International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 8, August 2013
ISSN 2319 - 4847
NUMERICAL SIMULATION OF HEAT
TRANSFER BY NATURAL CONVECTION IN A
STORAGE TANK
HARITI Rafika1, FEKIH Malika2, SAIGHI Mohamed3
1, 2, 3
Laboratory of Thermodynamics and Energetically Systems LTSE, Physics Faculty, University of Science and Technology
Houari Boumediene, U.S.T.H.B, Bab Ezzouar 16111, Algiers ALGERIA
ABSTRACT
Heat transfer by natural convection in storage tanks for LNG is extremely related to heat gains through the walls with thermal
insulation is not perfectly efficient. In this paper we present the study of natural convection in unsteady regime for natural gas in
aware phase using the fluent software. The gas is just on the surface of the liquid phase. The CFD numerical method used to
solve the system of equations is based on the finite volume method. This numerical simulation allowed us to determine the
temperature profiles, the stream function, the velocity vectors and the variation of the heat flux density in the vapor phase in the
LNG storage tank volume. The results obtained for a general configuration, by numerical simulation were compared to those
found in the literature.
Keywords: Numerical Simulation, Natural Convection, Heat Gains, Storage Tank, Liquefied Natural Gas.
1. INTRODUCTION
During the period storage of liquefied natural gas, stability is necessarily affected by natural convection along the walls of
the tank with thermal insulation is not perfectly efficient. Several studies have been devoted to the understanding of this
physical phenomenon by numerical simulation or an experimental works. Among these works we can also mentioned that
Evans et al [1] conducted a study in a cylindrical cavity partially filled with a liquid. Belssiotis [2] studied numerically
the unsteady natural convection in a cylindrical cavity containing water for a turbulent high Rayleigh number. Barzegar
et al [3] presented a numerical study in a storage tank filled with two types of LNG, to treat the heat transfer. Pham et al
[4] have carried the study of natural convection double diffusion in a square cavity containing LNG initially stratified.
The objective of this study is to know the influence of aspect ratio and boundary conditions on the thermal and dynamic
behavior of LNG vapor stored in tank.
2. MATHEMATICAL FORMULATION
The study domain considered is shown in Figure1, the aspect ratio AL = H / D. The lateral wall and the roof exchange
heat by convection and by radiation with the environment. For cons, the bottom of the tank is considered at the
temperature of the liquid LNG. The cavity containing the LNG vapor whose physical properties are constant, the fluid is
assumed Newtonian viscous dissipation is negligible, and the flow is incompressible boussinesq approximation is
counted. Given the axial symmetry, the problem is two-dimensional and heat transfer along the vertical walls is made by
natural convection.
Figure 1 Domain of Study
The Navies-Stokes equations governing the problem are studied:
 
 U  0
(1)
,
Continuity Equation
(2)
,
Equation of movement



U  
1 
 U   U    P   . U  T g
t
0
Volume 2, Issue 8, August 2013
Page 340
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 8, August 2013
ISSN 2319 - 4847
cp (


