Inviscid-Viscous Coupled Solution for Unsteady Flows Through Vibrating Blades: Part 2 — Computational Results

Author(s):  
L. He ◽  
J. D. Denton

A quasi 3-D inviscid-viscous coupled approach has been developed for unsteady flows around oscillating blades, as described in Part 1. To validate this method, calculations for several steady and unsteady flow cases with strong inviscid-viscous interactions are performed, and the results are compared with the corresponding experiments. Calculated results for unsteady flows around a bi-convex cascade and a fan tip section highlight the necessity of including viscous effects in predictions of turbomachinery blade flutter at transonic flow conditions.

1993 ◽  
Vol 115 (1) ◽  
pp. 101-109 ◽  
Author(s):  
L. He ◽  
J. D. Denton

A quasi-three-dimensional inviscid-viscous coupled approached has been developed for unsteady flows around oscillating blades, as described in Part 1. To validate this method, calculations for several steady and unsteady flow cases with strong inviscid-viscous interactions are performed, and the results are compared with the corresponding experiments. Calculated results for unsteady flows around a biconvex cascade and a fan tip section highlight the necessity of including viscous effects in predictions of turbomachinery blade flutter at transonic flow conditions.


Author(s):  
Ali H. Alhadidi ◽  
Mohammed F. Daqaq ◽  
Hamid Abderrahmane

This paper investigates exploiting a bi-stable restoring force to enhance the transduction of wake-galloping energy harvesters in unsteady flows. To that end, a harvester consisting of a piezoelectric cantilever beam augmented with a square-sectioned bluff body at the free end is considered. Two repulsive magnets located at the tip of the beam are used to introduce the bi-stable restoring force. Unsteadiness is generated in a wind tunnel using static-grid structures located in the upstream of the bluff body. Three different mesh screens with square bars are designed with different bar and mesh widths to control the Reynolds numbers and associated unsteadiness. A series of wind tunnel tests are then used to experimentally investigate the response of the harvester with and without the tip magnets. Results demonstrate that the bi-stable restoring force can be used to improve the output power of the harvester under unsteady flow conditions.


Author(s):  
Timothy C. Ayer ◽  
Joseph M. Verdon

A time-accurate Euler/Navier-Stokes analysis is applied to predict unsteady subsonic and transonic flows through a vibrating cascade. The intent is to validate this nonlinear analysis along with an existing linearized inviscid analysis via result comparisons for unsteady flows that are representative of those associated with blade flutter. The time-accurate analysis has also been applied to determine the relative importance of nonlinear and viscous effects on blade response. The subsonic results reveal a close agreement between inviscid and viscous unsteady blade loadings. Also, the unsteady surface pressure responses are essentially linear, and predicted quite accurately using a linearized inviscid analysis. For unsteady transonic flows, shocks and their motions cause significant nonlinear contributions to the local unsteady response. Viscous displacement effects tend to diminish shock strength and impulsive unsteady shock loads. For both subsonic and transonic flows, the energy transfer between the fluid and the structure is essentially captured by the first-harmonic component of the nonlinear unsteady solutions, but in transonic flows, the nonlinear first-harmonic and the linearized inviscid responses differ significantly in the vicinity of shocks.


2021 ◽  
Author(s):  
Le Wang ◽  
Alan Cuthbertson ◽  
Gareth Pender ◽  
Zhixian Cao

<p>Sediment transport and associated morphological changes in alluvial rivers occur primarily under unsteady flow conditions that are manifested as well-defined flood hydrograph events. At present, typical bed forms generated by such unsteady flows is far less studied and, thus, more poorly understood, than equivalent bed forms generated under steady flow conditions. In view of this, the objective of this work is to investigate the development of morphological bed features, and specifically variability in the length, height and steepness of bed forms that develop in a mobile coarse-sand bed layer under unsteady flow hydrographs under zero sediment feed conditions. A series of laboratory flume experiments is conducted within which different flow hydrograph events are simulated physically by controlling their shape, unsteadiness and magnitude. Experimental results indicate that different categories of bed forms such as dunes, alternate bars or transitional dune-bar structures develop within the erodible bed layer when subject to varying hydrograph flow conditions. Examination of relative importance of three parameters used to describe the hydrograph characteristics (i.e. asymmetry, unsteadiness and total water work) on bed form dimensional descriptors (i.e. wavelength, height and steepness) reveals that hydrograph unsteadiness and total water work are the primary and second-order controls on bed deformations or corresponding bed form dimensions. By contrast, hydrograph asymmetry appears to have minimal or negligible influence on bed form development in terms of their type and magnitude. Based on these findings, a physical model was developed and tested to describe the effect of unsteady flow hydrographs with varying unsteadiness and total water work on the nature and size of resulting bed forms that are generated in sand-bed layers. </p>


