Thermomechanical Response of LNG Concrete Tank to Cryogenic Temperatures
Исследуются железобетонные резервуары для хранения сжиженного природного газа, имеющие ряд преимуществ перед стальными (высокая криогенная прочность, сопротивление термошоку, усталости и потере устойчивости, огнеупорность и т.д.). Поскольку основным недостаткомжелезобетонных резервуаров является низ...
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| Veröffentlicht in: | Проблемы прочности |
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| Datum: | 2011 |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2011
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| Zitieren: | Thermomechanical Response of LNG Concrete Tank to Cryogenic Temperatures / L. Dahmani // Проблемы прочности. — 2011. — № 5. — С. 59-65. — Бібліогр.: 10 назв. — англ. |
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| author | Dahmani, L. |
| author_facet | Dahmani, L. |
| citation_txt | Thermomechanical Response of LNG Concrete Tank to Cryogenic Temperatures / L. Dahmani // Проблемы прочности. — 2011. — № 5. — С. 59-65. — Бібліогр.: 10 назв. — англ. |
| collection | DSpace DC |
| container_title | Проблемы прочности |
| description | Исследуются железобетонные резервуары для хранения сжиженного природного газа, имеющие ряд преимуществ перед стальными (высокая криогенная прочность, сопротивление термошоку, усталости и потере устойчивости, огнеупорность и т.д.). Поскольку основным недостаткомжелезобетонных резервуаров является низкая прочность при растяжении, для
оценки уровня термических растягивающих напряжений разработана численная модель, которая описывает их термомеханическое состояние при криогенных температурах с учетом температурных зависимостей теплофизических свойств бетона, в том числе теплопроводности и удельной теплоемкости.
Досліджуються залізобетонні резервуари для зберігання скрапленого природного газу, що мають ряд переваг порівняно зі стальними (висока кріогенна міцність, опір термошоку, втомі і втраті стійкості, вогнетривкість та ін.). Оскільки основним недоліком залізобетонних резервуарів є низька міцність при розтязі, для оцінки рівня термічних розтяжних напружень розроблено числову модель, яка описує їх термомеханічний стан за кріогенних температур з урахуванням температурних залежностей теплофізичних властивостей бетону, в тому числі теплопровідності та питомої теплоємності.
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UDC 539.4
Thermomechanical Response of LNG Concrete Tank to Cryogenic
Temperatures
L. Dahmani
Mouloud Mammeri University, Tizi-Ouzou, Algeria
lahlou_d@yahoo.fr
ÓÄÊ 539.4
Òåðìîìåõàíè÷åñêîå íàãðóæåíèå áåòîííîãî ðåçåðâóàðà ñî ñæèæåííûì
ïðèðîäíûì ãàçîì ïðè êðèîãåííûõ òåìïåðàòóðàõ
Ë. Äàõìàíè
Óíèâåðñèòåò èì. Ìóëóäà Ìàììåðè, Òèçè-Óçó, Àëæèð
Èññëåäóþòñÿ æåëåçîáåòîííûå ðåçåðâóàðû äëÿ õðàíåíèÿ ñæèæåííîãî ïðèðîäíîãî ãàçà, èìå-
þùèå ðÿä ïðåèìóùåñòâ ïåðåä ñòàëüíûìè (âûñîêàÿ êðèîãåííàÿ ïðî÷íîñòü, ñîïðîòèâëåíèå
òåðìîøîêó, óñòàëîñòè è ïîòåðå óñòîé÷èâîñòè, îãíåóïîðíîñòü è ò.ä.). Ïîñêîëüêó îñíîâíûì
íåäîñòàòêîì æåëåçîáåòîííûõ ðåçåðâóàðîâ ÿâëÿåòñÿ íèçêàÿ ïðî÷íîñòü ïðè ðàñòÿæåíèè, äëÿ
îöåíêè óðîâíÿ òåðìè÷åñêèõ ðàñòÿãèâàþùèõ íàïðÿæåíèé ðàçðàáîòàíà ÷èñëåííàÿ ìîäåëü, êî-
òîðàÿ îïèñûâàåò èõ òåðìîìåõàíè÷åñêîå ñîñòîÿíèå ïðè êðèîãåííûõ òåìïåðàòóðàõ ñ ó÷åòîì
òåìïåðàòóðíûõ çàâèñèìîñòåé òåïëîôèçè÷åñêèõ ñâîéñòâ áåòîíà, â òîì ÷èñëå òåïëîïðîâîä-
íîñòè è óäåëüíîé òåïëîåìêîñòè.
