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Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model
international journal of hydrogen energy xxx (xxxx) xxx
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Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model Yao Zheng a,b, Huawei Chang a,*, Yinan Qiu b, Chen Duan c, Jianye Chen a, Hong Chen b, Shuiming Shu a a
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China State Key Laboratory of Technologies in Space Cryogenic Propellants, Beijing 100028, China c Wuhan Second Ship Design and Research Institute, Wuhan 430064, China b
highlights A CFD model is built to predict liquid hydrogen flow boiling CHF under microgravity. Wall temperature and CHF location were compared for different gravity conditions. Effects of inlet velocity and inlet sub-cooling on the CHF of LH2 are investigated. The CHF location moves upstream with the decrease of the gravity-induced buoyancy.
article info
abstract
Article history:
Critical heat flux (CHF) of liquid hydrogen (LH2) flow boiling under microgravity is vital for
Received 16 August 2019
designing space cryogenic propellant conveying pipe since the excursion of wall temper-
Received in revised form
ature may cause system failure. In this study, a two-dimensional axisymmetric model
14 November 2019
based on the wall heat flux partition (WHFP) model was proposed to predict the CHF
Accepted 27 December 2019
condition under microgravity including the wall temperature and the CHF location. The
Available online xxx
proposed numerical model was validated to demonstrate a good agreement between the simulated and experimentally reported results. Then, the wall temperature distribution
Keywords:
and the CHF location under different gravity conditions were compared. In addition, the
Liquid hydrogen
WHFP and vapor-liquid distribution along the wall under microgravity were predicted and
Flow boiling
its difference with terrestrial gravity condition was also analysed and reported. Finally, the
Critical heat flux
effects of flow velocity and inlet sub-cooling on the wall temperature distributions were
Microgravity
analysed under microgravity and terrestrial gravity conditions, respectively. The results
Wall heat flux partition
indicate that the CHF location moves upstream about 5.25 m from 1g to 104g since the void
Numerical study
fraction near the wall reaches the breakpoint of CHF condition much earlier under the microgravity condition. Furthermore, the increase of the velocity and decrease of the subcooling have smaller effects on the CHF location during LH2 flow boiling under microgravity. © 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author. E-mail address: [email protected] (H. Chang). https://doi.org/10.1016/j.ijhydene.2019.12.197 0360-3199/© 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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Introduction In the past few decades, hydrogen/liquid hydrogen (LH2) has been extensively used in different fields, such as unmanned undersea vehicles, fuel cell vehicles, domestic heating devices, coolants for superconductors and cryogenic propellants, owing to its excellent specific impulse upon reaction with oxidants [1e4]. Deep space exploration vehicles should have the ability to store and refill cryogenic propellants, including LH2, during the rocket engine re-ignition in space [5e8]. Typically, cryogenic fluids are conveyed by an adiabatic pipeline, which seeks to minimise energy consumption [9]. The critical heat flux (CHF) condition is characterized by a sharp increasement of wall temperature due to the replacement of liquid adjacent to the heating surface. CHF is an important parameter for designing LH2 conveying pipes, as it determines the maximal allowable heat dissipation rate [10]; exceeding this maximal rate may seriously damage heating surfaces. Thus, understanding the differences of the mechanisms of CHF under microgravity condition with that under terrestrial gravity condition is critical for the successful development of LH2 conveying system under microgravity conditions. The vast majority of the previous CHF researches on boiling under microgravity condition focused on pool boiling. Most of these studies pointed out the occurrence of the CHF at very low heat fluxes, owing to the enormous bubble growth that occurred in the absence of gravitational force [11e13]. Hence, an urgent need in the studies of the flow boiling CHF under microgravity condition is to broaden the useful range of the nucleate boiling heat flux, as operating in the nucleate boiling region below CHF allows to attain both high nucleate boiling heat transfer coefficient and low surface temperature [14]. Ohta [15] obtained limited flow boiling CHF data under microgravity conditions with high inlet quality. However, local wall temperature distributions could not be measured because of the structure of the transparent heated wall. Ma and Chung [16] performed forced-convection boiling of FC-72 under microgravity conditions and observed a reduction in the CHF. However, for sufficiently high flow rates, the difference attributed to microgravity tended to decrease. Zhang et al. [17] conducted a flow boiling CHF experiment onboard a parabolic flight with FC-72. Their results suggested that, the CHF under microgravity is much smaller than the terrestrial one for low flow velocities. Verthier et al. [18] quenched a vertical glass tube by FC-72 during a parabolic flight, and the measured CHF under microgravity had almost the same magnitude compared with terrestrial gravity except for a larger wall superheating. As for cryogenic fluids, Kawanami et al. [19] conducted a liquid nitrogen (LN2) quenching experiment at a low mass velocity under microgravity condition by dropping from a tower at the Japan Microgravity Centre. The measured boiling curve revealed that the CHF under microgravity is about 0.8 times smaller than that under terrestrial condition. These experimental results indicated that LN2 contacted the inner wall earlier under microgravity. Liu et al. [20] conducted a flow boiling CHF experiment with LN2 in a horizontal small channel, the results indicated that both the departure from nucleate boiling (DNB) type and dryout type CHF are significantly affected by the gravity effect.
Flow boiling CHF experiments under microgravity are very complex and costly; therefore, numerical study based on CHF models can compromise readiness to future flow boiling experiments in the space environment. Different theoretical models have been proposed, including the interfacial lift-off model, the boundary layer separation model, and the dry out model et al. [19,21e26]. In recent years, multiphase computational fluid dynamics (CFD) modelling has been extensively used for prediction andvalidationtheflowboilingCHF.Thismethodcanalsoprovide insights into complicated mechanisms of vapor-liquid flows under terrestrial gravity conditions. Wang et al. [27] employed the lattice Boltzmann method to study the effect of merging bubbles on the flow boiling characteristics, and their results indicated the addition of surfactant to the CHF. Kim and Lee [28] numerically investigated the effects of wettability and inertia on flow boiling CHF, they found that the hydrophilic and hydrophobic channels enhanced the CHF at low and high mass fluxes, respectively. Li et al. [29] validated the Eulerian multiphase boiling model for a range of two-dimensional (2D) and threedimensional (3D) boiling flows by predicting nucleated boiling and the CHF. This model can reasonably well predict the location and the temperature increase for different CHF locations. Zhang et al. [30] embedded the Rensselaer Polytechnic Institute heat flux partition model into mixture multiphase models with userdefined functions (UDFs), and the improved model not only overcame theconvergence difficulty but also betterpredicted the CHF in comparison with the experimental measurements. Pothukuchi et al. [31] examined closure models by comparing the wall temperature predictions and the mean relative error for the CHF in a tube, and demonstrated that the error is within 15%. In addition, they identified the CHF location in an annulus and a rod bundle. Zhang et al. [32] developed a CFD model to validate their experiments conducted at a high-pressure CHF facility. The predictedCHFwasingoodagreementwithhighmassflux,yetthe deviation increased with decreasing mass flux. These authors assumed that the deviation occurred because the flow regime changed from bubbly to churn as the mass flux decreased. Zhang et al. [33] investigated the CHF of external reactor vessel cooling (ERVC), and their results agreed well with the experimental data obtained at the State Power Technology Research and Development Centre. Inaddition,thepressure,velocity, and void fraction distribution were also analysed. According to the literature survey, the existing studies on the CHF mainly focus on experimentation with normal temperature fluids under microgravity conditions or in-silico validation of the wall temperature distributions against the experimental data under terrestrial gravity conditions. There has been rarely attention paid to the CHF of LH2 flow boiling under microgravity. Understanding the difference of LH2 flow boiling CHF between microgravity and terrestrial gravity is essential for deep understanding of the LH2 flow boiling phenomenon under microgravity. Thence, simulations of flow boiling CHF with LH2 in a vertical pipeline were conducted. The primary goal of the present study was to predict the flow boiling CHF condition of LH2 under microgravity based on the Eulerian-Eulerian multiphase flow (EEMF) model and the WHFP model. Wall temperature and heat flux partitions in conjunction with the void fraction distribution were compared for microgravity and terrestrial gravity conditions.
Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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In addition, influence factors, such as inlet velocity and inlet sub-cooling, were also analysed.
