Adaptive strategy of transonic flows over vibrating blades with interblade phase angles

Abstract

SUMMARYAn error indicator and a locally implicit scheme with anisotropic dissipation model on dynamic quadrilateral-triangular mesh are developed to study transonic ows over vibrating blades with interblade phase angles. In the Cartesian co-ordinate system, the unsteady Euler equations with moving domain e ects are solved. The error indicator, in which uniÿed magnitudes of dynamic grid speed, substantial derivative of pressure, and substantial derivative of vorticity magnitude are incorporated to capture the unsteady wave behaviours and vortex-shedding phenomena due to unsteadiness. To assess the accuracy of the locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh, two ow calculations are performed. Based on the comparison with the related numerical and experimental data, the accuracy of the present approach is conÿrmed. According to the high-resolutional result on the adaptive mesh, the unsteady pressure wave, shock and vortex-shedding behaviours are clearly demonstrated.

Numerical Study of Turbulent Flows Over Vibrating Blades with Positive Interblade Phase Angle

“…Pressure contours and vorticity contours during the sixth cycle ((2MKτ -10π) = 0,π/6, π/3 and π/2) are plotted in Figs. Meanwhile, three compression waves which are located in front of leading edge of the lowest blade, on the rear part of From the above discussion and the corresponding pressure contour of author's previous Euler calculation [14], different flow behaviors are demonstrated. After comparing the pressure contours (Figs.…”

“…On the static triangular mesh, Hwang and Liu [16] developed the anisotropic dissipation model. In the author's previous study [14], the anisotropic dissipation model was extended on the dynamic quadrilateral-triangular mesh for inviscid flow calculations. In this article, the anisotropic dissipation model is extended on dynamic quadrilateral-triangular mesh for turbulent flow calculations.…”

“…(8), a locally implicit scheme [14,21] is implemented. (8), a locally implicit scheme [14,21] is implemented.…”

“…The unified magnitude of density gradient and unified magnitude of gradient of vorticity magnitude were incorporated to treat new node spacing of mesh remeshing [11], whereas a weighted function of vorticity magnitude was introduced to treat the boundary layer effect [12]. In the author's previous study [14], a refining error indicator was developed to study inviscid flows over vibrating blades. In the author's previous study [14], a refining error indicator was developed to study inviscid flows over vibrating blades.…”

Adaptive strategy of the supersonic turbulent flow over a backward‐facing step

“…In the author's previous inviscid study [23], an error indicator, which incorporated the uniÿed magnitudes of dynamic grid speed, substantial derivative of pressure and substantial derivative of vorticity magnitude was proposed and formulated as In the present turbulent study, the error indicator in Equation (17) is further improved to account for the viscous e ect, and the dynamic grid speed e ect is removed. The present error indicator is formulated as…”