Experimental Investigation of the Characteristics of Flow Boiling

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Thermodynamics, Transport, and Fluid Mechanics

Experimental Investigation on the Characteristics of Flow Boiling Oscillations in Vertical Mini-Channel Chong Li, Deqi Chen, Qi Lu, and Xueqiang He Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04890 • Publication Date (Web): 22 Mar 2018 Downloaded from http://pubs.acs.org on March 29, 2018

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Industrial & Engineering Chemistry Research

Experimental Investigation on the Characteristics of Flow Boiling Oscillations in Vertical Mini-Channel Chong Li 1, Deqi Chen*1,2, Qi Lu 1, Xueqiang He 1 (1. Key Laboratory of Low-grade Energy Utilization Technologies and Systems (Chongqing University), Ministry of Education, Chongqing 400044, China 2. Department of Power and Energy Engineering, Chongqing University, Chongqing, 400044, China;. ) * Corresponding author (Deqi Chen) Email: [email protected]; Tel and Fax: +86-23-65102052

ABSTRACT An experimental investigation is carried out to study the characteristics of flow boiling oscillation in a vertical mini-channel with the inner diameter of 2.15 mm. The working fluid is deionized water which is with the constant system pressure of 0.101 MPa. The characteristics of flow oscillation with different working conditions are analyzed in this paper. With other constant working conditions, it is found that the oscillation periods of the pressure drop and the wall temperature decrease with the inlet sub-cooling decreasing, while the fluctuation amplitude of pressure drop oscillations changes a little. The effects of heat flux and mass flux on the flow boiling oscillation are discussed with the equilibrium vapor quality (xe). Meanwhile, the xe which is at the onset of flow oscillation is affected by the mass flux. Finally, a new model which is based on the Flow Instability Ratio (FIR) is proposed to predict the onset of boiling two-phase flow oscillation, and a good agreement is achieved when comparing with the experimental results. Keywords: Flow boiling; Two-phase flow; Flow oscillations; Mini-channel

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NOMENCLATURE Nomenclature General symbol Q

the power (W)

k

the thermal conductivity (W (m k)-1)

U

the voltage (U)

p

the local pressure

I

the current (A)

f

the frequency of flow oscillations

-2

q

the heat flux (W m )

xe

the equilibrium quality

Gl

the mass flux (kg m-2s-1)

Co

the bubble confined coefficient

C

the perimeter of the inner cross section (m)

Nu

the Nusselt number

L

the length of heating section (m)

St

the Stanton number

D

the diameter of heating section (m)

Pe

the Peclet number

rc

the radius (m)

Subscripts -1

kw

the thermal conductivity (W (m k) )

w

wall

T

the temperature

tot

total

-3

Φ

the power density (W m )

in

inner

a

the constant

m

mixture

sub

subcooled

sat

saturated

FO

flow oscillations

h hfg cp,f

-1

the enthalpy (J kg ) -1

the latent heat of vaporization (J kg ) -1

the specific heat capacity (J (kg k) )

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1 INTRODUCTION Flow oscillations have been observed in many industries such as refrigeration systems, nuclear reactors, and two-phase flow heat exchangers. Fluctuation of hydraulic parameters can be caused significantly by them and consequently leading to the system’s failure. Over the years, flow oscillations have been studied and classified by many researchers due to its inherent nature 1-3. Ding et al. 4 have found three types of sustained dynamic instabilities (pressure drop type oscillations, density wave type oscillations and thermal oscillations) with refrigerant R-11 in a uniformly heated horizontal tube boiling system. It was found that the inlet pressure and the mass flow rate oscillated out of phase by 180° during pressure drop oscillations (PDO). Density wave type oscillations (DWO) appeared in the negative slope region after a transition period following the pressure drop type oscillations as is shown in Fig. 1. Thermal oscillations were defined in their studies as independent phenomena rather than accompaniments of pressure drop type oscillations. The random motion of the liquid/vapor transition point, i.e. the boundary between the two-phase mixture and the superheated vapour was considered by Ding et al. 4

which was as the main reason for the temperature variation within this region. Further,

R-22 was used by Liang et al. 5 to research the three types of oscillations in a horizontal straight tube evaporator, and then they obtained the onset of pressure drop and thermal oscillations, respectively. Wang et al. 6, 7 investigated the effect of imposed periodic mass flow rate and the heat flux on flow instabilities in subcooled flow boiling with R-134a and FC-72 in narrow flow passages. They indicated that the oscillatory flow boiling characteristics were significantly affected by the inlet liquid sub-cooling. Besides, the intermittent flow boiling for both refrigerants was observed because the imposed heat flux was close to the onset of unstable flow boiling. Furthermore, several studies which are focused on the geometry specification of two-phase flow channel have been done to investigate the effect of geometry specification on flow instability. You and Hassan

8

have studied the flow boiling

instability in a single micro-tube whose hydraulic diameter is 0.889 mm with and without inlet orifice. The reversed flow was believed as the major source of the flow instability, and two sizes (50% and 20% area ratio) of inlet orifices were investigated in the vertical

3



flow directions. They indicated that both these inlet orifices could control flow instability while the inlet orifice with 50% area ratio can show a better performance. Khodabandeh and Furberg 9 investigated that whether the different channel geometries and the height of a rectangular channel of fixed width have an effect on two phase flow instability at different diameter evaporator. The study showed that flow and temperature instability increased as the channel height decreasing. Refrigerants were used by all the works mentioned above, which were much different from water in physical properties such as the boiling point, surface tension and the latent heat of vaporization. The differences in physical properties between different working fluids might cause the different characteristics of two-phase flow in a certain flow channel. Therefore, the characteristics and the mechanisms of flow instability in refrigerants-based systems might not be applied to water-based systems.

To study the flow instability of water, researchers have set up many experiments and also obtained lots of conclusions. Wang et al.