T  
 U   T )   (   T )
t
(3)
And the boussinesq approximation is:
1 ψ
ur =
r z
,
   0 (1   (T  T0 ))
,
1 ψ
uz = 
r r
Velocity
,
Energy Equation
(4)
along r and z
The associated initial and boundary conditions are respectively:
At
ur = u z = ψ = 0
t=0
T (0, r, z) = T0
,
T 0 : The storage temperature of GNL equal 111K:
ψ
ψ
r=0 , z=0
ur = uz = ψ =
=
= 0
r
z
ψ ψ
ψ
ψ
r=R
,
z=H
ψ=
=
=0
ψ=
=
=0
Where
r=0
r z
T
|r=0 = 0
r
r=R , λ
r
,
T
|r= R = he (Tr= R  Ta )
r
z=0
z= H ,  λ
;
z
T (0, r, 0) = T0
T
|z= H = he (Tz= H  Ta )
z
3. RESULTS AND DISSCUTION
The system of equations is solved numerically by CFD method based on the finite volume method. LNG vapor phase
consists essentially of methane. The figure A shows the temperature profiles calculated for the form factors of the cavity
AL = 1/2, 1/4 and 1, which correspond to the different heights of vapor for Rayleigh numbers ranging
to Ra = 1.10
07
and Ra = 1.10
09
. We note that the temperature values are higher for the aspect ratio of AL = 1.
(a) Al=1/4
Ra = 1.10 07
(a) Al=1/4
Ra = 1.10 07
(a) Al=1/4
(b) AL =1/2 Ra = 1.10 08
Figure A. Profiles of Temperature
Ra = 1.10 07
Volume 2, Issue 8, August 2013
08
(b) AL =1/2 Ra = 1.10
Figure B. Stream function
(b) AL =1/2 Ra = 1.10 08
Figure C. Velocity Vectors
(c)
AL=1 Ra = 1.10 09
(c) AL=1 Ra = 1.10
09
(c) AL=1 Ra = 1.10 09
Page 341
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 8, August 2013
ISSN 2319 - 4847
Concerning stream functions shown in Figure B the fluid movement is unicellular and values are higher in the case of AL
= 1.The figure C shows the velocity vectors that describing the movement in the cavity, the fluid particles are heated on
the walls because of the heat input from outside to inside, stood along the last walls and takes higher values. Figure D
shows the variations of temperature profiles along the height (z), we always note that the increase in values over the
height is remarkable for the value of the higher elevation. Figure E introduce a very good agreement between our
calculations and measurements on site for temperature values. Figure F shows the comparison between the values of
velocity vectors for the three form factors of the tank, we can say that the values are higher for AL = 1. The density values
of heat fluxes are higher near the walls for the three form factors shown in Figure G, then begins to decrease because
those are the walls that heat the liquid. All figures shows strong and significant effect on the level of the LNG value
variation. Furthermore, concerning the values of velocity and stream functions we calculated are similar to those found by
other authors.
Tlng (AL=1)
Tlng (AL=1/2)
Tlng (AL=1/4)
300
250
Tlng(K)
200
150
100
0
0.2
0.4
Z(m)
0.6
0.8
1
Figure D. Temperature variation along z
AL = 1, AL = 1/2, AL = 1/4
Figure E. Temperature values
Calculated and measured (AL = 1)
V (m/s) AL=1
V(m/s) AL=1/2
V(m/s) AL=1/4
0.0001
8E-05
6E-05
V(m/s)
4E-05
2E-05
0
0
0.2
0.4
Z
0.6
0.8
1
Figure F. Comparison between the Velocity Vectors
AL = 1, AL = 1/2, AL = 1/4
200
Heat Flux Density (W/m2) AL=1
Heat Flux Density (W/m2) AL=1/2
Heat Flux Density (W/m2) AL=1/4
150
Heat Flux
Density
100
50
0
0
0.2
0.4 Z(m)
0.6
0.8
1
Figure G. Comparing the variation of the heat flux density
AL = 1, AL = 1/2, AL = 1/4
Volume 2, Issue 8, August 2013
Page 342
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 8, August 2013
ISSN 2319 - 4847
4. CONCLUSION
The study of natural convection in a storage tank is interesting from a practical point of view. In this study we presented a
numerical simulation to evaluate the temperature fields, the stream functions, velocity vectors and the variation of the
heat flux density in the gas phase of LNG. The results are in good agreement with the experimental readings observed in
actual operating conditions. The results presented in this work also show the sensitivity of the form factor AL
corresponding to different levels of tank, these results support the cause not completely filled storage tank and also avoid
low liquid levels during storage LNG.
5. NOMENCLATURE
D : Dimensional Diameter
H : Dimensional Height
Al : Form Factor H / D
T : Dimensional Temperature
Ta : Ambient Temperature
T0 : Storage Temperature of LNG
U : Dimensional Velocity
ψ : Dimensional Stream Fonction
ur : Dimensional Radial Velocity
u z :Dimensional Axial Velocity
3
Ra : Rayleigh Number, gβΔTH / aυ
p* : Hydrostatic Pressure, p+ρ0 gz
Pr : Prandtl Number, ν /a
β : Coefficient of Thermal Expansion
a : Thermal Diffusivity
λ : Thermal Conductivity
μ : Dynamic Viscosity
υ : Kinematic Viscosity
he : Thermal Coefficient of Heat Exchange
ρ : Volumetric Mass
Cp : Specific Heat Density
g : gravity
t : time
REFERENCES
[1] L.B.Evans, R.C.Reid.E.M.Drake, Transient Natural convection in Vertical Cylinder. Aiche J.14 (2) 251-259(1968).
[2] E. Papanicolaou, V. Blessiotis, Transient Natural Convection in a Cylindrical Enclosure at High Rayleigh Numbers.
Int. J. Heat Mass transfer (45) (2002) 1425-1444.
[3] C.T. Pham, S.Hartmann and J. P. Petit, Simultaneous heat and mass transfer in unsteady turbulent natural
convection: application to liquefied natural gas storage.10th International Heat Transfer, Conference Brighton (UK)
14-18 August 1994.
[4] A.Berzegar and.A.A.Dehgham (2009),Transient Thermal Behaviour of a Vertical Solar Storage Tank with a mantle
Heat Exchanger during no flow operation, Journal of applied fluid Mechanics, vol.2no.1PP.55-69,2009.
[5] D.Saury, N.Rouger, F.Djanna, F.Penot. Characterization turbulent flows for natural convection at large Rayleigh
Number. Francophone Symposium, Laser Techniques, CFTL 2008, 16 - 19 September 2008.
[6] Kuehn TH, Goldstein RJ (1976) Correlation equations for natural convection heat transfer between horizontal
cylinders. Int J Heat Mass Transfer 19, 1127-l 134.
[7] S. Battes, D. Morrison, Modeling the behavior of stratified LNG in storage tanks, Study of the rollover phenomenon,
Int. J. of Heat and Mass Transfer, Vol. 40, N° 8, 1997.
Volume 2, Issue 8, August 2013
Page 343