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Effect of insulation thickness on pressure evolution and thermal stratification in a cryogenic tank
Accepted Manuscript Effect of Insulation Thickness on Pressure Evolution and Thermal Stratification in a Cryogenic Tank Jeswin Joseph, Gagan Agrawal, Deepak Kumar Agarwal, J.C. Pisharady, S. Sunil Kumar PII: DOI: Reference:
S1359-4311(16)31144-9 http://dx.doi.org/10.1016/j.applthermaleng.2016.07.015 ATE 8613
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
31 March 2016 1 July 2016 2 July 2016
Please cite this article as: J. Joseph, G. Agrawal, D.K. Agarwal, J.C. Pisharady, S. Sunil Kumar, Effect of Insulation Thickness on Pressure Evolution and Thermal Stratification in a Cryogenic Tank, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.07.015
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Effect of Insulation Thickness on Pressure Evolution and Thermal Stratification in a Cryogenic Tank Jeswin Josepha, Gagan Agrawala, Deepak Kumar Agarwala*, J.C. Pisharadya, S. Sunil Kumara a
*
Liquid Propulsion Systems Centre, ISRO, Thiruvananthapuram, Kerala, India - 695 547,
Corresponding author. email: [email protected], ph: +91 471 256 7743, fax: +91
471 256 7039 Abstract A transient analytical, multi-phase, thermodynamic model of foam insulated liquid hydrogen tank is developed to understand the effect of insulation thickness on the evolution of tank pressure and liquid thermal stratification. The model is validated with experimental data reported in literature. Analyses are carried out for pressurization considering two scenarios: first case with tank vent port closed after pressurization to study the pressure evolution and the second case for a constant tank pressure of 3.0bar to study the growth of liquid thermal stratification. Both cases are investigated for different tank insulation thicknesses of 10mm, 20mm, 30mm and 40mm and with a pressurization gas temperature of 50K. Effects of variations in ambient wind velocity and presence of solar flux on self-pressurization profile of the tank are also analysed. The study shows that the reduction in insulation thickness leads to increase in stratified mass. The study also brings out significant increase in pressure rise when tank is insulated with lower insulation thickness. Keywords: Cryogenic Tank, Insulation, Thermal Stratification, Liquid Hydrogen, SelfPressurisation
1
Nomenclature A
Surface area (m2)
Cp
Specific heat (J/Kg-K)
D
Tank diameter (m)
d
Port diameter (m)
g
Gravity (m/s2)
H
Enthalpy (J/kg)
h
Heat transfer coefficient (W/m2-K)
hfg
Latent heat of vaporization (J/K)
k
Thermal conductivity (W/m-K)
m
Resident mass (Kg)
Nu
Nusselt number
Pr
Prandtl number
Gr
Grashof number
P
Pressure (Pa)
Q
Heat (J)
Ra
Rayleigh number
Re
Reynolds number
T
Temperature (K)
t
Time (s)
U
Boundary flow velocity (m/s)
x
Tank height (m)
Greek Symbols β
Coefficient of thermal expansion (K-1) 2
δ
Boundary layer thickness (m)
µ
Dynamic viscosity (Pa-s)
ʋ
Kinematic viscosity (m2/s)
ρ
Density (kg/m3)
σ
Surface tension (Kg/s2)
Subscripts a
Ambient
conv Convection int
Liquid-vapor interface
l
Liquid
s
Tank outer surface
u
Ullage
v
Vapor
w
Inner wall
3
4
1. Introduction Cryogenic propellants used for space missions are stored in foam-insulated tanks for long duration prior to lift-off. During this period, considerable amount of heat leak into the tank through the insulation which leads to the formation of natural convection boundary layer in the liquid close to tank surface. The heat leaked into the tank raises the temperature of the liquid in the boundary layer, resulting in movement of warm liquid cryogen from tank bottom to liquid-vapor interface along the tank wall due to buoyant force. Accumulation of warm liquid close to the interface creates a warm liquid zone at the top of the bulk liquid. Tank pressurization results in an additional heat input into the tank as pressurization sub-cools the bulk liquid and raises the liquid-vapor interface temperature, which rises the axial conduction heat flux through the interface. This conductive flux also influences the warm liquid zone by further increasing the liquid temperature. Tank pressurization with high temperature pressurant gas raises the tank wall temperature close to interface through convection in the ullage and subsequent tank wall conduction, which also adds to the heat flow into the warm liquid zone. The thickness of warm liquid zone increases with time as heat is pumped in and gives rise to axial temperature gradient in bulk liquid cryogen. This axial gradient in liquid temperature is called thermal stratification. Development of thermal stratification in a typical cryogenic propellant tank due to various external heat sources is depicted in Fig. 1. Cryogenic propellant tanks prepared for launch mission undergo typical operation sequence that include tank chilling, tank filling, boil-off, level correction, tank pressurization and hold, prior to lift-off. Boil-off operation essentially brings the propellant to saturation temperature based on the desired tank pressure. Level correction operation compensates the liquid level reduction due to boil-off by filling sub-cooled propellant from tank bottom, which marginally raises the tank pressure caused by ullage compression. During pressurization, interface 5
temperature increases based on saturation temperature corresponding to the tank pressure. Normally, tank pressurization ends about a minute prior to lift-off after which no operations are carried out until ignition of cryogenic engine. Engine ignition commences with regulated draining of propellant from the tank. During engine operation the tank pressure is maintained at a constant value to achieve uniform propellant flow rate. The desirable temperature of liquid propellant at pump inlet of cryogenic engine system is restricted by the pump cavitation limit, beyond which engine performance degrades significantly. Hence, the mass of liquid in warm zone that has a temperature above the pump cavitation limit is deemed unusable for the mission and is a liability to the payload capacity of the launch vehicle. This excess liquid mass that has to be loaded into the tank of a typical cryogenic propulsion system is called stratified mass of the propellant. Additionally, heat in-leak from ambient and tank pressurization play significant role in determining the pressure evolution inside the tank. Also, stratified mass and tank pressure can be controlled by proper insulation of cryogenic tank. Thus, it is important to have prior knowledge on the effect of insulation thickness on evolution of stratified mass and tank pressure for smooth operation of cryogenic engine. Several experimental and numerical studies on thermal stratification and pressure evolution in cryogenic tank have been reported in the literature. Schmidt et al [1] carried out experimental and numerical studies to investigate the liquid hydrogen stratification and pressurization in a super-insulated dewar. They assumed liquid column as a semi-infinite solid and compared their results to the experimental data. Tatom et al. [2] reported an experimental study on thermal stratification of liquid hydrogen in rocket propellants for bottom heating and side heating and suggested that bottom heating, if applied properly, may cause a considerable reduction in the stratification. Evans et al. [3] carried out the experimental study on the transient effects of natural convection inside enclosed fluids. Nein and Thompson [4] experimentally studied the pressurant requirements in cryogenic tanks of 6
various shapes and developed an analytical one-dimensional ullage stratification model to determine pressure requirements in cryogenic tanks. Li et al [5] numerically studied the thermodynamic effect of heat in-leak into cryogenic tank and backed the results with experimentation. The study concluded that thermal stratification exists only in sub-cooled liquid and heat in-leak depends on void fraction of fluid close to the tank wall. An experimental and numerical study was carried out by Ludwig et al. [6] showed the effect of sloshing on variation in tank pressure and liquid stratification. Hasan et al [7] conducted experiments in spherical liquid hydrogen tank to study the pressurisation of the tank, which showed that initial conditions of the tank plays significant role in tank pressure rise. Study carried out by Gursu et al. [8, 9] showed the significance of the thermal stratification on pressure rise rates. Tunc et al.[10] developed CFD model to simulate helium pressurisation effects in liquid oxygen tank. The study showed that pressure rise rates are significantly less when liquid oxygen tank is pressurised using gaseous helium. Stephens and Hanna [11] carried out analysis to study high heat flux effects on a horizontally-placed liquid hydrogen tank. The analysis showed that ullage mixing is dominant over wall to ullage heat transfer in determining the pressure evolution pattern in a cryogenic tank. Numerical simulations were carried out by Daigle et al [12] to analyse thermal stratification using ordinary differential equation solution and obtained good results with experiments. CFD studies carried out by Jazayeri and Khoei [13] showed thermal stratification in liquid oxygen and liquid nitrogen tanks depend mainly on natural convection flows. Grayson et al [14] modelled liquid hydrogen cryogenic tank of Saturn AS-203 flight experiment and simulated thermal stratification using CFD approach, which showed liquid temperatures under low gravity scenario. A numerical study was carried out by Lin and Hasan [15] which solve the steady state conservation equations for an axis-symmetric cylindrical enclosure, showed the effect of Rayleigh number, Prandtl number and wall heat flux on the characteristics of thermal 7
stratification in case of uniform sidewall heat flux. Tanyun et al. [16] performed a numerical simulation of the thermal stratification of liquid hydrogen inside the storage tank. The formulation was based on the vorticity-stream function method, and the surface temperature obtained was correlated with the heat flux, fluid level and time. Panzarella et al. [17] carried out numerical simulation with introducing the effect of thermal stratification in the liquid region to the effect of pressure rise on various heating conditions. The simulation was carried out using computationally-expensive Navier-Stokes differential equation solver. A numerical simulation for the convection currents in a rectangular enclosure was reported by Sun et al. [18] with volume base finite difference method. The study concluded the effect of increase in baffle size to the convection currents. Barsi et al. [19] carried out numerical calculation and experiment of the self-pressurization in liquid hydrogen tank. They considered the heat in the liquid is used for evaporation of liquid at interface and modeled the ullage gas phase as a lump in the respect of energy and mass. Ganguli et al. [20] performed an experimental and numerical study for stratification in fluid container taking working fluid as water. The study showed the higher stratification in less time with higher Rayleigh number. For insulation systems used in cryogenic tanks, studies were carried out by Arsonval [21], who proposed the insulation system for tank using double wall with vacuum annular section. This tank was later improved by Dewar [22] to store hydrogen liquid at 20.4 K. Several experimental studies were carried out by the researchers [23-27] to investigate the heat transfer in cryostat from ambient. Shu et al. [28] recommended for an optimal insulation of a nitrogen cryostat with a number of screen layers. These insulation systems are suitable for ground experiments. Cryogenic tank prepared for space missions are insulated with foam or MLI as reported by Kramer et al. [29].
