Solution of Navier-Stokes equations near the trailing edge of a plate

1986 ◽  
Vol 20 (4) ◽  
pp. 644-647
Author(s):  
V. V. Bogolepov
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations

scholarly journals Navier-Stokes Analysis of Unsteady Transonic Flows Through Gas Turbine Cascades With and Without Coolant Ejection

1997 ◽  
Author(s):  
T. Tanuma ◽  
N. Shibukawa ◽  
S. Yamamoto
Keyword(s):  
Gas Turbine ◽  
Stokes Equations ◽  
Viscous Flows ◽  
Navier Stokes ◽  
Implicit Time ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Turbine Cascades ◽  
Annular Cascade

An implicit time-marching higher-order accurate finite-difference method for solving the two-dimensional compressible Navier-Stokes equations was applied to the numerical analyses of steady and unsteady, subsonic and transonic viscous flows through gas turbine cascades with trailing edge coolant ejection. Annular cascade tests were carried out to verify the accuracy of the present analysis. The unsteady aerodynamic mechanisms associated with the interaction between the trailing edge vortices and shock waves and the effect of coolant ejection were evaluated with the present analysis.

On the flow near the trailing edge of a flat plate

1968 ◽  
Vol 306 (1486) ◽  
pp. 275-290 ◽  
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Multiplicative Constant ◽  
Boundary Layer Approximation ◽  
Uniform Shear

It is shown that the boundary layer approximation to the flow of a viscous fluid past a flat plate of length l , generally valid near the plate when the Reynolds number Re is large, fails within a distance O( lRe -3/4 ) of the trailing edge. The appropriate governing equations in this neighbourhood are the full Navier- Stokes equations. On the basis of Imai (1966) these equations are linearized with respect to a uniform shear and are then completely solved by means of a Wiener-Hopf integral equation. The solution so obtained joins smoothly on to that of the boundary layer for a flat plate upstream of the trailing edge and for a wake downstream of the trailing edge. The contribution to the drag coefficient is found to be O ( Re -3/4 ) and the multiplicative constant is explicitly worked out for the linearized equations.

scholarly journals The numerical solution of the asymptotic equations of trailing edge flow

1974 ◽  
Vol 340 (1620) ◽  
pp. 91-111 ◽  
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Asymptotic Equations ◽  
Displacement Thickness

According to Stewartson (1969, 1974) and to Messiter (1970), the flow near the trailing edge of a flat plate has a limit structure for Reynolds number Re →∞ consisting of three layers over a distance O (Re -3/8 ) from the trailing edge: the inner layer of thickness O ( Re -5/8 ) in which the usual boundary layer equations apply; an intermediate layer of thickness O ( Re -1/2 ) in which simplified inviscid equations hold, and the outer layer of thickness O ( Re -3/8 ) in which the full inviscid equations hold. These asymptotic equations have been solved numerically by means of a Cauchy-integral algorithm for the outer layer and a modified Crank-Nicholson boundary layer program for the displacement-thickness interaction between the layers. Results of the computation compare well with experimental data of Janour and with numerical solutions of the Navier-Stokes equations by Dennis & Chang (1969) and Dennis & Dunwoody (1966).

scholarly journals Some Modelling Issues on Trailing Edge Vortex Shedding

1999 ◽  
Author(s):  
Wei Ning ◽  
Li He
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Numerical Study ◽  
Independent Solution ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Averaged Equations ◽  
Edge Vortex

A numerical study has been carried out to investigate modelling issues on trailing edge vortex shedding. The vortex shedding from a circular cylinder and a VKI turbine blade is calculated using a 2-D unsteady multi-block Navier-Stokes solver. The unsteady stresses are calculated from the unsteady solutions. The distributions of the unsteady stresses are analysed and compared for the cylinder case and the cascade case, respectively. The time-averaged equations are then solved and the effectiveness of the “unsteady stresses” in suppressing trailing edge vortex shedding is checked. Finally, the time-independent solution produced by solving the time-averaged equations is compared with the time-averaged solution obtained by integrating the unsteady solutions. The numerical results have demonstrated that a time-independent vortex shedding solution can be achieved by solving the Navier-Stokes equations with the unsteady stresses and the time-averaged effects of the vortex shedding can be included.

scholarly journals Numerical Prediction of Trailing Edge Wake Shedding

1997 ◽  
Author(s):  
Andrea Arnone ◽  
Roberto Pacciani
Keyword(s):  
Vortex Shedding ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Mixing Length ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Turbine Stator ◽  
Edge Vortex ◽  
Stator Blade

A recently developed, time-accurate multigrid solver has been used to investigate the capability of predicting trailing edge vortex shedding by means of the Reynolds-Averaged Navier-Stokes equations and algebraic turbulence models. The study has been performed on a turbine stator blade for which experiments have recently been carried out. Calculations using a mixing-length based model for turbulence closure indicate the inception of shedding even on relatively coarse trailing edge (C-type) grids.

scholarly journals Numerical Study of Variable Camber Continuous Trailing Edge Flap at Off-Design Conditions

