# Fill-In and Boiling Transition Characteristics during the Liquid Oxygen Chill-Down Process in a Vertical Exit-Contracted Pipe

Authors: Jiaqi Zhang; Ke Wang; Lanwei Chen
Journal: International Journal of Aerospace Engineering
 (2022)

---

## Abstract

Liquid oxygen chill-down in a vertical exit-contracted pipe was investigated experimentally. The wall temperatures were recorded in detail to describe the filling and chill-down process of the experimental section. Two quenching fronts, the exit one and the inlet one, were detected, and their propagations were found. Results show that the chill-down process is controlled mainly by the formation and propagation of quenching front, which are determined by the pressure level. With the increase of pressure, the roles of both propagation of quenching front and inlet quenching front undergo decreasing. On the vertical section, the effect of circumferential position was discussed in detail and the dominant point was identified, which determines the boiling transition time of the dominated points on the current cross-section. Based on the experimental data, two correlations were suggested for dominant point and dominated points, respectively, to predict heat flux on Leidenfrost, heat transfer coefficient on Leidenfrost, and critical heat flux. One equation was approved to predict heat transfer coefficient on critical heat flux point for both sorts of points. All of these correlations could produce reliable predictions.


---

## Body

## 1. Introduction

Liquid oxygen (LO2) and liquid methane (LCH4) are characterized by low-cost, nontoxic, high performance compared to hypergolic propellants, and both of them could be produced on Mars [1, 2]. In this way, a number of projects have been put forward to support future exploration missions using this cryogenic propellant combination [3]. Systematical demonstrations indicated that for space propulsion using this combination, the primary technical risks included the cryogenic fluid management (CFM) and the low-pressure engine technology [4–6].A number of studies have been put forward to improve the technology readiness level (TRL) for CFM system [3]. For this system, cryogenic fluid could be the liquid phase when the container or pipe are cooled to the liquid temperature. In this way, cryogenic chill-down in the transportation pipe is one of the basic processes here, especially for refueling and transportation of the cryogenic propellants [7]. With the cryogenic fluid first flowing into the pipe with room temperature, flash vaporization would happen in the pipe. Figure 1 gives a typical process of cryogenic chill-down. With the pipe temperature decreasing, fluid pattern in the pipe undergoes film boiling, transition boiling, nucleate boiling, and single phase in sequence. These 4 flow patterns are divided by 3 boiling transition points, Leidenfrost (LFP), critical heat flux (CHF), and onset of nucleate boiling (ONB) [8].Figure 1
Typical boiling curve and flow patterns for chill-down process.A number of studies have been put forward to investigate the cryogenic chill-down in the transport pipeline. A series of visual studies have been put forward [9, 10], and based on them, a series of phenomenological models have been set up to model the cryogenic chill-down process [11, 12]. For setting up more reliable model, recently, a number of experimental studies have been performed [13–21] to correlate the heat transfer coefficients for various boiling patterns and boiling transition points (LFP, CHF). It is believed that in the current stage, correlations approved by Darr et al. [15, 16] could obtain general applications for transport pipe. Based on the improvement on models, a couple of reliable numerical results have been obtained [22, 23].For low-pressure cryogenic engine, the primary technical difficulty is the instable combustion associate with the two-phase injection produced by cryogenic chill-down [24]. As Figure 2 [25] shows, taking LO2 for example, before start-up, components upstream of point G would be chilled completely by LO2 outflow through the prechilling valve. During the start-up process, liquid propellant flows into the components downstream of point G in ambient temperature, which produces two-phase injection and instable combustion in the combustion chamber of the engine [24]. Basically, this phenomenon could be avoided by chilling the components downstream point G before start-up [26]. However, in most cases, the feasibility of this process is determined mainly by the engine procedure. Furthermore, it has been found that two-phase injection could not be avoided even after start-up process [27].Figure 2
Sketch of a typical low-pressure cryogenic engine [25].Cryogenic chill-down in low-pressure engine is characterized by the components downstream point G, with a flow contraction on the exit, known as injector, which could be reduced to an exit-contracted pipeline as Figure3 shows [8, 28]. This is much different from that in transportation pipe taking CFM system as the investigation background, without any flow contraction on the exit.Figure 3
Pipe with a contraction on the exit.In the previous studies, cryogenic chill-down in exit-contracted pipe has not been distinguished from cryogenic chill-down in transport pipe. A series of pioneered experimental studies on cryogenic chill-down in the horizontal exit-contracted pipe have been performed by the present authors [8, 28, 29]. Chill-down process was discussed, and boiling transition points were correlated. It has been found that boiling transition points could be well correlated by formats from pool boiling for the exit-contracted pipe, rather than formats from flow boiling from transport pipe [8]. However, the latest study showed that the quenching front seems to be formed in the center length in the horizontal exit-contracted pipe, then propagates to the both ends of the pipe during the chill-down process. In addition, gravity or the circumferential position (bottom, top, or side) plays significant role [29]. This induces extra difficulty to model the heat transfer and transition boiling points in exit-contracted pipe, which is much different from that in transport pipe [16].It has been concerned that the effects of both gravity and propagation of the quenching front play significant roles in the previous study that [29]. In the present study, for excluding the effect of gravity, vertical pipe would be applied instead of horizontal pipe. In this way, experimental study would be performed to investigate the chill-down process by a constant flow rate of LO2 in a vertical exit-contracted pipe. A series of tests with the same flow rate and various pressure in the pipe would be performed. Chill-down process would be tracked, by which the propagation of quenching front would be investigated. Based on these data, boiling transition points would be discussed, and qi and hi on these points would be correlated for vertical pipe section.


## 2. Experimental Methodology

### 2.1. Experimental Platform

Figure4 gives the experimental platform applied in the present study. It is the LO2 branch of a typical test platform for cryogenic engine. Compared to the previous one applied in the previous studies [8, 28], the present platform has been upgraded, where the previous 100 L/5.5 MPa LO2 tank is replaced by a 500 L/10 MPa one. Other parts of the present platform are the same with the previous ones. As shown in the figure, flow rate of the fluid is controlled by the Venturi nozzle.Figure 4
Experimental system of the present study.


### 2.2. Experimental Section and Measurement Approach

Figure5 gives the experimental section in detail. The shape of experimental section applied could be drawn in Figure 5(a), which also indicates the necessary sensors measuring the pressure and temperature of the fluid. As shown in the figure, a pressure sensor (PT301) and a temperature sensor (PT100) are set up on the experimental section to measure the pressure and temperature of the fluid, respectively, in the section. 13 To sensors (T-type thermocouples) were welded on the outer surface of the experimental section, and they were distributed on 5 cross-sections (various Lse) as Figure 5(a) shows. Figure 5(b) gives the cross-section (vertical) on Lse=1.55m, where the 2 sensors, denoted by 1.55-1 and 1.55-2, were welded on the bottom and south-side of the pipe, respectively. The cross-section (horizontal) for other Lse could be shown in Figure 5(c), which shows for every section, 3 sensors were set up on the west, south, and east of the pipe in turn (2 sensors on the west and south for Lse=0.3m, denoted by 0.3-1 and 0.3-2). To data were recorded by temperature scanner (EX32A). All of the above sensors are with the scan rate of 1000 Hz.Figure 5
Details on the experimental section, unit: mm.
(a)
Experimental section(b)
Cross-section onLse=1.55m(c)
Cross-section onLse=1,0.75,0.5m


### 2.3. Other Conditions

For minimizing the potential deviations including nitrogen solution in LO2 and flow rate oscillations, the test process were well designed and illustrated as shown in reference [1], which would not be repeated here.


## 2.1. Experimental Platform

Figure4 gives the experimental platform applied in the present study. It is the LO2 branch of a typical test platform for cryogenic engine. Compared to the previous one applied in the previous studies [8, 28], the present platform has been upgraded, where the previous 100 L/5.5 MPa LO2 tank is replaced by a 500 L/10 MPa one. Other parts of the present platform are the same with the previous ones. As shown in the figure, flow rate of the fluid is controlled by the Venturi nozzle.Figure 4
Experimental system of the present study.


## 2.2. Experimental Section and Measurement Approach

Figure5 gives the experimental section in detail. The shape of experimental section applied could be drawn in Figure 5(a), which also indicates the necessary sensors measuring the pressure and temperature of the fluid. As shown in the figure, a pressure sensor (PT301) and a temperature sensor (PT100) are set up on the experimental section to measure the pressure and temperature of the fluid, respectively, in the section. 13 To sensors (T-type thermocouples) were welded on the outer surface of the experimental section, and they were distributed on 5 cross-sections (various Lse) as Figure 5(a) shows. Figure 5(b) gives the cross-section (vertical) on Lse=1.55m, where the 2 sensors, denoted by 1.55-1 and 1.55-2, were welded on the bottom and south-side of the pipe, respectively. The cross-section (horizontal) for other Lse could be shown in Figure 5(c), which shows for every section, 3 sensors were set up on the west, south, and east of the pipe in turn (2 sensors on the west and south for Lse=0.3m, denoted by 0.3-1 and 0.3-2). To data were recorded by temperature scanner (EX32A). All of the above sensors are with the scan rate of 1000 Hz.Figure 5
Details on the experimental section, unit: mm.
(a)
Experimental section(b)
Cross-section onLse=1.55m(c)
Cross-section onLse=1,0.75,0.5m


## 2.3. Other Conditions

For minimizing the potential deviations including nitrogen solution in LO2 and flow rate oscillations, the test process were well designed and illustrated as shown in reference [1], which would not be repeated here.


## 3. Experimental Results

### 3.1. Basic Results

Four tests were performed, and related conditions and results could be listed in Table1. It shows that the present series of tests are all with the similar flow rate and various Ainj. With the decrease of Ainj (Exp. 1~4), pressure in the experimental section shows the increasing manner. This indicates that the Pss range is from 0.328 to 1.325 MPa.Table 1
Experimental conditions and results.
ParametersExp. 1Exp. 2Exp. 3Exp. 4Injector typeOrificePintlePintleOrificeAinj (mm)110.667.23312ṁ (kg/s, start)0.440.4350.4290.417ṁ (kg/s, end)0.450.4440.4380.426G (kg/(m2∙s), end)2546251324782411Re (end)259192270824319074329295Tp (K, end)101.5104112115Tsat−Tp (K, subcooling, end)1.652.063.39.64Ppeak (MPa, start)0.5860.8431.6783.049Pss (MPa, end)0.3280.410.771.325


### 3.2. Data Processing and Boiling Transition Points

Parameters in the pipe as well asTo data were measured for all of the four tests. By processing To data, Ti and qi were obtained because most discussions next would be based on these 2 parameters. Here, Ti would be determined according to reference [30], and qi would be obtained by numerical methods introduced in the previous studies [28], which would not be repeated here anymore.Based onTi and qi data, boiling curves could be drawn. In this way, boiling transition points, LFP, and CHF could be determined as well. These two points could be identified in the boiling curve easily, which indicate the minimum qi point and maximum qi point, respectively.


