Two-level discretizations of nonlinear closure models for proper orthogonal decomposition

Proper orthogonal decomposition has been successfully used in the reduced-order modeling of complex systems. Its original promise of computationally efficient, yet accurate approximation of coherent structures in high Reynolds number turbulent flows, however, still remains to be fulfilled. To balance the low computational cost required by reduced-order modeling and the complexity of the targeted flows, appropriate closure modeling strategies need to be employed. Since modern closure models for turbulent flows are generally nonlinear, their efficient numerical discretization within a proper orthogonal decomposition framework is challenging. This paper proposes a two-level method for an efficient and accurate numerical discretization of general nonlinear closure models for proper orthogonal decomposition reduced-order models. The two-level method computes the nonlinear terms of the reduced-order model on a coarse mesh. Compared with a brute force computational approach in which the nonlinear terms are evaluated on the fine mesh at each time step, the two-level method attains the same level of accuracy while dramatically reducing the computational cost. We numerically illustrate these improvements in the two-level method by using it in three settings: the one-dimensional Burgers equation with a small diffusion parameter ν = 10^?3, the two-dimensional flow past a cylinder at Reynolds number Re = 200, and the three-dimensional flow past a cylinder at Reynolds number Re = 1000.     

Insulation room for aero-acoustic experiments at moderate Reynolds and low Mach numbers

A non-expensive insulation box for aero-acoustic experiments at moderate Reynolds numbers Re < 2 × 10⁴ and low Mach numbers M < 0.2 is presented. Its performance is evaluated with particular attention to unwanted noise sources inherent to the flow facility. Objective acoustic parameters of the insulation box are assessed.     

A spectral-element discontinuous Galerkin lattice Boltzmann method for nearly incompressible flows

We present a spectral-element discontinuous Galerkin lattice Boltzmann method for solving nearly incompressible flows. Decoupling the collision step from the streaming step offers numerical stability at high Reynolds numbers. In the streaming step, we employ high-order spectral-element discontinuous Galerkin discretizations using a tensor product basis of one-dimensional Lagrange interpolation polynomials based on Gauss–Lobatto–Legendre grids. Our scheme is cost-effective with a fully diagonal mass matrix, advancing time integration with the fourth-order Runge–Kutta method. We present a consistent treatment for imposing boundary conditions with a numerical flux in the discontinuous Galerkin approach. We show convergence studies for Couette flows and demonstrate two benchmark cases with lid-driven cavity flows for Re = 400–5000 and flows around an impulsively started cylinder for Re = 550–9500. Computational results are compared with those of other theoretical and computational work that used a multigrid method, a vortex method, and a spectral element model.     

A computational study of the HyShot II combustor performance

Experimental and flight data for hypersonic air-breathing engines are both difficult and extremely expensive to obtain, motivating the use of computational models to enhance the understanding of the complex physics involved. Here, a comprehensive numerical study has been carried out for the HyShot II scramjet combustor. This study makes use of Reynolds Average Navier Stokes (RANS) based models and Large Eddy Simulation (LES) based models with semi-detailed reaction kinetics. In this investigation we focus on the underlying flow-mixing-combustion physics at different operating conditions tested in the High Enthalpy Shock Tunnel Göttingen (HEG). To account for the complex flow in the HEG facility a zonal approach is employed in which RANS is used to simulate the flow in the HEG nozzle and test-section, providing the necessary inflow boundary conditions for the combustor RANS and LES, being the focus of this analysis. Specifically, we here combine results from RANS and LES computations with data from the HEG experiments and the target HyShot II flight-tests at two different flight-altitudes (28 and 33 km). The LES model is observed to capture the experimental wall-pressure and heat-flux data very well for both the 33 and 28 km altitude cases, whereas the RANS model is only able to predict the wall-pressure and heat flux data for the 28 km altitude case. Based on the LES results, the flow at both altitudes is found to be unsteady, but with unsteady transitional flow features dominating the 33 km case. Moreover, these results show that the equivalence ratio is of key importance to the resulting flow, mixing and combustion physics, with richer mixtures being prone to transitional flow features. The LES results are also used to describe the flow physics in detail for both altitudes, and the key processes responsible for the transition between the two combustion modes observed.     

