Flow characteristics and instability analysis of pressure drop in parallel multiple microchannels

Accepted Manuscript Flow characteristics and instability analysis of pressure drop in parallel multiple microchannels Haojie Huang, Liang-ming Pan, Run-gang Yan PII: DOI: Reference:

S1359-4311(18)31224-9 https://doi.org/10.1016/j.applthermaleng.2018.06.083 ATE 12354

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

25 February 2018 6 June 2018 27 June 2018

Please cite this article as: H. Huang, L-m. Pan, R-g. Yan, Flow characteristics and instability analysis of pressure drop in parallel multiple microchannels, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/ j.applthermaleng.2018.06.083

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Flow characteristics and instability analysis of pressure drop in parallel multiple microchannels Haojie Huang, Liang-ming Pan*, Run-gang Yan Key Laboratory of Low-grade Energy Utilization Technologies and Systems (Chongqing University), Ministry of Education, Chongqing, 400044, China.

Abstract Instability analysis is vital for the safety of the system with microchannels, in which the microchannels could be used as a heat sink component with high heat efficiency. In this study, flow visualization and measurements of two-phase flow boiling in six parallel microchannels with a hydraulic diameter of 517 µm were conducted in order to investigate the dynamic instability in a microchannel system. The tests were performed in the range of mass flux 23.04 – 111.89 kg/ (m2·s), heat flux 4.2 – 67.7 kW/m2, inlet temperature 40 – 60 C and exit vapor quality -0.06 – 0.12. The wavelet decomposition method was used for the oscillation characteristic analysis and the signal noise was identified successfully within the decomposition process. Combination of time-domain and frequency-domain analysis as well as the high speed visualization were performed for the characteristics analysis of the pressure drop. Entropy method was first used for the flow instability analysis in the microchannel system and noticeable differences of stable and unstable flow states were found due to its inherent flow patterns in microchannel system. A strong bearing was found between the characteristic oscillation period of dynamic flow and the corresponding boiling number.

* Corresponding author: Tel: (+86) 23-65102280, Fax: (+86) 23-65102280, E–mail: [email protected]

Keywords: Microchannel, flow instability, wavelet decomposition, sampled entropy method, characteristic oscillation period.

1

Nomenclature a

Approximation coefficient

Δp

Pressure drop, kPa

Aw

Footprint area, m2

q

Heat flux, W/m²

Bo

Boiling number

r

Threshold value

d

Detailed coefficient or distance between two vectors

R

Correlation coefficient

f

1/T, oscillation frequency, Hz

S

Source signal

G

Mass flux, kg/(m2·s)

t

Time, s

H

Height of the channel, m

T

Temperature, C or oscillation periods, s

I

Electric current, A

ΔT

J

The maximum decomposition level

V

Electric voltage, V

L

Length of the channel, m

W

Width of the channel, m

m

Number of dimensions

x

Discrete time series of data

p

Pressure, kPa

X

Sequence vector

Greek symbols Scaling function φ

Wavelet function

σ

standard deviation of the data

Subscripts in Inlet loss Heat loss eff

Effective

2

Temperature difference between the test section and the surrounding, C

1

Introduction Interests in micro- and multi-channels have been increasingly prevalent due to their