10

presented a new type of dynamic instability

namely boiling onset oscillations in a stainless steel tube (Din=16mm) with high pressure (30-100 bar). This type of oscillations occurred only at high inlet sub-cooling condition as well as around the boiling point. The periods and amplitudes of this type of oscillations were much longer and larger than those of density wave and pressure drop type oscillations. Qu and Mudawar

11

have identiﬁed two types of instabilities of two-phase

hydrodynamic namely severe pressure drop oscillations and mild parallel channel instability. The severe pressure drop oscillations occurred at low heat fluxes due to the sudden generation of a significant amount of vapour at boiling incipience. While the mild parallel channel oscillations occurred at intermediate and high heat fluxes where the flow pattern fluctuated between slug and annular flow. Wu and Cheng 12 carried out a study of simultaneous visualization and showed that two-phase flow and single-phase liquid flow appeared alternatively in micro-channels, which led to large amplitude/long-period fluctuations with time in temperature, pressure and mass flux. The fluctuation periods were found to be dependent on channel size (31 s with hydraulic diameters of 158.8 µm while 141 s with hydraulic diameters of 82.8 µm), heat flux, and mass flux. As proposed by Balasubramanian et al. 13, flow boiling instability was influenced by the existent flow

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boiling regime and the most stable flow boiling process was offered by the annular flow regime. Wang et al.

14

identified two unstable flow boiling regimes with long-period

oscillations and short-period oscillations in temperature and pressure based on the heat-to-mass flux ratio (q/G), respectively. They tested a multi-microchannel heat sink which is consisted of eight parallel channels. The unstable flow boiling regime with long-period oscillations (more than 1s) and with short-period oscillations (less than 0.1 s) occurred when q/G = 0.96 ~ 2.14 kJ/kg and q/G>2.14 kJ/kg, respectively. Brutin et al.

15

made a flow pattern analysis and a stability delimitation of unsteady period in rectangular micro channels with a hydraulic diameter of 889 µm. Two types of behavior were observed: one was that a steady state was characterized by the pressure drop fluctuations with low amplitudes (from 0.5 to 5 kPa/m) and no characteristic frequency while the other was a non-stationary state of two-phase flow. As for the effect of bubble behaviors on flow oscillations, Chang and Pan

16

found that the length of bubble slug might

oscillate in unstable cases with reversed flow. Also it was found that the magnitude of pressure drop oscillations might be used as an index for the appearance of reversed flow. Bogojevic et al.

17

also indicated that the flow fluctuation was significantly affected by

bubble dynamic, which the shorter bubble lifetime resulted in higher frequency of fluctuations. On the other hand, bubbles with a long lifetime and slow growth rate resulted in a long two-phase period during the phase alternations. Furthermore, the influence factors on flow system stability are researched in recent years. Kandlikar et al. 18

performed an experiment on 1054×197 µm parallel rectangular micro-channels and

they found that the pressure drop elements partially reduced the flow instabilities while flow instabilities were increased by the artificial nucleation sites. Lee et al. 19 investigated flow instability in a vertical narrow rectangular channel with inlet throttling. They agreed with You and Hassan

8

that the stability of system was enhanced by increasing the inlet

throttling. What’s more, Qian et al.

20

,Guo et al.

21

and Xia et al.

22

also found that an

increase of system pressure would stabilize the system which is based on the RELAP5/MOD3.4 code. They indicated that the increase of inlet throttling coefficient would stabilize the system and enlarge the frequency. However, the increase of exit throttling would decrease the stability of the system and the frequency.

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Although many researchers have studied the flow oscillations with experimental and theoretical methods in recent years, most of the investigations are focused on the refrigerants-based micro systems and the improvement of enhancing the stability of two-phase flow. However, the criterion for the onset of flow oscillations of two-phase flow in mini-channel is still not clear. So, further study on the flow boiling in mini-channel is still necessary. Based on this situation, the objective of this paper is to experimentally investigate the characteristics of boiling two-phase flow oscillations in vertical mini channel, and to study the criterion for the onset of flow oscillations. In this paper, an experimental investigation is carried out to study the characteristics of boiling two-phase flow oscillations in a circular channel which the inner diameter is 2.15 mm. The characteristics of flow oscillations with different working conditions are analyzed in this paper. A new correlation of predicting the onset of flow oscillations which is based on the Flow Instability Ratio (FIR) is proposed in this paper.

2 EXPERIMENTAL APPARATUS The schematic diagram of the experimental loop system and the test-section can be shown in Fig. 2a and Fig. 2b, respectively. In this paper, the deionized water is used as the working fluid. The dissolved gas has been eliminated by heating the working fluid for more than 2 hours before the experimental study. The heating section of the test-section is made of stainless steel seamless cold drawn tube whose inner diameter is 2.15 mm. As is shown in Fig. 2b, two transparent sections which are equipped at the inlet and outlet of test-section are made of Polycarbonate with the length of 100 mm. The two transparent sections have the same inner diameter (2.15 mm) with that of test-section. Therefore, the inlet and the outlet throttling coefficient can be ignored in this study. The length of heating section is 300 mm and the thickness of heating wall is 0.925 mm. Seven T-type thermocouples with response time of 0.1 s are uniformly equipped along the heating section and the distance between each thermocouple is 50 mm. Two T-type thermocouples are equipped at the inlet and the outlet of test-section in order to measure the water temperature. The pressure of inlet and outlet is measured by two pressure transducers. The response time of pressure transducers is 0.2 s and the range is from 0

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kPa to 100 kPa. The test-section is heated by D.C. power (Uout = 0 ~ 12 V, Iout =0 ~ 2 kA). The flow patterns at outlet are captured by a high speed camera (Redlake-HG-100 K) with a micro-lens, and the recording speed is 5000 fps (frame per second) with an LED light which is used for illumination. As for the experimental loop system, the inlet working fluid is heated to 70°C, 75°C and 80°C by a cartridge preheater, and then driven by a centrifugal pump to flow into an orifice meter. The orifice meter has been calibrated before the experiment according to the working condition of flow rate. The range of flow rate is 6.5 kg/h ~ 40 kg/h during the experimental study, and the orifice meter is calibrated between 5 kg/h ~50 kg/h. The uncertainty of orifice meter is less than ±0.1% after calibration. As is shown in Fig. 2a, the driving power which is generated by the pump is adjusted to keep a constant mass flux with a buffer liquid tank under a certain working condition. The uncertainties of temperature measurements and pressure measurements are less than ±0.5°C and ±0.065% full scale, respectively. During this experimental study, all the measured parameters, including mass flux, heating power of test section, temperature and pressure are recorded by an Agilent acquisition system. All the uncertainties of those measurements are listed in Table 1 and the working conditions of experimental study are listed in Table 2.