### 3.3. Uncertainty

The present study focuses on the comparison between experimental values and predicted values forTLFP, qLFP, TCHF, and qCHF. The experimental values depend mainly on the To measurement, physical properties as well as the geometric parameter of the pipe. On the other hand, as shown in the correlations, the predicted values depend mainly on the measured pressure and geometric parameter of the pipe. These factors could be shown in Table 2. Furthermore, the respective mean absolute errors (MAE) can be defined as Equation (1) shows [31].
(1)MAE=1N∑Vexp−VpreVexp×100%.Table 2
Summary of the uncertainties.
ParametersUncertaintyFluid pressure (%)0.5Fluid temperature (K)1Outer wall temperature (K)1PipeDi and Do (mm)0.01Mass flow rate (%)1To (K)1Ti (K)2qi (%)5


### 3.4. Basic Chill-Down Process

Figure6 shows all of the Ti curves as well as Tp, Tsat, and Pp curves to show the chill-down process for Exp. 1. As shown in the figure, during the chill-down process, Tp, Tsat, and Pp curves show the similar manner with the curves recorded in the previous studies [8, 28]. It also shows that a typical Ti curve is composed by three sequent phases as follows.
(1)
Phase I: the initial linear decrease phase. In this phase,Ti decreases in a linear manner, which indicates the inner flow is on the film boiling. LFP, the transition point between film boiling and transition boiling, could be seen as the transition point between phases I and II as well(2)
Phase II: the sudden decrease followed by phase I. This phase is with the shortest period, in whichTi decreases dramatically. This phase involves both transition boiling section and nucleate boiling section, and CHF, the transition point between transition boiling and nucleate boiling, sometimes would be seen as the central point of it(3)
Phase III: the gradual decrease followed by phase II. In this phase,Ti decreases gradually, which indicates the inner flow is the single-phase flow. As shown in Figure 1, the transition point between phase II and phase III is denoted as ONB, which always indicates the end of chill-downFigure 6
Tested data curves for Exp. 1 (0.45 kg/s,Pss=0.328MPa).As shown in Figure6, for Exp. 1, Ti on Lse=1.55m decreases at first, followed by Lse=0.3m, 1 m, 0.75 m, and 0.5 m in turn. Similarly, LFP happens in Lse=1.55m at first, followed by Lse=0.3m, 1 m, 0.75 m, and 0.5 m in turn. This indicates that two quenching fronts (QF) are formed on the exit and inlet of the experimental section independently. In the current stage, the exact positions of them could not be decided yet. However, based on the current information, the characteristics of QF formation and propagation could be approved.It is evident that the QF formed near the exit propagates backward, from somewhere downstream ofLse=1.55m to the inlet section. It gets to Lse=1.55m, 1 m, 0.75 m, and 0.5 m in turn and produces boiling transitions on these points. On the other hand, the inlet QF propagates forward from the inlet section to the exit, and it gets to Lse=0.3m and produces boiling transition here. It has to be noted that QFs get to Lse=1.55m and Lse=0.3m almost simultaneously at 10 s. However, after that, it seems like that the inlet QF does not propagate forward, and the vertical section is chilled by the exit QF.As shown in Figure7, for Exp. 2, Ti on Lse=1.55m decreases at first, followed by Lse=1m, 0.75 m, 0.3 m, and 0.5 m in turn, and LFP shows the similar manner. However, as shown in Figure 8 and Table 3, for Exp. 3, Ti on Lse=1.55m decreases at first, followed by Lse=1m, 0.75 m, 0.5 m, and 0.3 m in turn, and LFP shows the similar manner. However, as shown in Figure 9 and Table 3, for Exp. 4, Ti on Lse=1.55m decreases at first. After that, Ti values on Lse=1m, 0.75 m, and 0.5 m decrease with the similar slope, which are obvious prior to Lse=0.3m. This indicates that QF on Lse=0.3m happens at first for Exp. 1, at the fourth place for Exp. 2, and at last for Exp. 3 and Exp. 4.Figure 7
Tested data curves for Exp. 2 (0.444 kg/s,Pss=0.41MPa).Figure 8
Tested data curves for Exp. 3 (0.438 kg/s,Pss=0.77MPa).Table 3
StatisticaltLFP/tCHF data (unit: s).
PositionExp. 1Exp. 2Exp. 3Exp. 40.3-110/11.922/23.613/18.98/11.70.3-211/13.722/25.916/21.39/130.5-129/33.123/26.712/18.36/9.10.5-228/33.222/26.812/18.75/9.50.5-330/33.225/2712/18.75/8.70.75-118/22.617/20.710/15.26/9.60.75-215/22.314/20.110/14.56/8.80.75-316/22.415/20.210/14.86/9.51-114/15.413/168/136/9.21-214/15.214/15.38/11.76/81-311/15.413/15.38/11.75/81.55-110/12.68/10.26/84/5.11.55-210/11.88/9.65/7.54/4.7Figure 9
Tested data curves for Exp. 4 (0.426 kg/s,Pss=1.325MPa).


### 3.5. Mechanisms of the Chill-Down Process and the Quenching Front Propagation

As discussed above, especially Table3, obviously, pressure plays significant role on the chill-down process. In another word, chill-down process is controlled by the formation and propagation of QFs, which is determined by the pressure level. In this way, the key point here is how to explain the relationship between pressure and the formation and propagation of QFs.Apparently, these relationships are obvious. For Exp. 1 and Exp. 2 (low pressure relatively), the propagation of the exit QF determines the LFP of the experimental section forLse=0.5m and its downstream, and LFP on Lse=0.3m are likely to be controlled by the inlet QF. For Exp. 3 (medium pressure relatively), it seems like that LFPs on all of the Lse points measured are controlled by the backward propagation of the exit QF. However, for Exp. 4 (high pressure relatively), the exit QF gets to Lse=1.55m. After that, QFs form almost simultaneously on all of the measured Lse points except Lse=0.3m; then, one of the QF (formed around Lse=0.5m) propagates to form LFP on Lse=0.3m.In this way, the overall chill-down process in the experimental section could be described. For low-pressure cases, as the LO2 flows into the experimental section, it produces intensive evaporation, and liquid core surrounded by the vapor flows to the exit. Because of the contraction on the pipe exit, outflow of the vapor-liquid mixture would be chocked to enhance the system pressure. Simultaneously, because the flow contraction is with high temperature, only vapor could flow out, which produces the liquid accumulation around the injector. As a result of liquid accumulation, heat transfer is enhanced, and QF is formed here at first. After that, QF moves from the exit of the pipe to the upstream of the experimental section. This process is similar with that discussion before [29]. For medium pressure cases, this process does not show obvious change. The only difference is that the duration is shortened by the enhancement of hFB produced by enhanced pressure. For high pressure relatively, the propagation of exit QF also plays significant role on the section near the exit. However, in most vertical section, QFs are formed almost simultaneously for all of the three Lse. This indicates that for this case, the role of QF propagation decreases.On the other hand, simultaneously, the inlet QF could be formed at the inlet of the experimental section. It plays significant role for low-pressure cases and decreasing roles with the increase of pressure. In addition, another possibility is the effects of inlet QF would be reduced by the corner of the experimental section near the inlet.Traditionally, QF propagates from the inlet to the outlet of the experimental section for transport pipe, and most correlations are independent on this characteristic [7]. However, recently, experimental studies on exit-contracted pipe show that the quenching front forms in the central length of the horizontal pipe [29]. In the present study, both inlet QF and outlet QF are found. This is different from the previous studies, in the transport pipe [7] or horizontal exit-contracted pipe [29].


## 3.1. Basic Results

Four tests were performed, and related conditions and results could be listed in Table1. It shows that the present series of tests are all with the similar flow rate and various Ainj. With the decrease of Ainj (Exp. 1~4), pressure in the experimental section shows the increasing manner. This indicates that the Pss range is from 0.328 to 1.325 MPa.Table 1
Experimental conditions and results.
ParametersExp. 1Exp. 2Exp. 3Exp. 4Injector typeOrificePintlePintleOrificeAinj (mm)110.667.23312ṁ (kg/s, start)0.440.4350.4290.417ṁ (kg/s, end)0.450.4440.4380.426G (kg/(m2∙s), end)2546251324782411Re (end)259192270824319074329295Tp (K, end)101.5104112115Tsat−Tp (K, subcooling, end)1.652.063.39.64Ppeak (MPa, start)0.5860.8431.6783.049Pss (MPa, end)0.3280.410.771.325


## 3.2. Data Processing and Boiling Transition Points

Parameters in the pipe as well asTo data were measured for all of the four tests. By processing To data, Ti and qi were obtained because most discussions next would be based on these 2 parameters. Here, Ti would be determined according to reference [30], and qi would be obtained by numerical methods introduced in the previous studies [28], which would not be repeated here anymore.Based onTi and qi data, boiling curves could be drawn. In this way, boiling transition points, LFP, and CHF could be determined as well. These two points could be identified in the boiling curve easily, which indicate the minimum qi point and maximum qi point, respectively.


## 3.3. Uncertainty

The present study focuses on the comparison between experimental values and predicted values forTLFP, qLFP, TCHF, and qCHF. The experimental values depend mainly on the To measurement, physical properties as well as the geometric parameter of the pipe. On the other hand, as shown in the correlations, the predicted values depend mainly on the measured pressure and geometric parameter of the pipe. These factors could be shown in Table 2. Furthermore, the respective mean absolute errors (MAE) can be defined as Equation (1) shows [31].
(1)MAE=1N∑Vexp−VpreVexp×100%.Table 2
Summary of the uncertainties.
ParametersUncertaintyFluid pressure (%)0.5Fluid temperature (K)1Outer wall temperature (K)1PipeDi and Do (mm)0.01Mass flow rate (%)1To (K)1Ti (K)2qi (%)5


## 3.4. Basic Chill-Down Process

Figure6 shows all of the Ti curves as well as Tp, Tsat, and Pp curves to show the chill-down process for Exp. 1. As shown in the figure, during the chill-down process, Tp, Tsat, and Pp curves show the similar manner with the curves recorded in the previous studies [8, 28]. It also shows that a typical Ti curve is composed by three sequent phases as follows.
(1)
Phase I: the initial linear decrease phase. In this phase,Ti decreases in a linear manner, which indicates the inner flow is on the film boiling. LFP, the transition point between film boiling and transition boiling, could be seen as the transition point between phases I and II as well(2)
Phase II: the sudden decrease followed by phase I. This phase is with the shortest period, in whichTi decreases dramatically. This phase involves both transition boiling section and nucleate boiling section, and CHF, the transition point between transition boiling and nucleate boiling, sometimes would be seen as the central point of it(3)
Phase III: the gradual decrease followed by phase II. In this phase,Ti decreases gradually, which indicates the inner flow is the single-phase flow. As shown in Figure 1, the transition point between phase II and phase III is denoted as ONB, which always indicates the end of chill-downFigure 6
Tested data curves for Exp. 1 (0.45 kg/s,Pss=0.328MPa).As shown in Figure6, for Exp. 1, Ti on Lse=1.55m decreases at first, followed by Lse=0.3m, 1 m, 0.75 m, and 0.5 m in turn. Similarly, LFP happens in Lse=1.55m at first, followed by Lse=0.3m, 1 m, 0.75 m, and 0.5 m in turn. This indicates that two quenching fronts (QF) are formed on the exit and inlet of the experimental section independently. In the current stage, the exact positions of them could not be decided yet. However, based on the current information, the characteristics of QF formation and propagation could be approved.It is evident that the QF formed near the exit propagates backward, from somewhere downstream ofLse=1.55m to the inlet section. It gets to Lse=1.55m, 1 m, 0.75 m, and 0.5 m in turn and produces boiling transitions on these points. On the other hand, the inlet QF propagates forward from the inlet section to the exit, and it gets to Lse=0.3m and produces boiling transition here. It has to be noted that QFs get to Lse=1.55m and Lse=0.3m almost simultaneously at 10 s. However, after that, it seems like that the inlet QF does not propagate forward, and the vertical section is chilled by the exit QF.As shown in Figure7, for Exp. 2, Ti on Lse=1.55m decreases at first, followed by Lse=1m, 0.75 m, 0.3 m, and 0.5 m in turn, and LFP shows the similar manner. However, as shown in Figure 8 and Table 3, for Exp. 3, Ti on Lse=1.55m decreases at first, followed by Lse=1m, 0.75 m, 0.5 m, and 0.3 m in turn, and LFP shows the similar manner. However, as shown in Figure 9 and Table 3, for Exp. 4, Ti on Lse=1.55m decreases at first. After that, Ti values on Lse=1m, 0.75 m, and 0.5 m decrease with the similar slope, which are obvious prior to Lse=0.3m. This indicates that QF on Lse=0.3m happens at first for Exp. 1, at the fourth place for Exp. 2, and at last for Exp. 3 and Exp. 4.Figure 7
Tested data curves for Exp. 2 (0.444 kg/s,Pss=0.41MPa).Figure 8
Tested data curves for Exp. 3 (0.438 kg/s,Pss=0.77MPa).Table 3
StatisticaltLFP/tCHF data (unit: s).
PositionExp. 1Exp. 2Exp. 3Exp. 40.3-110/11.922/23.613/18.98/11.70.3-211/13.722/25.916/21.39/130.5-129/33.123/26.712/18.36/9.10.5-228/33.222/26.812/18.75/9.50.5-330/33.225/2712/18.75/8.70.75-118/22.617/20.710/15.26/9.60.75-215/22.314/20.110/14.56/8.80.75-316/22.415/20.210/14.86/9.51-114/15.413/168/136/9.21-214/15.214/15.38/11.76/81-311/15.413/15.38/11.75/81.55-110/12.68/10.26/84/5.11.55-210/11.88/9.65/7.54/4.7Figure 9
Tested data curves for Exp. 4 (0.426 kg/s,Pss=1.325MPa).


