Time-domain CFD computation and analysis of acoustic attenuation performance of water-filled silencers

The multi-dimensional time-domain computational fluid dynamics(CFD) approach is extended to calculate the acoustic attenuation performance of water-filled piping silencers. Transmission loss predictions from the time-domain CFD approach and the frequency-domain finite element method(FEM) agree well with each other for the dual expansion chamber silencer, straight-through and cross-flow perforated tube silencers without flow. Then, the time-domain CFD approach is used to investigate the effect of flow on the acoustic attenuation characteristics of perforated tube silencers. The numerical predictions demonstrate that the mean flow increases the transmission loss, especially at higher frequencies, and shifts the transmission loss curve to lower frequencies.

Application of dual reciprocity boundary element method to predict acoustic attenuation characteristics of marine engine exhaust silencers

In marine engine exhaust silencing systems, the presence of exhaust gas flow influences the sound propagation inside the systems and the acoustic attenuation performance of silencers. In order to investigate the effects of three-dimensional gas flow and acoustic damping on the acoustic attenuation characteristics of marine engine exhaust silencers, a dual reciprocity boundary element method (DRBEM) was developed. The acoustic governing equation in three-dimensional potential flow was derived first, and then the DRBEM numerical procedure is given. Compared to the conventional boundary element method (CBEM), the DRBEM considers the second order terms of flow Mach number in the acoustic governing equation, so it is suitable for the cases with higher Mach number subsonic flow. For complex exhaust silencers, it is difficult to apply the single-domain boundary element method, so a substructure approach based on the dual reciprocity boundary element method is presented. The experiments for measuring transmission loss of silencers are conducted, and the experimental setup and measurements are explained. The transmission loss of a single expansion chamber silencer with extended inlet and outlet were predicted by DRBEM and compared with the measurements. The good agreements between predictions and measurements are observed, which demonstrated that the derived acoustic governing equation and the DRBEM numerical procedure in the present study are correct.

A Time-Domain Method for Hydroelastic Analysis of A Moored Oil Storage Vessel in Wind,Irregular Waves and Currents

The hydroelastic behavior of a moored oil storage vessel subjected to arbitrary time-dependent external loads,which include wind,waves,and currents with different incident directions,is investigated with the time-domain modal expansion method.First,the water boundary integral equations on the body surface of a quarter model,which can be obtained via the free-surface Green’s function method,are established.Then,the time-dependent elastic deflection of the moored oil storage vessel is expressed by a superposition of modal functions and corresponding modal amplitudes,and a Galerkin scheme is applied to derive the linear system of equations for the modal amplitudes.The second-order linear differential equations for modal amplitudes are solved via the fourth-order Runge−Kutta method.The present model is validated against existing frequency domain results for a truncated cylinder and a VLFS.Numerical calculations for the moored oil storage vessel are then conducted to obtain the time series of various modal amplitudes and elastic displacements of the measurement points and the corresponding spectra with different incident directions.

Numerical Research on The Nozzle Damping Effect by A Wave Attenuation Method

Nozzle damping is one of the most important factors in the suppression of combustion instability in solid rocket motors.For an engineering solid rocket motor that experiences combustion instability at the end of burning,a wave attenuation method is proposed to assess the nozzle damping characteristics numerically.In this method,a periodic pressure oscillation signal which frequency equals to the first acoustic mode is superimposed on a steady flow at the head end of the chamber.When the pressure oscillation is turned off,the decay rate of the pressure can be used to determine the nozzle attenuation constant.The damping characteristics of three other nozzle geometries are numerically studied with this method under the same operating condition.The results show that the convex nozzle provides more damping than the conical nozzle which in turn provides more damping than the concave nozzle.All the three nozzles have better damping effect than that of basic nozzle geometry.At last,the phase difference in the chamber is analyzed,and the numerical pressure distribution satisfies well with theoretical distribution.

