Generation of tones due to flow past a deep cavity: Effect of streamwise length

Shear flow past a deep cavity can generate self-sustained oscillations, including locked-on flow tones, due to coupling between the inherent instability of the separated shear layer and an acoustic mode of the cavity resonator. This investigation focuses on the dimensionless pressure amplitude response within a deep cavity, as a function of the streamwise length of the cavity opening; for each length, the pressure response is characterized over a wide range of dimensionless inflow velocity. Criteria for locked-on flow tones are assessed. They include a measure of the strength of lock-on, SoL and the quality factor Q. All self-excited oscillations are assessed using both of these criteria, in order to interpret dimensionless forms of the fluctuation pressure amplitude. The dimensionless pressure amplitude response of the cavity involves several successive regimes, due to variations of streamwise length L of the cavity opening. These regimes are defined in relation to L/θ, where θ is the momentum thickness of the inflow boundary layer. Below a minimum value of L/θ, flow tones cannot be generated. Furthermore, these regimes are defined in terms of the possible hydrodynamic modes (stages) of the unsteady shear layer and the acoustic modes of the deep cavity.     

Spatiotemporal representation of the dynamic modes in turbulent cavity flows

Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) were used to extract the coherent structures in turbulent cavity flows. The spatiotemporal representation of the modes was achieved by performing the circular convolution of a change of basis on the data sequence, wherein the transformation function was extracted from the POD or DMD. The spatiotemporal representation of the modes provided significant insight into the evolutionary behavior of the structures. Self-sustained oscillations arise in turbulent cavity flows due to unsteady separation at the leading edge. The turbulent cavity flow at Re_D = 12,000 and a length to depth ratio L/D = 2 was analyzed. The dynamic modes extracted from the data clarified the presence of self-sustained oscillations. The spatiotemporal representation of the POD and DMD modes that caused self-sustained oscillations revealed the prevalent dynamics and evolutionary behavior of the coherent structures from their formation at the leading edge to their impingement at the trailing edge. A local minimum in the mode amplitude representing the energy contributions to the flow was observed upon the impingement of coherent structure at the trailing edge. The modal energy associated with the periodic formation of organized coherent structures followed by their dissipation upon impingement revealed the oscillatory behavior over time.     

Nonaxisymmetric interaction of a spherical radiator in a fluid-filled permeable borehole

The Biot theory of poroelasticity along with the proper cylindrical/spherical wave-field transformations are used to investigate general (nonaxisymmetric) harmonic radiation from a spherical surface vibrating at the center of a fluid-filled circular cylindrical cavity embedded within a fluid-saturated porous elastic formation. This configuration, which is a realistic idealization of an acoustic logging tool suspended in a fluid-filled borehole, is of practical importance with a multitude of possible applications in seismic engineering and geophysics. The analytical results are illustrated with numerical examples in which the spherical source suspended at the center of a water-filled borehole embedded within water-saturated soils of distinct frame properties (i.e., soft or stiff soils), is excited in vibrational modes of various orders. The basic acoustic and elastic field quantities such as the resistive/reactive components of the modal acoustic radiation impedance load as well as the radial displacement and stress components induced within the surrounding formation for a pulsating (n = 0), an oscillating (n = 1), and a quadrupole-like (n = 2) spherical source are evaluated and discussed for representative values of the parameters characterizing the system. Special attention is paid to the effects of source excitation frequency, size, surface velocity profile, and internal impedance as well as soil type on the modal impedance values and the displacement/stress amplitudes. Limiting cases are considered and fair agreements with well-known solutions are obtained.     

Wake structures and vortex-induced vibrations of a long flexible cylinder—Part 1: Dynamic response

Results showing the dynamic response of a vertical long flexible cylinder vibrating at low mode numbers are presented in this paper. The model had an external diameter of 16 mm and a total length of 1.5 m giving an aspect ratio of about 94, with Reynolds numbers between 1200 and 12 000. Only the lower 40% of its length was exposed to the water current in the flume and applied top tensions varied from 15 to 110 N giving fundamental natural frequencies in the range from 3.0 to 7.1 Hz. Reduced velocities based on the fundamental natural frequency up to 16 were reached. The mass ratio was 1.8 and the combined mass–damping parameter about 0.05. Cross-flow and in-line amplitudes, x–y trajectories and phase synchronisation, dominant frequencies and modal amplitudes are reported. Cross-flow amplitudes up to 0.7 diameters and in-line amplitudes over 0.2 were observed with dominant frequencies given by a Strouhal number of 0.16.     

Numerical and experimental studies of temperature field characteristic inside an irregularly-shaped cavity of a space environment simulator system

Numerical and experimental methods were used to explore temperature and pressure distributions inside an irregularly-shaped cavity of a novel three-dimensional space environment simulator (SES) system. In order to obtain better temperature and pressure distributions, a plenum chamber and airflow diffusion perforated plate were adopted. Three-dimensional heat and mass transfer characteristics were analyzed using the Standard k–ε turbulence model. Simulation results revealed that the temperature and pressure distributions were greatly improved with improved diffusion configuration design, the temperature gradient decreased from 5 K to 1 K, and the pressure gradient decreased to 0.5% of the former value. Based on the simulation results, an improved experimental system for simulating space environment was set up. This experiment system could supply airflow with temperature ranging from 193 K to 353 K for simulating the real space environment. Experimental results showed that the temperature and pressure fields had smaller gradients across the surface and the inner cavity, which agreed considerably with the numerical results. The results of this study present useful information for the design of similar cavity structure.     