## 3.5. Mechanisms of the Chill-Down Process and the Quenching Front Propagation

As discussed above, especially Table3, obviously, pressure plays significant role on the chill-down process. In another word, chill-down process is controlled by the formation and propagation of QFs, which is determined by the pressure level. In this way, the key point here is how to explain the relationship between pressure and the formation and propagation of QFs.Apparently, these relationships are obvious. For Exp. 1 and Exp. 2 (low pressure relatively), the propagation of the exit QF determines the LFP of the experimental section forLse=0.5m and its downstream, and LFP on Lse=0.3m are likely to be controlled by the inlet QF. For Exp. 3 (medium pressure relatively), it seems like that LFPs on all of the Lse points measured are controlled by the backward propagation of the exit QF. However, for Exp. 4 (high pressure relatively), the exit QF gets to Lse=1.55m. After that, QFs form almost simultaneously on all of the measured Lse points except Lse=0.3m; then, one of the QF (formed around Lse=0.5m) propagates to form LFP on Lse=0.3m.In this way, the overall chill-down process in the experimental section could be described. For low-pressure cases, as the LO2 flows into the experimental section, it produces intensive evaporation, and liquid core surrounded by the vapor flows to the exit. Because of the contraction on the pipe exit, outflow of the vapor-liquid mixture would be chocked to enhance the system pressure. Simultaneously, because the flow contraction is with high temperature, only vapor could flow out, which produces the liquid accumulation around the injector. As a result of liquid accumulation, heat transfer is enhanced, and QF is formed here at first. After that, QF moves from the exit of the pipe to the upstream of the experimental section. This process is similar with that discussion before [29]. For medium pressure cases, this process does not show obvious change. The only difference is that the duration is shortened by the enhancement of hFB produced by enhanced pressure. For high pressure relatively, the propagation of exit QF also plays significant role on the section near the exit. However, in most vertical section, QFs are formed almost simultaneously for all of the three Lse. This indicates that for this case, the role of QF propagation decreases.On the other hand, simultaneously, the inlet QF could be formed at the inlet of the experimental section. It plays significant role for low-pressure cases and decreasing roles with the increase of pressure. In addition, another possibility is the effects of inlet QF would be reduced by the corner of the experimental section near the inlet.Traditionally, QF propagates from the inlet to the outlet of the experimental section for transport pipe, and most correlations are independent on this characteristic [7]. However, recently, experimental studies on exit-contracted pipe show that the quenching front forms in the central length of the horizontal pipe [29]. In the present study, both inlet QF and outlet QF are found. This is different from the previous studies, in the transport pipe [7] or horizontal exit-contracted pipe [29].


## 4. Film Boiling Heat Transfer and the Leidenfrost Point

In the present section, film boiling heat transfer, liquid rewetting, and LFP would be discussed forLse=0.5, 0.75 and 1 m. This is primary because these cross-sections are set on the vertical section, and the LFPs of them are primary controlled by the exit QF, at least for lower and medium pressure cases.


### 4.1. Basic Effect ofAinj

The experimentalΔTLFP, qLFP, and hLFP versus Ainj could be shown in Figure 10–12, respectively. It shows that, basically, with the decrease of Ainj, both qLFP and hLFP show the increasing manner (except some individual cases). On the other hand, with the decrease of Ainj, approximately, ΔTLFP shows the increase manner for Lse=0.5m, the decrease manner for Lse=0.75m, and increase-decrease manner for Lse=1m. This is similar with those indicated in reference [29].Figure 10
ExperimentalΔTLFP versus Ainj.Figure 11
ExperimentalqLFP versus Ainj.Figure 12
ExperimentalhLFP versus Ainj.


### 4.2. Evaluation of the Previous Correlations

Leidenfrost point (LFP), on which the liquid rewets the pipe wall, is known as the transition point from film boiling to transition boiling. This point is always identified as the point with the minimum heat flux. Historically, based on the flow instability theories, Zuber et al. [32] improved the basic correlation on qLFP as shown in Equation (2) (C1=0.09). After that, Berenson [33] approved Equation (3) (C2=0.425) to evaluate hFB, the heat transfer coefficient on film boiling, and suggested Equation (4) (CLFP=0.127) on LFP to evaluate ΔTLFP based on basic heat transfer equation, Equation (6). After that, most correlations on qLFP and ∆TLFP for both pool boiling and flow boiling were based on these 2 equations. In the previous studies, ΔTLFP and qLFP were tried to be correlated. In this way, Equation (4) and Equation (2) were applied to predict ΔTLFP and qLFP, respectively, for horizontal exit-contracted pipe [8, 29].
(2)qLFP=C1ρvHvlσvlgρl−ρvρl+ρv20.25,(3)hFB=C2kv3Hvlρvgρl−ρvμvΔTiσvl/gρl−ρv0.25,(4)ΔTLFP=TLFP−Tsat=CLFP⋅ELFP,(5)ELFP=ρvHvlkvgρl−ρvρl+ρv2/3σvlgρl−ρv1/2μvgρl−ρv1/3,(6)qi=hiΔTi.According to Equation (4), in the present study, for vertical experimental section, ΔTLFP could be plotted versus ELFP in Figure 13, where CLFP could be correlated to be 0.0576 and produces the MAE of 16.62%. As shown in the figure, the point distribution and constant CLFP do not show significant differences from the previous studies [29]. It shows that with the increase of Ainj, ΔTLFP shows the overall increasing manner for Lse=0.5m and overall decreasing manner for other Lse. This indicates the similar difficulties on correlation, which has been discussed in the previous studies in horizontal pipes [29].Figure 13
Experimental∆TLFP versus ELFP.On the other hand, Zuber’s correlation, Equation (2), indicates that on LFP, vapor was not produced rapidly enough to lift the interface as rapidly as it would normally collapse [34]. In this way, qLFP in the present study could be correlated by this equation as shown in Figure 14, where the constant C1 and MAE could be listed in Table 4. Generally speaking, as shown in Equation (2), the effects of fluid properties could be represented by the items in the abscissa of Figure 14, and the effects of circumferential position and Lse could be represented by the variable parameter C1, which has been correlated for every point. Obviously, it is not a general correlation. However, in the current stage, this equation is important to set up the basic outline for the following investigations.Figure 14
Correlation onqLFP by Equation (2).Table 4
Constants for every point in Equations (2), (3) and (11), respectively.
PointConstantC1MAE (%)ConstantC2MAE (%)C3MAE (%)0.5-10.055514.280.482810.160.0070311.240.5-20.06437.120.5736.290.009824.060.5-30.060711.200.52366.260.008284.060.75-10.059714.050.52816.400.007694.000.75-20.07485.450.713913.600.008354.190.75-30.050212.260.41215.720.0042813.651-10.0572∗10.490.4967∗7.090.006831.531-20.0749∗6.050.7384∗8.740.007251.631-30.086∗8.020.82644.470.009945.57∗, except Exp. 1.As shown in Figure14, basically, Equation (2) could produce reliable predictions on qLFP for Lse=0.5 and 0.75 m relatively. However, for Lse=1m, with the increase of ρvHvlσvlgρl−ρv/ρl+ρv20.25, qLFP shows the decreasing-increasing manner. Thus, from the view of point of correlation, Equation (2) could be used to produce qLFP for Lse=1m only on higher pressure (e.g., Pss≥0.4MPa). In this way, C1 items listed in Table 4 for Lse=1m were correlated for Exp. 2~4.


### 4.3. Correlations onhLFP

By the present set of data,hLFP could be correlated by Equation (3) as shown in Figure 15, where the constant C2 could be listed in Table 4. Basically, with the increase of pressure, the 2nd item of the right side of Equation (3) keeps increasing constantly, which is consistent to the experimental hLFP data.Figure 15
Correlation onhLFP by Equation (3).


### 4.4. Primary Effect Factors

According to Carbajo [35], liquid rewetting involves the effects of pressure, liquid subcooling, liquid and solid properties, surface conditions, and flow rate. However, in the present study, throughout all of the tests, only pressure shows the obvious variations. On the other hand, Lse and circumferential positions are obviously different for these points. In this way, the effects of pressure, Lse, and circumferential positions would be discussed in the present section.


#### 4.4.1. The Effects ofAinj or Pressure

The present series of tests are with the same flow rate. Thus, the effects ofAinj in the present study indicates the effects of pressure only. On the film boiling section, with the decrease of Ainj (increase of pressure), hFB keeps increasing because δFB keeps almost constant and kv keeps increasing as shown in Equation (7) [29].
(7)hFB=kvδFB.In this way, with the increase ofAinj, the slope of Ti decreasing increases for every point, and chill-down period (tLFP) would be shortened as well. As a result, both heat flux and heat transfer coefficient would be enhanced on film boiling section, which produces the overall increasing qLFP and hLFP for every point.These principles are very similar with those tendencies in horizontal exit-contracted pipe [29].


#### 4.4.2. The Effects ofLse

Traditionally,hLFP decreases with the increase of Lse according to the existing correlations [7]. However, in the present study, experimental data do not show the similar tendency. Comparison between Figures 14 and 15 shows that, for a certain test, both qLFP and hLFP increase with the increase of Lse, which is contrary to that in transport pipe [7]. Comparison among transport pipe [7], horizontal exit-contracted pipe [29], and vertical exit-contracted pipe indicates that the effects of Lse traditionally concerned are essentially more like the effects of Lqf, distance from the present point to the QF formation point. In this way, experimental results in reference [29] and in the present study could be explained well. Thus, it is necessary to denote that from the view of point of pipe length, Lqf plays the significant role on LFP instead of Lse.In general, for a certain test, along the directions of QF propagation,tLFP shows the increasing manner, compared to that qLFP and hLFP show the decreasing manner. This characteristic plays significant roles on the LFP. This indicates the basic principle, longer Lqf is corresponding to greater tLFP, lower qLFP and hLFP. This principle is always the case independent on Lse and the dominant QF, even for Lse=0.3m, on which even the LFP is controlled by various QF.For a certainLse, with the increase of Ainj, tLFP shows the decreasing manner, and qLFP and hLFP show the increasing manner. This indicates that with the increase of pressure, both hFB and M (magnitude of instable waves) undergo corresponding increase. According to results in horizontal exit-contracted pipe [29], LFP is controlled by the competition between heat transfer and the increase of M. However, according to the present study, QF propagation also plays a significant role on. In the present study, for Exp. 1~3, QF propagation could be well tracked according to the experimental data, which indicates that the latter one is the dominant factor. However, for Exp. 4, LFP happens almost simultaneously on Lse=0.5, 0.75, and 1 m, which indicates that the former is the dominant factor in this case.Another key point is where is the QFs formed. In the present study, both inlet QF and exit QF are identified. Analysis indicates that QF formation is controlled by the fill process of the cryogenic fluid in the exit-contracted pipe.


#### 4.4.3. The Effects of Circumferential Position

As shown in Table3, for every Lse, tLFP values for circumferential position (1, West; 2, South; 3, East) are quite similar to each other. This indicates the propagation of QF circumferentially also plays significant role. This is similar with those in horizontal exit-contracted pipe [29]. However, traditionally, circumferential position plays ignorable role in the vertical transport pipe [7]. In the present study, vertical section (Lse=1, 0.75, and 0.5 m), as shown in Table 4, could produce around 50% variation on hLFP and qLFP and qCHF for Lse=1 and 0.75 m and 30% for Lse=0.5m.In this way, for a certainLse, hFB always dominates the decrease of Ti on points 1~3. After that, once one of them gets to LFP, boiling transitions would happen immediately on other two points, which produces the hFB at that time as hLFP. In another word, on the same Lse cross-section, various points are with the similar tLFP.In this way, three points, 0.5-2, 0.75-2, and 1-3 are the dominant points forLse=0.5, 0.75, and 1 m, respectively, and determines the tLFP point on the present section in the present study. For other points (dominated points), during the chill-down process, qi and Ti keep decreasing, and hFB keeps increasing. Once LFP happens at tLFP on the dominant point on the same section, liquid rewetting would happen on the dominated points. Thus, qi, Ti, and hFB at that time would be identified as qLFP, TLFP, and hLFP.This implies that on a certainLse cross-section, the liquid rewetting mechanism for the dominant point is different from that for the dominated points. For the dominant point, liquid rewetting is more likely to be controlled by flow instability, which is similar with that on pool boiling or flow boiling. According to the series of data, this process is dominated by the QF propagation axially. However, for the dominated points, liquid rewetting is controlled by both the dominant point and the local heat transfer. This process is dominated by the QF propagation circumferentially.The difference between the dominant point and dominated points could be also found in the horizontal exit-contracted pipe. Obviously, because of the gravity, the dominant point is the bottom point for horizontal pipe [29]. However, for the vertical pipe, the effect of gravity could be ignored. According to Carbajo [35], liquid rewetting involves the effects of pressure, liquid subcooling, liquid and solid properties, surface conditions, and flow rate. In this way, on the same Lse cross-section, this sort of difference between the dominant point and dominated points is probably caused by the inner surface conditions.