applications in microelectronics. With the increase of electronic components density, higher demands for the capability and reliability of the heat sink are required. As a promising heat sink, extensive attention has been paid to microchannels due to their high surface-to-volume ratio, which contributes to provide high heat transfer coefficient, especially under phase change condition. The two-phase heat transfer could offer remarkable advantage over the single-phase heat exchange condition such as reduced flow rate and much higher degree of temperature uniformity. Both of these are critical for the performance of thermal management system. However, instabilities in two-phase flow referring hydraulic and thermal oscillations are the undesired phenomena, which may result in serious safety problems such as mechanical vibration of the system, and early attaining burn out condition[1]. Moreover, this problem augmented with the decrease of channel dimension due to the bubble evolution[2,3]. Instabilities in two-phase flow can be characterized by the maldistribution or fluctuation of the coolant, pressure and temperature oscillation, or intermittent flow reversal. As discussed in the review articles[4,5], they are usually grouped as the static instability and the dynamic ones based on the mechanism. A system is deemed as statically unstable if the system can work at a stable level which is different from previous condition after disturbance, such as the Ledinegg instability and the flow pattern-transition instability. The dynamic instability is defined as flow fluctuation sustained by the feedback among the temperature, pressure drop, flow rate and density changes. This type of instability can be classified as the density-wave oscillation, parallel-channel instability, pressure-drop oscillation and thermal and acoustic oscillation. Different mechanisms such as pressure wave propagation, thermodynamic nonequlibrium, flow regime change and kinematic wave propagation are involved in the complicated dynamic phenomena.[6] The Acoustic oscillation and densitywave oscillation are usually considered as “pure” dynamic oscillation while the others are usually a combination of two or more effects[7]. Regarding to the dynamic instabilities in two-phase flow, numerous theoretical and experimental researches have been conducted. Rapid bubble growth, bubble clogging, upstream compressibility, parallel channels interactions and reversed flow are regard as the major causes of dynamic instability[8]. Compared to macro channels, flow boiling in microchannels is more sensitive to the confined space. Review papers[9,10] suggested that the flow boiling instability in microchannels should be paid more attention and addressed properly. 3

Regarding the instability initiation criterion, Kew and Cornwell[11] defined the onset of flow instability when a bubble approaches the hydraulic diameter of a narrow channel. Brutin et al.[12] investigated the two-phase flow boiling phenomena in microchannels and proposed an instability criterion from their experimental observations. An unstable flow is defined by an oscillation amplitude larger than 1 kPa and an obvious characteristic frequency identified by spectrum analysis. Considering the force change in two-phase flow patterns in the microchannel system, two nondimensional groups related to the ratio of the evaporation momentum force to the inertia force and the ratio of evaporation momentum force to the surface tension were proposed by Kandlikar[13] to identify the flow boiling characteristics. Chang and Pan[14] studied the two-phase flow instability in a multiple parallel microchannel heat sink experimentally. The amplitude of pressure drop oscillation was used as an index of instability. A threshold of 6 kPa between the maximum instant pressure drop and the minimum instant pressure drop was found to be critical for the appearance of flow instability. Lee and Yao[15] proposed a parameter of system instability related to the ratio between the saturation temperature of the liquid and the bulk temperature of the liquid-phase at the exit. This system parameter suggests that instability will occur if the ratio is greater than unity. Based on the model proposed by Kandlikar[13], Lee et al.[16] proposed the ratio of backward evaporation momentum and forward liquid inertia force to characterize the flow instability. The flow would be stable if this ratio is less than unity. This model is valid for straight single channel and then expanded to channels with inlet orifice and expanding cross-section. However, Balasubramanian et al.[17] reported the limitation of this model for multiple microchannels with shared inlet and outlet plenums due to the interactions between the neighboring channels. They used this model in their experiments and found that it is applicable in the bubbly and slug flow regimes while inapplicable in transition or intermittent zones. Wang and Cheng[18,19] defined the unstable flow as the state that appreciable temporal variations of pressure or wall temperature are observed. Flow pattern maps were achieved in terms of the heat flux and mass flux as well as the exit thermodynamic quality. Since the flow instability decreases the thermohydraulic performance, the knowledge of instability threshold would be helpful in the design of two-phase heat exchangers[20]. However, due to the complexities associated with the interaction of the growing bubbles and the heating walls in microchannels as well as the flow coupling in multichannels, it is difficult to determine the onset of dynamic instability and distinguish the flow characteristics of a multichannel system when flow instability occurs. Clear demarcation of the stable and 4

unstable flow is required and some theoretical criteria or parameters that are suitable and meaningful for description of the flow boiling states need to be developed[8]. The goal of this paper is to define the initiation criterion of dynamic instability with a new method. The concept of entropy, related to the number of microscopic configurations of a thermodynamic system, and the sample entropy algorithm are introduced for the identification of flow boiling states in the microchannel system. The features such as flow patterns and oscillation characteristics are discussed in the present study.

