Acoustic Boundary Conditions Research Articles

Exponential stabilization of wave equation with acoustic boundary conditions and its application to memory‐type boundary

In this paper, we deal with the wave equation with acoustic boundary conditions. The exponential stabilization is obtained by Lyapunov approach and Riemannian geometry method. We then apply our main theorem to the wave equations with memory‐type acoustic boundary conditions, which is not available in the literature and give an example in the end.

Well-posedness and stability for Kirchhoff equation with non-porous acoustic boundary conditions

In this paper we prove the well-posedness to the wave equation of Kirchhoff type. Under a portion of the boundary, we consider the acoustic boundary conditions. We also prove the exponential stability of the energy associated to the problem. Our result generalize the previous literature where only the Carrier model was considered (when the nonlinearity involves the L2(Ω) norm) or the Kirchhoff model with porous acoustic boundary conditions. The main tool is the Faedo-Galerkin method. Due to the presence of acoustic boundary conditions, we can not use special basis and new estimates are necessary. To prove the stability we use integral estimates.

Robustness of Polynomial Stability of Damped Wave Equations

In this paper we present new results on the preservation of polynomial stability of damped wave equations under addition of perturbing terms. We in particular introduce sufficient conditions for the stability of perturbed two-dimensional wave equations on rectangular domains, a one-dimensional weakly damped Webster’s equation, and a wave equation with an acoustic boundary condition. In the case of Webster’s equation, we use our results to compute explicit numerical bounds that guarantee the polynomial stability of the perturbed equation.

A GENERAL DECAY RESULT FOR A VON KARMAN EQUATION WITH MEMORY AND ACOUSTIC BOUNDARY CONDITIONS

<abstract> We study a viscoelastic von Karman equation of memory type with acoustic boundary conditions. Utilizing some properties of convex functions and the perturbed energy method, we build a general decay result when the kernel function $ k $ is a very general type. This work extends and complements some previous decay results of solutions for von von Karman equations. </abstract>

Energy decay for a wave equation of variable coefficients with logarithmic nonlinearity source term

We investigate the variable-coefficient wave equation with nonlinear acoustic boundary conditions and logarithmic nonlinearity source term. In addition, the damping is nonlinear, and plays a role only in part of the boundary. Using the semigroup theory, we state the existence and uniqueness of the local solutions. Accordingly, we prove that under some assumptions on the initial data, the local solution can be extended to be global. Particularly, it has been shown that the decay rates of the system are given implicitly as solutions to a first-order ODE by applying the Riemannian geometry method.

On a nonlinear problem with Dirichlet and Acoustic boundary conditions

The aims of this paper are to establish theoretical analysis and numerical simulation for a nonlinear wave equation with mixed boundary conditions of Dirichlet and Acoustic type. The theoretical results are about: existence and uniqueness of global solutions, regularity and uniform stability of these global solutions and an exponential decay rate for energy. In the numerical context, simulations are presented using the finite element method in space (with linear and quadratic Lagrange basis), the Crank-Nicolson method in time and, for each discrete time, the Newton’s method is used to solve the nonlinear algebraic system. Furthermore, the energy exponential decay and convergence order (sub-optimal and optimal) are presented numerically.

Swirler geometry effects (dh/do ratio) on synthetic gas flames. Part 2: dynamic flame behaviour at external y altered acoustic conditions

In a combustion device, unsteady heat release causes acoustic energy to increase when acoustic damping (energy loss) is not that effective, and, as a result, thermo-acoustic flame instabilities occur. In this study, effects of the swirler dh/do ratio (at different swirl numbers) on dynamic flame behaviour of the premixed 20%CNG/30%H2/30%CO/20%CO2 mixture under externally altered acoustic boundary conditions and stability limits (flashback and blowout equivalence ratios) of such mixture were investigated in a laboratory-scale variable geometric swirl number combustor. Therefore, swirl generators with different dh/do ratios (0.3 and 0.5) and geometric swirl numbers (0.4, 0.6, 0.8, 1.0 1.2 and 1.4) were designed and manufactured. Acoustic boundary conditions in the combustion chamber were altered using loudspeakers, and flame response to these conditions was perceived using photodiodes and pressure sensors. Dynamic flame behaviour of respective mixture was evaluated using luminous intensity and pressure profiles. Results showed that the dh/do ratio has a minor impact on dynamic flame behaviour.