3 RESULTS AND DISCUSSION The boiling two-phase flow experiment is carried out by using above design and conditions. Bubble flow and slug flow can be observed clearly in this experiment. The characteristics of flow oscillations have been exhibited in the following sub-sections in detail.

3.1 Data Processing The imposed heat flux for the fluid flowing in the circular channels is calculated based on the total power input,

Qtot = UI

(1)

where Qtot is the total input power (W); U is the voltage (V) and I (A) is the current. Therefore, the heat flux can be obtained as follows,

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q = (Qtot − Qloss ) / CL

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(2)

where q is the heat flux (W/m2 ); Qloss is the heat loss (W); The heat loss value has been confirmed which is determined by using energy balance in the single phase experiments and conduct that the value is 3% before the experiment based on the thermal equilibrium experiment. C is the perimeter of the inner cross section (m) and L (m) is the length of the heating section. Moreover, the one dimensional heat conduction equation for the circular channel can be defined as follows,

∂T 1 ∂ ( kw rc w ) + Φ = 0 rc ∂rc ∂rc

(3)

where rc is the radius of the channel (m); kw is the thermal conductivity of the heating wall (W/mK); Tw is the temperature of the heating wall (°C) and Φ is the power density (W/m3). Also, the conditions for unique solution can be expressed as follows,

rc = rc ,out , Tw = Tw,out rc = rc,in ， k w

dTw CL = 0 drc

(4) (5)

The inner wall temperature can be expressed as follows,

Tw,in =

Φ 2 r + a ln r + a2 4kw c,in 1 c ,in

(6)

rc , inΦ Q + )r k wCL 2k w c ,in

(7)

a1 = (

a 2 = Tw,out +

Φrc2,out 4k w

− a11nrc ,out

(8)

Additionally, the mixing specific enthalpy of vapor and water at No. 7 (J/kg) can be calculated by the following equation,

hm 7 = hinlet +

qCz7 Gl A

(9)

where hinlet is the water specific enthalpy at inlet of the heating section (J/kg); Gl is the mass flux (kg/m2s); z7 is the distance from the inlet of the heating section to No. 7 (m) and A is the area of the inner cross section (m2 ).

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xe 7 =

hm 7 -hsat h fg

(10)

Where xe7 is the thermal equilibrium vapor quality at No. 7; hsat is the saturated water specific enthalpy (J/kg); hfg is the latent heat of vaporization (J/kg). The thermal equilibrium vapor quality at No. 7 is simplified by xe in the later sections.

In this paper, typical flow oscillations with different inlet sub-cooling, heat fluxes and mass fluxes are presented, respectively. For the stable flow conditions, no significantly periodic pressure drop is observed. As the heat flux increasing, more and more bubbles generate, grow up and coalesce in the narrow test-section (with the inner diameter of 2.15 mm) which result in the increase of pressure drop and flow oscillations. The most obvious characteristics of flow oscillations are periodicity and amplitude. Therefore, it is necessary to analyze the period and amplitude of flow fluctuations. Because the accurate period of fluctuation by time-domain analysis is difficult to obtain, the method of fast Fourier-transform is used in this paper to translate the time-domain analysis to the frequency-domain analysis.

3.2 The Effect of Sub-cooling on Flow Boiling Oscillations The characteristics of wall temperature oscillations, mass flux oscillations and pressure drop oscillations with different inlet sub-cooling as the flow oscillations occurring have been shown in Fig. 4. As is shown in Fig. 4a, the wall temperature ranges from 105°C to 118°C and the characteristics of wall temperature oscillations present three stages with other conditions unchanged in an oscillatory period, namely increasing stage, slightly fluctuating stage and decreasing stage. On the first stage, the wall is heated by imposed high heat flux, and the excess heat cannot be taken away by upstream subcooled fluid. Therefore, the wall temperature keeps increasing and the flow pattern is almost a single liquid phase at the outlet as is shown in Fig. 3a. As the wall temperature increasing to a certain degree of superheat, some small bubbles generate in the thermal boundary layer near the heated wall. With the mainstream temperature increasing, more and more bubbles generate from the heated wall. Then the bubbles coalesce to slugs with radial size which are comparable to the tube’s inner diameter (2.15 mm) as is shown in Fig. 3b. The

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dominant heat transfer mechanism for the heating wall changes from the single phase convective heat transfer to the nucleate boiling heat transfer. The excess heat is taken away by large latent heat of vaporization. The bubbles grow both in upstream and downstream and elongate rapidly in the respective directions, which result in reverse flow 14, 15, 19

as is shown in Fig. 3c and Fig. 3d. The wall temperature oscillations are in the

second slightly fluctuate stage. Wang et al.

14

also observed the similar phenomena that

the wall temperature kept a higher constant value with a long period. At some point, the slug is rapidly pushed out by the upstream liquid. The whole channel is refilled with the subcooled upstream liquid, which leads to the significant decrease of wall temperature, and the wall temperature oscillations are in the third decrease stage.