2

Experimental setup

2.1 Experimental loop

Fig. 1. Schematic diagram of the experimental apparatus. Similar to the flow loop introduced in our previous study[21], Fig. 1 shows the schematic diagram of the experimental apparatus, which could supply continuous deionized water to the microchannel test section at a desired condition. Deionized water was stored in a reservoir and has to be degassed with the help of a heater before experiment. Then, deionized water flowed through a filter and was pumped into a thermostatic bath that could provide a desired inlet temperature. The flow rate was recorded and stabilized by a feedback type flow meter (Bronkhorst mini CORI-FLOW). Single-phase and two-phase flow boiling tests 5

performed in the test section with different combinations of flow rate, inlet temperature and heating power. The flow phenomena were recorded visually through a high-speed camera (Phantom Miro M310) with a maximum of 12X lens (Navitar) and the flow parameters such as pressure were collected by the pressure transducer and differential pressure transducer, and then the signal was transferred to the data acquisition system (NI 9220 and NI 9213). Finally, the working fluid flowed into the condenser and returned into the reservoir after cooling to room temperature.

2.2 Test module

(b) Fig. 2. Detailed description of the test module. (a)Test module construction, (b) Cutaway view of the test module. (a)

As illustrated in Fig. 2, a detailed introduction of the test module as well as its cutaway view has been described. Six parallel rectangular microchannels with a length of 60 mm and a cross-section of 377×821 µm were machined on the top surface of the microchannel heat sink, which is a piece of oxygen-free cooper. Due to the excellent thermal conductivity, another piece of copper transferred the heat from 4 bottom cartridge heaters to the top microchannels where the heat was dissipated by the incoming liquid in the forms of sensible heat and latent heat. Two thermocouples were placed in the inlet and outlet plenums for the measurement of coolant temperature. In addition, 12 thermocouples which were separated by two rows, were inserted underneath the heat sink with a horizontal spacing of 10 mm and a vertical spacing of 4 mm. The pressure drop across the test piece was recorded by a differential pressure transducer while the inlet pressure was documented by a pressure transducer. G-10 fiberglass plastics were assembled around the heating sink for heat insulation. The test section was covered by a transparent quartz glass cover plate with high 6

thermal resistance for flow visualization. The working fluid flowed into the inlet plenum and experienced single-phase flow and two-phase flow boiling in the six parallel microchannels.

2.3 Experimental procedure Prior to experiments, adequate deionized water was injected into the reservoir and degassed by means of vigorous boiling for about an hour with the top exhaust valve opened. Before the investigation of two-phase flow instability experiments, a series of preliminary heat balance tests with single-phase flow under different mass flux were conducted in order to achieve the heating efficiency of the test section. The cooling degassed water was circularly pumped into the loop in the range of 23.04 - 111.89 kg/ (m2·s) while the flow rate was measured and controlled by the mass flow meter. The temperature of the working fluid in the inlet plenum was kept to a predetermined temperature by adjusting the power supply of the thermostatic bath. The temperature of the inlet plenum was controlled within the accuracy of 0.5C while the outlet pressure was stabilized at around atmosphere pressure. For a fixed mass flow rate and power input, various thermal parameters and flow patterns were recorded when steady state was reached. The steady state condition was assumed to be reached when the inlet temperature fluctuated within 0.5C for 10 minutes. Various methods have been used to estimate the heat loss in the micro/mini-channel heat transfer system. Generally, three kinds of methods are summarized as below: (1) Prior to conducting flow boiling experiments, the heat loss is estimated as a percentage of total heat supplied for a given flow rate through a set of single-phase tests. The mean heat loss percentages obtained in single-phase tests are used for flow boiling experiments at the same flow rate or all flow rate.[17,22–25] (2) The heat loss to the surrounding from the test section is evaluated from the difference between the total heat input and the sensible heat gained by the fluid under single-phase condition. To extend its applicability for two-phase flow, the heat loss is correlated linearly as a function of the average wall temperature or the temperature difference for each inlet condition, and extrapolated to those wall temperatures in flow boiling conditions.[26–28] (3) Electrical power is applied to the test section after evacuating the coolant in order to evaluate the heat loss at various wall temperatures in experiments. Once the temperature of test section reaches steady state, the temperature difference between the test section and the surrounding is recorded with its corresponding power input, which is entirely 7

