Bifurcation Analysis of Trailing Edge Angle for Aeroelastic System

2012 ◽  
Author(s):  
Cheng-Chi Wang ◽  
David T-W Lin ◽  
Her-Terng Yau
Keyword(s):  
Bifurcation Analysis ◽  
Trailing Edge ◽  
Aeroelastic System ◽  
Edge Angle

Dependence of steady Mach reflections on the reflecting-wedge trailing-edge angle

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1780-1782
Author(s):  
G. Ben-Dor ◽  
T. Elperin ◽  
H. Li ◽  
E. Vasiliev ◽  
A. Chpoun ◽  
...  
Keyword(s):  
Trailing Edge ◽  
Edge Angle

The influence of the trailing edge angle of the micro centrifugal impeller on the performance of the centrifugal compressor

2021 ◽  
pp. 1-15
Author(s):  
Xu Yu-dong ◽  
Li Cong ◽  
Lv Qiong-ying ◽  
Zhang Xin-ming ◽  
Mu Guo-zhen
Keyword(s):  
Centrifugal Compressor ◽  
Pressure Ratio ◽  
Centrifugal Impeller ◽  
Centrifugal Compressors ◽  
Trailing Edge ◽  
Sweep Angle ◽  
Impeller Blade ◽  
Bending Angle ◽  
Edge Angle ◽  
Isentropic Efficiency

In order to study the effect of the trailing edge sweep angle of the centrifugal impeller on the aerodynamic performance of the centrifugal compressor, 6 groups of centrifugal impellers with different bending angles and 5 groups of different inclination angles were designed to achieve different impeller blade trailing edge angle. The computational fluid dynamics (CFD) method was used to simulate and analyze the flow field of centrifugal compressors with different blade shapes under design conditions. The research results show that for transonic micro centrifugal compressors, changing the blade trailing edge sweep angle can improve the compressor’s isentropic efficiency and pressure ratio. The pressure ratio of the compressor shows a trend of increasing first and then decreasing with the increase of the blade bending angle. When the blade bending angle is 45°, the pressure ratio of the centrifugal compressor reaches a maximum of 1.69, and the isentropic efficiency is 67.3%. But changing the inclination angle of the blade trailing edge has little effect on the isentropic efficiency and pressure ratio. The sweep angle of blade trailing edge is an effective method to improve its isentropic efficiency and pressure ratio. This analysis method provides a reference for the rational selection of the blade trailing edge angle, and provides a reference for the design of micro centrifugal compressors under high Reynolds numbers.

Shock–boundary layer interaction and energetics in transonic flutter

2017 ◽  
Vol 832 ◽  
pp. 212-240 ◽  
Author(s):  
Pradeepa T. Karnick ◽  
Kartik Venkatraman
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Turbulence Model ◽  
Viscous Effects ◽  
Trailing Edge ◽  
Aeroelastic System ◽  
Number Range ◽  
Shock Reversal ◽  
Transonic Flutter ◽  
Flutter Boundary

We study the influence of shock and boundary layer interactions in transonic flutter of an aeroelastic system using a Reynolds-averaged Navier–Stokes (RANS) solver together with the Spalart–Allmaras turbulence model. We show that the transonic flutter boundary computed using a viscous flow solver can be divided into three distinct regimes: a low transonic Mach number range wherein viscosity mimics increasing airfoil thickness thereby mildly influencing the flutter boundary; an intermediate region of drastic change in the flutter boundary due to shock-induced separation; and a high transonic Mach number zone of no viscous effects when the shock moves close to the trailing edge. Inviscid transonic flutter simulations are a very good approximation of the aeroelastic system in predicting flutter in the first and third regions: that is when the shock is not strong enough to cause separation, and in regions where the shock-induced separated region is confined to a small region near the trailing edge of the airfoil. However, in the second interval of intermediate transonic Mach numbers, the power distribution on the airfoil surface is significantly influenced by shock-induced flow separation on the upper and lower surfaces leading to oscillations about a new equilibrium position. Though power contribution by viscous forces are three orders of magnitude less than the power due to pressure forces, these viscous effects manipulate the flow by influencing the strength and location of the shock such that the power contribution by pressure forces change significantly. Multiple flutter points that were part of the inviscid solution in this regime are now eliminated by viscous effects. Shock motion on the airfoil, shock reversal due to separation, and separation and reattachment of flow on the airfoil upper surface, also lead to multiple aerodynamic forcing frequencies. These flow features make the flutter boundary quantitatively sensitive to the turbulence model and numerical method adopted, but qualitatively they capture the essence of the physical phenomena.

