Computational analysis of canonical problems arising in the interaction of heated particles and a fluid
Keywords: Mechanical Engineering.

Numerical simulations of turbulent solid-particle-laden flows are challenging due to the simultaneous occurring of multiple phenomena spanning widely different scales. Presence of heat transfer, which occurs when the particulate phase is irradiated with radiation, complicates this problem further. An important application of multiphase particle-in-gas flow is that of a solid-particle-based, solar-thermal receiver to convert solar energy to electrical energy. To this end, the Predictive Science Academic Alliance Program (PSAAP) II at Stanford University, focuses on advancing the state-of-the-art in large-scale, predictive simulations of irradiated particle-laden turbulence relevant to concentrated solar power (CSP) systems. The aim of this thesis is to design and analyze a hierarchical set of increasingly complex and physically representative canonical problems that involve the interaction of subsets of the aforementioned physical phenomena. This thesis is divided into two parts -- the first dealing with the interaction of a single heated particle with an initially quiescent flow; the second dealing with the interaction of heated particle(s) with an initially uniform flow. In part I, the temporal evolution of the initial shock front and the low Mach flow field produced behind the front due to the presence of a spherical, finite-size heat energy source in a gas is investigated. The source of energy could either be some internal heat source within the sphere or radiation heating the sphere assuming that the fluid is optically thin. This leads to either a Dirichlet or a Robin boundary condition on the surface of the sphere. When the source is internal, the assumption is that the time-scale of heating is much smaller than the diffusion time scale of the fluid. While the study of the sphere is of physical interest, the analogous problems of a uniformly heated infinitely long cylindrical wire and an infinite plate are also considered. These problems serve as model problems to study and quantify finite-size effects, non-Boussinesq effects and compressibility effects without making any assumptions on the amount of heat addition from the sphere into the fluid. The study encompasses heating regimes where the Boussinesq approximation holds and regimes where it breaks down. At small times after the boundary conditions are imposed, compressibility effects are significant and a strong shock wave forms. This shock wave weakens as it moves away from the source eventually leading to an acoustic wave as the pressure settles everywhere to the ambient value for sufficiently large times. The features of this shock wave are analyzed in detail. Following the shock wave, the fluid motion occurs at a much lower speed which allows for a low Mach number formulation of the Navier-Stokes equations. In this low Mach regime, the resulting nonlinear energy equation is solved analytically using the method of Homotopy Perturbation Expansion. This leads to a weak decoupling of finite-size effects and non-Boussinesq effects thereby allowing the quantification of the individual impacts of both phenomena on the total solution. In part II, fully resolved simulations are first used to quantify the effects of heat transfer in the absence of buoyancy on the drag of a spatially fixed heated spherical particle at low particle Reynolds numbers (Re) in the range 0.001 to 10, in a variable property fluid. This analysis is carried out without making any assumptions on the amount of heat addition from the sphere and thus encompasses both, the heating regime where the Boussinesq approximation holds and the regime where it breaks down. The particle is assumed to have a low Biot number, which means that the particle is uniformly at the same temperature and has no internal temperature gradients. Large deviations in the value of the drag coefficient as the temperature of the sphere increases are observed. When Re is less than 0.01, these deviations are explained using a low Mach perturbation analysis as irrotational corrections to a Stokes-Oseen base flow. Correlations for the drag and Nusselt number of a heated sphere are proposed for the range of Reynolds numbers from 0.001 to 10, which fit the computationally obtained values with less than 1% and 3% errors respectively. These drag and Nusselt number correlations can be used in simulations of gas-solid flows where the accuracy of the drag law affects the prediction of the overall flow behavior. Finally, an analogy to incompressible flow over a modified sphere is demonstrated. Then, fully resolved simulations are used to quantify the effects of heat transfer in the presence of buoyancy on the drag of a spatially fixed heated spherical particle at low Reynolds numbers in the range 0.001 to 10 in a variable property fluid with the same assumptions as outlined before. A non-dimensional number called Buoyancy Induced Viscous Reynolds Number, which is analogous to the Grashof number, is derived using scaling analysis. No assumptions are made on the magnitude of this number either. The effects of the orientation of gravity relative to the free-stream velocity are also examined. Under appropriate constraints on the Buoyancy Induced Viscous Reynolds Number and the Reynolds number, the total drag on a heated sphere in the presence of buoyancy is shown to be, within 10\% error, the linear superposition of the drag computed in two canonical setups: one being the setup studied in chapter 9 and the other being natural convection. To demonstrate the effect of the drag modification due to heat transfer and buoyancy, the settling time and the settling velocity of a falling particle is shown using the proposed correlations. Then, heated spherical particles in infinite periodic arrays are considered. Drag enhancement is observed as the distance between particles decreases. However, the ratio of the viscous drag to the pressure drag on the sphere remains very close to 2:1. Finally, the individual effect of inertial, thermal, and clustering corrections to Stokes drag is evaluated on three sets of particle clusters extracted from the state-of-the-art point-particle simulations of the PSAAP-II channel. When compared to the true drag experienced by these particles in these clusters (as evaluated from particle-resolved simulations), just using Stokes' drag formula results in up to 18\% error which can be reduced to less than 2\% if the corrections proposed in this thesis are accounted for.