Physical model and methodology Physical model To numerically analyse the CHF state of LH2 in a vertical transportation pipeline under microgravity, a 2D axisymmetric model was developed, as shown in Fig. 1. The inner diameter (Di) was 0.2 m according to the actual LH2 conveying pipe of a rocket launching field, and the length was selected as 8 m to ensure the occurrence of the CHF phenomenon. The subcooled LH2 entered from the bottom and travelled upward through the pipeline. The flow boiling CHF condition could be divided into four regimes, i.e. single-phase convention, nucleate boiling, film boiling and post dry-out. In the liquid single-phase convection regime, the subcooled LH2 has not reached saturation temperature, hence a single-phase convective heat transfer was in dominant. As the LH2 flows
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further through the pipeline, the LH2 reached the saturation temperature and boiling occurred with more energy transferred from the heated wall, this regime was characterized by nucleate boiling. Then, the CHF occurred when heated wall was no longer wetted by boiling LH2 with the excursion of wall temperatures. And wall boiling departs from the nucleate boiling regime to the film boiling regime. While under microgravity condition, the CHF may occur much earlier when the vapor hydrogen gathered near the heated wall with the absence of gravity driven effect.
Methodology Wall heat flux partition model To describe the LH2 flow boiling CHF condition, the wall heat flux partition model developed by Kurual and Podowski was adopted. This model has proved its accuracy and reliability in simulating flow boiling with a variety of working fluids including cryogenic propellants [34e37]. When boiling occurs at a heated wall, different heat transfer mechanisms need to be modelled. The total heat flux from the wall to LH2 can be divided into three additive components, as shown in Fig. 2 [38]. qW ¼ qC þ qQ þ qE ;
(1)
where qC ; qQ ; qE are the convective heat flux, the quenching heat flux, and the evaporative heat flux in the single phase, respectively. Note that the heated wall surface is subdivided into the area covered by nucleating bubbles (Ab ) and the remaining portion covered by the liquid (1-Ab ). Therefore, the convective heat flux qC can be calculated as: qC ¼ hC ðTW Tl Þð1 Ab Þ
Fig. 1 e Schematic of the vertical conveying pipe and the flow states.
(2)
Fig. 2 e Wall heat flux partition model.
Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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here, hC is the single-phase heat transfer coefficient, TW and Tl are the wall and liquid temperatures, respectively. The quenching heat flux qQ is the cyclic averaged transient energy transfer related to the liquid filling the wall vicinity after the bubbles’ detachment, and is 2kl qQ ¼ pffiffiffiffiffiffiffiffiffiffiffi ðTw Tl Þ; pll td
(3)
where kl is the conductivity, td is the periodic time, and ll ¼ is the thermal diffusivity. The evaporative heat flux qE is qE ¼ Vd Nw rv hfv fd ;
kl rl Cpl
(4)
where Vd and fd represent the volume of the bubble based on the bubble departure diameter and the bubble departure frequency, respectively. Nw and rv are the active nucleate site density and vapor density, respectively. hfv is the latent heat of evaporation. In the wall heat flux partition model, the vapor temperature is assumed to be constant at the saturation temperature. However, at the CHF and post dry-out states, the space filled by the liquid near the heated wall is replaced by the vapor, accompanied by the excursion of the wall surface temperature and increasing vapor temperature. The WHFP model was thus extended by Lavieville et al. [39] to the following: qW ¼ qC;l þ qQ þ qE f ðal Þ þ ð1 f ðal ÞÞqC;v
(5)
The extra heat flux qC;v in this model represents the convective heat flux of the vapor phase, and it is qC;v ¼ hC;v ðTW Tv Þ
(7)
K ¼ 4:8e
(8)
Jasub 80
(9)
where Jasub is the sub-cooled Jacob number, which is defined as: rCpl DTsub ; Jasub ¼ rv hfv where DTsub ¼ Tsat Tl .
The empirical correlation defined by Tolubinski and Kostanchuk [44] was chosen to calculate the bubble departure diameter Dw as recommended in Refs. [1,42] for cryogenic fluids. 0
1
Dw ¼ min@0:0014; 0:0006e
DTsub 45:0
A
(12)
The frequency of the bubble departure fd for cryogenic fluids can be calculated by the following equation [45], which was also well verified in Ref. [42]. fd ¼
1 ¼ td
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4gðrl rv Þ ; 3rl CBD Dw
(13)
where CBD refers to the bubble drag coefficient in the boiling flow with the value of 1.
Interfacial momentum transfer model The interaction between the two phases was modelled by the interfacial forces, including the drag force, lift force, and turbulent dispersion force. In this study, the drag force was calculated as: 1 FD ¼ CD rp uR juR jAd ; 2
(14)
where the drag coefficient CD is the minimum of the viscous dis regime (Cvis D ) and the distorted regime (CD ): dis CD ¼ min Cvis D ; CD
(15)
The lift force was calculated from Drew’s equation [46]: (16)
where the lift force coefficient Cl can be estimated as:
The empirical constant K usually ranges from 1.8 to 5 based on Del Valle and Kenning’s findings [41]:
(11)
! up V! uq ! uq ; F lift ¼ Cl rq ap !
where the break points are av;1 ¼ 0:9,av;2 ¼ 0:95. The area of the bubble influence is defined as Nw pD2w Ab ¼ min 1; K 4
Nw ¼ Cn ðTW Tsat Þn
(6)
The convective heat transfer coefficient hC;v is computed from the wall function formulations. Taking the thin film boiling into consideration in the WHFP model, the function f ðal Þ can be estimated using the relation proposed by Ioilev et al. [40]: av av;1 ;1 ; f ðal Þ ¼ 1 f ðav Þ ¼ 1 max 0; min av;2 av;1
The nucleate site density NW is usually represented by a correlation based on the wall superheating and its applicability in simulating cryogenic fluids flow boiling has been validated in Refs. [1,36,42]. The empirical parameters n and C were set as 1.805 and 210, respectively, according to Lemmert and Chawla’s study [43]:
(10)
Cl ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 ðCl，lowRe Þ2 þ Cl，highRe ;
(17)
u q is the primary In which, rq is the primary phase density, ! phase velocity. ap is the secondary phase volume fraction, and ! u p is the secondary phase velocity. The turbulent dispersion force accounted for the interphase turbulent momentum transfer. In this study, The turbulent dispersion force was obtained as follows: ! ! F td;q ¼ F td;p ¼ CTD rq kq Vap ;
(18)
where rq is the primary phase density, kq is the turbulent kinetic energy in the primary phase, Vap is the gradient of the secondary phase volume fraction, and CTD was set to the default value of 1.
Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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The volumetric rate of energy transfer between the phases Qpq , was assumed to be a function of the temperature difference and the interfacial area Ai :
Qpq ¼ hpq Ai Tp Tq ;
(19)
where hpq is the volumetric heat transfer coefficient between the pth and qth phase. It is related to the Nusselt number of the pth phase, which is defined as follows: Nup ¼ 2:0 þ 0:6Rep1=2 Pr1=3 q ;
(20)
where Rep is the relative Reynolds number based on the up ! u q , diameter of the pth phase and the relative velocity ! and Pr is the Prandtl number of the qth phase: Prq ¼
cpq uq kq
(21)
In Fig. 3, the simulated wall temperature along the axial direction is compared with the experimental results from T1 to T7. Clearly, the simulation results are in a reasonably good agreement with the experimental data, especially in the nucleate boiling region, although the temperature near the exit is over predicted due to the early occurrence of the CHF in the simulation. In fact, the agreement between the simulation and experimental data became better if the wall heat flux was reduced to 9.76 W/cm2 in simulation. The deviation may be attributed to that the wall temperature at the CHF location increasing rapidly even with a very small increase in the wall heat flux at CHF condition. Thus, small fluctuations of the wall heat flux may result in large deviations of the wall temperature distribution near the CHF location. In general, the proposed model was considered to be effective for studying the CHF condition of LH2.