dissipated as heat loss. Then the relationship between the temperature difference and the corresponding power input is used to estimate the heat loss.[29–32] Mirmanto[33] estimated the heat loss with the second and third methods. It was reported that the two methods showed good agreement and the average heat loss was found to be about 6.8% of input power. This fixed heat loss ratio was used in their entire calculation, which corresponds to the first method. Alam et al. [30] reported the difference of heat losses estimated from the second and third methods is within 15% while a difference of five times was found by Jagirdar and Lee[34] due to the different heat dissipation passages. Considering the heat loss through top cover, the second method was used in our calculation. As can be seen in Fig. 3, the heat loss shows a good linearity on the temperature difference between the average wall temperature and the ambient temperature. Therefore, heat losses under flow boiling conditions were estimated by linear extrapolation at the same inlet conditions. The effective heat flux was then calculated from qeff 

VI  qloss Aw

where V is the voltage difference across the heating resistors and I is the corresponding current. Aw is the heat sink footprint area.

Fig. 3. Heat loss characterization curve.

8

(1)

All experimental signals such as the temperature, pressure, current and voltage as well as the mass flow rate were collected and sampled by a NI high-speed data acquisition system. A high-speed camera was mounted above the test section to record the visual information with a sampling rate of 500 fps (frames per second) when the flow instability happened. Table 1 shows the direct measurement uncertainties of the measurement instruments while the indirect measurement parameters such as heat flux and mass flux can be calculated by the propagation of uncertainty. Therefore, the uncertainty of mass flux is ± 0.61%. The uncertainty of effective heat flux, considering the heat loss error, ranges between ±1.8% and ±8.9% while the boiling number is in the range of ±1.9% to ±8.9%.

Table 1. The major parameters, instruments and uncertainties. Parameter

Explanations

Instruments

Uncertainties

V

Voltage measurement

Voltage module

±0.5%

I

Current measurement

Digital ammeter

±0.8%

T

Temperature

Type-K sheathed thermocouple

±0.5C

Mass flow rate Δp

Pressure drop

p

Pressure

L/W/H

Length/Width/Height

Mini CORI-FLOW M14

±0.2%

(Bronkhorst) Differential pressure transducer

±0.065%

(EJA110A, Yokogawa) Pressure transducer

±0.065%

(EJA430A, Yokogawa) Vernier caliper (SYNTEK)

±2 µm

2.4 Data reduction 2.4.1 Wavelet decomposition method Fast Fourier transform (FFT) method has been widely used in the analysis of flow characteristics. However, since useful information is usually coupled with noise in measurement and direct use of entropy analysis does not work well without de-noising[35], it is necessary to identify and remove the noise first. The discrete wavelet transform has been used in signal processing and shows its superior applications in the analysis of transient signals due to its localization properties in the time domain[36]. Characteristics coupled with the signal noise have been identified successfully with wavelet decomposition[30]. The wavelet transform can be expressed as a family of scaled and translated wavelets in order to capture different localization information embedded in a time series of signal data[37]. 9

For a sampled discrete signal function f (t ), t  1, 2, ... , N , its wavelet decomposition can be expressed as

f (t )   a jk jk (t )  k

0

 d

j  J k

 jk (t )

jk

(2)

where J  log 2 N is the maximum decomposition level, a jk and d jk are the approximation coefficients and detailed coefficients, respectively. At level j (or scale 2 j ), they can be derived from

a jk  2 j /2  f (t ),  (2 j t  k ) 