A nonparametric spectrum estimation method for dispersion and attenuation analysis of borehole acoustic measurements

Dispersion and attenuation analysis can be used to determine formation anisotropy induced by fractures,or stresses.In this paper,we propose a nonparametric spectrum estimation method to get phase dispersion characteristics and attenuation coefficient.By designing an appropriate vector filter,phase velocity,attenuation coefficient and amplitude can be inverted from the waveform recorded by the receiver array.Performance analysis of this algorithm is compared with Extended Prony Method(EPM)and Forward and Backward Matrix Pencil(FBMP)method.Based on the analysis results,the proposed method is capable of achieving high resolution and precision as the parametric spectrum estimation methods.At the meantime,it also keeps high stability as the other nonparametric spectrum estimation methods.At last,applications to synthetic waveforms modeled using finite difference method and real data show its efficiency.The real data processing results show that the P-wave attenuation log is more sensitive to oil formation compared to S-wave;and the S-wave attenuation log is more sensitive to shale formation compared to P-wave.

Effect of viscosity on stability and accuracy of the two-component lattice Boltzmann method with a multiple-relaxation-time collision operator investigated by the acoustic attenuation model

A two-component lattice Boltzmann method(LBM) with a multiple-relaxation-time(MRT) collision operator is presented to improve the numerical stability of the single relaxation time(SRT) model. The macroscopic and the momentum conservation equations can be retrieved through the Chapman–Enskog(C-E) expansion analysis. The equilibrium moment with the diffusion term is calculated, a diffusion phenomenon is simulated by utilizing the developed model, and the numerical stability is verified. Furthermore, the binary mixture channel model is designed to simulate the sound attenuation phenomenon, and the obtained simulation results are found to be consistent with the analytical solutions. The sound attenuation model is used to study the numerical stability and calculation accuracy of the LBM model. The simulation results show the stability and accuracy of the MRT model and the SRT model under different viscosity conditions. Finally,we study the influence of the error between the macroscopic equation of the MRT model and the standard incompressible Navier–Stokes equation on the calculation accuracy of the model to demonstrate the general applicability of the conclusions drawn by the sound attenuation model in the present study.

An analysis of seismic scattering attenuation in a random elastic medium

Seismic attenuation has been inherent media characteristics in which an interesting topic of research, for it reflects the seismic waves propagate. There are many factors that cause seismic wave attenuation, such as geometry attenuation caused by energy dissipating during propagation, friction attenuation by relative sliding among rock grains, and scattering attenuation by rock heterogeneity. In this paper we study P-wave scattering attenuation in a random elastic medium by numerical simulations from a statistical point of view. A random elastic medium model is built based on general stochastic process theory. Then a staggered-grid pseudo-spectral method is used to simulate wave propagation. Scattering attenuation is estimated by the spectral ratio method based on virtual detector records. Random elastic media numerical scatter results with various heterogeneity levels show that the higher heterogeneous levels cause greater scattering attenuation. When the scatter sizes are smaller than a wave length, the larger scatters give a greater attenuation. Finally, we propose a method to evaluate fluid-flow attenuation in porous media. The fluid- flow attenuation is derived from total attenuation and scattering attenuation in random porous media and the attenuation is estimated quantitatively. Results show that in the real seismic frequency range when the heterogeneous scale is about 10^1 meters （less than one wave length）, scattering attenuation is larger than fluid-tlow attenuation in random porous media and scattering attenuation is the main factor of seismic attenuation in real heterogeneous porous media.

Wave Attenuation Performance and the Influencing Factors of A Lower Arc-Plate Breakwater