1998 ◽  
Vol 120 (1) ◽  
pp. 112-121 ◽  
Author(s):  
T. C. Ayer ◽  
J. M. Verdon

A time-accurate Euler/Navier–Stokes analysis is applied to predict unsteady subsonic and transonic flows through a vibrating cascade. The intent is to validate this nonlinear analysis along with an existing linearized inviscid analysis via result comparisons for unsteady flows that are representative of those associated with blade flutter. The time-accurate analysis has also been applied to determine the relative importance of nonlinear and viscous effects on blade response. The subsonic results reveal a close agreement between inviscid and viscous unsteady blade loadings. Also, the unsteady surface pressure responses are essentially linear, and predicted quite accurately using a linearized inviscid analysis. For unsteady transonic flows, shocks and their motions cause significant nonlinear contributions to the local unsteady response. Viscous displacement effects tend to diminish shock strength and impulsive unsteady shock loads. For both subsonic and transonic flows, the energy transfer between the fluid and the structure is essentially captured by the first-harmonic component of the nonlinear unsteady solutions, but in transonic flows, the nonlinear first-harmonic and the linearized inviscid responses differ significantly in the vicinity of shocks.


2014 ◽  
Vol 905 ◽  
pp. 369-373
Author(s):  
Choo Tai Ho ◽  
Yoon Hyeon Cheol ◽  
Yun Gwan Seon ◽  
Noh Hyun Suk ◽  
Bae Chang Yeon

The estimation of a river discharge by using a mean velocity equation is very convenient and rational. Nevertheless, a research on an equation calculating a mean velocity in a river was not entirely satisfactory after the development of Chezy and Mannings formulas which are uniform equations. In this paper, accordingly, the mean velocity in unsteady flow conditions which are shown loop form properties was estimated by using a new mean velocity formula derived from Chius 2-D velocity formula. The results showed that the proposed method was more accurate in estimating discharge, when compared with the conventional formulas.


2005 ◽  
Vol 29 (2) ◽  
pp. 89-113 ◽  
Author(s):  
Niels Troldborg

A comprehensive computational study, in both steady and unsteady flow conditions, has been carried out to investigate the aerodynamic characteristics of the Risø-B1-18 airfoil equipped with variable trailing edge geometry as produced by a hinged flap. The function of such flaps should be to decrease fatigue-inducing oscillations on the blades. The computations were conducted using a 2D incompressible RANS solver with a k-w turbulence model under the assumption of a fully developed turbulent flow. The investigations were conducted at a Reynolds number of Re = 1.6 · 106. Calculations conducted on the baseline airfoil showed excellent agreement with measurements on the same airfoil with the same specified conditions. Furthermore, a more widespread comparison with an advanced potential theory code is presented. The influence of various key parameters, such as flap shape, flap size and oscillating frequencies, was investigated so that an optimum design can be suggested for application with wind turbine blades. It is concluded that a moderately curved flap with flap chord to airfoil curve ratio between 0.05 and 0.10 would be an optimum choice.


Author(s):  
C B Allen

A grid adaptation procedure suitable for use during unsteady flow computations is described. Transfinite interpolation is used to generate structured grids for the computation of steady and unsteady Euler flows past aerofoils. This technique is well suited to unsteady flows, since instantaneous grid positions and speeds required by the flow solver are available directly from the algebraic mapping. A different approach to grid adaptation is described, wherein adaptation is performed by redistributing the interpolation parameters, instead of the physical grid positions. This results in the adapted grid positions, and hence speeds, still being available algebraically. Grid adaptation during an unsteady computation is performed continuously by imposing an ‘adaptation velocity’ on grid points, thereby applying the adaptation over several time steps and avoiding the interpolation of the solution from one grid to another, which is associated with instantaneous adaptation. For both steady and unsteady flows the adapted grid technique is shown to produce sharper shock resolution for a very small increase in CPU (central processing unit) requirements.


2017 ◽  
Author(s):  
A. F. Totorean ◽  
S. I. Bernad ◽  
I. C. Hudrea ◽  
R. F. Susan-Resiga

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