Êëþ÷åâûå ñëîâà: òåðìîìåõàíè÷åñêèé ðàñ÷åò, ðåçåðâóàð äëÿ õðàíåíèÿ ñæè-
æåííîãî ãàçà, êðèîãåííàÿ òåìïåðàòóðà, áåòîí.
Introduction. This paper discusses the principal aspects of the numerical
evaluation of thermal stress induced by LNG (liquefied natural gas) in the concrete
tank.
Since low temperature applications imply thermal stresses, temperature
distribution data of thermal analysis is required in the coupled field analysis finally
to obtain and analyze thermal stresses. It is, therefore, proposed to solve a heat
conduction problem using finite element method to obtain temperature distribution
data of a concrete tank at cryogenic temperatures.
The basis for thermal analysis in ANSYS [1, 2] is a heat balance equation
obtained from the principle of conservation of energy. The finite element solution
performed via ANSYS yields nodal temperatures, and then uses the nodal
temperatures to obtain other thermal quantities. The elastic stresses, induced by
mechanical constraints and thermal strains resulting from the previous analysis,
have been calculated.
Finite Element Model. A solid concrete LNG tank model of 15 m radius and
30 m height shown in Fig. 1 is descretized with a 2D axisymetric finite element
model [3] as shown in Fig. 2. Its mechanical properties are given in Table 1.
© L. DAHMANI, 2011
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 5 59
A thermal version of the model was used to calculate the temperature profile
in the concrete tank; a structural version of the model then read the temperature
profile to calculate stresses.
A two-dimensional four-nodal quadrilateral element having thermal degree-
of-freedom (element type Plane 55 in ANSYS 8.0) is chosen for heat conduction
problem.
The distributions of thermal elastic stress components were then calculated by
switching the Plane 55 thermal element to Plane 42 structural element (Table 2)
which is used for 2-D modeling of solid structures [5–7].
The geometry, node locations, and the coordinate system for these elements
are shown in Figs. 3 and 4.
L. Dahmani
60 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 5
T a b l e 1
Mechanical Properties of Concrete
Physical parameters Values
Mass density � � 2400 kg/m3
Concrete compressive strength fc28 25� MPa
Concrete tensile strength ft 28 2 5� . MPa
Heat capacity C � 1000 J/(kg C�� )
Heat transfer coefficient � � 50 W/(m C2�� )
Thermal conductivity with
temperature [4]
T , �C �155 67. �10111. �59 44. �17 78. �23 39.
k , W/(m C�� ) 5.04 4.32 3.74 3.31 2.88
Fig. 1. Solid model (3D). Fig. 2. Finite element model (2D axisymetric).
T a b l e 2
Characteristics of Thermal and Structural Elements
Element Thermal Structural
Type Plane 55 Plane 42
Number of nodes 4 4
Number of DOF per node 1 2
Nature Temperature Displacement U X and UY
Transient Thermal Analysis. A transient thermal analysis determines the
temperature distribution and other thermal quantities under conditions that vary
over a period of time. Typical thermal quantities of interest are:
(i) the temperature distributions;
(ii) the amount of heat lost or gained;
(iii) thermal gradients;
(iv) thermal fluxes.
The mathematical solution for the axisymetrical element conduction heat
transfer is based on the first law of thermodynamics – energy conservation law [1,
2, 8, 9]
1
r r
k T r
T
r z
k T
T
z
c
T
t
�
�
�
�
�
�
�
�
�
�
�
( ) ( ) ,
�
�
� �
�
�
� � (1)
where � is the density of material, c is the heat capacity, and k is the thermal
conductivities of the concrete tank varying with temperature T.