Influence of nozzle spacing and diameter on acoustic radiation from supersonic jets in closely spaced arrays

Acoustic emissions were characterized for fourteen, 8 × 8 arrays of axisymmetric supersonic jets experimentally. The nozzle diameters ranged from 3.2 mm (1/8 in.) to 6.4 mm (1/4 in.) and the hole-to-hole spacing (S) over hole diameter (d), or the S/d ratios ranged from 1.44 to 3. The arrays were tested at several net pressure ratios ranging from 2 to 24. It was found that up to a critical net pressure ratio, the arrays radiated ultrasonic frequencies. Beyond this critical net pressure ratio the characteristic frequency decreased to lie within the audible range. Frequency response plots of the sound pressure indicate a broadband frequency peak generated by the turbulent mixing noise of the jet. At lower net pressure ratio (NPR) values, this broadband peak is similar to a single jet within the jet array. However, as the NPR continues to increase this frequency peak shifts to lower values which are similar to a single jet with an equivalent exit area of the entire array. Dimensional analysis revealed that at a critical net pressure ratio a dramatic reduction in the characteristic Strouhal number occurred. A small increase in the characteristic acoustic pressure was also observed at net pressure ratios below the critical net pressure ratio and a larger increase was observed at higher net pressure ratios. The critical net pressure ratio appeared to be a linear function of S/d for the nozzle arrays. A linear curve fit was applied to the measured critical net pressure ratio and this was compared to a theoretical model prediction. The experimental results revealed that the critical net pressure ratio is well predicted by the models.     

Dynamic features of a laser-induced cavitation bubble near a solid boundary

This paper deals with detailed features of bubble dynamics near a solid boundary. The cavitation bubble was created by using a Q-switched Nd: YAG laser pulse and observed using a high-speed camera (up to 100,000 frames per second). A hydrophone system was employed to monitor the acoustic signals generated by the transient pressure impulses and estimate the bubble oscillation periods. Experimental observations were carried out for bubbles with various maximum expanded radius R_max (between 1.0 mm and 1.6 mm) and stand-off distances, ds (defined as the distance between the solid boundary and the bubble center at inception) of 0.4 ? γ ? 3.0, and γ = ds/R_max. The existence of a solid boundary created asymmetry in the flow field and forced the bubble to collapse non-spherically, which finally brought forth the jet impact phenomenon. The dimensionless first and second oscillation periods were dependent on γ. A series of expansion and collapse of the bubble with cascading loss of energy were observed after the bubble had been generated. This study revealed that most bubbles lost about two-thirds of the total energy from the first maximum expansion to the second maximum expansion.     

Experimental examination of vortex-sound generation in an organ pipe: A proposal of jet vortex-layer formation model

Aero-dynamical models of sound generation in an organ pipe driven by a thin jet are investigated through an experimental examination of the vortex-sound theory. An important measurement requirement (acoustic cross-flow as an irrotational potential flow reciprocating sinusoidally) from the vortex-sound theory is carefully realized when the pipe is driven with low blowing pressures of about 60 Pa (jet velocities of about 10 m/s). Particle image velocimetry (PIV) is applied to measure the jet velocity and the acoustic cross-flow velocity over the mouth area at the same phase by quickly switching the jet drive and the loudspeaker-horn drive. The vorticity of the jet flow field and the associated acoustic generation term are evaluated from the measurement data. It is recognized that the model of the “jet vortex-layer formation” is more relevant to the sound production than the vortex-shedding model. The acoustic power is dominantly generated by the flow–acoustic interaction near the edge, where the acoustic cross-flow velocity takes larger magnitudes. The acoustic generation formula on the vortex sound cannot deny the conventional acoustical volume-flow model because of the in-phase relation satisfied between the acoustic pressure at the mouth and the acoustic volume flow into the pipe. The vortex layers formed along both sides of the jet act as the source of an accelerating force (through the “acceleration unbalance”) with periodically alternating direction to oscillate the jet flow and to reinforce the acoustic cross-flow at the pipe mouth.     

Two-phase electrohydrodynamic simulations using a volume-of-fluid approach: A comment

This comment refers to the article of Tomar et al. [1], which presents a numerical methodology of a continuum surface force formulation for simulating two-phase electrohydrodynamic flows. The present work shows, that due to the diffusive character of the Laplacian equation (? · (??₀E) = 0) with discontinuous physical properties (?(x, y, z)), different averaging methods (arithmetic and harmonic) for the fluid property in the transition region have to be applied. The correct choice of the averaging method depends on the orientation of the flux to the interface.An additional improvement is made by calculating the electric displacement D at the cell faces. This leads to a numerical solution independent of the spatial resolution as well as of the interfacial smearing. Simulation results of two different test cases show that the error of the numerical solution is in the order of machine precision.     