The characteristics of mass flux oscillations and pressure drop oscillations in an oscillatory period have been shown in Fig. 4a. The mass flux and the pressure drop oscillations are range from 988 kg/m2s to 1018 kg/m2s and 11 kPa to 28 kPa, respectively. They both present two stages, namely gradually increasing stage and rapidly decreasing stage while the phases of the two oscillations are out of phase by 180°. As the wall temperature keeping a relatively constant value, the bubbles generate gradually along the heating wall and coalesce to slugs as is shown from Fig. 3b to Fig. 3d, which lead to an increase in the flow resistance. Therefore, the pressure drop increases as is shown in Fig. 4a. As the pressure drop increasing to the maximum value, the slugs are rapidly pushed out by the upstream subcooled liquid, which lead to the decrease of the pressure drop. The flow pattern changes from slug flow to single phase liquid flow. With the unchanged pressure heat which is provided by the pump, the change of pressure drop in the text section due to the evolution of gas-liquid interface leads to the change of mass flux. As the pressure drop increasing, the mass flux decreases and vice versa. The phases of the two oscillations are always out of phase by 180°. In conclusion, the oscillations of wall temperature, pressure drop and mass flux are caused by the alternating flow patterns in the test channel. Therefore, the same periods of three oscillations are observed for 77s with Tin=70°C, Gl=1000 kg/m2s and q=210 kW/m2 in Fig. 4a.

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The characteristics of wall temperature oscillations, pressure drop oscillations and mass flux oscillations with different inlet sub-cooling can be shown in Fig. 4b and Fig. 4c which is compared with Fig. 4a (Tin=70°C). The same oscillating characteristics are obtained in the three figures. But the fluctuation periods of the wall temperature, the mass flux and the pressure drop decrease from 77 s (Tin=70°C) to 67 s (Tin=75°C) and 42 s (Tin=80°C). The inlet enthalpy (Hinlet) increases as the inlet sub-cooling degree decreasing, which leads to the two-phase section length increasing. The transformation from single liquid phase to vapor-liquid two-phase occurs in advance with other conditions unchanged. The first stage (increase stage) of wall temperature oscillations decreases rapidly from 38 s (Tin=70°C) to 31 s (Tin=75°C) and 15 s (Tin=80°C), while the second stage (slightly fluctuate stage) and the third stage (decrease stage) have a little change with inlet sub-cooling decreasing. Therefore, the total periods of flow oscillations decrease with the inlet sub-cooling degree decreasing. While the oscillation amplitude of mass flux and pressure drop changes a little with different sub-cooling as is shown in Fig. 4. The vapor quality increases as the sub-cooling decreasing with the constant heat flux, which causes the average pressure drop increasing with the increase of frictional pressure drop from 20 kPa to 22 kPa and 26.5 kPa. In addition, the average wall temperature increases from 111.5°C to 113.5°C and 115°C with the sub-cooling decreasing. As is shown in Fig. 4, the oscillation periods are significantly affected by the inlet sub-cooling, while the effect on the oscillation amplitude is ignorable in the experimental conditions. The average pressure drop increases slightly from 20 kPa to 26.5 kPa due to the increase of frictional pressure drop with inlet sub-cooling decreasing.

3.3 The Effect of Heat Flux on Flow Boiling Oscillations The effect of heat flux on flow boiling oscillations with Tin=80°C and Gl=1500 kg/m2s has been shown in Fig. 5a, 5b and 5c. The wall temperature, the mass flux and the pressure drop do not present the obvious oscillation phenomena with q=170 kW/m2 as is shown in Fig. 5a. And the xe with the increase of imposed heat flux has been shown in Fig. 6. The subcooled boiling is a dominant heat transfer mechanism with q=170 kW/m2 and the flow is almost the single liquid with very little bubbles in the thermal boundary layer near the heated wall as is shown in Fig. 3a. The bubbles are condensed quickly by

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the subcooled upstream flow and cannot grow up to larger bubbles. Therefore, the flow oscillation phenomenon does not occur.

As is shown in Fig. 5b and Fig. 5c, mass flux and pressure drop present the same obvious oscillation phenomena compared to the Fig. 4 with q=200 kW/m2 and q=220 kW/m2. The flow pattern at the outlet of test channel changes from isolate bubble flow (Fig. 3a) to slug flow (Fig. 3d) with heat flux increasing. The periods of the wall temperature oscillations decrease from 71 s to 46 s. Meanwhile, the periods of increasing stage decrease from 44 s to 28 s due to the increase of the length of two-phase section, while the periods of other two stages keep almost constant. The average wall temperature increases from 113°C to 115°C with other parameters being hold. In addition, the average pressure drop increases from 27.1 kPa to 28.4 kPa, which is caused by the increase of vapor quality with imposed heat flux increasing. As xe rising to nearly zero (q=200 kW/m2), plenty of bubbles generate in the main flow as is shown in Fig. 3c and Fig. 3d. Bubbles are departure from the heated wall and coalesce to larger bubbles even vapour slugs are in the flow channel. The incremental frictional pressure drop and acceleration pressure drop are larger than the decrease of gravitational pressure drop with the increase of imposed heat flux, which result in the increase of general pressure drop in Fig. 5b and Fig. 5c. And the correlation of xe and general pressure drop can be shown in Fig. 6. The red imaginary line shows the transition point of general pressure drop and the thermal equilibrium quality xeFO. Before the red imaginary line, the general pressure drop has a slight decline trend which is caused by the decrease of fluid density with the imposed heat flux increasing. The xe linear increases until the critical value xeFO, then the general pressure drop has a rapidly increase which is caused by the quickly generated bubbles and slugs in experimental section as is shown in Fig 3c. After xeFO, bubbles generate around the heating wall and grow up quickly to slip or departure from the heating wall which lead to the increase of general pressure drop. Meanwhile, the thermal equilibrium quality (xe) and pressure drop for onset of flow oscillations increase with mass flux increasing as is shown in Fig. 6.

