrigerants and other fluids. They mentioned that their model could be suggested for a wider use amongst engineers, but further validation with experimental data would add value to its robustness.
Son and Oh [61] investigated experimentally the condensation pressure drop characteristics for pure refrigerants R22, R134a, and a binary refrigerant mixture R410A without lubricating oil in a single circular microtube. Their test section consisted of 1220 mm length with horizontal copper tube of 3.38 mm outer diameter and 1.77 mm inner diameter. The researchers conducted their experiments at refrigerant mass flux (
Based on their experimental database and using a regression method with 108 data points,, their correlation provided a mean deviation of 2.31% and an average deviation of 8.7%.
Zhang et al. [62] presented the heat transfer characteristics of CO_{2} condensation in a minichannel condenser. The condenser consisted of seven tubes in parallel whose inner diameter was 0.9 mm that were thermally connected to two aluminium baseplates by using thermal glue. They obtained the CO_{2} condensation heat transfer coefficients, ranging from 1700 to 4500 W/(m^{2}.K) at saturation temperatures ranging from 5°C to 15°C, with average vapor qualities from 0.2 to 0.8, and, mass fluxes of 180, 360 and 540 kg/(m^{2}.s), respectively. Also, they found that the measured pressure drop over the condenser increased with the vapor quality and the mass flux, but decreased with the saturation temperature.
Garimella and Fronk [63] conducted a systematic series of experiments on condensation flow regimes, heat transfer, and pressure drop using innovative visualization and measurement techniques for condensation of synthetic and natural refrigerants and their azeotropic and zeotropic mixtures through microchannels with a wide range of diameters (0.1 <
Wang and Rose [64] investigated pressure drop and heat transfer during laminar annular flow condensation in microchannels. The annular laminar condensate flow permitted wholly theoretical solution without recourse to empirical input. Channel geometry, flow parameters and tube wall temperatures, local pressure gradient, and local heat transfercoefficient could be calculated as well as local quality and void fraction for laminar annular flow condensation in microchannels and for specified fluid. The researchers outlined the theory in this article, and discussed recent developments. They summarized and compared results for pressure drop and heat transfer for laminar annular flow condensation in microchannels with experimental data. They found that correlations of experimental data for both pressure drop and heat transfer could only be expected to have validity for fluids and conditions close to those used when obtaining the data on which the correlations were based. They found that the results for pressure gradient given by the annular laminar flow model were generally lower than those given by the correlations.
Liu et al. [65] presented experimental data for pressure drop and heat transfer during R152a condensation in square and circular microchannels with hydraulic diameters (
Wang et al. [66] calculated the frictional pressure gradient for the laminar annular flow condensation in microchannels. The laminar annular flow was the only flow regime permitting theoretical solution without having recourse to experimental data. The researchers made comparisons with correlations using experimental data for R134a. The correlations were different somewhat among themselves with the highest to lowest predicted friction pressure gradient ratio typically around 1.4 and nearer to 1 at high quality. The frictional pressure gradients given by the laminar annular flow solutions were lower than the correlations at lower quality and in fair agreement with the correlations at high quality. The frictional pressure gradient could not be directly observed and its evaluation from measurements required the nondissipative momentum or acceleration pressure gradient estimation. Methods used to estimate the nondissipative pressure gradient required void fraction and quality together with equations that related these and whose accuracy was difficult to quantify. Void fraction and quality could be readily found from the laminar annular flow solutions. They found significant differences between these and values from approximate equations.
Heo et al. [67] investigated the CO_{2} condensation pressure drop and heat transfer coefficient in a multiport microchannel with a hydraulic diameter (
Ganapathy et al. [68] presented a numerical model for the simulation of fluid flow characteristics and condensation heat transfer in a single microchannel. The researchers based their model on the volume of fluid approach that governed the hydrodynamics of the twophase flow. They governed the condensation characteristics using the phenomena physics and excluded any empirical expressions in the formulation. They modified the conventional governing equations for conservation of volume fraction and energy to include source terms, which accounted for the mass transfer at the liquid–vapor interface and the associated release of latent heat, respectively. They modeled a microchannel having characteristic dimension of 100 μm using a twodimensional computational domain. The working fluid was R134a and t he channel wall was maintained at a constant heat flux (
Heo et al. [70] presented comparison of condensation pressure drop and heat transfer of carbon dioxide (CO_{2}) in three various microchannels. The channels were rectangular, and the numbers of ports were 7, 19, and 23. The hydraulic diameters (
Murphy [71] investigated heat transfer and pressure drop during condensation of propane (R290) flowing through minichannels because condensation studies of hydrocarbons are important for applications in the petrochemical industry. For accurate design of heat transfer equipment for use in hydrocarbon processing, insights into the mechanisms of propane condensation are required. The researcher designed and fabricated an experimental facility to measure the frictional pressure drop and heat transfer coefficients during condensation of propane in vertical plain tubes with an inner diameter of 1.93 mm. He took measurements across the vaporliquid dome in nominal quality increments of 0.25 for two saturation temperatures (47°C and 74°C) and four mass flux conditions (75150 kg/(m^{2}.s)). He compared the data to the predictions of relevant correlations in the literature. Also, he used the data from his study to develop models for the frictional pressure drop and heat transfer coefficient based on the measurements and the underlying condensation mechanisms.