Comprehensive experimental and numerical studies have been undertaken to investigate wave energy dissipation performance and main influencing factors of a lower arc-plate breakwater. The numerical model, which considers nonlinear interactions between waves and the arc-plate breakwater, has been constructed by using the velocity wave- generating method, the volume of fluid (VOF) method and the finite volume method. The results show that the relative width, relative height and relative submergence of the breakwater are three main influencing factors and have significant influence on wave energy dissipation of the lower arc-plate open breakwater. The transmission coefficient is found to decrease with the increasing relative width, and the minimum transmission coefficient is 0.15 when the relative width is 0.45. The reflection coefficient is found to vary slightly with the relative width, and the maximum reflection coefficient is 0.53 when the relative width is 0.45. The transmission and reflection coefficients are shown to increase with the relative wave height for approximately 85% of the experimental tests when the relative width is 0.19 0.45. The transmission coefficients at relative submergences of 0.04, 0.02 and 0 are clearly shown to be greater than those at relative submergences of 0.02 and 0.04, while the reflection coefficient exhibits the opposite relationship. After the wave interacts with the lower arc-plate breakwater, the wave energy is mainly converted into transmission, reflection and dissipation energies. The wave attenuation performance is clearly weakened for waves with greater heights and longer periods.

A 1D time-domain method for in-plane wave motions in a layered half-space

A 1D finite element method in time domain is developed in this paper and applied to calculate in-plane wave motions of free field exited by SV or P wave oblique incidence in an elastic layered half-space. First, the layered half-space is discretized on the basis of the propagation characteristic of elastic wave according to the Snell law. Then, the finite element method with lumped mass and the central difference method are incorporated to establish 2D wave motion equations, which can be transformed into 1D equations by discretization principle and explicit finite element method. By solving the 1D equations, the displacements of nodes in any vertical line can be obtained, and the wave motions in layered half-space are finally determined based on the characteristic of traveling wave. Both the theoretical analysis and the numerical results demonstrate that the proposed method has high accuracy and good stability.

Second-Order Wave Diffraction Around 3-D Bodies by A Time-Domain Method

A time-domain method is applied to simulate nonlinear wave diffraction around a surface piercing 3-D arbitrary body. The method involves the application of Taylor series expansions and the use of perturbation procedure to establish the corresponding boundary value problems with respect to a time-independent fluid domain. A boundary element method based on B-spline expansion is used to calculate the wave field at each time step, and the free surface boundary condition is satisfied to the second order of wave steepness by a numerical integration in time. An artificial damping layer is adopted on the free surface for the removal of wave reflection from the outer boundary. As an illustration, the method is used to compute the second-order wave forces and run-up on a surface-piercing circular cylinder. The present method is found to be accurate, computationally efficient, and numerically stable.

Dispersion attenuation structure of the crust around the Weifang-Jiashan segment of the Tanlu fault zone in North China

On the condition that the velocity ratio of compressive wave to shear wave is stable during the propagating process of seismic wave, this paper develops an estimation method for medium quality factor based on single station＇s travel time difference between direct S and P waves and the first period signal of direct P wave. 8 774 high SNR wave data altogether recorded by 75 stations are analyzed. The results show that： （1） under the normal regional stress field, the quality factors QmsP in the stable tectonic area are higher than that in the active tectonic area around the Weifang-Jiashan section and its surrounding area in the Tanlu fault zone; （2） in the Juxian-Tancheng section the seismic wave attenuation is relatively quick, and the media is relatively broken, suggesting no tectonic stress accumulation; （3） the Xinyi-Sihong section is currently locking and in accumulating elastic strain energy stage, which has the deep environment and conditions of strong earthquake generation similar to those of the 1668 M8.5 Tancheng strong earthquake.

P-wave attenuation anisotropy in TI media and its application in fracture parameters inversion

The existence of aligned fractures in fluid-saturated rocks leads to obvious attenuation anisotropy and velocity anisotropy. Attenuation anisotropy analysis can be applied to estimate fracture density and scale, which provide important information for reservoir identification. This paper derives P-wave attenuation anisotropy in the ATI media where the symmetry axis is in the arbitrary direction theoretically and modifies the spectral ratio method to measure attenuation anisotropy in the ATI media, thus avoiding a large measurement error when applied to wide azimuth or full azimuth data. Fracture dip and azimuth can be estimated through attenuation anisotropy analysis. For small-scale fractures, fracture scale and fracture density can be determined with enhanced convergence if velocity and attenuation information are both used. We also apply the modified spectralratio method to microseismic field data from an oilfield in East China and extract the fracture dip through attenuation anisotropy analysis. The result agrees with the microseismie monitoring.