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3.4 The Effect of Mass Flux on Flow Boiling Oscillations The effect of mass flux on flow boiling oscillations with Tin=80°C and q=200 kW/m2 has been shown in Fig. 7a, 7b and 7c. As is shown in Fig. 7a and Fig. 7b, the characteristics of flow oscillations are the same with Fig. 4 and Fig. 5. The periods of the wall temperature increase from 42 s to 62 s with the mass flux increasing from 1000 kg/m2s to 1500 kg/m2s. Meanwhile, the periods of increasing stage increase from 14 s to 47 s due to the increase of the length of single phase section and the periods of slightly fluctuate stage decrease from 28 s to 15 s which is caused by the increase of driving head in test section with mass flux increasing. As other conditions being unchanged, the wall temperature decreases from 115°C to 113°C due to the mass flux increasing. The effect of mass flux on xe with Tin=80°C and q=200 kW/m2 has been shown in Fig. 8. The xe decreases from 0.017 to about zero as the mass flux increasing from 1000 kg/m2s to 1500 kg/m2s, and the length of two-phase section decreases while the single phase section increases in the test section which leads to the increase of flow oscillation periods. As the mass flux increasing from 1000 kg/m2s (xe>0) to 1500 kg/m2s (xeFO), the average pressure drop increases from 25 kPa to 27.1 kPa because of the extra gravitational pressure drop as is shown in Fig. 7a and Fig. 7b. While the wall temperature, the mass flux and the pressure drop do not present the obvious oscillation phenomena with Gl=2000 kg/m2s as is shown in Fig. 7c. The value of xe (-0.01) is much less than xeFO which is shown in Fig. 8, the bubbles are only generated near the heating wall as is shown in Fig 3a. Therefore, the flow oscillation phenomenon does not occur.

3.5 The Criterion of The Boundary of Flow Oscillations As the previous sections showing, the obvious oscillations of wall temperature and pressure drop are occurred in experimental section with specific mass flux and heat flux. The extra flow fluctuation has a distinctive effect on the heat transfer coefficient even leading to CHF in advance. Therefore, it is very important to determine the onset of flow oscillations in order to prevent the instability of flow system. In recent decades, researchers have proposed several criteria for identifying the onset of flow oscillations. These criteria were based on the onset of Nucleate Boiling (ONB), the Net Vapor

13



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Generation (NVG), the onset of Fully Developed Boiling (FDB) and the Flow Instability Ratio (FIR), which were proposed by Ghione et al.

23

and there were plenty of

experimental data (166) in narrow rectangular channels with low pressure. Firstly, the criterion based on the onset of Nucleate Boiling was discussed. The ONB was often predicted with the correlation of Bergles et al.

24

with the pressure range from 0.1

MPa to 13.8 MPa:

∆Tsat ,ONB

    q   = 0.556 1.156    p  1082 5    10   

 p  0.463 5   10 

0.0234

(12)

The criterion for the flow oscillations could be expressed as:

MTw−ONB = Tsat + ∆Tsat,ONB −Tw ≤ 0

(13)

The outcome with all the experimental data which was based on the Eq. (13) was negative, and they were too conservative to predict the boundary of flow oscillations for the maximum value -5.52 with the experimental data in Ghione et al.

23

. They indicated

that the formation of bubbles at the heating walls was a prerequisite for the flow instability so that the calculation values were too conservative. In this paper, the similar conclusion is obtained with the maximum value -0.93 and the mean value -3.85 of MTw-ONB. As is shown in Fig. 9, all the calculated values of MTw-ONB are much smaller than zero, which is too conservative to predict the onset of flow oscillations.

For the criterion based on the Net Vapor Generation (NVG), one of the most applied correlation was the Saha-Zuber correlation 25 which the pressure range was from 0.1 MPa to 13.8 MPa:

qDc p , f qD = = 455 k∆Tsub k∆H sub

if Pe ≤ 70000

(14)

q q = = 0.0065 Gl c p, f ∆Tsub Gl ∆H sub

if Pe > 70000

(15)

Nu =

St =

14


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Researchers proposed several prediction correlations based on Saha-Zuber correlation with the experiment condition. Siman et al.

26

introduced a sub-cooling correction factor

into the original S&Z correlations: Nu =

St =

 qD 11 .21  = 455 η sub = 455 0.55 +  k∆ Tsub ∆ Tsub  

 q 11 .21  = 0.0065 ηsub = 0.0065 0.55 +  Gl c p , f ∆ Tsub ∆ Tsub  

if Pe ≤ 70000

(16)

if Pe > 70000

(17)

Ghione et al. 23 proposed a possible OFI criterion which was called Net Vapor Generation Ratio (NVGR), it was given as follows:

NVGR =

H sat - H ∆H sub

(18)

The value which was smaller or equal to 1 indicated that the flow oscillations occurred in the experimental section. The results of Ghione et al. 23 showed that most of experimental data were smaller than 1, while some of cases did not predict flow oscillations with the Pe lower than 70000. In this paper, almost all the calculated Pe are lower than 70000 with the mean value 21766. The calculated NVGR also has the similar tendency that the error is larger compared to 1 with the Pe decreasing as is shown in Fig. 10. The two criteria which are based on NVG to predict the flow oscillations are not appropriate in this experiment condition as is shown in Fig. 10. The criterion based on the onset of Fully Developed Boiling (FDB) was hypothesized with high pressure. In this paper, this criterion is ignored for the system pressure with environmental pressure.

The most interested criterion was based on the global parameters. Whittle et al.

27

proposed a ratio R with low pressure to correlate the minima of the flow redistribution curve which was as follows:

R=

Tout − Tinlet Tsat − Tinlet

With the criterion of Bowring et al.