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A large number of experimental and numerical studies have been carried out and been reported in literature on thermal stratification, pressure evolution and insulation design of a cryogenic tank using different cryogenic liquids. However, a comprehensive investigation on the effect of insulation thickness on stratification and pressure evolution is absent in current literature. The present study focuses on developing a discretised lumped model strategy to simulate stratification phenomenon in a typical liquid hydrogen propellant tank used for space missions. The model is validated with the results reported in the literature. Effect of different tank insulation thicknesses on pressure evolution and thermal stratification are investigated. The study also brings out the effect of variations in wind velocity and presence of solar heat flux on self-pressurization of the tank. 2. Model Description A transient two-phase thermodynamic lumped model is developed using SINDA/FLUINT solver to simulate thermal stratification in a typical liquid hydrogen tank, having diameter of 4m, length of 7m, wall thickness of 4mm, various foam-insulation thicknesses of 10mm, 20mm, 30mm and 40mm, and liquid level filled upto 87% of the total height. The computational domain for the model is illustrated in Fig. 2. Thermal stratification in an axis-symmetric tank is caused due to complex two-dimensional boundary layer phenomenon, occurring close to tank wall. The current model simplifies this two-dimensional problem into one-dimensional lumped model, to predict the pressure evolution and bulk fluid temperatures during the occurrence of various thermodynamic transients in the tank. It is assumed that the boundary layer for natural convection forms within the liquid at nadir point of bottom dome. The tank surface and associated insulation are axially discretised in the same manner as bulk fluid within the tank. Surface discretizations are called nodes and fluid discretizations are called lumps, as seen in Fig. 2. 9
Ullage lumps are only axially discretised whereas liquid lumps are radially discretised into three parts. Liquid lumps close to the tank wall represent boundary flow zone where heat inleak into the tank raises the lump temperature in the zone, leading to boundary layer flow based on natural convection. The boundary layer flow in boundary zone creates a flow in radial direction, resulting in a region where fluid flows from interface towards tank bottom. This region is termed as return flow zone which constitutes the flow network for boundary layer flow phenomenon in the model. The third region is the core zone in the bulk liquid, which is radially most distant from the tank wall and having negligible flow along it. Heat transfer within this zone is predominantly due to simple fluid conduction, hence it is termed core conduction zone, as mentioned in Fig. 2. The stratified mass in current study is defined as the total mass of all fluid lumps having temperature in its axial layer, higher than pump cavitation limit of 23K. 3. Operational Sequence for Analysis As mentioned earlier, typical pre-flight tank operations include tank chilling, tank filling, boil-off, level correction, tank pressurization and tank hold. The transient analysis starts with level correction operation, assuming fluid at tank filling liquid temperature of 20.8K and tank pressure of 1.2bar at the end of boil-off. A steady-state analysis is carried out for initialisation of tank wall and foam insulation before transient execution. Insulation thermo-physical properties are shown in Table 1. Discrete values of thermal properties, shown in Table 1, are linearly interpolated. During level correction operation, the tank is filled with liquid hydrogen at 20.8K from the bottom of the tank, leading to rise in liquid fill level and subsequent increase in pressure from 1.2bar to 1.3bar in 5 minute duration. During this period, the growth of stratified layer is insignificant as saturation temperature of hydrogen at 1.3bar is only 21.1K. Tank 10
pressurization starts at time t=0s using gaseous hydrogen to raise the tank pressure to 3.0bar in 5 minutes. This results in significant stratification build-up close to liquid-vapor interface. As mentioned earlier, analyses are carried out considering two scenarios: first case with tank vent port closed after pressurization to study the pressure evolution, second case for a constant tank pressure after pressurisation at 3.0bar to study the thermal stratification growth. In both the cases, studies are carried out from tank pressurization at t=0s to t=300s and extended to 300s after pressurisation. These scenarios are investigated for varied insulation thickness of 10mm, 20mm, 30mm or 40mm while pressurant gas temperature is kept constant at 50K. Hydrogen properties are taken from NIST fluid property database [30]. 4. Mathematical Formulations 4.1 Conservation of Mass The net mass flow from a fluid node is equated to the rate of change of mass in the control volume as shown below.
Conservation of mass is ensured at each fluid node during each time-step of transient simulation. 4.2 Conservation of Momentum The governing equation for flow connectors is simply a complex form of Newton’s second law. The momentum conservation equation for a fluid connector is written as below:
Viscous coefficient ‘f’ is calculated using Churchill formulation [1]. Fluid nodes are connected by fluid connectors on which momentum conservation is imposed. 11
4.3 Conservation of Energy The energy conservation equation is expressed on the basis of the first law of thermodynamics. The rate of increase of internal energy in the control volume is equal to the difference between the rate of energy transport into the control volume and the rate of energy transport from the control volume. The energy conservation equation based on enthalpy can thus be written as below:
where Q, shown below, represents heat in-leak from ambient at boundary fluid nodes with heat transfer coefficient, h is described later in this section.
4.4 Equation of State Thermodynamic variables at a particular fluid lump are calculated using real fluid state equation with compressibility factor, Z, being an input from NIST database [30].
4.5 Boundary layer thickness and velocity The upward flow in boundary layer is determined by using the formulations developed by Tsuji et al. [31]. Since the liquid-side wall temperature is very close to the temperature of the liquid, formulations based on constant wall temperature, are shown as below.
where
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4.6 Heat and mass transfer across interface The model is used to analyze the evolution of liquid temperature inside the tank considering conduction, convection, heat and mass transfer across the interface. A schematic of the cryogenic tank showing various heat transfer mechanism is depicted in Fig. 2. Heat, from ullage to bulk liquid, transfers through interface. However, the heat transfer from ullage to interface and interface to liquid are equal. Heat transfer from the interface to liquid is expressed as:
The heat transfer from the ullage gas to interface is due to convection. Since, diffusing or condensing constituent carries its own individual enthalpy, there is an additional heat transfer across interface due to mass transfer of these species. Effective heat transfer from the ullage gas to interface is expressed as:
m and H are mass and enthalpy of fluid transfer across interface. m is positive for condensation and negative for vaporization of the liquid and is expressed as:
It has been assumed that the heat transfer is due to natural convection with the heat transfer coefficient being expressed by the correlations [32] as below.
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where:
and
Constant ‘C’ is 0.54 and 0.27 for heat transfer from ullage to interface and interface to liquid respectively. n = 0.25 and ‘KH’ (heat transfer adjustment factor) is set to 1.0. The length scale ‘ls’ is set to the diameter of the tank. 4.7 Heat transfer from wall to fluid Tank is pressurised with gaseous hydrogen and during pressurisation mixed convection heat transfer occurs in the tank ullage as a combination of force convection and natural. Heat transfer from tank wall to ullage gas during pressurisation is determined by using the formulation [33] described as below.
where:
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Heat transfer from wall to liquid is calculated using natural convection formulation reported by Rohsenow [34] and is described in Eq. 16.
4.8 Heat transfer from ambient Coefficient of convective heat transfer on tank surface is calculated by using Churchill and Bernstein [32] based formulation based. Heat transfer from outside is express below.
To calculate heat transfer from ambient to the tank wall, three dimensional transient heat conduction equations are solved considering the variation of thermal conductivity of the insulation with temperature. Three-dimensional transient heat conduction equation is given by following expression considering k as a function of temperature:
All the above mentioned heat transfer modes represent the mathematical thermal model which have been incorporated in the analyses. 4.9 Solution Methodology and Boundary Conditions
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Solution flow chart depicting the dependence of each parameter on different thermodynamic equations used in the present model is shown in Fig. 3. Major resultant parameters from the simulation are 3-D tank wall temperature distribution, fluid thermodynamic parameters (pressure, temperature, and density), fluid connector mass flow rates and interface mass transfer or evaporation/condensation rate. These parameters are inputs as well as outputs for different thermodynamic equations, discussed earlier in this section. Iterations for solution convergence are carried out for each time step of simulation, thereby forming a closed relation between the each parameter. Initial and boundary conditions used for the analyses are shown in Table 2. The input parameters used for the simulation are considered based on values and data from a typical launching mission. 5. Model Validation Ludwig et al. [6] carried out an experiment on pressurization of cryogenic tank filled with liquid nitrogen at an initial temperature and pressure of 77.7K and 1.06bar respectively. The dimensions of the cylindrical tank taken for the experiment are shown in Table 3. The mathematical formulations presented here are applied to the simulation of experimental study carried out by Ludwig et al. [6]. In the experiment, the tank is pressurized from 1.06bar to 3.0bar for duration of 52s using gaseous nitrogen. After 52s, tank pressure decreases and reaches 2.46bar at 200s. The numerical simulation of this experiment aims to capture the pressure evolution and liquid stratification and compared it with the experimental data reported. Figure 4 shows the comparison of measured tank pressure evolution with the simulated results. Figure 5 shows the liquid temperature along the tank height at different time instants of 0.0s, 52s and 200s. It can be seen from the Fig. 4 and Fig. 5 that initially liquid is at saturation condition of 77.7K. Subsequently, tank is pressurised from 1.06bar to 16
3.0bar in 52.0s and interface temperature increases from 77.7K to 87.9K which is the saturation temperature corresponding to the tank pressure. The reduction in pressure, after 52s, results in reduction in interface temperature and interface temperature at 200s is 85.7K. Figure 6 shows the rise in liquid temperature at a height of 0.445m and 0.450m from the tank bottom which illustrates a very good agreement with the experiment data. It is to be noted from the Figs. 4, 5 and 6 that simulated results are well validated with the experimental data. Hence, it proves the validity of numerical scheme used for the analysis for the effect of various parameters on liquid thermal stratification and pressure evolution inside the tank. 6. Results and Discussion A thermal stratification model is developed to analyse and discuss the two cases; (i) to determine the effect of insulation thickness on pressure evolution in liquid hydrogen cryogenic tank while pressurization port is closed after tank pressurization, named as pressure evolution studies and (ii) to determine the effect of insulation thickness on thermal stratification growth in liquid hydrogen cryogenic tank while tank pressure is maintained at 3.0bar after tank pressurization, named as liquid thermal stratification studies. The results simulated from the analyses are discussed below. It may be noted that the studies are carried out for the tank dimensions discussed in section 2. 6.1. Pressure Evolution Studies The transient analysis starts from tank pressurization process which commences at t=0 and lasts upto t=300s. After t=300s, the pressurization port is closed, thereby allowing the tank pressure to evolve under the influence of ullage heat-in leak. The analysis duration is extended by 300s after pressurization, i.e., up to t=600s. Analyses are carried out for different insulation thicknesses of 10mm, 20mm, 30mm and 40mm. The cases are analysed without solar heat flux effects and with wind velocity of 2m/s. The evolution of pressure for different 17
insulation thicknesses, subsequent to the pressurization for a pressurant gas temperature of 50K, is depicted in Fig. 7. It can be seen from Fig. 7 that there exists a pressure fall immediately after pressurization and is significant in tanks with higher insulation thickness. For 10mm insulation thickness over the tank, pressure fall is negligible. Pressure fall in a cryogenic tank after tank pressurization is due to the cooling of ullage gas and subsequent pressure rise is due to ambient heat in-leak in to the ullage overtaking the cooling rate. Figure 8 depicts the ullage temperature profile at t=0s, t=300s and t=600s, for 30mm insulated tank. From time t=0s to t=300s, there is a rise in ullage temperature, which is a consequence of pressurization whereas, ullage temperature decreases from time t=300s to t=600s, which results in tank pressure fall. Ullage temperature profile for different insulation thickness at t=300s and t=600s, is shown in Figs. 9a and 9b, respectively. It can be seen from Figs. 9a and 9b that the ullage temperature increases for insulation thicknesses 10mm and 20mm from t=300s to t=600s, whereas there is a decrease in ullage temperature when tank is 30mm and 40mm insulated. This is because the tank pressure at t=600s, for insulation thicknesses of 10mm and 20mm, is higher than that at t=300s, as can be seen in Fig. 7, which contributes to increase in ullage temperature at t=600s, seen in Fig. 9b. The tank pressure at t=600s is lower than 3bar for 30mm and 40mm insulated tanks, which contributes to decrease in ullage temperature. Heat input from the warm pressurant gas entering the tank, will raise the ullage gas temperature more than the tank wall temperature, resulting in loss of heat from ullage gas to the tank wall which causes the ullage temperature to reduce during pressurization, as seen in Figs. 9a, 9b and 10. The average heat flux values at t=300s and t=600s for different insulation thicknesses are shown in Fig. 11.