(3)

d jk  2 j /2  f (t ), (2 j t  k ) 

(4)

where <,> is the inner product. The  jk (t ) is a member of the set of expansion functions derived from a scaling function  (t ) , by translation and scaling using:

 jk (t )  2 j /2  (2 j t  k )

j, k  Z

(5)

The  jk (t ) is a member of the set of wavelets derived from a wavelet function (t ) , by translation and scaling using:

 jk (t )  2 j /2 (2 j t  k )

j, k  Z

(6)

In order to be a wavelet function,  (t ) has to satisfy the admissibility condition





 (t )dt  0



Since the wavelet decomposition depends on the choice of the wavelet basis, it is difficult to choose the optimal wavelet basis for the signal. Similar to the condition in the literature[38], Daubechies’s least symmetric wavelet of order four has been chosen in our analysis. In our study, the wavelet functions were used for the decomposition and the decomposition results were further analyzed with FFT.

2.4.2 Sample entropy analysis method The applications of entropy have been used in multi-phase flow field recently in order to quantify the degree of regularity and identify the flow pattern for its sensitivity to the flow pattern characteristics[39,40]. Generally, the entropy of a thermodynamic system represents the number of microscopic configurations and increases with the degree of disorder. There should be a difference in entropy when the flow boiling of a thermodynamic system changes 10

(7)

from stable state to an unstable state. The concept of sample entropy has been used for assessing the complexity of time-series signals successfully[41]. The sample entropy of a dataset of length N is defined as the negative natural logarithm of the conditional probability that two segments in the time series with m points having repeated itself with a tolerance r remain similar with m+1 points[42]. The algorithm of the sample entropy is as follows: a) For a one-dimensional discrete time series of data xi  ( x1 , x2 , ... xN ) , a mdimensional sequence vector is defined as: X (i)  [ x(i), x(i  1),..., x(i  m 1)], i  1 ~ N  m  1

(8)

b) The distance between two vectors is defined as:

d [ X (i), X ( j )]  max | x(i  k )  x(i  k ) | k  1 ~ m  1, i, j  1 ~ N  m  1, i  j

(9)

c) Count the number of the distance which is less than r

Cim (r ) 

1 num{d [ X (i), X ( j )]  r} N m

(10)

d) Average Ci (r ) from 1 ~ N  m  1 m

B m (r ) 

N  m 1 1 Cim (r )  N  m  1 i 1

m 1

e) Then increase the ?? to ??+1 and obtain Bi

(11)

(r ) . Consequently, the sample entropy

can be calculated as:

SampEn(m, r, N )   ln[ Bm1 (r ) / Bm (r )]

(12)

Generally, the accuracy and confidence of entropy estimation increases as the numbers of matches increase by choosing small m (short templates) and large r (wide tolerance), but the criteria would be too relaxed at the same time[42]. Pincus[43] found entropy estimation of a system could be achieved with relatively few data points for small m. Empirically, Costa et al. [44] found that their results were not closely related to the specific values of m and r. Satisfactory results are obtained with m ≤ 3 and r = 0.1~0.25σ in some physiologic analysis[45,46]. Here m = 2 and r = 0.1σ are chosen in our analysis, where σ is the standard deviation of the data.

11

3

Results and analysis

3.1 Noise signal identification

(a)

(b)

Fig. 4. Signal decomposition with discrete wavelet transform. (a) DWT tree; (b) Signal decomposition at level 4. Since the noise results from the system operation and the instruments uncertainties, which may affect the analysis result for suppressing the useful signal, the first step of the analysis is to identify the noise of a given system. A preliminary test of single-phase liquid flow (G = 82.52 kg/m2·s and Tin = 55C) without heating was carried out in the multiple microchannel system for the identification of the noise. The variation of the pressure drop between the inlet and outlet plenum was chosen as the flow instability index. Fig. 4a shows the discrete wavelet transform tree of the source signal with four levels while the Fig. 4b depicts the corresponding coefficients at each level. The source signal was first decomposed to the approximation coefficient a1 and the detailed coefficient d1 . Then the coefficient a1 was further decomposed to a2 and d 2 . Furthermore, the approximation coefficient a2 can be decomposed as a3 and d 3 while the a3 yields a4 and d 4 . Therefore, the source signal can be expressed as