Mikielewicz et al. [72] presented investigations of flow condensation with the use of the HFE7100 and HFE 7000 as a working fluids and their own condensation model inside tubes with account of nonadiabatic effects. Their model would be confronted with their own data for a new fluid HFE7000 and HFE 7100. One of the objectives of their study was to add data of HFE7100 and HFE7000 for minichannels because of the lack in published studies. This data was greatly interesting because of the very various thermo physical properties of such fluids compared to other substances commonly tested in minichannels. Another reason for understanding the behavior of two phase flow of the working fluids HFE7100 and HFE7000 was due to increased concerns of ozone depletion(ODP) and GWP (global warming potential), as increased knowledge of the performance of this fluids might contribute to HCFC and HFC refrigerants and might use in many other perspective ecological application like organic Rankine cycles. The researchers used a 2.23 mm circular vertical minichannel to measured both twophase pressure losses of the fluids HFE7100 and HFE7000. They found satisfactory consistency of discussed model with their own experimental data for condensation. Their presented model could be suggested for a wider use amongst engineers, but further validation with experimental data would add value to its robustness.
Sakamatapan and Wongwises [73] continued the authors’ previous work on the condensation of R134a flowing inside a multiport minichannel [74]. The researchers investigated experimentally the pressure drop’s characteristics during condensation for R134a flowing inside a multiport minichannel. Two kinds of multiport minichannels having 14 channels, one with a hydraulic diameter (
LópezBelchí et al. [75] studied condensing twophase flow pressure drop inside a minichannel tube with 1.16 mm inner hydraulic diameter with R1234yf, R134a and R32. According to the available data, most of the models checked capture the trend correctly. The researchers observed the pressure drop characteristics under mass flux (
where subscript
Eq. (69) for the friction factor in turbulent region was confirmed by Fang et al. [76, 77] and Brkic [78] to be the most accurate singlephase friction factor equation flow in smooth tubes.
Eq. (70) for the transition zone was obtained by linear interpolation (Xu and Fang [79]).
The correlation for
The experimental tests developed covered the range of,
Thome and Cioncolini [80] presented unified modeling suite convective boiling and condensation for annular flow in macro and microchannels. The researchers presented first unified suite of methods, illustrating in particular, the most recent updates. The annular flow suite included models to predict the entrained liquid fraction, void fraction, the wall shear stress and pressure gradient, and a turbulence model for momentum and heat transfer inside the annular liquid film. In particular, the turbulence model allowed prediction of the local liquid film thicknesses and the local heat transfer coefficients during convective evaporation and condensation. The benefit of a unified modeling suite was that all the included prediction methods were consistently formulated and were proven to work well together, and provided a platform for continued advancement based on the other models in the suite. The annular flow in convective condensation was established almost immediately at the channel inlet and persisted over most of the condensation process until the condensate flooded the channel.
Mikielewicz et al. [81] presented experimental investigations on pressure drop during the condensation in flow of HFE7000 in vertical minichannel of 2.23 mm inner diameter. The researchers scrutinized a new working fluid HFE7000, which had a strongly differing properties in comparison to the other fluids that were commonly used for studies in the minichannels. They observed the pressure drop characteristics under mass flux (
Kim and Mudawar [82] presented a review of databases and predictive methods for pressure drop in adiabatic, condensing and boiling mini/microchannel flows. Their study addressed the limited validity of most published methods to a few working fluids and narrow ranges of operating conditions by discussing the development of two consolidated mini/microchannel databases. The first database was for adiabatic and condensing flows, and consisted of 7115 frictional pressure gradient data points from 36 sources, and the second database for boiling flow, and consisted of 2378 data points from 16 sources. These researchers used these consolidated databases to assess the accuracy of previous models and correlations as well as to develop ‘universal’ correlations, which were applicable to a large number of fluids and very broad ranges of operating conditions.
IllánGómez et al. [83] studied condensing twophase flow pressure drop gradient and heat transfer coefficient (HTC) inside a minichannel multiport tube with R1234yf and R134a. The researchers used many models available in the literature to compare predictions of these two fluids. They analyzed experimental data to get the effect of saturation temperature, mass flux, vapor quality and fluid properties. HTC values of R1234yf seemed to be lower than R134a under similar conditions. They proposed a readjusted HTC model. Also, twophase flow pressure drops were lower in the case of the new refrigerant R1234yf.
RamírezRivera et al. [84] measured experimentally twophase flow pressure drop of R134a and R32 in condensation and evaporation fluid flow in a multiport extruded aluminium tube (MPEs) with
Goss et al. [87] investigated experimentally the pressure drop during the convective condensation of R134a inside eight round (
Table 1 presents a summary of the aforementioned previous studies on condensation pressure drop in microchannels and minichannels.






