An experimental study of flow boiling in minichannels at high reduced pressure

International Journal of Heat and Mass Transfer 110 (2017) 360–373

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An experimental study of flow boiling in minichannels at high reduced pressure A.V. Belyaev, A.N. Varava, A.V. Dedov ⇑, A.T. Komov The National Research University ‘‘MPEI”, Moscow, Krasnokazarmennaya, 14, Russia

a r t i c l e

i n f o

Article history: Received 13 October 2016 Received in revised form 27 February 2017 Accepted 14 March 2017 Available online 22 March 2017 Keywords: Flow boiling Hydrodynamics Heat transfer High reduced pressure

a b s t r a c t This paper presents an experimental setup and experimental data for heat transfer and pressure drops in flow boiling. Experimental study on hydrodynamics and heat transfer were performed for R113 and RC318 in two vertical channels with diameters of 1.36 and 0.95 mm and lengths of 200 and 100 mm, respectively. The inlet pressure-to-critical pressure ratio (reduced pressure) was pr = p/pcr = 0.15–0.9, the mass flux ranges were between 770 and 4800 kg/(m2 s), and inlet temperature varied from 30 to 180 °C. The primary regimes of flow boiling were obtained for conditions that varied from highly subcooled flows to saturated flows and include data for dryout onset. A comparison between the experimental and calculated data for pressure drops is presented. The influence of flow conditions (i.e., mass flow rate, pressure, inlet temperature, and the channel diameter) on the heat transfer coefficient and heat flux is presented in addition to a comparison between the experimental and calculated data for flow boiling heat transfer. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction An important trend in the development of new technologies is miniaturisation of technical objects, an effort that requires extensive background knowledge of hydrodynamics and heat transfer in single-phase convection and flow boiling in small-diameter channels. The ability to accurately predict the pressure drops and heat transfer and the choice of minichannel geometry and working conditions are important factors for design and selection of the optimal settings of heat exchangers. Experimental investigations conducted on fluid flow and flow boiling heat transfer in regular channels (d > 3 mm), showed that the heat transfer is determined by the interaction of two mechanisms: convection and boiling. Calculation of the heat transfer coefficient is performed in one of two ways. When one mechanism is dominant, the calculation is performed using the formulas for the respective components while neglecting the influence of the other mechanism. When convection and boiling are approximately the same, heat transfer is determined by addition or interpolation of these two mechanisms. The most well known methods in the literature for determining the heat transfer coefficient in forced fluid flow boiling through regular channels are Labuntsov’s [1] and

⇑ Corresponding author. E-mail address: [email protected] (A.V. Dedov). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.03.045 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.

Chen’s [2] methods. The peculiarities of heat transfer in subcooled flow boiling are described by Dedov in [3]. In minichannels (0.2 < d
3 mm [4]), peculiarities can result from the characteristic scale of the phenomena that occur in boiling flow and the linear scale of the channel. Investigations of heat transfer in mini- and micro-channels have been conducted for a long time. Before channels with a hydraulic diameter of
3 mm were highlighted as a ‘special’ type in the 1950–60s, a number of studies on fluid flow and heat transfer in subcooled and saturated forced flow boiling were performed. The most well-known studies are those of Ornatskiy and Kichigin [5] and Ornatskiy and Kriticheskiye [6], which investigated boiling heat transfer of water in a tube of d = 2 mm, under p = 1.0–22.5 MPa of pressure, with a mass flow rate of G = 5000–30,000 kg/(m2 s) and inlet subcooling from 200 to 5 °C. The results of these studies do not give reason to doubt that channels with diameters of 1–3 mm are regular channels. These experiments were conducted via traditional methods, i.e., using fixed parameters for subcooled inlet flow and changing the electrical load on the test section incrementally from regimes of single-phase convection to regimes of critical and supercritical thermal loads. Another accepted method for heat transfer research in a channel obtains experimental data for a saturated flow in the test section input by changing the steam quality (at fixed pressure, velocity, and heat flux) using an additional upstream pre-heater.

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361

Nomenclature d L G p V Pr T M Re Qlos q x cp hlg

diameter, m channel length, m mass flux, kg/(m2s) pressure, Pa volume flow rate, l/min Prandtl number temperature, K molar mass, g/mol Reynolds number heat losses, W heat flux, W/m2 vapour quality specific heat, J/(kgK) latent heat of evaporation, J/kg

Greek symbols a heat transfer coefficient, W/m2K Dp pressure difference, Pa DTs wall superheat, K

This method is generally accompanied by studies of the flow pattern and allows the allocation of flow regimes. A 1982 study by Lazarek and Black [7] was one of the first to measure the heat transfer coefficient, pressure drop and critical heat flux of saturated flow boiling with R113. Lazarek and Black performed this investigation in a circular vertical tube with an inner diameter of 3.15 mm, at pressures ranging from 0.13 to 0.41 MPa, with a mass flux of G = 125–750 kg/(m2s) and a heat flux from 14 to 380 kW/m2. The experiments began with inlet subcooled flow conditions in a two-part vertical test section heated by direct current. The results showed that heat transfer in saturated boiling is strongly dependent on heat flux but negligible in quality, which suggested that nucleate boiling controlled the heat transfer. As a result of data compilation, an empirical formula was derived for investigation of flow conditions in which the mechanism of boiling was predominant. The heat transfer coefficient in the formula is not dependent on the steam quality of fluid flow. The experimental results are in a good agreement with other empirical and semi-empirical correlations of various authors for regular tubes. Wambsganss et al. [8] described the results of studies on fluid flow and heat transfer for R113 in a tube with a 2.92 mm diameter using a test section heated by direct current and with subcooled inlet flow. The authors compared their results with values calculated from ten different empirical correlations, and the most precise results were calculated using the values from Lazarek and Black [7]. However, Wambsganss et al. observed a decrease in the heat transfer coefficient with increasing steam quality, probably due to partial drying out of the wall. Kew and Cornwell [9] conducted experiments on R141b in channels with diameters of 1.39, 2.87 and 3.69 mm. According to their data, the behaviour of the critical heat flux (CHF) for diameters of 2.87 and 3.67 mm is similar to that observed in regular channels. However, a difference appears for the 1.39 mm diameter tube. When quality is high, the CHF falls sharply because the channel is blocked by steam. Furthermore, Kew and Cornwell showed that the flow patterns in minichannels (isolated bubbles, confined bubbles and an annular slug flow regime) differ from patterns in regular channels. Comparison of Kew and Cornwell’s experimental data with other empirical correlations for regular channels has not yielded good results.

q r l k

density, kg/m3 surface tension, N/m dynamic viscosity, Hs/m2 thermal conductivity, W/mK

Subscripts calc calculated exp experimental boil boiling conv convective sub subcooled in inlet out outlet l liquid g gas w wall s saturated r reduced

