Patterns of Secondary Flow Field in a Circular Tube Caused by Corona Wind Using the Method of Characteristics

Abstract

Corona discharge is widely known as an effective method for improving the characteristics of the flow field and enhancing heat transfer. Distribution of charge density and electric field form a Coulomb body force which acts on the charged particles within the fluid and generates a secondary flow field. The thermal enhancing effects of corona wind are normally dominant in low Reynolds numbers or free convection problems. Although the governing differential equations of corona discharge are relatively simple, solving these equations by conventional computational methods does not yield a smooth solution for charge density and electric field. In particular, the results obtained from finite-volume method suffer from dispersion errors and fluctuations which lead to distorted values of electric body force, and consequently a distorted secondary flow. In this study, the corona discharge in a circular tube with the electrode positioned at the tube centerline is considered. An exact solution for charge density, electric field, and potential distribution along the radius of the tube has been derived analytically using a Lagrangian formulation for the charge density and the Method of Characteristics. It was found that the results of this method do not show any fluctuations or dispersion effects on charge density and electric field. The solution of the electric field provided a body force which was used in the Navier-Stokes equations to obtain the secondary flow in the cross section of the tube. In this paper, the electric and fluid flow fields are presented. The results are compared with those obtained by other computational methods and the differences are discussed.