S  a1  d1  a2  d2  d1  a3  d3  d2  d1  a4  d4  d3  d2  d1

(13)

As shown in Fig. 4b, the variance bands of the detailed coefficients d1 , d 2 and d 3 covers the range of (-0.05~0.05 kPa), (-0.05~0.05 kPa) and (-0.025~0.025 kPa) respectively. 12

d 4 and a4 have variance bands smaller than ±0.02 kPa. Since the measurement uncertainty of the pressure drop is ±0.065% of the measurement range (-10 ~ 30 kPa), d1 and d 2 can be considered to be the signal noise for the pressure drop measurement which are almost two times that of the measurement sensitivity. d 3 has the same variance amplitude of the measurement sensitivity while d 4 is smaller.

Fig. 5. Signal decomposition with discrete wavelet transform at level four. 2 ( G  82.52 kg/m  s , qeff  52.4 kW/m and Tin  55 C )

2

Fig. 5 depicts the variation of pressure drop with heat flux of 52.4 kW/m2 and its wavelet decomposition with 4 levels in a time span of 50 s. The detailed coefficients d1 to

d 2 show the noise components in the signal. d 3 equals to the measurement sensitivity while d 4 is smaller. The variance band of a4 is significantly larger than the sensitivity. These suggest that the source signal can be decomposed to level 3 and the source signals can be expressed with the approximation coefficient a3 after de-noising. It should be noted that the decomposition level that we should decompose might be different for each case. Since the variation of the pressure drop at each level represents the oscillation energy contributed to the 13

flow instability in the corresponding frequency range, useful approximation coefficients and detailed coefficients with amplitudes higher than that of the noise could be obtained from the decomposition results. Many researchers have reported two kinds of two-phase instability in their studies, the high amplitude with low frequency (HALF) oscillations and the low amplitude with high frequency (LAHF) oscillations[47–49]. However, the detailed coefficients of the results in our experiments shows that no significant oscillation characteristics larger than the noise are decomposed from the source signals. This means only HALF oscillations happened.

3.2 Flow characteristics analysis

Fig. 6. Temporal record of the pressure drop oscillations under different heat flux Fig. 6 shows the total pressure drop variation in a time span of 20 seconds under different heat flux. It shows that the variation of the pressure drop is relatively small at a heat flux of 32.5 kW/m2. The fluctuation amplitude starts to increase gradually as the heat flux 14

increases. The higher heat flux in two-phase flow leads to larger oscillation amplitude under same mass flux and inlet temperature due to the higher vapor generation rate. This figure displays an obvious periodic oscillation when the heat flux exceeds 40.3 kW/m2. However, it is difficult to define the onset of a periodic oscillation because the appreciable temporal variations of oscillation amplitude are strongly dependent on the max variation range and the instability initiation criteria are usually defined subjectively in previous studies.

Fig. 7. Visualization images of flow boiling under different heat flux. (Liquid flows from left 2 2 to right as shown in figures) (a) ~(c) qeff  35.8 kW/m and (d) ~ (f) qeff  40.3 kW/m . Fig. 7 shows the corresponding visualization images at the heat flux of 35.8 kW/m2 and 40.3 kW/m2, respectively. Phenomena of bubble nucleation, growth, condensation and reversed flow were recorded in different microchannels (see Fig. 7a ~ 6c) at the heat flux of 35.8 kW/m2 while explosive bubble growth and consecutive reversed flow were observed at the heat flux of 40.3 kW/m2 (see Fig. 7d ~ 6f). Bubbles expanded along the upstream direction in a certain single channel and then they were condensed by the incoming liquid at the heat flux of 35.8 kW/m2. However, no significant pressure drop was recorded for this case in the multichannel system (Fig. 6). It shows the limitation of the theoretic models that the onset of flow instability in a multichannel system is also defined by the observation of reversed flow in a single microchannel. The asynchronization phenomena of flow patterns in 15