Based on differential equation (1) with tacking into account of the spatial
temporal boundaries conditions, the heat balance for the structural nodes at time
( )t t� � is given by
[ ]{ �} [ ]{ } { },C T K T F� � (2)
where [ ]C is heat capacity matrix c, [ ]K is conductance matrix containing the
thermal conductivity terms (k) and heat exchange coefficients (�), { �}T is nodal
temperature rate vector � �T t, and { }F is thermal load vector ( temperature, etc.).
A transient thermal analysis follows basically the same procedures as a
steady-state thermal analysis. The main difference is that most applied loads in a
transient analysis are functions of time. To specify time-dependent loads, one can
divide the load-vs-time curve into load steps.
Thermal Boundary Conditions. A temperature of � �160 C was applied to
the inside wall and base of the concrete tank, and 50�C was applied to the outside
wall by convection with a film coefficient of 50 W/(m C2 �� ). The concrete initial
temperature is set to 20�C.
The temperature is obtained via the Galerkin finite element technique as
implemented by ANSYS software package [5].
Thermomechanical Response of LNG Concrete Tank ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 5 61
Fig. 3. Thermal 55 element. Fig. 4. Structural 42 element.
The Time Integration Parameter. The time integration parameter � relates
temperature difference to temperature rate:
T T t T t Tn n n n n n� �� � � �1 11� �( ) � � .� � (3)
Any value within 1 2 1� �� is unconditionally stable. That is, all solutions are
stable regardless of how large a time step �tn is chosen. In ANSYS the default
setting is � �1 2, known as the Crank–Nickolson technique. It is usable in the
majority of transient problems. For thermal shock problems with nonlinearities, a
higher value of � is recommended to avoid oscillations in time of the solution. For
the case of a brittle material like concrete, the Galerkin method was chosen with a
� � 2 3. Finally the reverse Euler integration scheme with � �1 would avoid
oscillations but requires finer time steps to achieve comparable accuracy. Details
about the algorithm are found in references [1, 10].
Thermal Results. The boundary conditions are implemented and the problem
is solved using Frontal solver in ANSYS 8.0. The temperature distribution results
are obtained in the general postprocessor. The results so obtained are plotted in
Figs. 5, 6, and 7 for the temperature profiles and in Fig. 8 for the thermal flux
vector. Figures 9, 10, 11, and 12 shows the temperature evolutions and profiles
across the wall thickness and the base of the tank respectively. The temperature
variations are nonlinear. This phenomenon can be attributed to the temperature
dependence of the thermal conductivity of the concrete.
62 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 5
L. Dahmani
Fig. 5. Temperature profile at time t � 10 h. Fig. 6. Temperature profile at time t � 20 h.
Fig. 7. Temperature profile at time t � 30 h. Fig. 8. Thermal flux vector at time t � 30 h.
Structural Analysis. Thermal-stress applications are treated within framework
of a so-called coupled-field analysis, which takes into account the interaction
between thermal expansion/contraction and mechanical stress. Since in the present
case strain does not influence on temperature, we are in a one way coupling
situation best handled by the indirect method, where nodal temperatures from a
(time transient) thermal analysis are applied at a specified time in the subsequent
(steady state) stress analysis. The direct method involving one (time transient)
thermomechanical analysis with a dedicated coupled field element may look
attractive, but is not practicable for larger models because of the huge amount of
cpu time and storage space required [10].
The change from thermal to structural analysis is easily achieved in ANSYS
as the element switch is automatic. Thermal 55 elements to structural 42 element
type.
The temperatures obtained from the previous analysis are now applied as a
load to determine thermal stresses and displacements.
Element of Plane 42 type can be used either as a plane element (plane stress or
plane strain) or as an axisymmetric element for a two dimensional modeling of
solid structures [5, 7]. The element is defined by four nodes having two degrees of
freedom at each node: translations in the nodal X and Y directions. The
geometry, node locations, and the coordinate system for this element are shown in
Fig. 4.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 5 63
Thermomechanical Response of LNG Concrete Tank ...
Fig. 9. Temperature variation across the wall. Fig. 10. Temperature profile across the wall.