#### 4.4.4. Summary on the Basic Effect Factors

As discussed above, the effects of pressure,Lse, and circumferential position could be summarized and concluded as follows.
(1)
For a certain point, the increase ofAinj produces overall increasing qLFP and hLFP and deceasing tLFP(2)
With the increase ofLqf, overall decreasing qLFP and hLFP and increasing tLFP could be obtained(3)
Because of the propagation of QF circumferentially, on a certainLse (cross-section), there are both dominant point and dominated points, which are controlled by flow instability and both dominant point and hFB and, respectively. In the present study, 0.5-2, 0.75-2, and 1-3 are the dominant points for these sections, respectively.


### 4.5. Discussions

#### 4.5.1. Correlations on the Dominant Points

From the view of point of correlation, all of these factors should be involved. For three dominant points, 0.5-2, 0.75-2, and 1-3, on which liquid rewetting is controlled by flow instability. According to Equation (2) and Table 4, C1 for them are correlated to be 0.0643, 0.0748, and 0.086, respectively. It shows that C1 increases linearly with the increase of Lse (decrease of Lqf). In this way, based on Equation (2), qLFP on the dominant points for Lse=0.5, 0.75, and 1 m could be correlated by Equation (8). This correlation could be approved for dominant points in vertical section.
(8)qLFP=0.0425+0.0434LseρvHvlσvlgρl−ρvρl+ρv20.25.As discussed above, in the present study,qLFP decreases with the decrease of Lse for Lse=0.5m and its downstream. In addition, on 1.55-2, the dominant point on Lse=1.55m, and the horizontal section, C1 was correlated to be 0.1335, which has not been given above. This indicates the C1 values along the QF propagation, from 0.1335 (Lse=1.55m) to 0.086 (Lse=1m), 0.0748 (Lse=0.75m), and finally, 0.0643 (Lse=0.5m). These series of values are consistent to the literature data, in which C1 was correlated to be 0.09 [32] for room-temperature fluid in pool boiling. At first, the deviation of C1 between the present study and reference [32] is mainly caused by the variations between the fill-in flow in the exit-contracted pipe and pool boiling. On the other hand, the decrease of C1 along the reverse direction of the flow in the experimental section pipe indicates the special characteristics of flow in the exit-contracted pipe.Similarly, according to Equation (3), C2 for 0.5-2, 0.75-2, and 1-3 are correlated to be 0.573, 0.7139, and 0.8264, respectively. Similar with qLFP, hLFP on the dominant points for Lse=0.5, 0.75, and 1 m could be correlated by Equation (9). This series of data is consistent to the literature data, in which C2 was correlated to be 0.425 [33] for room-temperature fluid in pool boiling.
(9)hFB=0.324+0.5068Lsekv3Hvlρvgρl−ρvμvΔTiσvl/gρl−ρv0.25.Compared to the literature data from room-temperature fluid in pool boiling, dominant points in the vertical section are with lowerqLFP, lower ΔTLFP, and higher hLFP. Basically, this sort of differences is mainly caused by the variations on the system pressure and flow condition. On the other hand, the similarity on C1 and C2 between for exit-contracted pipe and pool boiling indicates that flow instability is the primary dominant factor, and Lse also plays a certain role for the dominant points on the present vertical pipe.


#### 4.5.2. Correlations on the Dominated Points

For the dominated points, Equations (2) and (3) with constants listed in Table 4 could be suggested in the current stage. It has to be denoted that on this sort of points, liquid rewetting is not caused by local flow instability on this sort of points. On the contrary, the local instable wave has not been developed adequately. Result indicates that at tLFP, liquid rewetting happens on the dominant point on the current cross-section. Almost simultaneously, all of this cross-section is rewetted by the liquid as a result of QF propagation circumferentially from the dominant point. In this way, on the dominated points, as a result of being rewetted, qi, hi, and Ti at tLFP have to be denoted as parameters on LFP.


#### 4.5.3. Correlation Approach and Correlation Formats

In the previous studies,qLFP and ∆TLFP were tried to be correlated, and hLFP has not been tried to be correlated before [8]. In the present study, qLFP and hLFP (instead of ∆TLFP) are correlated. This is the new correlation approach. In the recent studies, correlation formats for Equations (2)–(4) were approved to correlate qLFP, hLFP, and ∆TLFP, respectively. The primary items in these equations could be plotted versus pressure as shown in Figure 16.Figure 16
Parameter combinations in Equations (2)–(4) versus pressure.ForΔTLFP, as discussed above, there are two difficulties on reliable correlation, which determines it would not be considered to be correlated in the current stage. The first one is, as shown in Figures 13 and 16, parameter combination, with the increase of pressure from ambient to around 2.5 MPa, ELFP in Equation (4) shows the increasing-decreasing manner, which indicates that it could not represent the effects of pressure. On the other hand, with the increase of pressure, the variations of ΔTLFP show different manners for various Lse. The primary reason is ELFP and Equation (4) are approved for pool boiling in ambient-pressure, which could not be applied in high pressure cases.For both dominant point and dominated points,qLFP and hLFP are well correlated on the vertical section. This is primarily because the basic effects including pressure, Lse, and circumferential position are well involved. At first, for dealing with the effect of circumferential position, dominant points were identified from dominated points, and they were correlated apart from each other. On the other hand, the effects of pressure and Lse are involved well in Equations (2)–(3) and Equations (8)–(9). Especially, as shown in Figure 16, in the effective LFP pressure range from ambient to around 2.5 MPa [8], the primary items in both Equations (2) and (3) (as well as (8) and (9)) increase consistently with the increase of pressure, which indicates that these equations could represent the effect of pressure well.


## 4.1. Basic Effect ofAinj

The experimentalΔTLFP, qLFP, and hLFP versus Ainj could be shown in Figure 10–12, respectively. It shows that, basically, with the decrease of Ainj, both qLFP and hLFP show the increasing manner (except some individual cases). On the other hand, with the decrease of Ainj, approximately, ΔTLFP shows the increase manner for Lse=0.5m, the decrease manner for Lse=0.75m, and increase-decrease manner for Lse=1m. This is similar with those indicated in reference [29].Figure 10
ExperimentalΔTLFP versus Ainj.Figure 11
ExperimentalqLFP versus Ainj.Figure 12
ExperimentalhLFP versus Ainj.


## 4.2. Evaluation of the Previous Correlations

Leidenfrost point (LFP), on which the liquid rewets the pipe wall, is known as the transition point from film boiling to transition boiling. This point is always identified as the point with the minimum heat flux. Historically, based on the flow instability theories, Zuber et al. [32] improved the basic correlation on qLFP as shown in Equation (2) (C1=0.09). After that, Berenson [33] approved Equation (3) (C2=0.425) to evaluate hFB, the heat transfer coefficient on film boiling, and suggested Equation (4) (CLFP=0.127) on LFP to evaluate ΔTLFP based on basic heat transfer equation, Equation (6). After that, most correlations on qLFP and ∆TLFP for both pool boiling and flow boiling were based on these 2 equations. In the previous studies, ΔTLFP and qLFP were tried to be correlated. In this way, Equation (4) and Equation (2) were applied to predict ΔTLFP and qLFP, respectively, for horizontal exit-contracted pipe [8, 29].
(2)qLFP=C1ρvHvlσvlgρl−ρvρl+ρv20.25,(3)hFB=C2kv3Hvlρvgρl−ρvμvΔTiσvl/gρl−ρv0.25,(4)ΔTLFP=TLFP−Tsat=CLFP⋅ELFP,(5)ELFP=ρvHvlkvgρl−ρvρl+ρv2/3σvlgρl−ρv1/2μvgρl−ρv1/3,(6)qi=hiΔTi.According to Equation (4), in the present study, for vertical experimental section, ΔTLFP could be plotted versus ELFP in Figure 13, where CLFP could be correlated to be 0.0576 and produces the MAE of 16.62%. As shown in the figure, the point distribution and constant CLFP do not show significant differences from the previous studies [29]. It shows that with the increase of Ainj, ΔTLFP shows the overall increasing manner for Lse=0.5m and overall decreasing manner for other Lse. This indicates the similar difficulties on correlation, which has been discussed in the previous studies in horizontal pipes [29].Figure 13
Experimental∆TLFP versus ELFP.On the other hand, Zuber’s correlation, Equation (2), indicates that on LFP, vapor was not produced rapidly enough to lift the interface as rapidly as it would normally collapse [34]. In this way, qLFP in the present study could be correlated by this equation as shown in Figure 14, where the constant C1 and MAE could be listed in Table 4. Generally speaking, as shown in Equation (2), the effects of fluid properties could be represented by the items in the abscissa of Figure 14, and the effects of circumferential position and Lse could be represented by the variable parameter C1, which has been correlated for every point. Obviously, it is not a general correlation. However, in the current stage, this equation is important to set up the basic outline for the following investigations.Figure 14
Correlation onqLFP by Equation (2).Table 4
Constants for every point in Equations (2), (3) and (11), respectively.
PointConstantC1MAE (%)ConstantC2MAE (%)C3MAE (%)0.5-10.055514.280.482810.160.0070311.240.5-20.06437.120.5736.290.009824.060.5-30.060711.200.52366.260.008284.060.75-10.059714.050.52816.400.007694.000.75-20.07485.450.713913.600.008354.190.75-30.050212.260.41215.720.0042813.651-10.0572∗10.490.4967∗7.090.006831.531-20.0749∗6.050.7384∗8.740.007251.631-30.086∗8.020.82644.470.009945.57∗, except Exp. 1.As shown in Figure14, basically, Equation (2) could produce reliable predictions on qLFP for Lse=0.5 and 0.75 m relatively. However, for Lse=1m, with the increase of ρvHvlσvlgρl−ρv/ρl+ρv20.25, qLFP shows the decreasing-increasing manner. Thus, from the view of point of correlation, Equation (2) could be used to produce qLFP for Lse=1m only on higher pressure (e.g., Pss≥0.4MPa). In this way, C1 items listed in Table 4 for Lse=1m were correlated for Exp. 2~4.


## 4.3. Correlations onhLFP

By the present set of data,hLFP could be correlated by Equation (3) as shown in Figure 15, where the constant C2 could be listed in Table 4. Basically, with the increase of pressure, the 2nd item of the right side of Equation (3) keeps increasing constantly, which is consistent to the experimental hLFP data.Figure 15
Correlation onhLFP by Equation (3).


## 4.4. Primary Effect Factors

According to Carbajo [35], liquid rewetting involves the effects of pressure, liquid subcooling, liquid and solid properties, surface conditions, and flow rate. However, in the present study, throughout all of the tests, only pressure shows the obvious variations. On the other hand, Lse and circumferential positions are obviously different for these points. In this way, the effects of pressure, Lse, and circumferential positions would be discussed in the present section.


### 4.4.1. The Effects ofAinj or Pressure

The present series of tests are with the same flow rate. Thus, the effects ofAinj in the present study indicates the effects of pressure only. On the film boiling section, with the decrease of Ainj (increase of pressure), hFB keeps increasing because δFB keeps almost constant and kv keeps increasing as shown in Equation (7) [29].
(7)hFB=kvδFB.In this way, with the increase ofAinj, the slope of Ti decreasing increases for every point, and chill-down period (tLFP) would be shortened as well. As a result, both heat flux and heat transfer coefficient would be enhanced on film boiling section, which produces the overall increasing qLFP and hLFP for every point.These principles are very similar with those tendencies in horizontal exit-contracted pipe [29].