Interesting experimental data were obtained by Wambsganss et al. [10] in their study using a circular channel with an inner diameter of 2.46 mm and a rectangular channel with linear parameters of 4.06  1.7 mm. Their experiments were performed on R12 and R113 at pressures ranging from 0.5 to 0.8 MPa, with vapour quality of x < 0.94, mass flux of G = 44–832 kg/(m2 s) and heat flux from 3.6 to 129 kW/m2. The results of this work show that when x < 0.2, the heat transfer coefficient does not depend on x. Tran et al. proposed their own formula in which the heat transfer coefficient depends on the boiling number, Weber number and the relationship of liquid density to vapour density. No geometrical effect was found. Results for flow boiling heat transfer in a tube with a 1 mm inner diameter using FC-72 as the working fluid were reported by Gugliermetti et al. [11]. This study aimed to identify the best correlation or model to predict the available experimental database. A comparison of several models and correlations available in the literature for both micro- and macro-scales was performed by the authors, with a focus on current preliminary analysis of saturated boiling conditions. Experimental data were collected in the pressure range of 3–5 bar, with mass flux from 800 to 1200 kg/m2s and thermal fluxes from 1.6 to 181 kW/m2. The best results in this preliminary analysis of saturated boiling points were obtained for the micro-scale empirical correlations of Li and Wu [12], with >91% of data within ±30% error and a mean absolute percent error (MAPE) of 13.4%. Among the macro-scale correlations, only the Chen correlation [2] presents good results has a lower degree of agreement with the experimental data. As mentioned previously, peculiarities exist in minichannels resulting from the characteristic scale of the phenomena that occur in boiling flow and the linear scale of the channel. Two-phase flow regimes become dominant in understanding the heat transfer mechanisms in these channels. Heat transfer calculated with the common formulas for regular channels does not agree well with experimental data for minichannels, if at all. Thus, new methods for determining heat transfer are needed. The available databases on two-phase heat transfer and hydrodynamics in channels of small diameter have led to a large number of studies that focus on analysis of previously performed studies. In these studies, the authors carefully assessed whether the existing calculation methods correspond to the various arrays of

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experimental data. The arithmetical mean and standard deviation are the criteria used in selection of the most accurate equations. At the same time, the authors attempted to identify universal equations that can be applied across the range of vapour quality. The literature that presents data and generalisations on flow boiling heat transfer and pressure drops in small diameter channels includes a number of reviews [12–21]. Analysis of the studies presented in these reviews shows that most of this research was performed in the range of relatively low mass velocities (less than 1000 kg/m2 s), with saturated flow at the inlet of a channel in the range of vapour quality 0–1 and at low or medium reduced pressure. For most studies, the flow regime was regulated using a pre-heater, with relatively low heat flux in the test section. This technique made it possible to create regimes of flow and boiling heat transfer that changed only slightly along the length of the tube. Such heat transfer conditions are typical for heat pipes. Features of the current study that are distinctive from previously performed studies are the following: – Stepwise increases of heat flux in the minichannel instead of the use of a pre-heater, which leads to liquid subcooling at the inlet. – Developed turbulent flow for which data were obtained in the mass velocity range of 770–4800 kg/(m2 s). – High reduced pressure. The technique chosen for the experiments in this study more closely resembled the heat transfer conditions in real heat exchangers than in many prior studies but led to a perceptible change in the flow patterns and heat transfer along the channel, which required careful interpretation of the experimental data. The aim of this work is to experimentally confirm the hypothesis that at high reduced pressures, two-phase flow regimes in minichannels become similar to those in regular channels. By primarily increasing the reduced pressure, the ratio of the specific volumes of vapour and liquid decreases and the characteristic internal scales of the two-phase flow become so small that in most practical cases, the two-phase flow specificity of small diameter channels disappears. At high reduced pressures, boiling begins at the lower wall overheating and the calculated values of the equilibrium vapour bubble radius are notably small. In that case, heat transfer in minichannels can be predicted via the common correlations used in regular channels. 2. Experimental setup and procedures 2.1. Experimental setup description The experimental setup is shown in Fig. 1. The hydraulic loop of the experimental setup allows it to maintain stable flow parameters at the inlet of the test section at pressures up to 2.7 MPa and temperatures up to 200 °C. A multistage centrifugal pump is used to circulate the working fluid (location 6 in Fig. 1). The mass flow rate was measured using two flow metres with large and small ranges (location 7). The flow metres were calibrated prior to testing, and the experimental dependence of the output current signal on the flow was determined. The measurement error of the flow rate was 2.2%. The working fluids in this study were R113 and RC318, which have critical temperatures of 214.3 °C and 115.2 °C and critical pressures of 3.41 MPa and 2.78 MPa, respectively. The saturation temperature, specific heat and critical pressure of these refrigerants are considerably lower than those of water, which allowed us to achieve the desired parameters with less energy. Before entering the test section (location 10 in Fig. 1), the working fluid was heated in a pre-heater (location 8). Subsequently, the

refrigerant was cooled via cooling water in a recuperative heat exchanger (location 12). Circuit pressure was increased using a thermocompressor (location 1). The pressure and pressure drops across the inlet and outlet of the test section were measured using a pressure sensor, and the pressure measurement accuracy was 1%. The inlet and outlet temperatures were measured with ChromelCopel cable thermocouples with a cable diameter of 0.7 mm. Prior to the experiments, calibration was performed as follows. Cold thermojunctions were placed in the Dewar vessel. Hot thermojunctions were placed in a metrological ‘Fluke 9173’ dry-block thermostat, which has an absolute error of temperature stabilisation of ±0.006 °C. As a result, the individual characteristics of the Chromel-Copel cable thermocouples were determined. The temperature measurement accuracy of flow was 1%. The test section was heated with alternating current. The electrical current strength was measured using an LA 55-P current transducer. The measurement error of the electric power was 1%. The test section is shown in Fig. 2. Two vertical stainless steel tubes were used with heated lengths of 200 and 100 mm, internal diameters of 1.36 and 0.95 mm, and external diameters of 1.60 and 1.23 mm, respectively. The tube was electrically insulated and hydraulically sealed using PTFE seals. Electrodes were soldered to the tube with silver. Inlet and outlet collectors were located on platforms made of kaprolon, which has low thermal conductivity, to minimise heat losses from the test section to the experimental setup. The design of the test section is temperature compensated, and the inlet collector has a vertical degree of freedom. The platform is mounted on two vertical metal rods on which it is able to slide. To avoid vibration and create stability for the test tube, the platform of the inlet collector is pressed by a spring along the rods towards the tube. Measurements of the wall temperatures are collected by six Chromel-Copel thermocouples. The wires (diameter 0.2 mm) were welded via lasers to the working area of the tube in six crosssections (T1-T6, see Table 1) on opposite sides of the tube. This mounting method for the thermocouples created low thermal inertia for the sensors and allowed measurement of the average temperature of the wall along its perimeter. The inner wall temperatures were calculated using a correction for the wall conductivity. The temperature measurement error was 1%. The temperatures of the cold junctions of the thermocouples mounted in a metal box were measured using a thermistor. The test section was isolated with fibreglass to avoid heat exchange with air. The inlet and outlet tubes of the circuit were made of steel and were thermally insulated. Heat losses were caused by free air convection and the thermal conductivity of the hydraulic circuit. The estimates of heat losses on the thermocouple lead wires showed that they can be neglected. Total heat losses (Qlos, the heat lost to the environment at a certain inlet temperature but without the thermal load on the test section) were determined in each regime. A temperature compensation method was used to determine heat losses. At the entrance to the minichannel, the required flow temperature was set at a fixed mass flow rate. The outlet flow temperature was lower because of heat losses in the test section. The heat losses were compensated by heating the minichannel with electrical power such that the inlet and outlet flow temperatures were equalised. Electrical power was calculated from the measured values of voltage and current in the test section P = UI, where U and I indicate the voltage and current. Fig. 3 shows the experimental values of the heat losses from the inlet temperature for the various volume flow rates. The measurement results show that the heat losses depend only weakly on the flow rate and are mostly affected by the inlet fluid temperature.