Fig. 11. Temperature variation across the base. Fig. 12. Temperature profile across the base.
Results and Discussion. According to the obtained results, the liquid of LNG
produced:
– a great thermal gradient between the interior and the exterior of the tank
(Figs. 6–11);
– a great thermal flux at the base-wall junction according to Fig. 8;
– a high values of tensile stresses (Fig. 16) which could worsen the static
behavior of the tank during the service by causing the cracking of the concrete and
enhancing the penetration of the liquid in the pores;
– a maximum shear forces at locations where thermal deformation is highly
restrained, such as the intersection between wall and base slab.
The risk could be prevented with the adoption of suitable measurements:
– the insertion of the reinforcements in the tension zones to strengthen the
concrete, thus reducing the formation of the cracks;
– providing prestress to control cracks;
– the use of a high performance concrete to increase resistance and to decrease
the permeability [4];
– the use of a good insulation material like lightweight insulating concrete
with a perlite aggregate (perlite concrete);
– introduce a special layer of steel (9% of nickel) interposed between the
liquid and the internal walls of the tank to decrease the thermal shock;
– using lightweight aggregate concrete can benefit the prevention of thermal
cracking. The lightweight aggregate concrete has larger strain at cracking, and
thus, can sustain more thermal deformation before cracking [4].
64 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 5
L. Dahmani
Fig. 13. Deformed shape (2D). Fig. 14. Deformed shape (3D).
Fig. 15. Deformed shape at the wall-base junction. Fig. 16. �Y stress profile.
Conclusions. This work deals with the peculiar aspects of the numerical
modeling of thermal induced stresses in the reinforced LNG concrete tank.
The ANSYS finite element code has been employed for performing a
sequential nonlinear transient thermal-structural analysis, taking into account the
thermal dependant properties of the concrete as thermal conductivity. As shown
from the results obtained. The LNG liquid generates a high temperature gradient
between the interior and the exterior of the wall tank; this induces the appearance
of high values of tensile stress that could worsen the static behaviour of the
concrete tank in a “full” condition due to liquid penetration and following pore
pressure rise and cracking of the concrete.
Moreover, these results provide the basis for further studies to get more
insight into the degree of damage and the safety aspects connected with thermally
induced stresses in the reinforced LNG concrete tank.
Ð å ç þ ì å
Äîñë³äæóþòüñÿ çàë³çîáåòîíí³ ðåçåðâóàðè äëÿ çáåð³ãàííÿ ñêðàïëåíîãî ïðèðîä-
íîãî ãàçó, ùî ìàþòü ðÿä ïåðåâàã ïîð³âíÿíî ç³ ñòàëüíèìè (âèñîêà êð³îãåííà
ì³öí³ñòü, îï³ð òåðìîøîêó, âòîì³ ³ âòðàò³ ñò³éêîñò³, âîãíåòðèâê³ñòü òà ³í.).
Îñê³ëüêè îñíîâíèì íåäîë³êîì çàë³çîáåòîííèõ ðåçåðâóàð³â º íèçüêà ì³öí³ñòü
ïðè ðîçòÿç³, äëÿ îö³íêè ð³âíÿ òåðì³÷íèõ ðîçòÿæíèõ íàïðóæåíü ðîçðîáëåíî
÷èñëîâó ìîäåëü, ÿêà îïèñóº ¿õ òåðìîìåõàí³÷íèé ñòàí çà êð³îãåííèõ òåìïå-
ðàòóð ç óðàõóâàííÿì òåìïåðàòóðíèõ çàëåæíîñòåé òåïëîô³çè÷íèõ âëàñòèâîñ-
òåé áåòîíó, â òîìó ÷èñë³ òåïëîïðîâ³äíîñò³ òà ïèòîìî¿ òåïëîºìíîñò³.
1. ANSYS Heat Transfer, User Guide for Rev. 5.0, DN-S221:50, 6 (1993).
2. ANSYS Thermal Analysis, Tutorial for Rev. 5.0, DN-T031:50, 6 (1992).
3. V. Adams and A. Askenazi, Building Better Products with Finite Element
Analysis, 1st edition, OnWord Press (1998), Chp. 14, pp. 411–423.