Numerical approaches and boundary conditions
Model validation Extensive literature survey has been performed to select suitable experimental data for model validation. However, no experimental data about LH2 has been published up to now. Therefore, liquid nitrogen (LN2) was selected as the working fluid for validating the proposed model, considering that some of its thermophysical properties are similar to those of LH2. The simulation results were validated against the experimental data published by Qi [10,47]. In the experiment, the length of the micro-tube was 250 mm, and its inner diameter was 0.531 mm. The inlet mass flux was 1062.7 kg/m2s. Seven T-type thermocouples (T1 to T7) were mounted in the tube at every 25 mm. In the simulation process, the geometrical and boundary conditions are completely consistent with the experiment. To reach the CHF state, the average heat flux in the experiment was slightly increased from 10.36 to 10.76 W/ cm2. When the wall temperature at T7 increased sharply, it indicated the occurrence of the CHF state. In the simulation, the wall heat flux is set as 10.76 W/cm2. The model validation results are shown in Fig. 3.
Results and discussions Prediction of CHF condition under microgravity Fig. 4 shows the wall temperature distribution along the axial direction with the inlet velocity at 1 m/s and inlet temperature at 18 K. Furthermore, a constant wall heat flux of 40,000 W is applied. It can be seen that, the CHF tends to occur much earlier and the wall temperature at the CHF location becomes higher with the decrease of gravity acceleration. The CHF location under microgravity (104g) is around 0.5 m from inlet, which is 5 m ahead that under terrestrial gravity. Besides, the predicted temperature at the CHF location is about 800 K under microgravity, which is 2.6 times larger than that under terrestrial gravity. Two types of the CHF characterisation, dryout and DNB, could reasonably explain the different wall temperature distributions in our study. Under microgravity, the absence of buoyancy subdues the bubble detachment and allows the bubbles to continue to propagate along the heating surface. As a result, the heat transfer between the heated wall and LH2 are restricted despite the presence of adequate bulk LH2 elsewhere within the pipeline. Under terrestrial gravity, 260
Experimental results Simulation results q=10.76W/cm2
220
Wall Temperature (K)
The structured grid of the computational domain was generated with the near wall mesh refined to fulfil the y þ requirement. The overall number of cells was 40,000, which was confirmed to be sufficient for the required calculation precision through cell independence analysis. For numerical computations, a steady-state solver based on pressure was adopted. The volume fraction equation was discretised using the modified HRIC algorithm, and second-order implicit discretisation was used for momentum and energy equations. Boundary conditions of the velocity inlet and pressure outlet were imposed. The wall heat flux was a constant 40,000 W, to ensure that the CHF occurred under both terrestrial and microgravity conditions. Saturation properties was assumed for both the LH2 and vapor phases at the atmospheric pressure. A no slip condition was imposed on the walls of the flow area. In this work, the Re-Normalisation Group (RNG) k-ε model along with non-equilibrium wall functions was adopted, and as in previous studies, it was shown to yield accurate CHF predictions.
Simulation results q=9.76W/cm2
180
140
100
60
0
50
100
150
200
250
Axial Position (mm)
Fig. 3 e Comparison of simulated and experimentally measured wall temperatures.
Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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Fig. 4 e Comparison of wall temperature along the axial direction.
the body force plays an important role in the bubble detachment near the heated wall. The CHF only occurs in highquality flows as the liquid film near the heated wall is consumed by evaporation. Under intermediate gravity (between 102ge0.1g), the CHF locations can be classified into the DNB-type CHF. The first wall temperature peak appears owing to the dispersed large bubble attached to the wall, while the second peak is related to the initial formation of the vapor layer alongside the heated wall. In general, the DNB-type CHF under microgravity precipitates larger wall temperature excursions, which potentially cause more serious damages to the heated wall compared with the terrestrial gravity scenario. As the wall heat fluxes (qW) can be subdivided into four parts, i.e. evaporation heat flux (qE), quenching heat flux (qQ), liquid phase heat flux (qC,l), and vapor phase heat flux (qC,v), it is instructive to compare wall heat flux partitions under microgravity and terrestrial gravity conditions. The results are illustrated in Fig. 5. Obviously, the evaporation heat flux dominates prior to the CHF in the nucleate boiling regime and decreases rapidly afterwards under both microgravity and terrestrial gravity conditions. The quenching heat flux is only significant near the upstream before the CHF, because it represents the transient energy of LH2 that fills the wall vicinity
after bubble detachment. In addition, the liquid phase heat flux remains insignificant throughout the pipeline. The vapor phase heat flux increases rapidly and reaches its maximum corresponding to the temperature excursion at the CHF location. For the terrestrial gravity condition, the evaporation heat flux contributes the most to the heat transfer process, which is more than 75% of the total heat flux before CHF. However, the vapor phase heat flux is dominant with 100% throughout the wall after CHF occurs under the microgravity condition. This difference may be also attributed to the different mechanisms of the CHF between microgravity and terrestrial gravity, as discussed in Fig. 4. To better understand the different mechanisms of the CHF under microgravity and terrestrial gravity conditions, the void fractions (hydrogen vapor volume fractions) along the radial direction from x ¼ 0.5 m to x ¼ 7.5 m are analysed in Fig. 6. Fig. 6(a) depicts that the void fraction near the wall ranges from 0.5 to 0.6 in the upstream section (0e2.5 m) of the pipeline under terrestrial gravity condition, which indicates the existence of a considerable amount of LH2 along the heated wall. As LH2 flows through the pipeline, the bulk and nearwall LH2 gradually evaporate and the void fraction increases in both regions. The CHF occurs when the void fraction reaches the breakpoint (in this case av ¼ 0.95 at the axial location of about 5.5 m in the near-wall regain). For the microgravity condition, the void fraction in the near-wall region steeply increases to the breakpoint at the axial position of about 0.5 m, and remains almost the same alongside the wall. Hence, the flow pattern is inverted annular flow. That is, the vapor film takes over the near-wall region and liquid exists only in the mainstream near the axial area. It can also be seen from Fig. 6(b) that the thickness of the vapor film increases from 0.05 mm to 0.18 mm from inlet to outlet. Under this circumstance, the heat flux from the heated wall to the bulk liquid can only be delivered through convective heat transfer between the two phases. The difference between the vapor-liquid distribution under different gravity conditions is shown in Fig. 7. Owing to the interfacial drag forces caused by the velocity difference in the axial direction, some vapor bubbles adjacent to the wall move to the centre of the pipeline in the terrestrial gravity scenario, which creates a path for the LH2 to replenish the cavity. By contrast, the drag forces between the liquid and vapor are negligible as the liquid and vapor phase have the same
Fig. 5 e Comparison of wall heat flux partitions (a: 1g; b: 10¡4g). Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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Fig. 6 e Comparison of void fractions in the radial direction (a: 1g; b: 10¡4g). velocity in microgravity scenario. Thus, the liquid and vapor are clearly stratified. This results in a deterioration of the heat transfer intensity and an increase of the wall temperature.
state under microgravity and terrestrial gravity conditions tend to be the same.
Effect of inlet sub-cooling on the CHF condition Effect of inlet velocity on the CHF condition After the comparison of the LH2 CHF condition under microgravity and terrestrial gravity conditions, the main influence factors for both conditions are analysed. Fig. 8 shows the wall temperature distributions with different inlet velocity. As can be seen, the CHF location shifts downstream with the increase of the inlet velocity, which means a positive correlation of CHF value with the inlet velocity in both conditions. However, the influence of inlet velocity on the CHF under terrestrial gravity is much more significant. The CHF location moves backwards about 2.5 m with every 0.5 m/s increasement in terrestrial gravity scenario. When the inlet velocity exceeds above 2 m/s, the CHF state disappears and is replaced by nucleate boiling throughout the pipeline. This is mainly because higher inlet velocity results in a larger inertia force, which can flush bubbles from the heated wall and create a path for LH2 to replenish the heated wall. For microgravity scenario, the CHF state remains even when the inlet velocity is up to 3 m/s and more temperature excursions appear at higher inlet velocity. In addition, the figure shows that when the velocity is large enough, the CHF
Another important factor that affects the CHF state is the inlet sub-cooling. Fig. 9 shows the wall temperature along the axial direction with different inlet sub-cooling. With the increase of the inlet sub-cooling, the CHF location shifts downstream under both the microgravity and terrestrial gravity conditions. This result indicates that higher inlet sub-cooling requires higher wall heat flux magnitude to reach the CHF state. For terrestrial gravity scenario, CHF location shifts downstream about 2 m with the inlet-subcooling changes. The CHF state may disappear when the inlet-subcooling is greater than 6 K. While for microgravity scenario, the CHF location moves 0.25 m backwards, which is much smaller than that in terrestrial gravity scenario. In addition, unlike the terrestrial gravity scenario, the temperature at CHF location in the microgravity scenario increases with higher inlet sub-cooling. On one hand, high inlet sub-cooling inhibits the evaporation of LH2; on the other hand, high sub-cooling tends to reduce the bubble diameter according to Eq. (14). Thus, the gap between the bubbles alongside the wall becomes smaller with higher inlet sub-cooling. By contrast, the temperature at CHF
Fig. 7 e Comparison of flow patterns and streamlines. Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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Fig. 8 e Wall temperature along the axial direction (a: 1g; b: 10¡4g).
