Microchannel heat exchangers offer the potential for high heat transfer coefficients; however, implementation challenges must be addressed to realize this potential. Maldistribution of phases among the microchannels and the changing phase velocities associated with phase change present design challenges. Flow maldistribution and oscillatory instabilities can affect transfer rates and pressure drops. In condensers, evaporators, absorbers, and desorbers, changing phase velocities can change prevailing flow regimes from favorable to unfavorable. Geometries with serpentine passages containing pin fins can be configured to maintain favorable flow regimes throughout the component for phase-change heat and mass transfer applications. Due to the possibility of continuous redistribution of the flow across the pin fins along the flow direction, maldistribution can also be reduced. These features enable high heat transfer coefficients, thereby achieving considerable compactness. The characteristics of two-phase flow through a serpentine passage with micro-pin fin arrays with diameter 350 μm and height 406 μm are investigated. An air–water mixture is used to represent two-phase flow through the serpentine test section, and flow features are investigated using high-speed photography. Improved flow distribution is observed in the serpentine geometry. Distinct flow regimes, different from those observed in microchannels, are also established. Void fraction and interfacial area along the length of the serpentine passages are compared with the corresponding values for microchannels. A model developed for the two-phase frictional pressure drops across this serpentine micro-pin fin geometry predicts experimental values with a mean absolute error (MAE) of 7.16%.

## Introduction

### Background.

Heat exchangers with microscale features have been shown to significantly enhance heat and mass transfer processes over conventional designs, resulting in efficient and compact geometries. Implementation of microchannel heat exchangers, however, poses two key challenges, associated with the maldistribution [1] of each of the phases among the microchannel array, changes in flow velocities associated with the change in quality of the two-phase flow. Such change in quality is observed in phase-change components such as condensers, evaporators, absorbers, and desorbers. The change in superficial velocities of each phase can change the flow regime from a favorable one to an unfavorable regime. Pin-fin arrays with varying geometry offer the potential to adapt the flow area in a microchannel array to address the challenges posed by the evolving flow characteristics. The use of micro-pin fin arrays in compact heat exchangers with two-phase flow is investigated here and their performance is compared with that seen with conventional microchannels.

Peles et al. [2] investigated the use of circular pin fins for applications in heat sinks for microelectromechanical systems. It was observed that the thermal resistance in micro-pin fins was comparable to that in microchannel geometries. Pressure drop correlations/models for single-phase flow across micro-pin fin arrays have been developed [35]. Kosar et al. [3] presented a friction factor and pressure drop correlation for flow of water over staggered and in-line circular/diamond-shaped micro-pin fins with a diameter and height of 100 μm. The ratio of the pitch-to-diameter in the array was 1.5. Their data spanned from 5 < Red < 110. Qu and Siu-Ho [4] developed a friction factor and pressure drop correlation for square pin fins for 40 < Red < 100. The square pin fins have a 200 × 200 μm cross section with a height of 670 μm and a pitch of 400 μm. Prasher et al. [5] investigated single-phase pressure drop in circular and square micro-pin fins with dimensions ranging from 50 to 150 μm. Experiments were conducted using water to yield a correlation that spanned a wide range of Reynolds numbers (5 < Red < 1000). (Data from Kosar et al. [3] were also considered while developing the pressure drop correlation for lower Re.) Flow over the pin fins was observed to transition from laminar flow at Red ≈ 100.

Nitrogen–water flow across pin fins was investigated by Krishnamurthy and Peles [6] using high-speed videography. The pin fins had a diameter height of 100 μm, with a pitch-to-diameter ratio of 1.5 and 5 < Re < 50. Four distinct flow regimes, bubbly slug, gas slug, bridged, and annular flow, were observed. Based on these data, they developed models to calculate the void fraction and pressure drop in two-phase flow across pin fins for Red < 40.

