Applied Thermal Engineering 173 (2020) 115265
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Numerical simulation and experiment verification of the static boil-off rate and temperature field for a new independent type B liquefied natural gas ship mock up tank
T
Sixian Wua, Yonglin Jua, , Jichao Lina, Yunzhun Fub ⁎
a b
Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China College of Mechanical Engineering, Shanghai University of Engineering Science, 333 Longteng Road, Shanghai 201620, China
HIGHLIGHTS
design and construction of a new independent type B LNG ship mock up tank is presented. • The 3D dynamic CFD model is proposed to calculate the boil-off gas (BOG) and the temperature field in the mock up tank. • AExperiments conducted to verify the CFD simulation results. • The deviationarebetween the simulation and experimental results is within 10%. • The effects of different working conditions on the BOG generation rate and the temperature field are investigated. • ARTICLE INFO
ABSTRACT
Keywords: New independent type B LNG ship Mock up tank Two-phase flow simulation Static evaporation rate
In this paper, a new independent type B liquefied natural gas (LNG) ship mock up tank with the net capacity of 40 m3 and an insulation thickness of 400 mm was taken as the research target. After reasonable simplification, two-phase flow and phase change heat transfer of cryogenic fluid in the mock up tank was simulated by using unsteady three-dimensional CFD method. Volume of fluid (VOF) model was selected to track the vapour-liquid interface, Lee model was used as the phase change model, and the influence of the static pressure on the phase change model was considered. The temperature distribution and the static boil-off gas (BOG) generation rate of the mock up tank was calculated, and working conditions of the simulated tank under different liquid levels and partial insulation system damage were discussed. The pressurization characteristics of the mock up tank under closed conditions was also studied. Comparing the simulation with the experimental results, it showed that this model could effectively simulate the evaporation process of cryogenic liquids in the mock up tank under stationary conditions, which provides an important reference for the design and improvement of the new independent type B LNG ship.
1. Introduction In recent years, with the global focus on the use of clean energy, the demand for natural gas (NG) has increasing grown due to its cleanburning, convenience and efficient application value [1-3]. LNG transportation is the most important means to solve cross-sea natural gas transportation trade between countries, it mainly carries out maritime transportation through LNG ships. Since the temperature difference between the LNG and the ambient air during the voyage is about 190 K, despite the prefect thermal insulation system, the generation of BOG is inevitable due to the heat ingress into the cargo containment
⁎
system (CCS). Therefore, the evaporation rate of the cargo tank is one of the most important indicators to measure the performance of the LNG ship, which reflects the insulation capacity of the LNG ship. In the design and construction of LNG ships, it is necessary to fully study the evaporation process, temperature distribution and flow characteristics of LNG in the CCS. The core component of LNG ship is the CCS. There are two basic types of CCSs: membrane type and independent type. The NO.96 and Mark III types developed by GTT (Gaz Transport and Technigaz, France) are the most common membrane type of CCSs and are currently employed in many LNG ships. Since membrane CCS has been widely
Corresponding author. E-mail address:
[email protected] (Y. Ju).
https://doi.org/10.1016/j.applthermaleng.2020.115265 Received 29 October 2019; Received in revised form 27 March 2020; Accepted 30 March 2020 Available online 01 April 2020 1359-4311/ © 2020 Elsevier Ltd. All rights reserved.
Applied Thermal Engineering 173 (2020) 115265
S. Wu, et al.
employed in many ships built over the past few decades, many researchers have conducted comprehensive studies on the membrane CCS. For instance, Bang et al. [4] and Choe et al. [5] studied the cryogenic reliability and mechanical properties of membrane CCS insulation system. Miana et al. [6] applied the CFD method to calculate the heat leakage and evaporation rate of the Mark III LNG ship using the reduced order model (ROM). Choi et al. [7] have experimentally studied the thermal properties of Mark III and NO.96 CCS insulation materials and steady-state thermal analysis of a CCS was investigated by numerical method. Lee et al. [8] used a multiphase flow model to study the diffusion speed and the vapor/liquid composition changes of LNG leakage in the modified NO. 96 CCS. Lee et al. [9] proposed a method for calculating the temperature of leaking LNG insulation wall of CCS by using the mathematical model of multi-phase flow with multiple gas species involving a porous medium and conjugate heat transfer and carried out model experiments. The results showed that the numerical results were in good agreement with the experimental results. Kang et al. [10] conducted experimental and numerical studies on thermal stratification of cryogenic liquids such as LNG and liquid hydrogen storage, the result show that thermal stratification is highly correlated with the thermal aspect ratio and this study showed that the thermodynamic behaviors resulting from thermal stratification were significantly different from those predicted by the homogeneous model. Lin et al. [11] proposed an equivalent conductive model with the combination of adjacent fluid layer and flowing BOG to replace the multiphase flow model in calculating temperature distribution and estimating evaporation rate of FSRU, testified by experimental results, which showed that the maximum relative error of BOR estimation was less than 4%. Yu et al. [12] proposed the use of glass composites to selectively enhance the PUF surface in the high thermal stress region of CCS, which could effectively reduce production costs, improved thermal insulation performance, and greatly improved the reliability of the thermal insulation board at the cryogenic temperature. Kim et al. [13] developed the impact isolation system of CCS by using glass fiber composite mat, which reduced the impact load transmission into the foam insulation board, and experimentally studied the effect of sloshing of glass fiber composites on the vibration isolation performance of CCS and optimized the design of vibration isolation system by numerical methods. Zakaria et al. [14-16] used ANSYS Fluent to simulate the fullscale LNG ship and estimated the generation of BOG in the cargo tank, but did not give a detailed introduction of the types of models and discretization methods for simulation. Because the flow and heat transfer characteristics of cryogenic fluids in CCSs and cryogenic storage tanks (such as LNG storage tanks) are very similar, the research on the cryogenic storage tanks can also guide the design and manufacture of CCS. A large number of researchers have studied cryogenic storage tanks in various aspects, Chen et al. [17] established a heat transfer model for LNG storage tanks using classical thermodynamics and heat transfer theories. The pressure and temperature changes in the LNG storage tank and the evaporation rate of the LNG storage tank were calculated and compared well with the measured evaporation rate and pressure changes. Because of the fuel loss situation of the LNG station, some approaches have been proposed. For example, the BOG of the LNG can be used to drive the generator or re-liquefied to reduce the gas pressure. Lee et al. [18]numerically investigated the pressure resistance of stainless-steel corrugation of LH2 tanks by using finite element methods and conducted series experimental tests. They developed and optimized a new anti-buckling glass fiber epoxy composite structure for liquefied hydrogen containers. A series of experimental studies [19-23] have carried out on cryogenic tanks, but they were basically in laboratory conditions and the geometric models of the tanks studied were very simple. Saleem et al.[24] studied the boiling mechanism and BOG generation process of full-scale land LNG tank based on ANSYS Fluent, the types of models and discretization methods used in the calculation were introduced in detail. Wang et al. [25-28] used the CFD method to study the transient thermal
Fig. 1. Typical midship section profile for the new independent type B LNG cargo.