28

(19) for the bubble detachment, Whittle et al.

proposed that the R could be expressed in terms of η and L/D:

15


27


RW =

1

Page 16 of 39

(20)

η 1+ L/D

The value of η was given for 25 with the experimental data

27

. While the value of 32.5

was usually suggested in the literature 29 and the Flow Instability Ratio (FIR) was defined as follows: FIR =

RW R

(21)

The FIR represented the degree of bubble departure before the onset of flow oscillations in the test section. If the ratio was smaller or equal to 1, the experimental condition was at the minimum of the flow redistribution curve which indicated that flow oscillations occurred. In this paper, the two values of η are verified in the Fig. 11a and Fig. 11b, respectively. As the η = 25 in Fig. 11a, the minimum value is 0.95 and the maximum is 1.13. While most of the values are greater than 1 and the mean value is 1.04. It can be shown in Fig. 11b that the outcome is with the η = 32.5 and most of the values fluctuate near 1 which indicates that this value is more suitable in this paper. While as the η = 32.5, the minimum value is 0.91, and the error is bigger compared to η = 25. Based on the ratio R which was proposed by Whittle et al, 27 a modified criterion was proposed by Stelling et al. 30:

RS =

1 D 1 1 + 0.25 L St

(22)

In this paper, the η (0.25/St) is verified with the experimental data and the outcome is shown in Fig. 11c. The calculated values are more compact compared to Fig. 11a and Fig. 11b, while almost all the values are larger than 1. The restriction of pipe diameter in bubble evolution does not be considered by all the criteria mentioned above, which significantly influences the bubble behavior in mini-channels. Therefore, the Co is introduced in the criterion which was proposed by Stelling et al. 30 to predict the onset of flow oscillations. The bubble confined coefficient is defined as follows,

16


Page 17 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


  σ  Co =  2  ( ρl − ρ g ) gDh 

1/ 2

(23)

The modified RCo can be obtained with the experimental data in this paper as follows,

RCo =

Co0.1 D 1 1 + 0.25 L St

(24)

The optimized FIR can be shown by the calculated values in Fig. 12. Almost all the calculated values are smaller than 1 and the minimum value is 0.974, which is much better with the η with 0.25/St or 32.5. The criterion for predicting the onset of flow oscillations is obtained as follows:

FIR =

Co0.1 Tout − Tinlet D 1 Tsat − Tinlet 1 + 0.25 L St

(23)

This criterion is satisfied with the low pressure and mass flux which is 700 kg/m2s-3000 kg/m2s with the inlet sub-cooling ranged for 20oC ~ 40oC. All the experimental parameters for onset of flow oscillations and the calculated values of criterion for flow oscillations are shown in table 3 and table 4, respectively. What should be mentioned is that the table 3 only shows the experimental conditions at the onset of flow oscillations, which occurs in subcooled boiling with bubbles sharply generating.

4 CONCLUSIONS An experimental study is carried out to investigate the characteristics of flow boiling oscillation with different working conditions, including different sub-cooling, mass fluxes and heat fluxes. A few conclusions are obtained as follows: (1) The characteristics of wall temperature oscillations, mass flux oscillations and pressure drop oscillations are analyzed in detail. The effect of working conditions on flow oscillations is discussed, which is combined with the visualization of two-phase flow and thermal equilibrium quality. The periods of mass flux oscillations and pressure drop oscillations decrease with sub-cooling decreasing and heat flux increasing, while the oscillation amplitude changes a little.

17



(2) The periods of wall temperature oscillations, mass flux oscillations and pressure drop oscillations increase with the initial mass flux increasing. Meanwhile, the thermal equilibrium quality (xe) and pressure drop for the onset of flow oscillation increase with the mass flux increasing. (3) A new FIR model coupled with Co is proposed to predict the onset of boiling two-phase flow oscillation. According to the comparison between the predicted and the experimental results, a good agreement is obtained in this study.

ACKNOWLEDGEMENT The authors are grateful for the support of the National Natural Science Foundation of China (No. 51206199); Project No. 106112017CDJQJ148806 is supported by the Fundamental Research Funds for the Central Universities.

18


Page 18 of 39

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REFERENCES 1.

Boure, J. A.; Bergles, A. E.; Tong, L. S., Review of two-phase flow instability.

Nuclear Engineering & Design 1973, 25, (2), 165-192. 2.

Chiapero, E. M.; Fernandino, M.; Dorao, C. A., Review on pressure drop oscillations

in boiling systems. Nuclear Engineering & Design 2012, 250, 436-447. 3.

Ruspini, L. C.; Marcel, C. P.; Clausse, A., Two-phase flow instabilities: A review.

International Journal of Heat & Mass Transfer 2014, 71, (3), 521-548. 4.

Ding, Y.; Kakaç, S.; Chen, X. J., Dynamic instabilities of boiling two-phase flow in a

single horizontal channel. Experimental Thermal and Fluid Science 1995, 11, (4), 327-342. 5.

Liang, N.; Shuangquan, S.; Tian, C.; Yan, Y. Y., Two-phase flow instabilities in

horizontal straight tube evaporator. Applied Thermal Engineering 2011, 31, (2-3), 181-187. 6.

Wang, S. L.; Chen, C. A.; Lin, T. F., Oscillatory subcooled flow boiling heat transfer

of R-134a and associated bubble characteristics in a narrow annular duct due to flow rate oscillation. International Journal of Heat and Mass Transfer 2013, 63, 255-267. 7.

Wang, S. L.; Chen, C. A.; Lin, Y. L.; Lin, T. F., Transient oscillatory saturated flow

boiling heat transfer and associated bubble characteristics of FC-72 over a small heated plate due to heat flux oscillation. International Journal of Heat and Mass Transfer 2012, 55, (4), 864-873. 8.

You, Q.; Hassan, I., Experimental investigation on flow boiling instability in a

microtube with and without an inlet orifice in vertical flow directions. Thermal Science and Engineering Progress 2017, 4, 18-29. 9.

Khodabandeh, R.; Furberg, R., Instability, heat transfer and flow regime in a

two-phase flow thermosyphon loop at different diameter evaporator channel. Applied Thermal Engineering 2010, 30, (10), 1107-1114. 10. Wang, Q.; Chen, X. J.; Kakaç, S.; Ding, Y., Boiling onset oscillation: a new type of dynamic instability in a forced-convection upflow boiling system. International Journal of Heat and Fluid Flow 1996, 17, (4), 418-423.

