Airfoils with separation and the resulting wakes

A viscous/inviscid interaction method is described and has been used to calculate flows around four distinctly different airfoils as a function of angle of attack. It comprises an inviscid-flow method based on conformal mapping, a boundary-layer procedure based on the numerical solution of differential equations and an algebraic eddy viscosity. The results are in close agreement with experiment up to angles close to stall. In one case, where the airfoil thickness is large, small difficulties were experienced and are described. The method is shown to be capable of obtaining results with large flow separation and quantifies the role of transition on the lift coefficient.

Download Full-text

Prediction of Viscous Effects in Steady Transonic Flow Past an Aerofoil

Aeronautical Quarterly ◽

10.1017/s0001925900008672 ◽

1979 ◽

Vol 30 (3) ◽

pp. 485-505 ◽

Cited By ~ 20

Author(s):

M.R. Collyer ◽

R.C. Lock

Keyword(s):

Boundary Layer ◽

Shock Waves ◽

Transonic Flow ◽

Lift Coefficient ◽

Inviscid Flow ◽

Viscous Effects ◽

Flow Past ◽

Boundary Layer Development ◽

Transition Position ◽

Realistic Representation

SummaryAn account is given of a numerical method for calculating transonic flow past an aerofoil with an allowance for viscous effects, providing that the boundary layer remains fully attached over the aerofoil surface. The method has been developed by combining, in an iterative manner, calculations of the inviscid flow with calculations of the compressible boundary layer and wake. The solution for the inviscid flow is obtained by an iterative scheme, originally established by Garabedian & Korn, which has been modified to give a more realistic representation of shock waves. The boundary-layer development is treated as laminar initially; at a certain transition position a turbulent boundary layer is assumed to develop, and this is determined by the lag-entrainment method of Green et al. Comparisons of the results from the numerical scheme with some experimental measurements are shown for various examples in which shock waves of moderate strength are present. The method predicts, with reasonable accuracy, both the detailed pressure distribution and the variation of drag coefficient with lift coefficient.

Download Full-text

Analysis of the Effect of Vortex Generator Spacing on Boundary Layer Flow Separation Control

Applied Sciences ◽

10.3390/app9245495 ◽

2019 ◽

Vol 9 (24) ◽

pp. 5495 ◽

Cited By ~ 4

Author(s):

Xin-kai Li ◽

Wei Liu ◽

Ting-jun Zhang ◽

Pei-ming Wang ◽

Xiao-dong Wang

Keyword(s):

Boundary Layer ◽

Wind Tunnel ◽

Kinetic Energy ◽

Flow Control ◽

Flow Separation ◽

Lift Coefficient ◽

Boundary Layer Separation ◽

Wind Tunnel Experiments ◽

Flow Separation Control ◽

Layer Separation

During the operation of wind turbines, flow separation appears at the blade roots, which reduces the aerodynamic efficiency of the wind turbine. In order to effectively apply vortex generators (VGs) to blade flow control, the effect of the VG spacing (λ) on flow control is studied via numerical calculations and wind tunnel experiments. First, the large eddy simulation (LES) method was used to calculate the flow separation in the boundary layer of a flat plate under an adverse pressure gradient. The large-scale coherent structure of the boundary layer separation and its evolution process in the turbulent flow field were analyzed, and the effect of different VG spacings on suppressing the boundary layer separation were compared based on the distance between vortex cores, the fluid kinetic energy in the boundary layer, and the pressure loss coefficient. Then, the DU93-W-210 airfoil was taken as the research object, and wind tunnel experiments were performed to study the effect of the VG spacing on the lift–drag characteristics of the airfoil. It was found that when the VG spacing was λ/H = 5 (H represents the VG’s height), the distance between vortex cores and the vortex core radius were approximately equal, which was more beneficial for flow control. The fluid kinetic energy in the boundary layer was basically inversely proportional to the VG spacing. However, if the spacing was too small, the vortex was further away from the wall, which was not conducive to flow control. The wind tunnel experimental results demonstrated that the stall angle-of-attack (AoA) of the airfoil with the VGs increased by 10° compared to that of the airfoil without VGs. When the VG spacing was λ/H = 5, the maximum lift coefficient of the airfoil with VGs increased by 48.77% compared to that of the airfoil without VGs, the drag coefficient decreased by 83.28%, and the lift-to-drag ratio increased by 821.86%.

Download Full-text

Separation and magnetohydrodynamics

Journal of Fluid Mechanics ◽

10.1017/s0022112069000292 ◽

1969 ◽

Vol 38 (3) ◽

pp. 481-498 ◽

Cited By ~ 25

Author(s):

John Buckmaster

Keyword(s):

Magnetic Field ◽

Boundary Layer ◽

Stagnation Point ◽

Linear Equations ◽

Inviscid Flow ◽

Transverse Magnetic ◽

Magnetic Reynolds Number ◽

Boundary Layer Equations ◽

Rear Stagnation Point

This paper is an investigation of MHD boundary layers in a transverse magnetic field when the magnetic Reynolds number (Rm) is small. The main purpose is to understand something about the suppression of separation by a strong magnetic field, with particular emphasis on the behaviour near a rear stagnation point. Given anO(1) inviscid flow it is shown that there is a critical value ofN, the interaction parameter, to completely suppress separation. This value is one half that proposed by Leibovich (1967), a discrepancy that is due to the non-regularity of the boundary-layer equations at a rear stagnation point, a possibility that Leibovich did not consider in his solution. Model linear equations suggest the true role of Leibovich's solution. The possibility of a viscous wake leaving the rear stagnation point is considered and it is suggested that one doesnotarise from vorticity generated in the boundary layer.