Krishnamurthy and Peles [7] presented the effect of pin diameter and pitch on flow regime. Two distinct mechanisms for the formation of bridged flow were observed. In the smaller test section, gas slugs trapping liquid bridges between pin fins was the main mechanism for bridge flow. In the larger test section, the break-up of larger liquid slugs resulted in the formation of liquid bridges. A parameter K, defined as the product of the Weber (We) and Euler (Eu) numbers, is proposed to predict the stability of the bridge flow: the bridge flow regime is stable at K ≪ 1 and unstable as K → 1.

A pressure drop model for the boiling of water through 200 × 200 μm square pin fins with a height of 670 μm and a pitch of 400 μm is presented by Qu and Siu-Ho [8]. The single-phase fluid flow friction factor correlation from Qu and Siu-Ho [4] in combination with the laminar liquid and vapor Lockhart and Martinelli [9] two-phase multiplier predicted their data well.

The studies mentioned thus far pertained to single-phase and adiabatic two-phase flow experiments. The pin-fin geometry has also been considered for heat sinks with boiling flows for high heat flux applications. Krishnamurthy and Peles [10] studied flow boiling in staggered micro-pin fin arrays with a diameter of 100 μm. Their experiments investigated different mass and heat fluxes, ranging from 346 to 794 kg m−2 s−1 and from 20 to 350 W cm−2, respectively. They developed a superposition model for the heat transfer coefficient. They also developed a flow regime map using visualization studies during flow boiling. McNeil et al. [11] conducted a comparative study on heat transfer and pressure drop for flow boiling between plane channels and channels with embedded inline pin fins. They found out that channels with pin fins performed slightly better than their counterparts in terms of heat transfer coefficient, although they suffered from a higher pressure drop. McNeil et al. [12] also investigated boiling of water through 1 × 1 × 1 mm square pin fins, with a pitch of 2 mm. It was observed that the two-phase frictional pressure drop correlations for tube bundles predicted the frictional pressure drop during boiling most accurately. Reeser et al. [13] investigated the flow boiling heat transfer and pressure drop for square micro-pin fin inline and staggered arrays. They used HFE-7200 and de-ionized water as working fluids. The square pin fins had a width and height of 153 and 305 μm, respectively.

Two-phase flow through an array of serpentine micro-pin fins is investigated here using visualization techniques. The performance of the serpentine micro-pin fin geometry is compared with that of conventional microchannels in two-phase flow applications. This comparison highlights the characteristics of different microscale features to enhance heat transfer in heat and mass exchangers with multiphase flow. Additionally, a pressure drop model for flow through serpentine micro-pin fin geometries is developed. This information is critical to the design of microscale absorbers, condensers, and other components with two-phase flow.

## Experimental Setup

The micro-pin fins have a diameter (d) of 350 μm, a depth of 406 μm, a transverse pitch (ST) of 1651 μm, and longitudinal pitch (SY) of 1430 μm. Transverse pitch is the pitch between pin fins in the direction perpendicular to flow, while longitudinal pitch is the pitch in the direction of flow. The dimensions of the micro-pin fins were chosen based on those used in microscale heat and mass exchangers in absorption heat pumps. The serpentine test section has seven ribs that act as baffles. The spacing between consecutive baffles decreases, as it is designed for condensing flows. The test section is fabricated by photochemical etching stainless steel 304. Air–water mixtures are used to simulate two-phase flow through the test section. Flow distribution, void fraction, and pressure drop of the two-phase mixture are investigated.

Figure 1 shows a schematic of the test facility used in this study. An overview of the instrumentation was presented by Hoysall et al. [1]. The supply tank is partially filled with distilled water, dyed red, and pressurized to 350 kPa using compressed air. The inlet air to the test section is drawn from the top of the pressurized tank, while water is drawn from the bottom. The flow rate of each stream is set using individual flow control valves and measured using the flow meters specified in Table 1. The air and water streams are then mixed through a T-section, following which the mixture flows into the inlet port of the test section. The air–water mixture then flows through the test section. At the outlet of the test section, the air–water mixture is collected in a storage tank. A high-speed camera (Photron FASTCAM Ultima 1024 with Nikon Micro-NIKKOR 105 mm lens) is used to record high-speed videos at specific locations along the length of the test section. In addition to flow visualization, the pressure drop across the test section is measured using a differential pressure transducer for each flow condition. The mixture mass quality varied between 0.0044 and 0.308. The mass fluxes through the test section range from 19 to 526 kg m−2 s−1. These mass fluxes and qualities represent those seen in ammonia–water microscale absorbers for heat pumps.