Fig. 9 e Wall temperature along the axial direction, for different inlet sub-cooling values (a: 1g; b: 10¡4g).
locations varies only little due to a similar void fraction around the CHF location for terrestrial gravity scenario.
Conclusions In the present work, a 2D axisymmetric model was developed to study the flow boiling CHF state of LH2 in a vertical pipeline under microgravity based on the EEMF model in conjunction with the WHFP model. The validation results demonstrate that the proposed model predicts reasonably well the distributions of wall temperature under CHF state. Then, the wall temperature distribution, wall heat flux partition, void fraction, as well as flow patterns under microgravity were predicted and compared with terrestrial conditions. In addition, different operating conditions, including flow velocity and inlet sub-cooling, were considered to further study the inconsistent CHF state under microgravity and terrestrial gravity conditions. The main findings of this study are as follows: The CHF location shifts downstream with the increase of the gravity acceleration owing to the differences between the dry-out and DNB type CHFs, which indicates a smaller heat flux demand in the low-gravity environment to reach the CHF state. The CHF under microgravity condition precipitates larger wall temperature excursions
(about 2.6 times larger than that under terrestrial gravity), which potentially does greater damage to the heated wall. In the absence of the gravity induced body force under the microgravity condition, the bubble detachment is suppressed, which causes bubbles to propagate along the surface. Hence, the vapor phase convective heat flux dominates the heat transfer between 0.5 m from inlet and outlet. By contrast, the evaporative heat flux dominates the heat transfer under terrestrial gravity with more than 75% of total heat flux before CHF. The void fraction breakpoint is reached in the downstream section of the pipeline at about 5.5 m under terrestrial gravity condition, while the value is about 0.5 m in the microgravity scenario. This is mainly because liquid and vapor phase have the same velocity in the microgravity scenario, which result in the bubbles gathering near the heating surface. Since the dry-out type CHF is harder to achieve with larger velocity, the inlet velocity can much more significantly affect the flow boiling CHF under the terrestrial gravity condition than that under the microgravity condition. When the velocity is large enough, the CHF state under microgravity and terrestrial gravity conditions tend to be the same. The critical temperature increases with larger inlet subcooling, owing to smaller bubble diameters and a
Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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narrower bubble gap in the microgravity scenario. In addition, the inlet sub-cooling has a greater influence on the CHF condition in the terrestrial gravity scenario.
Acknowledgement This work was supported by the National Natural Science Foundation of China (No. 51806071), the State Key Laboratory of Technologies in the Space Cryogenic Propellants (No. SKLTSCP1813) and the Fundamental Research Funds for the Central Universities, HUST (No. 2018JYCXJJ028).
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[14] Konishi C, Mudawar I. Review of flow boiling and critical heat flux in microgravity. Int J Heat Mass Transf 2015;80:469e93. [15] Ohta H. Experiments on microgravity boiling heat transfer by using transparent heaters. Nucl Eng Des 1997;175:167e80. [16] Ma Y, Chung JN. An experimental study of critical heat flux (CHF) in microgravity forced-convection boiling. Int J Multiph Flow 2001;27:1753e67. [17] Zhang H, Mudawar I, Hasan MM. Flow boiling CHF in microgravity. Int J Heat Mass Transf 2005;48:3107e18. [18] Verthier B, Celata GP, Zummo G, Colin C, Follet J. Effect of gravity on film boiling heat transfer and rewetting temperature during quenching. Microgravity Sci Technol 2009;21:185e91. [19] Kawanami O, Azuma H, Ohta H. Effect of gravity on cryogenic boiling heat transfer during tube quenching. Int J Heat Mass Transf 2007;50:3490e7. [20] Liu XF, Chen XY, Zhang QY, Wang SB, Hou Y, Chen L. Investigation on CHF of saturated liquid nitrogen flow boiling in a horizontal small channel. Appl Therm Eng 2017;125:1025e36. [21] Konishi C, Lee H, Mudawar I, Hasan MM, Nahra HK, Hall NR, et al. Flow boiling in microgravity: Part 2eCritical heat flux interfacial behavior, experimental data, and model. Int J Heat Mass Transf 2015;81:721e36. [22] Kutateladze S, Leont’ev A. Some applications of the asymptotic theory of the turbulent boundary layer. In: Proceedings of the third international heat transfer conference: Am. Inst. Chem. Engrs New York; 1966. p. 1e6. [23] Lee C, Mudawwar I. A mechanistic critical heat flux model for subcooled flow boiling based on local bulk flow conditions. Int J Multiph Flow 1988;14:711e28. [24] Huang C-N, Kharangate CR. A new mechanistic model for predicting flow boiling critical heat flux based on hydrodynamic instabilities. Int J Heat Mass Transf 2019;138:1295e309. [25] Xie HY, Yang D, Wang WY, Wan L, Li CM. An improved DNBtype critical heat flux prediction model for flow boiling at subcritical pressures in vertical rifled tube. Int J Heat Mass Transf 2019;132:209e20. [26] Hu H, Weibel JA, Garimella SV. A coupled wicking and evaporation model for prediction of pool boiling critical heat flux on structured surfaces. Int J Heat Mass Transf 2019;136:373e82. [27] Wang J, Cheng Y, Li XB, Li FC. Experimental and LBM simulation study on the effect of bubbles merging on flow boiling. Int J Heat Mass Transf 2019;132:1053e61. [28] Kim J, Lee JS. Numerical study on the effects of inertia and wettability on subcooled flow boiling in microchannels. Appl Therm Eng 2019;152:175e83. [29] Li H, Vasquez SA, Punekar H, Muralikrishnan R. Prediction of boiling and critical heat flux using an eulerian multiphase boiling model. In: ASME 2011 international mechanical engineering congress and exposition. American Society of Mechanical Engineers; 2011. p. 463e76. [30] Zhang YP, Zhang R, Tian WX, Su GH, Qiu SZ. Numerical prediction of CHF based on CFD methodology under atmospheric pressure and low flow rate. Appl Therm Eng 2019;149:881e8. [31] Pothukuchi H, Kelm S, Patnaik BSV, Prasad BVSSS, Allelein HJ. CFD modeling of critical heat flux in flow boiling: validation and assessment of closure models. Appl Therm Eng 2019;150:651e65. [32] Zhang R, Duarte JP, Cong TL, Corradini ML. Investigation on the critical heat flux in a 2 by 2 fuel assembly under low flow rate and high pressure with a CFD methodology. Ann Nucl Energy 2019;124:69e79.