Terahertz Time-Domain Spectroscopy method for optical parameter extraction of plastic materials

A method for extracting optical parameters of plastics materials based on terahertz time domain spectroscopy is presented. The transmission-type Terahertz Time-Domain Spectroscopy(THz TDS) system is adopted to detect the refractive index and extinction coefficient on different plastic materials. Then the corresponding spectral information is obtained by Fourier transform of the terahertz time domain waveform of the sampling points, including the corresponding amplitude and phase information of the waveform. The optical parameter extraction model is built. By using the simplex optimization method, the curves of the refractive index and extinction coefficient for the plastic material are obtained. The experimental samples are made of different plastic parallel plate materials. The experimental results show that the optimization of optical parameters can improve their extraction accuracy, and the error of refractive index is ±0.005. Extraction technology with the simplex optimization method of optical parameter based on THz TDS can help to extract the optical parameters of engineering plastics. It is of great significance for the research of terahertz nondestructive testing.

Stable attenuation-compensated reverse time migration and its application to land seismic data

Intrinsic attenuation of the earth causes energy loss and phase distortion in seismic wave propagation.To obtain high-resolution imaging results,these negative effects must be considered during reverse time migration(RTM).We can easily implement attenuation-compensated RTM using the constant Q viscoacoustic wave equation with decoupled amplitude attenuation and phase dispersion terms.However,the nonphysical amplitude-compensation process will inevitably amplify the high-frequency noise in the wavefield in an exponential form,causing the numerical simulation to become unstable.This is due to the fact that the amplitude of the compensation grows exponentially with frequency.In order to achieve stable attenuation-compensated RTM,we modify the analytic expression of the attenuation compensation extrapolation operator and make it only compensate for amplitude loss within the effective frequency band.Based on this modified analytic formula,we then derive an explicit time-space domain attenuation compensation extrapolation operator.Finally,the implementation procedure of stable attenuation-compensated RTM is presented.In addition to being simple to implement,the newly proposed attenuation-compensated extrapolation operator is superior to the conventional low-pass filter in suppressing random noise,which will further improve the imaging resolution.We use two synthetic and one land seismic datasets to verify the stability and effectiveness of the proposed attenuationcompensated RTM in improving imaging resolution in viscous media.

Using a Time-domain Higher-order Boundary Element Method to Simulate Wave and Current Diffraction from a 3-D Body

To study wave-current actions on 3-D bodies a time-domain numerical model was established using a higher-order boundary element method(HOBEM).By assuming small flow velocities,the velocity potential could be expressed for linear and higher order components by perturbation expansion.A 4th-order Runge-Kutta method was applied for time marching.An artificial damping layer was adopted at the outer zone of the free surface mesh to dissipate scattering waves.Validation of the numerical method was carried out on run-up,wave exciting forces,and mean drift forces for wave-currents acting on a bottom-mounted vertical cylinder.The results were in close agreement with the results of a frequency-domain method and a published time-domain method.The model was then applied to compute wave-current forces and run-up on a Seastar mini tension-leg platform.

Stochastic transient analysis of thermal stresses in solids by explicit time-domain method

Stochastic heat conduction and thermal stress analysis of structures has received considerable attention in recent years.The propagation of uncertain thermal environments will lead to stochastic variations in temperature fields and thermal stresses.Therefore,it is reasonable to consider the variability of thermal environments while conducting thermal analysis.However,for ambient thermal excitations,only stationary random processes have been investigated thus far.In this study,the highly efficient explicit time-domain method(ETDM)is proposed for the analysis of non-stationary stochastic transient heat conduction and thermal stress problems.The explicit time-domain expressions of thermal responses are first constructed for a thermoelastic body.Then the statistical moments of thermal displacements and stresses can be directly obtained based on the explicit expressions of thermal responses.A numerical example involving non-stationary stochastic internal heat generation rate is investigated.The accuracy and efficiency of the proposed method are validated by comparison with the Monte-Carlo simulation.