Koyama et al. [8]  1.114 mm (8 channels) 0.807 mm (19 channels) 
R134a  Horizontal 

The experimental data of frictional pressure drop agreed with the correlation of Mishima and Hibiki [9], while the correlations of Chisholm and Laird [10], Soliman et al. [11], and Haraguchi et al. [12], overpredicted. 
Garimella [13]  0.44.91 mm  R134a  Horizontal 

His flow regimebased models yield substantially better pressure drop predictions than the traditionally used correlations that were primarily based on airwater flows for large diameter tubes. 
Garimella et al. [14]  0.54.91 mm  R134a  Horizontal Considering the intermittent only, intermittent/discrete wavy annular transition, and annular only flow 

Presenting a multiple flowregime model for pressure drop during condensation. 
Haui and Koyama [25]  1.31 mm  CO_{2}  Horizontal 

The pressure drop was very small along the test section. The existing model failed to predict the experimental data. 
Cavallini et al. [26]  0.43 mm  high pressure (R410A), medium (R134a) and low pressure (R236ea)  Horizontal  No model is able to predict the frictional pressure gradient of the high pressure fluid R410A, several models accurately predict the medium pressure fluid R134a and a few satisfactorily estimate the low pressure refrigerant R236ea.  
Chowdhury et al. [27]  0.7 mm  R134a  Horizontal 

A unique process for fabrication of the microchannel involving milling and electroplating steps was adopted to maintain the channel geometry close to design values. 
Garimella [28]  1 mm  R134a 

Comparing different techniques for predicting the pressure drop during condensation.  
Agarwal and Garimella [29]  0.42 0.8 mm  R134a  Horizontal 

Their resulting model predicted 80% of the data within ±25%. The tube shape effect on pressure drop was demonstrated. 
Cavallini et al. [30]  0.96 mm  R134a  Horizontal  Presenting a model for calculation of the frictional pressure gradient during condensation or adiabatic liquidgas flow inside minichannels with different surface roughness.  
Cavallini et al. [32]  0.96 mm  R134a and R32  Horizontal  Presenting modification of the friction factor in the proposed model previously developed by Cavallini et al. [30] to take into consideration also effects due to wall roughness.  
Park and Hrnjak [33]  0.89 mm  CO_{2}  Horizontal 

Many correlations could predict their measured values of pressure drop relatively well such as the Mishima and Hibiki model [37]. 
Agarwal and Garimella [38]  100200 µm  R134a  Horizontal 

The pressure drop increased with increasing vapor quality, increasing mass flux and decreasing saturation temperature. 
Song et al. [39]  1.5 mm x 1.0 mm  FC72 and steam  Horizontal 

Presenting preliminary results from a new research program for making accurate heat transfer and pressure drop measurements during condensation in microchannels. 
Keinath and Garimella [40]  0.53 mm  R404a  Horizontal 

Presenting a novel and accurate methodology for the quantitative investigation of twophase flow regimes and flow parameters during condensation in minichannels. 
Fronk and Garimella [41]  100200 µm  CO_{2}  Horizontal 

Using the collected data to evaluate the applicability of correlations developed for larger hydraulic diameters and various fluids for predicting condensation heat transfer and pressure drop of CO_{2}. 
Kuo and Pan [42]  135 µm  steam  Horizontal  2.10×10^{−6}9.11×10^{−6} kg/s of steam for the uniform crosssection microchannel 2.10×10^{−6}5.93 ×10^{−6} kg/s of steam for the converging microchannel 
Their experimental data agreed well with the obtained correlations, with the maximum mean absolute errors of 6.4% for the twophase frictional multiplier. 
Goss et al. [44]  0.8 mm  R134a  Horizontal 

The pressure drop correlation proposed by Zang and Webb [45] gave the best results, with a deviation of 30%. 
Keinath and Garimella [46]  0.53.0 mm  R404A  The Garimella et al. [14] model tends to overpredict the pressure drop data. The poorest agreement is for the 3mm tube data. 