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[33] Zhang X, Hu T, Chen DQ, Zhong YK, Gao H. CFD simulation on critical heat flux of flow boiling in IVR-ERVC of a nuclear reactor. Nucl Eng Des 2016;304:70e9. [34] Li X, Gu A, Wang R. Numerical simulation of flow boiling of cryogenic liquids in tubes. In: Proceedings of the twentieth international cryogenic engineering conference (ICEC20). Elsevier; 2005. p. 865e8. [35] Li XD, Wei W, Wang RS, Shi YM. Numerical and experimental investigation of heat transfer on heating surface during subcooled boiling flow of liquid nitrogen. Int J Heat Mass Transf 2009;52:1510e6. [36] Chen JY, Zeng RR, Zhang XB, Qiu LM, Xie JL. Numerical modeling of flow film boiling in cryogenic chilldown process using the AIAD framework. Int J Heat Mass Transf 2018;124:269e78. [37] Murallidharan JS, Prasad BVSSS, Patnaik BSV, Hewitt GF, Badalassi V. CFD investigation and assessment of wall heat flux partitioning model for the prediction of high pressure subcooled flow boiling. Int J Heat Mass Transf 2016;103:211e30. [38] Kurul N, Podowski M. On the modeling of multidimensional effects in boiling channels. In: ANS proceeding of the 27th national heat transfer conference. New York: American Society of Mechanical Engineers; 1991. [39] Lavieville J, Quemerais E, Mimouni S, Boucker M, Mechitoua N. NEPTUNE CFD V1. 0 theory manual. Rapport interne EDF H-I81-2006-04377-EN Rapport NEPTUNE Nept_2004_L, vol. 1; 2006. [40] Ioilev A, Samigulin M, Ustinenko V, Kucherova P, Tentner A, Lo S, et al. Advances in the modeling of cladding heat transfer and critical heat flux in boiling water reactor fuel assemblies. In: Proc 12th international topical meeting on nuclear reactor thermal hydraulics. Pittsburgh, Pennsylvania, USA: NURETH-12; 2007. [41] Del Valle VH, Kenning D. Subcooled flow boiling at high heat flux. Int J Heat Mass Transf 1985;28:1907e20. [42] Li XD, Wang RS, Huang RG, Shi YM. Numerical investigation of boiling flow of nitrogen in a vertical tube using the twofluid model. Appl Therm Eng 2006;26:2425e32. [43] Lemmert M, Chawla J. Influence of flow velocity on surface boiling heat transfer coefficient. Heat Transf Boil 1977;237:247. [44] Tolubinsky V, Kostanchuk D. Vapour bubbles growth rate and heat transfer intensity at subcooled water boiling. Int Heat Tran Conf 1970;4. Begel House Inc. [45] Cole R. A photographic study of pool boiling in the region of the critical heat flux. AIChE J 1960;6:533e8. [46] Drew D, Lahey R. In particulate two-phase flow, vol. 509. Boston: ButterworthL Heinemann; 1993. p. 566. [47] Qi S, Zhang P, Wang R, Xu L. Flow boiling of liquid nitrogen in micro-tubes: Part IeThe onset of nucleate boiling, two-phase flow instability and two-phase flow pressure drop. Int J Heat Mass Transf 2007;50:4999e5016.
Ai : Interfacial area (m2) CBD: Bubble drag coefficient CD : Drag force coefficient Cl : Lift force coefficient Cp: Specific heat capacity (J/kg K) CTD : Constant 1 Di: Inner diameter of horizontal tube (m) Dw : Bubble departure diameter (m) fd : Frequency of bubble departure (s1) FD : Drag force (N) ! F : Lift force (N) !lift F td;q : Turbulent dispersion force (N) g: Gravitational acceleration (m/s2) hfv : Latent heat of evaporation (W/kg) Jasub : Subcooled Jacob number k: Turbulent kinetic energy (m2/s2) K, C, n: Constant L: Total length of horizontal tube (m) Nu: Nusselt number NW : Nucleate site density (m2) Pr: Prandtl number q: Heat flux (W/m2) Qpq : Volumetric rate of energy transfer between phases (W) Re: Reynolds number T: Temperature (K) td: Periodic time (s) u: Velocity (m/s) uR: Relative velocity of primary and secondary phase (m/s) x: Axial Location (m) DTsub : Subcooled temperature (K) Subscripts C: Convective E: Evaporative in: Inlet l: Liquid p: pth phase q: qth phase Q: Quenching sub: Subcooling sat: Saturation v: Vapor W: Wall Greek symbols a: Volume fraction k: Conductivity (W/m k) l: Diffusivity (m2/s) m: Dynamic viscosity (N s/m2) r: Density (kg/m3)
Nomenclature Ab : Area of influence (m2) Ad: Projected area of a typical particle (m2)
Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
Available online at www.sciencedirect.com
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Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model Yao Zheng a,b, Huawei Chang a,*, Yinan Qiu b, Chen Duan c, Jianye Chen a, Hong Chen b, Shuiming Shu a a
School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China State Key Laboratory of Technologies in Space Cryogenic Propellants, Beijing 100028, China c Wuhan Second Ship Design and Research Institute, Wuhan 430064, China b
highlights A CFD model is built to predict liquid hydrogen flow boiling CHF under microgravity. Wall temperature and CHF location were compared for different gravity conditions. Effects of inlet velocity and inlet sub-cooling on the CHF of LH2 are investigated. The CHF location moves upstream with the decrease of the gravity-induced buoyancy.
article info
abstract
Article history:
Critical heat flux (CHF) of liquid hydrogen (LH2) flow boiling under microgravity is vital for
Received 16 August 2019
designing space cryogenic propellant conveying pipe since the excursion of wall temper-
Received in revised form
ature may cause system failure. In this study, a two-dimensional axisymmetric model
14 November 2019
based on the wall heat flux partition (WHFP) model was proposed to predict the CHF
Accepted 27 December 2019
condition under microgravity including the wall temperature and the CHF location. The
Available online xxx
proposed numerical model was validated to demonstrate a good agreement between the simulated and experimentally reported results. Then, the wall temperature distribution
Keywords:
and the CHF location under different gravity conditions were compared. In addition, the
Liquid hydrogen
WHFP and vapor-liquid distribution along the wall under microgravity were predicted and
Flow boiling
its difference with terrestrial gravity condition was also analysed and reported. Finally, the
Critical heat flux
effects of flow velocity and inlet sub-cooling on the wall temperature distributions were
Microgravity
analysed under microgravity and terrestrial gravity conditions, respectively. The results
Wall heat flux partition
indicate that the CHF location moves upstream about 5.25 m from 1g to 104g since the void
Numerical study
fraction near the wall reaches the breakpoint of CHF condition much earlier under the microgravity condition. Furthermore, the increase of the velocity and decrease of the subcooling have smaller effects on the CHF location during LH2 flow boiling under microgravity. © 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author. E-mail address: [email protected] (H. Chang). https://doi.org/10.1016/j.ijhydene.2019.12.197 0360-3199/© 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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Introduction In the past few decades, hydrogen/liquid hydrogen (LH2) has been extensively used in different fields, such as unmanned undersea vehicles, fuel cell vehicles, domestic heating devices, coolants for superconductors and cryogenic propellants, owing to its excellent specific impulse upon reaction with oxidants [1e4]. Deep space exploration vehicles should have the ability to store and refill cryogenic propellants, including LH2, during the rocket engine re-ignition in space [5e8]. Typically, cryogenic fluids are conveyed by an adiabatic pipeline, which seeks to minimise energy consumption [9]. The critical heat flux (CHF) condition is characterized by a sharp increasement of wall temperature due to the replacement of liquid adjacent to the heating surface. CHF is an important parameter for designing LH2 conveying pipes, as it determines the maximal allowable heat dissipation rate [10]; exceeding this maximal rate may seriously damage heating surfaces. Thus, understanding the differences of the mechanisms of CHF under microgravity condition with that under terrestrial gravity condition is critical for the successful development of LH2 conveying system under microgravity conditions. The vast majority of the previous CHF researches on boiling under microgravity condition focused on pool boiling. Most of these studies pointed out the occurrence of the CHF at very low heat fluxes, owing to the enormous bubble growth that occurred in the absence of gravitational force [11e13]. Hence, an urgent need in the studies of the flow boiling CHF under microgravity condition is to broaden the useful range of the nucleate boiling heat flux, as operating in the nucleate boiling region below CHF allows to attain both high nucleate boiling heat transfer coefficient and low surface temperature [14]. Ohta [15] obtained limited flow boiling CHF data under microgravity conditions with high inlet quality. However, local wall temperature distributions could not be measured because of the structure of the transparent heated wall. Ma and Chung [16] performed forced-convection boiling of FC-72 under microgravity conditions and observed a reduction in the CHF. However, for sufficiently high flow rates, the difference attributed to microgravity tended to decrease. Zhang et al. [17] conducted a flow boiling CHF experiment onboard a parabolic flight with FC-72. Their results suggested that, the CHF under microgravity is much smaller than the terrestrial one for low flow velocities. Verthier et al. [18] quenched a vertical glass tube by FC-72 during a parabolic flight, and the measured CHF under microgravity had almost the same magnitude compared with terrestrial gravity except for a larger wall superheating. As for cryogenic fluids, Kawanami et al. [19] conducted a liquid nitrogen (LN2) quenching experiment at a low mass velocity under microgravity condition by dropping from a tower at the Japan Microgravity Centre. The measured boiling curve revealed that the CHF under microgravity is about 0.8 times smaller than that under terrestrial condition. These experimental results indicated that LN2 contacted the inner wall earlier under microgravity. Liu et al. [20] conducted a flow boiling CHF experiment with LN2 in a horizontal small channel, the results indicated that both the departure from nucleate boiling (DNB) type and dryout type CHF are significantly affected by the gravity effect.
