Part 4 — Two dimensional dynamic stall

1987 ◽  
Vol 91 (902) ◽  
pp. 72-88 ◽  
Author(s):  
G. J. Hancock ◽  
J. S. Y. Lam
Keyword(s):  
Limit Cycle ◽  
Dynamic Responses ◽  
Dynamic Stall ◽  
Two Dimensional ◽  
Linear Set ◽  
Impulsive Input ◽  
Aerodynamic Model ◽  
Aerodynamic Derivatives ◽  
Experimental Values ◽  
General Motion

Summary An axiomatic aerodynamic model has been developed for the general motion of a two dimensional aerofoil as it passes in and out of stall, which gives realistic unsteady loads as compared to experimental values. A non-linear set of aerodynamic derivatives with time delays have been derived from the axiomatic aerodynamics. ‘Actual’ and ‘predicted’ dynamic responses of an aerofoil, spring restrained in torsion, following an impulsive input show similar trends, including limit cycle oscillations, although there is a slight difference in frequency and a difference in the magnitude of the initial impulse required to trigger the limit cycle.

Dynamic responses of a two-dimensional flapping foil motion

2006 ◽  
Vol 18 (9) ◽  
pp. 098104 ◽  
Author(s):  
Xi-Yun Lu ◽  
Qin Liao
Keyword(s):  
Dynamic Responses ◽  
Two Dimensional ◽  
Flapping Foil

A New Global Spatial Discretization Method for Calculating Dynamic Responses of Two-Dimensional Continuous Systems With Application to a Rectangular Kirchhoff Plate

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
K. Wu ◽  
W. D. Zhu
Keyword(s):  
Boundary Conditions ◽  
Continuous System ◽  
Dynamic Responses ◽  
Kirchhoff Plate ◽  
Continuous Systems ◽  
Discretization Method ◽  
Two Dimensional ◽  
Spatial Discretization ◽  
Arbitrary Boundary ◽  
Discretization Methods

A new global spatial discretization method (NGSDM) is developed to accurately calculate natural frequencies and dynamic responses of two-dimensional (2D) continuous systems such as membranes and Kirchhoff plates. The transverse displacement of a 2D continuous system is separated into a 2D internal term and a 2D boundary-induced term; the latter is interpolated from one-dimensional (1D) boundary functions that are further divided into 1D internal terms and 1D boundary-induced terms. The 2D and 1D internal terms are chosen to satisfy prescribed boundary conditions, and the 2D and 1D boundary-induced terms use additional degrees-of-freedom (DOFs) at boundaries to ensure satisfaction of all the boundary conditions. A general formulation of the method that can achieve uniform convergence is established for a 2D continuous system with an arbitrary domain shape and arbitrary boundary conditions, and it is elaborated in detail for a general rectangular Kirchhoff plate. An example of a rectangular Kirchhoff plate that has three simply supported boundaries and one free boundary with an attached Euler–Bernoulli beam is investigated using the developed method and results are compared with those from other global and local spatial discretization methods. Advantages of the new method over local spatial discretization methods are much fewer DOFs and much less computational effort, and those over the assumed modes method (AMM) are better numerical property, a faster calculation speed, and much higher accuracy in calculation of bending moments and transverse shearing forces that are related to high-order spatial derivatives of the displacement of the plate with an edge beam.

Measurements of Apparent Mass Torque Coefficients of Two-Dimensional Centrifugal Impellers

1986 ◽  
Vol 108 (4) ◽  
pp. 407-413
Author(s):  
Y. Tsujimoto ◽  
K. Imaichi ◽  
T. Moritani ◽  
K. Kim
Keyword(s):  
Angular Velocity ◽  
Flow Rate ◽  
Potential Flow ◽  
Rotational Velocity ◽  
Apparent Mass ◽  
Two Dimensional ◽  
Drag Torque ◽  
Mean Flow ◽  
Experimental Values

