Phase Change Equation of State for FSI Applications

Transcription

1 15 th Internationa LS-DYNA Users Conference FSI / ALE Phase Change Equation of State for FSI Appications Mhamed Soui, Ramzi Messahe Lie Uniersity France Cyri Regan, Camie Ruiuc Ingeiance Technoogies, Agence de Bordeaux, France Bernard Cohen, Romain Ceyroe, Syain Dure EDF Direction Production Ingénierie Marne a Vaée France Abstract To simuate fast transient phenomena, one must consider reaistic compressibe fuid modes that take into consideration phase change, shock wae generation and its propagation. In an industria framework, such phenomena occur mosty near industria apparatuses such as pumps, propeers, impeers and contro aes. The rapid coapse of caitation produces strong shock waes that may harm the interacting structure. In this paper, we present the work on Homogeneous Equiibrium Mode (HEM) phase change mode impemented in the LS-DYNA that is compatibe its egacy ALE and FSI capabiities. Vaidation against experimenta data is shown through preiousy pubished test case of caitation in eastic water pipe. Introduction Under certain configurations, compressibe iquids the oca pressure may fa beow the urated pressure that gies rise to caitation. This situation can be encountered in industria appications such as Water Hammers and Under Water Exposion in nucear and marine industries, respectiey. The different transition regimes that occur in caitation phenomena (phase change, shock waes creation due to the coapse and its propagation) must be modeed in order to ead to reiabe and accurate resuts. From the existing approaches, we can distinguish two major categories: The Two-Fuid Modes [1,, 3] and the One-fuid Modes. In this paper, we present the Saure et a.[4] HEM one-fuid modes that has been recenty impemented in LS-DYNA due to their simpicity, easy impementation within existing codes (ALE and Lagrangian SPH), and finay, their abiity to mode phase changes in many industria appications, in particuar for water appications. The soed density and energy ariabes are mixture quantities expressed in function of the urated apor fraction. In order to cose the system, the appropriate EOS based on the mixture quantities is used such that the kinematic and the thermodynamic equiibrium are isfied; and aso the continuous phase change transitions. In an industria framework, such phenomena occur mosty near industria apparatuses such as pumps, propeers, impeers and contro aes. The rapid coapse of caitation produces strong shock waes that may harm the interacting structure. During the fuid structure interaction process, the fuid s pressure deforms the structure and the resuting deformation of the structure wi modify the fuid s properties such as the shock wae pressure and the shock speed [5, 6, 7], it is thus mandatory to consider FSI. In this paper, we present the work presented in detai in [6], on the impementation of HEM phase change mode in LS-DYNA and its aidation using ALE and FSI capabiities of the software. June 10-1, 018 1

2 15 th Internationa LS-DYNA Users Conference FSI / ALE Phase Change Modes This section presents the mode by Saure et a. [4] that has been impemented for modeing mode compex industria probem incuding phase change in compressibe fows, shock waes. The method is based on the foowing three main assumptions in the mixture region: 1- Mixture density and mixture interna energy are mean quantities of both iquid and apor phases. They are functions of apor fraction, urated iquid and apor iquid densities: ρ = α. ρ + (1 α ). α. ρ (1) Where α is the apour fraction defined by: e = Y. e + (1 Y ). e () α V = V 0 if ρ ρ = ρ ρ if ρ ρ ρ ρ 1if ρ ρ (3) Y, the apor mass fraction defined by ρ. α Y = (4) ρ T the temperature. - Liquid and apor phases are in kinematic equiibrium 3- The iquid and apor phases are in thermodynamic equiibrium ρ = ρ = ρ and T = T = T (5) Pressure, iquid density and apor density at uration state can be either proided by tabes obtained from experimenta database or deried anaytica equations. The atest one is seected in the LS-DYNA impemented ersion. For further detais on the specific case of water materia, the reader can refer to Messahe et a. [6] Figure 1 Discrete apor bubbes and Fringe ees of the apor fraction homogeneous mode representation (Eq.3 ). June 10-1, 018