Flow boiling CHF experiments under microgravity are very complex and costly; therefore, numerical study based on CHF models can compromise readiness to future flow boiling experiments in the space environment. Different theoretical models have been proposed, including the interfacial lift-off model, the boundary layer separation model, and the dry out model et al. [19,21e26]. In recent years, multiphase computational fluid dynamics (CFD) modelling has been extensively used for prediction andvalidationtheflowboilingCHF.Thismethodcanalsoprovide insights into complicated mechanisms of vapor-liquid flows under terrestrial gravity conditions. Wang et al. [27] employed the lattice Boltzmann method to study the effect of merging bubbles on the flow boiling characteristics, and their results indicated the addition of surfactant to the CHF. Kim and Lee [28] numerically investigated the effects of wettability and inertia on flow boiling CHF, they found that the hydrophilic and hydrophobic channels enhanced the CHF at low and high mass fluxes, respectively. Li et al. [29] validated the Eulerian multiphase boiling model for a range of two-dimensional (2D) and threedimensional (3D) boiling flows by predicting nucleated boiling and the CHF. This model can reasonably well predict the location and the temperature increase for different CHF locations. Zhang et al. [30] embedded the Rensselaer Polytechnic Institute heat flux partition model into mixture multiphase models with userdefined functions (UDFs), and the improved model not only overcame theconvergence difficulty but also betterpredicted the CHF in comparison with the experimental measurements. Pothukuchi et al. [31] examined closure models by comparing the wall temperature predictions and the mean relative error for the CHF in a tube, and demonstrated that the error is within 15%. In addition, they identified the CHF location in an annulus and a rod bundle. Zhang et al. [32] developed a CFD model to validate their experiments conducted at a high-pressure CHF facility. The predictedCHFwasingoodagreementwithhighmassflux,yetthe deviation increased with decreasing mass flux. These authors assumed that the deviation occurred because the flow regime changed from bubbly to churn as the mass flux decreased. Zhang et al. [33] investigated the CHF of external reactor vessel cooling (ERVC), and their results agreed well with the experimental data obtained at the State Power Technology Research and Development Centre. Inaddition,thepressure,velocity, and void fraction distribution were also analysed. According to the literature survey, the existing studies on the CHF mainly focus on experimentation with normal temperature fluids under microgravity conditions or in-silico validation of the wall temperature distributions against the experimental data under terrestrial gravity conditions. There has been rarely attention paid to the CHF of LH2 flow boiling under microgravity. Understanding the difference of LH2 flow boiling CHF between microgravity and terrestrial gravity is essential for deep understanding of the LH2 flow boiling phenomenon under microgravity. Thence, simulations of flow boiling CHF with LH2 in a vertical pipeline were conducted. The primary goal of the present study was to predict the flow boiling CHF condition of LH2 under microgravity based on the Eulerian-Eulerian multiphase flow (EEMF) model and the WHFP model. Wall temperature and heat flux partitions in conjunction with the void fraction distribution were compared for microgravity and terrestrial gravity conditions.
Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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In addition, influence factors, such as inlet velocity and inlet sub-cooling, were also analysed.
Physical model and methodology Physical model To numerically analyse the CHF state of LH2 in a vertical transportation pipeline under microgravity, a 2D axisymmetric model was developed, as shown in Fig. 1. The inner diameter (Di) was 0.2 m according to the actual LH2 conveying pipe of a rocket launching field, and the length was selected as 8 m to ensure the occurrence of the CHF phenomenon. The subcooled LH2 entered from the bottom and travelled upward through the pipeline. The flow boiling CHF condition could be divided into four regimes, i.e. single-phase convention, nucleate boiling, film boiling and post dry-out. In the liquid single-phase convection regime, the subcooled LH2 has not reached saturation temperature, hence a single-phase convective heat transfer was in dominant. As the LH2 flows
3
further through the pipeline, the LH2 reached the saturation temperature and boiling occurred with more energy transferred from the heated wall, this regime was characterized by nucleate boiling. Then, the CHF occurred when heated wall was no longer wetted by boiling LH2 with the excursion of wall temperatures. And wall boiling departs from the nucleate boiling regime to the film boiling regime. While under microgravity condition, the CHF may occur much earlier when the vapor hydrogen gathered near the heated wall with the absence of gravity driven effect.
Methodology Wall heat flux partition model To describe the LH2 flow boiling CHF condition, the wall heat flux partition model developed by Kurual and Podowski was adopted. This model has proved its accuracy and reliability in simulating flow boiling with a variety of working fluids including cryogenic propellants [34e37]. When boiling occurs at a heated wall, different heat transfer mechanisms need to be modelled. The total heat flux from the wall to LH2 can be divided into three additive components, as shown in Fig. 2 [38]. qW ¼ qC þ qQ þ qE ;
(1)
where qC ; qQ ; qE are the convective heat flux, the quenching heat flux, and the evaporative heat flux in the single phase, respectively. Note that the heated wall surface is subdivided into the area covered by nucleating bubbles (Ab ) and the remaining portion covered by the liquid (1-Ab ). Therefore, the convective heat flux qC can be calculated as: qC ¼ hC ðTW Tl Þð1 Ab Þ
Fig. 1 e Schematic of the vertical conveying pipe and the flow states.
(2)
Fig. 2 e Wall heat flux partition model.
Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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here, hC is the single-phase heat transfer coefficient, TW and Tl are the wall and liquid temperatures, respectively. The quenching heat flux qQ is the cyclic averaged transient energy transfer related to the liquid filling the wall vicinity after the bubbles’ detachment, and is 2kl qQ ¼ pffiffiffiffiffiffiffiffiffiffiffi ðTw Tl Þ; pll td
(3)
where kl is the conductivity, td is the periodic time, and ll ¼ is the thermal diffusivity. The evaporative heat flux qE is qE ¼ Vd Nw rv hfv fd ;
kl rl Cpl
(4)
where Vd and fd represent the volume of the bubble based on the bubble departure diameter and the bubble departure frequency, respectively. Nw and rv are the active nucleate site density and vapor density, respectively. hfv is the latent heat of evaporation. In the wall heat flux partition model, the vapor temperature is assumed to be constant at the saturation temperature. However, at the CHF and post dry-out states, the space filled by the liquid near the heated wall is replaced by the vapor, accompanied by the excursion of the wall surface temperature and increasing vapor temperature. The WHFP model was thus extended by Lavieville et al. [39] to the following: qW ¼ qC;l þ qQ þ qE f ðal Þ þ ð1 f ðal ÞÞqC;v
(5)
The extra heat flux qC;v in this model represents the convective heat flux of the vapor phase, and it is qC;v ¼ hC;v ðTW Tv Þ
(7)
K ¼ 4:8e
(8)
Jasub 80
(9)
where Jasub is the sub-cooled Jacob number, which is defined as: rCpl DTsub ; Jasub ¼ rv hfv where DTsub ¼ Tsat Tl .
The empirical correlation defined by Tolubinski and Kostanchuk [44] was chosen to calculate the bubble departure diameter Dw as recommended in Refs. [1,42] for cryogenic fluids. 0
1
Dw ¼ min@0:0014; 0:0006e
DTsub 45:0
A
(12)
The frequency of the bubble departure fd for cryogenic fluids can be calculated by the following equation [45], which was also well verified in Ref. [42]. fd ¼
1 ¼ td
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4gðrl rv Þ ; 3rl CBD Dw
(13)
where CBD refers to the bubble drag coefficient in the boiling flow with the value of 1.
