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• W2330169324 abstract "In this paper, the authors present a generalized compressible multiphase framework that allows for the specification of variable thermodynamic properties and flexibility of specifying physical equations of state for the mixture constituents. This methodology is an extension of an isothermal mixture model that has been developed by the authors and utilized for cavitation simulations. The authors maintain that the multiphase mixture models accurately capture the acoustics at the gas/liquid interface. The multiphase model is incorporated in a mixed element unstructured framework that permits to be locally refined in the interface region. The solution technique incorporates a parallel domain decomposition methodology for efficient 3D computations. Simulations of gas/liquid shock tubes, cavitating flowfields of a cylindrical headform and a high Reynolds number pump are discussed. 1.0 INTRODUCTION With the rapid development of computational fluid dynamic techniques for analyzing single phase flows and the evolution of parallel simulation technology, the focus is quickly changing towards analysis of the more complex multiphase flows. This is only fitting since most flows in nature and of practical importance in industrial applications are representative of two-phase flow. Examples of such flows can be found in boiling water and pressurized water nuclear reactors, internal combustion engines, heat exchangers, chemical reactors, cavitation in pumps, air conditioning and refrigeration systems and capillary transport in the human body etc. Most of the flows in the above-mentioned applications can be viewed as combinations of single-phase fluidic systems with one or multiple interfaces separating the different phases. In its most rigorous form, the analysis of these systems needs to be performed with a two-fluid model that solves for the mass, momentum and energy equations for each phase, supplemented with conditions that account for the constitutive relationships of the interfacial balance between phases and interfacial boundary conditions [1]. An alternate methodology to the two-fluid model consists of treating the multiphase flow regime as a AIAA-2001-2671, 15th CFD Conference, Anaheim, CA, June 11-14. 2001. t Research Scientist, Senior Member AIAA. Principal Scientist, Member AIAA. Copyright' 2001 by the authors. Published by AIAA with permission. mixture and procuring the interface as part of the flow solution. The advantage lies in solving one set of mass, momentum and energy equations for the mixture composition. These equations are generally supplemented with additional equations for the void or mass fraction of the mixture constituents [2]. There are typically two challenges associated with the use of mixture models for analyses of multiphase flow problems. The first challenge pertains to mathematical closure of the system in a consistent manner with the thermodynamics of the system and the second is related to the acoustics of the multiphase system. In particular, the acoustic speeds in gas-liquid type systems are very disparate and they follow a harmonic profile in the interface region where the mixture acoustic speed drops off rapidly [3]. This variation in acoustic speeds between the phases and the interface leads to flows exhibiting a large variation in local Mach number with supersonic flow regimes existing in the vicinity of the interface region. In the past, the authors [4,5] have presented a model for multi-fluid mixtures that was closed in a natural and mathematically consistent manner without the use of an ad hoc equation of state or the imposition of an artificial closure condition. The main feature of the model was that the interface dynamics were captured very accurately. In particular, the acoustics of the interface is thermodynamically consistent and agrees with classical theory. However, in the afore-mentioned model, compressibility was accounted for strictly at isothermal conditions i.e. only the variation in density due to fluctuations with pressure were considered. As a result, the energy equation completely decoupled from the system. In this paper, we extend our model to include compressibility effects due to temperature variations, and provide a general framework for solving multiphase flow problems with the flexibility of specifying the true equation of state for each fluid. This system is hyperbolic in nature and accommodates all regimes of problems from high-speed compressible classes of problems to low speed incompressible type flows. In multiphase systems, it is common to find the existence of both limits in different parts of the same flowfields. Our interest in the simulation of multiphase flow systems primarily stems from applications related to cavitating flowfields in turbopumps and marine propellers. The cavitation process is incorporated in our model through the use of finite rate source terms that trigger the formation of vapor/liquid based on the difference of the local pressure and the vapor pressure. The isothermal system accurately captures the dominant physics associated with cavitating flowfields when water is used as AIAA-2001-2671 1 American Institute of Aeronautics and Astronautics Ahuja and Hosangadi (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. the working fluid. However, temperature effects become important when cryogenic fluids are used as the working fluid. This is because these fluids operate in temperature regimes that are in proximity to the critical temperature. Therefore, the vapor pressure in cryogenic fluids can be very sensitive to changes in temperature. Hence, it becomes imperative to account for the energy balance while simulating cavitation in cryogenic pumps. It should be pointed out that there are many studies that have analyzed the thermodynamic effects on cavitation [6-8]. Most of these investigations have determined elaborate correlations that are difficult to incorporate in mathematical models used to simulate cavitating flowfields. Our model has been implemented in a generalized unstructured framework utilizing mixed element meshes. The advantage of the unstructured framework is two-fold [9]. First, it facilitates the modeling of complex shapes and provides flexibility in grid resolution especially close to the interface region. This becomes critical with turbomachinery flowfields where inducer/impeller blades can be highly skewed and twisted. The cavity/interface in such cases can take on highly irregular three dimensional shapes that have to be well resolved. Second, and more important, grid adaption can be used to capture the critical physics associated with the interfacial dynamics, thereby improving resolution where it is most needed [10]. For example, simulation of tip vortex type cavitation requires increasing resolution track the path of the tip vortex, as the low pressure in the vortex core leads to cavitation. The vortex trajectory is not known a priori and the grid needs to be adapted in successive iterations based on the calculated location of the vortex from the previous simulation. In summary, the major enhancement of the model we are presenting in this paper relates to the inclusion of temperature dependence on density variations of the respective phases. The only assumption regarding temperature is that the two phases are in local thermodynamic equilibrium. This permits an accurate description of the thermodynamics of the multiphase system along with fluid dynamic and acoustic characteristics. This extension provides us with the ability to model a wider range of problems that include cavitation in cryogenic pumps where traditional isothermal models fail, phase change in compressor pumps, deformation of blobs flying in supersonic regimes and shock tubes with mixtures of liquids and gases. In the next section, we provide details of our multiphase system. Following, will be a section on results utilizing the model introduced in the paper. The paper ends with concluding remarks on the model and the results. 2.0 MULTI-PHASE EQUATION SYSTEM 2.1 Generalized Nonisothermal Multiphase Model The multiphase system formulation including compressibility effects is presented in this section. In this derivation, we assume an equilibrium formulation i.e. we will work with one temperature for both fluids in a gas/liquid computational cell. There is flexibility for the user in specifying an equation of state for each phase. In the case of a liquid/incompressible phase, a stiff equation of state can be specified. The equations are presented in a form where the primitive variable set is updated at each integration step. This has several advantages: first, it makes the system amenable to preconditioning techniques. Second, by solving for pressure directly we can better handle the round-off error inherent in low speed flows. The governing Navier-Stokes equations along with a species transport equation can be expressed in the form" @default.
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• W2330169324 date "2001-06-11" @default.
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• W2330169324 title "Unstructured simulations of multi-phase mixtures with compressibility effects" @default.
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• W2330169324 doi "https://doi.org/10.2514/6.2001-2671" @default.
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