COMPUER FLUID DYNAMICS DEERMINAION OF INSIDE FLUID RESERVOIRS MOVEMENS COMPUER FLUID DYNAMICS DEERMINAION OF INSIDE FLUID RESERVOIRS MOVEMENS AND WALLS LOADS DURING EARHQUAKES Lecturer Eng. Ioan Sorin LEOVEANU, PhD. University ransilvania from Braşov REZUMA. Rezervoarele sunt construcţii destinate depozitării unei mari varietăţi de fluide, gaze lichefiate sau diverse gaze. În timpul proceselor de umplere, golire sau în cazul unui cutremur lichidele stocate în acestea vor dezvolta un sistem de încărcări dinamice care poate afecta integritatea structurii. Lucrarea propusă are ca scop utilizarea analizei numerice bazate pe calculul dinamicii fluidului (CFD) pentru a determina dinamica presiunii exercitate de fluid asupra rezervoarelor în timpul manevrării acestora. În lucrare s-a pus un accent deosebit pe efectul unei mişcări seismice având caracteristicile marilor cutremure din Vrancea, accelerogramele fiind ale ultimului mare cutremur. Se consideră că sistemul de forţe distribuite produse de mişcarea fluidului este format din forţe distribuite normale pe suprafaţa în contact cu fluidul (presiune impulsivă) şi dintr-un sistem de presiuni distribuite tangenţial pe suptafaţa de contact (presiune convectivă). Lucrarea îşi propune să pună în evidenţă complexitatea unor astfel de probleme. Cuvinte cheie: dinamica fluidului, cutremur, rezervoare, sistem de forţe, sarcină structurală. ABSRAC. Ground-supported reservoirs are used for a large variety of fluids and liquefied gases storages. During the processes of filling, empting and other exterior exceptional conditions the liquid develop a particular system of dynamic loading that can affect the integrity of the structure. he present papers consider a CFD analysis for establishing that effects of loading history of fluids that can take place on the walls of the reservoirs in the conditions of filling, empting and in the earthquake time. he pressure distribution on the walls is transformed in normal pressure (impulsive pressure) and in the tangent pressure with the walls (convective pressure) and applied to the structure of the reservoir. he verifications of the mathematical modeling were done using the acceleration spectra specifically to an earthquake with 7.4 magnitudes on Richter scale acting on both directions. his paper provides theoretical background for investigation of hydrodynamic pressure that is being developing during an earthquake in the liquid storage ground-supported rectangular container. Keywords: computer fluid dynamics, earthquake, reservoirs, loading system, structural loading. 1. INRODUCION Satisfactory performance of tanks during strong ground shaking is crucial for modern facilities. anks that were inadequately designed or detailed have suffered extensive damage during past earthquakes [2-7] or external exceptional loads. he knowledge of forces and pressure acting on the tanks walls during the earthquake, explosions, tsunami and other natural or military exceptional loads plays essential role in reliable and durable design of structure resistance tanks, which are made from steel or concrete and working at the soil level, inside the soil or over the soil level. From the last big earthquake the knowledge of the fluid movement inside the waste reservoirs and tank become more important until now. he use of prescriptions and codes get there limits in the cases of extreme conditions functional of that important buildings. he problems consist in loads system establishing for the geometry other that circular or rectangular and in the case of waves breaking walls inside the reservoir. he paper works try to overcome those problems by using the CFD modelling. he numerical methods frequently used for incompressible fluids are based on VOF or MAC method [8-10] and a large number of versions based on the two methods exist. In the paper we use the MAC method with some modifications from the boundary condition. We consider for the beginning the simple 2D analyses for a good and quick estimation of the differences between an analytic and numerical solution. he algorithm developed consider the free surface too facilities and the small walls deformations. he results obtained put in evidence the complexity of the problem and the importance of knowledge the liquid movement in the case when for some applications the fluid must be pumped from the reservoir in the moment when a quake take place. 2. NUMERICAL ANALYSIS In this paper we try to establish the pressure distribution dynamics on the walls of reservoirs using the constitutive Navier-Stokes system of differential equations for liquids and the fluid Buletinul AGIR nr. 2/2013 aprilie-iunie 19