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363

Fig. 1. Experimental setup: (1) thermocompressor, (2) tank, (3) and (5) filters, (4) balloon with refrigerant, (6) multistage centrifugal pump, (7) flow metres, (8) pre-heater, (9) roughing-down pump, (10) test section, (11) current transducer, (12) recuperative heat exchanger, and (13) bypass line.

The total heat losses under operating loads when boiling occurs can reach up to 20%. In this case, calculation of the heat flux density at the wall was performed using the electric power minus the heat losses calculated from the experimental function of the heat losses versus inlet temperature (see Fig. 3).

2.2. Data treatment During the experiments, the required parameters for the coolant at the inlet of the test section (i.e., pressure, temperature, and flow rate) were set, and starting from the minimum values, the electrical power was increased in increments of 5%. All measurements were collected using an automated data acquisition system. For each regime with fixed parameters, the maximum possible heating power value was applied, with the maximum limited by the maximum output of the power supply, the onset of dryout, or wall temperatures exceeding 350 °C. The distributions of inner wall temperature, fluid temperature, vapour quality, and heat transfer coefficient along the heated section were calculated as discrete values at each of the six thermocouple locations based on the measured values of wall temperatures, flow rates, and inlet and outlet liquid temperatures and pressures. The heat flux at each point was calculated as an average value along the tube using the values of the electric current and voltage drops across the heated section and the area of the inner surface of the heated section.

The mean local fluid enthalpy h at each thermocouple location was calculated from the heat balance equation. The local vapour quality x, assuming thermal equilibrium, is calculated as follows:

x¼

h  hl ; hg  hl

ð1Þ

where hl and hg are the enthalpies of the saturated liquid and saturated gas, respectively, evaluated at the local value of saturation temperature. The local heat transfer coefficient a at the location of each thermocouple is defined as follows:

a¼

q ; Tw  Tl

ð2Þ

where q is the inner wall heat flux to the fluid, Tw is the inner wall temperature, and Tl is the liquid temperature in the location of the thermocouple. Following the common method, the saturation temperature Ts is used as Tl in the quality region x > 0. Measurements of the distribution of the saturation temperature along the channel in the quality region were obtained via the pressure distribution. 2.3. Single-Phase heat transfer To check the validity of the present experimental method, a large array of single-phase heat transfer coefficients were used. The comparison between experimental and calculated singlephase data was presented without considering the heat losses, most of which were primarily due to the conductivity of the circuit

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in the cross-section of thermocouple T5 was used for comparison. Fig. 4 shows the generalisations for the single-phase heat transfer coefficients at the position of thermocouple T5. The experimental data (472 points) are in good agreement with the theoretical values calculated with Petuchov’s correlation modified by Gnielinski [22] and applicable for 2300 < Rel < 106 and 0.6 < Prl. Agreement between the experimental and calculated data confirmed the accuracy of both the primary and indirectly measured experimental values. 3. Results and discussion Experimental study on hydrodynamics and heat transfer were performed for R113 and RC318 in vertical channels with diameters of 1.36 and 0.95 mm and lengths of 200 and 100 mm, respectively. The parameters measured in the experiments were mass flow rate, pressure and temperature at the inlet and outlet of the test section, electric heating power, and temperature of the wall in six crosssections along the length of the minichannel. The experiments were performed for 195 regimes in which the inlet pressure-tocritical pressure ratio was pr = p/pcr = 0.15–0.9, the mass flux varied from 770 to 4800 kg/(m2 s), and the inlet temperature ranged from 30 to 180 °C. 3.1. Primary data

Fig. 2. Design of the test section for d = 1.36 mm.

and which predominated at the inlet portion of the test section where the greatest temperature difference occurred between the inlet and the heated components. Therefore, the wall temperature

Figs. 5–7 show the wall temperature in each of the six thermocouples T1-T6 versus the heating power used in typical regimes. All measurements were completed when CHF was reached. Analysis of the data graphs shows the area of convective heat transfer, nucleate boiling and film boiling. In Fig. 5, it can also be observed that the wall temperature was increased along the flow direction for a fixed electrical load. Figs. 6 and 7 show a regime in which the inlet temperature is close to the saturation temperature. Nucleate boiling was observed in the entire range of heat flux. Until the heat flux density reached at least q
110 kW/m2, nucleate boiling spread along the entire length of the minichannel. Furthermore, the heat transfer was reduced with increases in q. The wall temperature increased starting from cross-section T6. With increased thermal loads, the reduced heat transfer zone (film boiling) spread up to T3. Temperature dependencies in the cross-sections of T5 and T6 displayed inflection points in the area of film boiling. At these points, the wall temperature began to decrease as a result of intensification of heat transfer due to the possible irrigation of droplets on the wall from the flow core. Fig. 7 shows an enlarged-scale version of Fig. 6. In the region of q > 110 kW/m2, a significant temperature decrease (from crosssection T6 to T2) was observed before a sharp increase, which is shown in Fig. 6. In Fig. 7 and thereafter, these points are marked with ST. An intensification of heat transfer occurred, which led to a decrease in wall temperature. Nucleate boiling transformed into a new mode of heat transfer, probably as a result of combining vapour bubbles in conglomerates near the wall. As a result, the evaporation area of boundary layer inside the bubble increased. Further q increases led to film boiling. The experiments showed the influence of mass flow rate and inlet temperature on wall temperature and pressure drop. The wall temperatures at the thermocouple location T5 were selected because the heat losses at the outlet section of the channel are less than at the inlet. Figs. 8 and 9 show the effect of inlet temperature on the wall temperature and the pressure drop versus the heat flux. Fig. 8 clearly shows that increasing inlet temperature led to earlier boiling at a lower heat flux. In the convective region, the exper-

365

A.V. Belyaev et al. / International Journal of Heat and Mass Transfer 110 (2017) 360–373 Table 1 Coordinates of the cross-sections (mm). Diameter (mm)

T1

T2

T3

T4

T5

T6

1.36 0.95

40 20

70 35

100 50

130 65

160 80

190 95

Qlos, W

R113 d = 1.36 mm

30

Т, ºC 270

25 V, l/min 20

220

Т1 Т

film boiling

RС318 d = 1.36 mm G = 1900 kg/(m2s) pr = 0.52 Ts = 84º C Tin = 80 ÷ 81.5º C

Т2 Т Т3 Т Т4 Т

0.05 0.10

15

Т5 Т

170

0.15

10

Т6 Т

0.20 0.26

5 0 0

50

100

150

boiling, see Fig. 7

120

70

200

10

60

110

160

210

q, kW/m2

Тin, ºC

Fig. 6. Wall temperature versus heat flux.

