Numerical and asymptotic solutions for the supersonic flow near the trailing edge of a flat plate at incidence

1974 ◽  
Vol 63 (4) ◽  
pp. 641-656 ◽  
Author(s):  
P. G. Daniels
Keyword(s):  
Reynolds Number ◽  
Flat Plate ◽  
Analytic Solutions ◽  
Supersonic Stream ◽  
Angle Of Incidence ◽  
Trailing Edge ◽  
Order Of Magnitude ◽  
Stall Angle ◽  
High Reynolds ◽  
Critical Order

The equations which govern the flow at high Reynolds number in the vicinity of the trailing edge of a finite flat plate at incidence to a uniform supersonic stream are solved numerically using a finite-difference procedure. The critical order of magnitude of the angle of incidence α* for the occurrence of separation on one side of the plate is α* = O(R−¼) (Brown & Stewartson 1970), where R is a representative Reynolds number for the flow, and results are computed for three such values of α* which characterize the possible behaviour of the flow above the plate. The final set of computations leads to a numerical value for the trailing-edge stall angle α*s, the angle of incidence which just causes the flow to separate at the trailing edge of the plate. Analytic solutions are available in the form of asymptotic expansions near the trailing edge in terms of the scaled variable of order R−⅜. A multi-layer-type of expansion which occurs in the case α* = αs* is presented in detail for comparison with the computed solution.

Trailing-edge stall

1970 ◽  
Vol 42 (3) ◽  
pp. 561-584 ◽  
Author(s):  
S. N. Brown ◽  
K. Stewartson
Keyword(s):  
Boundary Layer ◽  
Complete Solution ◽  
Leading Edge ◽  
Asymptotic Solutions ◽  
Angle Of Incidence ◽  
Trailing Edge ◽  
Boundary Layer Equations ◽  
Order Of Magnitude ◽  
Stall Angle ◽  
Fundamental Equations

A study is made of the laminar flow in the neighbourhood of the trailing edge of an aerofoil at incidence. The aerofoil is replaced by a flat plate on the assumption that leading-edge stall has not taken place. It is shown that the critical order of magnitude of the angle of incidence α* for the occurrence of separation on one side of the plate is$\alpha^{*} = O(R^{\frac{1}{16}})$, whereRis a representative Reynolds number, for incompressible flow, and α* =O(R−¼) for supersonic flow. The structure of the flow is determined by the incompressible boundary-layer equations but with unconventional boundary conditions. The complete solution of these fundamental equations requires a numerical investigation of considerable complexity which has not been undertaken. The only solutions available are asymptotic solutions valid at distances from the trailing edge that are large in terms of the scaled variable of orderR−⅜, and a linearized solution for the boundary layer over the plate which gives the antisymmetric properties of the aerofoil at incidence. The value of α* for which separation occurs is the trailing-edge stall angle and an estimate is obtained from the asymptotic solutions. The linearized solution yields an estimate for the viscous correction to the circulation determined by the Kutta condition.

scholarly journals Trailing-edge dynamics and morphing of a deformable flat plate at high Reynolds number by time-resolved PIV

2014 ◽  
Vol 47 ◽  
pp. 41-54 ◽  
Author(s):  
M. Chinaud ◽  
J.F. Rouchon ◽  
E. Duhayon ◽  
J. Scheller ◽  
S. Cazin ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Flat Plate ◽  
High Reynolds Number ◽  
Trailing Edge ◽  
Time Resolved ◽  
High Reynolds

Vortex Shedding Analysis in the Wake of a Flat Plate at Low Incidence and Low Reynolds Number

2021 ◽  
Author(s):  
Bastav Borah ◽  
Anand Verma ◽  
Vinayak Kulkarni ◽  
Ujjwal K. Saha
Keyword(s):  
Reynolds Number ◽  
Velocity Field ◽  
Flat Plate ◽  
Vortex Shedding ◽  
Low Reynolds Number ◽  
General Tendency ◽  
Flat Plates ◽  
Trailing Edge ◽  
Low Reynolds ◽  
Low Incidence

Abstract Vortex shedding phenomenon leads to a number of different features such as flow induced vibrations, fluid mixing, heat transfer and noise generation. With respect to aerodynamic application, the intensity of vortex shedding and the size of vortices play an essential role in the generation of lift and drag forces on an airfoil. The flat plates are known to have a better lift-to-drag ratio than conventional airfoils at low Reynolds number (Re). A better understanding of the shedding behavior will help aerodynamicists to implement flat plates at low Re specific applications such as fixed-wing micro air vehicle (MAV). In the present study, the shedding of vortices in the wake of a flat plate at low incidence has been studied experimentally in a low-speed subsonic wind tunnel at a Re of 5 × 104. The velocity field in the wake of the plate is measured using a hot wire anemometer. These measurements are taken at specific points in the wake across the flow direction and above the suction side of the flat plate. The velocity field is found to oscillate with one dominant frequency of fluctuation. The Strouhal number (St), calculated from this frequency, is computed for different angles of attack (AoA). The shedding frequency of vortices from the trailing edge of the flat plate has a general tendency to increase with AoA. In this paper, the generation and subsequent shedding of leading edge and trailing edge vortices in the wake of a flat plate are discussed.

The Local Analytic Numerical Method for the Double Vortex Combustor Flow

1985 ◽  
Author(s):  
J. He ◽  
B. Q. Zhang
Keyword(s):  
Reynolds Number ◽  
Analytic Solutions ◽  
Navier Stokes ◽  
Hyperbolic Function ◽  
Navier Stokes Equation ◽  
One Dimensional ◽  
New Type ◽  
High Reynolds ◽  
The One ◽  
Coarse Grids

A new hyperbolic function discretization equation for two dimensional Navier-Stokes equation in the stream function vorticity from is derived. The basic idea of this method is to integrat the total flux of the general variable ϕ in the differential equations, then incorporate the local analytic solutions in hyperbolic function for the one-dimensional linearized transport equation. The hyperbolic discretization (HD) scheme can more accurately represent the conservation and transport properties of the governing equation. The method is tested in a range of Reynolds number (Re=100~2000) using the viscous incompressible flow in a square cavity. It is proved that the HD scheme is stable for moderately high Reynolds number and accurate even for coarse grids. After some proper extension, the method is applied to predict the flow field in a new type combustor with air blast double-vortex and obtained some useful results.

Bubble friction drag reduction in a high-Reynolds-number flat-plate turbulent boundary layer

2006 ◽  
Vol 552 (-1) ◽  
pp. 353 ◽  
Author(s):  
WENDY C. SANDERS ◽  
ERIC S. WINKEL ◽  
DAVID R. DOWLING ◽  
MARC PERLIN ◽  
STEVEN L. CECCIO
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Drag Reduction ◽  
Flat Plate ◽  
High Reynolds Number ◽  
Friction Drag ◽  
High Reynolds ◽  
Friction Drag Reduction

Asymmetric trailing-edge flows at high Reynolds number

1980 ◽  
Author(s):  
J. CLEARY ◽  
C. HORSTMAN ◽  
H. SEEGMILLER ◽  
P. VISWANATH
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Trailing Edge ◽  
High Reynolds
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