NUMERICAL PREDICTION OF
HIGHER SELF-PRESSURIZATION
RATES IN A TYPICAL STORAGE
VESSEL
HARI KRISHNA RAJ
PG Scholar, Department of Mechanical Engineering, TKM College of Engineering,
Kollam, Kerala-691005, India harikrishnaraj2007@gmail.com
JINAN S
PG Scholar, Department of Mechanical Engineering, TKM College of Engineering,
Kollam, Kerala-691005, India jinan6@gmail.com
Dr. K E REBY ROY
Asst. Professor, Department of Mechanical Engineering, TKM College of Engineering,
Kollam, Kerala-691005, India rebyroy@yahoo.com
Abstract:
Self-pressurization, as a result of vaporization can occur in many scientific and technical applications like cryogenic storage tanks, pressurized water reactors etc. Predictions of both the pressurization and vaporization rates are vital in defining design requirements conforming to the tank’s maximum working pressure and expected liquid losses. Predicting precisely the highly transient interface phenomenon due to mass transfer coupled with phase change due to evaporation is the major challenge encountered in modeling self-pressurization. The recent improvements of the multiphase flow modeling in the ANSYS FLUENT code make it now possible to simulate these mechanisms in detail without the need of user defined functions. The volume-of-fluid (VOF) method in conjunction with evaporation–condensation mass transfer model has been used here. In this paper we are extending the proven capability of VOF model for predicting higher self-pressurization rates due to phase change in storage vessels.
Keywords: Self-Pressurization; vaporization; CFD; VOF.
1. Introduction
The heat transfer associated with phase-change is complex phenomena encountered in engineering applications, such as boilers, pressure vessels etc. Accurate numerical investigation of the associated heat and mass transfer is an interesting area of research. However it is a difficult task to predict the mass transfer and the simultaneous heat transfer across the interface since the physical properties and the associated parameters differ on either sides of the interface.
from a rising drop in a solvent extraction process [Ohta and Suzuki, 1996]. Davidson and Rudman [9] have done coupling of VOF method with mass transfer. They calculated the mass transfer from a rising drop through a liquid column [Davidson and Rudman, 2002]. Schlottke et al. [7], Onea et al. [2] and Bothe et al. [5] used the VOF method for direct numerical simulation of interphase mass transfer [Onea et al., 2009]. Haelssig et al. [4] presented a VOF methodology for direct numerical simulation of interface dynamics and simultaneous interphase heat and mass transfer in systems with multiple chemical species [Haelssig et al., 2010].
Previous works reported in literature dealt with comparatively low pressurization rates. High self-pressurization rates can occur in critical engineering areas like pressurized water reactors of nuclear power plants in case of plant failure or in cryogenic storage vessels when suddenly exposed to high temperatures. Predicting the high pressure rise and pressurization rate in the above cases is a valuable date for structural design and for planning precautionary measure to avoid bursting of the pressure vessel. In the present work self-pressurization in a cylindrical vessel filled with water with high self-pressurization rate is investigated by VOF method in conjunction with evaporation –condensation mass transfer model.
2. Self-Pressurization Phenomenon
Self-pressurization phenomenon can be explained with the help of a tank partially filled with liquid as shown in Fig. 1. We can define two control volumes bounding the liquid and vapor phases. The saturated liquid vapor interface is a thin layer which allows for surface evaporation and heat transfer between the ullage gas and the liquid. Self-pressurization and the subsequent phase interaction is a coupled phenomenon of heat and mass transfer between the phases. Heat entering from the tank walls will be carried to the liquid vapor interface by natural convection generated by density gradients in the liquid. As the warmer fluid reaches the interface, evaporation will occur resulting in ullage compression and a subsequent rise in tank pressure.
Fig.1 Partially filled tank- two control volumes bounding each phase
3. CFD Modelling
With the advancement and recent development of CFD codes, a full set of fluid dynamic and multiphase flow equations can be solved numerically. The current study used commercial CFD code, ANSYS FLUENT, to solve the balance equation set via domain discretization, using control volume approach. These equations are solved by converting the complex partial differential equations into simple algebraic equations. An implicit method for solving the mass, momentum, and energy equations is used in this study. The
k
turbulence model with standard wall functionsa used due to their proven accuracies in solving multiphase problems. Effect of normal gravitational acceleration of is included.3.1. Geometry and Boundary conditions
much above the saturation temperature at one atmosphere. The effect of sensible heating before vaporization can also be incorporated with this boundary conditions. Geometry is modeled using GAMBIT 6.3. Structured quad mesh gives the best results in multi-phase calculations and hence the same is used for meshing. A mesh sensitivity analysis is performed that enabled the optimization of the mesh size. A total of 125000 cells are present.
