Over-Tip Choking and Its Implications on Turbine Blade Tip Aerodynamic Performance

At engine representative flow conditions a significant portion of flow over a high pressure turbine blade tip is transonic. In the present work, the choking flow behavior and its implications on over-tip leakage flow loss generation are computationally analyzed. An extensively developed RANS code (HYDRA) is adopted. Firstly a high speed linear cascade validation case is introduced, and the computations are compared with the experimental data to identify and establish the capability of the code in predicting the aerodynamics losses for a transonic turbine blade tip. The computational studies are then carried out for the blading configuration at different flow conditions ranging from a nearly incompressible to a nominal transonic one, enabling to establish a qualitatively consistent trend of the tip leakage losses in relation to the exit Mach number conditions. The results clearly show that the local choking sets a limiter for the over tip leakage mass flow, leading to a different leakage flow structure compared to that in a low speed and/or unchoked condition. The existence of tip choking effectively blocks the influence of the suction surface side on the over-tip flow, and hence leads to a breakdown of the pressure-driven mechanism, conventionally used in tip treatment and designs. The decoupling between blade loading and over tip leakage mass flow is clearly identified and highlighted. Furthermore, the realization of the loading-leakage flow decoupling indicates a possibility of a high-load blading design with a relatively low tip leakage loss. A high load blading is generated and analyzed to demonstrate the feasibility of such designs with a reduced tip leakage loss

Multigrid renormalization

We combine the multigrid (MG) method with state-of-the-art concepts from the variational formulation of the numerical renormalization group. The resulting MG renormalization (MGR) method is a natural generalization of the MG method for solving partial differential equations. When the solution on a grid of N points is sought, our MGR method has a computational cost scaling as O(log⁡(N)), as opposed to O(N) for the best standard MG method. Therefore MGR can exponentially speed up standard MG computations. To illustrate our method, we develop a novel algorithm for the ground state computation of the nonlinear Schrödinger equation. Our algorithm acts variationally on tensor products and updates the tensors one after another by solving a local nonlinear optimization problem. We compare several different methods for the nonlinear tensor update and find that the Newton method is the most efficient as well as precise. The combination of MGR with our nonlinear ground state algorithm produces accurate results for the nonlinear Schrödinger equation on N=1018grid points in three spatial dimensions

Variational quantum algorithms for nonlinear problems

We show that nonlinear problems including nonlinear partial di↵erential equations can be e- ciently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat nonlinearities eciently and by introducing tensor networks as a programming paradigm. The key concepts of the algorithm are demonstrated for the nonlinear Schr¨odinger equation as a canonical example. We numerically show that the variational quantum ansatz can be exponentially more ecient than matrix product states and present experimental proof-of-principle results obtained on an IBM Q device

Characteristics of a phylogenetically ambiguous, arsenic-oxidizing Thiomonas sp., Thiomonas arsenitoxydans strain 3As(T) sp. nov.

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Comparison of several optimisation strategies for robust turbine blade design

This paper addresses the problem of turbine blade shape optimization in the presence of geometric uncertainties. Several strategies are tested and compared on a two-dimensional compressor blade optimization process for which performance is assessed using a commercial Reynolds-averaged Navier-Stokes computational fluid dynamics code. In each case, a range of shape errors are considered that attempt to simulate foreign object damage, erosion damage, and manufacturing errors. These lead to stochastic performance measures that, in turn, are considered in a multi-objective optimization framework. Because of the long run times associated with Reynolds-averaged Navier-Stokes codes, use is also made of surrogate or response surface-based optimization methods to speed up the search processes. The paper shows that a range of techniques can be used to tackle this problem, but that no one method is clearly best overall. The practitioner is therefore cautioned against favoring a single approach for such design problems. Further research may help clarify these issue