A fast algorithm for inverse airfoil design using an efficient panel method for potential flow calculation is presented. The method employs linear vortex distributions on the panels and a consistent procedure for imposing the Kutta condition, thus eliminating the spurious aerodynamic loading that usually appears at a cusped trailing edge. The algorithm searches the airfoil ordinates attending to a given surface velocity distribution with fixed abscissas. It begins with a guessed starting shape and successively modifies it by an iterative process, such that the normal velocity vanishes and the calculated velocity distribution gradually approaches the required one. Each iteration is performed in two main steps: 1) the flow calculation step; 2) the geometrical marching step, where the calculated velocity distribution is compared with the required one and a transpiration model is applied to modify the current shape towards another one more close to the target shape. The geometrical marching is conducted by varying the panel slopes as a function of the normal velocity excess induced by the difference between the required and calculated velocities. A scheme is applied in order to close the body shape. Various test cases were carried out and are presented for the efficiency and robustness validation of the proposed inverse algorithm
This paper presents a low cost computational methodology for conceptual design optimization of axial-flow hydraulic turbines. The flow model away from the blade rows is considered axisymmetric, steady, and with cylindrical stream surfaces. The flow at the cross-sections behind the distributor and behind the runner is treated by means of the simplified radial equilibrium equation. The flow losses and deviations are assessed by using empirical correlations. Although simplified, the model allows the consideration of non-free vortex analysis at an early design stage. For reducing the set of design variables to be optimized, the runner blading stagger, camber, and chord-pitch ratio are parameterized in terms of their values at the hub, mean, and tip stations. The optimization problem consists in finding a basic geometry that maximizes the turbine efficiency, given the design flowrate, rotational speed and bounds for the design variables and also for the available head. Two optimization techniques have been applied: a standard sequential quadratic programming and a controlled random search algorithm. An application example is presented and discussed for the optimization of a real turbine model. The optimal solution is compared with the original turbine design, showing potential performance improvements.Although three-dimensional Navier-Stokes codes have allowed good performance predictions and contributed for decreasing the costs of turbomachine model tests, a considerable computational effort has still to be spent with grid generation and with the solution of the flow governing equations in each numerical investigation. This issue is even more important in the case of design optimization: when a geometrical change is made during the optimization process, complex meshes must be recalculated and the flow solver must be run again. This high effort prevents the incorporation of sophisticated Navier-Stokes simulations throughout the whole design procedure [2]. Actually, the analysis and design of turbomachines still require the use of simpler methodologies mainly in preliminary design phases, when the geometry is not yet completely defined. One example of a very simplified methodology is the mean streamline analysis for conceptual optimization of mixed-flow pumps [3]. For axial flow gas turbines, it is common JPE394
We have implemented an operational amplifier inductorless realization of the Chua's circuit. We have registered time series from its dynamical variables with the resistorRas the control parameter and varying from 1300Ωto 2000Ω. Experimental time series at fixedRwere used to reconstruct attractors by the delay vector technique. The flow attractors and their Poincaré maps considering parameters such as the Lyapunov spectrum, its subproduct the Kaplan-Yorke dimension, and the information dimension are also analyzed here. The results for a typical double scroll attractor indicate a chaotic behavior characterized by a positive Lyapunov exponent and with a Kaplan-Yorke dimension of 2.14. The occurrence of chaos was also investigated through numerical simulations of the Chua's circuit set of differential equations.
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