Iterative design for active control of fluid flow

This paper considers iterative controller design for planar Poiseuille flow by model unfalsification and controller redesign. The main contribution is to show that model-unfalsification-based iterative design can be useful in flow control problems. The a priori knowledge of the dynamics of the sampled system is obtained from the analytic approximation of the Navier-Stokes equations by a Galerkin method. Pole-positions, expected model orders and feasible dynamic variations are valuable prior knowledge which can be taken into account in the uncertainty-model unfalsification-based iterative design scheme developed

H/sub /spl infin// control of nonperiodic two-dimensional channel flow

This paper deals with finite-dimensional boundary control of the two-dimensional (2-D) flow between two infinite parallel planes. Surface transpiration along a few regularly spaced sections of the bottom wall is used to control the flow. Measurements from several discrete, suitably placed shear-stress sensors provide the feedback. Unlike other studies in this area, the flow is not assumed to be periodic, and spatially growing flows are considered. Using spatial discretization in the streamwise direction, frequency responses for a relevant part of the channel are obtained. A low-order model is fitted to these data and the modeling uncertainty is estimated. An H-infinity controller is designed to guarantee stability for the model set and to reduce the wall-shear stress at the channel wall. A nonlinear Navier-Stokes PDE solver was used to test the designs in the loop. The only assumption made in these simulations is that the flow is two dimensional. The results showed that, although the problem was linearized when designing the controller, the controller could significantly reduce fundamental 2-D disturbances in practice

High-speed flow with discontinuous surface catalysis

In a reacting gas flow both gas-phase chemical activity and surface catalysis can increase the rate of heat transfer from the gas to a solid surface. In particular, when there is a discontinuous change in the catalytic properties of the surface, there can be a very large increase in the local heat transfer rate. In this study numerical simulations have been performed for the laminar high-speed flow of a high-temperature, non-equilibrium reacting gas mixture over a flat plate. The surface of the plate is partly catalytic, with the leading region non-catalytic, and a discontinuous change in the catalytic properties of the surface at the catalytic junction. The surface is assumed to be isothermal, and cold relative to the free stream. The gas is assumed to be a mixture of molecular and atomic forms of a diatomic gas in an inert gas forming a thermal bath, giving a three-species mixture with dissociation and recombination of the reactive species. The calculations are performed for a gas with atomic and molecular oxygen in an argon bath, but a full range of gas-phase chemical and surface catalytic effects is considered. Kinetic schemes with frozen gas-phase chemistry, and partial or full recombination of atomic oxygen in the boundary layer are investigated. The catalytic nature of the surface material is given by a catalytic recombination rate coefficient, which varies from zero (non-catalytic) to one (fully catalytic), and the effects on the flow and the surface heat transfer of materials which are non-, partially, or fully catalytic are considered. A self-similar thin-layer analytical model of the change in the gas composition downstream of the catalytic junction is developed. For physically realistic (O(10-2)) values of the catalytic recombination rate coefficient, the predictions from this model of the surface values of the atomic oxygen mass fraction and the catalytic surface heat transfer rate are excellent when the only change in the composition of the gas comes from the surface catalysis, and reasonable when there is partial recombination of the gas in the boundary layer due to the gas-phase chemistry. In contrast, when the surface is fully catalytic, the streamwise diffusion terms play a significant role, and the model is not valid. These results should apply to other situations with an attached boundary layer with recombination reactions. A comparison is made between the calculated and experimental measurements of the heat transfer rate at the catalytic junction. With a kinetic scheme which allows partial recombination in the boundary layer, good agreement is found between the experimental and predicted values for surface materials which are essentially non-catalytic. For a catalytic material (platinum), the experimental and numerical heat transfer rates are matched to estimate the value of the catalytic recombination rate coefficient. The values obtained show a considerable amount of scatter, but are consistent with those found in the literature

Global optimisation-based control algorithms applied to boundary layer transition problems

Turbulent flow has a significantly higher drag than the corresponding laminar flow at the same flow conditions. The presence of turbulent flow over a large part of an aircraft therefore incurs a significant penalty of increased fuel consumption due to the extra thrust required. One possible way of decreasing the drag is to apply surface suction to delay the transition from laminar to turbulent flow. However, in order for the gain from the reduction in drag to outweigh the extra costs associated with the suction system, the suction must be distributed in an optimum, or near optimum, manner. In this paper two practical cases are considered. In the first of these a flat plate with panels whose positions are adjustable but do not overlap is treated. Since the cost function in this case is multi-modal, non-smooth and non-convex, methods for solving the optimisation problems necessary to design multi-panel suction systems based on direct search techniques are developed. In the second case considered the problem is that of linear distributed suction over the front part of an aerofoil. For this case, the computational load increases so significantly that in some cases it is not really feasible to continue the investigation using a single processor code. To overcome this, three parallel global optimisation algorithms are developed for the design of multi-panel suction systems on an aerofoil and it is shown that good solutions can be found efficiently

A simple redistribution vortex method (with accurate body forces)

A circulation redistribution scheme for viscous flow is presented. Unlike other redistribution methods, it operates by transferring the circulation to a set of fixed nodes rather than neighbouring vortex elements. A new distribution of vortex elements can then be constructed from the circulation on the nodes. The solution to the redistribution problem can be written explicitly as a set of algebraic formulae, producing a method which is simple and efficient. The scheme works with the circulation contained in the vortex elements only, and does not require overlap of vortex cores. With a body fitted redistribution mesh, smooth and accurate estimates of the pointwise surface forces can be obtained. The ability of the scheme to produce high resolution solution is demonstrated using a series of test problems <br/

Second-order kinetics for EC' reactions at a spherical microelectrode

A second-order (nonlinear) model is derived for steady-state kinetics of an EC' (catalytic electrochemical) reaction at a spherical microelectrode in the case where the electron transfer process is followed by a homogeneous chemical reaction regenerating the electroactive species. An asymptotic analysis of the model is performed, and the asymptotic results are compared with those from a numerical solution of the full nonlinear model. It is shown that in the fast reaction limit, where the current at the electrode takes its maximum possible value, the concentrations of the reactants are controlled by diffusion both close to and far from the electrode, with significant chemical activity occurring only in a narrow zone standing off the electrode. Also, it is shown that an equation obtained from a different asymptotic limit may be used to predict the limiting current at the microelectrode in all circumstances. The reasons for the surprising measure of agreement at the surface of the electrode are discussed, the predictions from the model of the limiting current are compared (favourably) with experimental results, and the model is compared with the standard pseudo-first-order model, which, although also based on a linearization of the governing equations, has a restricted range of validity