Energies ◽  
2019 ◽  
Vol 12 (16) ◽  
pp. 3185 ◽  
Author(s):  
Mohammed Abdul Raheem ◽  
Prasetyo Edi ◽  
Amjad A. Pasha ◽  
Mustafa M. Rahman ◽  
Khalid A. Juhany
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Computational Study ◽  
Advanced Technology ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Parabolic Profile ◽  
Trailing Edge Flap ◽  
Laminar Flow Control

Numerical simulations are performed to study the outboard airfoil of advanced technology regional aircraft (ATRA) wings with five different variable camber continuous trailing edge flap (VCCTEF) configurations. The computational study aims to improve the aerodynamic efficiency of the airfoil under cruise conditions. The design of outboard airfoil complies with the hybrid laminar flow control design criteria. This work is unique in terms of analysis of the effects of VCCTEF on the ATRA wing’s outboard airfoil during the off-design condition. The Reynolds–Averaged Navier–Stokes equations coupled with the Spalart-Allmaras turbulence model are employed to perform the simulations for the baseline case and VCCTEF configurations. The current computational study is performed at an altitude of 10 km with a cruise Mach number of 0.77 and a Reynolds number of 2.16 × 107. Amongst all five configurations of VCCTEF airfoils studied, a flap having a parabolic profile (VCCTEF 123) configuration shows the maximum airfoil efficiency and resulted in an increase of 6.3% as compared to the baseline airfoil.

Asymptotic analysis of a linearized trailing edge flow

1972 ◽  
Vol 6 (3) ◽  
pp. 327-347 ◽  
Author(s):  
K. Capell
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Wake Region ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Appl Math ◽  
Edge Flow

An Oseén type linearization of the Navier-Stokes equations is made with respect to a uniform shear flow at the trailing edge of a flat plate. Asymptotic expansions are obtained to describe a symmetrical merging flow for distances from the trailing edge that are, in a certain sense, large. Expansions for three regions are found:(i) a wake region,(ii) an inviscid region, and(iii) an upstream lower order boundary layer.The results are compared with those of Hakkinen and O'Neil (Douglas Aircraft Co. Report, 1967) and Stewartson (Proc. Roy. Soc. Ser. A 306 (1968)). They are further related to the results of Stewartson (Mathematika 16 (1969)) and Messiter (SIAM J. Appl. Math. 18 (1970)).

On the development of the wake behind the trailing edge of a flat plate

1970 ◽  
Vol 42 (3) ◽  
pp. 627-638 ◽  
Author(s):  
S. H. Smith
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Constant Velocity ◽  
Stokes Equations ◽  
Boundary Layer Theory ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations

A stream with constant velocity U is impulsively started at time t = 0 past the trailing edge of a semi-infinite flat plate. According to boundary-layer theory, it is found that the flow at a distance x downstream from the trailing edge is unaware of the presence of the plate when x > Ut; at time t = x/U there is then a discontinuity in the velocity normal to the plate. It is the neglect of diffusion parallel to the axis of the plate that introduces the discontinuity, and when the complete Navier–Stokes equations are considered for t ≃ x/U, a solution is found that can be matched with that gained from boundary-layer arguments.

scholarly journals Улучшение несущих свойств крыла на взлетно-посадочных режимах с помощью системы управления пограничным слоем с использованием актуаторов эжекторного типа

2018 ◽  
Vol 44 (15) ◽  
pp. 71
Author(s):  
А.В. Воеводин ◽  
А.А. Корняков ◽  
Д.А. Петров ◽  
А.С. Петров ◽  
Г.Г. Судаков
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Stokes Equations ◽  
Experimental Studies ◽  
Gas Jet ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Flow Past ◽  
Edge Based

AbstractA device making it possible to control of the flow past a wing at low flight speeds is proposed. The device comprises an ejector-type actuator that simultaneous sucks the boundary layer on the upper surface and blows a gas jet in the vicinity of the trailing edge. Based on the Reynolds-averaged Navier–Stokes equations, a mathematical model of an ejector-type actuator is developed and experimental studies are carried out.

scholarly journals Instability of local supersonic regions over a flat-sided airfoil with a blunt trailing edge

2021 ◽  
Vol 2103 (1) ◽  
pp. 012208
Author(s):  
A. Kuzmin
Keyword(s):  
Free Stream ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Blunt Trailing Edge ◽  
Computational Mesh ◽  
Free Stream Mach Number ◽  
The Given

Abstract The two-dimensional turbulent transonic flow over a symmetric flat-sided airfoil with a blunt trailing edge is studied numerically. Solutions of the Reynolds-averaged Navier-Stokes equations are obtained with a finite-volume solver on a fine computational mesh. The non-uniqueness of flow field in certain bands of the given free-stream Mach number and angle of attack is demonstrated. Intricate dependence of the lift coefficient on the free-stream parameters is discussed. Adverse free-stream parameters, which admit abrupt changes of the flow structure and lift, are identified.

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