A synthetic perturbative hypothesis for multiscale analysis of bluff-body wake instability

(Abstract

A new matched asymptotic expansion for the intermediate and far flow behind a finite body

An approximated Navier-Stokes steady solution is here presented for the two dimensional bluff body wake region that is intermediate between the field on the body scale LD, which includes the two symmetric counter-rotating eddies, and the ultimate far wake. The nonparallelism of the streamlines in the intermediate wake cannot yet be considered negligible. The R is of the order of the critical value for the onset of the first instability and the limiting behavior for large R is not considered. The solution is obtained by matching an inner solution—a Navier-Stokes expansion in powers of the inverse of the longitudinal coordinate—and an outer solution, which is a Navier-Stokes asymptotic expansion in powers of the inverse of the distance from the body. The matching is built on the criteria that, where the two solutions meet, the longitunal pressure gradients and the vorticities must be equal and the flow toward the inner layer must be equal to the outflow from the external stream. At high orders in the inner expansion solution, the lateral decay turns out to be algebraic. This approximate solution is here examined in relation to the class of asymptotic solutions that, in the past, were obtained by adopting the rapid decay principle, which implies an irrotational outer flow. The theme running through this paper is the necessity of the addition of this criterion to the equations of motion to build a solution that describes the intermediate wake. The present solution has been obtained by relaxing the imposition of the rapid decay principle. It can be concluded that, at Reynolds numbers as low as the first critical value and where the nonparallelism of the streamlines is not yet negligible, the division of the field into two basic parts—an inner vortical boundary layer flow and an outer potential flow—is spontaneously shown up to the second order of accuracy: at higher orders in the expansion solution the vorticity is first convected and then diffused in the outer field. If exploited to represent the basic flow of bluff body wakes, the analytical simplicity of this asymptotic expansion could be useful for the nonparallel analysis of the instability of two-dimensional wakes

Experimental assessment of drag reduction by traveling waves in a turbulent pipe flow

We experimentally assess the capabilities of an active, open-loop technique for drag reduction in turbulent wall flows recently introduced by Quadrio et al. [J. Fluid Mech., v.627, 161, (2009)]. The technique consists in generating streamwise-modulated waves of spanwise velocity at the wall, that travel in the streamwise direction. A proof-of-principle experiment has been devised to measure the reduction of turbulent friction in a pipe flow, in which the wall is subdivided into thin slabs that rotate independently in the azimuthal direction. Different speeds of nearby slabs provide, although in a discrete setting, the desired streamwise variation of transverse velocity. Our experiment confirms the available DNS results, and in particular demonstrates the possibility of achieving large reductions of friction in the turbulent regime. Reductions up to 33% are obtained for slowly forward-traveling waves; backward-traveling waves invariably yield drag reduction, whereas a substantial drop of drag reduction occurs for waves traveling forward with a phase speed comparable to the convection speed of near-wall turbulent structures. A Fourier analysis is employed to show that the first harmonics introduced by the discrete spatial waveform that approximates the sinusoidal wave are responsible for significant effects that are indeed observed in the experimental measurements. Practical issues related to the physical implementation of this control scheme and its energetic efficiency are briefly discussed.Comment: Article accepted by Phys. Fluids. After it is published, it will be found at http://pof.aip.or

A synthetic perturbative hypothesis for the multiscale analysis of the wake instability

The paper presents a nonparallel stability analysis of the intermediate region of the two-dimensional wake behind a bluff body. In particular, it analyzes the convective instabilities using a Wentzel-Kramers-Brillouin-Jeffreys method on a basic flow previously derived from intermediate asymptotics D. Tordella and M. Belan, Phys. Fluids 15, 1897, 2003. The multiscaling is carried out to explicitly account for the effects associated to the lateral momentum dynamics at a given Reynolds number. These effects are an important feature of the base flow and are included in the perturbative equation as well as in the associated modulation equation. At the first order in the multiscaling, the disturbance is locally tuned to the property of the instability, as can be seen in the zero-order theory near-parallel parametric Orr-Sommerfeld treatment. This leads to a synthetic analysis of the nonparallel correction of the instability characteristics. The system is, in fact, considered to be locally perturbed by waves with a wave number that varies along the intermediate wake and which is equal to the wave number of the dominant saddle point of the zero order dispersion relation, taken at different Reynolds numbers. In this study, the Reynolds number is thus the only parameter. It is shown that the corrections to the frequency, and to the temporal and spatial growth rates are remarkable in the first part of the intermediate wake and lead to absolute instability in regions that extend to about ten body scales. The correction increases with the Reynolds number and agrees with data from laboratory and numerical experiments in literature. An eigenfunction and eigenvalue asymptotic analysis for the far wake is included, which is in excellent agreement with the complete problem