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It can be seen from Figs. 10 and 11 that heat in-leak into the ullage at t=300s is negative, denoting net loss of heat from ullage gas to the tank wall after pressurization. Negative heat flux at t=300s represents the tendency of tank pressure to fall whereas positive heat flux at t=600s shows the tendency of tank pressure to rise, which is in agreement with pressure evolution plot, shown in Fig.7. The pressurant mass flow rate required to pressurize the tank for different tank insulation thicknesses are shown in Fig. 12. It is evident from Fig. 12 that more pressurant mass flow is required to achieve similar pressure rise rate for the tank with more insulation thickness. This is because of lower heat in-leak into the ullage for higher tank insulation thickness, leading to slower temperature rise, and consequently, slower pressure rise. The liquid-vapor interface mass transfer rates at t=300s and t=600s for different tank insulation thicknesses, are shown in Table 4. Negative values show evaporation whereas positive values show condensation. It can be seen that condensation dominates during pressurization in well-insulated tanks. This is due to the sudden increase in pressure of ullage gas, which is initially close to saturation temperature. Low heat in-leak into the liquid due to high insulation thickness, also favours condensation. Mass transfer across interface depends on tank pressurization, which gives rise to condensation, and liquid heat in-leak, giving rise to evaporation. As insulation reduces, increase in evaporation is observed at t=300s and t=600s as liquid heat in-leak dominates the tank pressurization effect on interface mass transfer. 6.1.1 Study of Variations in Ambient Conditions A parametric study is carried out with 30mm insulated tank to determine the effect of different wind velocities and effect of presence of solar radiation. Wind velocities of 1m/s, 2m/s, 3m/s and 4m/s are considered in initial study without considering solar heat flux over 19
the tank. Self-pressurization pattern of the tank for various wind velocities are shown in Fig. 13. It is seen from Fig. 13 that pressure fall rate, immediately after tank pressurization, reduces non-linearly when wind velocity increases. It is also noted from Fig. 13 that for higher wind velocities, the rate of pressure fall is similar, resulting in closer pressure value at t=600s. This is because higher wind velocities increase the heat transfer coefficient over the insulation outer surface, as discussed in equations 22-24, and increases its temperature closer to ambient temperature of 300K, as shown in Table 5. Increase in outer temperature of insulation is marginal if wind velocity keeps on increasing because of constant ambient boundary temperature. Heat in-leak into the tank, and consequently its self-pressurization rate shown in Fig. 13, is a result of conductive heat transfer through the insulation which is directly dependent on insulation outer temperature, shown in Table 5. Similar impact is seen when the cryogenic tank is exposed to solar heat flux of 330W/m2. Comparison of pressure profiles for analyses carried out with and without solar heat load over the tank is shown in Fig. 14. As discussed earlier, heat in-leak is the main source of self-pressurization of the tank. Presence of constant heat flux over the insulation outer surface results in rise in insulation outer temperature, resulting in higher conductive heat flux through the insulation and subsequent rise in heat in-leak. Maximum temperature of 312K at insulation surface is observed when solar flux of 330W/m2 is present as opposed to 286K observed in the absence of it. This resulted in ullage heat in-leak and tank pressure values of 24.9W/m2 and 2.96bar at t=600s for simulation with solar flux, against values of 18.2W/m2 and 2.91bar for simulation without solar flux. 6.2. Liquid Thermal Stratification Studies 20
Similar to the previous analysis, the transient analysis is carried out to study the liquid thermal stratification and stratified mass evolution in the liquid hydrogen tank for different insulation thicknesses of 10mm, 20mm, 30mm and 40mm using 50K pressurant gas temperature. The studies are carried out without solar heat flux effects and with wind velocity of 2m/s. After t=300s, the tank pressure is maintained at peak pressure of 3.0bar by operating the tank port in pressurization or venting mode. The analysis duration is extended by 300s after pressurization, i.e., up to t=600s. While the tank is pressurized from t=0s to t=300s and subsequently maintained at peak pressure of 3.0bar, the liquid temperature in core conduction zone raises due to heat in-leak into liquid hydrogen. Liquid core temperature along the tank height is depicted in Fig. 15 for different time instant of t=0s, t=300s and t=600s where 30mm insulated tank and 50K pressurant gas temperature are used. Liquid temperature profiles in core conduction zone at t=300s and t=600s for different insulation thicknesses are shown in Figs. 16(a) and 16(b), respectively. It is evident from Figs. 16(a) and 16(b) that the temperature of the liquid bulk increases at a faster rate for lesser insulation thickness. This is because of high level of heat in-leak into the bulk liquid as seen in Table 6. Due to ambient heat in-leak and conduction flux from interface into the liquid, the liquid lumps close to liquid-vapor interface reach saturation, as can be seen in Figs. 16(a) and 16(b). This is prominent in 10mm insulated tank where heat flux levels into the liquid are high, as seen in Table 6. The interface mass transfer rate at t=300s and t=600s for different insulation thicknesses are also shown in Table 6. It is clear that condensation is the dominant mode of mass transfer during pressurization while evaporation is the dominant mode when tank pressure is maintained.
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The stratified mass is defined as the mass of liquid having temperature higher than pump cavitation limit of 23K. The stratified mass evolution for different tank insulation thicknesses is shown in Fig. 17. It is evident from Fig. 17 that stratified mass increases slowly in well-insulated tanks, as a consequence of low heat in-leak, seen in Table 6. It is also observed during pressurization that the stratified mass increases at a faster rate compared to that during fixed pressure scenario after pressurization. The reason is due to the continuous increase in interface temperature during pressurization, leading to continuous increase in conductive heat flux from interface to the liquid, in addition to the ambient heat in-leak into the tank through the insulation. The pressurant gas requirement to maintain the tank pressure at peak value of 3.0bar is also investigated through the analysis. The pressurant gas mass flow rates to maintain 3.0bar pressure in the tank for different insulation thickness are shown in Fig. 18. It can be seen that more pressurant gas is required to maintain the tank pressure at 3.0 bar when tank insulation thickness is higher. It is also seen in the figure that pressurant mass flow rate is negative for lower tank insulation thicknesses, which means the tank is being vented to maintain the pressure at 3bar. As seen in pressure evolution studies shown in Fig. 7, after pressurization, the tank pressure falls faster if the tank is well insulated, which is due to lower ullage heat in-leak. Higher the pressure fall, more is the pressurant mass required to maintain the tank pressure. The pressure evolution for lower insulation thicknesses, shown in Fig. 7, indicates that tank has to be vented to compensate for pressure rise due to ullage heat in-leak. 7. Conclusion A transient, two-phase, thermodynamic model of liquid hydrogen cryogenic propellant tank used in a typical launch mission is developed to understand the effect of insulation thickness on the tank pressure and thermal stratified mass evolution. The model is validated with 22
transient pressure and liquid temperature data from experiments reported in literature [6]. Following are the salient conclusions drawn from the analyses: 1. Lower insulation thickness over cryogenic tanks leads to higher heat in-leak into ullage gas, causing tank pressure to rise significantly. 2. Tank pressure, which influences the interface temperature, has significant influence on the stratified mass evolution. Higher tank pressure leads to higher liquid stratified mass. 3. Lower thickness of tank insulation results in higher stratified mass due to higher liquid heat in-leak from the ambient, causing payload penalty in propellant tanks used in launch vehicles. 4. Lower tank insulation thickness results in less pressurant mass required for tank pressurization due to higher ullage heat in-leak. Subsequently, higher ullage mass need to be vented to maintain constant tank pressure after pressurization. 5. Tank outer surface temperature is influenced by ambient conditions and solar flux, and affects the heat in-leak and subsequently, the tank pressure. Though higher tank insulation thickness is required to minimize the liquid stratified mass and ullage pressure rise, optimization for insulation thickness should be carried out considering other parameters such as increase in insulation mass with higher insulation thickness and condensation or ice-formation over the tank insulation for lower insulation thickness. While designing the insulation and its thickness, one should also keep in mind the constraints imposed on mission critical parameters like tank pressure and temperature limits due to flight trajectory.
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8. References: [1]
Schmidt, A. F., Purcell, J. R., Wilson, W. A., Smith, R. V., 1960. An experimental study concerning the pressurization and stratification of liquid hydrogen, Advances in Cryogenic Engineering, Springer US, pp. 487-497.
[2]
Tatom, J. W., Brown, W. H., Knight, L. H., Coxe, E. F., 1964. Analysis of thermal stratification of LH2 in rocket propellant tank, Advances in Cryogenic Engineering, vol. 9, pp. 265–272.
