Browsing by Subject "compressible"
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Item A Preliminary Study to Assess Model Uncertainties in Fluid Flows(2011-08-08) Delchini, Marc OlivierIn this study, the impact of various flow models is assessed under free and forced convection: compressible versus incompressible models for a Pressurized Water Reactor, and Darcy's law vs full momentum equation for High Temperature Gas Reactor. Euler equations with friction forces and a momentum and energy source/sink are used. The geometric model consists of a one-dimensional rectangular loop system. The fluid is heated up and cooled down along the vertical legs. A pressurizer and a pump are included along the horizontal legs. The compressible model is assumed to be the most accurate model in this study. Simulations show that under forced convection compressible and incompressible models yield the same transient and steady-state. As free convection is studied, compressible and incompressible models have different transient but the same final steady-state. As Darcy's law is used, pressure and velocity steady-state profiles yield some differences compared to the compressible model both under free and forced convections. It is also noted some differences in the transient.Item A rigorous compressible streamline formulation for black oil and compositional simulation(Texas A&M University, 2007-04-25) Osako, IchiroIn this study for the first time we generalize streamline models to compressible flow using a rigorous formulation while retaining most of its computational advantages. Our new formulation is based on three major elements and requires only minor modifications to existing streamline models. First, we introduce a relative density for the total fluids along the streamlines. This density captures the changes in the fluid volume with pressure and can be conveniently and efficiently traced along streamlines. Thus, we simultaneously compute time of flight and volume changes along streamlines. Second, we incorporate a density-dependent source term in the streamline saturation/composition conservation equation to account for compressibility effects. Third, the relative density, fluid volumes and the time-of-flight information are used to incorporate cross-streamline effects via pressure updates and remapping of saturations. Our proposed approach preserves the 1-D nature of the conservation calculations and all the associated advantages of the streamline approach. The conservation calculations are fully decoupled from the underlying grid and can be carried out using large time steps without gridbased stability limits. We also extend the streamline simulation to compositional modeling including compressibility effects. Given the favorable computational scaling properties of streamline models, the potential advantage for compositional simulation can be even more compelling. Although several papers have discussed compositional simulation formulation, they all suffer from a major limitation, particularly for compressible flow. All of the previous works assume, either explicitly or implicitly, that the divergence of total flux along streamlines is negligible. This is not only incorrect for compressible flow but also introduces inconsistency between the pressure and conservation equations. We examine the implications of these assumptions on the accuracy of compositional streamline simulation using a novel and rigorous treatment of compressibility. We demonstrated the validity and practical utility of our approach using synthetic and field examples and comparison with a finite difference simulator. Throughout the validation for compositional model, we found out the importance of finer segments discretizations along streamlines. We introduce optimal coarsening of segments to minimize flash calculations on each segment while keeping the accuracy of finer segments.Item Effect of Inhomogeneity and Unsteadiness on the Stability of High-Speed Shear Flows(2014-07-09) Bertsch, Rebecca LynneIn hypersonic flows, turbulence critically influences mass and momentum transport, mixing, heat transfer and acoustic noise generation. In contrast to incompressible flow, in high speed flows pressure is a true thermodynamic variable and flowthermodynamic interactions render the investigations extremely challenging. Most studies to date have been performed on steady, uniform or homogeneous shear flows leading to important insight on the flow physics. In most real world applications,flows of practical importance will exhibit unsteadiness and strong inhomogeneity. To date, investigations of unsteadiness and inhomogeneity in high-speed flows are rare. The goal of this dissertation is to study and understand these non-ideal effects when pertinent to shear flows. Towards this goal, we perform three distinct studies: (a) examination of time reversal characteristics of linear inviscid mass, momentum, energy and state equation in compressible flows; (b) Linear analysis (RDT) of compressibility effects on instabilities in temporally periodic (unsteady) homogeneous shear flow; and (c) Numerical investigation of small perturbation evolution in compressible Kolmogorov (inhomogeneous) shear flow. The first study shows that even with the additional governing equations required in the high-speed regime, the inviscid flow field is still reversible. This justifies the use of temporal periodicity to investigate the effect of unsteadiness. The second study presents a detailed analysis of the pressure equation in temporally periodic homogeneous shear flow. The analysis and numerical results show unsteady uniform shear exhibits two stages of evolution due to the changing behavior of pressure. These stages are analogous to the first two stages of evolution established in steady shear. The third stage seen in steady shear is not achieved by periodic shear flow. The final study shows that the evolution of small perturbations in spatially periodic Kolmogorov flow is influenced by: i) the initial compressibility parameter, M_(g0), ii) the initial perturbation orientation, and iii) the stream normal location. Ultimately, the final study supports the postulate that all shear flows exhibit perturbation stability boundary classifications seen in homogeneous shear flows. The findings of this research further our understanding of the effects of unsteadiness and inhomogeneity in realistic flows, which will aid in the development of improved computational tools.Item Turbulence Modeling for Compressible Shear Flows(2012-11-15) Gomez Elizondo, Carlos Arturo 1981-Compressibility profoundly affects many aspects of turbulence in high-speed flows - most notably stability characteristics, anisotropy, kinetic-potential energy interchange and spectral cascade rate. Many of the features observed in compressible flows are due to the changing nature of pressure. Whereas for incompressible flows pressure merely serves to enforce incompressibility, in compressible flows pressure becomes a thermodynamic variable that introduces a strong coupling between energy, state, and momentum equations. Closure models that attempt to address compressibility effects must begin their development from sound first-principles related to the changing nature of pressure as a flow goes from incompressible to compressible regime. In this thesis, a unified framework is developed for modeling pressure-related compressibility effects by characterizing the role and action of pressure at different speed regimes. Rapid distortion theory is used to examine the physical connection between the various compressibility effects leading to model form suggestions for the pressure-strain correlation, pressure-dilatation and dissipation evolution equation. The pressure-strain correlation closure coefficients are established using fixed point analysis by requiring consistency between model and direct numerical simulation asymptotic behavior in compressible homogeneous shear flow. The closure models are employed to compute high-speed mixing-layers and boundary layers in a differential Reynolds stress modeling solver. The self-similar mixing-layer profile, increased Reynolds stress anisotropy and diminished mixing-layer growth rates with increasing relative Mach number are all well captured. High-speed boundary layer results are also adequately replicated even without the use of advanced thermal-flux models or low Reynolds number corrections. To reduce the computational burden required for differential Reynolds stress calculations, the present compressible pressure-strain correlation model is incorporated into the algebraic modeling framework. The resulting closure is fully explicit, physically realizable, and is a function of mean flow strain rate, rotation rate, turbulent kinetic energy, dissipation rate, and gradient Mach number. The new algebraic model is validated with direct numerical simulations of homogeneous shear flow and experimental data of high-speed mixing-layers. Homogeneous shear flow calculations show that the model captures the asymptotic behavior of direct numerical simulations quite well. Calculations of plane supersonic mixing-layers are performed and comparison with experimental data shows good agreement. Therefore the algebraic model may serve as a surrogate for the more computationally expensive differential Reynolds stress model for flows that permit the weak-equilibrium simplification.