Inverse design of internally cooled turbine blades based on the heat adjoint equation

Figures & data

Figure 1. Domain geometry and nomenclature.

Figure 2. Test 1: geometry.

Figure 3. Test 1: geometry and temperature field.

Figure 4. Test 1: convergence history of x_c = a₁, Y_c = b₁, R_c = r₁ (left) and of the objective function residuals (right) vs. optimization step.

Table 1. Composite hollow cylinder test. Comparison between numerical and theoretical value of main parameters.

	a1 (mm)	b1 (mm)	r1 (mm)	Q (W m^−2)	Tb (K)
Theoretical	0	0	25	2044.79	337.230
Numerical	0.303	0.012	24.933	2044.54	337.234
Error	5.22·10^−3(*)	2.07· 10^−4(*)	0.27%	0.012%	0.0012%
Note: *The absolute error has been scaled to the external cylinder radius rb.

Figure 5. Test Mark II: initial (a) and final (b) grid and cooling passage pattern, initial (c) and final (d) temperature field.

Figure 6. Test Mark II: heat transfer coefficient fitting (left) and comparison of the surface temperature obtained by the inverse problem and the target temperature distribution (right). Note: Symbols refer to the experimental data and solid lines to numerical results).

Figure 7. Test Mark II: convergence history of L²-norm of gradient residuals (left) and of the objective function residuals (right) vs. optimization step.