1,735 research outputs found
Theory of pressure acoustics with boundary layers and streaming in curved elastic cavities
The acoustic fields and streaming in a confined fluid depend strongly on the
acoustic boundary layer forming near the wall. The width of this layer is
typically much smaller than the bulk length scale set by the geometry or the
acoustic wavelength, which makes direct numerical simulations challenging.
Based on this separation in length scales, we extend the classical theory of
pressure acoustics by deriving a boundary condition for the acoustic pressure
that takes boundary-layer effects fully into account. Using the same
length-scale separation for the steady second-order streaming, and combining it
with time-averaged short-range products of first-order fields, we replace the
usual limiting-velocity theory with an analytical slip-velocity condition on
the long-range streaming field at the wall. The derived boundary conditions are
valid for oscillating cavities of arbitrary shape and wall motion as long as
the wall curvature and displacement amplitude are both sufficiently small.
Finally, we validate our theory by comparison with direct numerical simulation
in two examples of two-dimensional water-filled cavities: The well-studied
rectangular cavity with prescribed wall actuation, and the more generic
elliptical cavity embedded in an externally actuated rectangular elastic glass
block.Comment: 18 pages, 5 figures, pdfLatex, RevTe
Two-way coupling of FENE dumbbells with a turbulent shear flow
We present numerical studies for finitely extensible nonlinear elastic (FENE)
dumbbells which are dispersed in a turbulent plane shear flow at moderate
Reynolds number. The polymer ensemble is described on the mesoscopic level by a
set of stochastic ordinary differential equations with Brownian noise. The
dynamics of the Newtonian solvent is determined by the Navier-Stokes equations.
Momentum transfer of the dumbbells with the solvent is implemented by an
additional volume forcing term in the Navier-Stokes equations, such that both
components of the resulting viscoelastic fluid are connected by a two-way
coupling. The dynamics of the dumbbells is given then by Newton's second law of
motion including small inertia effects. We investigate the dynamics of the flow
for different degrees of dumbbell elasticity and inertia, as given by
Weissenberg and Stokes numbers, respectively. For the parameters accessible in
our study, the magnitude of the feedback of the polymers on the macroscopic
properties of turbulence remains small as quantified by the global energy
budget and the Reynolds stresses. A reduction of the turbulent drag by up to
20% is observed for the larger particle inertia. The angular statistics of the
dumbbells shows an increasing alignment with the mean flow direction for both,
increasing elasticity and inertia. This goes in line with a growing asymmetry
of the probability density function of the transverse derivative of the
streamwise turbulent velocity component. We find that dumbbells get stretched
referentially in regions where vortex stretching or bi-axial strain dominate
the local dynamics and topology of the velocity gradient tensor.Comment: 20 pages, 10 Postscript figures (Figures 5 and 10 in reduced quality
A ducted wind turbine simulation model for building simulation
Power production is shifting away from centralized generation plants to production of heat and power at the point of demand. A technology that may play a part in this shift is the ducted wind turbine (DWT). The emergence of small building integrated micro turbines opens up the possibility of utilizing the differential pressures occurring around buildings for local power production. This paper describes work to develop and test a simple mathematical model of a ducted wind turbine and its integration within a building simulation tool. A case study in which the simulation model will be used to analyse of the likely power output from a building incorporating ducted wind turbines within the façade is also presented
Precise fabrication of ultra violet dielectric dispersion compensating mirrors
The present contribution is concentrated on an improved method to manufacture dielectric dispersion compensating mirrors in the ultra violet (UV) range by applying a novel online phase monitoring device. This newly developed measurement tool monitors the group delay (GD) and group delay dispersion (GDD) of the electromagnetic field in situ during the deposition of the layer system. Broad band monitoring of the phase enhances the accuracy in the near infrared spectral range (NIR), significantly. In this study, the correlation of the GDD in the NIR and in the UV spectral range is investigated. A design synthesis is introduced to achieve optimum reflection and GDD target values in the UV and NIR. This requires a similar behavior of both bands according to deposition errors, to guarantee switching off the UV GDD target band proper, while monitoring the GDD in the NIR spectral range. The synthesis results in a design, characterized by a GDD of -100fs2±20fs2 between 330nm and 360nm in the UV and by -450fs2±10fs2 within 820nm to 870nm in the NIR. The fabricated sample, applying an ion beam sputtering process, consists of a 9μm layer stack of Hafnium oxide and Silicon dioxide. The first layers of the stack are switched and controlled by a conventional in situ spectrometric broad band monitoring in conjunction with a forward re-optimization algorithm, which also manipulates the layers remaining for deposition at each switching event. To accomplish the demanded GDD-spectra, the last layers are controlled by the novel in situ GDD monitor. © 2015 SPIE.DFG/EXC/QUESTDFG/13N1155
Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube.
