Question

Induced inflow ratio, \lambda_i/\lambda_n 1.5 1 0.5 2 0 0 2 4 Special case of induced inflow for \alpha = 0^\circ Exact solution -----\"High-speed\" approximation 6 8 10 Forward speed ratio, \mu/\lambda_n Figure 2.24 Induced inflow ratio at the rotor disk \lambda_i/\lambda_n as a function of forward speed ratio \mu/\lambda_n for \alpha = 0. Figure 1: Figure 2.24 Problem 4 (25 points) Compare the results from the iterative solution of the inflow equation to the exact analytical inflow equation for the case of \alpha = 0. You need to do this problem using two approaches: (i) you may use either the fixed point iterative method or the Newton-Raphson method (don't need to do both), and (ii) use Matlab's fzero function like I demonstrated in class. Plot your results from the two approaches and from the approximate solution in a manner similar to Fig. 2.24 in the book. Determine the conditions (if any) under which these iterative methods fail. The results from your two approaches should be close to the exact solution in Fig. 2.24. Submit your equations, plots, and code with your HW.

          Induced inflow ratio, \lambda_i/\lambda_n
1.5
1
0.5
2
0
0
2
4
Special case of induced inflow for \alpha = 0^\circ
Exact solution
-----\"High-speed\" approximation
6
8
10
Forward speed ratio, \mu/\lambda_n
Figure 2.24 Induced inflow ratio at the rotor disk \lambda_i/\lambda_n as a function of forward speed
ratio \mu/\lambda_n for \alpha = 0.
Figure 1: Figure 2.24
Problem 4 (25 points)
Compare the results from the iterative solution of the inflow equation to the exact analytical
inflow equation for the case of \alpha = 0. You need to do this problem using two approaches: (i)
you may use either the fixed point iterative method or the Newton-Raphson method (don't
need to do both), and (ii) use Matlab's fzero function like I demonstrated in class. Plot your
results from the two approaches and from the approximate solution in a manner similar to
Fig. 2.24 in the book. Determine the conditions (if any) under which these iterative methods
fail. The results from your two approaches should be close to the exact solution in Fig. 2.24.
Submit your equations, plots, and code with your HW.

Induced inflow ratio, /1.5
1
0.5
2
0
0
2
4
Special case of induced inflow for α= 0^∘Exact solution
—–Ḧigh-speedäpproximation
6
8
10
Forward speed ratio, μ/Figure 2.24 Induced inflow ratio at the rotor disk /as a function of forward speed
ratio μ/for α= 0.
Figure 1: Figure 2.24
Problem 4 (25 points)
Compare the results from the iterative solution of the inflow equation to the exact analytical
inflow equation for the case of α= 0. You need to do this problem using two approaches: (i)
you may use either the fixed point iterative method or the Newton-Raphson method (don't
need to do both), and (ii) use Matlab's fzero function like I demonstrated in class. Plot your
results from the two approaches and from the approximate solution in a manner similar to
Fig. 2.24 in the book. Determine the conditions (if any) under which these iterative methods
fail. The results from your two approaches should be close to the exact solution in Fig. 2.24.
Submit your equations, plots, and code with your HW.

Added by Daniel J.

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