and pressurization behaviors of liquid hydrogen or liquid oxygen tank based on multiphase flow model. It was also pointed out that the CFD method had strong adaptability in the numerical simulation of the cryogenic propellant system and had been widely used in thermal and pressurization researches. As stated above, many researchers have conducted a large number of experimental and numerical studies both on the membrane-type CCSs and simple-structure cryogenic storage tanks and achieved a series of valuable results. However, there is less literatures on the study of the new independent type B CCSs. Fig. 1 shows the typical midship section profile for the new independent type B LNG cargo tank. The liquid cargo tank is prismatic and is connected and fixed to the inner hull by support members and chocks. The insulation layer is fixed to the surface of the cargo tank body by bolts. The cargo load and temperature stress of the tank body are directly transmitted to the inner hull of the ship through the support member without affecting the insulation system. It is a typical independent self-supporting type. Besides, at the bottom of the cargo tank, a void space for inspection and repair is designed between the insulation and the inner hull to facilitate the maintenance. Fig. 2 shows the typical midship section profile for two main conventional LNG cargo (membrane-type and MOSS independent spherical type). Comparing Fig. 1 with Fig. 2, it can be found that the new independent type B CCS has outstanding advantages in terms of easy construction and installation, reducing hull load-bearing, reducing liquid cargo sloshing and leakage, and facilitating detection and maintenance, compared with the membrane-type CCS. Compared with the MOSS type CCS, the new independent type B CCS has a higher utilization ratio of cabin space and higher navigation stability due to its low center of gravity structure. In our previous paper, the system design and the preliminary thermal analysis of the insulation system were presented for the new independent B-type CCS. [29]. A steady-state CFD model of the new independent type B CCS insulation system was developed to calculate the BOG of the cargo tank and the temperature distribution of the insulation system. However, the flow and heat transfer characteristics of the cryogenic fluid in the CCS was not studied in detail. To summarize the discussion above, there are few experimental and numerical studies on the independent type B CCS in the literature and few detailed studies on the two-phase flow and phase-change heat transfer of cryogenic fluids in the CCS and cryogenic tank. In this present paper, a new independent B-type CCS mock up tank using the new type (PUF) insulation materials and a cryogenic test platform are designed and built to test the temperature distribution and evaporation rate of the mock up tank. In addition, a 3D dynamic CFD model of the mock up tank is developed to comprehensively study the two-phase 2
Applied Thermal Engineering 173 (2020) 115265
S. Wu, et al.
Fig.2. Typical midship section profile for two main conventional LNG carrier: (a) membrane-type; (b) MOSS independent spherical type.
flow and phase-change heat transfer characteristics of the cryogenic fluid. The temperature distribution of the mock up tank and the static BOG generation rate are calculated and the effects of different filling ratios and insulation system damage on the evaporation characteristics of the mock up tank are also considered.
Energy equation:
( E) + t
For the vapor-liquid two-phase flow in the mock up tank, the accurate determination of the vapor-liquid interface is extremely necessary. The volume of fluid (VOF) method is widely used to simulate two or more immiscible phases. It is also the preferred method for tracking the vapor-liquid interface in the literature. Therefore, in this paper, choosing the VOF model as the multiphase model to study the vaporliquid two-phase flow and mass transfer characteristics.
is the density, u is the velocity vector, p is the pressure, µ is
FCSF = 2
lv
·[µ ( u +
T
u )] + FCSF
l
(4)
+
g g
(5)
µ=
l µl
+
g µg
(6)
E=
n n En
n= 1 2 n=1
n n
(7)
The En for each phase is calculated from its specific heat and temperature. Volume fraction equation: As the volume fraction equation is shared by each phase respectively, it has the following form for the vapor phase:
t
(
v v)
+
·(
v v
u ) = mlv
m vl
(8)
where mlv and m vl are the evaporation and condensation rates, respectively.
(1)
2.2. Phase change model
(2)
The Lee model is widely used as the phase change model to simulate the evaporation-condensation process, i.e. to calculate the mass transfer terms mlv and m vl in the volume fraction equation, which can be
Momentum equation:
p+ g+
v v Cl v
l l
2
In general, the governing equations in VOF model are based on N-S equations, the effects of gravity and surface tension are considered in the calculation. The governing equations in VOF model are as follows: Continuity equation:
·( u u ) =
+ +
The energy (E ) and temperature (T ) are taken as mass-averages. E is calculated from:
= 1, the computational cell is completely filled with the liquid phase; (2) l = 0 , the computational cell is completely filled with the vapor phase; (3) 0 < l < 1,the computational cell is partially filled with the liquid phase
( u) + t
v
=
l
·( u ) = 0
l l Cv
×
here, lv is the surface tension coefficient, C is the surface curvature. The subscript l is the liquid phase and v is the vapor phase. Since there may be two phases in some computational cells, the volume average equation is often used to calculate the viscosity and density in the transport equation for VOF model.
The VOF model is applicable to the case where the sum of the volume fractions of all components is one in each computational cell. By defining the volume fraction of each phase, the movement of each phase can be tracked and the interface between each phase can be determined. The multiphase model in this paper is a vapor-liquid twophase model, assuming that the volume fraction of liquid phase is l and the volume fraction of vapor phase is v in each computational cell, the following three situations may occur in each computational cell:
+
(3)
where
l
2.1. Governing equations
t
·(keff T ) + mlg hlg
the dynamic viscosity, g is the gravitational acceleration, FCSF is the surface tension term, E is the energy, T is the temperature, keff is the effective thermal conductivity. FCSF is calculated by the continuum surface force (CSF) model [30]:
2. CFD model
(1)
·[ u ( E + p)] =
3
Applied Thermal Engineering 173 (2020) 115265
S. Wu, et al.
describe as follows: If Tl > Tsat (evaporation):
mlv = coeff ×
l l
(Tl
Tsat ) Tsat
(9)
If Tv < Tsat (condensation):
m vl = coeff ×
v v
(Tsat Tv ) Tsat
(10)
where coeff is the accommodation coefficient, and Tsat is the saturation temperature, it is the temperature for a corresponding saturation pressure at which the phase change occurs. In the Lee model, coeff is called mass transfer intensity factor or relaxation time(s−1). This is a tunable parameter. Kharangate et al. [31] stated that the range of coeff is very wide, the difference of coeff in different literatures is very large, ranging from 0.1 to 1 × 107(s−1). The optimal value of coeff depends on many factors, including but not limited to specific phase change procedure, flow velocity, mesh size and time step. For the evaporation performance of cryogenic fluids in storage tanks, some literatures [24,32-34], which used the Lee model as phase change model, have demonstrated that the simulation results are almost independent of coeff values. In the present study, considering four cases of coeff equal to 0.1, 0.2, 1, 5, respectively. It is found that the change of coeff has almost no effect on the temperature distribution, vapor fraction and BOG generation rate. Considering the stability and efficiency of calculation, we take coeff = 1 in the CFD simulations. Due to the large vertical height of the simulated tank, the influence of hydrostatic pressure on the saturation temperature of liquid cannot be ignored. Therefore, a polynomial is defined to describe the change of the saturation temperature of liquid with pressure. The following expression, with R2 = 0.9999 is used in the Lee model to calculate Tsat for liquid nitrogen:
Tsat = 7.249 × 10 (K)
16p3
4.994 × 10
(R2=0.9999)
10p 2
+ 0.0001629p + 65.21 (11)
2.3. Turbulence model Considering that the flow pattern in the mock up tank is mainly caused by natural convection, the Ra number in the calculation domain is about 1018 much larger than the critical Ra number (1 0 8) (Ra = g 2cp qw l 4 /µ 2 ), turbulence model is considered in the present study. Combined with the application of each turbulence model provided by ANSYS Fluent and referring to Refs. [24,35], the standard k model is selected as the turbulence model, enhanced wall treatment is used as the wall function.