Buoyancy-driven turbulent mixing of fluids of slightly different densities [At = Δρ/(2〈ρ〉) = 1.15×10−2] in a long circular tube tilted at an angle θ = 15° from the vertical is studied at the local scale, both experimentally from particle image velocimetry and laser induced fluorescence measurements in the vertical diametrical plane and numerically throughout the tube using direct numerical simulation. In a given cross section of the tube, the axial mean velocity and the mean concentration both vary linearly with the crosswise distance z from the tube axis in the central 70% of the diameter. A small crosswise velocity component is detected in the measurement plane and is found to result from a four-cell mean secondary flow associated with a nonzero streamwise component of the vorticity. In the central region of the tube cross section, the intensities of the three turbulent velocity fluctuations are found to be strongly different, that of the streamwise fluctuation being more than twice larger than that of the spanwise fluctuation which itself is about 50% larger than that of the crosswise fluctuation. This marked anisotropy indicates that the turbulent structure is close to that observed in homogeneous turbulent shear flows. Still in the central region, the turbulent shear stress dominates over the viscous stress and reaches a maximum on the tube axis. Its crosswise variation is approximately accounted for by a mixing length whose value is about one-tenth of the tube diameter. The momentum exchange in the core of the cross section takes place between its lower and higher density parts and there is no net momentum exchange between the core and the near-wall regions. A sizable part of this transfer is due both to the mean secondary flow and to the spanwise turbulent shear stress. Near-wall regions located beyond the location of the extrema of the axial velocity (|z|≳0.36 d) are dominated by viscous stresses which transfer momentum toward (from) the wall near the top (bottom) of the tube
Crossflow instability of finite Bödewadt flows: transients and spiral waves
The flow in an enclosed rotating cylinder with a stationary lower end wall is investigated numerically. For fast rotation rates, the flow in the interior is primarily in the azimuthal direction, with an angular momentum distribution very close to that corresponding to solid-body rotation for
about the inner-half radius. The differential rotation sets up a large-scale circulation that is primarily present in the boundary layers on the rotating top and sidewalls and the stationary bottom wall, with a very weak effusive component throughout the bulk interior providing a matching between the boundary layer flows on the top and bottom. The top end wall boundary layer has a profile that very
closely matches the von Kármán solution for a rotating disk boundary layer; it is stable and very robust to finite disturbances for all rotation rates considered. The boundary layer on the stationary bottom end wall has a profile that agrees with the Bödewadt solution for a stationary disk with an
ambient flow in solid-body rotation. This boundary layer is not robust, suffering crossflow instability to multiarmed spiral waves via a supercritical Hopf bifurcation, as well as being susceptible to axisymmetric circular waves that travel radially inward where the boundary layer profile is most
inflectional. In the absence of any external forcing, the circular waves are transitory, but low amplitude forcing can sustain them indefinitely, whereas the spiral waves are essentially unaffected by the external forcing.Peer ReviewedPostprint (published version
Sand as Maxwell's demon
We consider a dilute gas of granular material inside a box, kept in a
stationary state by shaking. A wall separates the box into two identical
compartments, save for a small hole at some finite height . As the gas is
cooled, a second order phase transition occurs, in which the particles
preferentially occupy one side of the box. We develop a quantitative theory of
this clustering phenomenon and find good agreement with numerical simulations
Cavitation inception of a van der Waals fluid at a sack-wall obstacle
Cavitation in a liquid moving past a constraint is numerically investigated
by means of a free-energy lattice Boltzmann simulation based on the van der
Waals equation of state. The fluid is streamed past an obstacle and, depending
on the pressure drop between inlet and outlet, vapor formation underneath the
corner of the sack-wall is observed. The circumstances of cavitation formation
are investigated and it is found that the local bulk pressure and mean stress
are insufficient to explain the phenomenon. Results obtained in this study
strongly suggest that the viscous stress, interfacial contributions to the
local pressure, and the Laplace pressure are relevant to the opening of a vapor
cavity. This can be described by a generalization of Joseph's criterion that
includes these contributions. A macroscopic investigation measuring mass flow
rate behavior and discharge coefficient was also performed. As theoretically
predicted, mass flow rate increases linearly with the square root of the
pressure drop. However, when cavitation occurs, the mass flow growth rate is
reduced and eventually it collapses into a choked flow state. In the cavitating
regime, as theoretically predicted and experimentally verified, the discharge
coefficient grows with the Nurick cavitation number
Branching of the Falkner-Skan solutions for λ < 0
The Falkner-Skan equation f'" + ff" + λ(1 - f'^2) = 0, f(0) = f'(0) = 0, is discussed for λ < 0. Two types of problems, one with f'(∞) = 1 and another with f'(∞) = -1, are considered. For λ = 0- a close relation between these two types is found. For λ < -1 both types of problem allow multiple solutions which may be distinguished by an integer N denoting the number of zeros of f' - 1. The numerical results indicate that the solution branches with f'(∞) = 1 and those with f'(∞) = -1 tend towards a common limit curve as N increases indefinitely. Finally a periodic solution, existing for λ < -1, is presented.
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