Paolo Luchini

Resistance of a grooved surface to parallel flow and cross-flow

A study is undertaken of both parallel flow and cross-flow in the viscous sublayer generated by a fluid streaming along a grooved surface, with the aim of clarifying the phenomena that underlie the reduction of turbulent drag by such surfaces. A quantitative characterization of the effectiveness of different groove profiles in retarding secondary cross-flow is given in terms of the difference of two ‘protrusion heights’. Analytical calculations of limit cases and a boundary-element computer code for the analysis of general profiles are illustrated, and several examples are presented and discussed.

Optical guiding in an FEL

Abstract Guiding of laser light by FEL amplifiers is studied in the framework of the linearized Boltzmann equation. The eigenmodes of the coupled Boltzmann and Maxwell equations are analyzed. An approximate approach based on the WKB solution of the transverse mode equation enables us to investigate the eigenvalue structure in terms of the prescribed electron beam transverse distribution.

A deferred-correction multigrid algorithm based on a new smoother for the Navier-Stokes equations

Abstract An algorithm which brings together the techniques of multigrid and deferred correction through their common relationship with imperfect Newton iteration manages to combine the ease of calculation of a low-order with the accuracy of a high-order difference approximation of any given differential-equation problem. A stable explicit Gauss-Seidel relaxation algorithm for the ψ-ζ Navier-Stokes equations based on an appropriate kind of “upwinding” of ψ- as well as ζ-derivatives, especially developed for use as a multigrid smoother in this context, is presented and the complete algorithm is tested on the standard conservative second-order discretization of the driven-cavity problem.

Use of indeterminate Padè approximations in the analysis of diffraction at the mirror edges of an optical resonator

A method is presented for analysis of the diffraction of waveguide modes at the open end of a two-dimensional metallic waveguide, based on a rational approximation of the field diffracted outside the open end. We believe that this method can be used for waveguides with nonplane walls, and it should prove a useful tool in the analysis of optical resonators.

Compressible flow in a hovercraft air cushion

A solution of the compressible fluid-dynamic equations describing the two-dimensional, inviscid, subsonic fluid-dynamic field in the peripheral jets of a hovercraft at zero forward speed is presented. The analysis is made in the hodograph plane in which the motion equation is linear and enables one to write the solution of the problem as a sum of elementary separable solutions of the equation. The stream function is expressed as a Fourier series whose coefficients can be calculated numerically with ease. The comparison of the results with those of a different representation, valid only in the incompressible case, shows that the two solutions coincide

A fast conformal mapping algorithm with no FFT

Abstract An algorithm is presented for the computation of a conformal mapping discretized on a non-uniformly spaced point set, useful for the numerical solution of many problems of fluid dynamics. Most existing iterative techniques, both those having a linear and those having a quadratic type of convergence, rely on the fast Fourier transform ( FFT) algorithm for calculating a convolution integral which represents the most time-consuming phase of the computation. The FFT, however, definitely cannot be applied to a non-uniform spacing. The algorithm presented in this paper has been made possible by the construction of a calculation method for convolution integrals which, despite not using an FFT, maintains a computation time of the same order as that of the FFT. The new technique is successfully applied to the problem of conformally mapping a closely spaced cascade of airfoils onto a circle, which requires an exceedingly large number of points if it is solved with uniform spacing.

Resistance of a Grooved Surface to Parallel and Cross Flow Calculated by B.E.M.

A study is described of both parallel and cross flow in the viscous sublayer generated by a fluid streaming along a grooved surface, with the aim of clarifying the phenomena that underlie the reduction of turbulent drag by such surfaces. A quantitative characterization of the effectiveness of different groove profiles in retarding secondary cross flow is given in terms of the difference of two “protrusion heights.” The development of a B.E.M. computer code for the analysis of general profiles is illustrated, and several examples are presented and discussed.

Electric-Discharge Excited Blast Waves in a Flat Subsonic Nozzle

The persistence of pressure waves generated by an electric discharge in the throat of a subsonic nozzle is studied analytically and numerically with particular reference to the operation of the high-power EUREKA excimer laser under construction at the national Italian ENEA Frascati laboratories. The attention is focused on transverse waves traveling parallel to the discharge electrodes. After some analytical estimates, a quasi-twodimensional numerical simulation is presented of the propagation of these waves in the anticipated geometry of the discharge chamber of the EUREKA laser. The possibility of reflection of pressure waves on the thermal slug left behind by the previous discharge is also considered. N a high-power, high-repetition-rate excimer laser, gas flows at a subsonic speed through a nozzle of elongated cross section in the throat of which an electric discharge is periodically fired with a repetition rate of the order of 1 kHz. Only about 1% of the energy released by the discharge is usefully converted into electromagnetic waves in the laser cavity positioned at the throat of the nozzle. All of the remaining energy instantaneously heats up the gas, with respect to the propagation time of sound, and produces blast waves that, if still present in the discharge chamber when the next pulse fires, may cause instability of the following discharges. A one-dimensional picture of the phenomenon is shown in Fig. 1. The initial instantaneous temperature and pressure increase subsequently divides up into three waves: an entropy wave (the thermal slug), which travels with the main flow velocity V\ and forward and backward pressure waves with velocity V + a and V — a, respectively (a being the speed of sound). In the simplified one-dimensional situation depicted in Fig. 1, these waves propagate out and do not interfere with following discharges if only enough time is allowed for all three waves to abandon the discharge volume. Provided that V<a/2, the slowest wave is the entropy wave; therefore, this criterion may be expressed figuratively by saying that the gas where one discharge has occurred must be washed out of the discharge volume before another discharge may be fired. However, various circumstances may disrupt such an ideal behavior: 1) If the pressure waves are strong enough to behave as shock waves, the entropy change through the backward wave may change the thermodynamical state of the gas arriving at the discharge section. 2) Obstacles or bends in the feed and exhaust ducts may reflect the waves back onto the discharge section. 3) Transverse waves, propagating at an angle with respect to the flow direction, may be excited by disuniformities in the discharge and come back on reflection by the lateral walls. Problem 1 is not a major concern for the typical energy release during a discharge of the order of 50 -s-100 J/l under a gas pressure of the order of some atmospheres. The shock strength can be calculated from the equation of state of an ideal gas to be given by

Effects of bending on free electron laser performance

Abstract The ability of electromagnetic radiation to follow bends of the electron beam path in a high-gain free electron laser is investigated by considering the mode structure of propagation inside a bent undulator. For this purpose the mode equation, previously studied in the context of optical guiding in a straight undulator, is modified so as to account for bending. A qualitative criterion for the significance of the bending effect is given, based on the identification of the relevant dimensionless parameter. Quantitative results are then obtained by solving approximately the mode equation of a bent undulator through an extension of the Rayleigh-Ritz variational technique. Diagrams of amplification rate vs bending parameter are given.

An Analysis of Optical Resonators with Tapered-Reflectivity Mirrors

In recent years many attempts have been undertaken to devise approximate analytical descriptions of unstable optical resonators. The starting point for a large part of this work has been the analysis of plane resonators carried out by Weinstein1,2.