[3]
Evans, L. B., Stefany, N. E., 1966. An experimental study of transient heat transfer to liquids in cylindrical enclosures, Chem. Eng. Prog. Symposium Ser., Vol. 62, No. 64, pp 209- 215.
[4]
Nein, M. E., Thompson, J. F., 1966. Experimental and analytical studies of cryogenic propellant tank pressurant requirements, George C Marshall Space Flight Center, NASA TN D-3177
[5]
Li, X., Xie, G., Wang, R., 2010. Experimental and numerical investigations of fluid flow and heat transfer in a cryogenic tank at loss of vacuum, Journal of Heat and Mass Transfer, Vol. 46(4), pp.395-404.
[6]
Ludwig, C., Dreyer, M. E., Hopfinger, E. J., 2013. Pressure variations in a cryogenic liquid storage tank subjected to periodic excitations. International Journal of Heat and Mass Transfer, Vol. 66: 223-234.
[7]
Hasan, M. M., Lin, C. S., Vandresar, N. T., 1991. Self-pressurization of a flightweight liquid hydrogen storage tank subjected to low heat flux, NASA Technical Memorandum 103804
[8]
Gursu, S., Sherif, S. A., Veziroglu, T. N., Sheffield, J. W., 1993. Analysis and optimization of thermal stratification and self-pressurization effects in liquid hydrogen
24
storage systems—Part 1: Model development, ASME Journal of Energy Resources Technology, Vol. 115(3), pp.221-227. [9]
Gursu, S., Sherif, S. A., Veziroglu, T. N., Sheffield, J. W., 1993. Analysis and optimization of thermal stratification and self-pressurization effects in liquid hydrogen storage systems—Part 2: Model results and conclusions, ASME Journal of Energy Resources Technology, Vol.115(3), pp.228-231.
[10] Tunc, G., Wagner, H., Bayazitoglu, Y., 2001. Space shuttle upgrade liquid oxygen Tank thermal stratification, 35th AIAA Thermophysics Conference Proceedings, Anaheim, CA [11] Stephens, C. A., Hanna, G. J., 1991. Thermal modelling and analysis of a cryogenic tank design exposed to extreme heating profiles, NASA Contractor Report 186012, Dryden Flight Research Facility. [12] Daigle, M. J., Smelyanskiy, V. N., Boschee, J., Foygel, M., 2013. Temperature stratification in a cryogenic fuel tank, Journal of Thermophysics and Heat Transfer, Vol 27(1), pp-116-126 [13] Jazayeri, S. A., Khoei, E. M. H., 2008. Numerical comparison of thermal stratification due natural convection in densified LOX and LN2 tanks, American Journal of Applied Sciences Vol 5(12) pp 1773-1779 [14] Grayson, G. D., Lopez, A., Chandler, F. O., Hastings, L. J., Tucker, S. P., 2006. Cryogenic
tank
modelling
for
the
Saturn
AS-203
experiment,
42nd
AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Sacramento California [15] Lin, C. S., Hasan, M. M., 1990. Numerical investigation of the thermal stratification in cryogenic tanks subjected to wall heat flux, AIAA-90-2375, NASA Tech. Memo. 103194. 25
[16] Tanyun, Z., Zhongpin, H., and Li, S., 1996. Numerical simulation of thermal stratification in liquid hydrogen, Advances in Cryogenic Engineering, Vol. 41, pp. 155– 161. [17] Panzarella, C. H., Kassemi, M., 2003. On the validity of purely thermodynamic descriptions of two-phase cryogenic fluid storage tanks, Journal of Fluid Mechanics, Vol. 484, pp. 41-68. [18] Sun, Y. S., Emery, A. F.,1997. Effects of wall conduction, internal heat sources and an internal baffle on natural convection heat transfer in a rectangular enclosure, International Journal of Heat and Mass Transfer Vol. 40, pp. 915–929. [19] Barsi, S., and Kassemi, M., 2008. Numerical and experimental comparisons of the selfpressurization behaviour of an lh2 tank in normal gravity, Journal of Cryogenics, Vol. 48, pp. 122-129. [20] Ganguli, A. A., Pandit, A. B.,Joshi, J. B., Vijayan, P. K., 2011. Hydrodynamic and heat transfer characteristics of a centrally heated cylindrical enclosure: CFD simulations and experimental measurements, Chemical Engineering Research, 89,2024–2037. [21] Arsonval, A. D., 1888. Research report, Roy. Soc. Biol, 40, p. 136 [22] Dewar, J., 1898. Storage of liquid hydrogen, Proc. Roy. Soc. 63, p. 256. [23] Caplin, A. D., Cayless, A. T., 1986. Simple numerical modelling technique for cryostat design, Journal of Cryogenics Vol. 26, pp. 678–681. [24] Mende, F. F., 1989. Broad-neck liquid helium cryostat. Journal of Cryogenics Vol. 29, pp. 998–1001. [25] Buhler, S., 1994. Thermal conduction through a vented support, Journal of Physics III France. [26] Casse, J. L., Woestenburg, E. E. M., 1986. Thermal model for a hybrid cryostat, Journal of Cryogenics Vol. 26, pp. 454–458. 26
[27] Anzelka, P., 1993. Numerical modelling in cryostat design, Journal of Cryogenics Vol. 33, pp. 953–958. [28] Shu, Q. S., Fats, R. W., Hart, H. L., 1985. An experimental study of heat transfer in multilayer insulation systems from room temperature to 77 K, 1st International Cryogenics Conference [29] Kramer, T. J., Brogren, E. W., Siegel, B. L., 1984. Evaluation of propellant tank insulation concepts for low-thrust chemical propulsion systems, NASA Lewis Research Centre, Contract Report no. 168321 [30] webbook.nist.gov/chemistry/fluid/ [31] Tsuji, T., Nagano, Y., 1989. Velocity and temperature measurements in a natural convection boundary layer along a vertical flat plate, Experimental Thermal and Fluid Science, 2(2), pp.208-215. [32] Incropera, F. P., Dewitt, D. P., 1985. Fundamentals of heat and mass transfer, John Wiley & Sons, Inc., Chap. 7. [33] Woodfield, P. L., Monde, M. and Mitsutake, Y., 2006. Measurement of averaged heat transfer coefficient in high pressure vessel during charging with hydrogen, Nitrogen and Argon gas, Journal of Thermal Science and Technology, No. 06-0272, DOI 10.1299/jtst.2.180. [34] Rohsenow, W.M., A method of correlating heat-transfer data for surface boiling liquids, Transactions of ASME, Vol. 74, pp. 969-975, 1952.
27
List of figures Figure 1
Schematic of thermal stratification phenomenon in a cryogenic tank
Figure 2
Computational model of thermal stratification in cryogenic tank
Figure 3
Flow chart depicting solution procedure
Figure 4
Model validation with literature : Tank pressure
Figure 5
Model validation with literature : Liquid temperature along the tank height
Figure 6
Model validation with literature : Transient liquid temperature rise
Figure 7
Evolution of pressure for different tank insulation thicknesses
Figure 8
Ullage gas temperature profile during different instances for 30mm insulated tank
Figure 9
Ullage gas temperature profile for different tank insulation thicknesses at (a) t=300s and (b) t=600s
Figure 10
Ullage heat in-leak for 30mm insulation thickness
Figure 11
Ullage heat in-leak at t=300s and t=600s for different insulation thicknesses
Figure 12
Pressurant gas flow rate during pressurization for different insulation thicknesses
Figure 13
Self-pressurization profile for different wind velocities
Figure 14
Pressure profile for cases with and without solar heat flux
Figure 15
Liquid core temperature profile during different instances for 30mm insulated tank with tank pressure maintained after pressurization
Figure 16
Liquid core temperature profile for different tank insulation thicknesses at (a) t=300s and (b) t=600s
Figure 17
Thermal stratified mass evolution in liquid for different insulation thicknesses
Figure 18
Pressurant gas flow rate to maintain the pressure at 3bar for different insulation thicknesses 28
List of Tables Table 1
Thermo-physical properties of insulation material
Table 2
Initial and boundary conditions for the analyses
Table 3
Details of experimental tank used by Ludwig et al. [6]
Table 4
Interface mass evaporation rate and liquid heat in-leak at t=300s and t=600s for different insulation thicknesses
Table 5
Maximum temperature at insulation outer surface, ullage heat in-leaks and tank pressures at t= 600s for cases with different wind velocities
Table 6
Interface mass evaporation rate at t=300s and t=600s for different insulation thicknesses
29
Fig. 1
30
Fig. 2
31
Fig. 3
32
9. Fig. 4
33
Fig. 5
34
Fig. 6
35
Fig. 7
36
Fig. 8
37
Fig. 9 38
Fig. 10
39
Fig. 11
40
Fig. 12
41
Fig. 13
42
Fig. 15
43
Fig. 15
44
Fig. 16 45
Fig. 17
46
Fig. 18
47
Table 1 Property, Unit
Values
Density, kg/m3
35 755 (90K)
Specific Heat, J/Kg.K
1942 (283K) 2234 (298K) 2121 (323K) 0.0097 (90K)
Conductivity, W/m.K
0.0349 (283K) 0.0382 (298K) 0.048 (323K)
48
Table 2 Tank Height (m)
7
Tank Diameter (m)
4
Liquid Fill Level (%)
87
Ambient Temp. (K)
300
Ambient Wind Vel. (m/s)
2
Pressurant Gas Temp. (K)
50
Working fluid
Hydrogen
Pressurant gas
Hydrogen
Initial Liquid Temp. (K)
20.8
Initial Ullage Temp. (K)
21.0
49
Table 3 Total height
0.65m
Liquid height
0.455m
Tank diameter
0.296m
Working fluid
Nitrogen
Pressurant gas
Nitrogen
Pressurant gas temperature
294K
50
Table 4 Insulation Thickness (mm)
Mass Transfer Rate at t=300s (g/s)
Mass Transfer Rate at t=600s (g/s)
Average Heat in-leak in Liquid (W/m2)
10
-0.9
-1.43
405
20
-0.5
-0.6
230
30
0.4
-0.45
161.3
40
0.7
-0.34
124.9
51
Table 5 1
2
3
4
275
286
290
292
Ullage Heat in-Leak (W/m )
15.8
18.2
19.4
19.9
Tank Pressure (bar)
2.903
2.916
2.924
2.927
Wind Velocity (m/s) Max. Temp. at Insulation Surface (K) 2
52
Table 6 Insulation Thickness (mm)
Mass Transfer Rate at t=300s (g/s)
Mass Transfer Rate at t=600s (g/s)
Average Heat in-leak in liquid (W/m2)
10
-0.9
-1.48
426.3
20
-0.5
-0.66
242.5
30
0.4
-0.51
169.4
40
0.7
-0.36
131.2
53
S1359-4311(16)31144-9 http://dx.doi.org/10.1016/j.applthermaleng.2016.07.015 ATE 8613
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
31 March 2016 1 July 2016 2 July 2016
Please cite this article as: J. Joseph, G. Agrawal, D.K. Agarwal, J.C. Pisharady, S. Sunil Kumar, Effect of Insulation Thickness on Pressure Evolution and Thermal Stratification in a Cryogenic Tank, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.07.015
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effect of Insulation Thickness on Pressure Evolution and Thermal Stratification in a Cryogenic Tank Jeswin Josepha, Gagan Agrawala, Deepak Kumar Agarwala*, J.C. Pisharadya, S. Sunil Kumara a
*
Liquid Propulsion Systems Centre, ISRO, Thiruvananthapuram, Kerala, India - 695 547,
Corresponding author. email: [email protected], ph: +91 471 256 7743, fax: +91
