Aeroacoustics of shear layers in internal flows : closed branches and wall perforations

Flow induced pulsations in resonant pipe networks have been observed in many technical applications, such as natural gas transport systems, steam lines of nuclear power plants and re-heat steam lines of boilers. These pulsations, which present a serious threat to the integrity of the systems, have been identifed as self-sustained aeroacoustic oscillations driven by the instability of the flow.The main goal of the proposed research is the prediction of the coupling of acoustic waves with shear layers formed by ow separation in internal flows and the design of remedial measures. We consider here, in particular, the shear layers formed at the opening of closed branches along a pipe and shear layers formed by grazing/bias ow along/through wall perforations.Although there are extensive studies in literature on the pulsations generated by the separating ow along a closed side branch, the configurations with the flow entering or leaving the side branch have not been recognized as source of pulsations. In our study, strong flow induced pulsations have been observed experimentally in configurations with a mean ow entering a side branch or flowing out of a side branch. When flow induced pulsations occur, wall vibrations can be significant amplitude limiting losses. Therefore, we propose an analytical model for the acoustical energy losses due to wall vibrations induced by an oscillating side branch. The study of the aeroacoustics of complex pipe systems was initiated considering a row of closed side branches placed along a main pipe. Systems with up to 15 shallow side branches produces flow induced pulsations in which the shear layer instability couples with a longitudinal acoustic standing wave along the main pipe. The side branches are not resonant. The whistling observed in such a system is similar to that observed in a main steam line along which a row of safety valves is placed. It is also a model for a corrugated pipe as used in risers for natural gas production. Our experiments and theoretical analysis demonstrate that the aeroacoustic sources are located near the acoustic pressure nodes of the longitudinal acoustic modes. A prediction model for the whistling behavior has been proposed, which is based on the \energy balance" between the acoustic sources and the acoustic losses. Experiments carried out on pipe systems with deep closed side branches show that these systems displays strong trapped modes. These systems have been used to test design rules aiming at a reduction of pulsation levels. The most commonly used solution, detuning the side branch length, appears to be inefficient in multiple deep side branch systems. We propose a semi-empirical model for the prediction of the self-sustained oscillations in pipe systems with closed deep side branches with rounded edged T-junctions. It can predict the oscillation amplitude of a system of six deep side branches within 50% and the oscillation frequency within 2%, for the first hydrodynamic mode. It strongly overestimates the amplitude of higher hydrodynamic modes. In car mufflers, liners of the aircraft engine and liners protecting the walls of combustion chambers, perforated walls are used to absorb sound. The sound absorption is due to the interaction of acoustic waves with the shear layers formed by grazing or/and bias flow. The sound absorption depends strongly on the shape of the perforations and on the ratio of bias to grazing flow velocity. In the low Strouhal number limit, the acoustic resistance (real part of the impedance) of a perforation is observed to be proportional to the steady-state resistance. A high value of the steady-state resistance leads to high pressure losses across the perforation. The design of an efficient acoustic damper requires an optimization between acoustic and fluid dynamic performances. Both resistance (real part of the impedance) and reactance (imaginary part of the impedance) due to a grazing-bias flow display an oscillating behavior as function of the Strouhal number. In particular, at high Strouhal numbers, positive (sound absorption) and negative (sound production) values of resistance are observed. The geometry of the perforation determines the whistling behavior at high Strouhal numbers. This operating condition should be avoided in technical applications. Analytical models of the steady flow and of the low frequency aeroacoustic behavior of a two-dimensional wall perforation are proposed allowing a quasi-steady prediction for the sound absorption at low Strouhal numbers. They compare favorably with the experiments

Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields

In the present study we consider planar piecewise linear vector fields with two zones separated by the straight line $x=0$. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, we provide a canonical form for these systems assuming that each linear system has center, a real one for $y<0$ and a virtual one for $y>0$, and such that the real center is a global center. Then, working with a first order piecewise linear perturbation we obtain piecewise linear differential systems with three crossing limit cycles. Second, we see that a sliding cycle can be detected after a second order piecewise linear perturbation. Finally, imposing the existence of a sliding limit cycle we prove that only one adittional crossing limit cycle can appear. Furthermore, we also characterize the stability of the higher amplitude limit cycle and of the infinity. The main techniques used in our proofs are the Melnikov method, the Extended Chebyshev systems with positive accuracy, and the Bendixson transformation.Comment: 24 pages, 7 figure