Fig. 1
Fig. 1
Close modal
Table 1

Instrument specifications

ParameterInstrumentRangeUncertainty
Inlet air volumetric flow rateRotameter0.4–8.0 × 10−5 m3 s−15%
Inlet water volumetric flow rateRotameter0.2–2.6 × 10−6 m3 s−14%
Test section differential pressureDifferential pressure transducer0–175 kPa0.245 kPa
TemperatureT-type thermocouple3–673 K0.25 K
ParameterInstrumentRangeUncertainty
Inlet air volumetric flow rateRotameter0.4–8.0 × 10−5 m3 s−15%
Inlet water volumetric flow rateRotameter0.2–2.6 × 10−6 m3 s−14%
Test section differential pressureDifferential pressure transducer0–175 kPa0.245 kPa
TemperatureT-type thermocouple3–673 K0.25 K

Figure 2(a) presents an image of the test section used in this study, with a detailed view of the micro-pin fins shown in Fig. 2(b). Seven baffles guide the flow along the component in a serpentine path. The baffles have a thickness of 1.6 mm. The geometry is designed for condensing flow or flow in an absorber, where the quality of the flow decreases from the inlet to the outlet. Hence, the spacing between the baffles is progressively decreased. For flow in an evaporator or desorber, where the flow quality increases, the inlet and outlet can be interchanged such that the cross-sectional area increases from the inlet to the outlet. Details of the micro-pin fin geometry are provided in Fig. 2(c). The test section is sealed by compressing the etched sheet against a Plexiglas plate using a metal plate as shown in Fig. 3. The assembly consists of a top plate, a Plexiglas plate, two gaskets, and a bottom plate. The test section is placed in a slot machined in the bottom plate and sealed by compressing the gaskets around it using the Plexiglas plate. Further details of the assembly are presented in Ref. [1].

Fig. 2
Fig. 2
Close modal
Fig. 3
Fig. 3
Close modal

### Flow Visualization.

Videos were recorded at 250 frames per second at a shutter speed of 1/1000 second and a resolution of 1024 × 512 pixels. Flow videos capturing the entire width of the test section are recorded for 4 s for each test condition at four different locations along the length, which enables the tracking of changes in flow characteristics along the length. Figure 4(a) presents a representative image of the flow in Window 1 at a mass flux of 38.52 kg m−2 s−1 and a quality of 0.062. Several liquid bridges are observed in the central area of Fig. 4(a). Similar flow characteristics were also observed by Krishnamurthy and Peles [6], who referred to it as bridge flow. Water was observed to aggregate around the pin fins and the edges of the shim. At low air flow rates, a bubbly flow regime was observed, with bubbles smaller than the fin pitch (Fig. 4(b)). At higher air flow rates, the flow regime transitions to gas-slug flow, where the presence of large bubbles encompassing multiple pins between them is observed (Fig. 4(c)). The differentiation between bubbly and gas-slug regimes is challenging because both small and large bubbles can be observed at the same time. Therefore, the presence of any large bubbles in the flow indicates gas-slug flow. As the superficial velocity of air increases, the flow transitions to bridge flow (Fig. 4(d)). At high air and water flow rates, annular flow is observed (Fig. 4(e)).