Determination of density and concentration from fluorescent images of a gas flow

A fluorescent image analysis procedure to determine the distribution of species concentration and density in a gas flow is proposed. The fluorescent emission is due to the excitation of atoms/molecules of a gas that is intercepted by an electron blade. The intensity of the fluorescent light is proportional to the local number density of the gas. When the gas flow is a mixture of different species, this proportionality can be exploited to extract the contribution associated to the species from the spectral superposition acquired by a digital camera. This yields a method that simultaneously reveals species concentrations and mass density of the mixture. The procedure is applied to two under-expanded sonic jets discharged into a different gas ambient - Helium into Argon and Argon into Helium - to measure the concentration and density distribution along the jet axis and across it. A comparison with experimental and numerical results obtained by other authors when observing under-expanded jets at different Mach numbers is made with the density distribution along the axis of the jet. This density distribution appears to be self-similar.Comment: New figures in portable .eps forma

A High-Precision and Low-Cost Dew Point Equipment with Fuzzy Control System

The control of environmental conditions in some sectors of the industry is essential since the variation of these parameters can influence the quality of the manufactured product. For this, it is necessary to use measuring equipment with high precision, and when referring to the measurement of relative humidity, the dew point meter is indispensable. The chilled mirror method for measure °Cdp is the one of the most accurate that exists in the market, but these devices typically are high cost, hampering access to small businesses. The chilled mirror method basically consists of a PID (Proportional Integral Derivative) control of the temperature of a Peltier module based on the reading of the light intensity generated from the reflection of a light source. In this context, the proposal of this work is to develop a high precision and low cost device, operating in the range of -20 to 20°Cdp, replacing the traditional PID control by a Fuzzy control system, providing better accuracy in control, thus making a viable product mainly for small and medium-sized companies. The results presented show the feasibility of the proposal of this work, obtaining 98.9% accurate readings when compared with a reference equipment, and a maximum deviation observed was of 0.02°Cdp, thus proving its precision. Another point to note is the low cost of the equipment, approximately US$ 120.00, thus reaching the proposed objective

The Hydrodynamics of Astrophysical jets: Scaled Experiments and Numerical Simulations

Context. In this paper we study the propagation of hypersonic hydrodynamic jets (Mach number >5) in a laboratory vessel and make comparisons with numerical simulations of axially symmetric flows with the same initial and boundary conditions. The astrophysical context is that of the jets originating around young stellar objects (YSOs). Aims. In order to gain a deeper insight into the phenomenology of YSO jets, we performed a set of experiments and numerical simulations of hypersonic jets in the range of Mach numbers from 10 to 20 and for jet-to-ambient density ratios from 0.85 to 5.4, using different gas species and observing jet lengths of the order of 150 initial radii or more. Exploiting the scalability of the hydrodynamic equations, we intend to reproduce the YSO jet behaviour with respect to jet velocity and elapsed times. In addition, we can make comparisons between the simulated, the experimental, and the observed morphologies. Methods. In the experiments the gas pressure and temperature are increased by a fast, quasi-isentropic compression by means of a piston system operating on a time scale of tens of milliseconds, while the gas density is visualized and measured by means of an electron beam system. We used the PLUTO software for the numerical solution of mixed hyperbolic/parabolic conservation laws targeting high Mach number flows in astrophysical fluid dynamics. We considered axisymmetric initial conditions and carried out numerical simulations in cylindrical geometry. The code has a modular flexible structure whereby different numerical algorithms can be separately combined to solve systems of conservation laws using the finite volume or finite difference approach based on Godunov-type schemes. Results. The agreement between experiments and numerical simulations is fairly good in most of the comparisons. The resulting scaled flow velocities and elapsed times are close to the ones shown by observations. The morphologies of the density distributions agree with the observed ones as well. Conclusions. The laboratory and the simulated hypersonic jets are all pressure matched, i.e. their axial regions are almost isentropic at the nozzle exit. They maintain their collimation for long distances in terms of the initial jet radii, without including magnetic confinement effects. This yields a qualitatively good agreement with the observed YSO jet morphologies. It remains to be seen what happens when non-axially symmetric perturbations of the flow are imposed at the nozzle, both in the experiment and in the simulation