3 15 th Internationa LS-DYNA Users Conference FSI / ALE Vapor Phase α = 1 Pressure in the iquid region is computed using the modified Tait EOS P = ρ( T ). R. T (6) R is the specific gas constant for apour (for water R= J.Kg -1.K -1 ) Mixture Phase 0 < α < 1 In the mixture region, pressure and temperature of both iquid and apor phases are assumed to be in equiibrium. ρ = ρ = ρ = ρ (T ) and T = T = T = T Using equations (1-4), the interna energy in the mixture, e(t ) is gien by (6) e = ( α. ρ. e + (1. α ). ρ. e ) / ρ( T ) (7) and the speed of sound in c the mixture by Wais equation [14] 1 ρ. c α 1. αv = + (8) ρ. c ρ. c L L A noninear procedure is deeoped to soe for the mixture temperature and the apour fraction to isfy equiibrium equation for the interna energy equation (7). For mixture region the pressure is gien by: P = P (9) Numerica Simuation In this section we present aidation against an experimenta study of caitation in eastic water pipes. This test case is compex is a sense that it incudes non-inear and compex muti-physics effects such as FSI, phase change and soid-soid contacts. Thus, it represents an idea case to aidate the impemented phase change mode and its conjugate appication with the egacy capabiities of LS-DYNA. Some researchers tried to simpify the probem and treated it in a two steps decouped manner: first, by assuming that the structure is rigid and soing the fuid probem to obtain fuid pressure; then secondy, by appying the resuting fuid pressure oad on the deformabe structure. This strategy ed to an oer-estimation of the pressure wae eocity that wi be compared to experimenta data by Tijsseing et a., 1996 [8]. In figures and 3 we show a description and a sketch of the numerica setup, respectiey. The mode is composed of 17,90 ALE hexahedra soid eements (Haquist [15] ) for the water, 5160 Lagrangian hexahedra soid eements for both the rigid stee rod, the impact end pug and the remote end cap and 44,0 0 0 Beytschko Lin Tsay she eements for the fu singe ebow pipe system, Haf of the mode is simuated by considering the X Y pane symmetry. A sketch of the mode is shown in Fig. 3. The numerica pressure at ocation PT6 is potted and compared to experimenta data, which shows good correation. June 10-1, 018 3

4 15 th Internationa LS-DYNA Users Conference FSI / ALE Figure : One-ebow pipe system (numerica aues in mm are not to scae)[8] Figure 3: Sketch of the numerica mode [6] Figure 4: Absoute pressure at sensor PT6: Experimenta resuts Tijsseing et a., [8], ( --), numerica resuts with eastic pipes ( ). June 10-1, 018 4

5 15 th Internationa LS-DYNA Users Conference FSI / ALE Concusion In this paper, HEM phase change mode impemented mode is presented and its aidation shows good agreement between strongy couped simuations and experimenta resuts. It shows that combination of HEM phase change mode and ALE formuation and FSI capabiities of LS-DYNA used for modeing mutiphase fows in interaction with structures incuding phase change and shock wae due to the coapse of the caitation can be modeed accuratey. This ast point is of crucia interest in industria engineering for the design and the conception of safer pipe systems and the improement of its performance. Indeed, once numerica simuations are aidated with experimenta test resuts, compex systems incuding FSI phenomenon with phase change can be numericay simuated. References [1] V. Ahuja, V. Hosangadi, S. Arunajatesan, Simuation of caitation fows using hybrid unstructured meshes, Journa of Fuids Engineering 40 (001) doi: / [] I. Senocak, W. Shyy, A pressure-based method for turbuent caitating fow computations, Journa of Computationa Physics 176 (00) [3] S. Venkateswaran, J. W. Lindau, R. F. Kunz, C. L. Merke, Computation of mutiphase mixture fows with compressibe effects, Journa of Computationa Physics 180 (00) [4] R. Saure, J. P. Cocchi, P. B. Buter, Numerica study of caitation in the wake of a hyper-eocity underwater projectie, Computer Methods in Appied Mechanics and Engineering 15 (4) (1999) [5] A. R. Simpson, Large water hammer pressures due to coumn separation in soping pipes, Ph.D. Thesis, Uniersity of Michigan, USA (1986). [6] R. Messahe, B. Cohen, M. Soui, M. Moatamedi, Fuid-structure inter- action for water hammers effects in petroeum and nucear pants, The Internationa Journa of Mutiphysics 5 (011) [7] Messahe, R., Regan, C., Soui, M., Ruiu, C. Numerica inestigation of homogeneous equiibrium mode and fuid-structure interaction for mutiphase water fows in pipes, Internationa Journa of Mutiphase Fow, o. 98, pp , Year 018. [8] A. S. Tijsseing, A. E. Vardy, D. Fan, Fuid-structure interaction and caitation in a singe-ebow pipe system, Journa of Fuids and Structures 10 (1996) [9] G. B. Wais, One-dimensiona two-phase fow McGraw-Hi, [10] J. O. Haquist, LS-DYNA Theory Manua, LSTC, Liermore Software Technoogy Corporation CA (USA) (8 015). June 10-1, 018 5