Fig. 3. (a) 3D model of the No.3 tank of the type B LNG ship (unit: mm); (b) 1 / 4 3D model of the mock up tank and the naming of each feature surface; (c) mesh implementation.
a finer mesh is required near the top vent to accurately measure the flow characteristics. The top vent includes 21 node points, so there are 20 cells at the boundary of the top vent. In the implementation of the CFD model, considering that the flow of the liquid nitrogen in the mock up tank is driven by natural convection, using the Boussinesq approximation to calculate the density of liquid nitrogen can achieve faster convergence. This approximation regards density as constant, except buoyancy term in the momentum T ) is used to eliminate equation, where = m (1 from the buoyancy term. The nitrogen is considered as the ideal gas. The PISO algorithm is used for the pressure-velocity coupling, the governing equations are discretized by using the second order upwind method. Volume fraction equation is discretized by using the geometric reconstruction scheme. The convergence criterion is set at 1 × 10−4 for the residuals of the continuity equation, momentum equation, volume fraction and turbulence equations. A convergence criterion of 1 × 10−8 is used for the energy equation. The time step of the transient calculation is set to 5 × 10−3 s.
2.4. Numerical implementation Fig. 3(a) shows the No.3 tank of the type B LNG ship. The mock up tank is constructed according to the scale of 1:1000. Considering the symmetry of the mock up tank, only 1/4 part of it is simulated. The reasonably simplified 3D model of the mock up tank without insulation system is shown in Fig. 3(b), and the symmetry plane is Z = 0 . The Yblock method is mainly used to divide the computational area into structural grids, and the grid is encrypted on the wall. Fig. 3(c) shows the result of mesh implementation. In addition, in order to simulate the heat and mass transfer phenomenon near the vapor–liquid interface more accurately, the mesh near the interface also needs to be encrypted. According to the experimental results of reference [36], the equilibrium boil-off process is via surface evaporation controlled by 3 delicate mechanisms within 5–10 mm of the liquid surface. Therefore, we encrypt the mesh within 0.02 m around the interface, and the grid thickness is 0.004 m. It is to be noted that the vent size is small (0.1 m diameter) compared to the dimensions of the mock up tank. Therefore, 4
Applied Thermal Engineering 173 (2020) 115265
S. Wu, et al.
2.5. Initial and boundary conditions
transfer coefficient hi, c at the corresponding position of the mock up tank can be calculated after several iterations. After that, the total heat leakage of the insulation system can be calculated by imitating the method in the reference [29]. Therefore, according to the equation Qtot = UA (Tair Tfliud) , the overall heat transfer coefficient (U ) can be determined as 0.086 W /(m2 · K ) when the insulation layer is 400 mm and the thermal conductivity is 0.025 W /(m · K ) .
In the initialization, the operating pressure is set as 1 atm and the temperature in all the computational zone is firstly set as 77.35 K, the initial level is patched to the height at which the mock up tank filling ratio is 98%. This paper mainly studies the internal two-phase flow and phase change heat transfer performance of the liquid nitrogen in the mock up tank, in order to simplify the CFD simulation, the mock up tank without insulation system is studied. In the natural gas industry, the heat entering the storage tank is usually calculated by
Qtot = UA (Tair
3. Experimental investigation In order to study the evaporation characteristics and temperature distribution of the new independent type B CCS and to validate the CFD model, a mock up tank test platform was built. Considering the safety of the experiment, liquid nitrogen was adopted as the cryogenic working substance. liquid nitrogen is usually used as a safer liquid for liquefied natural gas [37]. The mock up tank is designed with reference to the CCS in the middle of the new independent type B LNG ship designed by HudongZhonghua Shipbuilding (Group) Co., Ltd., and is constructed according to the scale of 1:1000. The thermal insulation materials and the structure of insulation layer are the same as the actual ship. Fig. 4(a) shows the mock up tank (without insulation system), the mock up tank is prismatic and the tank material is 9% nickel steel which has perfect performance at cryogenic. In terms of three-dimensional size, the mock up tank is 4.96 m long, 3.8 m wide and 2.75 m high. The wall thickness of the tank is 8 mm and the capacity of the mock up tank is about 40 m3. The insulation system is directly installed on the outer surface of the mock up tank and the thickness of insulation layer is 400 mm. Since the simulation cabin is fixed, the sloshing effect is neglected in the experiment. According to the GB/T 18443.5-2010, the static evaporation rate test of the cryogenic tank mainly includes two methods: flowmeter method and weighing method. Considering the large size of the mock up tank, the flowmeter method is appropriately used to measure the evaporation rate. During the experiment, the mass flow rate of the BOG was measured by a gas mass flowmeter installed at the vent of the top of the mock up tank, and the flowmeter accuracy was 1.5%. Fig. 4(b) shows the structure of insulation layer and installation diagram of temperature sensors (PT100). They are installed on the outer surface of the tank, the inner surface of the insulation layer, the middle of the insulation layer and the outer surface of the insulation layer. In addition to obtaining the temperature distribution of the insulation layer, in order to obtain the temperature distribution data of different parts of the mock up tank, and considering the symmetrical structure of the mock up tank, six characteristic surfaces of A, B, C, E, F and G are selected to arrange the temperature sensor. Fig. 4(c) shows the arrangement diagram for temperature sensors. In addition, two pressure sensors are installed at the top vent of the mock up tank to monitor the pressure in the tank, and two guided wave radars are installed in the tank to measure the liquid nitrogen level height.