In-plane free vibration of a single-crystal silicon ring

In this paper the natural frequencies and the associated mode shapes of in-plane free vibration of a single-crystal silicon ring are analyzed. It is found that the Si(1 1 1) ring is two-dimensionally isotropic in the (1 1 1) plane for elastic constants but three-dimensionally anisotropic, while the Si(1 0 0) ring is fully anisotropic. Hamilton’s principle is used to derive the equations of vibration, which is a set of partial differential equations with coefficients being periodic in polar variable. Expressing the radial and tangential displacements in sinusoidal form with non-predetermined amplitudes, and through the integration with respect to the circumferential variable, the original governing equations in partial differential form can be converted into the amplitude equations in ordinary differential form. The exact expressions for frequencies and mode shapes are obtained. It is found that for Si(1 0 0) rings the frequencies of a pair of modes, which are equal for an isotropic ring, split due to the anisotropic effect only for the second in-plane vibration mode. The phenomena of frequency splitting and degenerate modes can be proved either based on the conservation of averaged mechanical energy or by the concept of crystallographic symmetry groups. When the single-crystal silicon is replaced by the polycrystalline silicon, which is isotropic in elastic constants, the derived equations for frequencies correctly predict the vanishing of the phenomenon of frequency splitting.     

Dual-element directional shock wave attenuators

This study explores the interaction between shock waves and dual-element porous plates used to ameliorate the hazardous effects of these waves. Tests were performed in a shock tube to determine the effects that a pair of porous plates with directional resistance properties had on the initial peak pressure and impulse amelioration experienced by an end wall. Mild steel test specimens, ranging in porosity values from 6.6% to 41.1%, were mounted two at a time at different spacings in the test section. Each plate had directional properties, i.e. resistance to flow was different for flow coming from either side. Four plates were used, and 48 plate configurations were tested. Side wall and end wall pressure measurements and schlieren photographs were taken of the interactions. Tests were run at Mach numbers of 1.23, 1.35 and 1.42. The separation distances between the plate specimens were varied between 30 mm and 60 mm; however, the distance between the downstream plate and the end wall was kept constant at 140 mm for all tests.Both the initial peak pressure and impulse amelioration values were found to be dependant on the plate combination porosity. As the porosity of the combination increased, the amelioration values decreased. Complementary plate combinations produced differing results as different wave interactions occur when plate positions were interchanged. The porosity of the combined plates was found to have an overriding influence on the end wall peak pressure and impulse amelioration values when compared to the effect that plate arrangement (i.e. geometrical influences) had. Impulse amelioration values were found to increase as the separation distance between plates were increased. The amplitude of the end wall pressure trace was found to increase as the incident Mach number was increased. The significant attenuation of the incident shock wave obtained during this study is attributed to the system of multiple reflected and transmitted waves that are produced by the presence of the plate specimens in series. This increases the frequency of shock wave and barrier interactions, when compared to just using a single barrier.     

Large-eddy simulation of thermal fatigue in a mixing tee

Temperature fluctuations occur due to thermal mixing of hot and cold streams in the T-junctions of the piping system in nuclear power plants, which may cause thermal fatigue of piping system. In this paper, three-dimensional, unsteady numerical simulations of coolant temperature fluctuations at a mixing T-junction of equal diameter pipes were performed using the large eddy simulation (LES) turbulent model. The experiments used in this paper to benchmark the simulations were performed by Hitachi Ltd. The calculated normalized mean temperatures and fluctuating temperatures are in good agreement with the measurements. The influence of the time-step ranging from 100 Hz to 1000 Hz on the numerical simulation results was explored. The simulation results indicate that all the results with different frequencies agree well with the experimental data. Finally, the attenuation of fluctuation of fluid temperature was also investigated. It is found that, drastic fluctuation occurs within the range of less than L/D = 4.0; the fluctuation of fluid temperature does not always attenuate from the pipe center to the wall due to the continuous generation of vortexes. At the top wall, the position of L/D = 1.5 has a minimum normalized mean temperature and a peak value of root-mean square temperature, whereas at the bottom wall, the position having the same characteristics is L/D = 2.0.     