471 256 7039 Abstract A transient analytical, multi-phase, thermodynamic model of foam insulated liquid hydrogen tank is developed to understand the effect of insulation thickness on the evolution of tank pressure and liquid thermal stratification. The model is validated with experimental data reported in literature. Analyses are carried out for pressurization considering two scenarios: first case with tank vent port closed after pressurization to study the pressure evolution and the second case for a constant tank pressure of 3.0bar to study the growth of liquid thermal stratification. Both cases are investigated for different tank insulation thicknesses of 10mm, 20mm, 30mm and 40mm and with a pressurization gas temperature of 50K. Effects of variations in ambient wind velocity and presence of solar flux on self-pressurization profile of the tank are also analysed. The study shows that the reduction in insulation thickness leads to increase in stratified mass. The study also brings out significant increase in pressure rise when tank is insulated with lower insulation thickness. Keywords: Cryogenic Tank, Insulation, Thermal Stratification, Liquid Hydrogen, SelfPressurisation
1
Nomenclature A
Surface area (m2)
Cp
Specific heat (J/Kg-K)
D
Tank diameter (m)
d
Port diameter (m)
g
Gravity (m/s2)
H
Enthalpy (J/kg)
h
Heat transfer coefficient (W/m2-K)
hfg
Latent heat of vaporization (J/K)
k
Thermal conductivity (W/m-K)
m
Resident mass (Kg)
Nu
Nusselt number
Pr
Prandtl number
Gr
Grashof number
P
Pressure (Pa)
Q
Heat (J)
Ra
Rayleigh number
Re
Reynolds number
T
Temperature (K)
t
Time (s)
U
Boundary flow velocity (m/s)
x
Tank height (m)
Greek Symbols β
Coefficient of thermal expansion (K-1) 2
δ
Boundary layer thickness (m)
µ
Dynamic viscosity (Pa-s)
ʋ
Kinematic viscosity (m2/s)
ρ
Density (kg/m3)
σ
Surface tension (Kg/s2)
Subscripts a
Ambient
conv Convection int
Liquid-vapor interface
l
Liquid
s
Tank outer surface
u
Ullage
v
Vapor
w
Inner wall
3
4
1. Introduction Cryogenic propellants used for space missions are stored in foam-insulated tanks for long duration prior to lift-off. During this period, considerable amount of heat leak into the tank through the insulation which leads to the formation of natural convection boundary layer in the liquid close to tank surface. The heat leaked into the tank raises the temperature of the liquid in the boundary layer, resulting in movement of warm liquid cryogen from tank bottom to liquid-vapor interface along the tank wall due to buoyant force. Accumulation of warm liquid close to the interface creates a warm liquid zone at the top of the bulk liquid. Tank pressurization results in an additional heat input into the tank as pressurization sub-cools the bulk liquid and raises the liquid-vapor interface temperature, which rises the axial conduction heat flux through the interface. This conductive flux also influences the warm liquid zone by further increasing the liquid temperature. Tank pressurization with high temperature pressurant gas raises the tank wall temperature close to interface through convection in the ullage and subsequent tank wall conduction, which also adds to the heat flow into the warm liquid zone. The thickness of warm liquid zone increases with time as heat is pumped in and gives rise to axial temperature gradient in bulk liquid cryogen. This axial gradient in liquid temperature is called thermal stratification. Development of thermal stratification in a typical cryogenic propellant tank due to various external heat sources is depicted in Fig. 1. Cryogenic propellant tanks prepared for launch mission undergo typical operation sequence that include tank chilling, tank filling, boil-off, level correction, tank pressurization and hold, prior to lift-off. Boil-off operation essentially brings the propellant to saturation temperature based on the desired tank pressure. Level correction operation compensates the liquid level reduction due to boil-off by filling sub-cooled propellant from tank bottom, which marginally raises the tank pressure caused by ullage compression. During pressurization, interface 5
temperature increases based on saturation temperature corresponding to the tank pressure. Normally, tank pressurization ends about a minute prior to lift-off after which no operations are carried out until ignition of cryogenic engine. Engine ignition commences with regulated draining of propellant from the tank. During engine operation the tank pressure is maintained at a constant value to achieve uniform propellant flow rate. The desirable temperature of liquid propellant at pump inlet of cryogenic engine system is restricted by the pump cavitation limit, beyond which engine performance degrades significantly. Hence, the mass of liquid in warm zone that has a temperature above the pump cavitation limit is deemed unusable for the mission and is a liability to the payload capacity of the launch vehicle. This excess liquid mass that has to be loaded into the tank of a typical cryogenic propulsion system is called stratified mass of the propellant. Additionally, heat in-leak from ambient and tank pressurization play significant role in determining the pressure evolution inside the tank. Also, stratified mass and tank pressure can be controlled by proper insulation of cryogenic tank. Thus, it is important to have prior knowledge on the effect of insulation thickness on evolution of stratified mass and tank pressure for smooth operation of cryogenic engine. Several experimental and numerical studies on thermal stratification and pressure evolution in cryogenic tank have been reported in the literature. Schmidt et al [1] carried out experimental and numerical studies to investigate the liquid hydrogen stratification and pressurization in a super-insulated dewar. They assumed liquid column as a semi-infinite solid and compared their results to the experimental data. Tatom et al. [2] reported an experimental study on thermal stratification of liquid hydrogen in rocket propellants for bottom heating and side heating and suggested that bottom heating, if applied properly, may cause a considerable reduction in the stratification. Evans et al. [3] carried out the experimental study on the transient effects of natural convection inside enclosed fluids. Nein and Thompson [4] experimentally studied the pressurant requirements in cryogenic tanks of 6
various shapes and developed an analytical one-dimensional ullage stratification model to determine pressure requirements in cryogenic tanks. Li et al [5] numerically studied the thermodynamic effect of heat in-leak into cryogenic tank and backed the results with experimentation. The study concluded that thermal stratification exists only in sub-cooled liquid and heat in-leak depends on void fraction of fluid close to the tank wall. An experimental and numerical study was carried out by Ludwig et al. [6] showed the effect of sloshing on variation in tank pressure and liquid stratification. Hasan et al [7] conducted experiments in spherical liquid hydrogen tank to study the pressurisation of the tank, which showed that initial conditions of the tank plays significant role in tank pressure rise. Study carried out by Gursu et al. [8, 9] showed the significance of the thermal stratification on pressure rise rates. Tunc et al.[10] developed CFD model to simulate helium pressurisation effects in liquid oxygen tank. The study showed that pressure rise rates are significantly less when liquid oxygen tank is pressurised using gaseous helium. Stephens and Hanna [11] carried out analysis to study high heat flux effects on a horizontally-placed liquid hydrogen tank. The analysis showed that ullage mixing is dominant over wall to ullage heat transfer in determining the pressure evolution pattern in a cryogenic tank. Numerical simulations were carried out by Daigle et al [12] to analyse thermal stratification using ordinary differential equation solution and obtained good results with experiments. CFD studies carried out by Jazayeri and Khoei [13] showed thermal stratification in liquid oxygen and liquid nitrogen tanks depend mainly on natural convection flows. Grayson et al [14] modelled liquid hydrogen cryogenic tank of Saturn AS-203 flight experiment and simulated thermal stratification using CFD approach, which showed liquid temperatures under low gravity scenario. A numerical study was carried out by Lin and Hasan [15] which solve the steady state conservation equations for an axis-symmetric cylindrical enclosure, showed the effect of Rayleigh number, Prandtl number and wall heat flux on the characteristics of thermal 7
stratification in case of uniform sidewall heat flux. Tanyun et al. [16] performed a numerical simulation of the thermal stratification of liquid hydrogen inside the storage tank. The formulation was based on the vorticity-stream function method, and the surface temperature obtained was correlated with the heat flux, fluid level and time. Panzarella et al. [17] carried out numerical simulation with introducing the effect of thermal stratification in the liquid region to the effect of pressure rise on various heating conditions. The simulation was carried out using computationally-expensive Navier-Stokes differential equation solver. A numerical simulation for the convection currents in a rectangular enclosure was reported by Sun et al. [18] with volume base finite difference method. The study concluded the effect of increase in baffle size to the convection currents. Barsi et al. [19] carried out numerical calculation and experiment of the self-pressurization in liquid hydrogen tank. They considered the heat in the liquid is used for evaporation of liquid at interface and modeled the ullage gas phase as a lump in the respect of energy and mass. Ganguli et al. [20] performed an experimental and numerical study for stratification in fluid container taking working fluid as water. The study showed the higher stratification in less time with higher Rayleigh number. For insulation systems used in cryogenic tanks, studies were carried out by Arsonval [21], who proposed the insulation system for tank using double wall with vacuum annular section. This tank was later improved by Dewar [22] to store hydrogen liquid at 20.4 K. Several experimental studies were carried out by the researchers [23-27] to investigate the heat transfer in cryostat from ambient. Shu et al. [28] recommended for an optimal insulation of a nitrogen cryostat with a number of screen layers. These insulation systems are suitable for ground experiments. Cryogenic tank prepared for space missions are insulated with foam or MLI as reported by Kramer et al. [29].
