Showing papers by "Mark H. Carpenter published in 2011"

Computational Modeling of Roughness-Based Laminar Flow Control on a Subsonic Swept Wing

Abstract: A combination of parabolized stability equations and secondary instability theory has been applied to a low-speed swept airfoil model with a chord Reynolds number of 7.15 million, with the goal of evaluating this methodology in the context of transition prediction for a known configuration for which roughness-based crossflow transition control has been demonstrated under flight conditions. Nonlinear parabolized stability equations computations indicate that progressive reduction in the growth of the linearly most amplified stationary crossflow mode can be achieved via increasingly stronger control input corresponding to the first harmonic of the target mode. The reduction in the target mode amplitude is accompanied by reduced linear growth rates of the high-frequency secondary instabilities that lead to rapid breakdown of the laminar flow. The secondary instability predictions based on secondary instability theory are shown to agree well with those based on the parabolized stability equations. The possibility of overcontrol is also assessed, and it is found that premature transition due to excessive control can be avoided by keeping the control amplitude below a certain threshold. The nonlinear development of the most unstable Z-mode secondary instability is traced using the parabolized stability equation method, so as to yield physics-based prediction of crossflow-dominated transition.

Computational Study of Laminar Flow Control on a Subsonic Swept Wing Using Discrete Roughness Elements

Abstract: A combination of parabolized stability equations and secondary instability theory has been applied to a low-speed swept airfoil model with a chord Reynolds number of 7.15 million, with the goals of (i) evaluating this methodology in the context of transition prediction for a known configuration for which roughness based crossflow transition control has been demonstrated under flight conditions and (ii) of analyzing the mechanism of transition delay via the introduction of discrete roughness elements (DRE). Roughness based transition control involves controlled seeding of suitable, subdominant crossflow modes, so as to weaken the growth of naturally occurring, linearly more unstable crossflow modes. Therefore, a synthesis of receptivity, linear and nonlinear growth of stationary crossflow disturbances, and the ensuing development of high frequency secondary instabilities is desirable to understand the experimentally observed transition behavior. With further validation, such higher fidelity prediction methodology could be utilized to assess the potential for crossflow transition control at even higher Reynolds numbers, where experimental data is currently unavailable.

Energy Stable WENO Schemes of Arbitrary Order

Abstract: A systematic approach for constructing Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference schemes of arbitrary order is presented. The new class of schemes is proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. We also present new weight functions and constraints on their parameters, which provide consistency and much faster convergence of the high-order ESWENO schemes to their underlying linear schemes. Furthermore, the improved weight functions guarantee that the ESWENO schemes are design-order accurate for smooth solutions with arbitrary number of vanishing derivatives and provide much better resolution near strong discontinuities than the conventional counterparts. Numerical results show that the new ESWENO schemes are stable and significantly outperform the corresponding WENO schemes of Jiang and Shu in terms of accuracy, while providing essentially non-oscillatory solutions near strong discontinuities.