different channels should be taken into consideration in the multiple microchannel system. Due to the conjugation effect in a multichannel system, it showed stable flow characteristic at this stage even with reversed flow happening in a certain channel. As the heat flux increased to 40.3 kW/m2 (Fig. 7d ~ 6f), the evolution of elongated bubbles dominated the flow and obvious pressure fluctuations were recorded. Due to the increased heat flux, the subcooling of the liquid decreased and the liquid was gradually heated along the channel. The quick release of the superheated energy from the nucleation sites and the evaporation of the liquid film around the bubble contributed to the explosive bubble growth and induced a sharp increase of the vapor pressure. In addition, the release of the superheated liquid energy when the paired bubbles coalesced led to the bubble explosion phenomenon, as shown in Fig. 7e. Considering both the film evaporation and pressure limitation effects, the exponential bubble growth in slug flow was modeled by Li et al.[50]. Due to the quick expansion in the axial direction, the pressure limitation effect on bubble growth in a microchannel is found to weaken the evaporation effect significantly. The formation and depletion of the thin liquid film underneath the elongated bubbles were recorded by the high speed-camera. It was found that the thin liquid film underneath a bubble was not depleted simultaneously. It depleted from the nose of a bubble to the end. Due to the high contribution of the liquid film evaporation to the heat transfer process, it might be taken into consideration for modeling heat transfer process in future studies. Fig. 8 shows the typical characteristics of the pressure drop under different heat flux with Fast Fourier transform after de-noising. High amplitude with low frequency oscillations are illustrated in the analysis. The oscillation frequency starts from nearly zero to 0.68 Hz and then decreases with the increase of heat flux while the oscillation amplitude augments with increased heat flux. The transition of the characteristic frequency could be used to identify the instability status of the system. However, it is only effective when appreciable and reasonable oscillation amplitude is well defined. Due to the complicated conjugation effect of the flow in multiple microchannel configuration, the oscillation energy may distribute uniformly in a wide range of frequency. There may be several characteristic frequencies or sometimes no typical frequencies can be identified from the FFT results. A different method that could represent the flow states at different working conditions is needed and introduced subsequently.

16

Fig. 8. Frequency domain characteristics of the pressure drop under different heat flux.

3.3 Instability analysis with sample entropy The flow characteristics have a close relationship with the pressure fluctuation signal in the flow boiling experiments. The bubble evolution processes such as nucleation, free growth, confined growth, flow reversal and sweep-out are sensitive to the pressure fluctuation signal in the microchannel system. The applications of information entropy such as sample entropy and multi-scale entropy for the characteristic identification have been used widely in physiological field and multiphase flow due to its ability in assessing the complexity of timeseries signals. Since the flow instability mainly refers to the transition of bubbly flow to elongated flow in our microchannel system, the entropy of the state in which instability occurs would differ from that of the stable flow. The sample entropy algorithm introduced in the data reduction section was used for the calculation of temporal records of pressure drop after de-noising.

