tailieunhanh - Calculation of transonic flows around profiles with blunt and angled leading EDGES

Transonic flow is a mixed flow of subsonic and supersonic regions. Because of this mixture, the solution of transonic flow problems is obtained only when solving the differential equations of motion with special treatments for the transition from subsonic region to supersonic region and vice versa. We built codes solving the full potential equation and Euler equations by applying the finite difference method and finite volume method, and also associated with software Fluent to consider the viscous effects. | Vietnam Journal of Mechanics, VAST, Vol. 38, No. 1 (2016), pp. 1 – 13 DOI: CALCULATION OF TRANSONIC FLOWS AROUND PROFILES WITH BLUNT AND ANGLED LEADING EDGES Hoang Thi Bich Ngoc∗ , Nguyen Manh Hung University of Science and Technology, Vietnam 1 Hanoi ∗ E-mail: hoangthibichngoc@ Received December 07, 2014 Abstract. Transonic flow is a mixed flow of subsonic and supersonic regions. Because of this mixture, the solution of transonic flow problems is obtained only when solving the differential equations of motion with special treatments for the transition from subsonic region to supersonic region and vice versa. We built codes solving the full potential equation and Euler equations by applying the finite difference method and finite volume method, and also associated with software Fluent to consider the viscous effects. The analysis of results calculated for cases of transonic flow over profiles with blunt and angled leading edges shows more clearly the physical nature of the gas - solid interaction at leading edges in the mixed flow and the optimal application of each profile in transonic flows. Keywords: Transonic flow, finite volumes, finite differences, blunt LE, angled LE. 1. INTRODUCTION In order to solve transonic flows (with free flow Mach numbers M∞ ≥ ), it is necessary to use the equations of compressible flow. In the assumption of potential flow, differential equations of compressible flow are Euler equations and full potential equation. For incompressible flows (with Mach numbers M∞ < ), by considering the constant density, the Euler equations and the full potential equation are reduced to the Laplace equation of potential (elliptic form). Whatever the method, the transonic problem needs to treat the transition from subsonic flow zones to supersonic flow zones and vice versa. Motion differential equations in this transition zone change back and forth from elliptic form to hyperbolic form. The appearance of a

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