(12)
Tfliud)
where, Qtot is the heat entering the storage tank, U is the overall heat transfer coefficient, A is the tank surface area, Tair is the ambient air temperature, Tfliud is the fluid temperature in the storage tank. Therefore, the third boundary condition is adopted in this paper, in which the convective heat transfer coefficient is set as the overall convective heat transfer coefficient (U ), and the ambient air temperature (Tair ) is consistent with the average temperature during the experiment. In addition, in order to simplify boundary condition, it is assumed that the overall heat transfer coefficient (U ) and the ambient air temperature (Tair ) of each surface of the mock up tank are the same and do not change with time. In order to roughly calculate the total heat leakage through the insulation system to determine the overall heat transfer coefficient (U ), it is assumed that the fluid temperature () is the saturated temperature of liquid nitrogen, the ambient air temperature is set to 290 K, according to the daily average temperature during the experiment. The natural convection heat transfer coefficient hi, c of each surface of the insulation system is determined by the empirical equation of the natural convection in an infinite space: For the side of the mock up tank, the following heat transfer correlation is recommended to calculate the Nusselt number:
Nu = C (Grair Prair )n C = 0.59, n = 1/4 (1.43 × 10 4 Grair 3 × 109) C = 0.0292, n = 0.39 (3 × 109 Grair 2 × 1010) C = 0.11, n = 1/3 (Grair > 2 × 1010)
(13)
For the bottom of the mock up tank (Cold surface down), the following heat transfer correlation is recommended to calculate the Nusselt number:
Nu = (10 4 Nu = (107
0.54(Grair Prair )1/4 Grair Prair 107) 0.15(Grair Prair )1/4 Grair Prair 1011)
4. Model validation
(14)
According to the specifications of filling ratio in the actual voyage of LNG ships, the initial filling ratio of the mock up tank is 98% in the experiment, which means that all the other surfaces of the mock up tank except the surface A have good contact with the liquid nitrogen. The temperature of those surfaces is basically equal to the saturation temperature of the liquid nitrogen and does not change with time basically. Therefore, the temperature distribution of the surface A and the region of nitrogen is mainly considered to reflect the temperature characteristics of the mock up tank in this study. Four kinds of mesh with the number of cells 837397, 644152, 527,172 and 426,702 are used in this paper. The results of the mesh independence validation of the mock up tank are shown in Fig. 5. When the average temperature of the surface A and the BOG generation rate of the mock up tank reaches steady state, the results show that the
For the up of the mock up tank (Cold surface up), the following heat transfer correlation is recommended to calculate the Nusselt number:
Nu = 0.27(Grair Prair )1/4 (105 Grair Prair 1010) where, Grair =
Tl3
g V vair 2
, Nu =
(15) hi, c l air
.
In the above equation, air is the thermal conductivity of air, g is the acceleration of gravity, vair is the dynamic viscosity of air, V is the volume expansion coefficient of air, T is the temperature difference between the wall of insulation layer and the external environment, Prair is the Prandtl number of air, l is the surface characteristic length, Grair is the Grashof number of air. According to the above equation, the natural convection heat 5
Applied Thermal Engineering 173 (2020) 115265
S. Wu, et al.
Fig. 4. (a) Mock up cargo tank (without insulation system); (b) Installation diagram of temperature sensors in the insulation layer; (c) Arrangement diagram for temperature sensors.
(426702 cells)
(527172 cells)
(a)
(644152 cells)
(837397 cells)
(b) Fig. 5. Results of the mesh independence validation: (a) Temperature contours of four kinds of mesh, (b) Average temperature of the surface A and the BOG generation rate as a function of time.
6
Applied Thermal Engineering 173 (2020) 115265
S. Wu, et al.
Fig. 6. Experimental data of the mock up tank: (a) Trend of temperature in the insulation layer on surface A; (b) Temperature distribution in the insulation layer of the mock up tank; (c) Plot of ambient temperature and mass of BOG with time during testing; (d) Trend of pressure in the mock up tank.
maximum difference of the four grids is less than 0.5%. Therefore, considering the simulation accuracy and efficiency, it is appropriate to use the grids of 644,152 cells to calculate. In order to obtain the steady evaporation rate and temperature distribution in the experiment and according to the GB/T 18443.52010, the mock up tank is allowed to stand for 48 h before the test. The data of the flowmeter and the temperature sensor for 24 h is recorded during the test. Fig. 6(a) and Fig. 6(b) show the trend of temperature in the insulation layer on the surface A and the temperature distribution in the insulation layer of the mock up tank. It can be seen that during the testing, the fluctuation of the temperature inside the insulation layer is extremely small, and the temperature distribution inside the insulation layer of each surface is basically the same. The surface A and E are not completely immersed in liquid nitrogen, so their temperatures are higher than those of other surfaces. Fig. 6(c) and (d) show the plot of the ambient temperature, the BOG generation rate and the pressure in the mock up tank with time during the testing. It can be seen that during the testing, the pressure in the mock up tank is almost constant, and the trend of BOG generation rate is basically consistent with the trend of the ambient temperature. The ambient temperature rises, the BOG generation rate also increases. Considering the large size of the mock up tank, the 24 h 3D dynamic CFD simulation of the mock up tank requires a lot of computing resources and long computation time, which is difficult to achieve in engineering. Our research mainly focuses on the temperature distribution and evaporation rate of the mock up tank after reaching the thermal steady state and the process of reaching the thermal steady state, so it is not necessary to carry out the whole process simulation. After theoretical analysis and reference to the experimental data, it can
Fig. 7. Results of average surface temperature of the mock up tank and the mass flow rate of BOG calculated by numerical method.
be known that the mock up tank basically reaches thermal steady state when the temperature distribution of the mock up tank and the BOG generation rate hardly change with time in a period of time. Fig. 7 illustrates the numerical results of average temperature of each surface and the BOG generation rate with time. After about 20 min, the average temperature of each surface and the BOG generation rate basically reach a steady state. It should be noted that the BOG generation rate here refers to the whole tank, not to the 1/4 tank, the calculation of the BOG generation rate in the following section is the same.
7
Applied Thermal Engineering 173 (2020) 115265
S. Wu, et al.
5. Results and discussion 5.1. The flow and heat transfer performances Fig. 9(a) shows the temperature contours for the mock up tank at about 60 min. It can be seen that there is a significant temperature gradient along the tank height in the nitrogen region, while the temperature of the liquid nitrogen region is almost constant. Fig. 9(b) and (e) shows the velocity contours for the mock up tank at about 60 min corresponding to the Fig. 9(a) and velocity vector graph of the symmetrical surface of the mock up tank. Due to the heat leakage, the density of the liquid nitrogen changes, and the density gradient causes natural convection of the liquid nitrogen in the tank. It can be clearly seen that there is a counter-clockwise circulation. The cold fluid with higher density sinks in the center of the tank (surface of symmetry) and replaces the hot fluid with lower density at the bottom. The hot fluid rises along the side wall to replace the cold fluid at the top. The natural convection effectively eliminates the temperature gradient of liquid nitrogen. Therefore, the BOG generation rate and temperature distribution reach a steady state when the mock up tank displays prefect mixing performance. Fig. 9(c) shows the temperature contours near the liquid-vapor interface corresponding to Fig. 9(e), temperature difference of the vapor and liquid near the interface is very small, which also proves that the Lee model was applied properly. In order to more clearly reflect the relationship between the flow circulation and the liquid temperature in the mock up tank, Fig. 9(d) shows the temperature contours in the mock up tank (The range of temperature in the contours is adjusted, and the temperature contours of the vapor phase region is ignored.). It can be found that the temperature distribution in the liquid phase region is consistent with the velocity distribution. Fig. 9(f) shows the phase contours for the mock up tank at about 60 min. It can be seen that there is no bubbles formation in the liquid nitrogen region, so it is concluded that there is only surface evaporation without nuclear boiling in the mock up tank. This is due to the perfect insulation system of the mock up tank. model is used as the turIt is found that when the standard k bulence model for simulation, the selection of wall functions has a great impact on the temperature distribution prediction of the mock up tank. Fig. 10 shows the results of the average temperature of surface A and the BOG generation rate by using (a): Standard wall function, (b): Enhanced wall treatment and (c): Enhanced wall treatment (considering the thermal effect). The choice of the wall function really has a significant influence on the temperature distribution and has no significant effect on the BOG generation rate. The comparison with the experimental results shows that the enhanced wall treatment can more accurately predict the temperature distribution. This conclusion also confirms that the choice of wall function has an effect on the simulation results, especially on the prediction of heat transfer [38]. Combined with Fig. 7 and Fig. 10, the generation characteristics of BOG in general cryogenic storage tanks can be generally analyzed. The generation of BOG is caused by the heat from the outside. Initially, part of the heat entering the mock up tank is used as sensible heat to raise the temperature of vapor and liquid in the tank; the other part is used as latent heat to generate the BOG. With time going on, once the natural convection is gradually established and fully developed in the whole liquid region, as mentioned above, the region of the liquid will generally show uniform temperature. The heat ingress into tank is basically used as latent heat, i.e. generating the BOG.