### 4.4.2. The Effects ofLse

Traditionally,hLFP decreases with the increase of Lse according to the existing correlations [7]. However, in the present study, experimental data do not show the similar tendency. Comparison between Figures 14 and 15 shows that, for a certain test, both qLFP and hLFP increase with the increase of Lse, which is contrary to that in transport pipe [7]. Comparison among transport pipe [7], horizontal exit-contracted pipe [29], and vertical exit-contracted pipe indicates that the effects of Lse traditionally concerned are essentially more like the effects of Lqf, distance from the present point to the QF formation point. In this way, experimental results in reference [29] and in the present study could be explained well. Thus, it is necessary to denote that from the view of point of pipe length, Lqf plays the significant role on LFP instead of Lse.In general, for a certain test, along the directions of QF propagation,tLFP shows the increasing manner, compared to that qLFP and hLFP show the decreasing manner. This characteristic plays significant roles on the LFP. This indicates the basic principle, longer Lqf is corresponding to greater tLFP, lower qLFP and hLFP. This principle is always the case independent on Lse and the dominant QF, even for Lse=0.3m, on which even the LFP is controlled by various QF.For a certainLse, with the increase of Ainj, tLFP shows the decreasing manner, and qLFP and hLFP show the increasing manner. This indicates that with the increase of pressure, both hFB and M (magnitude of instable waves) undergo corresponding increase. According to results in horizontal exit-contracted pipe [29], LFP is controlled by the competition between heat transfer and the increase of M. However, according to the present study, QF propagation also plays a significant role on. In the present study, for Exp. 1~3, QF propagation could be well tracked according to the experimental data, which indicates that the latter one is the dominant factor. However, for Exp. 4, LFP happens almost simultaneously on Lse=0.5, 0.75, and 1 m, which indicates that the former is the dominant factor in this case.Another key point is where is the QFs formed. In the present study, both inlet QF and exit QF are identified. Analysis indicates that QF formation is controlled by the fill process of the cryogenic fluid in the exit-contracted pipe.


### 4.4.3. The Effects of Circumferential Position

As shown in Table3, for every Lse, tLFP values for circumferential position (1, West; 2, South; 3, East) are quite similar to each other. This indicates the propagation of QF circumferentially also plays significant role. This is similar with those in horizontal exit-contracted pipe [29]. However, traditionally, circumferential position plays ignorable role in the vertical transport pipe [7]. In the present study, vertical section (Lse=1, 0.75, and 0.5 m), as shown in Table 4, could produce around 50% variation on hLFP and qLFP and qCHF for Lse=1 and 0.75 m and 30% for Lse=0.5m.In this way, for a certainLse, hFB always dominates the decrease of Ti on points 1~3. After that, once one of them gets to LFP, boiling transitions would happen immediately on other two points, which produces the hFB at that time as hLFP. In another word, on the same Lse cross-section, various points are with the similar tLFP.In this way, three points, 0.5-2, 0.75-2, and 1-3 are the dominant points forLse=0.5, 0.75, and 1 m, respectively, and determines the tLFP point on the present section in the present study. For other points (dominated points), during the chill-down process, qi and Ti keep decreasing, and hFB keeps increasing. Once LFP happens at tLFP on the dominant point on the same section, liquid rewetting would happen on the dominated points. Thus, qi, Ti, and hFB at that time would be identified as qLFP, TLFP, and hLFP.This implies that on a certainLse cross-section, the liquid rewetting mechanism for the dominant point is different from that for the dominated points. For the dominant point, liquid rewetting is more likely to be controlled by flow instability, which is similar with that on pool boiling or flow boiling. According to the series of data, this process is dominated by the QF propagation axially. However, for the dominated points, liquid rewetting is controlled by both the dominant point and the local heat transfer. This process is dominated by the QF propagation circumferentially.The difference between the dominant point and dominated points could be also found in the horizontal exit-contracted pipe. Obviously, because of the gravity, the dominant point is the bottom point for horizontal pipe [29]. However, for the vertical pipe, the effect of gravity could be ignored. According to Carbajo [35], liquid rewetting involves the effects of pressure, liquid subcooling, liquid and solid properties, surface conditions, and flow rate. In this way, on the same Lse cross-section, this sort of difference between the dominant point and dominated points is probably caused by the inner surface conditions.


### 4.4.4. Summary on the Basic Effect Factors

As discussed above, the effects of pressure,Lse, and circumferential position could be summarized and concluded as follows.
(1)
For a certain point, the increase ofAinj produces overall increasing qLFP and hLFP and deceasing tLFP(2)
With the increase ofLqf, overall decreasing qLFP and hLFP and increasing tLFP could be obtained(3)
Because of the propagation of QF circumferentially, on a certainLse (cross-section), there are both dominant point and dominated points, which are controlled by flow instability and both dominant point and hFB and, respectively. In the present study, 0.5-2, 0.75-2, and 1-3 are the dominant points for these sections, respectively.


## 4.4.1. The Effects ofAinj or Pressure

The present series of tests are with the same flow rate. Thus, the effects ofAinj in the present study indicates the effects of pressure only. On the film boiling section, with the decrease of Ainj (increase of pressure), hFB keeps increasing because δFB keeps almost constant and kv keeps increasing as shown in Equation (7) [29].
(7)hFB=kvδFB.In this way, with the increase ofAinj, the slope of Ti decreasing increases for every point, and chill-down period (tLFP) would be shortened as well. As a result, both heat flux and heat transfer coefficient would be enhanced on film boiling section, which produces the overall increasing qLFP and hLFP for every point.These principles are very similar with those tendencies in horizontal exit-contracted pipe [29].


## 4.4.2. The Effects ofLse

Traditionally,hLFP decreases with the increase of Lse according to the existing correlations [7]. However, in the present study, experimental data do not show the similar tendency. Comparison between Figures 14 and 15 shows that, for a certain test, both qLFP and hLFP increase with the increase of Lse, which is contrary to that in transport pipe [7]. Comparison among transport pipe [7], horizontal exit-contracted pipe [29], and vertical exit-contracted pipe indicates that the effects of Lse traditionally concerned are essentially more like the effects of Lqf, distance from the present point to the QF formation point. In this way, experimental results in reference [29] and in the present study could be explained well. Thus, it is necessary to denote that from the view of point of pipe length, Lqf plays the significant role on LFP instead of Lse.In general, for a certain test, along the directions of QF propagation,tLFP shows the increasing manner, compared to that qLFP and hLFP show the decreasing manner. This characteristic plays significant roles on the LFP. This indicates the basic principle, longer Lqf is corresponding to greater tLFP, lower qLFP and hLFP. This principle is always the case independent on Lse and the dominant QF, even for Lse=0.3m, on which even the LFP is controlled by various QF.For a certainLse, with the increase of Ainj, tLFP shows the decreasing manner, and qLFP and hLFP show the increasing manner. This indicates that with the increase of pressure, both hFB and M (magnitude of instable waves) undergo corresponding increase. According to results in horizontal exit-contracted pipe [29], LFP is controlled by the competition between heat transfer and the increase of M. However, according to the present study, QF propagation also plays a significant role on. In the present study, for Exp. 1~3, QF propagation could be well tracked according to the experimental data, which indicates that the latter one is the dominant factor. However, for Exp. 4, LFP happens almost simultaneously on Lse=0.5, 0.75, and 1 m, which indicates that the former is the dominant factor in this case.Another key point is where is the QFs formed. In the present study, both inlet QF and exit QF are identified. Analysis indicates that QF formation is controlled by the fill process of the cryogenic fluid in the exit-contracted pipe.


## 4.4.3. The Effects of Circumferential Position

As shown in Table3, for every Lse, tLFP values for circumferential position (1, West; 2, South; 3, East) are quite similar to each other. This indicates the propagation of QF circumferentially also plays significant role. This is similar with those in horizontal exit-contracted pipe [29]. However, traditionally, circumferential position plays ignorable role in the vertical transport pipe [7]. In the present study, vertical section (Lse=1, 0.75, and 0.5 m), as shown in Table 4, could produce around 50% variation on hLFP and qLFP and qCHF for Lse=1 and 0.75 m and 30% for Lse=0.5m.In this way, for a certainLse, hFB always dominates the decrease of Ti on points 1~3. After that, once one of them gets to LFP, boiling transitions would happen immediately on other two points, which produces the hFB at that time as hLFP. In another word, on the same Lse cross-section, various points are with the similar tLFP.In this way, three points, 0.5-2, 0.75-2, and 1-3 are the dominant points forLse=0.5, 0.75, and 1 m, respectively, and determines the tLFP point on the present section in the present study. For other points (dominated points), during the chill-down process, qi and Ti keep decreasing, and hFB keeps increasing. Once LFP happens at tLFP on the dominant point on the same section, liquid rewetting would happen on the dominated points. Thus, qi, Ti, and hFB at that time would be identified as qLFP, TLFP, and hLFP.This implies that on a certainLse cross-section, the liquid rewetting mechanism for the dominant point is different from that for the dominated points. For the dominant point, liquid rewetting is more likely to be controlled by flow instability, which is similar with that on pool boiling or flow boiling. According to the series of data, this process is dominated by the QF propagation axially. However, for the dominated points, liquid rewetting is controlled by both the dominant point and the local heat transfer. This process is dominated by the QF propagation circumferentially.The difference between the dominant point and dominated points could be also found in the horizontal exit-contracted pipe. Obviously, because of the gravity, the dominant point is the bottom point for horizontal pipe [29]. However, for the vertical pipe, the effect of gravity could be ignored. According to Carbajo [35], liquid rewetting involves the effects of pressure, liquid subcooling, liquid and solid properties, surface conditions, and flow rate. In this way, on the same Lse cross-section, this sort of difference between the dominant point and dominated points is probably caused by the inner surface conditions.


## 4.4.4. Summary on the Basic Effect Factors

As discussed above, the effects of pressure,Lse, and circumferential position could be summarized and concluded as follows.
(1)
For a certain point, the increase ofAinj produces overall increasing qLFP and hLFP and deceasing tLFP(2)
With the increase ofLqf, overall decreasing qLFP and hLFP and increasing tLFP could be obtained(3)
Because of the propagation of QF circumferentially, on a certainLse (cross-section), there are both dominant point and dominated points, which are controlled by flow instability and both dominant point and hFB and, respectively. In the present study, 0.5-2, 0.75-2, and 1-3 are the dominant points for these sections, respectively.


## 4.5. Discussions

### 4.5.1. Correlations on the Dominant Points

From the view of point of correlation, all of these factors should be involved. For three dominant points, 0.5-2, 0.75-2, and 1-3, on which liquid rewetting is controlled by flow instability. According to Equation (2) and Table 4, C1 for them are correlated to be 0.0643, 0.0748, and 0.086, respectively. It shows that C1 increases linearly with the increase of Lse (decrease of Lqf). In this way, based on Equation (2), qLFP on the dominant points for Lse=0.5, 0.75, and 1 m could be correlated by Equation (8). This correlation could be approved for dominant points in vertical section.
(8)qLFP=0.0425+0.0434LseρvHvlσvlgρl−ρvρl+ρv20.25.As discussed above, in the present study,qLFP decreases with the decrease of Lse for Lse=0.5m and its downstream. In addition, on 1.55-2, the dominant point on Lse=1.55m, and the horizontal section, C1 was correlated to be 0.1335, which has not been given above. This indicates the C1 values along the QF propagation, from 0.1335 (Lse=1.55m) to 0.086 (Lse=1m), 0.0748 (Lse=0.75m), and finally, 0.0643 (Lse=0.5m). These series of values are consistent to the literature data, in which C1 was correlated to be 0.09 [32] for room-temperature fluid in pool boiling. At first, the deviation of C1 between the present study and reference [32] is mainly caused by the variations between the fill-in flow in the exit-contracted pipe and pool boiling. On the other hand, the decrease of C1 along the reverse direction of the flow in the experimental section pipe indicates the special characteristics of flow in the exit-contracted pipe.Similarly, according to Equation (3), C2 for 0.5-2, 0.75-2, and 1-3 are correlated to be 0.573, 0.7139, and 0.8264, respectively. Similar with qLFP, hLFP on the dominant points for Lse=0.5, 0.75, and 1 m could be correlated by Equation (9). This series of data is consistent to the literature data, in which C2 was correlated to be 0.425 [33] for room-temperature fluid in pool boiling.
(9)hFB=0.324+0.5068Lsekv3Hvlρvgρl−ρvμvΔTiσvl/gρl−ρv0.25.Compared to the literature data from room-temperature fluid in pool boiling, dominant points in the vertical section are with lowerqLFP, lower ΔTLFP, and higher hLFP. Basically, this sort of differences is mainly caused by the variations on the system pressure and flow condition. On the other hand, the similarity on C1 and C2 between for exit-contracted pipe and pool boiling indicates that flow instability is the primary dominant factor, and Lse also plays a certain role for the dominant points on the present vertical pipe.


