What are the factors necessary for flow separation? Explain its consequences.
For flow separation to occur, there should be two factors. One is the presence of viscosity and the other is adverse pressure gradient. In inviscid flow, you can never expect flow separation even if there is adverse pressure gradient. Flow separation can be averted if the flow has significant energy to overcome the adverse pressure gradient. Sometimes, energizing the flow by introducing turbulence helps out to avert this. When flow separates, the pressure drag component increases. Therefore, in airfoils major efforts have to be taken to prevent such a separation.
Consider a velocity potential given by phi = x^2 - z^2. Determine the streamfunction of this flow and plot it using MATLAB. Also plot the velocity potential contour and streamlines on the same graph.
clear all; [x z] = meshgrid(0:0.04:3); velocitypotential = x.^2 - z.^2; contourf(x,z,velocitypotential,100); title('Contours of Velocity Potential'); set(gca,'fontsize',20); hold on; figure(2); [x z] = meshgrid(0:0.08:3); velocitypotential = x.^2 - z.^2; contourf(x,z,velocitypotential,100); title('Contours of Velocity Potential'); set(gca,'fontsize',20); hold on; startx = 0:0.08:3; starty = 0:0.08:3; u = -2*x; w = 2*z; streamline(x,z,u,w,startx,starty); title('Contour Plot of Velocity Potential with Streamlines'); figure(3); streamline(x,z,u,w,startx,starty); hold on; quiver(x,z,u,w,1.5); set(gca,'fontsize',20); title('Streamlines with Velocity Vectors');
Discuss the effect of camber on the lift coefficient vs angle of attack graph.
Camber does not contribute towards altering the slope of the lift coefficient vs angle of attack graph. It merely affects the zero lift angle of attack. A positive camber shifts the zero lift angle of attack towards the negative side and vice versa for a negative camber. However restraints should be kept on the maximum camber that is allotted to an airfoil. Always having higher camber is not preferred. For one thing, manufacturing would be difficult. The other more aerodynamic reason would be that flow separation possibility would increase considerably. A careful trade-off between various factors should be kept in mind while designing airfoils.