Fluid mechanics approach to acoustic liner design

Fluid mechanics approach to acoustic liner desig

SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x)

In this paper we prove the special bounded variation regularity of the gradient of a viscosity solution of the Hamilton-Jacobi equation partial derivative(t)u + H(t, x, D(x)u) = 0 in Omega subset of [0, T] x R-n under the hypothesis of uniform convexity of the Hamiltonian H in the last variable. This result extends the result of Bianchini, De Lellis, and Robyr obtained for a Hamiltonian H = H(D(x)u) which depends only on the spatial gradient of the solution

SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian

In this paper we consider a viscosity solution u of the Hamilton-Jacobi equation partial derivative(t)u + H(D(x)u) = 0 in Omega subset of [0,T] x R-n. where H is smooth and convex. We prove that when d(t,center dot) := H-p(D(x)u(t,center dot)), H-p := del H is BV for all t epsilon [0, T] and suitable hypotheses on the Lagrangian L hold, the Radon measure divd(t,center dot) can have Cantor part only for a countable number of t's in [0,T]. This result extends a result of Robyr for genuinely nonlinear scalar balance laws and a result of Bianchini, De Lellis and Robyr for uniformly convex Hamiltonians

3_D modeling using TLS and GPR techniques to characterize above and below-ground wood distribution in pyroclastic deposits along the Blanco River (Chilean Patagonia)

To date, the study of in-stream wood in rivers has been focused mainly on quantifying wood pieces deposited above the ground. However, in some particular river systems, the presence of buried dead wood can also represent an important component of wood recruitment and budgeting dynamics. This is the case of the Blanco River (Southern Chile) severely affected by the eruption of Chait\ue9n Volcano occurred between 2008 and 2009. The high pyroclastic sediment deposition and transport affected the channel and the adjacent forest, burying wood logs and standing trees. The aim of this contribution is to assess the presence and distribution of wood in two study areas (483 m2 and 1989 m2, respectively) located along the lower streambank of the Blanco River, and covered by thick pyroclastic deposition up to 5 m. The study areas were surveyed using two different devices, a Terrestrial Laser Scanner (TLS) and a Ground Penetrating Radar (GPR). The first was used to scan the above surface achieving a high point cloud density ( 48 2000 points m-2) which allowed us to identify and measure the wood volume. The second, was used to characterize the internal morphology of the volcanic deposits and to detect the presence and spatial distribution of buried wood up to a depth of 4 m. Preliminary results have demonstrated differences in the numerousness and volume of above wood between the two study areas. In the first one, there were 43 wood elements, 33 standing trees and 10 logs, with a total volume of 2.96 m3 (109.47 m3 km-1), whereas the second one was characterized by the presence of just 7 standing trees and 11 wood pieces, for a total amount of 0.77 m3 (7.73 m3 km-1). The dimensions of the wood elements vary greatly according to the typology, standing trees show the higher median values in diameter and length (0.15 m and 2.91 m, respectively), whereas the wood logs were smaller (0.06 m and 1.12 m, respectively). The low dimensions of deposited wood can be probably connected to their origin, suggesting that these elements were generated by toppling and breaking of surrounding dead trees. Results obtained with the GPR confirm the ability of this instrument to localize the presence and distribution of buried wood. From the 3- D analysis it was possible to assess the spatial distribution and to estimate, as first approach, the volume of the buried wood which represents approximately 0.04% of the entire volcanic deposit. Further analysis will focus on additional GPR calibration with different wood sizes for a more accurate estimation of the volume. The knowledge of the overall wood amount stored in a fluvial system that can be remobilized over time, represent an essential factor to ensure better forest and river management actions

Grain Sorghum Response to Band Applied Zinc Fertilizer

Zinc (Zn) is one of the micronutrients found to be deficient in Kansas. The objective of this study was to evaluate the response of grain sorghum to Zn fertilization using strip trials. The experiment was set up in Manhattan, KS, in 2015. The experimental design consisted of two strips, one with Zn fertilizer and the other without, with five replications. Zn fertilizer was applied as starter in combination with ammonium polyphosphate at the rate of 0.5 lb Zn/a. Plant tissue samples were collected to determine Zn content. Grain yield was recorded by combine equipped with yield monitor. No significant differences were found for sorghum grain yield. Grain Zn content increased with Zn fertilization. Zn fertilization may be considered for future studies in food biofortification