### 4.5.2. Correlations on the Dominated Points

For the dominated points, Equations (2) and (3) with constants listed in Table 4 could be suggested in the current stage. It has to be denoted that on this sort of points, liquid rewetting is not caused by local flow instability on this sort of points. On the contrary, the local instable wave has not been developed adequately. Result indicates that at tLFP, liquid rewetting happens on the dominant point on the current cross-section. Almost simultaneously, all of this cross-section is rewetted by the liquid as a result of QF propagation circumferentially from the dominant point. In this way, on the dominated points, as a result of being rewetted, qi, hi, and Ti at tLFP have to be denoted as parameters on LFP.


### 4.5.3. Correlation Approach and Correlation Formats

In the previous studies,qLFP and ∆TLFP were tried to be correlated, and hLFP has not been tried to be correlated before [8]. In the present study, qLFP and hLFP (instead of ∆TLFP) are correlated. This is the new correlation approach. In the recent studies, correlation formats for Equations (2)–(4) were approved to correlate qLFP, hLFP, and ∆TLFP, respectively. The primary items in these equations could be plotted versus pressure as shown in Figure 16.Figure 16
Parameter combinations in Equations (2)–(4) versus pressure.ForΔTLFP, as discussed above, there are two difficulties on reliable correlation, which determines it would not be considered to be correlated in the current stage. The first one is, as shown in Figures 13 and 16, parameter combination, with the increase of pressure from ambient to around 2.5 MPa, ELFP in Equation (4) shows the increasing-decreasing manner, which indicates that it could not represent the effects of pressure. On the other hand, with the increase of pressure, the variations of ΔTLFP show different manners for various Lse. The primary reason is ELFP and Equation (4) are approved for pool boiling in ambient-pressure, which could not be applied in high pressure cases.For both dominant point and dominated points,qLFP and hLFP are well correlated on the vertical section. This is primarily because the basic effects including pressure, Lse, and circumferential position are well involved. At first, for dealing with the effect of circumferential position, dominant points were identified from dominated points, and they were correlated apart from each other. On the other hand, the effects of pressure and Lse are involved well in Equations (2)–(3) and Equations (8)–(9). Especially, as shown in Figure 16, in the effective LFP pressure range from ambient to around 2.5 MPa [8], the primary items in both Equations (2) and (3) (as well as (8) and (9)) increase consistently with the increase of pressure, which indicates that these equations could represent the effect of pressure well.


## 4.5.1. Correlations on the Dominant Points

From the view of point of correlation, all of these factors should be involved. For three dominant points, 0.5-2, 0.75-2, and 1-3, on which liquid rewetting is controlled by flow instability. According to Equation (2) and Table 4, C1 for them are correlated to be 0.0643, 0.0748, and 0.086, respectively. It shows that C1 increases linearly with the increase of Lse (decrease of Lqf). In this way, based on Equation (2), qLFP on the dominant points for Lse=0.5, 0.75, and 1 m could be correlated by Equation (8). This correlation could be approved for dominant points in vertical section.
(8)qLFP=0.0425+0.0434LseρvHvlσvlgρl−ρvρl+ρv20.25.As discussed above, in the present study,qLFP decreases with the decrease of Lse for Lse=0.5m and its downstream. In addition, on 1.55-2, the dominant point on Lse=1.55m, and the horizontal section, C1 was correlated to be 0.1335, which has not been given above. This indicates the C1 values along the QF propagation, from 0.1335 (Lse=1.55m) to 0.086 (Lse=1m), 0.0748 (Lse=0.75m), and finally, 0.0643 (Lse=0.5m). These series of values are consistent to the literature data, in which C1 was correlated to be 0.09 [32] for room-temperature fluid in pool boiling. At first, the deviation of C1 between the present study and reference [32] is mainly caused by the variations between the fill-in flow in the exit-contracted pipe and pool boiling. On the other hand, the decrease of C1 along the reverse direction of the flow in the experimental section pipe indicates the special characteristics of flow in the exit-contracted pipe.Similarly, according to Equation (3), C2 for 0.5-2, 0.75-2, and 1-3 are correlated to be 0.573, 0.7139, and 0.8264, respectively. Similar with qLFP, hLFP on the dominant points for Lse=0.5, 0.75, and 1 m could be correlated by Equation (9). This series of data is consistent to the literature data, in which C2 was correlated to be 0.425 [33] for room-temperature fluid in pool boiling.
(9)hFB=0.324+0.5068Lsekv3Hvlρvgρl−ρvμvΔTiσvl/gρl−ρv0.25.Compared to the literature data from room-temperature fluid in pool boiling, dominant points in the vertical section are with lowerqLFP, lower ΔTLFP, and higher hLFP. Basically, this sort of differences is mainly caused by the variations on the system pressure and flow condition. On the other hand, the similarity on C1 and C2 between for exit-contracted pipe and pool boiling indicates that flow instability is the primary dominant factor, and Lse also plays a certain role for the dominant points on the present vertical pipe.


## 4.5.2. Correlations on the Dominated Points

For the dominated points, Equations (2) and (3) with constants listed in Table 4 could be suggested in the current stage. It has to be denoted that on this sort of points, liquid rewetting is not caused by local flow instability on this sort of points. On the contrary, the local instable wave has not been developed adequately. Result indicates that at tLFP, liquid rewetting happens on the dominant point on the current cross-section. Almost simultaneously, all of this cross-section is rewetted by the liquid as a result of QF propagation circumferentially from the dominant point. In this way, on the dominated points, as a result of being rewetted, qi, hi, and Ti at tLFP have to be denoted as parameters on LFP.


## 4.5.3. Correlation Approach and Correlation Formats

In the previous studies,qLFP and ∆TLFP were tried to be correlated, and hLFP has not been tried to be correlated before [8]. In the present study, qLFP and hLFP (instead of ∆TLFP) are correlated. This is the new correlation approach. In the recent studies, correlation formats for Equations (2)–(4) were approved to correlate qLFP, hLFP, and ∆TLFP, respectively. The primary items in these equations could be plotted versus pressure as shown in Figure 16.Figure 16
Parameter combinations in Equations (2)–(4) versus pressure.ForΔTLFP, as discussed above, there are two difficulties on reliable correlation, which determines it would not be considered to be correlated in the current stage. The first one is, as shown in Figures 13 and 16, parameter combination, with the increase of pressure from ambient to around 2.5 MPa, ELFP in Equation (4) shows the increasing-decreasing manner, which indicates that it could not represent the effects of pressure. On the other hand, with the increase of pressure, the variations of ΔTLFP show different manners for various Lse. The primary reason is ELFP and Equation (4) are approved for pool boiling in ambient-pressure, which could not be applied in high pressure cases.For both dominant point and dominated points,qLFP and hLFP are well correlated on the vertical section. This is primarily because the basic effects including pressure, Lse, and circumferential position are well involved. At first, for dealing with the effect of circumferential position, dominant points were identified from dominated points, and they were correlated apart from each other. On the other hand, the effects of pressure and Lse are involved well in Equations (2)–(3) and Equations (8)–(9). Especially, as shown in Figure 16, in the effective LFP pressure range from ambient to around 2.5 MPa [8], the primary items in both Equations (2) and (3) (as well as (8) and (9)) increase consistently with the increase of pressure, which indicates that these equations could represent the effect of pressure well.


## 5. New Correlation onqCHF and Discussions on the Critical Heat Flux Point

### 5.1. Basic Effect ofAinj

Figure17–19 shows the basic experimental data, where ∆TCHF, qCHF, and hCHF are plotted versus Ainj, respectively. With the decrease of Ainj, ΔTCHF shows the overall decreasing manner, and both qCHF and hCHF show the overall increasing-decreasing manner, primarily. This is similar with the results in the previous study for horizontal exit-contracted pipe [29].Figure 17
ExperimentalΔTCHF versus Ainj.Figure 18
ExperimentalqCHF versus Ainj.Figure 19
ExperimentalhCHF versus Ainj.


### 5.2. Evaluations on the Previous Correlations

In the previous studies, Equation (10) from transport pipe was recommended by the present authors to predict ΔTCHF for horizontal exit-contracted pipe [8, 28]. However, this equation was demonstrated to produce great deviations when predicting the previous set of data, where more detailed To was measured [29].
(10)ΔTCHF=TCHF−Tsat=1.345×10−5B,(11)B=Hvlρvgσvlρl−ρvρv20.25.Figure20 plots the experimental ΔTCHF versus parameter B in the present study. These figures show very similar with Figure 13. In this way, similar difficulties on correlations with LFP could be found, which could be discussed next.Figure 20
ExperimentalΔTCHF versus B.In the previous study, new correlations onqCHF have been approved for horizontal exit-contraction pipe [29] as shown in Equation (12) (Equation (13) is another version). This equation involves the effects of Lse and circumferential by constant C3, the effects of ul by ul−0.1149, and the effects of fluid properties by other items. In the present study, qCHF values could be correlated by Equation (13) as shown in Figure 21, where the constant C3 could be listed in Table 4, which indicates correlation equation approved from the horizontal exit-contracted pipe would be used in the present vertical exit-contracted pipe.
(12)qCHF=C3ul0.1149ρv0.1262Hvlρl‐ρvσvl0.1667ρl0.5405,(13)qCHFρvHvlul=C3ρlρvul0.250.8738σvlρlul2Dbu0.3333.Figure 21
Correlation onqCHF by Equation (12).


### 5.3. New Correlation onhCHF

For LFP, bothqLFP and hLFP could be correlated by the existing correlation format. In this way, ΔTLFP could be obtained correspondingly. This approach could be adopted when discussing CHF point. In this way, the possibility of correlating hCHF should be evaluated well. Basically, a number of correlations on heat transfer coefficient for nucleate boiling were approved in the previous studies.Forster-Zuber correlation was applied widely to predict heat transfer for nucleate boiling in pool [36]. In this correlation, the variation between saturation pressure on Ti (temperature inner wall), Psi, and Pp (pressure in the pipe) was assumed to vary linearly versus subcooling ΔTi, (Ti−Tsat), as Equation (14) shows. In this way, heat transfer coefficient could be predicted by Equation (15), where constant C4 indicates C·kFZ0.75. Experimental results show that in the present study, most TCHF values are higher than the critical temperature, which gives the constant Psi values. Of course, another possibility is this series of equations were approved for low-pressure cases. Nevertheless, this reduces the role of kFZ as shown in Equation (14), and the effects of kFZ could be just represented by C4 in Equation (15).
(14)Psi−Pp=kFZΔTi,(15)hNB=C4ρl0.5cpl0.125kl1.125Prl0.333ρv0.25Hvl0.25μvl0.625σvl0.5ΔTi.Comparison shows that, as shown in Equation (15), for CHF, with the increase of pressure, ρl0.5cpl0.125kl1.125Prl0.333/ρv0.25Hvl0.25μvl0.625σvl0.5 shows the overall increasing manner; however, ΔTCHF shows the contrary manner, which produces extra difficulties on correlation. In this way, the parameter combination could be revised as Equation (16) shows, and the present set of data could be plotted as shown in Figure 22. It shows that hCHF could be correlated by Equation (17), which produces the overall MAE of 2.3% and the max deviation 13.4%. The deviation bar has been plotted in the figure, where the red lines show the ±2% deviation on the present figure, and ±17.9% for the hCHF data.
(16)hCHF=C4ρv0.25Hvl0.25μvl0.625σvl0.5ρl0.5cpl0.125kl1.125Prl0.333ΔTCHFN,(17)hCHF=19511.9ρv0.25Hvl0.25μvl0.625σvl0.5ρl0.5cpl0.125kl1.125Prl0.333ΔTCHF0.6588.Figure 22
Correlation onhCHF by Equation (17).