8
A large number of experimental and numerical studies have been carried out and been reported in literature on thermal stratification, pressure evolution and insulation design of a cryogenic tank using different cryogenic liquids. However, a comprehensive investigation on the effect of insulation thickness on stratification and pressure evolution is absent in current literature. The present study focuses on developing a discretised lumped model strategy to simulate stratification phenomenon in a typical liquid hydrogen propellant tank used for space missions. The model is validated with the results reported in the literature. Effect of different tank insulation thicknesses on pressure evolution and thermal stratification are investigated. The study also brings out the effect of variations in wind velocity and presence of solar heat flux on self-pressurization of the tank. 2. Model Description A transient two-phase thermodynamic lumped model is developed using SINDA/FLUINT solver to simulate thermal stratification in a typical liquid hydrogen tank, having diameter of 4m, length of 7m, wall thickness of 4mm, various foam-insulation thicknesses of 10mm, 20mm, 30mm and 40mm, and liquid level filled upto 87% of the total height. The computational domain for the model is illustrated in Fig. 2. Thermal stratification in an axis-symmetric tank is caused due to complex two-dimensional boundary layer phenomenon, occurring close to tank wall. The current model simplifies this two-dimensional problem into one-dimensional lumped model, to predict the pressure evolution and bulk fluid temperatures during the occurrence of various thermodynamic transients in the tank. It is assumed that the boundary layer for natural convection forms within the liquid at nadir point of bottom dome. The tank surface and associated insulation are axially discretised in the same manner as bulk fluid within the tank. Surface discretizations are called nodes and fluid discretizations are called lumps, as seen in Fig. 2. 9
Ullage lumps are only axially discretised whereas liquid lumps are radially discretised into three parts. Liquid lumps close to the tank wall represent boundary flow zone where heat inleak into the tank raises the lump temperature in the zone, leading to boundary layer flow based on natural convection. The boundary layer flow in boundary zone creates a flow in radial direction, resulting in a region where fluid flows from interface towards tank bottom. This region is termed as return flow zone which constitutes the flow network for boundary layer flow phenomenon in the model. The third region is the core zone in the bulk liquid, which is radially most distant from the tank wall and having negligible flow along it. Heat transfer within this zone is predominantly due to simple fluid conduction, hence it is termed core conduction zone, as mentioned in Fig. 2. The stratified mass in current study is defined as the total mass of all fluid lumps having temperature in its axial layer, higher than pump cavitation limit of 23K. 3. Operational Sequence for Analysis As mentioned earlier, typical pre-flight tank operations include tank chilling, tank filling, boil-off, level correction, tank pressurization and tank hold. The transient analysis starts with level correction operation, assuming fluid at tank filling liquid temperature of 20.8K and tank pressure of 1.2bar at the end of boil-off. A steady-state analysis is carried out for initialisation of tank wall and foam insulation before transient execution. Insulation thermo-physical properties are shown in Table 1. Discrete values of thermal properties, shown in Table 1, are linearly interpolated. During level correction operation, the tank is filled with liquid hydrogen at 20.8K from the bottom of the tank, leading to rise in liquid fill level and subsequent increase in pressure from 1.2bar to 1.3bar in 5 minute duration. During this period, the growth of stratified layer is insignificant as saturation temperature of hydrogen at 1.3bar is only 21.1K. Tank 10
pressurization starts at time t=0s using gaseous hydrogen to raise the tank pressure to 3.0bar in 5 minutes. This results in significant stratification build-up close to liquid-vapor interface. As mentioned earlier, analyses are carried out considering two scenarios: first case with tank vent port closed after pressurization to study the pressure evolution, second case for a constant tank pressure after pressurisation at 3.0bar to study the thermal stratification growth. In both the cases, studies are carried out from tank pressurization at t=0s to t=300s and extended to 300s after pressurisation. These scenarios are investigated for varied insulation thickness of 10mm, 20mm, 30mm or 40mm while pressurant gas temperature is kept constant at 50K. Hydrogen properties are taken from NIST fluid property database [30]. 4. Mathematical Formulations 4.1 Conservation of Mass The net mass flow from a fluid node is equated to the rate of change of mass in the control volume as shown below.
Conservation of mass is ensured at each fluid node during each time-step of transient simulation. 4.2 Conservation of Momentum The governing equation for flow connectors is simply a complex form of Newton’s second law. The momentum conservation equation for a fluid connector is written as below:
Viscous coefficient ‘f’ is calculated using Churchill formulation [1]. Fluid nodes are connected by fluid connectors on which momentum conservation is imposed. 11
4.3 Conservation of Energy The energy conservation equation is expressed on the basis of the first law of thermodynamics. The rate of increase of internal energy in the control volume is equal to the difference between the rate of energy transport into the control volume and the rate of energy transport from the control volume. The energy conservation equation based on enthalpy can thus be written as below:
where Q, shown below, represents heat in-leak from ambient at boundary fluid nodes with heat transfer coefficient, h is described later in this section.
4.4 Equation of State Thermodynamic variables at a particular fluid lump are calculated using real fluid state equation with compressibility factor, Z, being an input from NIST database [30].
4.5 Boundary layer thickness and velocity The upward flow in boundary layer is determined by using the formulations developed by Tsuji et al. [31]. Since the liquid-side wall temperature is very close to the temperature of the liquid, formulations based on constant wall temperature, are shown as below.
where
12
4.6 Heat and mass transfer across interface The model is used to analyze the evolution of liquid temperature inside the tank considering conduction, convection, heat and mass transfer across the interface. A schematic of the cryogenic tank showing various heat transfer mechanism is depicted in Fig. 2. Heat, from ullage to bulk liquid, transfers through interface. However, the heat transfer from ullage to interface and interface to liquid are equal. Heat transfer from the interface to liquid is expressed as:
The heat transfer from the ullage gas to interface is due to convection. Since, diffusing or condensing constituent carries its own individual enthalpy, there is an additional heat transfer across interface due to mass transfer of these species. Effective heat transfer from the ullage gas to interface is expressed as:
m and H are mass and enthalpy of fluid transfer across interface. m is positive for condensation and negative for vaporization of the liquid and is expressed as:
It has been assumed that the heat transfer is due to natural convection with the heat transfer coefficient being expressed by the correlations [32] as below.
13
where:
and
Constant ‘C’ is 0.54 and 0.27 for heat transfer from ullage to interface and interface to liquid respectively. n = 0.25 and ‘KH’ (heat transfer adjustment factor) is set to 1.0. The length scale ‘ls’ is set to the diameter of the tank. 4.7 Heat transfer from wall to fluid Tank is pressurised with gaseous hydrogen and during pressurisation mixed convection heat transfer occurs in the tank ullage as a combination of force convection and natural. Heat transfer from tank wall to ullage gas during pressurisation is determined by using the formulation [33] described as below.
where:
14
Heat transfer from wall to liquid is calculated using natural convection formulation reported by Rohsenow [34] and is described in Eq. 16.
4.8 Heat transfer from ambient Coefficient of convective heat transfer on tank surface is calculated by using Churchill and Bernstein [32] based formulation based. Heat transfer from outside is express below.
To calculate heat transfer from ambient to the tank wall, three dimensional transient heat conduction equations are solved considering the variation of thermal conductivity of the insulation with temperature. Three-dimensional transient heat conduction equation is given by following expression considering k as a function of temperature:
All the above mentioned heat transfer modes represent the mathematical thermal model which have been incorporated in the analyses. 4.9 Solution Methodology and Boundary Conditions
15
Solution flow chart depicting the dependence of each parameter on different thermodynamic equations used in the present model is shown in Fig. 3. Major resultant parameters from the simulation are 3-D tank wall temperature distribution, fluid thermodynamic parameters (pressure, temperature, and density), fluid connector mass flow rates and interface mass transfer or evaporation/condensation rate. These parameters are inputs as well as outputs for different thermodynamic equations, discussed earlier in this section. Iterations for solution convergence are carried out for each time step of simulation, thereby forming a closed relation between the each parameter. Initial and boundary conditions used for the analyses are shown in Table 2. The input parameters used for the simulation are considered based on values and data from a typical launching mission. 5. Model Validation Ludwig et al. [6] carried out an experiment on pressurization of cryogenic tank filled with liquid nitrogen at an initial temperature and pressure of 77.7K and 1.06bar respectively. The dimensions of the cylindrical tank taken for the experiment are shown in Table 3. The mathematical formulations presented here are applied to the simulation of experimental study carried out by Ludwig et al. [6]. In the experiment, the tank is pressurized from 1.06bar to 3.0bar for duration of 52s using gaseous nitrogen. After 52s, tank pressure decreases and reaches 2.46bar at 200s. The numerical simulation of this experiment aims to capture the pressure evolution and liquid stratification and compared it with the experimental data reported. Figure 4 shows the comparison of measured tank pressure evolution with the simulated results. Figure 5 shows the liquid temperature along the tank height at different time instants of 0.0s, 52s and 200s. It can be seen from the Fig. 4 and Fig. 5 that initially liquid is at saturation condition of 77.7K. Subsequently, tank is pressurised from 1.06bar to 16
3.0bar in 52.0s and interface temperature increases from 77.7K to 87.9K which is the saturation temperature corresponding to the tank pressure. The reduction in pressure, after 52s, results in reduction in interface temperature and interface temperature at 200s is 85.7K. Figure 6 shows the rise in liquid temperature at a height of 0.445m and 0.450m from the tank bottom which illustrates a very good agreement with the experiment data. It is to be noted from the Figs. 4, 5 and 6 that simulated results are well validated with the experimental data. Hence, it proves the validity of numerical scheme used for the analysis for the effect of various parameters on liquid thermal stratification and pressure evolution inside the tank. 6. Results and Discussion A thermal stratification model is developed to analyse and discuss the two cases; (i) to determine the effect of insulation thickness on pressure evolution in liquid hydrogen cryogenic tank while pressurization port is closed after tank pressurization, named as pressure evolution studies and (ii) to determine the effect of insulation thickness on thermal stratification growth in liquid hydrogen cryogenic tank while tank pressure is maintained at 3.0bar after tank pressurization, named as liquid thermal stratification studies. The results simulated from the analyses are discussed below. It may be noted that the studies are carried out for the tank dimensions discussed in section 2. 6.1. Pressure Evolution Studies The transient analysis starts from tank pressurization process which commences at t=0 and lasts upto t=300s. After t=300s, the pressurization port is closed, thereby allowing the tank pressure to evolve under the influence of ullage heat-in leak. The analysis duration is extended by 300s after pressurization, i.e., up to t=600s. Analyses are carried out for different insulation thicknesses of 10mm, 20mm, 30mm and 40mm. The cases are analysed without solar heat flux effects and with wind velocity of 2m/s. The evolution of pressure for different 17
insulation thicknesses, subsequent to the pressurization for a pressurant gas temperature of 50K, is depicted in Fig. 7. It can be seen from Fig. 7 that there exists a pressure fall immediately after pressurization and is significant in tanks with higher insulation thickness. For 10mm insulation thickness over the tank, pressure fall is negligible. Pressure fall in a cryogenic tank after tank pressurization is due to the cooling of ullage gas and subsequent pressure rise is due to ambient heat in-leak in to the ullage overtaking the cooling rate. Figure 8 depicts the ullage temperature profile at t=0s, t=300s and t=600s, for 30mm insulated tank. From time t=0s to t=300s, there is a rise in ullage temperature, which is a consequence of pressurization whereas, ullage temperature decreases from time t=300s to t=600s, which results in tank pressure fall. Ullage temperature profile for different insulation thickness at t=300s and t=600s, is shown in Figs. 9a and 9b, respectively. It can be seen from Figs. 9a and 9b that the ullage temperature increases for insulation thicknesses 10mm and 20mm from t=300s to t=600s, whereas there is a decrease in ullage temperature when tank is 30mm and 40mm insulated. This is because the tank pressure at t=600s, for insulation thicknesses of 10mm and 20mm, is higher than that at t=300s, as can be seen in Fig. 7, which contributes to increase in ullage temperature at t=600s, seen in Fig. 9b. The tank pressure at t=600s is lower than 3bar for 30mm and 40mm insulated tanks, which contributes to decrease in ullage temperature. Heat input from the warm pressurant gas entering the tank, will raise the ullage gas temperature more than the tank wall temperature, resulting in loss of heat from ullage gas to the tank wall which causes the ullage temperature to reduce during pressurization, as seen in Figs. 9a, 9b and 10. The average heat flux values at t=300s and t=600s for different insulation thicknesses are shown in Fig. 11.