The effect of the convective momentum transfer on the acoustic boundary condition of perforated liners with grazing mean flow

The interaction of sound with sound-permeable hard walls subjected to grazing mean flow is investigated with a focus on the sound-induced exchange of streamwise momentum between the mean flow and the wall. Two generic wall types have to be distinguished, the homogeneously permeable wall and the wall with clearly separated openings, which is a more realistic model of technically feasible walls. To begin with, the focus is on the shear stress that drives the dynamics of the shearing mean flow over the homogeneous wall. This is analyzed by means of two simple mathematical models of shear stress diffusion, which come as two equivalent pairs of differential equations either for the acoustic shear stress and the wall-normal displacement, or for the streamwise and the wall-normal components of the acoustic velocity. The physical analysis is concentrated on the relation between shear stress and the wall-normal displacement of the fluid elements, which determines the effective admittance of the wall. The shear stress is represented by the momentum transfer impedance which is defined as the ratio between the acoustic wall shear stress and the in-wall velocity evaluated at the wall. It turns out that the strong increase of the acoustic wall shear stress due to transfer of mean flow momentum to the wall is the dominating mechanism which affects the effective admittance of the wall. Nevertheless, the suitability of the momentum transfer impedance as part of a complete boundary condition of the wall is questioned. The disagreement between the predicted momentum transfer impedance and some rare experimental data obtained with real inhomogeneous walls is considered as a strong indication that some further mechanisms are invoked by the inhomogeneity of real walls which are briefly discussed with regard to future studies.

Global solutions of wave equations with multiple nonlinear source terms under acoustic boundary conditions

Under the acoustic boundary conditions, the initial boundary value problem of a wave equation with multiple nonlinear source terms is considered. This paper gives the energy functional of regular solutions for the wave equation and proves the decreasing property of the energy functional. Firstly, the existence of a global solution for the wave equation is proved by the Faedo–Galerkin method. Then, in order to obtain the nonexistence of global solutions for the wave equation, a new functional is defined. When the initial energy is less than zero, the special properties of the new functional are proved by the method of contraction. Finally, the conditions for the nonexistence of global solutions of the wave equation with acoustic boundary conditions are analyzed by using these special properties.

Influence of cavitation on the acoustic boundary conditions in water hammer experiments

A water hammer event is created by stopping a flow in a pipeline using a fast closing valve. The pressure is measured at three different positions upstream the valve. Cavitation occurs close to the valve and is detected by vapour pressure in the pipeline. Frequencies in the liquid part of the pipe were measured and statistically evaluated in order to analyse whether cavitation acts as a boundary condition of acoustics.Without cavitation one side of the pipe is an open end, while the other side is a closed end. In presence of cavitation the cavity should act like an open end due to the high change of acoustic impedance from liquid to gaseous phase. Therefore it is expected that the oscillating behavior is changing from an open/close to an open/open system. The measured frequencies indeed show a change towards an open/open configuration. It is shown that cavitation acts as a boundary condition in this system.

Prediction of vibration radiation noise from shell of straw crushing machine

In order to predict the radiation noise of the vibrating shell of the straw crusher in the design phase, the computational fluid dynamics–discrete element coupling method is initially used to simulate the airflow–straw coupled flow field in the straw crusher, and the pulsating pressure generated by the coupled flow field is applied to the inner surface of the shell of the crusher. Then, the harmonic response of the shell is analyzed, and its results are used to be the acoustic boundary condition. Finally, the finite element and acoustic boundary element combined test methods are used to predict vibration noise of the straw crusher shell. The results indicate that the produced vibration noise of the straw crusher shell changes as the excitation frequency of the rotor rotation changes. The maximum vibration noise is achieved at the excitation fundamental frequency, and radiation noises at the harmonic frequencies decrease as the frequency increases. The simulated value of the sound pressure level of each measuring point at the excitation fundamental frequency and harmonic frequencies is basically the same as those of the experiment. Moreover, it is found that the maximum difference between the simulated and experimental value of measuring points is 1.69 dB(A). Therefore, it is concluded that the numerical model of the vibration radiation noise is accurate. The vibration noise of the shell at the inlet is the largest, and the main noise source of the vibration radiation noise is the dipole sound source of the rotating hammer rotor. The corresponding design method provides the reference for the low-noise design of straw crushers.