Fig. 3. Heat losses versus inlet temperature.

Nu/Nucalc

d=0,95 mm

1.20

Т, ºC 95

start of boiling

d=1,36 mm

1.15

Т1

1.10

Т2 90

1.05

Т3

1.00

Т4

0.95

Т5

85

ST

0.90

Т6

0.85

80

0.80 0

10,000

20,000

30,000

40,000

50,000

10

60,000

60

R113 d = 1.36 mm G = 3570 kg/(m2s) pr = 0.59; Tin = 124º C Ts = 178º C

200

180

160

210

Fig. 7. Wall temperature versus heat flux (scale enlarged from Fig. 6).

Fig. 4. Generalisation of single-phase convection experimental data.

Т, ºC

110

q, kW/m2

Re

Т1

Т, ºC

Т3

R113 d = 1.36 mm G ≈ 2300 kg/(m2s) pr = 0.68 Тs = 188º C Т5

film boiling

Т2

270

Т4 nucleate boiling

Т5

160

Т6 single phase convection

220 Tin, ºC 55 89 125 168 180 d = 0.95 mm 88

170

140

120

120 0

100

200

300

P, W Fig. 5. Wall temperature versus heating power.

400

70

0

100

200

300

400

500

600

q, kW/m2 Fig. 8. Wall temperature versus heat flux.

700

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∆p, kPa

RC318 d = 1.36 mm G = 1800 ÷ 2570 kg/(m2s) pr = 0.685 Тs = 96º C

34

30

∆p, kPa

RC318 d = 1.36 mm Tin = 62.2 ÷ 65º C pr = 0.685

80

60 G, kg/(m2s)

Tin , ºC

film boiling

31 49 64 80 92

26

22

3950 40

2900 2230 1450

20

770 0

18 0

50

100

150

200

250

300

0

350

50

100

150

q,

q, kW/m2

200

250

300

Fig. 11. Pressure drop versus heat flux.

Fig. 9. Pressure drop versus heat flux.

imental points have the same slope, which indicates a constant heat transfer coefficient, as justified under conditions with a constant flow rate. Comparison of the diameters in Fig. 8 for inlet temperature Tin = 88–89 °C shows that if all other parameters were fixed, diameter reduction led to an increase of heat flux corresponding to the transition from convection to nucleate boiling and to an increase of CHF. Fig. 9 demonstrates the behaviour of the pressure drops in the convection and boiling regions versus heat flux. In single-phase convection, the pressure drop was reduced due to a reduction in liquid viscosity. When boiling began, the pressure drop began to grow, and with decreasing subcooling, it began earlier. The effect of mass flow rate on wall temperature and pressure drop versus heat flux is shown in Figs. 10 and 11. In the convective heat transfer region, Fig. 10 shows the characteristic change of the curve inclination versus the flow rate. Convective HTC depends on the flow rate, and therefore, the curves have different inclinations. After the single-phase convective region, all data points gather on the boil line. Fig. 11 shows that the increasing mass flow rate increased the pressure drop. The data on pressure drops presented in Figs. 9 and 11 are typical for conditions of subcooled flow boiling. The pressure effect on the wall temperature versus heat flux is presented in Fig. 12. Increasing the pressure and therefore the saturation temperature at all other fixed flow parameters increased the CHF and wall temperature in the flow boiling regime (see Fig. 13).

Т, ºC 210 190

R113 d = 1.36 mm G = 2700 kg/(m2s) Tin ≈ 85º C Т5

p, kPa 500 1000 1500 1750 2000 2300

170 150 130 110 90 0

100

200

300

400

Fig. 12. Wall temperature in section T5 versus heat flux at different pressures.

∆p, kPa

R113 d = 0.95 mm G ≈ 3200 ÷ 3800 kg/(m2s) pr = 0.68 Тs = 188º C

110 100 90

Тin , ºC 57 exp 87 129 160 175 calc

70

RC318 d = 0.95 mm pr = 0.52 Тs = 83º C Тin = 46.5 ÷ 49º C Т5

90

75

G, kg/(m2s) 3600 2550 1950

60

500

q, kW/m2

80

Т, ºC

350

kW/m2

60 50 40 0

200

400

600

800

1000

q, kW/m2 Fig. 13. Pressure drop versus heat flux compared with calculation using the homogeneous model; s marks the ONB.

3.2. Pressure drop generalisation

45 0

100

200 q,

300

kW/m2

Fig. 10. Wall temperature versus heat flux.

400

Measurements of the pressure drops in the test section were collected in each regime. Typical measurement results are presented in Figs. 9 and 11 and show the total pressure drops in the channel plus in the inlet and outlet collectors.

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Generalisation of the experimental data on pressure drops for flow boiling was performed using the homogeneous model, which is justified under the conditions of high pressure and subcooling. Calculation of the hydraulic friction coefficient in the channel was performed using Filonenko’s formula: 2

n ¼ ð1:821 lg Re  1:64Þ :

ð3Þ

Calculation of the hydraulic friction coefficients in the inlet and outlet collectors was performed based on the construction geometry with consideration of the pressure drops in the confusor and diffuser [23]. Special tests for determining the hydraulic friction coefficients were conducted to correct calculation errors because of the design features of the inlet and outlet sections. For each minichannel and working fluid, data were obtained for the pressure drops depending on the flow rate. Subsequently, the hydraulic friction coefficients for the inlet and outlet sections were corrected using the data tests. The pressure drop was calculated using the Darcy-Weisbach formula:

Dp ¼ n

G2 L ; 2 d

ð4Þ

and Eq. (3), where the dynamic viscosity l(T) in the Re number was
 w , and T w was calcalculated using the average temperature l T l þT 2 culated as the average value along the minichannel according to the wall temperatures in the thermocouple locations T w ¼ T 1 þT 26þ...þT 6 out and T l ¼ T in þT . 2 Good agreement was observed between the calculations and the experimental data in the regimes with high subcooling, high mass velocities and reduced pressure, primarily in the channel with the smaller diameter. A match with the calculations was also observed in the regime with low subcooling and high reduced pressure. Analysis of the generalisation showed that liquid subcooling to the saturation temperature at the inlet had a strong influence on the calculation agreement with the experimental data for the homogeneous model. Fig. 15 shows that the effect of temperature on the pressure drop depended on the heat flux compared with the calculation for the homogeneous model, where the onset of nucleate boiling (ONB) is marked by the symbol s. With increasing inlet temperature, the experimental points in the boiling region exceeded those of the calculation, which was caused by the pressure drop increase due to bubbles released from viscous fluid sublayer. When this phenomenon occurred, the flow pattern ceased to satisfy the conditions of the homogeneous model.