Interfacial momentum transfer model The interaction between the two phases was modelled by the interfacial forces, including the drag force, lift force, and turbulent dispersion force. In this study, the drag force was calculated as: 1 FD ¼ CD rp uR juR jAd ; 2
(14)
where the drag coefficient CD is the minimum of the viscous dis regime (Cvis D ) and the distorted regime (CD ): dis CD ¼ min Cvis D ; CD
(15)
The lift force was calculated from Drew’s equation [46]: (16)
where the lift force coefficient Cl can be estimated as:
The empirical constant K usually ranges from 1.8 to 5 based on Del Valle and Kenning’s findings [41]:
(11)
! up V! uq ! uq ; F lift ¼ Cl rq ap !
where the break points are av;1 ¼ 0:9,av;2 ¼ 0:95. The area of the bubble influence is defined as Nw pD2w Ab ¼ min 1; K 4
Nw ¼ Cn ðTW Tsat Þn
(6)
The convective heat transfer coefficient hC;v is computed from the wall function formulations. Taking the thin film boiling into consideration in the WHFP model, the function f ðal Þ can be estimated using the relation proposed by Ioilev et al. [40]: av av;1 ;1 ; f ðal Þ ¼ 1 f ðav Þ ¼ 1 max 0; min av;2 av;1
The nucleate site density NW is usually represented by a correlation based on the wall superheating and its applicability in simulating cryogenic fluids flow boiling has been validated in Refs. [1,36,42]. The empirical parameters n and C were set as 1.805 and 210, respectively, according to Lemmert and Chawla’s study [43]:
(10)
Cl ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 ðCl，lowRe Þ2 þ Cl，highRe ;
(17)
u q is the primary In which, rq is the primary phase density, ! phase velocity. ap is the secondary phase volume fraction, and ! u p is the secondary phase velocity. The turbulent dispersion force accounted for the interphase turbulent momentum transfer. In this study, The turbulent dispersion force was obtained as follows: ! ! F td;q ¼ F td;p ¼ CTD rq kq Vap ;
(18)
where rq is the primary phase density, kq is the turbulent kinetic energy in the primary phase, Vap is the gradient of the secondary phase volume fraction, and CTD was set to the default value of 1.
Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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The volumetric rate of energy transfer between the phases Qpq , was assumed to be a function of the temperature difference and the interfacial area Ai :
Qpq ¼ hpq Ai Tp Tq ;
(19)
where hpq is the volumetric heat transfer coefficient between the pth and qth phase. It is related to the Nusselt number of the pth phase, which is defined as follows: Nup ¼ 2:0 þ 0:6Rep1=2 Pr1=3 q ;
(20)
where Rep is the relative Reynolds number based on the up ! u q , diameter of the pth phase and the relative velocity ! and Pr is the Prandtl number of the qth phase: Prq ¼
cpq uq kq
(21)
In Fig. 3, the simulated wall temperature along the axial direction is compared with the experimental results from T1 to T7. Clearly, the simulation results are in a reasonably good agreement with the experimental data, especially in the nucleate boiling region, although the temperature near the exit is over predicted due to the early occurrence of the CHF in the simulation. In fact, the agreement between the simulation and experimental data became better if the wall heat flux was reduced to 9.76 W/cm2 in simulation. The deviation may be attributed to that the wall temperature at the CHF location increasing rapidly even with a very small increase in the wall heat flux at CHF condition. Thus, small fluctuations of the wall heat flux may result in large deviations of the wall temperature distribution near the CHF location. In general, the proposed model was considered to be effective for studying the CHF condition of LH2.
Numerical approaches and boundary conditions
Model validation Extensive literature survey has been performed to select suitable experimental data for model validation. However, no experimental data about LH2 has been published up to now. Therefore, liquid nitrogen (LN2) was selected as the working fluid for validating the proposed model, considering that some of its thermophysical properties are similar to those of LH2. The simulation results were validated against the experimental data published by Qi [10,47]. In the experiment, the length of the micro-tube was 250 mm, and its inner diameter was 0.531 mm. The inlet mass flux was 1062.7 kg/m2s. Seven T-type thermocouples (T1 to T7) were mounted in the tube at every 25 mm. In the simulation process, the geometrical and boundary conditions are completely consistent with the experiment. To reach the CHF state, the average heat flux in the experiment was slightly increased from 10.36 to 10.76 W/ cm2. When the wall temperature at T7 increased sharply, it indicated the occurrence of the CHF state. In the simulation, the wall heat flux is set as 10.76 W/cm2. The model validation results are shown in Fig. 3.
Results and discussions Prediction of CHF condition under microgravity Fig. 4 shows the wall temperature distribution along the axial direction with the inlet velocity at 1 m/s and inlet temperature at 18 K. Furthermore, a constant wall heat flux of 40,000 W is applied. It can be seen that, the CHF tends to occur much earlier and the wall temperature at the CHF location becomes higher with the decrease of gravity acceleration. The CHF location under microgravity (104g) is around 0.5 m from inlet, which is 5 m ahead that under terrestrial gravity. Besides, the predicted temperature at the CHF location is about 800 K under microgravity, which is 2.6 times larger than that under terrestrial gravity. Two types of the CHF characterisation, dryout and DNB, could reasonably explain the different wall temperature distributions in our study. Under microgravity, the absence of buoyancy subdues the bubble detachment and allows the bubbles to continue to propagate along the heating surface. As a result, the heat transfer between the heated wall and LH2 are restricted despite the presence of adequate bulk LH2 elsewhere within the pipeline. Under terrestrial gravity, 260
Experimental results Simulation results q=10.76W/cm2
220
Wall Temperature (K)
The structured grid of the computational domain was generated with the near wall mesh refined to fulfil the y þ requirement. The overall number of cells was 40,000, which was confirmed to be sufficient for the required calculation precision through cell independence analysis. For numerical computations, a steady-state solver based on pressure was adopted. The volume fraction equation was discretised using the modified HRIC algorithm, and second-order implicit discretisation was used for momentum and energy equations. Boundary conditions of the velocity inlet and pressure outlet were imposed. The wall heat flux was a constant 40,000 W, to ensure that the CHF occurred under both terrestrial and microgravity conditions. Saturation properties was assumed for both the LH2 and vapor phases at the atmospheric pressure. A no slip condition was imposed on the walls of the flow area. In this work, the Re-Normalisation Group (RNG) k-ε model along with non-equilibrium wall functions was adopted, and as in previous studies, it was shown to yield accurate CHF predictions.
Simulation results q=9.76W/cm2
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Fig. 3 e Comparison of simulated and experimentally measured wall temperatures.
Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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Fig. 4 e Comparison of wall temperature along the axial direction.
the body force plays an important role in the bubble detachment near the heated wall. The CHF only occurs in highquality flows as the liquid film near the heated wall is consumed by evaporation. Under intermediate gravity (between 102ge0.1g), the CHF locations can be classified into the DNB-type CHF. The first wall temperature peak appears owing to the dispersed large bubble attached to the wall, while the second peak is related to the initial formation of the vapor layer alongside the heated wall. In general, the DNB-type CHF under microgravity precipitates larger wall temperature excursions, which potentially cause more serious damages to the heated wall compared with the terrestrial gravity scenario. As the wall heat fluxes (qW) can be subdivided into four parts, i.e. evaporation heat flux (qE), quenching heat flux (qQ), liquid phase heat flux (qC,l), and vapor phase heat flux (qC,v), it is instructive to compare wall heat flux partitions under microgravity and terrestrial gravity conditions. The results are illustrated in Fig. 5. Obviously, the evaporation heat flux dominates prior to the CHF in the nucleate boiling regime and decreases rapidly afterwards under both microgravity and terrestrial gravity conditions. The quenching heat flux is only significant near the upstream before the CHF, because it represents the transient energy of LH2 that fills the wall vicinity
after bubble detachment. In addition, the liquid phase heat flux remains insignificant throughout the pipeline. The vapor phase heat flux increases rapidly and reaches its maximum corresponding to the temperature excursion at the CHF location. For the terrestrial gravity condition, the evaporation heat flux contributes the most to the heat transfer process, which is more than 75% of the total heat flux before CHF. However, the vapor phase heat flux is dominant with 100% throughout the wall after CHF occurs under the microgravity condition. This difference may be also attributed to the different mechanisms of the CHF between microgravity and terrestrial gravity, as discussed in Fig. 4. To better understand the different mechanisms of the CHF under microgravity and terrestrial gravity conditions, the void fractions (hydrogen vapor volume fractions) along the radial direction from x ¼ 0.5 m to x ¼ 7.5 m are analysed in Fig. 6. Fig. 6(a) depicts that the void fraction near the wall ranges from 0.5 to 0.6 in the upstream section (0e2.5 m) of the pipeline under terrestrial gravity condition, which indicates the existence of a considerable amount of LH2 along the heated wall. As LH2 flows through the pipeline, the bulk and nearwall LH2 gradually evaporate and the void fraction increases in both regions. The CHF occurs when the void fraction reaches the breakpoint (in this case av ¼ 0.95 at the axial location of about 5.5 m in the near-wall regain). For the microgravity condition, the void fraction in the near-wall region steeply increases to the breakpoint at the axial position of about 0.5 m, and remains almost the same alongside the wall. Hence, the flow pattern is inverted annular flow. That is, the vapor film takes over the near-wall region and liquid exists only in the mainstream near the axial area. It can also be seen from Fig. 6(b) that the thickness of the vapor film increases from 0.05 mm to 0.18 mm from inlet to outlet. Under this circumstance, the heat flux from the heated wall to the bulk liquid can only be delivered through convective heat transfer between the two phases. The difference between the vapor-liquid distribution under different gravity conditions is shown in Fig. 7. Owing to the interfacial drag forces caused by the velocity difference in the axial direction, some vapor bubbles adjacent to the wall move to the centre of the pipeline in the terrestrial gravity scenario, which creates a path for the LH2 to replenish the cavity. By contrast, the drag forces between the liquid and vapor are negligible as the liquid and vapor phase have the same
Fig. 5 e Comparison of wall heat flux partitions (a: 1g; b: 10¡4g). Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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Fig. 6 e Comparison of void fractions in the radial direction (a: 1g; b: 10¡4g). velocity in microgravity scenario. Thus, the liquid and vapor are clearly stratified. This results in a deterioration of the heat transfer intensity and an increase of the wall temperature.