Fig. 8. The locations of the four typical temperature sensors on the surface A of the mock up tank.
Fig. 8 shows the locations of the four typical temperature sensors on the surface A of the mock up tank. Tab. 1 lists the experimental and numerical results of the temperature, the BOG generation rate and the Boil-off rate (BOR) when the temperature distribution and the BOG generation rate reach thermal steady state. BOR is the daily evaporation rate, which is often used as an index to evaluate the insulation performance of cryogenic tanks. The BOR is calculated by
BOR =
Q × 3600 × 24 1000 × hLN2 × V × LN2 ×
× 100%
(16)
where, Q is the total heat leakage of the mock up tank, hLN2 is the latent heat of vaporization of liquid nitrogen, V is the total volume of the simulation tank, LN2 is the density of liquid nitrogen, is the filling rate of liquid nitrogen in the simulation tank. From the Table 1., it can be seen that the numerical results are almost consistent with the experimental results, the deviation between the simulation and experimental results is within 10%, which indicates that the model presented above can accurately predict the temperature field and evaporation rate of the mock up tank. The main source of the deviation is the calculation of the heat leakage of the mock up tank. In the experiment, the insulation system of the mock up tank is made up of many insulation blocks, and the gap between blocks is filled with glass wool and other insulation materials. In the numerical calculation, when calculating the overall heat transfer coefficient (U), the insulation system is simply regarded as a whole, its insulation performance is better than that of the actual experiment, so the heat leakage is smaller than the experiment.
Table 1 Experimental and numerical results of the temperature and the BOG. Items
Experimental results
Numerical results
Point A Point B Point C Point D Average temperature of surface A BOG BOR
81.5 85.8 79.8 81.9 /
82.75 83.58 81.51 80.85 84.45
K K K K
0.0078 kg/s 1.71%
K K K K K
5.2. Effect of filling ratio In the actual voyage of LNG ships, the period of navigation is generally longer, and the evaporation of liquid cargo in the CCS is unavoidable, the liquid level will gradually decrease. Therefore, it is significant to study the variation of the BOG generation rate and temperature distribution in the mock up tank at different liquid levels.
0.00715 kg/s 1.58%
8
Applied Thermal Engineering 173 (2020) 115265
S. Wu, et al.
Fig. 9. The flow and heat transfer performances of liquid nitrogen in the mock up tank: (a) Temperature contours at about 60 min; (b) Velocity contours at about 60 min; (c) Temperature contours of the symmetrical surface at about 60 min; (d) Temperature contours of the symmetrical surface at about 60 min (Liquid phase); (e) Velocity vector graph of the symmetrical surface at about 60 min (Liquid phase); (f) Phase contours at about 60 min.
Fig. 11(a) displays the temperature distribution along the tank height at the symmetrical surface of the mock up tank with the filling ratios of 98% and 58%, respectively. As can be seen from the graph, for the temperature distribution, regardless of the filling ratio of 98% or
58%, the temperature of the liquid nitrogen region hardly changes with the height, while the temperature of the nitrogen region increases with the height. Compared with the 98% filling ratio, the average temperature of the surface A is about 15 K higher. It should be noticed that 9
Applied Thermal Engineering 173 (2020) 115265
S. Wu, et al.
Table 2 The heat leakage of every surface of the 1/4 mock up tank at different filling ratios. Heat leakage of every surface of the 1/4 mock up tank
Filling ratio = 98%
Filling ratio = 58%
A B C E F G Total
60.84 W 91.49 W 70.94 W 44.38 W 72.39 W 22.28 W 362.32 W
53.07 W 85.3 W 70.94 W 40.67 W 67.94 W 22.28 W 340.2 W
It is worth noting that although the heat transfer conditions of the inner wall of the mock up tank have changed (liquid convective heat transfer or vapor convective heat transfer) under different filling ratios, the most important part of the thermal resistance in the heat transfer process between the mock up tank and the ambient air is the heat conduction resistance (insulation system). Therefore, the heat transfer temperature difference between the inner wall of the mock up tank and the ambient air is the main factor that determines the heat transfer rate of the mock up tank under different filling ratios.
Fig. 10. Results of the average temperature of the surface A and the BOG generation rate by using different wall function.
the temperature gradient near the wall is very large. The reason for this phenomenon is that this region is in the boundary layer of the natural convection, and the boundary condition of the surface A is the third kind of boundary condition. Fig. 11(b) shows the variation of the BOG generation rate with time at filling ratios of 98% and 58%, respectively. When the generation rate of BOG reaches a steady state, the BOG generated when the filling ratio is 98% is about 6% more than that of 58%. Table 2. lists the detailed data of the heat ingress on each surface of the mock up tank. It is noted that the heat leakage of the surface C and the surface G is consistent. This is because, whether at 98% or 58%, the surface C and the surface G are completely immersed in the liquid nitrogen. The heat leakage of other surfaces is higher at 98% filling ratio than at 58% filling ratio. This is due to at 58% filling ratio, all or part of these surfaces are in contact with the nitrogen vapor for heat transfer. Thus, the temperature of the inner wall of the mock up tank at these surfaces increases, thus reducing the heat transfer temperature difference. According to the Eq. (12), the heat leakage also decreases. However, the reduction of the heat transfer temperature difference is not significant, it can be seen from the Fig. 11(a). Therefore, the reduction of the heat leakage is not significant, so the difference of the BOG generation rate between the 98% filling ratio and 58% filling ratio is also not remarkable.
5.3. Effect of insulation system damage In the actual voyage of LNG ships, the insulation system of CCSs may be damaged. Therefore, it is of great significance to study the influence of the insulation system damage on the temperature distribution and BOG generation rate of CCSs. In order to fully discuss the effect of insulation system damage on the temperature field and BOG generation rate of the mock up tank, the damage of the insulation system above and below the liquid level is respectively studied. It is assumed that the area of the damaged insulation system is 0.3 m2, which is located at the center of the top surface and the bottom surface of the mock up tank respectively. In addition, it is assumed that the damage of the insulation system is complete, that means the inner shell of the mock up tank directly exchanges heat with the ambient air. Therefore, the boundary conditions of the insulation system damage area need to be redefined. Considering that the natural convection is the heat transfer form between the inner shell and the ambient air, the boundary condition at the insulation system damage area is defined as the third kind boundary condition.
