R. V R Pandya

Analytical description of particle/droplet-laden turbulent flows

Abstract Various existing analytical descriptions for predicting turbulent flows laden with solid particles or liquid droplets are reviewed here. The main focus is on a collisionless dispersed phase, however, the two-way coupling effects are considered and discussed. The review of various methods is conducted by dividing them into two main categories. The first category includes direct numerical simulation (DNS), large-eddy simulation, and stochastic modelling, which are collectively called the ‘Lagrangian description’. The second category, under the ‘Eulerian description’, includes Reynolds averaged Navier–Stokes (RANS) and probability density function (pdf) modelling. The emphasis is placed on application of these approaches for both understanding and prediction of turbulent dispersed phase. The discussion is focused on merits and limitations of these approaches and the nature of predictions offered by them. The mathematical aspects of RANS and pdf modelling are presented in greater detail. The important role of DNS generated data in the development and assessment of other approaches is discussed with the aid of some representative examples in particle-laden homogeneous turbulent flows.

Temperature statistics in particle-laden turbulent homogeneous shear flow

Abstract Direct numerical simulation is utilized to generate temperature field statistics in particle-laden incompressible homogeneous shear turbulent flows in the presence of mean temperature gradients. The particle density is much larger than the fluid density and the particle volume fraction is small. The particle–particle collisions are ignored, however, both one- and two-way couplings are considered. The effects of the mass loading ratio, the particle time constant, the ratio of specific heats, and the orientation of the mean temperature gradient on the fluid and particle temperature statistics are investigated. The results indicate that the increase of the mass loading ratio or the particle time constant generally tends to decrease the magnitudes of the temperature variance and the turbulent heat flux of both the carrier and the dispersed phases. The increase of the ratio of specific heats increases the particle temperature variance but demonstrates an opposite effect on the fluid. The magnitude of the turbulent heat flux of the fluid is not influenced by the change of the ratio of specific heats whereas that of the particles increases with the increase of this ratio. Further analysis of the results shows that the correlation of the temperature of the particles and the temperature of the fluid at the location of the particles decreases with the increase of the ratio of specific heats or the particle time constant and increases with the increase of the mass loading ratio. The mechanisms responsible for these variations are discussed by examining the budgets of the temperature variance and turbulent heat flux for both phases.

PROBABILITY DENSITY FUNCTION MODELING OF EVAPORATING DROPLETS DISPERSED IN ISOTROPIC TURBULENCE

A statistical closure scheme is used to obtain an approximate equation for probability density function to predict the statistical properties of interest of collisionless evaporating droplets suspended in isothermal isotropic turbulent flows. The resulting Fokker-Planck equation has nonlinear, time-dependent drift and diffusion coefficients that depend on the statistical properties of the droplet slip velocity. Approximate analytical expressions for these properties are derived, and the equation is solved numerically after implementing the path-integral approach. The time evolution of various statistical properties related to the droplet diameter are then calculated

Kinetic equation for particle transport and heat transfer in nonisothermal turbulent flows

The physical situation of two-phase nonisothermal turbulent fluid flows laden with nonevaporating spherical particles is considered. A closed kinetic equation for the transport of particles and their temperature is derived by solving the involved closure problem using the functional method. The equation is exact when the fluctuations of fluid flow variables along the particle path are distributed as Gaussian. For the case of homogeneous turbulent flows, macroscopic equations describing the time evolution of statistical properties related to particle velocity and temperature are obtained by taking various moments of the closed kinetic equation

Deterministic and Probabilistic Approaches for Prediction of Two-Phase Turbulent Flow in Liquid-Fuel Combustors

This chapter analyzes the deterministic approach of direct numerical simulation (DNS) and the probabilistic approach of probability density function (PDF) modeling. These approaches are implemented for the prediction of droplet dispersion and polydispersity in liquid–fuel combustors. These modeling approaches are used for predicting two-phase turbulent flows. The DNS is focused on generating information useful in designing the experiment on the backward-facing step with countercurrent flow, which closely represents the dump combustor flow situation. DNS allows the quantification and visualization of various effects arising because of the different inlet flow conditions, Stokes number of the dispersed phase, and strength of the countercurrent flow. The DNS data are valuable in the development and assessment of predictive models. The chapter discusses the development of PDF model for a general situation of turbulent flow laden with evaporating droplets. This model is in the form of a closed equation, which governs the transport of the probability density of droplet position, velocity, temperature, and diameter.

Current Issues in Analytical Description of Particle/Droplet-Laden Turbulent Flows

The particle/droplet-laden turbulent flows occur in many important natural and technological situations, e.g., cloud [1], aerosol transport and deposition [2], spray combustion [3, 4], fluidized bed combustion [5], plasma spray coating and synthesis of nanoparticles [6]. Undoubtedly, turbulence itself remains as a difficult and unsolved problem of classical mechanics despite many persistent efforts by physicists and engineers. The presence of particles/droplets (hereafter simply referred to as particles) further adds to the complexity of the turbulence. The particle behavior in turbulent flows gives rise to many interesting phenomena, such as, turbophoresis [7], turbulent thermal diffusion and barodiffusion [8, 9], preferential distribution, and anomaly and intermittency [9, 10]. It is challenging to come up with a unique predictive theory for the particle phase which is useful for engineering purposes and also capable in quantifying various related phenomena.Copyright