Download presentation

Presentation is loading. Please wait.

1
**Boundary Layer Analyses**

Module 3.4: Wind Engineering L. Sankar School of Aerospace Engineering

2
**Outline Thwaites Method for Computing Laminar Boundary Layers**

Michel’s Transition Criterion Head’s method for Turbulent Flow Squire-Young Formula for Drag Prediction See for background material.

3
Thwaites’ method I This is an empirical method based on the observation that most laminar boundary layers obey the following relationship. Ref: Thawites, B., Incompressible Aerodynamics, Clarendon Press, Oxford, 1960: Thwaites recommends A = 0.45 and B = 6 as the best empirical fit.

4
**Thwaites’ Method II The above equation may be analytically integrated**

yielding For blunt bodies such as airfoils, the edge velocity ue is zero at x=0, the stagnation point. For sharp nosed geometries such as a flat plate, the momentum thickness q is zero at the leading edge. Thus, the term in the square bracket always vanishes. The integral may be evaluated, at least numerically, when ue is known.

5
Thwaites’ method III After q is found, the following relations are used to compute the shape factor H.

6
Thwaites’ method IV After q is found, we can also find skin friction coefficient from the following empirical curve fits:

7
**MATLAB Code from PABLO %--------Laminar boundary layer**

lsep = 0; trans=0; endofsurf=0; theta(1) = sqrt(0.075/(Re*dueds(1))); i = 1; while lsep ==0 & trans ==0 & endofsurf ==0 lambda = theta(i).^2*dueds(i)*Re; % test for laminar separation if lambda < -0.09 lsep = 1; itrans = i; break; end; H(i) = fH(lambda); L = fL(lambda); cf(i) = 2*L./(Re*theta(i)); if i>1, cf(i) = cf(i)./ue(i); end; i = i+1; % test for end of surface if i> n endofsurf = 1; itrans = n; break; end; K = 0.45/Re; xm = (s(i)+s(i-1))/2; dx = (s(i)-s(i-1)); coeff = sqrt(3/5); f1 = ppval(spues,xm-coeff*dx/2); f1 = f1^5; f2 = ppval(spues,xm); f2 = f2^5; f3 = ppval(spues,xm+coeff*dx/2); f3 = f3^5; dth2ue6 = K*dx/18*(5*f1+8*f2+5*f3); theta(i) = sqrt((theta(i-1).^2*ue(i-1).^6 + dth2ue6)./ue(i).^6); % test for transition rex = Re*s(i)*ue(i); ret = Re*theta(i)*ue(i); retmax = 1.174*(rex^ *rex^(-0.54)); if ret>retmax trans = 1; itrans = i;

8
**Reationship between l and H**

function H = fH(lambda); if lambda < 0 if lambda==-0.14 lambda=-0.139; end; H = /(lambda+0.14); elseif lambda >= 0 H = *lambda *lambda.^2;

9
**Skin Friction function L = fL(lambda); if lambda < 0**

end; L = *lambda +(0.018*lambda)./(lambda+0.107); elseif lambda >= 0 L = *lambda - 1.8*lambda.^2; We invoke (or call this function) at each i-location as follows: H(i) = fH(lambda); L = fL(lambda); cf(i) = 2*L./(Re*theta(i));

10
**Transition prediction**

A number of methods are available for predicting transition. Examples: Eppler’s method Michel’s method Wind turbine designers and laminar airfoil designers tend to use Eppler’s method Aircraft designers tend to use Michel’s method.

11
**Michel’s Method for Transition Prediction**

% test for transition rex = Re*s(i)*ue(i); ret = Re*theta(i)*ue(i); retmax = 1.174*(rex^ *rex^(-0.54)); if ret>retmax trans = 1; itrans = i; end;

12
Turbulent Flow A number of CFD methods, and integral boundary layer methods exist. The most popular of these is Head’s method. This method is used in a number of computer codes, including PABLO.

13
**Head’s Method Von Karman Momentum Integral Equation:**

A new shape parameter H1: Evolution of H1 along the boundary layer: These two ODEs are solved by marching from transition location to trailing edge.

14
**Empirical Closure Relations**

Ludwig-Tillman relationship: Turbulent separation occurs when H1 = 3.3

15
**Coding Closure Relations in Head’s Method**

function y=H1ofH(H); if H <1.1 y = 16; else if H <= 1.6 y = *(H-1.1).^(-1.287); y = *(H ).^(-3.064); end; function H=HofH1(H1); if H1 <= 3.32 H = 3; elseif H1 < 5.3 H = *(H1-3.3).^(-0.326); else H = *(H1-3.3).^(-0.777); end function cf = cfturb(rtheta,H); cf = 0.246*(10.^(-0.678*H))*rtheta.^(-0.268);

16
**Drag Prediction Squire-Young Formula**

Similar presentations

Presentation is loading. Please wait....

OK

Anoop Samant Yanyan Zhang Saptarshi Basu Andres Chaparro

Anoop Samant Yanyan Zhang Saptarshi Basu Andres Chaparro

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on the greatest dictator of the world Ppt on centring point Nose anatomy and physiology ppt on cells Ppt on marketing management project Ppt on target marketing Ppt on obesity prevention in children Ppt on computer software and languages Free ppt on germination of seeds Ppt on virtual file system Animated ppt on magnetism quiz