Fig. 4
Fig. 4
Close modal

### Data Reduction.

An image analysis tool for the serpentine pin fin geometry was developed on the matlab platform to process a large number of images in a short time. The flow images were rotated and cropped as shown in Fig. 4(a). The red regions represent the liquid regions, the dark circles are the microscale pin fins, while the gray regions represent air. These images are converted to an red, blue, green format. The captured images are processed using the algorithm shown in Fig. 5, which is similar to that used by Hoysall et al. [1], but modified to map the pin fins in the present study. Air bubbles often aggregated at the edges and corners of the ribs that guide the flow in the shim, resulting in the inability of taking flow images with only liquid in the test section. Therefore, a “no flow” image is used to map pins for this test section. A red threshold was used to differentiate between air and water to identify the liquid regions. Once the liquid regions are identified, the image is converted to a binary black and white image with liquid in black and gas in white, as shown in Fig. 5. This binary image is further processed using a two-dimensional median filter that removes noise from the image. Figure 6 presents a filtered image combined with information about the pin fin locations. The window void fraction is calculated using Eq. (1). The number of air pixels is divided by the pixels of total area available for flow. The mean window void fraction for each frame in the video is calculated as

Fig. 5
Fig. 5
Close modal
Fig. 6
Fig. 6
Close modal
$αwin=1Nframes∑1Nframe(∑Pixair∑Pixflow area)$
(1)
The Canny edge detector is used to identify interfaces between air and water, which are shown in red in Fig. 6. The curvature of the air water interface is neglected, and the interface is assumed to be a straight line. This underpredicts the total area as the interface has some curvature due to surface tension. The interfacial area intensity, defined as the interfacial area per unit volume, is calculated as shown in Eq. (2) and is the number of interface pixels divided by the total number of pixels. This quantity is proportional to the total interfacial area. These images are further processed to observe the flow distribution and the interface distribution through the serpentine test section
$IAIntensity=1Nframes∑1Nframes(∑Pixint∑Pixflow area)$
(2)
The uncertainty associated with this analysis is quantified using Eq. (3). The first two terms account for uncertainty in the red threshold, by observing the change in void fraction for a 10% change in threshold. The third and fourth terms account for the uncertainty due to the wrong identification of a pixel as liquid or air. Equation (3) presents the uncertainty in the measurement of void fraction of a channel for a representative data point
$UαFlow=(ΔαFlow,110%)2+(ΔαFlow,90%)2+(ΔαFlow,+1)2+(ΔαFlow,−1)2UαFlow=(−0.015)2+(0.0184)2+(−4.54×10−6)2+(4.54×10−6)2UαFlow=0.0237αFlow=0.736±0.0237$
(3)
A similar method is used to calculate the uncertainty in the interfacial area. A sample of the uncertainty in the interfacial area is shown in the below equation
$UIA=(ΔIA,110%)2+(ΔIA,90%)2+(ΔIA,+1)2+(ΔIA,−1)2UIA=(0.00439)2+(−0.00542)2+(−4.54×10−6)2+(4.54×10−6)2UIA=0.00698IAintensity=0.0765±0.00698$
(4)

## Results and Discussion

### Flow Regimes, Void Fraction, and Interfacial Area.

The average void fraction variation does not change significantly along the length, as shown in Fig. 7. The values of void fraction of each window are within the uncertainty bands and do not show any appreciable dependence on phase superficial velocities. This measured void fraction is compared with predictions of correlations in the literature [6,1416], as shown in Fig. 8. All these correlations predict the measured values with reasonable accuracy. Among these, only the correlation of Krishnamurthy and Peles [6] was developed for pin fins. The Kawahara et al. [14] correlation worked the best and predicted all points within an accuracy of 25%. The Winkler et al. [15] correlation is able to predict cases with high void fraction more accurately than those with lower void fraction. The Schrage et al. [16] correlation developed for vertical flow across tube bundles is able to correctly predict trends, but underpredicts most values. It should also be noted that this correlation depends on Froude number, which is used when the gravitational force is important. However, gravity has not been observed to influence the flow through microscale geometries such as those under consideration.