### 5.4. Primary Effect Factors

Similar with LFP, the effects of pressure,Lse, and circumferential positions would be discussed in the present section.


#### 5.4.1. The Effect ofAinj or Pressure

CHF point could be recorded in a wide range from the ambient-pressure to around 4.0 MPa. Basically, as shown in Section5.1, in this pressure range, with the decrease of Ainj (increase of pressure), primarily, qCHF, ΔTCHF, and hCHF show the overall constant or increase-decrease manner. These factors are consistent to those approved in the previous studies [8, 29].


#### 5.4.2. The Effects ofLse

For LFP, at leastqLFP shows the obviously decreasing manner with the increase of Lqf. However, for the experimental data on qCHF and hCHF, the effects of Lse do not show the obvious regulations. In this way, correlations on these parameters do not involve Lse. At least, this indicates Lse plays ignorable roles on bubble separation.


#### 5.4.3. The Effects of Circumferential Position

The effect of circumferential position on CHF is similar to that of LFP. As shown in Table3, for every Lse, tCHF values for various circumferential positions (1, West; 2, South; 3, East) are quite similar to others. This indicates that the propagation of bubble separation “front” circumferentially plays significant roles on the CHF for a certain Lse cross-section. In addition, for a certain Lse, various circumferential positions are with various qCHF, hCHF, and TCHF. This indicates that, similar with LFP, for a certain Lse, there are both dominant point and dominated points. As shown in Table 3, dominant points for bubble separation (CHF), 0.5-2, 0.75-2, and 1-3 are same with those for liquid rewetting (LFP). This is because on the current cross-section, Ti on the dominant point decreases prior to other points, not only on film boiling section but also on transition boiling section. In this way, Ti on the dominant point is always the lowest on the current cross-section and dominates the boiling transitions on the current cross-section.


#### 5.4.4. Summaries on the Basic Factors

As discussed above, the effects of pressure,Lse, and circumferential position could be summarized and concluded as follows.
(1)
For a certain point, the increase of pressure produces overall decreasingqCHF, hCHF, and deceasing tCHF(2)
The effect ofLse plays ignorable roles on CHF, including qCHF and hCHF(3)
Similar with LFP, because of the propagation of bubble separation front circumferentially, on a certainLse (cross-section), there are both dominant point and dominated points, which are controlled by flow instability and both heat transfer and the dominant points. In the present study, 0.5-2, 0.75-2, and 1-3 are the dominant points for these sections, respectively


### 5.5. Discussions

#### 5.5.1. Correlation on the Dominant Points

From the view of point of correlation, the effects of both pressure and circumferential position should be involved. The related strategy is similar with that for LFP, by which the dominant points and dominated points would be discussed, respectively.As shown in Equation (12) and Table 4, in the present correlation on qCHF, C3 is correlated to be 0.00982, 0.00835, and 0.00994 for dominant points, 0.5-2, 0.75-2, and 1-3, respectively. This shows that C3 for 0.5-2 is well consistent to that for 1-3, which shows around 16% greater than that for 0.75-2. Of course, there is also another possibility that 0.75-2 is not the exactly dominant point. Nevertheless, for the dominant points in the vertical section, qCHF could be correlated by Equation (12), in which C3 could be suggested to be 0.00935, which produces the deviation within ±12%, referring Figure 21.Correlation format as Equation (12) shows for qCHF is much different from that in the pool boiling, in which qCHF was correlated to be linear versus parameter B as shown in Equation (11) [37]. Equation (12) was approved by the present authors, which represents the effects of bubble size and fluid properties by parameter combination and the effects of Lse and circumferential position by C3 [29]. Figure 21 shows that on the dominant points of the vertical section, qCHF is primarily controlled by bubble size and fluid properties, which are determined primarily by system pressure. In this way, on the vertical section of the present study, qCHF could be well correlated by Equation (12) with the C3 of 0.00935. Here, previous flow instability theories could not be used here, which has been discussed before [29].On the other hand, Equation (17) gives good correlations on hCHF for both dominant points and dominated points. With the increase of pressure, all of the parameters including qCHF, ΔTCHF, and hCHF show the overall decreasing manner. In this way, a new parameter combination has been set up referring F-Z equation, as shown in Equation (16), and reliable correlations have been obtained by Equation (17).


#### 5.5.2. Correlation on the Dominated Points

In the current stage, Equation (12) and C3 listed in Table 4 could be suggested to predict qCHF values for the dominated points. Similar with LFP, on this sort of points, bubble separation is not caused by local flow instability. Result indicates that at tCHF, bubble separation happens on the dominant point of the current cross-section. Almost simultaneously, bubbles are separated from the inner wall on all of this cross-section as a result of bubble separation front propagation circumferentially. In this way, on the dominated points, as a result of being separated, qi, hi, and Ti at tCHF have to be denoted as parameters on CHF.


#### 5.5.3. Correlation Formats and Analyses

In the previous studies,qCHF and ΔTCHF were always correlated [8]. However, in the present study, qCHF and hCHF were tried to be correlated instead of ΔTCHF. This is the new correlation approach, similar with LFP. The primary parameter combinations in Equation (11), (12), and (17), used to predict ΔTCHF, qCHF, and hCHF, respectively, could be plotted versus pressure in Figure 23.Figure 23
Pressure versus parameter combinations for CHF.As shown in Figure23, for ΔTCHF, the correlation difficulties are more or less similar to those for ΔTLFP. The key point is the primary parameter combination B in Equation (11) could not represent the effect of pressure.ForqCHF, analysis shows that the effects of pressure and circumferential position should be involved. In the present study, the strategies are similar with those for LFP. For involving the effect of circumferential position, dominant points and dominated points are identified. Results show that qCHF could be well correlated by Equation (12). For three dominant points, C3 in Equation (12) is approved to be 0.00935, and for dominated points, C3 in Equation (12) is listed in Table 4. On the other hand, parameter combination in Equation (12) decreases linearly with the increase of pressure as shown in Figure 23. This indicates the effect of pressure, determining bubble size, and fluid properties could be represented well by this correlation.ForhCHF, Equation (17) could be suggested for both dominant points and dominated points. It shows that on the vertical section, it is determined by ΔTCHF and fluid properties, which are dominated by pressure.


## 5.1. Basic Effect ofAinj

Figure17–19 shows the basic experimental data, where ∆TCHF, qCHF, and hCHF are plotted versus Ainj, respectively. With the decrease of Ainj, ΔTCHF shows the overall decreasing manner, and both qCHF and hCHF show the overall increasing-decreasing manner, primarily. This is similar with the results in the previous study for horizontal exit-contracted pipe [29].Figure 17
ExperimentalΔTCHF versus Ainj.Figure 18
ExperimentalqCHF versus Ainj.Figure 19
ExperimentalhCHF versus Ainj.


## 5.2. Evaluations on the Previous Correlations

In the previous studies, Equation (10) from transport pipe was recommended by the present authors to predict ΔTCHF for horizontal exit-contracted pipe [8, 28]. However, this equation was demonstrated to produce great deviations when predicting the previous set of data, where more detailed To was measured [29].
(10)ΔTCHF=TCHF−Tsat=1.345×10−5B,(11)B=Hvlρvgσvlρl−ρvρv20.25.Figure20 plots the experimental ΔTCHF versus parameter B in the present study. These figures show very similar with Figure 13. In this way, similar difficulties on correlations with LFP could be found, which could be discussed next.Figure 20
ExperimentalΔTCHF versus B.In the previous study, new correlations onqCHF have been approved for horizontal exit-contraction pipe [29] as shown in Equation (12) (Equation (13) is another version). This equation involves the effects of Lse and circumferential by constant C3, the effects of ul by ul−0.1149, and the effects of fluid properties by other items. In the present study, qCHF values could be correlated by Equation (13) as shown in Figure 21, where the constant C3 could be listed in Table 4, which indicates correlation equation approved from the horizontal exit-contracted pipe would be used in the present vertical exit-contracted pipe.
(12)qCHF=C3ul0.1149ρv0.1262Hvlρl‐ρvσvl0.1667ρl0.5405,(13)qCHFρvHvlul=C3ρlρvul0.250.8738σvlρlul2Dbu0.3333.Figure 21
Correlation onqCHF by Equation (12).


## 5.3. New Correlation onhCHF

For LFP, bothqLFP and hLFP could be correlated by the existing correlation format. In this way, ΔTLFP could be obtained correspondingly. This approach could be adopted when discussing CHF point. In this way, the possibility of correlating hCHF should be evaluated well. Basically, a number of correlations on heat transfer coefficient for nucleate boiling were approved in the previous studies.Forster-Zuber correlation was applied widely to predict heat transfer for nucleate boiling in pool [36]. In this correlation, the variation between saturation pressure on Ti (temperature inner wall), Psi, and Pp (pressure in the pipe) was assumed to vary linearly versus subcooling ΔTi, (Ti−Tsat), as Equation (14) shows. In this way, heat transfer coefficient could be predicted by Equation (15), where constant C4 indicates C·kFZ0.75. Experimental results show that in the present study, most TCHF values are higher than the critical temperature, which gives the constant Psi values. Of course, another possibility is this series of equations were approved for low-pressure cases. Nevertheless, this reduces the role of kFZ as shown in Equation (14), and the effects of kFZ could be just represented by C4 in Equation (15).
(14)Psi−Pp=kFZΔTi,(15)hNB=C4ρl0.5cpl0.125kl1.125Prl0.333ρv0.25Hvl0.25μvl0.625σvl0.5ΔTi.Comparison shows that, as shown in Equation (15), for CHF, with the increase of pressure, ρl0.5cpl0.125kl1.125Prl0.333/ρv0.25Hvl0.25μvl0.625σvl0.5 shows the overall increasing manner; however, ΔTCHF shows the contrary manner, which produces extra difficulties on correlation. In this way, the parameter combination could be revised as Equation (16) shows, and the present set of data could be plotted as shown in Figure 22. It shows that hCHF could be correlated by Equation (17), which produces the overall MAE of 2.3% and the max deviation 13.4%. The deviation bar has been plotted in the figure, where the red lines show the ±2% deviation on the present figure, and ±17.9% for the hCHF data.
(16)hCHF=C4ρv0.25Hvl0.25μvl0.625σvl0.5ρl0.5cpl0.125kl1.125Prl0.333ΔTCHFN,(17)hCHF=19511.9ρv0.25Hvl0.25μvl0.625σvl0.5ρl0.5cpl0.125kl1.125Prl0.333ΔTCHF0.6588.Figure 22
Correlation onhCHF by Equation (17).


## 5.4. Primary Effect Factors

Similar with LFP, the effects of pressure,Lse, and circumferential positions would be discussed in the present section.


### 5.4.1. The Effect ofAinj or Pressure

CHF point could be recorded in a wide range from the ambient-pressure to around 4.0 MPa. Basically, as shown in Section5.1, in this pressure range, with the decrease of Ainj (increase of pressure), primarily, qCHF, ΔTCHF, and hCHF show the overall constant or increase-decrease manner. These factors are consistent to those approved in the previous studies [8, 29].


### 5.4.2. The Effects ofLse

For LFP, at leastqLFP shows the obviously decreasing manner with the increase of Lqf. However, for the experimental data on qCHF and hCHF, the effects of Lse do not show the obvious regulations. In this way, correlations on these parameters do not involve Lse. At least, this indicates Lse plays ignorable roles on bubble separation.


### 5.4.3. The Effects of Circumferential Position

The effect of circumferential position on CHF is similar to that of LFP. As shown in Table3, for every Lse, tCHF values for various circumferential positions (1, West; 2, South; 3, East) are quite similar to others. This indicates that the propagation of bubble separation “front” circumferentially plays significant roles on the CHF for a certain Lse cross-section. In addition, for a certain Lse, various circumferential positions are with various qCHF, hCHF, and TCHF. This indicates that, similar with LFP, for a certain Lse, there are both dominant point and dominated points. As shown in Table 3, dominant points for bubble separation (CHF), 0.5-2, 0.75-2, and 1-3 are same with those for liquid rewetting (LFP). This is because on the current cross-section, Ti on the dominant point decreases prior to other points, not only on film boiling section but also on transition boiling section. In this way, Ti on the dominant point is always the lowest on the current cross-section and dominates the boiling transitions on the current cross-section.