18
It can be seen from Figs. 10 and 11 that heat in-leak into the ullage at t=300s is negative, denoting net loss of heat from ullage gas to the tank wall after pressurization. Negative heat flux at t=300s represents the tendency of tank pressure to fall whereas positive heat flux at t=600s shows the tendency of tank pressure to rise, which is in agreement with pressure evolution plot, shown in Fig.7. The pressurant mass flow rate required to pressurize the tank for different tank insulation thicknesses are shown in Fig. 12. It is evident from Fig. 12 that more pressurant mass flow is required to achieve similar pressure rise rate for the tank with more insulation thickness. This is because of lower heat in-leak into the ullage for higher tank insulation thickness, leading to slower temperature rise, and consequently, slower pressure rise. The liquid-vapor interface mass transfer rates at t=300s and t=600s for different tank insulation thicknesses, are shown in Table 4. Negative values show evaporation whereas positive values show condensation. It can be seen that condensation dominates during pressurization in well-insulated tanks. This is due to the sudden increase in pressure of ullage gas, which is initially close to saturation temperature. Low heat in-leak into the liquid due to high insulation thickness, also favours condensation. Mass transfer across interface depends on tank pressurization, which gives rise to condensation, and liquid heat in-leak, giving rise to evaporation. As insulation reduces, increase in evaporation is observed at t=300s and t=600s as liquid heat in-leak dominates the tank pressurization effect on interface mass transfer. 6.1.1 Study of Variations in Ambient Conditions A parametric study is carried out with 30mm insulated tank to determine the effect of different wind velocities and effect of presence of solar radiation. Wind velocities of 1m/s, 2m/s, 3m/s and 4m/s are considered in initial study without considering solar heat flux over 19
the tank. Self-pressurization pattern of the tank for various wind velocities are shown in Fig. 13. It is seen from Fig. 13 that pressure fall rate, immediately after tank pressurization, reduces non-linearly when wind velocity increases. It is also noted from Fig. 13 that for higher wind velocities, the rate of pressure fall is similar, resulting in closer pressure value at t=600s. This is because higher wind velocities increase the heat transfer coefficient over the insulation outer surface, as discussed in equations 22-24, and increases its temperature closer to ambient temperature of 300K, as shown in Table 5. Increase in outer temperature of insulation is marginal if wind velocity keeps on increasing because of constant ambient boundary temperature. Heat in-leak into the tank, and consequently its self-pressurization rate shown in Fig. 13, is a result of conductive heat transfer through the insulation which is directly dependent on insulation outer temperature, shown in Table 5. Similar impact is seen when the cryogenic tank is exposed to solar heat flux of 330W/m2. Comparison of pressure profiles for analyses carried out with and without solar heat load over the tank is shown in Fig. 14. As discussed earlier, heat in-leak is the main source of self-pressurization of the tank. Presence of constant heat flux over the insulation outer surface results in rise in insulation outer temperature, resulting in higher conductive heat flux through the insulation and subsequent rise in heat in-leak. Maximum temperature of 312K at insulation surface is observed when solar flux of 330W/m2 is present as opposed to 286K observed in the absence of it. This resulted in ullage heat in-leak and tank pressure values of 24.9W/m2 and 2.96bar at t=600s for simulation with solar flux, against values of 18.2W/m2 and 2.91bar for simulation without solar flux. 6.2. Liquid Thermal Stratification Studies 20
Similar to the previous analysis, the transient analysis is carried out to study the liquid thermal stratification and stratified mass evolution in the liquid hydrogen tank for different insulation thicknesses of 10mm, 20mm, 30mm and 40mm using 50K pressurant gas temperature. The studies are carried out without solar heat flux effects and with wind velocity of 2m/s. After t=300s, the tank pressure is maintained at peak pressure of 3.0bar by operating the tank port in pressurization or venting mode. The analysis duration is extended by 300s after pressurization, i.e., up to t=600s. While the tank is pressurized from t=0s to t=300s and subsequently maintained at peak pressure of 3.0bar, the liquid temperature in core conduction zone raises due to heat in-leak into liquid hydrogen. Liquid core temperature along the tank height is depicted in Fig. 15 for different time instant of t=0s, t=300s and t=600s where 30mm insulated tank and 50K pressurant gas temperature are used. Liquid temperature profiles in core conduction zone at t=300s and t=600s for different insulation thicknesses are shown in Figs. 16(a) and 16(b), respectively. It is evident from Figs. 16(a) and 16(b) that the temperature of the liquid bulk increases at a faster rate for lesser insulation thickness. This is because of high level of heat in-leak into the bulk liquid as seen in Table 6. Due to ambient heat in-leak and conduction flux from interface into the liquid, the liquid lumps close to liquid-vapor interface reach saturation, as can be seen in Figs. 16(a) and 16(b). This is prominent in 10mm insulated tank where heat flux levels into the liquid are high, as seen in Table 6. The interface mass transfer rate at t=300s and t=600s for different insulation thicknesses are also shown in Table 6. It is clear that condensation is the dominant mode of mass transfer during pressurization while evaporation is the dominant mode when tank pressure is maintained.
21
The stratified mass is defined as the mass of liquid having temperature higher than pump cavitation limit of 23K. The stratified mass evolution for different tank insulation thicknesses is shown in Fig. 17. It is evident from Fig. 17 that stratified mass increases slowly in well-insulated tanks, as a consequence of low heat in-leak, seen in Table 6. It is also observed during pressurization that the stratified mass increases at a faster rate compared to that during fixed pressure scenario after pressurization. The reason is due to the continuous increase in interface temperature during pressurization, leading to continuous increase in conductive heat flux from interface to the liquid, in addition to the ambient heat in-leak into the tank through the insulation. The pressurant gas requirement to maintain the tank pressure at peak value of 3.0bar is also investigated through the analysis. The pressurant gas mass flow rates to maintain 3.0bar pressure in the tank for different insulation thickness are shown in Fig. 18. It can be seen that more pressurant gas is required to maintain the tank pressure at 3.0 bar when tank insulation thickness is higher. It is also seen in the figure that pressurant mass flow rate is negative for lower tank insulation thicknesses, which means the tank is being vented to maintain the pressure at 3bar. As seen in pressure evolution studies shown in Fig. 7, after pressurization, the tank pressure falls faster if the tank is well insulated, which is due to lower ullage heat in-leak. Higher the pressure fall, more is the pressurant mass required to maintain the tank pressure. The pressure evolution for lower insulation thicknesses, shown in Fig. 7, indicates that tank has to be vented to compensate for pressure rise due to ullage heat in-leak. 7. Conclusion A transient, two-phase, thermodynamic model of liquid hydrogen cryogenic propellant tank used in a typical launch mission is developed to understand the effect of insulation thickness on the tank pressure and thermal stratified mass evolution. The model is validated with 22
transient pressure and liquid temperature data from experiments reported in literature [6]. Following are the salient conclusions drawn from the analyses: 1. Lower insulation thickness over cryogenic tanks leads to higher heat in-leak into ullage gas, causing tank pressure to rise significantly. 2. Tank pressure, which influences the interface temperature, has significant influence on the stratified mass evolution. Higher tank pressure leads to higher liquid stratified mass. 3. Lower thickness of tank insulation results in higher stratified mass due to higher liquid heat in-leak from the ambient, causing payload penalty in propellant tanks used in launch vehicles. 4. Lower tank insulation thickness results in less pressurant mass required for tank pressurization due to higher ullage heat in-leak. Subsequently, higher ullage mass need to be vented to maintain constant tank pressure after pressurization. 5. Tank outer surface temperature is influenced by ambient conditions and solar flux, and affects the heat in-leak and subsequently, the tank pressure. Though higher tank insulation thickness is required to minimize the liquid stratified mass and ullage pressure rise, optimization for insulation thickness should be carried out considering other parameters such as increase in insulation mass with higher insulation thickness and condensation or ice-formation over the tank insulation for lower insulation thickness. While designing the insulation and its thickness, one should also keep in mind the constraints imposed on mission critical parameters like tank pressure and temperature limits due to flight trajectory.
23
8. References: [1]
Schmidt, A. F., Purcell, J. R., Wilson, W. A., Smith, R. V., 1960. An experimental study concerning the pressurization and stratification of liquid hydrogen, Advances in Cryogenic Engineering, Springer US, pp. 487-497.
[2]
Tatom, J. W., Brown, W. H., Knight, L. H., Coxe, E. F., 1964. Analysis of thermal stratification of LH2 in rocket propellant tank, Advances in Cryogenic Engineering, vol. 9, pp. 265–272.
[3]
Evans, L. B., Stefany, N. E., 1966. An experimental study of transient heat transfer to liquids in cylindrical enclosures, Chem. Eng. Prog. Symposium Ser., Vol. 62, No. 64, pp 209- 215.