General Decay Result for a Type III Thermoelastic Coupled System with Acoustic Boundary Conditions in the Presence of Distributed Delay

General Decay Result for a Type III Thermoelastic Coupled System with Acoustic Boundary Conditions in the Presence of Distributed Delay

New general stability for a variable coefficient thermo-viscoelastic-coupled system of second sound with acoustic boundary conditions

In this paper, we consider a variable coefficient thermo-viscoelastic-coupled system of second sound with acoustic boundary conditions, where the heat conduction is given by Cattaneo’s law. We establish a general decay of energy-associated solutions under a class of generality of the relaxation function. Our result extends the various decay results obtained for problems with or without thermo-viscoelasticity.

A categorization of marginally stable thermoacoustic modes based on phasor diagrams

Phasor diagrams are utilized to plot and analyze thermoacoustic modes in a duct with ideal closed/open acoustic boundary conditions that contains a velocity-sensitive flame. Inspection of phasor diagrams that represent fluctuations of velocity, pressure, heat release rate and characteristic wave amplitudes at the flame elicits characteristic features of marginally stable, intrinsic thermoacoustic (ITA) modes: the sign of velocity fluctuations and the sign of the gradient of pressure fluctuations change across the flame. These sign changes result from a reversal of direction of the velocity phasor across the flame, affected by unsteady heat release exactly out-of-phase with respect to upstream velocity fluctuations and of sufficient strength. Unlike alternative methods proposed for the identification of ITA modes, the proposed categorization does not involve a parameter sweep, but relies on an analogy with the structure of ITA modes in an anechoic environment. The phasor diagram also elucidates that continuous transitions from acoustic to ITA modes and vice versa can be achieved by an increase or decrease of the gain of the flame transfer function. The representation of acoustic wave propagation in terms of phasors facilitates the formulation of a compact dispersion relation of the thermoacoustic configuration under consideration. The value of the transitional gain of the flame transfer function, where acoustic/ITA transitions occur, may be deduced easily from the dispersion relation. A plot of solution branches of acoustic and ITA modes illustrates how the respective mode transitions, and how they can be related to the well-known quarter wave modes of a closed/open resonator. It is observed that under variation of transfer function gain and phase, marginally stable eigenmodes may occur at almost any frequency, not only at frequencies that correspond to the quarter-wave modes.

Investigation and validation of the dynamic response of an acoustically levitated particle using the lattice Boltzmann method

The stable levitation of an analyte sample in an acoustic levitator is a primary requirement for accurate x-ray characterization of its scientific structure. A rigid particle oscillates in an under-damped manner when introduced into the node of established standing acoustic waves. This investigation has employed the lattice Boltzmann method (LBM), a computational fluid dynamics technique, for the analysis of such rigid particle dynamics in acoustic levitation. The simulation uses the two dimensional and nine velocity (D2Q9) Bhatnagar–Gross–Krook formulation to levitate a rigid 1.6 mm diameter nylon (ρ = 1150 kg/m3) particle in the air at standard pressure and temperature conditions. The presented work is the first reported simulation of realistic acoustic levitator boundary conditions using the LBM. The simulation can capture the particle–fluid interactions that produce dynamic levitation at less than one-period timescale in the ultrasonic frequency regime. An experiment was conducted by levitating a 1.6 mm-diameter nylon sphere to estimate the oscillations, and the oscillating frequency was found to be 50 Hz. The dynamic simulation results are consistent with experimental results for particle oscillations within the same order of magnitude, indicating that LBM formulation can be successfully used to study acoustic levitation to understand and mitigate particle jitter. The distortion of the acoustic field due to a levitating particle’s presence was also analyzed to demonstrate how the presence of the particle can disrupt adjacent levitating nodes.

Directional sound source modeling using the adjoint Euler equations in a finite-difference time-domain approach.