19



11. Qu, W.; Mudawar, I., Measurement and prediction of pressure drop in two-phase micro-channel heat sinks. International Journal of Heat and Mass Transfer 2003, 46, (15), 2737-2753. 12. Wu, H. Y.; Cheng, P., Visualization and measurements of periodic boiling in silicon microchannels. International Journal of Heat and Mass Transfer 2003, 46, (14), 2603-2614. 13. Balasubramanian, K.; Jagirdar, M.; Lee, P. S.; Teo, C. J.; Chou, S. K., Experimental investigation of flow boiling heat transfer and instabilities in straight microchannels. International Journal Of Heat And Mass Transfer 2013, 66, 655-671. 14. Wang, G.; Cheng, P.; Wu, H., Unstable and stable flow boiling in parallel microchannels and in a single microchannel. International Journal of Heat and Mass Transfer 2007, 50, (21-22), 4297-4310. 15. Brutin, D.; Topin, F.; Tadrist, L., Experimental study of unsteady convective boiling in heated minichannels. International Journal of Heat and Mass Transfer 2003, 46, (16), 2957-2965. 16. Chang, K. H.; Pan, C., Two-phase flow instability for boiling in a microchannel heat sink. International Journal Of Heat And Mass Transfer 2007, 50, (11-12), 2078-2088. 17. Bogojevic, D.; Sefiane, K.; Duursma, G.; Walton, A. J., Bubble dynamics and flow boiling instabilities in microchannels. International Journal Of Heat And Mass Transfer 2013, 58, (1-2), 663-675. 18. Kandlikar, S. G.; Kuan, W. K.; Willistein, D. A.; Borrelli, J., Stabilization of flow boiling in microchannels using pressure drop elements and fabricated nucleation sites. Journal of Heat Transfer 2006, 128, (4), 389. 19. Lee, J.; Jo, D.; Chae, H.; Chang, S. H.; Jeong, Y. H.; Jeong, J. J., The characteristics of premature and stable critical heat flux for downward flow boiling at low pressure in a narrow rectangular channel. Experimental Thermal and Fluid Science 2015, 69, 86-98. 20. Qian, L.; Ding, S.; Qiu, S., Research on two-phase flow instability in parallel rectangular channels. Annals of Nuclear Energy 2014, 65, 47-59. 21. Guo, Y.; Huang, J.; Xia, G. L.; Zeng, H. Y., Experiment investigation on two-phase flow instability in a parallel twin-channel system. Annals Of Nuclear Energy 2010, 37, (10), 1281-1289.

20


Page 20 of 39

Page 21 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


22. Xia, G. L.; Peng, M. J.; Guo, Y., Research of two-phase flow instability in parallel narrow multi-channel system. Annals Of Nuclear Energy 2012, 48, 1-16. 23. Ghione, A.; Noel, B.; Vinai, P.; Demazière, C., Criteria for onset of flow instability in heated vertical narrow rectangular channels at low pressure: An assessment study. International Journal of Heat and Mass Transfer 2017, 105, 464-478. 24. Bergles, A. E.; Rohsenow, W. M., The determination of forced-convection surface-boiling heat transfer. Journal of Heat Transfer 1964, 86, (3), 365-372. 25. Saha, P.; Zuber, N., Point of net vapor generation and vapor void fraction in subcooled boiling. Scripta Book Co., Washington, DC; Georgia Inst. of Technology, Atlanta: 1974; p Medium: X; Size: Pages: 175-179. 26. Siman-Tov, M.; Felde, D. K.; McDuffee, J. L.; Yoder, G. L. J., Static flow instability in subcooled flow boiling in parallel channels. ; Oak Ridge National Lab., TN (United States): 1995; p Medium: ED; Size: 22 p. 27. Whittle, R. H.; Forgan, R., A correlation for the minima in the pressure drop versus flow-rate curves for sub-cooled water flowing in narrow heated channels. Nuclear Engineering & Design 1967, 6, (1), 89-99. 28. Bowring, R. W., Physical model based on bubble detachment and calculation of steam voidage in the subcooled region of a heated channel. 1962. 29. Roglansribas, J., Analyses of Flow Excursion Experiments Relevant to Research Reactors: Revisited. 30. Stelling, R.; Mcassey, E. V.; Dougherty, T.; Yang, B. W., The onset of flow instability for downward flow in vertical channels. Journal of Heat Transfer 1996, 118, (3), 709-714.

21



Table and Figure Captions: Table Captions: Table 1 Measuring Uncertainties Table 2 Working Conditions of Experimental Study Table 3 The Experimental Parameter for Onset of Flow Oscillations Table 4 The Calculated Values of Different Criterions for Flow Oscillations

Figure Captions: Fig. 1 the schematic boundaries of flow instability Fig. 2 the schematic diagram of experimental loop system and test-section Fig. 3 The evolution from small bubbles to slugs Fig. 4 The effect of sub-cooling on flow boiling oscillations (Gl=1000 kg/m2s, q=210 kW/m2) Fig. 5 The effect of heat flux on flow boiling oscillations (Tin=80°C, Gl=1500 kg/m2s) Fig. 6 The correlation of xe and general pressure drop Fig. 7 The effect of mass flux on flow boiling oscillations (Tin=80°C, q=200 kW/m2) Fig. 8 xe with different mass flux Fig. 9 The criterion basde on ONB Fig. 10 The criterion based on NVG Fig. 11 The FIR for the Whittle relation with the different η (a: η=25; b: η=32.5; c: η=0.25/St) Fig. 12 The revised criterion of flow oscillations

22


Page 22 of 39

Page 23 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1 Measuring Uncertainties

