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.

Part I: Some experiences on simple panel methods applied to attached and separated flows

1987 ◽  
Vol 91 (908) ◽  
pp. 350-359 ◽  
Author(s):  
H. B. Tou ◽  
G. J. Hancock
Keyword(s):  
Piecewise Linear ◽  
Separated Flows ◽  
Surface Singularity ◽  
List Type ◽  
Trailing Edge ◽  
Kutta Condition ◽  
First Order ◽  
Panel Methods ◽  
Total Head ◽  
Order Surface

Summary Simple first order surface singularity methods based on: (i) Smith and Hess uniform source panels plus a uniform vorticity around aerofoil profile, (ii) piecewise linear vorticity around aerofoil profile, with different assumption for Kutta condition, have been applied to attached flows and separated flows past an aerofoil/spoiler configuration, assuming an inviscid model. For separated flows, piecewise linear vorticity methods give reasonable results as long as small panel elements are taken in the region of the separations at the spoiler tip and aerofoil trailing edge. The Smith and Hess method gives results which do not agree too closely with the vorticity methods. There is doubt concerning uniqueness. Results have been compared using two different wake models; in one, the total head inside the wake is taken to be uniform, in the second, the static pressures along the separation streamlines are taken to be uniform. There appears to be a difference of about 5% in CL. It is not known why.

Experimental Investigation of Compressor Cascade Wakes

1982 ◽  
Author(s):  
D. E. Hobbs ◽  
J. H. Wagner ◽  
J. F. Dannenhoffer ◽  
R. P. Dring
Keyword(s):  
Experimental Investigation ◽  
Boundary Layers ◽  
Potential Flow ◽  
Compressor Cascade ◽  
Trailing Edge ◽  
Airfoil Surface ◽  
Flow Solver ◽  
Cascade Flow ◽  
Wake Modeling

This report discusses a cascade wake experiment intended to improve wake modeling in an airfoil analysis. The experiment included extensive measurements of the near and far wakes, trailing edge boundary layers, and airfoil surface static pressures. The measured wake displacement surface and computed boundary layers were used in conjunction with a cascade potential flow solver to demonstrate the feasibility of modeling the viscous aspects of cascade flow.

scholarly journals Note on the Physical Basis of the Kutta Condition in Unsteady Two-Dimensional Panel Methods

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
M. La Mantia ◽  
P. Dabnichki
Keyword(s):  
Pressure Difference ◽  
Energy Requirements ◽  
Aquatic Species ◽  
Biological Applications ◽  
Velocity Difference ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Wing Motion ◽  
Panel Methods ◽  
New Formulation

Force generation in avian and aquatic species is of considerable interest for possible engineering applications. The aim of this work is to highlight the theoretical and physical foundations of a new formulation of the unsteady Kutta condition, which postulates a finite pressure difference at the trailing edge of the foil. The condition, necessary to obtain a unique solution and derived from the unsteady Bernoulli equation, implies that the energy supplied for the wing motion generates trailing-edge vortices and their overall effect, which depends on the motion initial parameters, is a jet of fluid that propels the wing. The postulated pressure difference (the value of which should be experimentally obtained) models the trailing-edge velocity difference that generates the thrust-producing jet. Although the average thrust values computed by the proposed method are comparable to those calculated by assuming null pressure difference at the trailing edge, the latter (commonly used) approach is less physically meaningful than the present one, as there is a singularity at the foil trailing edge. Additionally, in biological applications, that is, for autonomous flapping, the differences ought to be more significant, as the corresponding energy requirements should be substantially altered, compared to the studied oscillatory motions.

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

Viscous tails in Hele-Shaw flow

1971 ◽  
Vol 46 (3) ◽  
pp. 569-576
Author(s):  
C. J. Wood
Keyword(s):  
Reynolds Number ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Quantitative Discrepancy ◽  
Edge Flow ◽  
Hele Shaw Cell

An experiment has been performed, using pulsed dye injection on an aerofoil in a Hele-Shaw cell. The purpose was to observe the form of the trailing-edge flow when the Reynolds number was high enough to permit separation and the initiation of a Kutta condition. The experiment provides a successful confirmation of the existence of a ‘viscous tail’ as predicted by Buckmaster (1970) although there is an unexplained quantitative discrepancy.

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.

scholarly journals A Review on Generation and Mitigation of Airfoil Self-Induced Noise

2021 ◽  
Vol 90 (1) ◽  
pp. 163-178
Author(s):  
Mohamed Ibren ◽  
Amelda Dianne Andan ◽  
Waqar Asrar ◽  
Erwin Sulaeman
Keyword(s):  
Parametric Design ◽  
Acoustic Scattering ◽  
Feedback Mechanism ◽  
Flow Topology ◽  
Trailing Edge ◽  
Airfoil Surface ◽  
Design Concepts ◽  
Acoustic Control ◽  
Passive Acoustic ◽  
And Control

A review on passive acoustic control of airfoil self-noise by means of porous trailing edge is presented. Porous surfaces are defined using various terms such as porosity, permeability, resistivity, porosity constant, dimensionless permeability, flow control severity and tortuosity. The primary purpose of this review paper is to provide key findings regarding the sources and mitigation techniques of self-induced noise generated by airfoils. In addition, various parametric design concepts were presented, which are critically important for porous-airfoil design specifications. Most research focus on experimentation with some recent efforts on numerical simulations. Detail study on flow topology is required to fully understand the unsteady flow nature. In general, noise on the airfoil surface is linked to the vortex shedding, instabilities on the surface, as well as feedback mechanism. In addition, acoustic scattering can be minimized by reducing extent of the porous region from the trailing edge while increasing resistivity. Moreover, blowing might also be another means of reducing noise near the trailing edge. Ultimately, understanding the flow physics well provides a way to unveil the unknowns in self-induced airfoil noise generation, mitigation, and control.