CREAIVIAE, INVENICĂ, ROBOICĂ dynamics inside the tank based on a given acceleration spectra of a quake. In this case the earth movement processes imposed by quake modify the equilibrium of fluid stored in the tank and the fluid speed, shape and pressure change in accord with the external loads. he geometry and system of loading acting on the liquid volume stored in the tank is getting in the figure 1 for an analyzed more simple case. he shape of free surface of liquid was modeled using marker and cell method (MAC) in accord with the Marangony flow and the resulting maps pressures on the walls are in accord with the complex moving fluid conditions. he governing equations of fluid, considered in present work and the work hypothesis are: l) he flow is 2-D, incompressible and laminar. 2) Each thermal property of incompressible fluid is constant. 3) he walls deformations are small and the structure move between the earthquakes with the instant acceleration of the quake. 4) he time computed effects of the quake on the tank is double 5) he heat dissipation and the turbulent indices are calculated only in the fluid control volume. hen the general differential equation for conservative lows can be given as: 20 v v j i S t xi xj xi xi x j x j (1) he definitions of the letters,, and S are done in the table 1 where is the viscosity of the fluid, g x and g y the gravitational acceleration, /( c) the heat diffusivity and v x, v y, v z, and the fluid speed on x, y and z direction, the density and the temperature of the fluid walls will have the same acceleration as the walls cells. Boundary conditions. he fluid in contact with the walls will be accelerating with the same acceleration that acts on the wall. In our case, with the consideration that the walls are rigid and there deformation is neglected, the fluid in the cells near the walls will have the same speed like the wall. he general equations used are given in able 1. Boundary condition on cells in contact with the walls. For fluid flow analysis, either the slip wall condition or the no-slip wall condition is adopted [9, 10], according to the size of a cell and the magnitude of velocity. When the walls move, the convection coefficient between fluid and solid boundary is calculated, based on Re x and Pr numbers in the fluid cells. he heat flow equation is used only to calculate the fluid temperature distribution variation in the quake action. For water and other liquids the temperature is not important but for oils and liquefied gases the knowledge of fluid temperature and pressure becomes important. he equations for boundary domain in contact with solid walls become: u u u u p u v w uax t x y x x v v v v p u v w vay t x y z y (2) w w w w p u v w waz t x y z z v ui v j wk where a X,a Y and a Z are the spectrum of quake accelerations transmitted to the walls. In accord with the 3) hypothesis, that accelerations will be take in calculus equal with the earthquake accelerations. Γ S Continuity 0 0 Moment Energy v i velocity on x i direction v j velocity on x j direction w k velocity on x k direction temperature able 1 Buletinul AGIR nr. 2/2013 aprilie-iunie μ μ c g x i g x j g xk q he free boundary of the fluid. On free surface, the sum of tangential stresses must be zero and the sum of normal stresses must be equal to the applied stresses or pressures. he tangential and normal stress conditions are applied on free surface [7, 10]. Where u, v, w are the x, y and z component of velocity; n x, n y and n z are the unit vectors which refer to the local tangential and normal direction of the surface, respectively. he definition of φ follows the former expression, that is, φ a = (p ext )/ρ γ R m ; while μ represents kinematics viscosity; γ is the surface tension function of temperature; p ext is the pressure of gas phase inside the tank and, R m is the local mean radius of the free surface. he free surface temperature time variation is considerate nulle. angential stress condition for 2D modelling: u v 2 2 u v 2 nx n ( ) i y n j y nx x y y x t x i x j x k (3)
COMPUER FLUID DYNAMICS DEERMINAION OF INSIDE FLUID RESERVOIRS MOVEMENS Fig. 1. he acceleration specters considerate in the problem modelling. Normal stress condition for 2D simulation: 2 u u v 2 v a nx nx n i y n j y x y x y 2 angential stress condition for 3D modelling: u v 2 2 u v 2 nx n ( ) i y ny nx x y y x u w 2nz n j x xy z x t u w 2 2 u w 2 nx n ( ) i y nz nx x z z x u v 2nx n j y xz y x t v w 2 2 w v 2 ny n ( ) i z nz ny y z y z v w 2nz n j y yz z y t Normal stress condition for 3D simulation: 2 u 2 v 2 w u v nx ny nz 2nxny x y z y x u w v w 2nn x z 2nn y z a z x z y (4) (5) (6) (7) (8) Initial and load conditions. Because the problem is time dependent, the initial conditions consist in imposing null speed value for v x and v y and the gas pressure equal with the atmospheric pressure at sea level. he temperature was considerate equal with 20 o C on the air interface and 15 o C on the walls interfaces and in this conditions the buoyancy movements inside the fluid is considerate. After the first time step, the quake event is considerate and the spectra given in the figure 1 was applied on the liquid/solid boundary and the inside initial fluid speed distribution is considerate in accord with Figure 1. 