Bohdal et al. [48]  0.13.30 mm  R134a  Horizontal 

The pressure drop in twophase flow during R134a condensation is dependent on: the agent type, process parameters and the structure of twophase flow. 
Bohdal et al. [49]  0.313.30 mm  R134a and R404A  Horizontal 

The pressure drop during the condensation of the R134a and R404A refrigerants is described in a satisfactory manner with Friedel [6] and Garimella [13] correlations. 
Bohdal et al. [50]  0.313.30 mm  R134a, R404a and R407C  Horizontal 

The pressure drop during the condensation of the R134a, R404a and R407C refrigerants is described in a satisfactory manner with Friedel [6] and Garimella [13] correlations. 
Alshqirate et al. [51]  0.6, 1.0, and 1.6 mm  CO_{2} 

Using the dimensional analysis technique to develop correlations for Nusselt numbers and pressure drops.  
Kim and Mudawar [52]  1 mm  FC72 and water (counter flow)  Horizontal  For FC72, For water, mass flow rate = 36 g/s 
Their new model accurately captured the pressure drop and heat transfer coefficient data in both magnitude and trend, evidenced by mean absolute error values of 3.6% and 9.3%, respectively. 
Kim et al. [53]  1 mm  FC72 and water (counter flow)  Horizontal  For FC72, For water, 
The homogenous flow model provides far more accurate predictions of pressure drop than the separated flow models. Among the separated flow models, Kim et al. [53] achieve better predictions with those for adiabatic and mini/microchannels than those for flow boiling and macrochannels. 
Rose and Wang [54]  R134a  laminar annular flow  The momentum pressure gradient is not small in comparison with the friction pressure gradient. The friction pressure gradient in the annular flow case is appreciably smaller than given by the earlier correlations. 

Fronk and Garimella [55]  1.435 mm  Ammonia (NH_{3})  Horizontal 

The coupled influences of ammonia properties and microscale geometry were outside the applicable range of most condensation pressure drop and heat transfer models. Additional reliable data pressure drop and heat transfer for smaller tube diameters and with working fluids like ammonia were necessary. 
Charun [56]  1.4, 1.6, 1.94, 2.3 and 3.3 mm  R404A  Horizontal 

The pressure drop during the R404A refrigerant condensation is satisfactorily described by the Friedel [6] and Garimella [13] correlations. 
Kim and Mudawar [57]  0.0695 6.22 mm  17 various working fluids (air/CO_{2}/N_{2}water mixtures, N_{2}–ethanol mixture, R12, R22, R134a, R236ea, R245fa, R404A, R410A, R407C, propane, methane, ammonia, CO_{2}, and water) 

Proposing a new universal approach to predict twophase frictional pressure drop for adiabatic and condensing mini/microchannel flows.  
Zhang et al. [59]  1.088 and 1.289 mm  R22, R410A and R407C  Horizontal 

Two phase pressure drop and condensation heat transfer coefficients of R22 and R407C are equivalent but both higher than those of R410A. R410A a s a substitute for R22, has more advantages than R407C in view of the characteristics of condensation pressure drop and heat transfer. 
Mikielewicz et al. [60]  Presenting a general method for calculation of twophase flow pressure drop in flow boiling and flow condensation because flow boiling and flow condensation are often regarded as two opposite or symmetrical phenomena, however their description with a single correlation have yet to be suggested.  
Son and Oh [61]  1.77 mm  R22, R134a and R410A 

The condensation pressure drop of R134a is higher than that of R22 and R410A for the same mass flux. Presenting a new pressure drop model where the Chisholm factor ( 