Fig. 7
Fig. 7
Close modal
Fig. 8
Fig. 8
Close modal

Flow maldistribution was observed to be a limiting factor in the microchannel passage arrays investigated by Hoysall et al. [1]. Quantifying the flow distribution in the serpentine micro-pin fin geometry under consideration here is more challenging. Figure 9 presents the time-averaged distribution of liquid in the serpentine section. The two-phase flow direction is top right to bottom left, as shown in Fig. 9. Regions with liquid constantly flowing through them are shown in red, while a blue color represents regions with no liquid flow at any time. The edges experience higher liquid flow, while the core areas exhibit higher gas flow. The brightly colored regions around the pins show the liquid aggregated around the pins due to surface forces. A trace of bridge flow is observed where the pins are connected by a bridgelike structure in a highlighted color.

Fig. 9
Fig. 9
Close modal

Figure 10 presents the distribution of the flow along the length of the test section observed through four different windows for a representative case. As mentioned earlier, the flow area decreases along the test section, because it is designed for condensing flows. The flow area decreases from 9.58 × 10−6 m2 in the first pass to 4.17 × 10−6 m2 in the last. As air–water mixtures were used in this study, the superficial velocities of the two phases increase significantly along the serpentine length of the test section. This enables the study of different flow regimes in different sections of the sheet. It is observed that all the windows appear to have an air core and liquid flowing close to the edges. Liquid was observed to aggregate around the pin fins in all the sections due to the effects of surface tension.

Fig. 10
Fig. 10
Close modal

Interfacial area is critical to the condensation heat and mass transfer. Hoysall et al. [1] measured the interfacial area in two microchannel shim designs and observed the increase in interfacial area with improved mixing of the two phases. Figure 11 compares interfacial area intensity observed in the present serpentine test section to that observed in the microchannel geometries studied by Hoysall et al. [1]. Figure 11(a) presents the interfacial area intensity in the microchannel test sections. Window “0” corresponds to the shim without mixing features, while windows 1–4 correspond to values for the microchannel test section with mixing features presented in Ref. [1]. It should be noted that all the three designs being compared have the same overall width and length. The interfacial area intensity in the serpentine test section is presented in Fig. 11(b). The interfacial area intensity for the serpentine test section was observed to be much higher than the corresponding value for the microchannel test sections. This indicated that the gas and liquid phases interact more vigorously in the serpentine section than in the microchannel section.

Fig. 11
Fig. 11
Close modal

The time-averaged distribution of interfacial area is presented in Fig. 12(a) for the same data set as Fig. 9. A comparison of Figs. 9 and 12(a) shows that the interfaces between air and water were concentrated in regions with high liquid flow. Liquid aggregation around pins also facilitated mixing between the two phases, as observed in the high concentration of interfaces in regions surrounding pin fins. Interfaces formed in the bridge flow regime were also observed to be significant. As liquid flows away from a bridge structure, it is replenished by liquid flowing toward the bridge. This led to liquid bridges being sustained for long periods as observed in Fig. 12(a). The presence of some stagnant and slow moving bubbles close to the edges of the test section leads to a high concentration of interfacial area in the region. Such bubbles do not contribute to the improved performance, but highlight the region close to the edges.

Fig. 12
Fig. 12
Close modal

Figure 12(b) presents the distribution of interface area in window 4. The section analyzed has a narrow flow area, resulting in higher velocities of air and water in the test section. The flow regime observed in this section is annular flow. Interfacial area is again concentrated in regions with higher liquid flow. Annular flow results in air–water interfaces between pins; unlike bridge flow, these flow regimes have intense mixing between the two phases. This was also observed in Ref. [6]. The interfaces in bridges are clearly observed in the time-averaged map, as the bridges are constantly replenished and remain in the same location. The interfaces in annular flow are more widely spread and not concentrated in the same location.