17

Fig. 9. The calculated sample entropy of pressure fluctuation vs boiling number. (a) Present experimental data; (b) Experimental data from paper[21]. Fig. 9 shows the calculated sample entropy of pressure drop in a wide range of inlet temperature, mass flux and heat flux. The dimensionless boiling number ( Bo  q / Gh fg ) is used since it is the ratio of heat exchanged with the surrounding environment to the heat that would vaporize the input liquid into vapor completely. Since the stages of bubble nucleating, growing and being swept out to the exit plenum are relatively more stochastic than the periodic reversed flow results from the evolution of elongated bubbles, the entropy of the pressure drop in the early stages of flow boiling would show a higher value. Fig. 9a displays the calculated sample entropy of each case in present work. The same symbol represents the same inlet temperature and mass flux with increasing heat flux. As the heat flux increases at constant inlet temperature and mass flux, sharp decreases of the sample entropy for each set of cases at a certain condition are observed from this map. Generally, a noticeable difference is also found for all cases. As it is shown in this figure, experimental cases under stable states have values of sample entropy higher than 2.0. Instabilities of the flow boiling in the microchannel system occur when the sample entropy values are lower than 2.0. It can be concluded that sample entropy value at about 2.0 is regarded as the flow instability criterion for our multiple microchannel system. At the same time, experimental data from the paper[21] was analyzed with the same method, as illustrated in Fig. 9b. The same symbol represents the same inlet temperature and mass flux with increasing heat flux, or the same inlet temperature and heat flux with decreasing mass flux. A small variation of the sample entropy for each set of cases under stable states is observed from this figure. As the boiling number increases, sharp decreases of the sample entropy for each set of cases are also observed. The demarcation of the stable and unstable flow can be determined to be about 2.4. 18

It can be concluded that the value of instability criterion calculated from sample entropy might be different for various microchannel systems as well as the different parameters that are chosen for the calculation of the sample entropy. Nevertheless, the differentiation of the stable flow and unstable flow should be obvious in the microchannel system and the sample entropy algorithm could be used for the identification of flow instability.

3.4 Oscillation characteristic analysis

Fig. 10 Comparison of present experimental results with those in the literature. Fig. 10 displays the comparison of the characteristic oscillation periods in our experiments with those in the experiments conducted by Wang et al.[18]. The present experimental results were obtained over a range of inlet temperatures from 40 to 60C, mass flux from 23.04 to 111.89 kg/ (m2·s), heat flux from 4.22 to 67.69 kW/m2 and exit vapor quality from -0.06 to 0.12. Both of the two results show the strong linear dependence of the characteristic oscillation periods on the boiling number. A linear fitting was made for all experimental data and the linear relationship shows a good agreement for both experiments. The range of boiling number in our experiments is smaller than that of Wang’s experiments since they 19

conducted their experiments from bubbly flow to elongated flow and annular/mist flow. However, annular/mist flow boiling was not employed in our experiments for the purpose of avoiding CHF. Wang et al. also reported that the oscillation period of the microchannel temperature is dependent on the heat-to-mass flux ratio while independent of the heat flux. The pressure drop oscillation period was theoretically analyzed by Kuang et al.[51] with a lumped oscillator model and it was found to be a function of the upstream compressible volume, system pressure, channel geometry, channel number and the liquid density. As can be seen from Fig. 10, a higher boiling number corresponds to a larger oscillation period. Besides the influence of those fixed parameters in a microchannel system, the thermal parameters such as heat flux and mass flux also show influence on the pressure drop oscillation characteristic, represented by the slope of the fitting line. The thermal parameters affect the oscillation characteristic through the considerable vapor generation, which is comparable to the upstream compressible volume. Compared with conventional channel system, this effect plays a more significant role in a microchannel system.

4 Conclusions Flow visualization and measurements were conducted in a wide range of inlet temperature, mass flux and heat flux in order to study the characteristics of flow boiling in multiple microchannels systems. The following conclusions can be summarized: 1. With the help of wavelet decomposition method, signal noise and the characteristics of flow oscillations were analyzed. Only oscillations with high amplitude and low frequency were observed in the experiments. 2. The concept of entropy was introduced to depict the flow boiling state in microchannel system and the sample entropy algorithm showed a good identification when flow instability occurs. It reveals that the state function of the microchannel system changes noticeably when instability occurs. 3. The depletion of liquid film underneath a bubble occurred from the bubble nose to the end. 4. The oscillation period of flow instability has a strong bearing on the boiling number.

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Acknowledgments The authors are grateful for the support of the Natural Science Foundation of China (Grant Nos.: 51676020, 51376201) and Natural Science Foundation Project of CQ CSTC (Grant No. cstc2015jcyjB0588).

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