state under microgravity and terrestrial gravity conditions tend to be the same.
Effect of inlet sub-cooling on the CHF condition Effect of inlet velocity on the CHF condition After the comparison of the LH2 CHF condition under microgravity and terrestrial gravity conditions, the main influence factors for both conditions are analysed. Fig. 8 shows the wall temperature distributions with different inlet velocity. As can be seen, the CHF location shifts downstream with the increase of the inlet velocity, which means a positive correlation of CHF value with the inlet velocity in both conditions. However, the influence of inlet velocity on the CHF under terrestrial gravity is much more significant. The CHF location moves backwards about 2.5 m with every 0.5 m/s increasement in terrestrial gravity scenario. When the inlet velocity exceeds above 2 m/s, the CHF state disappears and is replaced by nucleate boiling throughout the pipeline. This is mainly because higher inlet velocity results in a larger inertia force, which can flush bubbles from the heated wall and create a path for LH2 to replenish the heated wall. For microgravity scenario, the CHF state remains even when the inlet velocity is up to 3 m/s and more temperature excursions appear at higher inlet velocity. In addition, the figure shows that when the velocity is large enough, the CHF
Another important factor that affects the CHF state is the inlet sub-cooling. Fig. 9 shows the wall temperature along the axial direction with different inlet sub-cooling. With the increase of the inlet sub-cooling, the CHF location shifts downstream under both the microgravity and terrestrial gravity conditions. This result indicates that higher inlet sub-cooling requires higher wall heat flux magnitude to reach the CHF state. For terrestrial gravity scenario, CHF location shifts downstream about 2 m with the inlet-subcooling changes. The CHF state may disappear when the inlet-subcooling is greater than 6 K. While for microgravity scenario, the CHF location moves 0.25 m backwards, which is much smaller than that in terrestrial gravity scenario. In addition, unlike the terrestrial gravity scenario, the temperature at CHF location in the microgravity scenario increases with higher inlet sub-cooling. On one hand, high inlet sub-cooling inhibits the evaporation of LH2; on the other hand, high sub-cooling tends to reduce the bubble diameter according to Eq. (14). Thus, the gap between the bubbles alongside the wall becomes smaller with higher inlet sub-cooling. By contrast, the temperature at CHF
Fig. 7 e Comparison of flow patterns and streamlines. Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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Fig. 8 e Wall temperature along the axial direction (a: 1g; b: 10¡4g).
Fig. 9 e Wall temperature along the axial direction, for different inlet sub-cooling values (a: 1g; b: 10¡4g).
locations varies only little due to a similar void fraction around the CHF location for terrestrial gravity scenario.
Conclusions In the present work, a 2D axisymmetric model was developed to study the flow boiling CHF state of LH2 in a vertical pipeline under microgravity based on the EEMF model in conjunction with the WHFP model. The validation results demonstrate that the proposed model predicts reasonably well the distributions of wall temperature under CHF state. Then, the wall temperature distribution, wall heat flux partition, void fraction, as well as flow patterns under microgravity were predicted and compared with terrestrial conditions. In addition, different operating conditions, including flow velocity and inlet sub-cooling, were considered to further study the inconsistent CHF state under microgravity and terrestrial gravity conditions. The main findings of this study are as follows: The CHF location shifts downstream with the increase of the gravity acceleration owing to the differences between the dry-out and DNB type CHFs, which indicates a smaller heat flux demand in the low-gravity environment to reach the CHF state. The CHF under microgravity condition precipitates larger wall temperature excursions
(about 2.6 times larger than that under terrestrial gravity), which potentially does greater damage to the heated wall. In the absence of the gravity induced body force under the microgravity condition, the bubble detachment is suppressed, which causes bubbles to propagate along the surface. Hence, the vapor phase convective heat flux dominates the heat transfer between 0.5 m from inlet and outlet. By contrast, the evaporative heat flux dominates the heat transfer under terrestrial gravity with more than 75% of total heat flux before CHF. The void fraction breakpoint is reached in the downstream section of the pipeline at about 5.5 m under terrestrial gravity condition, while the value is about 0.5 m in the microgravity scenario. This is mainly because liquid and vapor phase have the same velocity in the microgravity scenario, which result in the bubbles gathering near the heating surface. Since the dry-out type CHF is harder to achieve with larger velocity, the inlet velocity can much more significantly affect the flow boiling CHF under the terrestrial gravity condition than that under the microgravity condition. When the velocity is large enough, the CHF state under microgravity and terrestrial gravity conditions tend to be the same. The critical temperature increases with larger inlet subcooling, owing to smaller bubble diameters and a
Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197
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narrower bubble gap in the microgravity scenario. In addition, the inlet sub-cooling has a greater influence on the CHF condition in the terrestrial gravity scenario.
Acknowledgement This work was supported by the National Natural Science Foundation of China (No. 51806071), the State Key Laboratory of Technologies in the Space Cryogenic Propellants (No. SKLTSCP1813) and the Fundamental Research Funds for the Central Universities, HUST (No. 2018JYCXJJ028).
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Ai : Interfacial area (m2) CBD: Bubble drag coefficient CD : Drag force coefficient Cl : Lift force coefficient Cp: Specific heat capacity (J/kg K) CTD : Constant 1 Di: Inner diameter of horizontal tube (m) Dw : Bubble departure diameter (m) fd : Frequency of bubble departure (s1) FD : Drag force (N) ! F : Lift force (N) !lift F td;q : Turbulent dispersion force (N) g: Gravitational acceleration (m/s2) hfv : Latent heat of evaporation (W/kg) Jasub : Subcooled Jacob number k: Turbulent kinetic energy (m2/s2) K, C, n: Constant L: Total length of horizontal tube (m) Nu: Nusselt number NW : Nucleate site density (m2) Pr: Prandtl number q: Heat flux (W/m2) Qpq : Volumetric rate of energy transfer between phases (W) Re: Reynolds number T: Temperature (K) td: Periodic time (s) u: Velocity (m/s) uR: Relative velocity of primary and secondary phase (m/s) x: Axial Location (m) DTsub : Subcooled temperature (K) Subscripts C: Convective E: Evaporative in: Inlet l: Liquid p: pth phase q: qth phase Q: Quenching sub: Subcooling sat: Saturation v: Vapor W: Wall Greek symbols a: Volume fraction k: Conductivity (W/m k) l: Diffusivity (m2/s) m: Dynamic viscosity (N s/m2) r: Density (kg/m3)
Nomenclature Ab : Area of influence (m2) Ad: Projected area of a typical particle (m2)
Please cite this article as: Zheng Y et al., Prediction of liquid hydrogen flow boiling critical heat flux condition under microgravity based on the wall heat flux partition model, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.12.197