Fig. 11. Effect of filling ratio: (a) Temperature distribution along the tank height with the filling ratios of 98% and 58%, respectively; (b) Variation of BOG mass flow rate with time at filling ratios of 98% and 58%, respectively.
10
Applied Thermal Engineering 173 (2020) 115265
S. Wu, et al.
Fig. 12. Temperature contours of the insulation system with 0.3 m3 breakage at about 60 min: (a) Partial damage on the surface A, (b) Partial damage on the surface C.
The temperature is 290 K, which is consistent with the experimental condition and the convective heat transfer coefficient can be calculated according to Eqs. (14) and (15). For the case of the insulation system of the surface A damaged, the convection heat transfer coefficient in the damaged area can be calculated by the Eq. (15); for the case of insulation system of surface C damaged, the convection heat transfer coefficient in the damaged area can be calculated by the Eq. (14). Through calculating, in the case of the insulation system of the surface A damaged, UA damage = 2.234W/(m2 K ) ; in the case of the insulation system of the surface C damaged, UC damage = 2.094W/(m2 K ) . The remaining settings in the CFD simulation are consistent with those mentioned above. The temperature contours of the mock up tank when there is a partial damage of the insulation layer is shown in Fig. 12. When the insulation layer of surface A is damaged, the maximum temperature of the damaged area reaches about 250 K, and the average temperature of the surface A is about 86.85 K, which is about 2 K higher than the undamaged insulation system. When the insulation layer of the surface C is damaged, the maximum temperature of the damaged area reaches about 86 K, and the average temperature of the surface C is about 77.45 K, which is about 0.1 K higher than the undamaged insulation system. This illustrates that the partial damage of the insulation system has little effect on the overall temperature distribution of the mock up tank, and there is only an obvious temperature rise in the damaged region. Fig. 13 shows the variation of the BOG generation rate with time when the insulation system is damaged. When the insulation system of the surface A is damaged, the BOG generation rate increases by about 8% compared with that when the insulation system is not damaged, and when the insulation system of the surface C is damaged, the BOG generation rate increases by about 20% compared with that when the insulation system is not damaged. This is because when the insulation system of the surface A is damaged, the heat transfer with the damaged region is the nitrogen in the top region of the mock up tank. The main form of the heat transfer is the natural convection of the vapor phase. Therefore, the heat transfer coefficient is low and less heat ingress into the mock up tank, the increase of the BOG generation rate is relatively less; when the insulation system of the surface C is damaged, the heat transfer with the damaged region is the liquid nitrogen at the bottom region of the mock up tank, the liquid nitrogen will boil vigorously. The
Fig. 13. Variation of the BOG generation rate with time when the insulation system is damaged.
heat transfer form is mainly phase change heat transfer, and the heat transfer coefficient is large. The increase of the BOG generation rate is relatively more. The phase contours shown in Fig. 14 can well reflect the phase change characteristics when the insulation system of the mock up tank is damaged. When the insulation layer of the surface A is damaged, no bubbles are generated in the liquid nitrogen region of the tank, and the phase change mainly occurs at the vapor-liquid interface. When the insulation layer of the surface C is damaged, it can be seen that nucleate boiling occurs at the damaged insulating system region, and bubbles gradually float upward until the vapor-liquid interface disappears. 5.4. The pressurization characteristics of the closed mock up tank According to the GB/T 18443.5-2010, the evaporation rate of the mock up tank was measured by the flowmeter method in the
11
Applied Thermal Engineering 173 (2020) 115265
S. Wu, et al.
Fig. 14. Phase contours of the mock up tank at about 60 min: (a) Partial damage on the surface A, (b) Partial damage the surface C.
small part is used for latent heat to generate BOG, thus restraining the generation of BOG.
experiment. Therefore, during the testing, the vent on the top of the mock up tank needs to be opened all the time. However, the liquid cargo tank will not always be in the state of pressure relief during the voyage, so it is necessary to study the pressurization characteristics when the vent of the mock up tank is closed. Fig. 15 shows the flow and heat transfer performances of the closed mock up tank. Fig. 15(a)–(c) shows the temperature contours, temperature contours of the surface A of the closed mock up tank and temperature contours of the surface A of the non-closed mock up tank. According to the temperature contours, there is no significant difference between the closed and non-closed mock up tank in 60 min. Fig. 15(d) shows the velocity contours. As for the velocity contours, it can be noted that there are obvious differences between closed and non-closed tanks in the top of the liquid phase region. In this region, a weak central jet is formed. Under this effect, the thermal stratification will gradually form in the closed tank rather than in the non-closed tank [10,39]. Fig. 15(e) shows the pressurization characteristics of the tank and the variation of nitrogen mass as function of time. Initially, the evaporation of the liquid nitrogen in the mock up tank was intense, which led to the increase of pressure, and the increase of pressure also increased the saturation temperature of the liquid nitrogen, thus inhibiting the evaporation of the liquid nitrogen and even leading to the condensation of nitrogen in the tank. After about 5 min, it can be seen that the change trend of pressure in the mock up tank is almost the same as that of nitrogen mass in the mock up tank. After about 15 min, the increase of the pressure and the nitrogen mass gradually reaches steady state, because the mock up tank is closed, the increase rate of nitrogen mass is the BOG generation rate. It can be seen from Fig. 15(f) and (g) that at 5 min, there is not fully developed natural convection in the mock up tank, and the temperature contours and velocity contours are not reach steady state; at 10 min, it can be seen that the velocity contours gradually presents the trend of fully developed natural convection. By calculation, the BOG generation rate of the whole tank is about 0.000024 kg/s, the evaporation rate is about 0.0053%. Compared with the mock up tank at constant pressure, the BOG generation rate decreases greatly. The main reason is that the saturation temperature of the liquid nitrogen in the mock up tank rises with the increase of pressure, so that most of the heat leakage is used for sensible heat, raising the temperature of the liquid nitrogen to reach the saturation temperature under the corresponding pressure, while only a
5.5. Comparison of evaporation characteristics between LNG and liquid nitrogen Considering the safety of the experiment, liquid nitrogen was generally used instead of LNG as the working substance in the cryogenic experiment. In order to better simulate the BOG generation rate and temperature distribution of the mock up tank in the actual voyage, and to simplify the simulation process reasonably, pure methane is properly considered as the representation of LNG in this analysis, while other conditions (initial and boundary conditions, etc.) remain unchanged. Fig. 16(a) and (c) shows the temperature contours and velocity contours for the mock up tank at about 60 min (pure methane). It can be found that the temperature and velocity contours of the mock up tank in the Fig. 16(a) and (c) is consistent with the Fig. 16(b) and (d) except for the difference in value. Therefore, it is safe and appropriate to use liquid nitrogen instead of LNG to research the flow and heat transfer characteristics of LNG in the actual CCS. Fig. 16(c) shows the plot of the BOG generation rate with time when the working substance is the liquid nitrogen and methane. It can be seen that the trend of BOG generation is almost the same whether it is methane or liquid nitrogen. After about 20 min, the BOG generation rate basically reaches a steady state. It is also proved that the CFD model presented in this paper is general. In addition, when the working substance is methane, the BOG generation rate is about 1/4 of that when the working substance is liquid nitrogen, and the BOR of the liquid nitrogen tank is about 1.58% while that of the LNG tank is 0.816%. There are two main reasons for this difference. Firstly, it is the difference of latent heat between methane and liquid nitrogen. Under the same external heat transfer conditions, the latent heat of liquefied natural gas is about 510 kJ/kg, and the latent heat of liquid nitrogen is about 199 kJ/kg, therefore, relatively more nitrogen vapor is generated. Secondly, because the saturation temperature of methane is higher than that of liquid nitrogen, under the same external ambient temperature and convention heat transfer conditions, the heat ingress into liquid nitrogen tank is larger than that of LNG tank.