3. SOLUION AND RESULS As an example case we will assume the ground supported rectangular endlessly tank with L = 24 m length and H = 12 m height and with uniform concrete thickness of 0.25 m. he tank is filled with water until h = 6 m in the first application and h = 11.50 m in the second application.. he processing of the fluid flow inside the waste reservoirs become usefully not only for structural design of reservoirs but even in the extremely important processes that consist in adsorption of liquid from the tank when the earthquake take place. he speed, pressure and vortices generate by earthquake can disturb the pump system and affect the processes evolution. he importance of knowledge of liquid movement in the tanks consists in the possibility to establish more accurately the dynamics of that engineering construction and design an active dumping system protection. We consider that the industrial and civil engineering application of the CFD modelling of fluid flow inside the closes domain loaded can get new solutions in the design of waste reservoirs systems. Buletinul AGIR nr. 2/2013 aprilie-iunie 21
CREAIVIAE, INVENICĂ, ROBOICĂ a) t = 1s b) t = 2s c) t = 3s d) t = 4s e) t = 1s f) t = 2s g) t = 3s h) t = 6s Fig. 2: a-d pressure distribution for filled tank H = L; e-h pressure distribution for half filled tank. a) t = 1s b) t = 2 s c) t = 3 s d) t = 4 s e) t = 5 s f) t = 6 s g) t = 7 s h) t = 8 s i) t = 9 s j) t = 10 s h) t = 11 s l) t = 12 s n) t = 16 s m) t = 19 s o) t = 22 s Fig. 3. he u speed distribution in the fluid during the analyzed earthquake. p) = 23 s 22 Buletinul AGIR nr. 2/2013 aprilie-iunie
COMPUER FLUID DYNAMICS DEERMINAION OF INSIDE FLUID RESERVOIRS MOVEMENS a) t = 1 s b) t = 2 s c) t = 3 s d) t = 4 s e) t = 5 s f) t = 6 s g) t = 14 s h) t = 19 s i) t = 23 s j) t = 29 s Fig. 4. he internal heat distribution inside fluid. a) t = 1s b) t = 2s c) t = 3s d) t = 4s e) t = 5s f) t = 6s g) t = 7s h) t = 8s i) t = 9s j) t = 10s h) t = 35s k) t = 40s Fig. 5. he pressure distribution inside the liquid area: a-d L = 24 m, H = 12 m; e-h L = 48 m, H = 12 m; e-f speed v evolution inside the fluid area. Buletinul AGIR nr. 2/2013 aprilie-iunie 23
CREAIVIAE, INVENICĂ, ROBOICĂ a) t = 1s b) t = 2s c) t = 4s d) t = 5s e) t = 1s f) t = 7s g) t = 14s h) t = 40s Fig. 6: a-d the distribution of viscous heat generation; e-h the speed v x distribution in the liquid. REFERENCES [1] Kotrasová, K., Kormaníková, E., Design of liquid storage tank made from composite material, In: Proceedings of 7-th European Conference. RANSCOM 2007. [2] Králik, J., Králik, J.,jr.: Deterministic and probilistic analysis of compressor foundation and soil interaction. Zborník z přednášek ze II. konference s mezinárodní účastí Dynamicky namáhané konstrukce Dyna 2008, Brno 2008. [3] Melcer, J.: Amplitude and frequency composition of seismic load due to transport around transport ways. Zborník DYN-WIND 2003, SvF ŽU ále, 19.-22. mája 2003, ISBN 80-8070-066-4. [4] IIK-GSDMA, 2005: Guidelines for seismic design of liquid storage tanks provisions with commentary and explanatory examples. Kanpur, Indian Institute of echnology Kanpur, 2005. [5] EN 1998-4: 2006 Eurocode 8. Design of structures for earthquake resistance. Part 4: Silos, tanks and pipelines. CEN, Brussels, 2006. [6] M., Rappaz, M., Bellet, M., Devile, Numerical Modeling in Material science and Engineering.Springer, 2002. [7] S. V. Patankar: Numerical Heat ransfer and Fluid Flow, McGraw-Hill, New York, (1980), 79. [8] B. D. Nichols and C. W. Hirt: J. Computational Physics, 8 (197 l), 434. [9] Leoveanu I. S. ierean, M. H.. Advenced numerical method. Application in metal modelling. (in Roumanian) Ed. Universitatii ransilvania din Braşov, 2009. [10] Vizman D., Cristea A., Sofonea V.. Metode numerice avansate. Ed. Eurobit. imişoara, 2008. Lecturer Eng. Ioan Sorin LEOVEANU, PhD. University ransilvania from Braşov About the author Mechanical Engineer of the University ransilvania from Braşov, the Managerial Industrial Program with Welding Especiality and PhD in residual stresses and strains modelling and technology optimisation. He worked at the Industrial ractors Design and Research Institute at ICPA Braşov to havy and mediun Bulldozers prototips design and other Earth Moving Machineries prototipes and series products. From 1988 he work at ransilvania University at Materials Science and Engineering Faculty and from 2010 he work in the area of Civile Engineering at ransilvania University. He publish monographis in the area of Optimization echnology and ransport Phenomenon involved in the Welding and Engineering area and articles in diverses journals and national and international conferences. Here research topics. Modelling the physical processes involved in welding phenomenons using Finite Volume and Finite Elements Method for Modelling the Exceptional Loads induced in Builings by Earth Quakes, Wind and Explosions. 24 Buletinul AGIR nr. 2/2013 aprilie-iunie