Download Full-text

Calculation of the Flow Along the S1 Stream Surface With Inviscid-Viscous Interaction Method

Volume 1: Turbomachinery ◽

10.1115/88-gt-62 ◽

1988 ◽

Author(s):

Kang Shun ◽

Huang Yongshen ◽

Wang Zhongqi

Keyword(s):

Boundary Layer ◽

Turbulent Boundary Layer ◽

Iterative Method ◽

Rate Equation ◽

Iteration Method ◽

Inviscid Flow ◽

Experimental Results ◽

Interaction Method ◽

Stream Surface ◽

Entrainment Coefficient

As an extension of the author’s previous work, this paper proposes a mixed iterative method for calculating the interactions of boundary layer with inviscid flow on S1 stream surface. It is shown from the comparison with experimental results that the iteration method given in this paper has a high calculation accuracy. In addition, the rate equation of the entrainment coefficient adapted for the turbulent boundary layer in the S1 stream surface has been established in this paper. The predicted results show that taking this equation as the supplemental equation for solving the turbulent boundary layer on cascade blades can improve the accuracy of calculation of the turbulent boundary layer on cascade blades.

Download Full-text

Interacting Turbulent Boundary Layer over a Wavy Wall

Journal of Heat Transfer ◽

10.1115/1.3450876 ◽

1978 ◽

Vol 100 (4) ◽

pp. 678-683 ◽

Cited By ~ 2

Author(s):

A. Polak ◽

M. J. Werle

Keyword(s):

Boundary Layer ◽

Turbulent Boundary Layer ◽

Eddy Viscosity ◽

Relaxation Method ◽

Inviscid Flow ◽

Reynolds Numbers ◽

Flow Conditions ◽

Boundary Layer Equations ◽

Eddy Viscosity Model ◽

Turbulence Effects

This paper is concerned with the two-dimensional supersonic flow of a thick turbulent boundary layer over a train of relatively small wave-like protuberances. The flow conditions and the geometry are such that there exists a strong interaction between the viscous and inviscid flow. Here the interacting boundary layer equations are solved numerically using a time-like relaxation method with turbulence effects represented by the inclusion of the eddy viscosity model of Cebeci and Smith. Results are presented for flow over a train of up to six waves for Mach numbers of 2.5 and 3.5, Reynolds numbers of 10 and 32 × 106/meter, and wall temperature ratios Tw/T0 of 0.4 and 0.8. Limited comparisons with independent experimental and analytical results are also given.

Download Full-text

Numerical Simulation of Flow Around Airfoil With Non-Linear RANS Model

Volume 1A: Symposia, Part 2 ◽

10.1115/ajkfluids2015-02777 ◽

2015 ◽

Cited By ~ 1

Author(s):

Wei Qun ◽

Chen Hongxun ◽

Ma Zheng

Keyword(s):

Flow Separation ◽

Eddy Viscosity ◽

General Purpose ◽

Shear Strain Rate ◽

Eddy Viscosity Model ◽

Ansys Cfx ◽

Non Linear ◽

Attached Flow ◽

Wind Turbine Airfoil ◽

Large Flow

The standard k-ε eddy viscosity model is the most commonly used model in computational fluid dynamics and perform well in application, but less effective for flows with high mean shear rate or massive separation. An non-linear eddy viscosity k-ε model was developed to compensate the deficit, in which the Cμ determined by an expression of shear strain rate rather than a constant on the base of experimental and DNS data. Two-dimensional CFD simulations were carried out by proposed NL k-ε model and standard k-ε model for wind-turbine airfoil S809 with the general purpose CFD code ANSYS CFX 12.1. Results show that standard k-ε can predict the flow around the airfoil for angles of attack with attached flow, but is not qualified for flow at angles of attack with strong flow separation, whereas non-linear k-ε model can improve the accuracy of the performance coefficients to some extent, and when large flow separation generates, non-linear k-ε model can improve the accuracy of pressure distribution around the airfoil and simulate the flow separation more correctly.

Download Full-text

A Statistical Study of Process Variables to Optimize a High Speed Curtain Coater: Part I

TAPPI Journal ◽

10.32964/tj8.1.20 ◽

2009 ◽

Vol 8 (1) ◽

pp. 20-26 ◽

Cited By ~ 1

Author(s):

PEEYUSH TRIPATHI ◽

MARGARET JOYCE ◽

PAUL D. FLEMING ◽

MASAHIRO SUGIHARA

Keyword(s):

Boundary Layer ◽

Experimental Design ◽

High Speed ◽

Statistical Study ◽

Process Variables ◽

High Speeds ◽

The Stability ◽

Air Removal ◽

Removal System

Using an experimental design approach, researchers altered process parameters and material prop-erties to stabilize the curtain of a pilot curtain coater at high speeds. Part I of this paper identifies the four significant variables that influence curtain stability. The boundary layer air removal system was critical to the stability of the curtain and base sheet roughness was found to be very important. A shear thinning coating rheology and higher curtain heights improved the curtain stability at high speeds. The sizing of the base sheet affected coverage and cur-tain stability because of its effect on base sheet wettability. The role of surfactant was inconclusive. Part II of this paper will report on further optimization of curtain stability with these four variables using a D-optimal partial-facto-rial design.

Download Full-text