Quantity

Uncertainty

Temperature

±0.5°C

pressure/pressure drop

±0.065%

liquid-phase flow rate

±0.1%

DC power voltage

±0.5%

DC power current

±0.5%

Heat flux

±0.7%

23



Page 24 of 39

Table 2 Working Conditions of Experimental Study

Din (mm)

Tinlet (℃) 70

75

2.15 80

Number of

q (kW/m2)

Gl (kg/m2s)

xeFO

50-210

700

-0.01129

17

50-220

1000

-0.01223

18

50-200

700

-0.01287

16

50-220

1000

-0.00989

18

50-330

1500

-0.00711

15

50-330

2000

-0.00715

12

50-410

2500

-0.0069

11

50-190

700

-0.01026

15

50-220

1000

-0.01005

18

50-230

1500

-0.00743

12

50-270

2000

-0.00766

9

50-360

2500

-0.00739

11

50-450

3000

-0.00666

13

24


runs

Page 25 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3 The Experimental Parameter for Onset of Flow Oscillations

Tinlet (℃）

Gl (kg/m2s)

q (kW/m2)

Tout (℃)

Pe

70

704

130.52

94.3

8805.79

70

1014

179.00

96.1

12686.04

70

2032

383.19

94.2

25422.62

70

2532

489.50

94.9

31694.62

75

711

110.81

95.8

8889.94

75

1012

148.83

94.9

12666.00

75

1512

230.93

94.8

18919.41

75

2019

320.34

95.5

25260.91

75

2525

393.10

94.9

31594.21

75

3034

448.04

93.9

37957.80

80

707

90.28

96.3

8844.28

80

1013

130.26

96.8

12680.21

80

1500

189.08

96.9

18764.51

80

1995

261.51

97.9

24964.46

80

2504

328.20

96.7

31335.39

80

3018

398.65

97.0

37766.54

25



Page 26 of 39

Table 4 The Calculated Values of Different Criterions for Flow Oscillations FIR

FIR

FIR

FIR

(η=25)

(η=32.5)

(η=0.25/St)

(η=0.279/St)

14.95

1.054

1.010

1.015

0.995

2.73

9.57

0.982

0.941

0.995

0.980

-6.73

2.03

5.12

1.058

1.014

1.019

0.999

-7.20

1.38

3.84

1.029

0.987

1.016

0.998

-1.45

4.79

15.84

1.025

0.983

1.010

0.992

-2.28

4.46

12.59

1.069

1.025

1.009

0.987

-5.36

3.00

8.21

1.079

1.035

1.019

0.997

-5.49

1.82

5.63

1.041

0.998

1.017

0.998

-3.98

1.71

4.78

1.072

1.028

1.021

0.999

-1.86

1.83

4.45

1.127

1.080

1.024

0.999

-1.60

5.07

18.62

1.046

1.003

1.019

1.000

-0.93

2.95

12.26

1.016

0.975

1.013

0.996

-1.70

1.96

8.35

1.011

0.969

1.009

0.993

-2.98

0.83

5.06

0.954

0.915

1.004

0.993

-4.15

1.19

4.88

1.018

0.976

1.016

1.000

-3.79

0.88

3.89

1.003

0.962

1.014

0.999

MTw-ONB

NVGR,sz

NVGR,sm

-9.54

5.84

-2.61

26


Page 27 of 39

12

Single-phase Steam

10

Two-phase

Single-phase Liquid

DWO

Pressure drop ∆P

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


8

PDO+ DWO

6

ONB

4

OFI

2 0 0

5

10 flux G Mass

15

20

Fig. 1 the schematic boundaries of flow instability 4

27


25


100 mm

Fig. 2a The schematic diagram of experimental loop system Transparent Section

Toutlet Pout

-

50 mm

T7

50 mm

T6

50 mm

T5

50 mm

T4

Din

Heating Section

50 mm

T3

50 mm

T2

T1

+ Pin

Tinlet

100 mm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Transparent Section

Fig. 2b The schematic diagram of test-section Fig. 2 The schematic diagram of experimental loop system and test-section

28


Page 28 of 39

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Fig. 3a Isolated small bubbles

Fig. 3b Isolated big bubbles

Fig. 3c Big bubbles and slugs

Fig. 3d Long slugs

Fig. 3 The evolution from small bubbles to slugs

29



Fig. 4a Tin=70℃

Fig. 4b Tin=75℃

Fig. 4c Tin=80℃

Fig. 4 The effect of sub-cooling on flow boiling oscillations (Gl=1000 kg/m2s, q=210 kW/m2)

30


Page 30 of 39

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Fig. 5a q=170 kW/m2

Fig. 5b q=200 kW/m2

Fig. 5c q=220 kW/m2

Fig. 5 The effect of heat flux on flow boiling oscillations (Tin=80°C, Gl=1500 kg/m2s)

31



Fig. 6 The correlation of xe and general pressure drop

32


Page 32 of 39

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Fig. 7a Gl=1000 kg/m2s

Fig. 7b Gl=1500 kg/m2s

Fig. 7c Gl=2000 kg/m2s

Fig. 7 The effect of mass flux on flow boiling oscillations (Tin=80℃, q=200 kW/m2)

33



Fig. 8 xe with different mass fluxes

34


Page 34 of 39

Page 35 of 39 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 9 The criterion basde on ONB

35



Fig. 10 The criterion based on NVG

36


Page 36 of 39

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a

b

c

Fig. 11 The FIR for Whittle relation with the different η (a: η=25; b: η=32.5; c: η=0.25/St)

37



Fig. 12 The revised criterion of flow oscillations

38


Page 38 of 39

Page 39 of 39

Table of Contents (TOC) Graphic:

2

60

∆P(kPa)

Gl(kg/m s)

50

1950

40

1900

30

2

2000

1850 800

1000

1200

1400

∆P(kPa)

2050

Gl(kg/m s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


20 1600

t (s)

The flow oscillation characteristics of pressure drop and mass flux

39


Experimental Investigation of the Characteristics of Flow Boiling

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