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Numerical Solutions to the Taylor

# Numerical Solutions to the Taylor - Project Gas Dynamics ID...

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Project : Gas Dynamics ID : 1000711176 Name : Krushit Shah Project: Numerical Solutions to the Taylor-Maccoll Equation 1 Outline The goal of this project is to determine a numerical solution to the Taylor-Maccoll equation for a given value of the free-stream Mach number and shock angle. An incomplete numerical code written in MATLAB is included in this document. The project requires you to 1. Determine the velocity at the shock front. 2. Complete the routine “Tmac.m”, which is called by the variable step time integrator “ode15i”. 2 Data . The shock angle is bita = 50 The free-stream mach number is Minf = 5. The isentropic index is gamma = 1.4. 3 Find Determine the cone angle (theta_c) for the given conditions. Submit its numerical value plus the program you used to evaluate it.

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Project : Gas Dynamics ID : 1000711176 Name : Krushit Shah Numerical Solutions to the Taylor-Maccol Equation

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Unformatted text preview: Project : Gas Dynamics ID : 1000711176 Name : Krushit Shah Complition “Tmac.m” Project : Gas Dynamics ID : 1000711176 Name : Krushit Shah Final Solution Project : Gas Dynamics ID : 1000711176 Name : Krushit Shah Solution Solution Project : Gas Dynamics ID : 1000711176 Name : Krushit Shah Step 1 From theta- bita- Minf relation we find the value of theta For bita = 50 & Minf = 5, Theta = 35 Step 2 For Mach no M Mn1 = Minf*sin(bita) Mn1 = 3.8 from the Table A2 for Normal shock M = 4.407 Step 3 After getting the theta & M we find Vprime’ = [ 2/(gamma-1)*M^2]^-1/2 Vprime’ = 0.8917 Step 4 From geometry of fig we find the Vprime’r = 0.5731. As shown in fig the Vtheta component is opposite from the Vr vector so take the Vtheta is Negative Vprime’(theta) = -0.1502 Project : Gas Dynamics ID : 1000711176 Name : Krushit Shah...
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