Cross-correlation Doppler global velocimetry (CC-DGV)

A flow velocimetry method, cross-correlation Doppler global velocimetry (CC-DGV), is presented as a robust, simplified, and high dynamic range implementation of the Doppler global/planar Doppler velocimetry technique. A sweep of several gigahertz of the vapor absorption spectrum is used for each velocity sample, with signals acquired from both Doppler-shifted scattered light within the flow and a non-Doppler shifted reference beam. Cross-correlation of these signals yields the Doppler shift between them, averaged over the duration of the scan. With presently available equipment, velocities from 0 ms⁻¹ to over 3000 ms⁻¹ can notionally be measured simultaneously, making the technique ideal for high speed flows. The processing routine is shown to be robust against large changes in the vapor pressure of the iodine cell, benefiting performance of the system in facilities where ambient conditions cannot be easily regulated. Validation of the system was performed with measurements of a model wind turbine blade boundary layer made in a 1.83 m by 1.83 m subsonic wind tunnel for which laser Doppler velocimetry (LDV) measurements were acquired alongside the CC-DGV results. CC-DGV uncertainties of ±1.30 ms⁻¹, ±0.64 ms⁻¹, and ±1.11 ms⁻¹ were determined for the orthogonal stream-wise, transverse-horizontal, and transverse-vertical velocity components, and root-mean-square deviations of 2.77 ms⁻¹ and 1.34 ms⁻¹ from the LDV validation results were observed for Reynolds numbers of 1.5 million and 2 million, respectively. Volumetric mean velocity measurements are also presented for a supersonic jet, with velocity uncertainties of ±4.48 ms⁻¹, ±16.93 ms⁻¹, and ±0.50 ms⁻¹ for the orthogonal components, and self-validation done by collapsing the data with a physical scaling.     

A miniaturized prototype of resonant banana-shaped photoacoustic cell for gas sensing

A resonant photoacoustic cell intended for laser-spectroscopy gas sensing is represented. This cell is a miniature imitation of a macro-scale banana-shaped cell developed previously. The parameters, which specify the cavity shape, are chosen so as not only to provide optimal cell operation at a selected acoustic resonance but also to reduce substantially the cell sizes. A miniaturized prototype cell (the volume of acoustic cavity of ∼5 mm³) adapted to the narrow diffraction-limited beam of near-infrared laser is produced and examined experimentally. The noise-associated measurement error and laser-initiated signals are studied as functions of modulation frequency. The background signal and the useful response to light absorption by the gas are analyzed in measurements of absorption for ammonia in nitrogen flow with the help of a pigtailed DFB laser diode oscillated near a wavelength of 1.53 μm. The performance of prototype operation at the second longitudinal acoustic resonance (the resonance frequency of ∼32.9 kHz, Q-factor of ∼16.3) is estimated. The noise-limited minimal detectable absorption normalized to laser-beam power and detection bandwidth is ∼8.07 × 10⁻⁸ cm⁻¹ W Hz^−1/2. The amplitude of the background signal is equivalent to an absorption coefficient of ∼2.51 × 10⁻⁵ cm⁻¹. Advantages and drawbacks of the cell prototype are discussed. Despite low absorption-sensing performance, the produced miniaturized cell prototype shows a good capability of gas-leak detection.     

A deconvolution enhancement of the Navier–Stokes-αβ model

A deconvolution enhancement of the Navier–Stokes-αβ model for turbulent flow is introduced. The energy and energy-dissipation rate for the enhanced model are derived. It is also shown that the consistency error, relative to the Navier–Stokes equations, and the microscale of the enhanced model are less than those of the Navier–Stokes-αβ model. The proposed model is used to simulate the Taylor–Green vortex problem and results show a qualitatively improved representation of the mean-square vorticity when compared to the Navier–Stokes-αβ model. Numerical studies of the energy spectrum and the alignment between the vorticity and the eigenvectors of the stretching tensor for three-dimensional turbulent flows with Re = 200 are used to explore the utility of the model. A benchmark problem of a two-dimensional channel flow over a step for Re = 600 also indicates that this model can be applied to more general flows than those involving periodic boundary conditions.     

Estimating health related costs and savings from balcony acoustic design for road traffic noise

A multi-faceted study is conducted with the objective of estimating the potential fiscal savings in annoyance and sleep disturbance related health costs due to providing improved building acoustic design standards. This study uses balcony acoustic treatments in response to road traffic noise as an example. The study area is the State of Queensland in Australia, where regional road traffic noise mapping data is used in conjunction with standard dose–response curves to estimate the population exposure levels. The background and the importance of using the selected road traffic noise indicators are discussed. In order to achieve the objective, correlations between the mapping indicator (L_{A10 (18 hour)}) and the dose response curve indicators (L_den and L_night) are established via analysis on a large database of road traffic noise measurement data. The existing noise exposure of the study area is used to estimate the fiscal reductions in health related costs through the application of simple estimations of costs per person per year per degree of annoyance or sleep disturbance. The results demonstrate that balcony acoustic treatments may provide a significant benefit towards reducing the health related costs of road traffic noise in a community.     

Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation

Many applications lead to large systems of linear equations with dense matrices. Direct matrix-vector products become prohibitive, since the computational cost increases quadratically with the size of the problem. By exploiting specific kernel properties fast algorithms can be constructed.A directional multilevel algorithm for translation-invariant oscillatory kernels of the type K(x, y) = G(x ? y)e^?k∣x?y∣, with G(x ? y) being any smooth kernel, will be presented. We will first present a general approach to build fast multipole methods (FMMs) based on Chebyshev interpolation and the adaptive cross approximation (ACA) for smooth kernels. The Chebyshev interpolation is used to transfer information up and down the levels of the FMM. The scheme is further accelerated by compressing the information stored at Chebyshev interpolation points using ACA and QR decompositions. This leads to a nearly optimal computational cost with a small pre-processing time due to the low computational cost of ACA. This approach is in particular faster than performing singular value decompositions.This does not address the difficulties associated with the oscillatory nature of K. For that purpose, we consider the following modification of the kernel K^u = K(x, y)e^??ku·(x?y), where u is a unit vector (see Brandt [1]). We proved that the kernel K^u can be interpolated efficiently when x ? y lies in a cone of direction u. This result is used to construct an FMM for the kernel K.Theoretical error bounds will be presented to control the error in the computation as well as the computational cost of the method. The paper ends with the presentation of 2D and 3D numerical convergence studies, and computational cost benchmarks.     

Relationship between Electroencephalogram variation and subjective annoyance under noise exposure

The relationship between Electroencephalogram (EEG) variation and subjective annoyance was investigated with 70 dBA white noise and pure tones at 160 Hz, 500 Hz and 4000 Hz being selected as exposed noise sources. The results indicate that when the duration of noise was less than 6 s, Average Power of Electroencephalogram (APEEG) varied irregularly. When the noise lasted for 5 min, the sum of the relative APEEG of θ wave and the relative APEEG of α wave increased with the subjective annoyance increasing under noise exposures. The maximum power of θ wave appeared in the frontal region, while the maximum power of α wave appeared in the occipital region. Up to the fifth minute after noise exposure, more than two APEEG maximums of θ wave appeared, and the time points of maximum occurrence shifted forwards slowly following the increase of exposed noise frequency. The interval between two time points of maximum occurrence was reduced with the increase of the exposed noise frequency.     

Nonlinear parameter estimation in water-saturated sandy sediment with difference frequency acoustic wave

Difference frequency acoustic wave from nonlinear interaction of two primary acoustic waves at frequencies of 76 and 114 kHz was utilized with a parametric acoustic array theory to estimate the nonlinearity parameter of water-saturated sandy sediment. Such nonlinearity parameter can be used as background information for the nonlinear acoustic investigation of bottom or sub-bottom profiling in the ocean sandy sediments. Because of its lower attenuation the difference frequency acoustic wave method can be usefully applied to estimate the nonlinearity parameter of ocean sediment in the ocean as well as under laboratory conditions. The nonlinearity parameter β for the water-saturated sandy sediment used as a reference in this study was estimated as β = 80.5 ± 5.1 at the difference frequency of 38 kHz. It was agreed very well with that estimated at the difference frequency of 67 kHz, when two primary frequencies were 137 and 204 kHz. The estimated nonlinearity parameter of water-saturated sandy sediment in this study was also compared and analyzed with those estimated in previously published literatures. It was suggested that the difference frequency wave method used to estimate the nonlinearity parameter of water-saturated sandy sediment can be employed as a good method to estimate the nonlinearity parameters of fluid-like granular media.     

Temperature dependence of dc corona and charge-carrier entrainment in a gas flow channel

Current–voltage (I–V) data for positive and negative polarity point-to-plane geometries are reported for gas flows transverse to the axis of the emitters. Air and nitrogen flows of 0–5 m/s were considered in the experiments and temperatures in ranges of 213–493 K in nitrogen and 283–493 K in air. Entrainment of charge carriers from the individual corona and positive–negative polarity emitter-pairs was considered towards understanding the static elimination process for downstream targets in the gas flows.     