### Pressure Drop Correlation.

Correlations for single-phase pressure drop across micro-pin fins have been developed in earlier studies. Table 2 presents a brief overview of the various geometries investigated in the literature and their applicability. Krishnamurthy and Peles [6] presented a new two-phase multiplier to predict pressure drop for two-phase flow through micro-pin fins. Qu and Siu-Ho [8] observed that the Lockhart and Martinelli [9] two-phase multiplier accurately predicted the two-phase pressure drop through pin fins. The other studies presented in Table 2 developed correlations to predict the pressure drop in single-phase flow. The liquid and gas Reynolds numbers in the present study varied from 7 to 198 and 15 to 424, respectively. The frictional pressure drop across the serpentine test section is calculated as shown in the below equation

Table 2

Pressure drop model comparison

AuthorPin dimensions (μm)Re range
Krishnamurthy and Peles [6]d = 100, H = 100, P/d = 1.5Red < 40
Qu and Siu-Ho [8]Lp = 200, H = 670, ST/L = 2, SY/L = 237 < Red < 86
Prasher et al. [5]50 ≤ d, Lp ≤ 150, 155 ≤ H ≤ 310, 2 ≤ ST/d ≤ 3.6, 3.6 ≤ SY/d ≤ 440 < Red < 1000
AuthorPin dimensions (μm)Re range
Krishnamurthy and Peles [6]d = 100, H = 100, P/d = 1.5Red < 40
Qu and Siu-Ho [8]Lp = 200, H = 670, ST/L = 2, SY/L = 237 < Red < 86
Prasher et al. [5]50 ≤ d, Lp ≤ 150, 155 ≤ H ≤ 310, 2 ≤ ST/d ≤ 3.6, 3.6 ≤ SY/d ≤ 440 < Red < 1000
$ΔP=ΔPin+ΔPpin+ΔPbend+ΔPgravity+ΔPout$
(5)

The ΔPpin represents the frictional pressure drop due to two-phase flow through the micro-pin fin arrays. The ΔPbend represents the pressure drop due to the guiding baffles that direct the flow through the serpentine test section, causing a 180 deg change in the flow direction that accounts for about 3% of total pressure drop. There are seven such bends in the test section with a progressively decreasing flow cross section. ΔPgravity is the change in pressure due to gravity. The contribution due to gravity is very small and accounts for about −1% of total pressure drop. As the flow is downward, this term has a negative value. ΔPin is the frictional pressure loss around micro-pin fins as the flow enters from the inlet port and crosses the first baffle. Similarly, ΔPout accounts for the frictional losses around the micro-pin fins between the last baffle and the outlet port. Losses associated with the expansion and contraction of the two-phase mixture from the inlet port into the inlet header and outlet header to outlet port were observed to be negligible.

Flow between baffles is assumed to be in the horizontal direction. The pressure drop around the baffle is modeled as flow through a 180 deg pipe bend as modeled by Chisholm [17]. The mass flux is calculated based on the minimum area in the baffle gap. The corresponding single-phase pressure drop is calculated as shown in Eq. (6), where KBL0 is the single-phase loss coefficient for the bend
$ΔPL0=KBL0G22ρL$
(6)
The two-phase pressure drop is calculated as shown in the below equation
$ΔPbend=ΨL0ΔPL0$
(7)
ΨL0 is the two-phase multiplier given in the below equation
$ΨL0=1+(ρLρG−1)[B180x(1−x)+x2]$
(8)
where x is the quality and B is an empirical constant given by Eqs. (9) and (10). B90 and B180 represent the values for 90 deg and 180 deg bends. B180 is derived from B90 as outlined in Ref. [17]; KBL0,90 has a value of 0.3
$B180=1+B902$
(9)
$B90=1+2.2KBL0,90(2+RD)$
(10)

The hydraulic diameter for flow around the pin fins is used as the diameter (D) in Eq. (10). Half the baffle opening length is used as the bend radius (R), which represents the mean radius for all the paths along which the flow bends.

The pressure drop due to gravity (ΔPgravity) is calculated as shown in Eq. (11). The void fraction model from Kawahara et al. [14] is used as it was observed to best predict the measured void fraction in the experiments
$ΔPgravity=−[αρg+(1−α)ρl]gh$
(11)

The pressure drop around the micro-pin fins is calculated by subtracting ΔPgravity and ΔPbend from ΔPtotal. Figure 13 presents the contributions of frictional, baffle, and gravitational components toward the total pressure drop. The x-axis shows ten selected data points from the test matrix in increasing order of pressure drop. It is observed that the frictional pressure drop for flow through the micro-pin fin array is the dominant contribution. Gravity has a negative contribution as the test section is in a downward flow configuration. The magnitude of the gravitational component is higher at lower qualities due to the higher liquid fraction.

