A class of unsteady free convection flows over a differentially cooled horizontal surface is considered. The cooling, specified in terms of an imposed negative buoyancy or buoyancy flux, varies laterally as a step function with a single step change. As thermal boundary layers develop on either side of the step change, an intrinsically unsteady, boundary-layer-like flow arises in the transition ...

Considerable progress in development and application of CFD for aeroengine internal flow systems has been made in recent years. CFD is regularly used in industry for assessment of air systems, and the performance of CFD for basic axisymmetric rotor/rotor and stator/rotor disc cavities with radial throughflow is largely understood and documented. Incorporation of three dimensional (3D) geometric...

We study the role of unsteady lift in the context of flapping wing bird flight. Both aerodynamicists and biologists have attempted to address this subject, yet it seems that the contribution of unsteady lift still holds many open questions. The current study deals with the estimation of unsteady aerodynamic forces on a freely flying bird through analysis of wingbeat kinematics and near wake flo...

This paper presents a nonlinear solver based on the Newton-Krylov methods, where the Newton equations are solved by Krylov-subspace type approaches. We focus on the solution of unsteady systems, in which the temporal terms are discretized by the backward Euler method using finite difference. To save computational cost, an adaptive time stepping is used to minimize the number of time steps. The ...

This paper presents an adjoint method for the optimum shape design of unsteady flows. The goal is to develop a set of discrete unsteady adjoint equations and their corresponding boundary conditions for both the time accurate and non-linear frequency domain methods. First, this paper presents the complete formulation of the time dependent optimal design problem. Second, we present the time accur...

This paper presents the formulation of a dual time stepping procedure to solve the equations of fully implicit Runge–Kutta schemes. In particular themethod is applied toGauss and Radau 2A schemes with either two or three stages. The schemes are tested for unsteady flows over a pitching airfoil modeled by both the Euler and the unsteady Reynolds averaged Navier Stokes equations. It is concluded ...

We present a new algorithm for combining a fully anisotropic goal-oriented mesh adaptation with the transient fixed point method for unsteady problems. The minimization of the error on a functional provides both the density and the anisotropy (stretching) of the optimal mesh. This method is used for specifying the mesh for a time subinterval from the state and the adjoint. The global transient ...

this paper presents the results of numerical simulations of the laminar and turbulent flows inside diverging channels using random vortex methods (rvm). random vortex method is a mesh-free method which solves unsteady vorticity equation instead of solving navier-stokes equations directly to determine the velocity field. in this paper, the velocity potential, which is used as the initial conditi...