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LUl SV You have been chosen as the chief designer of a supersonic wind tunnel. The test section should have a 0.5 m x 0.5 m cross-section of length 1 m, with a design Mach number of 2.0. The tunnel is to be driven by a compressor, which is guaranteed to do work on the working fluid with an adiabatic efficiency of 1 = 0.92. The adiabatic efficiency is defined as Shock Test Section Figure 1: Single-throat Supersonic Tunnel The above diagram shows a "blow down\" single-throat supersonic wind tunnel. The compressor is located upstream of the throat section (with cross sectional area A,). The cross-sectional area of the test section is Az (which should be as big as possible to accommodate large test models). You are to use the most simple-minded design: using a normal shock located at the end of the test section where the cross-sectional area A, is very close to Az, The air is exhausted back into the room at exit station 4. Use subsecripts s and s, to indicate conditions immediately before and after the normal shock, respectively, 1. Determine values for cross-sectional areas Ay (which equals Ay) and Ajy. 2. Calculate the lengths of the converging and diverging segments before and after the test section. 3. Determine the total pressure ratio of the fan (pgs/pe1) and power rating for your fan, and therefore the rating of the motor yvou need to drive the fan. 4. Calculate the Reynolds number in the test section based on tunnel height. 5. Show that your design satisfies mass and energy conservation laws between the inlet and exit, and discuss the advantages and disadvantages of a large exit cross-sectional area Ay. In each step, outline your objective and constraints and justify your design choices. 6. The depth of the tunnel is constant (D = 0.5m). The height is symmetric with respect to the centerline. The cross-sectional area change is achieved by choosing the half-height function y(z). Design a smooth function to avoid excessive gradient in the converging and diverging parts of the tunnel, especially in the diverging part, where Page 1 of 2 there is adverse pressure gradient. Also, we need to maintain the flow in the test section to be as uniformly 1-dimensional as possible. In practice, we would need a round-rectangular transition duct to connect the fan exit to the tunnel section. For simplicity, we neglect that part of the design. 7. Once you have determined your y(r) either using a discretely defined array of (x,y) pairs or piecewise-continuous analytic formulas, calculate and plot M, p, T', p, and V' as a function of x along the centerline based on quasi-1D flow. 8. The wind tunnel is to be bolted to a foundation on the ground. Caleulate the force that the bolts and the foundation have to withstand due to the 'thrust' of the tunnel