Apparent mass torque coefficients for fluctuations of flow rate and angular velocity are determined experimentally for two-dimensional centrifugal impellers. Nearly sinusoidal fluctuations of flow rate and angular velocity are produced by using crank mechanisms, and the resulting unsteady torque on the impeller is measured. The torque is divided into components in-phase and out-of-phase with the displacements. The in-phase components are used to determine the apparent mass coefficients. Drag torque coefficients are defined and used to represent the out-of-phase components. The tests are conducted under various frequencies and amplitudes of the fluctuations with zero mean flow rate and rotational velocity. The apparent mass torque coefficients are compared with theoretical values obtained under the assumption of a two-dimensional potential flow. The experimental values are 5 to 20 percent larger than the theoretical ones and no appreciable effects of the frequency and the amplitude are observed within the range of the experiments.

The Effect of Structural Parameters on Response Characteristics of Aeroelastic System in the Presence of Dynamic Stall

2021 ◽  
Author(s):  
Zhan Qiu ◽  
Fuxin Wang
Keyword(s):  
Limit Cycle ◽  
Structural Parameters ◽  
Dynamic Pressure ◽  
Angle Of Attack ◽  
Dynamic Stall ◽  
System Response ◽  
Structural Stiffness ◽  
Aeroelastic System ◽  
Equilibrium Angle ◽  
Minimum Angle

Abstract The effect of structural paramters on the response and aerodynamic stiffness characteristics of the free aeroelastic system under the influence of dynamic stall is investigated adopting CFD (Computational Fluid Dynamics) method. The equilibrium angle of the spring and the structural stiffness are taken as parameters of interest. Systems with small equilibrium angles enter the symmetric limit-cycle state more quickly after a Hopf bifurcation and experience dynamic stall in both directions, rather than slowly decreasing in minimum angle of attack and remaining in the asymmetric limit-cycle state before dynamic stall in the opposite direction, as is the case with systems with large spring equilibrium angles. Thus, aerodynamic stiffness of system with large equilibrium angles can be more significantly influenced by the change in aerodynamic moment characteristics at the minimum angle of attack. Furthermore, by increasing the initial angular velocity, we find that the system response all becomes symmetric limit cycle and therefore the aerodynamic stiffness appears to have a monotonically increasing characteristic. As to the effect of structural stiffness, it is found that the limit cycle amplitude first increases with structural stiffness after bifurcation, then the amplitude is unchanged with varying structural stiffness at higher Mach number. Energy maps show that the parametric distribution of the energy transfer contributes to this phenomenon. Moreover, when entering the symmetric limit cycle state, the structural stiffness no longer has a significant effect on the aerodynamic stiffness of the system, as the increase in the aerodynamic stiffness is determined solely by the increase in dynamic pressure without the effect of changes in moment characteristics.

Improved Two-Dimensional Dynamic Stall Prediction with Structured and Hybrid Numerical Methods

2011 ◽  
Vol 56 (4) ◽  
pp. 1-12 ◽  
Author(s):  
K. Richter ◽  
A. Le Pape ◽  
T. Knopp ◽  
M. Costes ◽  
V. Gleize ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Numerical Method ◽  
High Speed ◽  
Turbulence Modeling ◽  
Turbulence Models ◽  
Boundary Layer Transition ◽  
Dynamic Stall ◽  
Two Dimensional ◽  
Layer Transition ◽  
The Impact

A joint comprehensive validation activity on the structured numerical method elsA and the hybrid numerical method TAU was conducted with respect to dynamic stall applications. To improve two-dimensional prediction, the influence of several factors on the dynamic stall prediction was investigated. The validation was performed for three deep dynamic stall test cases of the rotor blade airfoil OA209 against experimental data from two-dimensional pitching airfoil experiments, covering low-speed and high-speed conditions. The requirements for spatial discretization and for temporal resolution in elsA and TAU are shown. The impact of turbulence modeling is discussed for a variety of turbulence models ranging from one-equation Spalart–Allmaras-type models to state-of-the-art, seven-equation Reynolds stress models. The influence of the prediction of laminar/turbulent boundary layer transition on the numerical dynamic stall simulation is described. Results of both numerical methods are compared to allow conclusions to be drawn with respect to an improved prediction of dynamic stall.

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