Zhang et al. [62]  0.9 mm  CO_{2} 

The measured pressure drop over the condenser increases with the mass flux and the vapor quality, but decreases with the saturation temperature.  
Garimella and Fronk [63]  0.1 < 
synthetic and natural refrigerants and their azeotropic and zeotropic mixtures  These experiments resulted in flowregimebased heat transfer and pressure drop models with very good predictive capabilities for such microchannel geometries.  
Wang and Rose [64]  R134a, ammonia (NH_{3})  laminar annular flow  Results for pressure gradient given by the annular laminar flow model are generally lower than those given by the correlations.  
Liu et al. [65]  1.152 mm (circular) 0.952 mm (square) 
R152a  Horizontal 

Channel geometry has little effect on frictional pressure gradients. Koyama et al. [8] underestimates the square and circular microchannels data while Agarwal and Garimella [29] overestimate the square microchannel data. Predictions of Cavallini et al. [30] show large rootmeansquare errors for data in both square and circular microchannels. 
Wang et al. [66]  R134a  laminar annular flow  The frictional pressure gradients given by the laminar annular flow solutions are in fair agreement with the correlations at high quality and lower than the correlations at lower quality.  
Heo et al. [67]  1.5 mm  CO_{2}  Horizontal 

The Mishima and Hibiki model [37] showed mean deviation of 29.1%. 
Ganapathy et al. [68]  100 μm  R134a  constant heat flux 

Using the volume of fluid approach. The mean absolute error (MAE) is 8.1% for twophase frictional pressure drop against a recent universal predictive approach by Kim and Mudawar [57]. 
Heo et al. [70]  1.5, 0.78, and 0.68 mm for the 7, 23, and 19 ports  CO_{2}  Horizontal 

The Mishima and Hibiki model [37] has a mean deviation of ±30.1% for the frictional pressure drop. 
Murphy [71]  1.93 mm  Propane (R290)  Vertical 

The results and the corresponding correlations contribute to the understanding of condensation of hydrocarbon. 
Mikielewicz et al. [72]  2.23 mm  HFE7000 and HFE7100  Vertical  Satisfactory consistency of discussed model with their own experimental data for condensation has been found. The presented model can be suggested for a wider use amongst engineers, but further validation with experimental data would add value to its robustness. 

Sakamatapan and Wongwises [73]  1.1 mm (14 channels), 1.2 mm (8 channels)  R134a  Horizontal 

Proposing a new twophase friction factor correlation using the equivalent Reynolds number ( 
LópezBelchí et al. [75]  1.16 mm  R1234yf, R134a and R32  Horizontal 

Presenting a new correlation model with a mean absolute relative deviation (MARD) value of 8.32% reducing the best correlation MARD by more than 34%. 
Thome and Cioncolini [80]  Annular flow  Presenting unified modeling suite for annular flow, convective boiling and condensation in macro and microchannels.  
Mikielewicz et al. [81]  2.23 mm  HFE7000  Vertical 

The comparisons of the experimental results with the inhouse developed model for twophase flow pressure drop with inclusion of nonadiabatic effects show satisfactory agreement. 
Kim and Mudawar [82]  Presenting a review of databases and predictive methods for pressure drop in adiabatic, condensing and boiling mini/microchannel flows.  
IllánGómez et al. [83]  1.16 mm  R1234yf, and R134a  Horizontal 

Pressure drop for R1234yf is by 57% lower than for R134a. The existing models are able to predict frictional pressure drop reasonably well. 
RamírezRivera et al. [84]  0.715 and 1.16 mm  R134a and R32  Horizontal  For condensing flow 
Friedel [6] and MüllerSteinhagen and Heck [85] predict satisfactorily well the experimental pressure drop data. The Souza and Pimenta correlation [86] estimates the experimental pressure gradient data very well with multiport tubes of The Cavallini et al. model [26] presents the best prediction performance. Cavallini et al. [26] and Zhang and Webb [45] predicted with reasonable accuracy the experimental twophase flow pressure drop data. 
Goss et al. [87]  0.77 mm  R134a  Horizontal 