Fig. 14 shows the effect of pressure on the correspondence between the calculations for the homogenous model and the experimental data. At low reduced pressure pr = 0.29, a great increase in pressure drop and a discrepancy with the calculations after the ONB were observed. With reduced pressure pr = 0.52 and other constant flow parameters, the calculations for the homogenous model agreed with the experimental data. Fig. 14 clearly shows that when other the flow parameters and thermal loads were fixed, the pressure increase resulted in a significant reduction in the pressure drop of the coolant and reduced pumping costs. The calculations according to the homogeneous model allowed generalisation of the data, mainly in the range of high reduced pressure pr  0.5. Subcooling affected the convergence of the experimental and calculated data to a lesser degree because for each particular pressure, a temperature boundary of model applicability exists. Increasing pressure leads to an expansion of the heat flux ranges (up to q
qcr) and a decrease in the mass flow rate (down to G  850 kg/(m2 s)) and subcooling (down to Tsub  10 °C) for which the homogeneous model is applicable. Generalisation of the regimes in which a strong discrepancy exists between the calculation and the experiment when boiling is impossible within the homogeneous model. It is necessary to consider the changes in the flow pattern along the length of the minichannel.

4. Flow boiling heat transfer The local heat transfer coefficients of the six cross-section thermocouple locations T1-T6 (see Table 1) were determined based on the primary data. The temperature difference between the wall and the liquid was used to determine the heat transfer coefficient q = a(TwTl). The liquid temperature in each cross-section was determined based on the thermal balance. Fig. 15 shows the heat flux density versus wall overheating DTs = (Tw  Ts) for an almost saturated liquid at the inlet defined in the cross-sections of thermocouple locations T1, T2, T4, and T5. In this regime, the liquid boiled uniformly along the length of the channel. All of the points fall approximately on one dependency. The flow boiling pattern remained nearly unchanged, which is characteristic of low subcooling. The influence of convection on heat transfer was minimal. It is possible to obtain various regimes of flow and boiling along the channel at one value of the heat flux density. The last two points in the cross-section T5 are the precritical points. These points are marked with ST (see Fig. 7). In this

q,kW/(m2K) ∆p, kPa 60

ST

RC318 d=0.95 mm ρw ≈ 1930 kg/(m2s) Тin ≈ 46 ºC

50

pr = p/pcr

40

Тs=58 ºC Тsub ≈12 ºC

30

Тs=83 ºC Тsub ≈37 ºC

RС318 d = 0.95 mm Тin = 93º C ∆Tsub = 3 ÷ 4º C G = 2600 kg(m2s) Тs = 96º C pr = 0.685

100

0.29 calc 0.52 calc

Т1 Т2 Т4

20

Т5

10 0

50

100

150

200

250

q, kW/m2 Fig. 14. Pressure effect on pressure drop versus heat flux compared with calculation using the homogeneous model; s marks the ONB.

10 1

ΔTs

10

Fig. 15. Heat flux versus wall overheating for an almost-saturated liquid at the inlet of the channel.

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regime, we visually observed the effect when the wall temperature fell prior to the critical heat flux as a result of intensification of the heat transfer. Fig. 16 shows the dependency of a(q) for highly subcooled flow in cross-section T5, which is a typical example of the influence of mass flow rate on heat transfer at high subcooling. The dependence of a(q) on the mass flow rate is clearly visible, and the separation of the curves in the boiling region can be explained by the continuing influence of convection on heat transfer. The transitions from convection to boiling occur at the point where the slope of the curves changes, according to a specific law of dependency a  qn where n  0.4. Data on the mass flow rate effects obtained in the test sections with different diameters are compared in Fig. 17. The two regimes with low mass velocities have drops in the wall temperatures (points ST), after which a sharp deterioration of heat transfer occurred. For the data obtained in the test section of the larger diameter tube, the separation of the dependencies a(q) remained in the area of nucleate boiling. However, the dependencies with high mass flow rates (G > 3000 kg/(m2 s)) were located on one boiling curve. It can be assumed that as the diameter decreases, the role of the convective component in the heat transfer balance increases. Decreasing the mass flow rate (G < 3000 kg/(m2 s)) for the data collected in the minichannel with a larger diameter resulted in separation of the dependencies a(q) and a more rapid increase of the heat transfer coefficient versus heat flux. Such behaviour of the dependencies a(q) in Fig. 17 could be explained by the combined influence of the flow parameters (i.e., pressure, subcooling to the saturation temperature, and mass flow rate) and the diameter of the channel on the contribution of the individual components in the heat transfer balance. For the regime with mass flux of G = 2700 kg/(m2 s) and diameter d = 1.36 mm (indicated by the solid line), a change in the slope of the dependence a(q) was observed in the boiling region for q > 180 kW/m2. The change in slope is obviously a result of the conversion of the flow pattern and the boiling mechanism. Further decreases in the mass flow rate led to regimes that were characterised by intensification of heat transfer, which led to a decrease in the temperature of the wall (points ST) before the crisis of boiling occurred. In Fig. 17, these regimes are marked with a dashdotted line. The effect of liquid subcooling on the boiling curves q(DTs) in cross-section T5 is shown in Fig. 18. Increasing the inlet temperature leads to a change in the flow patterns and boiling regimes along the length of the channel. At the inlet temperature

α,kW/(m2K)

α ~ q0,4

RС318 d = 1.36 mm Тin = 46.5 ÷ 50º C ∆Tsub ≈ 50º C Тs = 96º C pr = 0.685 Т5

10

G, kg/(m2s) 3600 2700 2000 1400 850

1 10

100 q, kW/m2

1000

Fig. 16. Effect of mass flow rate on heat transfer coefficient versus heat flux for highly subcooled flow boiling.

α,kW/(m2K)

R113 Тs = 188º C pr = 0.68 Т5

ST

20

G, kg/(m2s) 3500 2500 1800 4600 3200 2700 1600 1000

d = 0.95 mm Тin = 161 ÷ 163º C d = 1.36 mm Тin = 161 ÷ 168º C

180 2 30

q, kW/m2

300

Fig. 17. Effect of channel diameter on heat transfer coefficient versus heat flux with various mass flow rates.

q, kW/m2 RС318 d = 1.36 mm Тs = 96º C G = 1900 kg/(m2s) pr = 0.685 Т5

200

Tin , ºC 31 48 62 78 91 47

pr = 0.29 Тs = 57º C G = 1400, kg/(m2s)

ST

20

1

ΔTs

6

Fig. 18. Effect of subcooling on heat flux dependency versus wall overheating.

