Starting from the basic principles, derive an expression to compute the lift coefficient when the free stream Mach number equals to 0.8.
Added by Melissa D.
Step 1
It is defined as: \[ C_L = \frac{L}{q S} \] where \( L \) is the lift force, \( q \) is the dynamic pressure, and \( S \) is the reference area of the airfoil or aircraft. Show more…
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Adi S.
Consider an airfoil in a Mach 0.5 freestream. At a given point on the airfoil, the local Mach number is 0.86. Calculate the pressure coefficient at that point. [Note: In an incompressible flow, the pressure coefficient at any point in the flow is a unique function of the local velocity at that point and the freestream velocity. In the present problem, we see that the Mach number is the relevant property for a compressible flow—not velocity. The pressure coefficient for an inviscid compressible flow is a unique function of the local Mach number and the freestream Mach number.]
Consider a flat plate airfoil in supersonic flow. The real drag coefficient should be a sum of wave drag and friction drag: C_D = c_d + C_f, where C_f is the friction drag, which is assumed to be a constant. And C_D = (4α^2)/(√(M_∞^2-1)) for a given freestream Mach number M_∞ > 1.2. Write the expression of lift-to-drag ratio (C_L/C_D), find the value of α when this ratio is maximum, and (C_L/C_D)_max.
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