### 5.4.4. Summaries on the Basic Factors

As discussed above, the effects of pressure,Lse, and circumferential position could be summarized and concluded as follows.
(1)
For a certain point, the increase of pressure produces overall decreasingqCHF, hCHF, and deceasing tCHF(2)
The effect ofLse plays ignorable roles on CHF, including qCHF and hCHF(3)
Similar with LFP, because of the propagation of bubble separation front circumferentially, on a certainLse (cross-section), there are both dominant point and dominated points, which are controlled by flow instability and both heat transfer and the dominant points. In the present study, 0.5-2, 0.75-2, and 1-3 are the dominant points for these sections, respectively


## 5.4.1. The Effect ofAinj or Pressure

CHF point could be recorded in a wide range from the ambient-pressure to around 4.0 MPa. Basically, as shown in Section5.1, in this pressure range, with the decrease of Ainj (increase of pressure), primarily, qCHF, ΔTCHF, and hCHF show the overall constant or increase-decrease manner. These factors are consistent to those approved in the previous studies [8, 29].


## 5.4.2. The Effects ofLse

For LFP, at leastqLFP shows the obviously decreasing manner with the increase of Lqf. However, for the experimental data on qCHF and hCHF, the effects of Lse do not show the obvious regulations. In this way, correlations on these parameters do not involve Lse. At least, this indicates Lse plays ignorable roles on bubble separation.


## 5.4.3. The Effects of Circumferential Position

The effect of circumferential position on CHF is similar to that of LFP. As shown in Table3, for every Lse, tCHF values for various circumferential positions (1, West; 2, South; 3, East) are quite similar to others. This indicates that the propagation of bubble separation “front” circumferentially plays significant roles on the CHF for a certain Lse cross-section. In addition, for a certain Lse, various circumferential positions are with various qCHF, hCHF, and TCHF. This indicates that, similar with LFP, for a certain Lse, there are both dominant point and dominated points. As shown in Table 3, dominant points for bubble separation (CHF), 0.5-2, 0.75-2, and 1-3 are same with those for liquid rewetting (LFP). This is because on the current cross-section, Ti on the dominant point decreases prior to other points, not only on film boiling section but also on transition boiling section. In this way, Ti on the dominant point is always the lowest on the current cross-section and dominates the boiling transitions on the current cross-section.


## 5.4.4. Summaries on the Basic Factors

As discussed above, the effects of pressure,Lse, and circumferential position could be summarized and concluded as follows.
(1)
For a certain point, the increase of pressure produces overall decreasingqCHF, hCHF, and deceasing tCHF(2)
The effect ofLse plays ignorable roles on CHF, including qCHF and hCHF(3)
Similar with LFP, because of the propagation of bubble separation front circumferentially, on a certainLse (cross-section), there are both dominant point and dominated points, which are controlled by flow instability and both heat transfer and the dominant points. In the present study, 0.5-2, 0.75-2, and 1-3 are the dominant points for these sections, respectively


## 5.5. Discussions

### 5.5.1. Correlation on the Dominant Points

From the view of point of correlation, the effects of both pressure and circumferential position should be involved. The related strategy is similar with that for LFP, by which the dominant points and dominated points would be discussed, respectively.As shown in Equation (12) and Table 4, in the present correlation on qCHF, C3 is correlated to be 0.00982, 0.00835, and 0.00994 for dominant points, 0.5-2, 0.75-2, and 1-3, respectively. This shows that C3 for 0.5-2 is well consistent to that for 1-3, which shows around 16% greater than that for 0.75-2. Of course, there is also another possibility that 0.75-2 is not the exactly dominant point. Nevertheless, for the dominant points in the vertical section, qCHF could be correlated by Equation (12), in which C3 could be suggested to be 0.00935, which produces the deviation within ±12%, referring Figure 21.Correlation format as Equation (12) shows for qCHF is much different from that in the pool boiling, in which qCHF was correlated to be linear versus parameter B as shown in Equation (11) [37]. Equation (12) was approved by the present authors, which represents the effects of bubble size and fluid properties by parameter combination and the effects of Lse and circumferential position by C3 [29]. Figure 21 shows that on the dominant points of the vertical section, qCHF is primarily controlled by bubble size and fluid properties, which are determined primarily by system pressure. In this way, on the vertical section of the present study, qCHF could be well correlated by Equation (12) with the C3 of 0.00935. Here, previous flow instability theories could not be used here, which has been discussed before [29].On the other hand, Equation (17) gives good correlations on hCHF for both dominant points and dominated points. With the increase of pressure, all of the parameters including qCHF, ΔTCHF, and hCHF show the overall decreasing manner. In this way, a new parameter combination has been set up referring F-Z equation, as shown in Equation (16), and reliable correlations have been obtained by Equation (17).


### 5.5.2. Correlation on the Dominated Points

In the current stage, Equation (12) and C3 listed in Table 4 could be suggested to predict qCHF values for the dominated points. Similar with LFP, on this sort of points, bubble separation is not caused by local flow instability. Result indicates that at tCHF, bubble separation happens on the dominant point of the current cross-section. Almost simultaneously, bubbles are separated from the inner wall on all of this cross-section as a result of bubble separation front propagation circumferentially. In this way, on the dominated points, as a result of being separated, qi, hi, and Ti at tCHF have to be denoted as parameters on CHF.


### 5.5.3. Correlation Formats and Analyses

In the previous studies,qCHF and ΔTCHF were always correlated [8]. However, in the present study, qCHF and hCHF were tried to be correlated instead of ΔTCHF. This is the new correlation approach, similar with LFP. The primary parameter combinations in Equation (11), (12), and (17), used to predict ΔTCHF, qCHF, and hCHF, respectively, could be plotted versus pressure in Figure 23.Figure 23
Pressure versus parameter combinations for CHF.As shown in Figure23, for ΔTCHF, the correlation difficulties are more or less similar to those for ΔTLFP. The key point is the primary parameter combination B in Equation (11) could not represent the effect of pressure.ForqCHF, analysis shows that the effects of pressure and circumferential position should be involved. In the present study, the strategies are similar with those for LFP. For involving the effect of circumferential position, dominant points and dominated points are identified. Results show that qCHF could be well correlated by Equation (12). For three dominant points, C3 in Equation (12) is approved to be 0.00935, and for dominated points, C3 in Equation (12) is listed in Table 4. On the other hand, parameter combination in Equation (12) decreases linearly with the increase of pressure as shown in Figure 23. This indicates the effect of pressure, determining bubble size, and fluid properties could be represented well by this correlation.ForhCHF, Equation (17) could be suggested for both dominant points and dominated points. It shows that on the vertical section, it is determined by ΔTCHF and fluid properties, which are dominated by pressure.


## 5.5.1. Correlation on the Dominant Points

From the view of point of correlation, the effects of both pressure and circumferential position should be involved. The related strategy is similar with that for LFP, by which the dominant points and dominated points would be discussed, respectively.As shown in Equation (12) and Table 4, in the present correlation on qCHF, C3 is correlated to be 0.00982, 0.00835, and 0.00994 for dominant points, 0.5-2, 0.75-2, and 1-3, respectively. This shows that C3 for 0.5-2 is well consistent to that for 1-3, which shows around 16% greater than that for 0.75-2. Of course, there is also another possibility that 0.75-2 is not the exactly dominant point. Nevertheless, for the dominant points in the vertical section, qCHF could be correlated by Equation (12), in which C3 could be suggested to be 0.00935, which produces the deviation within ±12%, referring Figure 21.Correlation format as Equation (12) shows for qCHF is much different from that in the pool boiling, in which qCHF was correlated to be linear versus parameter B as shown in Equation (11) [37]. Equation (12) was approved by the present authors, which represents the effects of bubble size and fluid properties by parameter combination and the effects of Lse and circumferential position by C3 [29]. Figure 21 shows that on the dominant points of the vertical section, qCHF is primarily controlled by bubble size and fluid properties, which are determined primarily by system pressure. In this way, on the vertical section of the present study, qCHF could be well correlated by Equation (12) with the C3 of 0.00935. Here, previous flow instability theories could not be used here, which has been discussed before [29].On the other hand, Equation (17) gives good correlations on hCHF for both dominant points and dominated points. With the increase of pressure, all of the parameters including qCHF, ΔTCHF, and hCHF show the overall decreasing manner. In this way, a new parameter combination has been set up referring F-Z equation, as shown in Equation (16), and reliable correlations have been obtained by Equation (17).


## 5.5.2. Correlation on the Dominated Points

In the current stage, Equation (12) and C3 listed in Table 4 could be suggested to predict qCHF values for the dominated points. Similar with LFP, on this sort of points, bubble separation is not caused by local flow instability. Result indicates that at tCHF, bubble separation happens on the dominant point of the current cross-section. Almost simultaneously, bubbles are separated from the inner wall on all of this cross-section as a result of bubble separation front propagation circumferentially. In this way, on the dominated points, as a result of being separated, qi, hi, and Ti at tCHF have to be denoted as parameters on CHF.


## 5.5.3. Correlation Formats and Analyses

In the previous studies,qCHF and ΔTCHF were always correlated [8]. However, in the present study, qCHF and hCHF were tried to be correlated instead of ΔTCHF. This is the new correlation approach, similar with LFP. The primary parameter combinations in Equation (11), (12), and (17), used to predict ΔTCHF, qCHF, and hCHF, respectively, could be plotted versus pressure in Figure 23.Figure 23
Pressure versus parameter combinations for CHF.As shown in Figure23, for ΔTCHF, the correlation difficulties are more or less similar to those for ΔTLFP. The key point is the primary parameter combination B in Equation (11) could not represent the effect of pressure.ForqCHF, analysis shows that the effects of pressure and circumferential position should be involved. In the present study, the strategies are similar with those for LFP. For involving the effect of circumferential position, dominant points and dominated points are identified. Results show that qCHF could be well correlated by Equation (12). For three dominant points, C3 in Equation (12) is approved to be 0.00935, and for dominated points, C3 in Equation (12) is listed in Table 4. On the other hand, parameter combination in Equation (12) decreases linearly with the increase of pressure as shown in Figure 23. This indicates the effect of pressure, determining bubble size, and fluid properties could be represented well by this correlation.ForhCHF, Equation (17) could be suggested for both dominant points and dominated points. It shows that on the vertical section, it is determined by ΔTCHF and fluid properties, which are dominated by pressure.


## 6. Conclusion

LO2 chill-down in a vertical exit-contracted pipe was studied experimentally. Wall temperature was detected in detail (various Lse and circumferential position, 1-east, 2-south, and 3-west) to investigate the filling and chill-down process. The filling and chill-down process was described in detail, on which the propagation of quenching front (QF) was detected. Two QFs were found, one for the exit QF and another for the inlet QF. It has been found that the chill-down process is controlled mainly by the formation and propagation of QFs, which are determined by the pressure level. Based on the experimental data, qLFP, hLFP, qCHF, and hCHF were correlated, respectively, for the vertical section. Primary conclusions could be listed as follows.
(1)
During LO2 chill-down process in the vertical exit-contracted pipe, both exit QF and inlet QF are detected. Results show that on most cases, the propagation of the exit QF dominates the liquid rewetting for Lse=0.5m and its downstreams(2)
For both LFP and CHF, circumferential position plays significant roles. On the vertical section, because of the proportions of QF or bubble separation front circumferentially, when LFP or CHF happens on the dominant point, LFP or CHF would happen on the same cross-section (dominated points) in a short period. On the dominant points, LFP is controlled by the flow instability, and CHF is controlled by the bubble size and fluid properties. However, on the dominated points, both LFP and CHF are determined by the dominant points and heat transfer themselves(3)
BothΔTLFP and ΔTCHF have not been tried to be correlated. A series of difficulties have been discussed. At first, these two parameters are not independent themselves, and they are both determined by other parameters. On the other hand, the current parameter combinations could not represent the effects of pressure in such a wide range of pressure(4)
Equations (8) and (9), involving the effects of pressure and Lse could be suggested to predict qLFP, and hLFP on the dominant points. Equations (2) and (3), with the similar formats with Equations (8) and (9) could be suggested to predict qLFP and hLFP on the dominated points by constant in Table 4(5)
ForqCHF, Equation (12) would be suggested, with C3 of 0.00935 for dominant points and C3 listed in Table 4 for dominated points. Equation (17) could be strongly suggested to predict hCHF for both sorts of points.



---

*Source: 5899199-2022-08-23.xml*