Fig. 13
Fig. 13
Close modal

### Model Development.

The Reynolds number is calculated as shown in the below equation
$Red=Gdpinμ$
(12)
The mass flux (G) is calculated based on Amin as shown in the below equation
$G=m˙Amin$
(13)
Amin is the minimum cross-sectional area defined in the below equation
$Amin=ST−dSTSBH$
(14)

where SB is the spacing between the baffles.

The single-phase (liquid) pressure drop is presented in the below equation
$ΔPL,pin,i=fiN[Gi(1−x)]22ρl$
(15)

where f is the single-phase Darcy friction factor, and N is the number of pin rows in the flow direction.

The pressure drop across the micro-pin fins is calculated as shown in the below equation
$ΔPpin=∑i=1Nbaffle−1ΦL,i2ΔPL,pin,i$
(16)

where ΔPL,pin is the single-phase pressure drop around the micro-pin fins and ΦL2 is the two-phase multiplier. ΔPpin is calculated using Eqs. (11)(16). ΔPin is the frictional pressure drop around the pins between the inlet port and the first baffle. ΔPout is the frictional pressure drop around the pins between the last baffle and the outlet port. ΔPin and ΔPout are both calculated using the same method as ΔPpin. The corresponding numbers of pin rows are Npin, Nin, and Nout. Flow between the baffles is assumed to be in the horizontal direction. Npin is the number of pin rows in the horizontal direction of flow. Nin and Nout are the number of pin rows in the vertical direction between the inlet and outlet.

The two-phase multiplier is calculated as shown in the below equation, where C is a parameter obtained by the regression of the frictional contribution for flow around the micro-pin fins obtained from the overall pressure drop measurements in the test section as described earlier
$ΦL2=1+CX+1X2$
(17)

Figure 14 presents the comparison of the measured pressure drop data with the various two-phase pressure drop models.

Fig. 14
Fig. 14
Close modal

### Comparison With the Literature.

As mentioned earlier, the pressure drop around the pin fins is calculated by subtracting ΔPgravity and ΔPbend from ΔPtotal. This pin fin pressure drop is then compared to those in the literature. Krishnamurthy and Peles [6] used the expression 0.0358 × Re to calculate C. This value of C underpredicts the pressure drops from the present study and leads to a mean absolute error (MAE) of 37.5% as shown in Fig. 14(a). Qu and Siu-Ho [8] used a value of 5 for C, which predicts the pressure drop from the present study within a reasonable MAE of 12.5% as shown in Fig. 14(b), but the model was developed only for cases with Re < 86. The data presented in this work have ReL ≤ 198 and ReG ≤ 424, which is beyond the range of applicability of their correlation. The Reynolds number for the serpentine geometry increases as the spacing between baffles keeps decreasing along the length of the test section. While the correlation is able to accurately predict the pressure drop of the model, there is a need to develop a method to predict the two-phase pressure drop over a larger range of Reynolds numbers. Of the various friction factor correlations for micro-pin fins in the literature, the one developed by Prasher et al. [5] was found to be applicable for Reynolds numbers up to 1000.

### Pressure Drop Model.

Based on the previously mentioned discussion and comparison of the results from the present study with the literature, a regression analysis was performed on the pin–fin portion of the two-phase pressure drop deduced from the measurements to develop a new two-phase multiplier of the form shown in Eq. (17). The corresponding single-phase pressure drop was calculated using the correlation of Prasher et al. [5]. The regression analysis revealed that the pressure drop around the pins was predicted best by a value of 20 for C. Figure 15 compares the measured pressure drop with the pressure drop predicted using the developed two-phase multiplier. The MAE for the model is 7.16% indicating a very good agreement with the measured data. Table 3 summarizes the pressure drop models used and their predictions. On comparison with a microchannel array with the same footprint, it is observed that the pressure drop through the serpentine test section is 2.7–4.1 times higher. The higher pressure drop is due to the increased flow length of the serpentine path that the fluid follows. This higher pressure drop represents the tradeoff required to overcome the limitations due to maldistribution. It should be noted that a heat and mass exchanger with maldistribution will need to be oversized to compensate for maldistribution, which will in turn increase the pressure drop in the microchannel component as well. The choice of geometry between these two should be assessed based on the design requirements and the penalties of maldistribution.