An adjoint-based approach for synthesizing complex sound sources by discrete, grid-based monopoles in finite-difference time-domain simulations is presented. Previously, Stein, Straube, Sesterhenn, Weinzierl, and Lemke [(2019). J. Acoust. Soc. Am. 146(3), 1774-1785] demonstrated that the approach allows one to consider unsteady and non-uniform ambient conditions such as wind flow and thermal gradient in contrast to standard methods of numerical sound field simulation. In this work, it is proven that not only ideal monopoles but also realistic sound sources with complex directivity characteristics can be synthesized. In detail, an oscillating circular piston and a real two-way near-field monitor are modeled. The required number of monopoles in terms of the sound pressure level deviation between the directivity of the original and the synthesized source is analyzed. Since the computational effort is independent of the number of monopoles used for the synthesis, also more complex sources can be reproduced by increasing the number of monopoles utilized. In contrast to classical least-square problem solvers, this does not increase the computational effort, which makes the method attractive for predicting the effect of sound reinforcement systems with highly directional sources under difficult acoustic boundary conditions.

Energy decay for variable coefficient viscoelastic wave equation with acoustic boundary conditions in domains with nonlocally reacting boundary

In this article, we study a variable coefficients viscoelastic wave equation with acoustic boundary conditions in domains with nonlocally reacting boundary. By constructing suitable Lyapunov functionals and using the energy compensation method, we prove that under suitable conditions on the initial data and the relaxation function, the energy of the system has an explicit and general decay rate.&#x0D; For more information see https://ejde.math.txstate.edu/Volumes/2020/95/abstr.html

Optimal decay rates for the acoustic wave motions with boundary memory damping

A linear wave equation with acoustic boundary conditions (ABC) on a portion of the boundary and Dirichlet conditions on the rest of the boundary is considered. The (ABC) contain a memory damping with respect to the normal displacement of the boundary point. In this paper, we establish polynomial energy decay rates for the wave equation by using resolvent estimates.

A residual a posteriori error estimate for the time–domain boundary element method

This article investigates residual a posteriori error estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable estimates for Dirichlet and acoustic boundary conditions which hold for a large class of discretizations. Efficiency of the error estimate is shown for a natural discretization of low order. Numerical examples confirm the theoretical results. The resulting adaptive mesh refinement procedures in 3d recover the adaptive convergence rates known for elliptic problems.

Numerical Investigation of Combustion Instabilities in a Single-Element Lean Direct Inject Combustor Using Flamelet Based Approaches

Abstract In this paper, high-fidelity large eddy simulations (LES) along with flamelet-based combustion models are assessed to predict combustion dynamics in low-emission gas turbine combustor. A model configuration of a single-element lean direct injection (LDI) combustor from Purdue University (Huang et al., 2014, “Combustion Dynamics Behavior in a Single-Element Lean Direct Injection (LDI) Gas Turbine Combustor,” 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Cleveland, OH, July 28–30.) is used for the validation of simulation results. Two combustion models based on the flamelet concept, i.e., steady diffusion flamelet (SDF) model and flamelet generated manifold (FGM) model are employed to predict combustion instabilities. Simulations are carried out for two equivalence ratios of φ = 0.6, and 0.4. The results in the form of mode shapes, peak to peak pressure amplitude and power spectrum density (PSD) are compared with the experimental data of Huang et al. (2014, “Combustion Dynamics Behavior in a Single-Element Lean Direct Injection (LDI) Gas Turbine Combustor,” 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Cleveland, OH, July 28–30.). The effect of variation in the time-step size hence acoustic courant number is studied. Further, two numerical solver options, i.e., pressure-based segregated solver and pressure-based coupled solver, are used to understand their effect on the solution convergence regarding the number of time-steps required to reach the limit cycle of the pressure oscillations. A truncated (half) domain simulation is performed by applying an appropriate acoustic impedance boundary condition at the truncated location. Overall, the simulation results compare well with the experimental data and trends are captured accurately in all simulations. It builds confidence in flamelet-based combustion models for the use in combustion instability modeling which is traditionally done using finite rate chemistry models based on reduced kinetics.