Qiqi Wang

Optimal Design and Tolerancing of Compressor Blades Subject to Manufacturing Variability

This paper presents a computational approach for optimal robust design and tolerancing of turbomachinery compressor blades that are subject to geometric variability. This approach simultaneously determines the optimal blade geometry and manufacturing tolerances to minimize the overall cost of producing and operating the resulting compressor blades. A pathwise sensitivity method is used to compute gradient information that is in turn used to optimize the design and tolerances. Results for a two-dimensional subsonic compressor are presented, demonstrating the significant performance improvements that can be achieved using the proposed approach.

Multiple Shooting Shadowing for Sensitivity Analysis of Chaotic Systems and Turbulent fluid flows

Sensitivity analysis methods are important tools for research and design with computational models like CFD. Traditional sensitivity analysis methods are unable to compute useful gradient information for long time averaged quantities in chaotic dynamical systems, such as high fidelity simulations of turbulent fluid flows. The Least Squares Shadowing (LSS) method has been used to compute useful gradient information for a number of chaotic systems, including a simulation of homogeneous isotropic turbulence. However, some LSS gradient calculations for the Kuramoto-Sivshinsky (K-S) equation and the Lorenz 96 system have a systematic error due to breaks in the assumption of ergodicity. Since these systems have similar characteristics to turbulent fluid flows, this ergodicity breaking error must be minimized. This paper proposes a new approach using LSS, Multiple Shooting Shadowing (MSS), which uses the multiple shooting implementation of LSS to reduce the size of the ergodicity breaking error by not running the multiple shooting algorithm to full convergence. This way, gradients are computed from an ensemble of solutions, rather than the shadow direction alone, making the method more robust to the ergodicity breaking error. In this paper, MSS is demonstrated for the K-S equation and it is found that MSS cannot fix the systematic error of LSS when the system has a wide range of chaotic time scales.

Simultaneous Robust Design and Tolerancing of Compressor Blades

The manufacturing processes used to create compressor blades inevitably introduce geometric variability to the blade surface. In addition to increasing the performance variability, it has been observed that introducing geometric variability tends to reduce the mean performance of compressor blades. For example, the mean adiabatic efficiency observed in compressor blades with geometric variability is typically lower than the efficiency in the absence of variability. This “mean-shift” in performance leads to increased operating costs over the life of the compressor blade. These detrimental effects can be reduced by using robust optimization techniques to optimize the blade geometry. The impact of geometric variability can also be reduced by imposing stricter tolerances, thereby directly reducing the allowable level of variability. However, imposing stricter manufacturing tolerances increases the cost of manufacturing. Thus, the blade design and tolerances must be chosen with both performance and manufacturing cost in mind.This paper presents a computational framework for performing simultaneous robust design and tolerancing of compressor blades subject to manufacturing variability. The manufacturing variability is modelled as a Gaussian random field with non-stationary variance to simulate the effects of spatially varying manufacturing tolerances. The statistical performance of the compressor blade system is evaluated using the Monte Carlo method. A gradient based optimization scheme is used to determine the optimal blade geometry and distribution of manufacturing tolerances.Copyright

Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization

We investigate the Lyapunov spectrum of separated flows and their dependence on the numerical discretization. The chaotic flow around the NACA 0012 airfoil at low Reynolds number and large angle of attack is considered to that end, and t-, h- and p-refinement studies are performed to examine each effect separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. In particular, the asymptotic Lyapunov spectrum for time refinement is achieved for CFL numbers as large as

A Non-Intrusive Algorithm for Sensitivity Analysis of Chaotic Flow Simulations

\mathcal{O}(10^1-10^2)

Optimization with LES -- algorithms for dealing with sampling error of turbulence statistics

, whereas the system continues to become more and more chaotic even for meshes that are much finer than the best practice for this type of flows.

Sensitivity analysis on chaotic dynamical system by Non-Intrusive Least Square Shadowing (NI-LSS)

We demonstrate a novel algorithm for computing the sensitivity of statistics in chaotic flow simulations to parameter perturbations. The algorithm is non-intrusive but requires exposing an interface. Based on the principle of shadowing in dynamical systems, this algorithm is designed to reduce the effect of the sampling error in computing sensitivity of statistics in chaotic simulations. We compare the effectiveness of this method to that of the conventional finite difference method.

Unsteady Adjoint of Pressure Loss for a Fundamental Transonic Turbine Vane

Optimization with Large Eddy Simulations (LES) can be challenging due to noisy objective function. This noise is because of the sampling error of turbulent statistics. It decays slowly as computation cost increases, therefore is significant in most simulations. It is often unpredictable due to chaotic dynamics of turbulence, in that it can be totally different for almost identical simulations. In this paper we evaluate several optimization algorithms that are designed to handle noisy objective functions by testing it on the Lorenz equations, a low dimensional chaotic dynamical system. Bayesian optimization, one of the better performing algorithms, is then adapted to minimize drag in a turbulent channel flow. Our optimization algorithm simultaneously runs several simulations, each parallelized to thousands of cores, in order to utilize additional concurrency offered by today’s supercomputers.