Investigation of three-pulse photon echo in thick crystal using finite-difference time-domain method

This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works.The influence of thickness on the three-pulse photon echo＇s amplitude and efficiency is analyzed with the Maxwell-Bloch equations solved by finite-difference timedomain method.We demonstrate that the amplitude of three-pulse echo will increase with the increasing of thickness and the optimum thickness to generate three-pulse photon echo is 0.3 cm for Tm^（3＋）：YAG when the attenuation of the input pulse is taken into account.Meanwhile,we find the expression 0.09 exp（α＇L）,which is previously employed to describe the relationship between echo＇s efficiency and thickness,should be modified as 1.3 · 0.09 exp（2.4 ·α＇L） with the propagation of echo considered.

Attenuation-compensated reverse time migration of GPR data constrained by resistivity

The high-frequency electromagnetic waves of ground-penetrating radar(GPR)attenuate severely when propagated in an underground attenuating medium owing to the influence of resistivity,which remarkably decreases the resolution of reverse time migration(RTM).As an effective high-resolution imaging method,attenuation-compensated RTM(ACRTM)can eff ectively compensate for the energy loss caused by the attenuation related to media absorption under the influence of resistivity.Therefore,constructing an accurate resistivity-media model to compensate for the attenuation of electromagnetic wave energy is crucial for realizing the ACRTM imaging of GPR data.This study proposes a resistivity-constrained ACRTM imaging method for the imaging of GPR data by adding high-density resistivity detection along the GPR survey line and combining it with its resistivity inversion profile.The proposed method uses the inversion result of apparent resistivity data as the GPR RTM-resistivity model for imposing resistivity constraints.Moreover,the hybrid method involving image minimum entropy and RTM is used to estimate the medium velocity at the diff raction position,and combined with the distribution characteristics of the reflection in the GPR profile,a highly accurate velocity model is built to improve the imaging resolution of the ACRTM.The accuracy and eff ectiveness of the proposed method are verified using the ACRTM test of the GPR simulated data of a typical attenuating media model.On this basis,the GPR and apparent resistivity data were observed on a field survey line,and use the GPR resistivity-constrained ACRTM method to image the observed data.A comparison of the proposed method with the conventional ACRTM method shows that the proposed method has better imaging depth,stronger energy,and higher resolution,and the obtained results are more conducive for subsequent data analysis and interpretation.

Optical simulation of in-plane-switching blue phase liquid crystal display using the finite-difference time-domain method

The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell＇s equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.

Frequency-dependent attenuation of P and S waves in Yunnan region

We analyzed digital seismogram data of 5668 earthquakes that occurred in Yunnan region between July of 1999 and December of 2003. Among the 22 seismic stations, six ones, namely Baoshan, Yongsheng, Lijiang, Heqing, Yimen, and Luquan, were selected and their attenuations of P and S waves were measured by using the extended coda-normalization method. The six stations were classified into three regions according to their location, that is, Baoshan area, Yongsheng-Lijiang-Heqing (YLH) area and Luquan-Yimen (LY) area. The values of QS-1 and QP-1 are expressed as QS-1=0.00867 f-0.86, QP-1=0.01155 f-0.93, QS-1=0.01824 f-0.92, QP-1=0.02288 f-0.92, and QS-1=0.01647 f-0.91, QP-1=0.02826 f-0.97 in Baoshan, YLH, LY areas respectively. The attenuation of YLH, LY are closer to each other, however, Baoshan area is apparently lower. Comparing attenuation in the three areas with other areas of the world using the same method, it is suggested that the attenuations of P and S waves in YLH and LY areas are close to Kanto of Japan, but much higher than southeast of South Korea. The QS-1 and QP-1 in Baoshan area are slightly higher than southeastern South Korea. Furthermore, the results indicate that our QS-1 in Yunnan area is close to others by analyzing the coda attenuation.