12
Applied Thermal Engineering 173 (2020) 115265
S. Wu, et al.
Fig. 15. The flow and heat transfer performances of the closed mock up tank: (a) Temperature contours at about 60 min; (b) Temperature contours of the surface A at about 60 min (Closed tank); (c) Temperature contours of the surface A at about 60 min (non-closed tank); (d) Velocity contours at about 60 min; (e) Pressurization characteristics of the tank and the variation of nitrogen mass as function of time; (f) Temperature and velocity contours at about 5 min; (g) Temperature and velocity contours at about 10 min;
6. Conclusion
(1) This model has high prediction accuracy for the BOG generation rate and the temperature distribution calculation of the mock up tank, and can well analyze and calculate the variations of the internal flow and heat transfer characteristics of the mock up tank under different filling ratios, insulation layer damage and closure of the mock up tank vent, as well as the BOG generation rate and temperature distribution. (2) It is also found that when the liquid nitrogen of the mock up tank is fully mixed by natural convection, the BOG generation rate and
In this paper, experimental and numerical studies have been carried out on the mock up tank of the new independent type B LNG ship. The internal two-phase flow and phase-change heat transfer of the mock up tank which is fixed in the laboratory have been studied in detail by using CFD method. The BOG generation rate and temperature distribution of the mock up tank have been calculated and verified by experiments. Several main conclusions are obtained as following:
13
Applied Thermal Engineering 173 (2020) 115265
S. Wu, et al.
Fig. 16. The flow and heat transfer performances of liquid methane in the mock up tank: (a) Temperature contours at about 60 min (methane); (b) Temperature contours at about 60 min (nitrogen); (c) Velocity contours at about 60 min (methane); (d) Velocity contours at about 60 min (nitrogen); (e) The BOG generation rate as a function of time.
temperature distribution will reach steady state; when the insulation system above the liquid level is damaged, the phase change phenomenon in the tank is only confined to the surface evaporation, when the insulation system below the liquid level is damaged, nucleate boiling will occur in the tank. (3) The evaporation rate in the closed mock up tank is considerably lower than that in the mock up tank at constant pressure, but the pressure will gradually increase and threaten the safe voyage of the LNG ship. (4) The simulation results illustrate that the evaporation rate measured by using liquid nitrogen as the working substance is about two times of the evaporation rate of LNG.
[3] G. Guan, Y. Lin, Y. Chen, An optimisation design method for cryogenic pipe support layout of LNG-powered ships, J. Mar. Eng. Technol. 16 (2017) 45–50, https://doi. org/10.1080/20464177.2016.1276389. [4] C.S. Bang, C.H. Park, D.G. Lee, Optimum glass fiber volume fraction in the adhesive for the Al-SUS adhesively bonded joints at cryogenic temperatures, Compos. Struct. 108 (2014) 119–128, https://doi.org/10.1016/j.compstruct.2013.08.018. [5] J. Choe, K.H. Kim, D. Lee, C.S. Bang, D.G. Lee, Glass composite vibration isolating structure for the LNG cargo containment system, Compos. Struct. 107 (2014) 469–475, https://doi.org/10.1016/j.compstruct.2013.08.013. [6] M. Miana, R. Legorburo, D. Díez, Y.H. Hwang, Calculation of boil-off rate of liquefied natural gas in mark III tanks of ship carriers by numerical analysis, Appl. Therm. Eng. 93 (2016) 279–296, https://doi.org/10.1016/j.applthermaleng.2015. 09.112. [7] S.W. Choi, J.U. Roh, M.S. Kim, W. Il Lee, Analysis of two main LNG CCS (cargo containment system) insulation boxes for leakage safety using experimentally defined thermal properties, Appl. Ocean Res. 37 (2012) 72–89, https://doi.org/10. 1016/j.apor.2012.04.002. [8] J.H. Lee, Y.J. Kim, S. Hwang, Computational study of LNG evaporation and heat diffusion through a LNG cargo tank membrane, Ocean Eng. 106 (2015) 77–86, https://doi.org/10.1016/j.oceaneng.2015.06.045. [9] H.B. Lee, B.J. Park, S.H. Rhee, J.H. Bae, K.W. Lee, W.J. Jeong, Liquefied natural gas flow in the insulation wall of a cargo containment system and its evaporation, Appl. Therm. Eng. 31 (2011) 2605–2615, https://doi.org/10.1016/j.applthermaleng. 2011.04.028. [10] M. Kang, J. Kim, H. You, D. Chang, Experimental investigation of thermal stratification in cryogenic tanks, Exp. Therm. Fluid Sci. 96 (2018) 371–382, https://doi. org/10.1016/j.expthermflusci.2017.12.017. [11] Y. Lin, C. Ye, Y. Yun Yu, S. Wei Bi, An approach to estimating the boil-off rate of LNG in type C independent tank for floating storage and regasification unit under different filling ratio, Appl. Therm. Eng. 135 (2018) 463–471, https://doi.org/10. 1016/j.applthermaleng.2018.02.066. [12] Y.H. Yu, B.G. Kim, D.G. Lee, Cryogenic reliability of the sandwich insulation board for LNG ship, Compos. Struct. 95 (2013) 547–556, https://doi.org/10.1016/j. compstruct.2012.07.007. [13] K.H. Kim, S.H. Yoon, D.G. Lee, Vibration isolation of LNG containment systems due to sloshing with glass fiber composite, Compos. Struct. 94 (2012) 469–476, https:// doi.org/10.1016/j.compstruct.2011.08.008. [14] M.S. Zakaria, K. Osman, A.A. Yusof, M.H. Mohd Hanafi, M.N.A. Saadun, M.Z.A. Manaf, Parametric analysis on boil-off gas rate inside liquefied natural gas storage tank, J. Mech. Eng. Sci. 6 (2014) 845–853, https://doi.org/10.15282/jmes.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work is supported partly by the Ministry of Industry and Information Technology, PRC. References [1] N. Arcuri, R. Bruno, P. Bevilacqua, LNG as cold heat source in OTEC systems, Ocean Eng. 104 (2015) 349–358, https://doi.org/10.1016/j.oceaneng.2015.05.030. [2] Y. Lin, Y. Yu, G. Guan, Research on energy efficiency design index for sea-going LNG carriers, J. Mar. Sci. Appl. 13 (2014) 430–436, https://doi.org/10.1007/ s11804-014-1282-6.
