hw7 - 3 Consider the problem o± shock refection ±rom a...

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MAE135 Homework No. 7 Spring 2010 Date Assigned: Tuesday, May 18, 2010 Due date: 5:00 pm, Tuesday, May 25, 2010 PROBLEM 1 (10 points) 1 2 1 2 3 20 o 10 o 10 o M 1 =3.0 p 1 =1.0 atm M 1 =3.0 p 1 =1.0 atm (a) (b) Consider the two supersonic turns shown above. In case (a), the flow is turned to 20 deg by one wedge. In case (b), two successive turns, each with 10-deg deflection, turn the flow to a final angle of 20 deg. The Mach number of the incoming flow is M 1 = 3 . 0 and its static pressure is p 1 = 1 . 0 atm. All the shocks are of the “weak-solution” type. (a) For case (a), calculate M , p , and p 0 in region 2. (b) For case (b), calculate M , p , and p 0 in regions 2 and 3. (c) If you were to consider the above two designs for an inlet to an engine, which design is more efficient? Provide a short justification. Problem 3 (10 points) 1 2 20 o M 1 =4.0 p 1
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Unformatted text preview: 3 Consider the problem o± shock refection ±rom a fat wall. The refection ±rom regions 2 to 3 happens because in region 3 the fow must become parallel to the upper wall. ²or the conFguration shown above ( M 1 = 4, θ = 20 o ), Fnd M and p in regions 2 and 3. Consider the “weak solution” only. PROBLEM 3 (10 points) y x 1 M 1 = 2 y i x i y= 0.1 x 2 M An isentropic compression turn occurs ±or 0 ≤ x ≤ 1 and has the shape y = 0 . 1 x 2 No ±urther turning occurs ±or x > 1. The incoming Mach number is M 1 = 2. (a) Calculate the coordinates ( x i , y i ) o± the intersection o± the Frst and last Mach waves o± the compression. (b) Determine the Mach number M 2 downstream o± the isentropic compression 1...
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