A flow suction mechanism is created at the trailing edge of a thin flat plate of...

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A flow suction mechanism is created at the trailing edge of a thin flat plate of length L as sketched below. The flow slightly above the plate can be described by a potential flow Ue(x)=M/2π(L-x) where M is the suction strength and the flow very near the plate forms a laminar boundary layer. (1) Use Karman integral equation with a 3rd order polynomial considering pressure gradient to find an expression for the wall shear stress Twi(x) (2) Apply Thwaite's method get another estimation Tw2(x) using the single à parameter solution. (3) Analyze the results in (2) or evaluate it at a few points to show how the wall stress evolves along x. (4) If we take U₂(0) to approximate a uniform incoming flow, compare the finding in (3) to Blasius solution. Do you see a faster or slower growth of wall shear stress along x? Explain the effect of trailing edge suction on manipulating the wall stress? 2 0.25 0.20 0.14 0.12 0.10 0.08 0.064 0.048 0.032 0.016 0 -0.008 -0.016 -0.024 1 -0.032 3.0 2.0 l 1.0 0 -0.10 S() 0.500 0.463 0.404 0.382 0.359 0.333 0.313 0.291 0.268 0.244 0.220 0.208 0.195 0.182 0.168 a -0.05 0 H(2) 2.00 2.07 2.18 2.23 2.28 2.34 2.39 2.44 2.49 2.55 2.61 2.64 2,67 2.71 2.75 O 0.05 X -0.040 -0.048 -0.052 -0.056 -0.060 -0.064 -0.068 -0.072 -0.076 -0.080 -0.084 -0.086 -0.088 -0.090 " THWAITES POHLHAUSEN EXACT 0.10 0.15 H l 0.153 0.138 0.130 0.122 0.113 0.104 0.095 0.085 0.072 0.056 0.038 0.027 0.015 0 (Separation) S(X) 0.20 4.0 3.0 2.0 1.0 H 0.25 2.81 2.87 2.90 2.94 2.99 3.04 3.09 3.15 3.22 3.30 3.39 3.44 3.49 3.55 H(X) A flow suction mechanism is created at the trailing edge of a thin flat plate of length L as sketched below. The flow slightly above the plate can be described by a potential flow Ue(x)=M/2π(L-x) where M is the suction strength and the flow very near the plate forms a laminar boundary layer. (1) Use Karman integral equation with a 3rd order polynomial considering pressure gradient to find an expression for the wall shear stress Twi(x) (2) Apply Thwaite's method get another estimation Tw2(x) using the single à parameter solution. (3) Analyze the results in (2) or evaluate it at a few points to show how the wall stress evolves along x. (4) If we take U₂(0) to approximate a uniform incoming flow, compare the finding in (3) to Blasius solution. Do you see a faster or slower growth of wall shear stress along x? Explain the effect of trailing edge suction on manipulating the wall stress? 2 0.25 0.20 0.14 0.12 0.10 0.08 0.064 0.048 0.032 0.016 0 -0.008 -0.016 -0.024 1 -0.032 3.0 2.0 l 1.0 0 -0.10 S() 0.500 0.463 0.404 0.382 0.359 0.333 0.313 0.291 0.268 0.244 0.220 0.208 0.195 0.182 0.168 a -0.05 0 H(2) 2.00 2.07 2.18 2.23 2.28 2.34 2.39 2.44 2.49 2.55 2.61 2.64 2,67 2.71 2.75 O 0.05 X -0.040 -0.048 -0.052 -0.056 -0.060 -0.064 -0.068 -0.072 -0.076 -0.080 -0.084 -0.086 -0.088 -0.090 " THWAITES POHLHAUSEN EXACT 0.10 0.15 H l 0.153 0.138 0.130 0.122 0.113 0.104 0.095 0.085 0.072 0.056 0.038 0.027 0.015 0 (Separation) S(X) 0.20 4.0 3.0 2.0 1.0 H 0.25 2.81 2.87 2.90 2.94 2.99 3.04 3.09 3.15 3.22 3.30 3.39 3.44 3.49 3.55 H(X)