Bi-fidelity approximation for uncertainty quantification and sensitivity analysis of irradiated particle-laden turbulence.

Abstract

Efficiently performing predictive studies of irradiated particle-laden turbulent flows has the potential of providing significant contributions towards better understanding and optimizing, for example, concentrated solar power systems. As there are many uncertainties inherent in such flows, uncertainty quantification is fundamental to improve the predictive capabilities of the numerical simulations. For large-scale, multiphysics problems exhibiting high-dimensional uncertainty, characterizing the stochastic solution presents a significant computational challenge as many methods require a large number of high-fidelity solves. This requirement results in the need for a possibly infeasible number of simulations when a typical converged high-fidelity simulation requires intensive computational resources. To reduce the cost of quantifying highdimensional uncertainties, we investigate the application of a non-intrusive, bi-fidelity approximation to estimate statistics of quantities of interest associated with an irradiated particle-laden turbulent flow. This method relies on exploiting the low-rank structure of the solution to accelerate the stochastic sampling and approximation processes by means of cheaper-to-run, lower fidelity representations. The application of this bi-fidelity approximation results in accurate estimates of the QoI statistics while requiring a small number of high-fidelity model evaluations.Turbulent flow laden with inertial particles, or droplets, in the presence of thermal radiation is encountered in a wide range of natural phenomena and industrial applications. For instance, it is well established that turbulence-driven particle inhomogeneity plays a fundamental role in determining the rate of droplet coalescence and evaporation in ocean sprays [2] and atmospheric clouds [3]. Another example is found when studying fires, in which turbulence, soot particles, and radiation are strongly interconnected resulting in very complex physical processes [4]. From an industrial point of view, important applications include the atomization of liquid fuels in combustion chambers [5], soot formation in rocket engines [6], and more recently, volumetric particle-based solar receivers for energy harvesting [7].Even in the simplest configuration, e.g., homogeneous isotropic turbulence, particle-laden turbulent flow is known to exhibit complex interactions between the carrier and dispersed phases in the form of preferential concentration and turbulence modulation [8]. Preferential concentration is the phenomenon by which heavy particles tend to avoid intense vorticity regions and accumulate in regions of high strain rate, while turbulence modulation refers to the alteration of fluid flow characteristics in the near-field region of particle clusters as a result of two-way coupling effects, e.g., enhanced dissipation, kinetic energy transfer, or formation of wakes and vortexes. The physical complexity is further increased by the simple addition of solid walls as turbophoresis [9], i.e., tendency of particles to migr...