Characterization of typical aeroelastic sections under combined structural concentrated nonlinearities

2021 ◽  
pp. 107754632110001
Author(s):  
José Augusto I da Silva ◽  
Flávio D Marques
Keyword(s):  
Time Integration ◽  
Unsteady Aerodynamics ◽  
Nonlinear Effects ◽  
Free Play ◽  
Control Surface ◽  
Trailing Edge ◽  
Aeroelastic System ◽  
Practical Applications ◽  
Structural Nonlinearities ◽  
The Stability

Structural nonlinearities are usually present in aeroelastic systems. The analysis of this system commonly comprises a study involving only one type of nonlinearity, influencing a particular motion of the airfoil. However, practical applications of aeroelastic systems can be affected by different types of structural nonlinearities. It becomes essential to study the stability of the aeroelastic system under these conditions to assess more real operational flight procedures. In this context, this article presents an investigation of a typical aeroelastic section response with trailing edge control surface subjected to combinations of concentrated structural nonlinearities. Different nonlinear scenarios involving cubic hardening stiffness in pitching and free play, free play with preload, and slip dry friction in the trailing edge control surface motion are analyzed. The mathematical model is based on linear unsteady aerodynamics coupled to a three-dof typical aeroelastic section. Hopf bifurcations diagrams are obtained from direct time integration of the equation of motion. The post-flutter limit cycle oscillations are investigated, revealing supercritical and subcritical bifurcations. A complete parametric study of the nonlinear parameters is carried out, thereby allowing a sensitivity analysis of each nonlinear scenario. The results show that aeroelastic tailoring considering the mild post-flutter behavior can be achieved through an appropriate choice of combined nonlinear effects. Moreover, combined nonlinearities can mitigate the undesired subcritical aeroelastic responses caused by free play.

The wave drag at zero lift of slender delta wings and similar configurations

1956 ◽  
Vol 1 (3) ◽  
pp. 337-348 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Uniform Distribution ◽  
Present Method ◽  
Wave Drag ◽  
The Body ◽  
Slender Body ◽  
Trailing Edge ◽  
Slender Body Theory ◽  
Edge Angle ◽  
Finite Wing ◽  
Body Theory

Ward's slender-body theory of supersonic flow is applied to bodies terminating in either (i) a single trailing edge at right angles to the oncoming supersonic stream, or (ii) two trailing edges at right angles to one another as well as to the oncoming stream, or (iii) a cylindrical section with two or four identical fins equally spaced round it. The wave drag at zero lift, D, is given by the expression $\frac {D}{\frac {1}{2}\rho U^2} &=& \frac {1}{2\pi}\int^l_0 \int^l_0 log\frac{1}{|s-z|}S^{\prime \prime}(s)S^{\prime \prime}(z)dsdz - \\ &-& \frac{S^\prime (l)}{\pi}\int^l_0 log \frac {l}{l-z}S^{\prime \prime}(z)dz + \frac{S^{\prime 2}(l)}{2\pi} \{ log \frac{l}{(M^2-1)^{1|2}b}+k \} $ where l is the length of the body, b the semi-span of the trailing edge (or length of trailing edge of a single fin), and S(z) is the cross-sectional area of the body at a distance z behind the apex. The constant k depends on the distribution of trailing-edge angle along the span for each trailing-edge configuration. In case (i) it is 1·5 for a uniform distribution of trailing-edge angle and 1·64 for an elliptic distribution. In case (ii) it is 1·28 for a uniform distribution and 1·44 for an elliptic distribution. Study of case (iii) indicates that interference effects due to the presence of the body reduce the drag of the fins. For example, with a uniform distribution of trailing-edge angle, k for two fins falls from 1·5 in the absence of a body to 1·06 when the body radius equals the trailing-edge semi-span, while k for four fins falls from 1·28 to 0·45 under the same conditions.Where ordinary finite-wing theory is applicable, the present method must agree with it for small $(M^2-1)^{1|2}b|l$, and this is confirmed by two examples (§3), but within the limit imposed by slenderness the present method is of course more widely applicable, as well as simpler, than finite-wing theory.It is not known experimentally whether slender-body theory gives accurate predictions of drag at zero lift, for the shapes here discussed, under the conditions for which on theoretical grounds it might be expected to do so. It should be noted that, although tests have not yet been made on ideally suitable bodies, no clear the drag is therefore twice that of a wing made up of two of them. The final stages of the process cannot be represented by slender-body theory, but the initial trend may well be indicated fairly accurately.

Bifurcation analysis of an aeroelastic system with concentrated nonlinearities

2011 ◽  
Vol 69 (1-2) ◽  
pp. 57-70 ◽  
Author(s):  
Abdessattar Abdelkefi ◽  
Rui Vasconcellos ◽  
Flavio D. Marques ◽  
Muhammad R. Hajj
Keyword(s):  
Bifurcation Analysis ◽  
Aeroelastic System

scholarly journals On the Kutta Condition in Potential Flow over Airfoil

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Farzad Mohebbi ◽  
Mathieu Sellier
Keyword(s):  
Potential Flow ◽  
Trailing Edge ◽  
Airfoil Surface ◽  
Kutta Condition ◽  
Edge Angle ◽  
Panel Methods ◽  
Flow Potential ◽  
Novel Method ◽  
Elliptic Grid Generation ◽  
Fast Procedure

This paper proposes a novel method to implement the Kutta condition in irrotational, inviscid, incompressible flow (potential flow) over an airfoil. In contrast to common practice, this method is not based on the panel method. It is based on a finite difference scheme formulated on a boundary-fitted grid using an O-type elliptic grid generation technique. The proposed algorithm uses a novel and fast procedure to implement the Kutta condition by calculating the stream function over the airfoil surface through the derived expression for the airfoils with both finite trailing edge angle and cusped trailing edge. The results obtained show the excellent agreement with the results from analytical and panel methods thereby confirming the accuracy and correctness of the proposed method.

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