Microfluidic acoustic trapping force and stiffness measurement using viscous drag effect

It has recently been demonstrated that it was possible to individually trap 70 μm droplets flowing within a 500 μm wide microfluidic channel by a 24 MHz single element piezo-composite focused transducer. In order to further develop this non-invasive approach as a microfluidic particle manipulation tool of high precision, the trapping force needs to be calibrated to a known force, i.e., viscous drag force arising from the fluid flow in the channel. However, few calibration studies based on fluid viscosity have been carried out with focused acoustic beams for moving objects in microfluidic environments.In this paper, the acoustic trapping force (F_trapping) and the trap stiffness (or compliance k) are experimentally determined for a streaming droplet in a microfluidic channel. F_trapping is calibrated to viscous drag force produced from syringe pumps. Chebyshev-windowed chirp coded excitation sequences sweeping the frequency range from 18 MHz to 30 MHz is utilized to drive the transducer, enabling the beam transmission through the channel/fluid interface for interrogating the droplets inside the channel. The minimum force (F_min,trapping) required for initially immobilizing drifting droplets is determined as a function of pulse repetition frequency (PRF), duty factor (DTF), and input voltage amplitude (V_in) to the transducer. At PRF = 0.1 kHz and DTF = 30%, F_min,trapping is increased from 2.2 nN for V_in = 22 V_pp to 3.8 nN for V_in = 54 V_pp. With a fixed V_in = 54 V_pp and DTF = 30%, F_min,trapping can be varied from 3.8 nN at PRF = 0.1 kHz to 6.7 nN at PRF = 0.5 kHz. These findings indicate that both higher driving voltage and more frequent beam transmission yield stronger traps for holding droplets in motion.The stiffness k can be estimated through linear regression by measuring the trapping force (F_trapping) corresponding to the displacement (x) of a droplet from the trap center. By plotting F_trapping – x curves for certain values of V_in (22/38/54 V_pp) at DTF = 10% and PRF = 0.1 kHz, k is measured to be 0.09, 0.14, and 0.20 nN/μm, respectively. With variable PRF from 0.1 to 0.5 kHz at V_in = 54 V_pp, k is increased from 0.20 to 0.42 nN/μm. It is shown that a higher PRF leads to a more compliant trap formation (or a stronger F_trapping) for a given displacement x. Hence the results suggest that this acoustic trapping method has the potential as a noninvasive manipulation tool for individual moving targets in microfluidics by adjusting the transducer’s excitation parameters.     

Mechanical characterization of sintered piezo-electric ceramic material using scanning acoustic microscope

Lead Zirconate Titanate (PZT) is a piezo-electric ceramic material that needs to be characterized for its potential use in microelectronics. Energy dispersive X-ray analysis (EDX) is conducted to determine the chemical composition of the PZT ceramics. The scanning electron microscope (SEM) is performed to study the surface morphology, grain structure and grain boundaries. The SEM image helps us to understand the surface wave propagation and scattering phenomena by the PZT and the reason for its anisotropy and inhomogeneity due to the grain structure. In this paper scanning acoustic microscopy at 100 MHz excitation frequency is conducted for determining mechanical properties of PZT. Earlier works reported only the longitudinal wave speed in PZT while in this paper longitudinal, shear and surface acoustic wave speeds of sintered PZT are measured from its acoustic material signature (AMS) curves, also known as V(z) curves. AMS or V(z) curve is the variation of the output voltage as a function of the distance between the acoustic lens focal point and the reflecting surface. The average velocities of longitudinal, shear and surface acoustic waves in a PZT specimen are determined from its V(z) curve generated at 100 MHz excitation frequency and found to be over 5000 m/s, over 3000 m/s and between 2500 and 3000 m/s, respectively. From these velocities all elastic constants of the specimen are obtained.     

Synchrotron quantification of ultrasound cavitation and bubble dynamics in Al–10Cu melts

Knowledge of the kinetics of gas bubble formation and evolution under cavitation conditions in molten alloys is important for the control casting defects such as porosity and dissolved hydrogen. Using in situ synchrotron X-ray radiography, we studied the dynamic behaviour of ultrasonic cavitation gas bubbles in a molten Al–10 wt% Cu alloy. The size distribution, average radius and growth rate of cavitation gas bubbles were quantified under an acoustic intensity of 800 W/cm² and a maximum acoustic pressure of 4.5 MPa (45 atm). Bubbles exhibited a log-normal size distribution with an average radius of 15.3 ± 0.5 μm. Under applied sonication conditions the growth rate of bubble radius, R(t), followed a power law with a form of R(t) = αt^β, and α = 0.0021 & β = 0.89. The observed tendencies were discussed in relation to bubble growth mechanisms of Al alloy melts.