Fig.2 Meshed geometry as displayed in FLUENT
3.2. Modeling Multi-Phase
The numerical simulations presented in this work are based on the ANSYS FLUENT volume-of-fluid (VOF), which is a Euler-Euler two fluid model method. The Eulerian modeling is based on mass-weighted averaged mass and momentum transport equations for all phases, gas and liquid. The VOF model is designed for two or more immiscible fluids in which the position of the interface between the fluids is of interest. In the VOF model, a single set of momentum equations is shared by the fluids, and the volume fraction of each of the fluids in each computational cell is tracked throughout the domain. One set of Navier-Stokes equations for the gas-liquid mixture together with two volume fraction equations and turbulence model equations are solved in this model. Transport equations are used to track the motion of liquid–vapour boundary and both the phases share a common velocity field. VOF method in conjunction with evaporation–condensation mass transfer model has been used to simulate mass transfer by phase change. The liquid-vapor mass transfer is governed by the vapor transport equation.
3.3. Modeling Assumption
The flow is assumed to be transient, and the pressure based solver is used. Standard wall functions have been selected and the effect of drag, lift and slip interaction has not been investigated. Initially it is assumed that ullage volume is completely filled with vapor and the liquid zone is completely filled with water.
3.4. Solution Strategy and Convergence
4. CFD Analysis and Results
4.1. Validation of the code
Pressurization in liquid hydrogen tank investigated by Jaeheon Sim et al. [6] is used for validation [Jaeheon et al., 2011]. A 50% filled liquid hydrogen vessel is heated uniformly on all its sides. Self-pressurization due to evaporation occurs as a result of the heat flux. As reported in the paper the saturation pressure after 1000 seconds and 2000 seconds is 101750 and 102350 Pascal respectively. The saturation pressure after the corresponding time interval obtained using the present methodology is 101820 and 102374 Pa respectively. Results obtained from the present methodology are in good agreement with the published results.
4.2. Results and Discussions
4.2.1Pressurization rate
Since the liquid is in sub cooled state initially sensible heating takes place during the initial stages. Once the temperature attains saturation temperature anywhere in the liquid domain, phase change starts to occur. As a result vapour fraction of water vapour increases. Hence pressurization occurs since the container is enclosed. The pressurization rate is as given in Figure3. With time the liquid near the wall attains saturation temperature and vaporization takes place near the wall and the vapour rises to the liquid vapour interface, thus increasing turbulence and convection in the liquid zone. As a result heat transfer to the liquid zone increases and phase change rate also increases which in turn increases the pressurization rate. The pressurization rate increases with time as initial boiling or phase change near the wall changes to bulk boiling of the liquid with increase in temperature. From graph it is evident that the pressurization rate plot has an accelerating slope with time.
Fig.3 Pressurization rate variation with time
4.2.2 Vapour fraction
increases. The liquid level falls to five cm approximately from top. In this particular instance there is presence of vapour at the bottom of tank. This is due to vaporization near the lower portions of tank and the subsequent stratification and turbulence in the liquid domain. At 12 seconds presence of vapour throughout the domain is evident.
Fig.4 Contour of vapour fraction of the container during the first 12 seconds of simulation
4.2.3 Mass transfer rate
The variation of mass transfer rate with time is shown in Figure 6 and the mass transfer contour for first 12 seconds is as shown in Figure 7.During the initial stages no phase change occurs as sensible heating alone takes place. With time, temperature of liquid reaches the saturation temperature at the bottom of the tank and near the liquid vapour interface and hence phase change is initiated in these regions. This region widens and phase change occurs throughout the wall which encloses the liquid phase. The mass transfer rate will be in a slow pace during the initial stages. With time the bulk of the fluid reaches saturation temperature and the thermal stratification increases and proportionally the mass transfer rate also increases.
Fig.6 variation of mass transfer rate with time
5. Conclusion and Scope for Future Work
VOF multiphase model method in conjunction with evaporation–condensation mass transfer model of ANSYS FLUENT is a useful tool in studying higher self-pressurization rates associated with phase change. The results obtained are encouraging. The predictions using this methodology need to be checked with experiments.
Acknowledgement
The authors gratefully acknowledge the Department of Mechanical Engineering, TKM College of Engineering, Kollam, for making available the facilities at CFD centre, which helped to complete the work successfully.
Reference
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