Fig. 15
Fig. 15
Close modal
Table 3

Two phase flow pressure drop model evaluation

AuthorsfDarcyCXMAE (%)
Krishnamurthy and Peles [6]1166.6 $Red−1.489$0.035 8 × Re$(μLμG)0.745 (1−xx)0.256 (ρGρL)0.5$37.51
Qu and Siu-Ho [8]20.09 $Red−0.547$5$(μLμG)0.274 (1−xx)0.727 (ρGρL)0.5$11.44
Prasher et al. [5]$14(Hd)0.724 (SY−dd)−0.442 (ST−dd)−0.245 Red−0.58$20$(μLμG)0.29 (1−xx)0.71 (ρGρL)0.5$7.16
AuthorsfDarcyCXMAE (%)
Krishnamurthy and Peles [6]1166.6 $Red−1.489$0.035 8 × Re$(μLμG)0.745 (1−xx)0.256 (ρGρL)0.5$37.51
Qu and Siu-Ho [8]20.09 $Red−0.547$5$(μLμG)0.274 (1−xx)0.727 (ρGρL)0.5$11.44
Prasher et al. [5]$14(Hd)0.724 (SY−dd)−0.442 (ST−dd)−0.245 Red−0.58$20$(μLμG)0.29 (1−xx)0.71 (ρGρL)0.5$7.16

## Conclusion

Two-phase flow through a serpentine micro-pin fin geometry was visually investigated. The micro-pin fins allowed for redistribution of the two phases, resulting in an improved flow distribution in the sheets. Some maldistribution was still observed in the pin–fin geometry, as the vapor phase was observed to predominantly flow through the center of the test section. The serpentine geometry had higher mixing of the two phases compared to the microchannel design of same size. Hence, it is better suited for components with mass transfer between the two phases. Microchannel void fraction models from the literature were found to accurately predict the void fraction through the test section. The frictional pressure drop through the pin fins was the largest contributor to the overall pressure drop across the serpentine test section. A new method to calculate two-phase pressure drop across a serpentine pin fin geometry was developed. It was observed that a Chisholm parameter of 20 in the two-phase multiplier accurately predicted two-phase pressure drop through the pin fins.

## Acknowledgment

Financial support for this work from the Advanced Research Projects Agency-Energy—U.S. Department of Energy is gratefully acknowledged.

## Funding Data

• Advanced Research Projects Agency (Grant No. DE-AR0000370).

## Nomenclature

d =

diameter (m)

Eu =

Euler number

g =

gravitation acceleration (m s−2)

G =

mass flux (kg m−2 s−1)

H =

pin height (μm)

IA =

interfacial area (m2 m−3)

L =

pin edge length (μm)

N =

number

P =

pressure (kPa)

Pix =

pixels

Re =

Reynolds number

S =

pitch (μm)

We =

Weber number

x =

quality

X =

Martinelli parameter

### Greek Symbols

Greek Symbols
α =

void fraction (%)

μ =

viscosity (kg m−1 s−1)

ρ =

density (kg m−3)

σ =

standard deviation (%)

Φ =

two-phase multiplier

Ψ =

two-phase multiplier for bend

### Subscripts

Subscripts
air =

air

avg =

average

ch =

channel

d =

pin diameter

G =

gas

h =

hydraulic

int =

interface

intensity =

intensity

L =

liquid

p =

pin

T =

transverse direction

win =

window

Y =

longitudinal direction

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