Tin = 31–62 °C (corresponding to subcooling 65–16 °C), the boiling curves (which are typical for boiling conditions in subcooled flow) meet in a common dependency. The boiling curves with lower subcooling, including those for the relatively small reduced pressure, display a different dependence. The differences can be explained by possible changes in the flow pattern and reduced impact of the forced convection on the intensity of heat transfer. The regime with input temperatures close to Ts (Tin = 91 °C) is characterised by increasing heat flux with nearly constant DTs. In this case, developed boiling is the dominant heat transfer mechanism, and the influence of convection is minimal. The last ST point in this regime is the pre-crisis point and shows the wall temperature decrease before the crisis. Four regimes obtained in the two test sections with the same flow parameters for subcooled boiling are compared in Fig 19. The data are presented for cross-sections T4 (d = 1.36 mm) and T5 (d = 0.95 mm), which correspond to the same related heated length. The experimental curves a(q) for the different diameters and the same inlet temperatures correspond to each other within the measurement accuracy. Diameter had a negative effect on critical heat flux. Fig. 20 shows the typical dependency a(q) for the regimes in which the inlet temperature is close to the saturation temperature of the liquid. The data are presented for different diameters, reduced pressures, and mass flow rates, and for various crosssections of the minichannel.

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α,kW/(m2K)

RС318 Тs = 83º C pr = 0.52

∆p, kPa 30 28

Tin, ºC, G, kg/(m2s)

10

d = 1.36 mm Т4

31, 2200

d = 0.95 mm Т5

32, 2500

47, 2200

film boiling in cross section Т2 RС318 pr = 0.685 Tin = 96º C; G = 1800, kg/(m2s) Тs = 96º C d = 0.95 mm

ST in cross section Т2

26 24

Exp 47, 2500

22 20 0

1 10

100

50

100

150

q, kW/m2

1000

q, kW/m2

Fig. 21. Pressure drop versus heat flux.

Fig. 19. Effect of subcooling and diameter on heat transfer coefficient versus heat flux for subcooled flow.

α,kW/(m2K)

RС318 film boiling onset ST Tin , ºC; G, kg/(m2s)

10

pr = 0.52 Тs = 83º C d = 0.95 mm

80, 2500 Т5

pr = 0.685 Тs = 96º C d = 0.95 mm

96, 1800, Т2

pr = 0.685 Тs = 96º C d = 1.36 mm

film boiling

92, 1900 Т6

in the heat transfer coefficient and the pressure drop are associated with each other and indicate changes in flow patterns. In these modes, it is possible to control the growth of dry spots to obtain film boiling along the entire length of the minichannel. In this study, a variety of flow boiling regimes for uniform heating of the tube walls were observed in the vertical minichannels. Most of them are typical for conventional channels. For limited cases, the wall temperature dependences of the possible flow patterns are summarised in the graphical diagrams shown in Fig. 22. (a) Low liquid subcooling at the inlet and a comparatively low mass flow rate: In this case, with increases in the heat flux, it was possible to obtain the next regimes of flow boiling, i.e., boiling of subcooled liquid C-O, developed boiling O-D, boiling at the annular flow pattern D-F, ST transition regime

1 10

100

1000

q, kW/m2 Fig. 20. Heat transfer coefficient versus heat flux when inlet temperature is close to saturation temperature.

The dependences a(q) begin at the regime of developed boiling. The boiling lines have approximately the same inclination. Furthermore, with increasing heat flux, the boiling curves abruptly approach the boiling mode ST. In this case, the wall temperature fell at 1–2 °C (or in the mode illustrated for cross-section T6, 2.5 °C). The wall temperature might decrease only as a result of heat transfer intensification on the inner surface of the tube. The intensification of boiling can be caused by two factors: (1) an increase of the evaporation zone in the vicinity of dry spots (by either an increase in the number of nucleation sites or a geometric increase in the evaporation zone due to the merging of bubbles) or (2) an increase in the heat transfer in the flow core, which is possible when the flow pattern changes as a result of the steam core formation. Further increase of the thermal load in the ST regime did not lead to a corresponding increase of the heat transfer coefficient. Fig. 20 shows several points with approximately the same values for the heat transfer coefficient. A detailed analysis of the pressure drop dependencies versus heat flux for these regimes allows the identification of the corresponding transition zones. For the regime with an inlet temperature Tin = 96 °C, shown in Fig. 20 for crosssection T2 (indicating the change in flow pattern along the entire channel length), the graph of pressure drop versus heat flux (Fig. 21) shows the increase in pressure drop in the boiling region, minimal changes in values in the regime ST, and further increases with the transition to the film boiling. It is obvious that the changes

Fig. 22. Diagram of basic flow boiling patterns: xb.s. - vapour quality at boiling onset, xcr - crisis of heat transfer, Tw - wall temperature, T f - mean temperature of the fluid in the flow core, and Ts - saturation temperature.

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E-F, film boiling F-G, droplet deposition on the wall of the channel from the flow core G-H, and superheated vapour H-I. (b) High liquid subcooling at the inlet and high mass flow rate: With increases in heat flux, the next regimes are observed, namely, subcooled boiling C-F and crisis of heat transfer F-O. For the regimes studied, it can be stated that with increasing reduced pressure, liquid subcooling and mass flow rate, the flow boiling patterns tend towards case b. The E–F region expands as the diameter decreases. At point C, where the transition from the convective heat transfer to boiling occurs, the wall temperature is changed in different ways. In case b, the wall temperature decrease is not observed, in contrast to case a in which this decrease does occur. This observation suggests that in case a, nucleate boiling significantly affects the heat transfer in the C-O region, unlike case b.

q, kW/m2

R113 d=1.36 mm pr=0.59 Тs=180 ºC Тin= 167 ºC G ≈ 1800 kg/(m2s) Т5 exp calculation by (5), (8) (11), (13) (14) (15) [21]

350 300 250 200 150 100 50

x

0.10

ð5Þ

It is assumed that convective heat transfer has the same effect as in the single-phase turbulent flow:

qconv ¼ aconv ðT w  T l Þ;

ð6Þ

where aconv for turbulent flow is calculated with Petuchov’s correlation modified by Gnielinski [22]:

Nu ¼



ðn=8ÞðRe  1000ÞPr

Prl 1 þ 12:7ðn=8Þ1=2 ðPr2=3  1Þ Prw

0:25 ð7Þ

2

In the literature, the most studied regime of boiling in a minichannel is the developed boiling regime, which is characterised by low subcooling at the inlet and moderate mass velocities. Such regimes were partially observed in this study and described in the previous section and are presented via graphic generalisation in Fig. 23a. The developed boiling in our experiments was observed at low mass velocities and inlet temperatures close to saturation. The known methods [2,3,7,8,10,21,24,25] of calculating heat transfer in flow boiling deemed most appropriate for the conditions and parameters of the current experiments were selected to generalise the regimes of developed boiling. The works of Lazarek and Black [7] and Wambsganss et al. [10] are two of the first in which the empirical formulas were obtained for flow boiling of the refrigerants in minichannels. In [20], it is shown that among the 28 existing correlations of flow boiling heat transfer, the Fang [21] correlation makes the best predictions for all 397 experimental data points. Analyses of primary data results showed that convection has a significant effect on heat transfer. Therefore, to create a calculation method for heat transfer in subcooled flow boiling with high mass flux, it is necessary to consider both the heat transfer from the wall due to evaporation in the bottom of the bubble and the convective heat transfer from the wall surface not occupied by bubbles. Considering the small size of the bottoms of the bubbles and the lack of experimental data in these conditions with respect to the number of active nucleation sites on the wall, the only possible approach is

0.00

q ¼ qboil þ qconv :

n ¼ ð1:821 lg Re  1:64Þ :

5. Generalisation of flow boiling

0 -0.10

to neglect the contact area of the vapour-wall compared with the wall surface. In such conditions, it is possible to assert the independence of the heat transfer mechanisms of single-phase convection and evaporation. The studies by Dedov et al. [3,25] developed such an approach in creating a calculation method for heat transfer in subcooled flow boiling with high mass flux and suggested a calculation correlation in the following form:

0.20

Fig. 23. Heat flux versus vapour quality for the regime with developed boiling.

