Numerical Study of Unsteady Flow Around Airfoil With Spoiler

Abstract

A discrete vortex model based on the panel method has been developed to simulate the two-dimensional unsteady separated flow generated by the rapid deployment of a spoiler on the upper surface of an airfoil. This method represents the boundary surfaces by distributing piecewise linear-vortex and constant source singularities on discrete panels. The wake of the spoiler and airfoil is represented by discrete vortices. At each sharp edge, a vortex sheet is used to feed discrete vortices at every time-step to form the downstream wake. The length and strength of each shed vortex sheet are determined by the continuity equation and a condition such that the flow, the net force, and the pressure difference across the vortex sheet are zero. The flow patterns behind the spoiler at different time-steps are presented. The pressure distributions on the airfoil based on the unsteady Bernoulli’s equation are compared, where possible, with the experimental results and other computational results. The adverse lift effects have been obtained, and similar effects have been measured in experiments.

Unsteady Pressure Field Investigation of an Axial Fan—Inlet and Outlet Unsteady Pressure Field Measurement

“…The pressure oscillation frequency depends on the fan rotational speed. The detailed analysis of the unsteady pressure can be found in Xu and Yeung (1998). In this work, the above formulation will be used to explain the measurement results in the following sections.…”

“…According to the study by Xu and Yeung (1998), the pressure downstream of a rotation machine and a airfoil moving spoiler can be simulated by using the vortex method. The pressure oscillations downstream of the fan are significantly affected by many factors, including the environmental conditions during the testing.…”

“…Consider the velocity induced by the vortices at the point (r , θ ) in the stationary coordinate system. If the fan blade bounded vortex strength is γ , according to the basic formulation discussed (Xu and Yeung, 1998), the velocity induced by γ downstream of the fan can be expressed in Fourier series as:…”

“…The vortex shedding rate can be calculated by using Helmholz theorem (Xu and Yeung, 1998), that is the total circulation change around the fan blade which is equal to the total shed vortices form the trailing edge within unit time. Then the velocity induced by the vortices shed from the fan blade trailing edge γ w can be expressed as:…”

Unsteady Pressure Field Investigation of an Axial Fan—Blade Unsteady Pressure Field Measurement

“…To analyze the unsteady pressure field, a vortex singularity method (Xu and Yeung, 1998) should be used. Assuming that the flow is two-dimensional within the same radial plan, consider the velocity induced by the vortices at the point (r, θ ) in the stationary coordinate system.…”