J. Ortega-Casanova

Lift and drag characteristics of a cascade of flat plates in a configuration of interest for a tidal current energy converter: Numerical simulations analysis

Numerical simulations of the three-dimensional flow through a cascade of flat plates are conducted to analyze its lift and drag characteristics in a configuration of interest for a particular type of tidal hydrokinetic energy converter. To that end, the turbulent model parameters in the computational fluid dynamics code are validated against experimental data for the flow around an isolated plate at different angles of incidence and the same Reynolds number used in the cascade. The lift and drag coefficients of a plate in the cascade, as well as the effective nondimensional power extracted from the tidal current, are compared to the corresponding values for an isolated plate. These results are used as a guide for the design of the optimum configuration of the cascade (angle of attack, blade speed, and solidity) which extracts the maximum power from a tidal current for a given reference value of the Reynolds number.

Experimental study on sand bed excavation by impinging swirling jets

The excavation performance of swirling jets impinging normally against a sand bed from several distances is described. A specially-designed nozzle with adjustable swirl vanes was used to generate swirling jets of various swirl intensities. Two sand beds of different grain size distributions were considered. The main scour patterns on the sand bed produced by the swirling jets were measured by image processing of photographs of the bed illuminated by a laser sheet. The velocity profiles of the swirling jets at the nozzle exit were measured using Laser Doppler Anemometry for various test conditions. The scour patterns were then analysed in relation to the details of the velocity profile of the swirling jets, their Reynolds numbers and the distances from the nozzle to the bed. The optimum jet features resulting from the different swirl nozzles and the best impinging distances for sea bed excavation are identified and discussed.

Confined swirling jet impingement on a flat plate at moderate Reynolds numbers

The behavior of a swirling jet issuing from a pipe and impinging on a flat smooth wall is analyzed numerically by means of axisymmetric simulations. The axial velocity profile at the pipe outlet is assumed flat while the azimuthal velocity profile is a Burger’s vortex characterized by two non-dimensional parameters; a swirl number S and a vortex core length δ. We concentrate on the effects of these two parameters on the mechanical characteristics of the flow at moderate Reynolds numbers. Our results for S=0 are in agreement with Phares et al. [J. Fluid Mech. 418, 351 (2000)], who provide a theoretical determination of the wall shear stress under nonswirling impinging jets at high Reynolds numbers. In addition, we show that the swirl number has an important effect on the jet impact process. For a fixed nozzle-to-plate separation, we found that depending on the value of δ and the Reynolds number Re, there is a critical swirl number, S=S∗(δ,Re), above which recirculating vortex breakdown bubbles are observed...

Three-dimensional transitions in a swirling jet impinging against a solid wall at moderate Reynolds numbers

We consider the three-dimensional structure of a q-vortex interacting with a solid surface perpendicular to its axis. We use a direct numerical simulation based on a potential vector formulation with a Fourier decomposition in azimuthal modes for a Reynolds number equal to 100. This method is specially suited for the study of the nonlinear stability of axially symmetric flows because one may follow the raising of the different nonaxisymmetric modes from numerical noise, their nonlinear development, and their nonlinear interactions. For the given Reynolds number we find that there exists several transitions as the swirl number is increased, including the development of nonaxisymmetric instabilities for different azimuthal modes, and the formation of a vortex breakdown bubble that turns the flow axisymmetric again. We analyze these transitions and characterize them as a function of the swirl number for different distances of the incoming vortex to the wall.

A pseudospectral based method of lines for solving integro-differential boundary-layer equations. Application to the mixed convection over a heated horizontal plate

Abstract The method of lines is well suited for solving numerically parabolic boundary-layer equations because it avoids the numerical difficulties associated to the integration of the continuity equation, which is subsumed into the momentum equations as an integral of the main velocity component. To deal with these integrals, as well as with any other integral operator entering the boundary layer equations in some particular problems, it is very efficient to discretize the transversal coordinate using pseudospectral methods. The resulting ordinary differential equations (ODEs) can be then written in a very compact form, suitable for general-purpose methods and software developed for the numerical integration of ODEs. We present here such a numerical method applied to the boundary-layer equations governing the mixed convection over a heated horizontal plate. These parabolic equation can be written in such a way that the natural convection appears as an integro-differential term in the usual horizontal momentum equation, so that the discretization by pseudospectral methods of the vertical coordinate derivative is very appropriate. Several Matlab based solvers are compared to integrate the resulting ODEs. To validate the numerical results they are compared with analytic solutions valid near the leading edge of the boundary-layer.

A numerical method for the study of nonlinear stability of axisymmetric flows based on the vector potential

We develop in this paper a numerical method to simulate three-dimensional incompressible flows based on a decomposition of the flow into an axisymmetric part, in terms of the stream function and the circulation, and a non-axisymmetric part in terms of a potential vector function. The method is specially suited for the study of nonlinear stability of axially symmetric flows because one may follow neatly the raising of the different non-axisymmetric modes, their nonlinear development, and their nonlinear interaction. The numerical technique combines finite differences on a non-uniform grid in the axial direction, a Chebyshev spectral collocation technique in the radial direction, and a Fourier spectral method in the azimuthal direction for the non-axisymmetric vector potential. As an example to check the efficiency and accuracy of the method we apply it to the flow inside a rotating circular pipe, and compare the resulting travelling waves with previous stability results for this problem, for different values of the Reynolds and the swirl numbers.

On the efficiency of a numerical method with periodic time strides for solving incompressible flows

An explicit numerical method to solve the unsteady incompressible flow equations consisting on N small time steps Δt between each two much larger time steps (Δt)1 is considered. The stability and efficiency of the method is first analyzed using the one-dimensional diffusion equationl. It is shown that the use of a time step Δt slightly smaller than the critical one (Δt)c, given by numerical stability allows lo periodically take a much larger time step (stride) that speeds-up the advance in time in a numerical stable scheme. In particular, the stability analysis shows that for a given value of the stride (Δt)1, there is an optimum value of the small time step for which the computational speed is the fastest (N is a minimum), being this speed significantly larger than the corresponding one for an explicit method using (Δt)c only. The efficiency of the method is discussed for different time discretization schemes. The numerical method is then used to solve a particular incompressible flow. It is shown that the method is significantly (about three times) faster than a standard explicit scheme, and yields the same time evolution of the flow (within spatial accuracy). Further, it is shown that a much more higher computational speed and efficiency is reached if one combines an implicit scheme for the periodic strides with the explicit small time steps. With this combination one can speed-up the computations in more than one order of magnitude with the same resolution.

Inviscid evolution of incompressible swirling flows in pipes: The dependence of the flow structure upon the inlet velocity field

This paper analyses the influence of the inlet swirl on the structure of incompressible inviscid flows in pipes. To that end, the inviscid evolution along a pipe of varying radius with a central body situated inside the pipe is studied for three different inlet swirling flows by solving the Bragg-Hawthorne equation both asymptotically and numerically. The downstream structure of the flow changes abruptly above certain threshold value s of the swirl parameter (L). In particular, there exist a value Lr above which a near-wall region of flow reversal is formed downstream, and a critical value Lf above which the axial vortex flow breaks down. It is shown that the dependence upon the pipe geometry of these critical values of the swirl parameter varies strongly with the inlet azimuthal velocity profile considered. An excellent agreement between asymptotic and numerical results is found.