To calculate qboil under the conditions of developed boiling in Eq. (5), it is expedient to use the correlation proposed by Yagov [24]:

hlg DT s k2 DT 3s 1þ mrT s 2Ri T 2s
 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  1 þ 1 þ 800B þ 400B

!

qboil ¼ 3:43  104

B¼

hlg ðqg mÞ3=2

rðkT s Þ1=2

ð8Þ

;

ð9Þ

where all properties are defined at the saturation temperature Ts. For calculation of qboil under conditions of subcooled flow boiling, based on the results of Dedov et al. [25], it is possible to use the modified correlation (8):

hlg DT s k2 DT 3s 1þ mrT s 2Ri T 2s
 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  1 þ 1 þ 800B þ 400B :

!

qboil ¼ 0:47  104

ð10Þ

The generalisation of the experimental data was also performed with Chen’s [2] correlation, and in general, it reflects Eq. (5).

a ¼ Eaconv þ Saboil

ð11Þ

aconv ¼ 0:023Re0:8 Pr0:4 kl =d aboil ¼ 0:00122 ( E¼

X¼

!

0:49 k0:79 c0:45 l p;l ql 0:24 r0:5 l0:29 hlg q0:24 g l

DT 0:24 Dp0:75 s s

ð12Þ

if x 6 0:1  0:736 2:35 X1 þ 0:213 ; if x > 0:1

1;

 0:9  0:5 qg 1x x ql

ll lg

!0:1 ;

S¼

1 1 þ 2:35  106 Re1:17

Based on the fact that the experimental data were obtained under conditions of high reduced pressures on the refrigerants, instead of the original empirical correlation (12) [26] used to calculate the heat transfer due to boiling (aboil) in Eq. (11), Cooper’s [27] empirical correlation is a better choice. 0:55 0:5 0:67 aboil ¼ 55p0:12 ð0:4343log10 pr Þ M q r

ð13Þ

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This correlation (13) was obtained for refrigerants and other fluids in saturated nucleate pool boiling at a wide range of reduced pressures (pr = 0.001–0.9). Fig. 23 shows the comparison of the experimental data with the values of heat flux density calculated as a function of vapour quality in the regime with the flow parameters most appropriate for developed boiling conditions. In Eq. (5), qboil was calculated using Eq. (8). The results of the calculations using Eqs. (5), (8) and (11), (13) are in good agreement with the experiment. The calculations using the correlations of Fang [21], Lazarek and Black [7]

Nu ¼ 30Re0:857 Bo0:714

ð14Þ

and Tran et al. [10] 0:3

a ¼ 840ðBo2 Wel Þ ðql =qg Þ

qcalc/qexp

equations (5) and (10)

1.90 1.60 1.30 1.00 0.70 0.40 0.10 -2

0:4

-1.5

-1

ð15Þ

do not correspond to the experimental results, and therefore, their use in the generalisation does not make sense. Obviously, this situation occurs because these correlations were obtained for smaller ranges of mass velocities (up to G  800 kg/(m2 s)) and pressures (up to pr  0.2). No formulas more suitable for this study’s range of parameters were found in the literature. The generalisation of the regimes with developed boiling and the same diameter, pressure and working fluid in the location of thermocouple T6 at different mass flow rates is presented in Fig. 24. In conditions of low subcooling in the region of positive values of vapour quality, the calculations using Eqs. (5), (8) and (11), (13) are within the acceptable range of 30% deviation. For x < 0, the data scatter increases. Flow boiling regimes with high subcooling had their own characteristics. Forced convection has a strong influence on the dependency q(DTs), and liquid boils at a higher wall overheating [3]. For generalisation of the regimes with high subcooling, formula (5) was used in which the heat transfer by boiling qboil was calculated using Yagov’s modified correlation (10). The results of data generalisation for flow boiling at high reduced pressures for both diameters and both liquids are presented in Fig. 25–27 as the ratio of the calculated density of the heat flux to the experimental value (in cross-sections T1-T6) versus vapour quality. The results of the generalisation of the subcooled flow boiling regimes, which were calculated using Eqs. (5) and (10), are shown in Fig. 25. The calculations include 1587 points, of which 1442 (91%) are within the acceptable 30% range of deviation. The main array of the data lies in the negative range of vapour quality. Most of the points lying in the region of positive values of x were

x

-0.5

0

0.5

Fig. 25. Generalisation of the experimental data for subcooled flow boiling; qcalc/ qexp versus local vapour quality.

qcalc/qexp

equations (5) and (8)

1.90 1.60 1.30 1.00 0.70 0.40 -1

-0.75

-0.5

-0.25 x

0

0.25

0.5

Fig. 26. Generalisation of the experimental data for developed boiling; qcalc/qexp versus local vapour quality.

qcalc/qexp

equations (11) and (13)

2.80 2.50 2.20 1.90 1.60

qcalc/qexp

R113 d = 1.36 mm pr = 0.59 Тs ≈ 179º C Тin ≈ 154 ÷ 170º C Т6

2.20 1.90 1.60

G, kg/(m2s) 4600 3570 2700 1800 4600 3570 2700 1800

1.30 1.00 0.70 0.40 0.10 -0.20

-0.10

0.00

0.10

0.20

x Fig. 24. Comparison of calculated data with experimental data for flow boiling. Filled markers show calculation via Eqs. (5) and (8); unfilled markers indicate calculation using Eqs. (11) and (13).

1.30 1.00 0.70 0.40 0.10 -2

-1.5

-1

x

-0.5

0

0.5

Fig. 27. Generalisation of the experimental data for subcooled and saturated boiling; qcalc/qexp versus local vapour quality.

obtained with RC318 under relatively low reduced pressure pr = 0.52 in the test section with a diameter of 1.36 mm and with an inlet temperature close to the saturation temperature. The remainder were obtained under conditions of weak local subcooling (in cross-sections T4-T6), but the inlet flow parameters were typical for flow boiling regimes with high subcooling.

