1,720,999 research outputs found
A simple redistribution vortex method (with accurate body forces)
No full textA 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/
Active control of flows with trapped vortices
No full textAn approach to developing active control strategies for high Reynolds number flows with trapped vortices is presented. The problem considered is the stabilisation of the vortex in a special cavity on the airfoil using suction as an actuator. The flow dynamics are modelled by the parallel discrete vortex method capable of handling wall irregularities, arbitrary boundary conditions, and turbulence. System identification is performed based on the open-loop analysis with the constant flow rate suction. Feedback control results show that a properly designed linear PI controller prevents the large-scale vortex shedding from the cavity region and reduces considerably flow unsteadiness in the downstream boundary layer
Recurrence of travelling waves in transitional pipe flow
No full textThe recent theoretical discovery of families of unstable travelling-wave solutions in pipe flow at Reynolds numbers lower than the transitional range, naturally raises the question of their relevance to the turbulent transition process. Here, a series of numerical experiments are conducted in which we look for the spatial signature of these travelling waves in transitionary flows. Working within a periodic pipe of 5D (diameters) length, we find that travelling waves with low wall shear stresses (lower branch solutions) are on a surface in phase space which separates initial conditions which uneventfully relaminarize and those which lead to a turbulent evolution. This dividing surface (a separatrix if turbulence is a sustained state) is then minimally the union of the stable manifolds of all these travelling waves. Evidence for recurrent travelling-wave visits is found in both 5D and 10D long periodic pipes, but only for those travelling waves with low-to-intermediate wall shear stress and for less than about 10% of the time in turbulent flow at Re = 2400. Given this, it seems unlikely that the mean turbulent properties such as wall shear stress can be predicted as an expansion solely over the travelling waves in which their individual properties are appropriately weighted. Instead the onus is on isolating further dynamical structures such as periodic orbits and including them in any such expansion
Second-order kinetics for EC' reactions at a spherical microelectrode
No full textA 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
Flow along a long thin cylinder
Full text linkTwo different approaches have been used to calculate turblent flow along a long thin culinder where the flow is aligned with the cylinder. A boundary-layer code is used to predict the mean flow for very long cylinders (length to ratio of up to O(106)), with the effects of the turbulence estimated through a turbulence model. Detailed comparison with experimental results shows that the mean properties of the flow are predicted within experimental accuracy. The boundary-layer model predicts that, sufficiently far downstream, the surface shear stress will be (almost) constant. This is consistent with experimental results from long cylinders in the form of sonar arrays. A periodic Navier-Stokes problem is formulated, and solutions generated for the boundary-layer model and experiments. Strongly turbulent flow occurs only near the surface of the cylinder, with relatively weak turbulence over most of the boundary layer. For a thick boundary layer with the boundary-layer thickness much larger than the cylinder radius, the mean flow is effectively constant near the surface, in both temporal and spatial frameworks, while the outer flow continues to develop in time or space. Calculations of the circumferentially averaged surface pressure spectrum sho that, in physical terms, as the radius of the cylinder decreases, the surface noise from the turbulence increases, with the maximum noise at a Reynolds number of O(103). An increase in noise with a decrease in radius (Reynolds number) is consistent with experimental results
Numerical simulation of Görtler vortices in hypersonic compression ramps
No full textA numerical study of the formation and evolution of Görtler type vortices over a compression ramp under an hypersonic flow is presented. Numerical predictions in laminar compression ramps (body/body-flaps configurations) usually require the inclusion of three-dimensional effects to correlate separation lengths with experimental measurements. Moreover, in the presence of large recirculation regions, the heat transfer calculated over the compression ramp severely underestimate experimental values. This discrepancy could be explained at least in part by the presence and effects of centrifugal disturbances. Indeed the regular striation patterns in heat transfer rates seen in experiments suggest this. In the present work numerical simulations were carried out over three-dimensional 15° compression ramps in a laminar hypersonic flow at Mach 6.85 and a Reynolds number per unit length of 2.45 × 106 m?1. The relatively high Görtler numbers obtained suggested that Görtler vortices might be important. In most cases, a spanwise periodic velocity perturbation is imposed on the flat plate ahead of separation. However for one case, which had a grid with a higher spanwise resolution, a regular striation pattern emerged without forcing. In this case, the pattern had a wavelength comparable to that found in experiments and as predicted from linear theory. A spanwise variation of 5–15% in the heat transfer close to the centreline was obtained in this case
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