4. L. Dahmani, A. Khennan, K. Salah, “Behavior of the reinforced concrete at
cryogenic temperature,” Cryogenics, 47, 517–525 (2007).
5. ANSYS 8.0. The General-Purpose Finite Element Software. Documentation
(2003).
6. E. Madenci and I. Guven, The Finite Element Method and Applications in
Engineering Using ANSYS, Springer, New York (2006).
7. S. Moaveni, Finite Element Analysis: Theory and Application with ANSYS,
Pearson Education Inc., New Jersey (2003).
8. F. Kreith and M. S. Bohn, Principles of Heat Transfer, Harper & Row, New
York (1986).
9. John H. Lienhard IV and John H. Lienhard V, A Heat Transfer Textbook,
Third Edition, Phlogiston Press, Cambridge, Massachusetts (2008).
10. R. Chavan, A Thermomechanical Analysis of the Central Column Tiles,
CRPP/EPFL – Lausanne, Internal Report INT 195/99 (1998–1999).
Received 29. 03. 2010
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 5 65
Thermomechanical Response of LNG Concrete Tank ...
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| id | nasplib_isofts_kiev_ua-123456789-95207 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-02T11:52:53Z |
| publishDate | 2011 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Dahmani, L. 2016-02-17T19:48:20Z 2016-02-17T19:48:20Z 2011 Thermomechanical Response of LNG Concrete Tank to Cryogenic Temperatures / L. Dahmani // Проблемы прочности. — 2011. — № 5. — С. 59-65. — Бібліогр.: 10 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/95207 539.4 Исследуются железобетонные резервуары для хранения сжиженного природного газа, имеющие ряд преимуществ перед стальными (высокая криогенная прочность, сопротивление термошоку, усталости и потере устойчивости, огнеупорность и т.д.). Поскольку основным недостаткомжелезобетонных резервуаров является низкая прочность при растяжении, для оценки уровня термических растягивающих напряжений разработана численная модель, которая описывает их термомеханическое состояние при криогенных температурах с учетом температурных зависимостей теплофизических свойств бетона, в том числе теплопроводности и удельной теплоемкости. Досліджуються залізобетонні резервуари для зберігання скрапленого природного газу, що мають ряд переваг порівняно зі стальними (висока кріогенна міцність, опір термошоку, втомі і втраті стійкості, вогнетривкість та ін.). Оскільки основним недоліком залізобетонних резервуарів є низька міцність при розтязі, для оцінки рівня термічних розтяжних напружень розроблено числову модель, яка описує їх термомеханічний стан за кріогенних температур з урахуванням температурних залежностей теплофізичних властивостей бетону, в тому числі теплопровідності та питомої теплоємності. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Thermomechanical Response of LNG Concrete Tank to Cryogenic Temperatures Термомеханическое нагружение бетонного резервуара со сжиженным природным газом при криогенных температурах Article published earlier |
| spellingShingle | Thermomechanical Response of LNG Concrete Tank to Cryogenic Temperatures Dahmani, L. Научно-технический раздел |
| title | Thermomechanical Response of LNG Concrete Tank to Cryogenic Temperatures |
| title_alt | Термомеханическое нагружение бетонного резервуара со сжиженным природным газом при криогенных температурах |
| title_full | Thermomechanical Response of LNG Concrete Tank to Cryogenic Temperatures |
| title_fullStr | Thermomechanical Response of LNG Concrete Tank to Cryogenic Temperatures |
| title_full_unstemmed | Thermomechanical Response of LNG Concrete Tank to Cryogenic Temperatures |
| title_short | Thermomechanical Response of LNG Concrete Tank to Cryogenic Temperatures |
| title_sort | thermomechanical response of lng concrete tank to cryogenic temperatures |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/95207 |
| work_keys_str_mv | AT dahmanil thermomechanicalresponseoflngconcretetanktocryogenictemperatures AT dahmanil termomehaničeskoenagruženiebetonnogorezervuarasosžižennymprirodnymgazomprikriogennyhtemperaturah |