Journal of Combustion

Volume 2016, Article ID 8306839, 13 pages

http://dx.doi.org/10.1155/2016/8306839

## A Numerical Study on the Oscillating Flow Induced by an Acoustic Field around Coal Particles

^{1}North China Electric Power University, Baoding 071003, China^{2}North China Electric Power University, Beijing 102206, China

Received 25 May 2016; Accepted 26 July 2016

Academic Editor: Xiang Wang

Copyright © 2016 Genshan Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In order to investigate the acoustically driven oscillating flow around coal particles in the power plant boiler, the two-dimensional, unsteady mass and momentum conservation equations for laminar flow in spherical coordinates are developed numerically. The velocity field, axial pressure gradient, shear stress, and flow separation angle on the particle surface are carefully analyzed with different values of acoustic Reynolds number and Strouhal number. The minimum frequency required for flow separation is also investigated with different SPL (sound pressure level). The axial pressure gradient, shear stress, and separation angle on the surface are proportional to the magnitude of the oscillating flow velocity at low frequency (~50 Hz). However, those physical quantities have different values at high frequency (~5000 Hz), due to the combined effect of curvature and the flow acceleration.

#### 1. Introduction

Over the years, considerable researches have been carried out on oscillating flows over bodies of various shapes because of the related engineering application [1]. The rates of heat and mass transfer from the sphere are enhanced by the oscillation of the surrounding fluid. This phenomenon has good potential in some areas, such as the pulse combustion [2], food refrigeration [3], and heat exchanger [4, 5].

The theoretical study of oscillating flow over sphere dates back to the work of Bassett [6]. An experiment had been conducted by Odar and Hamilton [7] on oscillating flow over a sphere in attempt to modify Bassett’s solution. Mei [8] proposed a general dynamic equation including the quasisteady drag, history force, and added-mass force in the time domain for particle motions at finite Reynolds number (order of several hundred). It was found that the form of history force obtained performed consistently better than that of Odar and Hamilton. Chang and Maxey [9] investigated the oscillating flow over a sphere with the frequency up to 10 Hz and the Reynolds numbers up to 16.7, by using the numerical calculation method. They found that, at very low Reynolds number, separation took place during the deceleration period and there was no separation during the acceleration period. Then, Alassar [10] extended the Reynolds number to 200 with the series truncation method and had careful analyses on the separation angle and the wake length. Alassar [10] also investigated the phenomenon of second motion (acoustic streaming) created by the oscillating flow over a sphere, by solving the full Navier-Stokes equations. However, all the researches above on oscillating flow over a sphere have one thing in common that the maximum excursion of sphere over one period of the flow is small, compared to the characteristic size of the particles.

When an acoustic field is applied to enhance the combustion and the heat and mass transfer to and from coal particles, the maximum excursion is large compared to the characteristic size of the coal particles. In this case, Pozrikidis [11] investigated the problem of viscous oscillating flow over a particle at low Reynolds numbers (order of ten), by solving the unsteady stokes equation with boundary-integral method. Ha [12] studied the oscillating flow driven by high-intensity acoustic field over a spherical particle (the diameter is 100 *μ*m) in the air. Some issues were discussed as well, such as the flow structure, axial pressure gradient, shear stress, and flow separation on the particle surface. Oscillating flow driven by a standing wave around a solid particle (the diameter is at the nanoscale) was investigated by Sadhal [13].

In this paper, the two-dimensional, unsteady mass and momentum conservation equations for laminar flow are solved for the oscillating flow induced by an acoustic field around coal particles. The parameters of flue gas in the real power plant boiler are also taken into account. The flow velocity, axial pressure gradient, shear stress, and flow separation on the coal particle surface are analyzed in different Reynolds numbers and Strouhal numbers. Although there is not much about the mechanism of acoustic enhancement of heat and mass transfer from coal particles, this study highlights its good application prospect in the power plant boiler.

#### 2. The Model

##### 2.1. Governing Equation and Physical Model

The general differential equations can be written as [14]where , are the radial velocity and tangential velocity, respectively. is the source term and its expression in the radial is different from that in tangential directions, as shown in Table 1.