A B-Spline Higher-Order Panel Method Applied to Two-Dimensional Lifting Problem

2003 ◽  
Vol 47 (04) ◽  
pp. 290-298
Author(s):  
Chang-Sup Lee ◽  
Justin E. Kerwin
Keyword(s):  
Present Method ◽  
Gaussian Quadrature ◽  
Solution Process ◽  
Higher Order ◽  
Panel Method ◽  
Pressure Jump ◽  
Two Dimensional ◽  
Kutta Condition ◽  
B Spline ◽  
Panel Methods

A higher-order panel method based on B-spline representation for both the geometry and the solution is developed for the solution of the flow around two-dimensional lifting bodies. The influence functions due to the normal dipole and the source are separated into the singular and nonsingular parts; then the former is integrated analytically, whereas the latter is integrated using Gaussian quadrature. Through a desingularization process, the accuracy of the present method can be increased without limit to any order by selecting a proper numerical quadrature. A null pressure jump Kutta condition at the trailing edge is found to be effective in stabilizing the solution process and in predicting the correct solution. Numerical experiments indicate that the present method is robust and predicts the pressure distribution around lifting foils with far fewer panels than existing low-order panel methods.

Sound diffraction at a trailing edge

1981 ◽  
Vol 108 ◽  
pp. 443-460 ◽  
Author(s):  
S. W. Rienstra
Keyword(s):  
Vortex Shedding ◽  
Pulse Wave ◽  
Layer Structure ◽  
Harmonic Wave ◽  
Sound Field ◽  
Edge Condition ◽  
Trailing Edge ◽  
Kutta Condition ◽  
High Reynolds ◽  
Sound Diffraction

The diffraction of externally generated sound in a uniformly moving flow at the trailing edge of a semi-infinite flat plate is studied. In particular, the coupling of the sound field to the hydrodynamic field by way of vortex shedding from the edge is considered in detail, both in inviscid and in viscous flow.In the inviscid model the (two-dimensional) diffracted fields of a cylindrical pulse wave, a plane harmonic wave and a plane pulse wave are calculated. The viscous proess of vortex shedding is represented by an appropriate trailing-edge condition. Two specific cases are compared, in one of which the full Kutta condition is applied, and in the other no vortex shedding is permitted. The results show good agreement with Heavens’ (1978) observations from his schlieren photographs, and confirm his conclusions. It is further demonstrated, by an explicit expression, that the sound power absorbed by the wake may be positive or negative, depending on Mach number and source position. So the process of vortex shedding does not necessarily imply an attenuation of the sound.In the viscous model a high-Reynolds-number approximation is constructed, based on a triple-deck boundary-layer structure, matching the harmonic plane wave outer solution to a known incompressible inner solution near the edge, to obtain the viscous correction to the Kutta condition.

A theoretical model for multiply connected wings

1998 ◽  
Vol 9 (6) ◽  
pp. 607-634
Author(s):  
P. BASSANINI ◽  
C. M. CASCIOLA ◽  
M. R. LANCIA ◽  
R. PIVA
Keyword(s):  
Three Dimensional ◽  
Inviscid Flow ◽  
Linear Functional Equation ◽  
Trailing Edge ◽  
Vortex Sheets ◽  
Kutta Condition ◽  
Multiply Connected ◽  
Flow Solution ◽  
Multiplicative Factor

Steady incompressible inviscid flow past a three-dimensional multiconnected (toroidal) aerofoil with a sharp trailing edge TE is considered, adopting for simplicity a linearized analysis of the vortex sheets that collect the released vorticity and form the trailing wake. The main purpose of the paper is to discuss the uniqueness of the bounded flow solution and the role of the eigenfunction. A generic admissible flow velocity u has an unbounded singularity at TE; and the physical flow solution requires the removal of the divergent part of u (the Kutta condition). This process yields a linear functional equation along the trailing edge involving both the normal vorticity ω released into the wake, and the multiplicative factor of the eigenfunction, a1. Uniqueness is then shown to depend upon the topology of the trailing edge. If δTE=[empty ], as, for example, in an annular-aerofoil configuration, both ω and a1 are uniquely determined by the Kutta condition, and the bounded flow u is unique. If δTE≠[empty ], as, for example, in a connected-wing configuration, there is an infinity of bounded flows, parametrized by a1. Numerical results of relevance for these typical configurations are presented to show the different role of the eigenfunction in the two cases.

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