14
Applied Thermal Engineering 173 (2020) 115265
S. Wu, et al. 6.2014.10.0080. [15] M.S. Zakaria, K. Osman, M.N.M. Musa, Boil-off gas formation inside large scale liquefied natural gas (LNG) tank based on specific parameters, Appl. Mech. Mater. 229–231 (2012) 690–694, https://doi.org/10.4028/www.scientific.net/AMM.229231.690. [16] M.S. Zakaria, K. Osman, M.N.A. Saadun, M.Z.A. Manaf, M.H. Mohd, Hanafi, Computational simulation of boil-off gas formation inside liquefied natural gas tank using evaporation model in ANSYS fluent, Appl. Mech. Mater. 393 (2013) 839–844, https://doi.org/10.4028/www.scientific.net/AMM.393.839. [17] Q.S. Chen, J. Wegrzyn, V. Prasad, Analysis of temperature and pressure changes in liquefied natural gas (LNG) cryogenic tanks, Cryogenics (Guildf). 44 (2004) 701–709, https://doi.org/10.1016/j.cryogenics.2004.03.020. [18] D. Lee, S.H. Yoon, K.H. Kim, I. Choi, D.G. Lee, Composite anti-buckling structure for the corrugations of liquefied hydrogen containers, Compos. Struct. 95 (2013) 492–499, https://doi.org/10.1016/j.compstruct.2012.07.004. [19] D. Boukeffa, M. Boumaza, M.X. Francois, S. Pellerin, Experimental and numerical analysis of heat losses in a liquid nitrogen cryostat, Appl. Therm. Eng. 21 (2001) 967–975, https://doi.org/10.1016/S1359-4311(00)00098-3. [20] O. Khemis, M. Boumaza, M. Ait Ali, M.X. Francois, Experimental analysis of heat transfers in a cryogenic tank without lateral insulation, Appl. Therm. Eng. 23 (2003) 2107–2117, https://doi.org/10.1016/S1359-4311(03)00164-9. [21] O. Khemis, R. Bessaïh, M.A. Ali, M.X. François, Measurement of heat transfers in cryogenic tank with several configurations, Appl. Therm. Eng. 24 (2004) 2233–2241, https://doi.org/10.1016/j.applthermaleng.2004.02.002. [22] T. Kanazawa, K. Kudo, A. Kuroda, N. Tsui, Experimental study on heat and fluid flow in LNG tank heated from the bottom and the sidewalls, Heat Transf. - Asian Res. 33 (2004) 417–430, https://doi.org/10.1002/htj.20031. [23] M. Belmedani, A. Belgacem, R. Rebiai, Analysis of natural convection in liquid nitrogen under storage conditions, J. Appl. Sci. 8 (2008) 2544–2552, https://doi. org/10.3923/jas.2008.2544.2552. [24] A. Saleem, S. Farooq, I.A. Karimi, R. Banerjee, A CFD simulation study of boiling mechanism and BOG generation in a full-scale LNG storage tank, Comput. Chem. Eng. 115 (2018) 112–120, https://doi.org/10.1016/j.compchemeng.2018.04.003. [25] L. Wang, S. Ye, Y. Ma, J. Wang, Y. Li, CFD investigation on helium pressurization behaviors in liquid hydrogen tank, Int. J. Hydrogen Energy. 42 (2017) 30792–30803, https://doi.org/10.1016/j.ijhydene.2017.10.145. [26] L. Wang, Y. Ma, Y. Wang, F. Xie, Y. Li, Investigation on pressurization behaviors of two-side-insulated cryogenic tank during discharge, Int. J. Heat Mass Transf. 102 (2016) 703–712, https://doi.org/10.1016/j.ijheatmasstransfer.2016.06.045. [27] L. Wang, Y. Li, Z. Zhao, Z. Liu, Transient thermal and pressurization performance of
[28] [29] [30] [31] [32]
[33] [34]
[35] [36] [37] [38] [39]
15
LO 2 tank during helium pressurization combined with outside aerodynamic heating, Int. J. Heat Mass Transf. 62 (2013) 263–271, https://doi.org/10.1016/j. ijheatmasstransfer.2013.03.021. L. Wang, Y. Li, C. Li, Z. Zhao, CFD investigation of thermal and pressurization performance in LH 2 tank during discharge, Cryogenics (Guildf). 57 (2013) 63–73, https://doi.org/10.1016/j.cryogenics.2013.05.005. W.C. Niu, G.L. Li, Y.L. Ju, Y.Z. Fu, Design and analysis of the thermal insulation system for a new independent type B LNG carrier, Ocean Eng. 142 (2017) 51–61, https://doi.org/10.1016/j.oceaneng.2017.06.067. J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. (1992), https://doi.org/10.1016/0021-9991(92) 90240-Y. C.R. Kharangate, I. Mudawar, Review of computational studies on boiling and condensation, Int. J. Heat Mass Transf. 108 (2017) 1164–1196, https://doi.org/10. 1016/j.ijheatmasstransfer.2016.12.065. R. Zhou, W.L. Zhu, Z. Hu, S. Wang, H. Xie, X. Zhang, Simulations on effects of rated ullage pressure on the evaporation rate of liquid hydrogen tank, Int. J. Heat Mass Transf. 134 (2019) 842–851, https://doi.org/10.1016/j.ijheatmasstransfer.2019. 01.091. O. Kartuzova, M. Kassemi, Self - Pressurization and Spray Cooling Simulations of the Multipurpose Hydrogen Test Bed (MHTB) Ground - Based Experiment, (2019). O. Kartuzova, M. Kassemi, CFD modeling of the Multipurpose Hydrogen Test Bed (MHTB) self-pressurization and spray bar mixing experiments in normal gravity: Effect of the accommodation coefficient on the tank pressure51st, AIAA/SAE/ASEE Jt. Propuls. Conf. (2015) 1–24. S. Roh, G. Son, G. Song, J. Bae, Numerical study of transient natural convection in a pressurized LNG storage tank, Appl. Therm. Eng. 52 (2013) 209–220, https://doi. org/10.1016/j.applthermaleng.2012.11.021. C. Beduz, R.G. Scurlock, Evaporation mechanisms and instabilities in cryogenic liquids, Adv. Cryog. Eng. 39 (1994) 1749–1757, https://doi.org/10.1007/978-14615-2522-6_214. T. Olewski, L. Vechot, S. Mannan, Study of the vaporization rate of liquid nitrogen by smalland medium-scale experiments, Chem. Eng. Trans. (2013), https://doi.org/ 10.3303/CET1331023. ANSYS Academic Research, ANSYS Fluent Theory Guide, ANSYS Help Syst. (2018). S.B. Vishnu, S. Bhowmick, B.T. Kuzhiveli, Experimental and numerical investigation of stratification and self pressurization in a high pressure liquid nitrogen storage tank, Energy Sour. Part A Recover. Util. Environ. Eff. (2019) 1–15, https://doi. org/10.1080/15567036.2019.1651424.