Doctor of Philosophy (PhD)


Mechanical Engineering

Document Type



In the first part, an optimization strategy is described that combines high-fidelity simu- lations with response surface construction, and is applied to pulsed film cooling for turbine blades. The response surface is constructed for the film cooling effectiveness as a function of duty cycle, in the range of DC between 0.05 and 1, and pulsation frequency St in the range of 0.2-2, using a pseudo-spectral projection method. The jet is fully modulated and the blowing ratio, when the jet is on, is 1.5 in all cases. Overall 73 direct numerical sim- ulations (DNS) using spectral element method were performed to sample the film cooling effectiveness on a Clenshaw-Curtis grid in the design space. It is observed that in the parameter space explored a global optimum exists, and in the present study, the best film cooling effectiveness is found at DC = 0.14 and St = 1.03. In the same range of DC and St, four other local optimums were found. The gradient-based optimization algorithms are argued to be unsuitable for the current problem due to the non-convexity of the objective function. In the second part, the effect of randomness of blowing ratio on film cooling performance is investigated by combining direct numerical simulations with a stochastic collocation ap- proach. The blowing ratio variations are assumed to have a truncated Gaussian distribution with mean of 0.3 and the standard variation of approximately 0.1. The parametric space is discretized using Multi-Element general Polynomial Chaos (ME-gPC) with five elements where general polynomial chaos of order 3 is used in each element. Direct numerical simula- tions were carried out using spectral/hp element method to sample the governing equations in space and time. The probability density function of the film cooling effectiveness was obtained and the standard deviation of the adiabatic film cooling effectiveness on the blade surface was calculated. A maximum standard deviation of 15% was observed in the region within a four-jet-diameter distance downstream of the exit hole. The spatially-averaged adiabatic film cooling effectiveness was 0.23 0.02. The calculation of all the statistical properties were carried out as off-line post-processing. Overall the computational strategy is shown to be very effective with the total computational cost being equivalent to solving twenty independent direct numerical simulations that are performed concurrently. In the third part, an accurate and efficient finite difference method for solving the incompressible Navier-Stokes equations on curvilinear grids is developed. This method combines the favorable features of the staggered grid and semi-staggered grid approaches. A novel symmetric finite difference discretization of the Poisson-Neumann problem on curvilinear grids is also presented. The validity of the method is demonstrated on four benchmark problems. The Taylor-Green vortex problem is solved on a curvilinear grid with highly skewed cells and a second-order convergence in .-norm is observed. The mixed convection in a lid-driven cavity is solved on a highly curvilinear grid and excellent agreement with literature is obtained. The results for flow past a cylinder are compared with the existing experimental data in the literature. As the fourth case, three dimensional time-dependent incompressible flow in a curved tube is solved. The predictions agree well with the measured data, and validate the approach used.



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Committee Chair

Acharya, Sumanta