[4]
Nein, M. E., Thompson, J. F., 1966. Experimental and analytical studies of cryogenic propellant tank pressurant requirements, George C Marshall Space Flight Center, NASA TN D-3177
[5]
Li, X., Xie, G., Wang, R., 2010. Experimental and numerical investigations of fluid flow and heat transfer in a cryogenic tank at loss of vacuum, Journal of Heat and Mass Transfer, Vol. 46(4), pp.395-404.
[6]
Ludwig, C., Dreyer, M. E., Hopfinger, E. J., 2013. Pressure variations in a cryogenic liquid storage tank subjected to periodic excitations. International Journal of Heat and Mass Transfer, Vol. 66: 223-234.
[7]
Hasan, M. M., Lin, C. S., Vandresar, N. T., 1991. Self-pressurization of a flightweight liquid hydrogen storage tank subjected to low heat flux, NASA Technical Memorandum 103804
[8]
Gursu, S., Sherif, S. A., Veziroglu, T. N., Sheffield, J. W., 1993. Analysis and optimization of thermal stratification and self-pressurization effects in liquid hydrogen
24
storage systems—Part 1: Model development, ASME Journal of Energy Resources Technology, Vol. 115(3), pp.221-227. [9]
Gursu, S., Sherif, S. A., Veziroglu, T. N., Sheffield, J. W., 1993. Analysis and optimization of thermal stratification and self-pressurization effects in liquid hydrogen storage systems—Part 2: Model results and conclusions, ASME Journal of Energy Resources Technology, Vol.115(3), pp.228-231.
[10] Tunc, G., Wagner, H., Bayazitoglu, Y., 2001. Space shuttle upgrade liquid oxygen Tank thermal stratification, 35th AIAA Thermophysics Conference Proceedings, Anaheim, CA [11] Stephens, C. A., Hanna, G. J., 1991. Thermal modelling and analysis of a cryogenic tank design exposed to extreme heating profiles, NASA Contractor Report 186012, Dryden Flight Research Facility. [12] Daigle, M. J., Smelyanskiy, V. N., Boschee, J., Foygel, M., 2013. Temperature stratification in a cryogenic fuel tank, Journal of Thermophysics and Heat Transfer, Vol 27(1), pp-116-126 [13] Jazayeri, S. A., Khoei, E. M. H., 2008. Numerical comparison of thermal stratification due natural convection in densified LOX and LN2 tanks, American Journal of Applied Sciences Vol 5(12) pp 1773-1779 [14] Grayson, G. D., Lopez, A., Chandler, F. O., Hastings, L. J., Tucker, S. P., 2006. Cryogenic
tank
modelling
for
the
Saturn
AS-203
experiment,
42nd
AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Sacramento California [15] Lin, C. S., Hasan, M. M., 1990. Numerical investigation of the thermal stratification in cryogenic tanks subjected to wall heat flux, AIAA-90-2375, NASA Tech. Memo. 103194. 25
[16] Tanyun, Z., Zhongpin, H., and Li, S., 1996. Numerical simulation of thermal stratification in liquid hydrogen, Advances in Cryogenic Engineering, Vol. 41, pp. 155– 161. [17] Panzarella, C. H., Kassemi, M., 2003. On the validity of purely thermodynamic descriptions of two-phase cryogenic fluid storage tanks, Journal of Fluid Mechanics, Vol. 484, pp. 41-68. [18] Sun, Y. S., Emery, A. F.,1997. Effects of wall conduction, internal heat sources and an internal baffle on natural convection heat transfer in a rectangular enclosure, International Journal of Heat and Mass Transfer Vol. 40, pp. 915–929. [19] Barsi, S., and Kassemi, M., 2008. Numerical and experimental comparisons of the selfpressurization behaviour of an lh2 tank in normal gravity, Journal of Cryogenics, Vol. 48, pp. 122-129. [20] Ganguli, A. A., Pandit, A. B.,Joshi, J. B., Vijayan, P. K., 2011. Hydrodynamic and heat transfer characteristics of a centrally heated cylindrical enclosure: CFD simulations and experimental measurements, Chemical Engineering Research, 89,2024–2037. [21] Arsonval, A. D., 1888. Research report, Roy. Soc. Biol, 40, p. 136 [22] Dewar, J., 1898. Storage of liquid hydrogen, Proc. Roy. Soc. 63, p. 256. [23] Caplin, A. D., Cayless, A. T., 1986. Simple numerical modelling technique for cryostat design, Journal of Cryogenics Vol. 26, pp. 678–681. [24] Mende, F. F., 1989. Broad-neck liquid helium cryostat. Journal of Cryogenics Vol. 29, pp. 998–1001. [25] Buhler, S., 1994. Thermal conduction through a vented support, Journal of Physics III France. [26] Casse, J. L., Woestenburg, E. E. M., 1986. Thermal model for a hybrid cryostat, Journal of Cryogenics Vol. 26, pp. 454–458. 26
[27] Anzelka, P., 1993. Numerical modelling in cryostat design, Journal of Cryogenics Vol. 33, pp. 953–958. [28] Shu, Q. S., Fats, R. W., Hart, H. L., 1985. An experimental study of heat transfer in multilayer insulation systems from room temperature to 77 K, 1st International Cryogenics Conference [29] Kramer, T. J., Brogren, E. W., Siegel, B. L., 1984. Evaluation of propellant tank insulation concepts for low-thrust chemical propulsion systems, NASA Lewis Research Centre, Contract Report no. 168321 [30] webbook.nist.gov/chemistry/fluid/ [31] Tsuji, T., Nagano, Y., 1989. Velocity and temperature measurements in a natural convection boundary layer along a vertical flat plate, Experimental Thermal and Fluid Science, 2(2), pp.208-215. [32] Incropera, F. P., Dewitt, D. P., 1985. Fundamentals of heat and mass transfer, John Wiley & Sons, Inc., Chap. 7. [33] Woodfield, P. L., Monde, M. and Mitsutake, Y., 2006. Measurement of averaged heat transfer coefficient in high pressure vessel during charging with hydrogen, Nitrogen and Argon gas, Journal of Thermal Science and Technology, No. 06-0272, DOI 10.1299/jtst.2.180. [34] Rohsenow, W.M., A method of correlating heat-transfer data for surface boiling liquids, Transactions of ASME, Vol. 74, pp. 969-975, 1952.
27
List of figures Figure 1
Schematic of thermal stratification phenomenon in a cryogenic tank
Figure 2
Computational model of thermal stratification in cryogenic tank
Figure 3
Flow chart depicting solution procedure
Figure 4
Model validation with literature : Tank pressure
Figure 5
Model validation with literature : Liquid temperature along the tank height
Figure 6
Model validation with literature : Transient liquid temperature rise
Figure 7
Evolution of pressure for different tank insulation thicknesses
Figure 8
Ullage gas temperature profile during different instances for 30mm insulated tank
Figure 9
Ullage gas temperature profile for different tank insulation thicknesses at (a) t=300s and (b) t=600s
Figure 10
Ullage heat in-leak for 30mm insulation thickness
Figure 11
Ullage heat in-leak at t=300s and t=600s for different insulation thicknesses
Figure 12
Pressurant gas flow rate during pressurization for different insulation thicknesses
Figure 13
Self-pressurization profile for different wind velocities
Figure 14
Pressure profile for cases with and without solar heat flux
Figure 15
Liquid core temperature profile during different instances for 30mm insulated tank with tank pressure maintained after pressurization
Figure 16
Liquid core temperature profile for different tank insulation thicknesses at (a) t=300s and (b) t=600s
Figure 17
Thermal stratified mass evolution in liquid for different insulation thicknesses
Figure 18
Pressurant gas flow rate to maintain the pressure at 3bar for different insulation thicknesses 28
List of Tables Table 1
Thermo-physical properties of insulation material
Table 2
Initial and boundary conditions for the analyses
Table 3
Details of experimental tank used by Ludwig et al. [6]
Table 4
Interface mass evaporation rate and liquid heat in-leak at t=300s and t=600s for different insulation thicknesses
Table 5
Maximum temperature at insulation outer surface, ullage heat in-leaks and tank pressures at t= 600s for cases with different wind velocities
Table 6
Interface mass evaporation rate at t=300s and t=600s for different insulation thicknesses
29
Fig. 1
30
Fig. 2
31
Fig. 3
32
9. Fig. 4
33
Fig. 5
34
Fig. 6
35
Fig. 7
36
Fig. 8
37
Fig. 9 38
Fig. 10
39
Fig. 11
40
Fig. 12
41
Fig. 13
42
Fig. 15
43
Fig. 15
44
Fig. 16 45
Fig. 17
46
Fig. 18
47
Table 1 Property, Unit
Values
Density, kg/m3
35 755 (90K)
Specific Heat, J/Kg.K
1942 (283K) 2234 (298K) 2121 (323K) 0.0097 (90K)
Conductivity, W/m.K
0.0349 (283K) 0.0382 (298K) 0.048 (323K)
48
Table 2 Tank Height (m)
7
Tank Diameter (m)
4
Liquid Fill Level (%)
87
Ambient Temp. (K)
300
Ambient Wind Vel. (m/s)
2
Pressurant Gas Temp. (K)
50
Working fluid
Hydrogen
Pressurant gas
Hydrogen
Initial Liquid Temp. (K)
20.8
Initial Ullage Temp. (K)
21.0
49
Table 3 Total height
0.65m
Liquid height
0.455m
Tank diameter
0.296m
Working fluid
Nitrogen
Pressurant gas
Nitrogen
Pressurant gas temperature
294K
50
Table 4 Insulation Thickness (mm)
Mass Transfer Rate at t=300s (g/s)
Mass Transfer Rate at t=600s (g/s)
Average Heat in-leak in Liquid (W/m2)
10
-0.9
-1.43
405
20
-0.5
-0.6
230
30
0.4
-0.45
161.3
40
0.7
-0.34
124.9
51
Table 5 1
2
3
4
275
286
290
292
Ullage Heat in-Leak (W/m )
15.8
18.2
19.4
19.9
Tank Pressure (bar)
2.903
2.916
2.924
2.927
Wind Velocity (m/s) Max. Temp. at Insulation Surface (K) 2
52
Table 6 Insulation Thickness (mm)
Mass Transfer Rate at t=300s (g/s)
Mass Transfer Rate at t=600s (g/s)
Average Heat in-leak in liquid (W/m2)
10
-0.9
-1.48
426.3
20
-0.5
-0.66
242.5
30
0.4
-0.51
169.4
40
0.7
-0.36
131.2
53