The pressure drop increases with an increase in ( 
3. Recommendations for future studies
Finally, recommendations for future studies will be given. These new points can be expected to be the research focus in the coming years. Studying the condensation pressure drop in microscales can be done using:
The experiments with new kinds of noncircular shapes like trapezoidal, elliptical,.., etc. To the best of the authors’ knowledge, the study of condensation pressure drop in microscales of elliptic crosssection is not yet tackled in literature. Only recently a new interest has been devoted to the elliptical crosssection, produced by mechanical fabrication in metallic microchannels for practical applications in MEMS. Also, the experimental study of the condensation pressure drop in microscales can be done with using various triangular cross sections such as right isosceles triangular.
The experiments with new kinds of environmentally friendly refrigerants such as HDR14, which is low global warming fluid for replacement of R245fa. The GWP is an index used to compare the potential of gases to produce a greenhouse effect and the reference is CO_{2} with a value of 1. HDR14 has a global warming potential (GWP) of only 7, much lower than the value of 930 of R245fa (both considering a period time horizon of 100 years). Also, HDR14 has a much lower atmospheric life time (0.1 year) in comparison with the atmospheric life time of R245fa (7.6 years).
The experiments with oil in the refrigerant loop (refrigerant/lubricant mixture) at various concentrations. For example, AkhavanBehabadi et al. [88] utilized polyolester oil (POE) as the lubricant in R600a/POE mixture to study experimentally the heat transfer characteristics of flow condensation.
The experiments with new types of working fluids such as refrigerant/lubricant/nanoparticles mixture. For example, AkhavanBehabadi et al. [88] used R600a/ polyolester oil (POE)/CuO nanorefrigerant to study experimentally the heat transfer characteristics of flow condensation. Nanorefrigerant is a type of nanofluid where a refrigerant is used as the base fluid [89]. Recently, Dalkiliç and coworkers [90, 91] presented a review paper on nanorefrigerants.
The experiments with new types of refrigerant blends. For instance, new refrigerant blends, like R417A, are becoming very important due to the possibility of using them in R22 systems with only minor changes (dropin refrigerants) [92]. R417A is the composition with mass fractions of 46.6% R125, 50% R134a, and 3.4% R600. Also, we can carry out the experiments with new kinds of refrigerant blends like R1234yf and R1234ze(E) as constituents as well as blends of old refrigerants with HydroFluoroOlefin (HFO) refrigerants. These blends can be azeotropic blends or zeotropic blends like zeotropic mixture R32/R1234ze(E). R32 (CH_{2}F_{2}) is flammable and has for this reason not been used pure.
Similar to recent work on condensation in macroscales at microgravity conditions [93, 94], studies on condensation pressure drop in microscales at microgravity conditions can be done. These studies will be important because future manned space missions will be expected to greatly increase the space vehicle's weight, size, and heat dissipation requirements. An effective means to reducing both weight and size is replacing singlephase thermal management systems with twophase counterparts that capitalize upon both sensible and latent heat of the coolant rather than sensible heat alone. This shift is expected to yield orders of magnitude enhancements in condensation heat transfer coefficients. A major challenge to this shift is the reliable tools lack for accurate prediction of heat transfer coefficient and twophase pressure drop in reduced gravity.
4. Summary and conclusions
This paper provides a comprehensive, uptodate review in a chronological order on the research progress made on condensation pressure drop in microscales. Also, studies on condensation pressure drop in microscales are summarized in a table. At the end, some suggestions for future work are presented. Therefore, the present study can not only be used as the starting point for the researcher interested in condensation pressure drop in microscales, but it also includes recommendations for future studies on condensation pressure drop in microscales.
Nomenclature
C ; coefficient in LockhartMartinelli parameter ()
Re ; Reynolds number ()
RR ; relative roughness of the tube, Eq. (26)
Su; Suratman number ()
T ; temperature, ^{o}C
U ; velocity, m/s
W ; parameter, Eq. (17)
We ; Weber number ()
x ; mass quality ()
X ; LockhartMartinelli parameter ()
Z ; parameter, Eq. (18)
Greek Symbols
α; void fraction ()
∆; difference
ϕ^{2} ; twophase frictional multiplier ()
μ; dynamic viscosity, kg/m.s
ρ; density, kg/m^{3}
σ; surface tension, N/m
ψ; dimensionless surface tension term ()
Subscripts
bubble; bubble
cond; condenser
cr; critical
d; diameter
eq; equivalent
g; gas
gc ; gas core
go ; gas phase with total mass flow rate
h ; hydraulic
i; inner
in; inlet
l; liquid
lo ; liquid phase with total mass flow rate
m; mean
sat; saturation
slug ; slug
transition transition
tube; tube
UC; unit cell
unit cell unit cell
tp; twophase
Acknowledgments
Professor Ahmet Selim Dalkilic wishes to thank King Mongkut’s University of Technology Thonburi (KMUTT) for providing him with a Postdoctoral fellowship. Professor Somchai Wongwises wishes to thank the "Research Chair Grant" National Science and Technology Development Agency, the Thailand Research Fund and the National Research University Project for the support.
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