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The results of the generalisation of the developed boiling regimes, which were calculated using Eqs. (5) and (8), are shown in Fig. 26. The calculations include 1364 points, of which 1241 (91%) are within the acceptable 30% range of deviation. The main array of the data fits into the vapour quality range of 0.25 < x < 0.25. Certain points correspond to negative values of x, up to x = 1 and were obtained for small values of G and local x at the entrance of the minichannel (T1–T3). The intensity of the heat transfer is defined by the flow parameters and flow patterns. At the same values of vapour quality, depending on the values of the mass flux and subcooling to the saturation temperature at the inlet, it is possible to obtain the flow patterns and heat transfer corresponding to both subcooled and developed boiling along the length of the channel. Comparison of the results of calculations using Eqs. (11) and (13) with our own experimental data was performed on all regimes, including saturated and subcooled flow boiling. This approach does not consider the type of boiling regime. The results are presented in Fig. 27. It was compared 3319 data points, 1541 (46.4%) of which are within the 30% range of deviation. The main portion of the calculated data, which matches the experiment, lies within the vapour quality range from 0.5 to 0.25. As observed from the results of the data generalisation, the division of the regimes by boiling type and selection of appropriate calculation methods works better than the universal approaches of Chen [2] and other authors. In this study, certain regimes were obtained in which heat transfer has distinctive features. These regimes could not be generalised with the known correlations presented in the existing literature and were mostly obtained in the minichannel with a diameter of 0.95 mm. Fig. 28 shows a comparison of the calculated values of the heat flux density with the experimental values versus the vapour quality in cross-section T5 for the demonstration regime with highly subcooled flow boiling and a high mass flow rate. The graph shows a linear increase of the experimental values of the heat flux versus the vapour quality. It can be assumed that the strong influence of forced convection suppresses nucleate boiling on the channel wall. The estimates show that under high reduced pressure, the size of the vapour bubbles is 108 m and the thickness of the viscous sub-layer is 106 m, and hence, the formation of vapour bubbles within the viscous sub-layer is possible. In the graph of the pressure drop versus the heat flux density (Fig. 29) for the presented regime, when q > 400 kW/m2, an increase in the pressure drop was observed, which indicated the release of the vapour bubbles to the flow core from the viscous sub-layer. A group of such

q, kW/m2 2,500

R113 d=0.95 mm pr=0.68 Тs=188 ºC Тin= 86 ºC G ≈ 3300 kg/(m2s) Т5

2,000 1,500

∆p, kPa 55 R113 d = 0.95 mm pr = 0.68 Тs =188º C Тin = 86º C G ≈ 3300 kg/(m2s)

50

45 0

200

400

600

Fig. 29. Experimental pressure drop versus heat flux.

regimes with ‘suppressed boiling’, which displayed the characteristic features and strong influence of convection, was identified. This heat transfer regime was observed primarily in the test section with diameter d = 0.95 mm and with R113. The dependence of the heat flux versus the vapour quality compared with the calculations using formulas (5), (8) and (11), (13) is shown in Fig. 30 for the regimes in which a transition occurred from heat transfer with saturated boiling to the regime ST. When x > 0.08, the calculated data deviate strongly downward from the experimental data, which occurred due to decreases in the wall temperature. The regime ST was determined in both minichannels. In the 1.36 mm minichannel, the duration of the regime did not exceed 1–2 steps of the heat load (1–2 points) before a sharp increase was observed in the wall temperature. The duration of the regime in the other minichannel (d = 0.95 mm) was substantially longer, as shown in Fig. 30. This group of regimes requires a detailed study that must be conducted in the future. All of the boiling regimes were approximately divided into four groups depending on the combination of mass flow rate G and subcooling to the saturation temperature at the inlet of the test section DTsub. Fig. 31 shows a map of the boiling regimes where the ‘existence’ areas of developed boiling, subcooled boiling, suppressed boiling, and the regime ST are presented. The black points with decreasing DTsub indicate the approximate boundary of subcooled boiling completion and the transition to developed boiling. A region with a transition boiling regime also appears between them. The unfilled rhombus points indicate the beginning border of the

exp

q, kW/m2

calculation by

100

x = 0.08

RC318 d=0.95 mm pr=0.685 Тs=96,5 ºC Тin= 95,5 ºC G ≈ 2000 kg/(m2s) Т2

(5), (10) (11), (13)

800

q, kW/m2

80

(7)

saturated boiling

60

1,000

40

500

20

exp

regime ST

calculation by (5), (8)

0

(11), (13)

0 -1.1

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

x Fig. 28. Heat flux density versus vapour quality for the regime with highly subcooled flow boiling.

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

x Fig. 30. Heat flux density versus vapour quality for the saturated boiling and regime ST.

A.V. Belyaev et al. / International Journal of Heat and Mass Transfer 110 (2017) 360–373

373

characteristics in minichannel from the results obtained in conventional tubes was not observed.

G, kg/(m2s)

subcooled boiling

5,000

developed boiling

4,000

suppressed boiling (obtained on d = 0.95 mm) possibility of the regime ST

Acknowledgements This work was supported by RSF Grant 16-19-10457.

3,000

References 2,000

1,000

0 0

20

40

60

80

100

120

140

∆Tsub Fig. 31. Map of the boiling regimes: solid line – subcooled boiling above, dashed line – developed boiling inside, dotted line – ST regime inside.

developed boiling regime. The unfilled circular points show the completion border of the depressed boiling regime, after which the subcooled boiling regime usually begins with decreasing DTsub. The asterisk points indicate a possible transition from developed boiling to the regime ST. The length of the regime ST along the channel depended on the flow parameters and the diameter of the minichannel and did not usually exceed the output half of the channel length. All of these points, except for the unfilled circular points, form nominal boundaries (indicated by lines: solid line - black circular points, dashed line - unfilled rhombus points, dotted line - asterisk points) of the completion and beginning of the boiling regimes. 6. Conclusions This paper presented the results of an investigation of flow boiling heat transfer of R113 and RC318 in two vertical channels with diameters of 1.36 and 0.95 mm and lengths of 200 and 100 mm, respectively, under different combinations of reduced pressure, liquid subcooling, mass flux and heat load. These governing parameters were varied within the following ranges: pr = 0.15–0.9, mass flux G = 770–4800 kg/(m2 s), inlet fluid temperature Tin = 30– 180 °C, and q from boiling onset up to crisis (maximal value of CHF was qcr = 907 kW/m2). The analyses examined the influence of the various flow parameters on the heat transfer of subcooled flow boiling in the channels with small diameters. The results for wall temperature, pressure drop and heat transfer data for various parameters are typical for subcooled flow boiling. For the full range of flow parameters, univocal influences of mass flow rate, pressure diameter and fluid subcooling on heat transfer, pressure drop and CHF were observed. Increases in mass flow rate and pressure extend the heat flux range in the convection regime and enhance CHF, and inlet temperature increase and mass flow rate decrease lead to the opposite effect. When other flow parameters and heat flux are fixed, increases of pressure result in a significant reduction in pressure drop. The paper presented comparisons between the experimental and calculated data for flow boiling heat transfer. The results of the data generalisation allowed us to conclude that division of regimes by boiling type is more appropriate than the universal approaches presented in the previous literature. It was shown that for high reduced pressure (pr > 0.4) qualitative differences in flow boiling and convection heat transfer

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