• International Journal of Aeronautical and Space Sciences
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• v.14 no.3
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• pp.210-214
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• 2013

The sensitivity of transonic flow past a Whitcomb airfoil to deflections of an aileron is studied at free-stream Mach numbers from 0.81 to 0.86 and vanishing or negative angles of attack. Solutions of the Reynolds-averaged Navier-Stokes equations are obtained with a finite-volume solver using the $k-{\omega}$ SST turbulence model. The numerical study demonstrates the existence of narrow bands of the Mach number and aileron deflection angles that admit abrupt changes of the lift coefficient at small perturbations. In addition, computations reveal free-stream conditions in which the lift coefficient is independent of aileron deflections of up to 5 degrees. The anomalous behavior of the lift is explained by interplay of local supersonic regions on the airfoil. Both stationary and impulse changes of the aileron position are considered.

• Journal of the Semiconductor & Display Technology
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• v.8 no.3
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• pp.31-37
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• 2009

This paper presents one and two dimensional simulation results with discontinuous features (shocks) of capacitively coupled rf plasmas. The model consists of the first two and three moments of the Boltzmann equation for the ion and electron fluids respectively, coupled to Poisson's equation for the self-consistent electric field. The local field and drift-diffusion approximations are not employed, and as a result the charged species conservation equations are hyperbolic in nature. Hyperbolic equations may develop discontinuous solutions even if their initial conditions are smooth. Indeed, in this work, secondary electron emission is shown to produce transient electron shock waves. These shocks form at the boundary between the cathodic sheath (CS) and the quasi-neutral (QN) bulk region. In the CS, the electrons emitted from the electrode are accelerated to supersonic velocities due to the large electric field. On the other hand, in the QN the electric field is not significant and electrons have small directed velocities. Therefore, at the transition between these regions, the electron fluid decelerates from a supersonic to a subsonic velocity in the direction of flow and a jump in the electron velocity develops. The presented numerical results are consistent with both experimental observations and kinetic simulations.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.4
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• pp.601-613
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• 2017

An adjoint-based error estimation and mesh adaptation study is conducted for two-dimensional viscous flows on unstructured hybrid meshes. The error in an integral output functional of interest is estimated by a dot product of the residual vector and adjoint variable vector. Regions for the mesh to be adapted are selected based on the amount of local error at each nodal point. Triangular cells in the adaptive regions are refined by regular refinement, and quadrangular cells near viscous walls are bisected accordingly. The present procedure is applied to single-element airfoils such as the RAE2822 at a transonic regime and a diamond-shaped airfoil at a supersonic regime. Then the 30P30N multi-element airfoil at a low subsonic regime with a high incidence angle (${\alpha}=21deg.$) is analyzed. The same level of prediction accuracy for lift and drag is achieved with much less mesh points than the uniform mesh refinement approach. The detailed procedure of the adjoint-based mesh refinement for the multi-element airfoil case show that the basic flow features around the airfoil should be resolved so that the adjoint method can accurately estimate an output error.

• International Journal of Aeronautical and Space Sciences
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• v.15 no.3
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• pp.232-240
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• 2014

Transonic flow past a NASA SC(2)-0710 airfoil with deployments of a spoiler up to $6^{\circ}$ was studied numerically. We consider angles of attack from $-0.6^{\circ}$ to $0.6^{\circ}$ and free-stream Mach numbers from 0.81 to 0.86. Solutions of the unsteady Reynolds-averaged Navier-Stokes equations were obtained with a finite-volume solver using several turbulence models. Both stationary and time-dependent deployments of the spoiler were examined. The study revealed the existence of narrow bands of the Mach number, angle of attack, and spoiler deflection angle, in which the flow was extremely sensitive to small perturbations. Simulations of 3D flow past a swept wing confirmed the flow sensitivity to small perturbations of boundary conditions.