Two-degree-of-freedom vortex-induced vibrations using a force assisted apparatus

We report results from two-degree-of-freedom vortex-induced vibration tests on a flexibly mounted, rigid, smooth cylinder in cross-flow. The tests are performed for six in-line natural frequency to transverse natural frequency ratios. The Reynolds number based on diameter ranged from 11 000 to 60 000. To reduce structural damping in both directions, an apparatus utilizing two linear motors was used. Increasing the in-line to transverse frequency ratio caused a shift in the peak amplitude response to increasingly higher reduced velocities; and at a frequency ratio of 1.9, two distinct response peaks appear, in agreement with earlier experiments by Sarpkaya in 1995. Other comparisons are made with the low mass-damping, two-degree-of-freedom experiments by Jauvtis and Williamson in 2004. The frequency ratio affects the phase lag between transverse and in-line oscillations and hence the shape of the cylinder orbital.     

Experimental analysis of the quasi-static and dynamic torsional behaviour of shape memory alloys

This paper investigates experimentally the quasi-static and dynamic torsional behaviour of shape memory alloys wires under cyclic loading. A specifically designed torsional pendulum made of a Ni–Ti wire is described. Results on the quasi-static behaviour of the wire obtained using this setup are presented, giving an overall view of the damping capacity of the material as function of the amplitude of the loading (imposed torsional angle), the frequency and the temperature. The dynamical behaviour is then presented through measured frequency response function between forcing angle at the top of the pendulum and the difference between top and bottom rotation angles in the vicinity of the first eigenfrequency of the wire, i.e. in the range [0.3 Hz, 1 Hz]. The softening-type non-linearity and its subsequent jump phenomenon, predicted theorically by the decrease of the effective stiffness when martensite transformation starts is clearly evidenced and analysed.     

Dynamic mode decomposition of turbulent cavity flows for self-sustained oscillations

Self-sustained oscillations in a cavity arise due to the unsteady separation of boundary layers at the leading edge. The dynamic mode decomposition method was employed to analyze the self-sustained oscillations. Two cavity flow data sets, with or without self-sustained oscillations and possessing thin or thick incoming boundary layers (Re_D = 12,000 and 3000), were analyzed. The ratios between the cavity depth and the momentum thickness (D/θ) were 40 and 4.5, respectively, and the cavity aspect ratio was L/D = 2. The dynamic modes extracted from the thick boundary layer indicated that the upcoming boundary layer structures and the shear layer structures along the cavity lip line coexisted with coincident frequency space but with different wavenumber space, whereas structures with a thin boundary layer showed complete coherence among the modes to produce self-sustained oscillations. This result suggests that the hydrodynamic resonances that gave rise to the self-sustained oscillations occurred if the upcoming boundary layer structures and the shear layer structures coincided, not only in frequencies, but also in wavenumbers. The influences of the cavity dimensions and incoming momentum thickness on the self-sustained oscillations were examined.     

Dynamic mode decomposition of turbulent cavity flows for self-sustained oscillations

Self-sustained oscillations in a cavity arise due to the unsteady separation of boundary layers at the leading edge. The dynamic mode decomposition method was employed to analyze the self-sustained oscillations. Two cavity flow data sets, with or without self-sustained oscillations and possessing thin or thick incoming boundary layers (Re_D = 12,000 and 3000), were analyzed. The ratios between the cavity depth and the momentum thickness (D/θ) were 40 and 4.5, respectively, and the cavity aspect ratio was L/D = 2. The dynamic modes extracted from the thick boundary layer indicated that the upcoming boundary layer structures and the shear layer structures along the cavity lip line coexisted with coincident frequency space but with different wavenumber space, whereas structures with a thin boundary layer showed complete coherence among the modes to produce self-sustained oscillations. This result suggests that the hydrodynamic resonances that gave rise to the self-sustained oscillations occurred if the upcoming boundary layer structures and the shear layer structures coincided, not only in frequencies, but also in wavenumbers. The influences of the cavity dimensions and incoming momentum thickness on the self-sustained oscillations were examined.     

Numerical evaluation of turbulence models for dense to dilute gas–solid flows in vertical conveyor

A two-fluid model (TFM) of multiphase flows based on the kinetic theory and small frictional limit boundary condition of granular flow was used to study the behavior of dense to dilute gas–solid flows in vertical pneumatic conveyor. An axisymmetric 2-dimensional, vertical pipe with 5.6 m length and 0.01 m internal diameter was chosen as the computation domain, same to that used for experimentation in the literature. The chosen particles are spherical, of diameter 1.91 mm and density 2500 kg/m³. Turbulence interaction between the gas and particle phases was investigated by Simonin's and Ahmadi's models and their numerical results were validated for dilute to dense conveying of particles. Flow regimes transition and pressure drop were predicted. Voidage and velocity profiles of each phase were calculated in radial direction at different lengths of the conveying pipe. It was found that the voidage has a minimum, and gas and solid velocities have maximum values along the center line of the conveying pipe and pressure drop has a minimum value in transition from dense slugging to dilute stable flow regime. Slug length and pressure fluctuation reduction were predicted with increasing gas velocity, too. It is shown that solid phase turbulence plays a significant role in numerical prediction of hydrodynamics of conveyor and the capability of particles turbulence models depends on tuning parameters of slip-wall boundary condition.     

Quantitative imaging of acoustically coupled flows over symmetrically located side branches

Fully turbulent inflow past symmetrically located side branches mounted in a duct can give rise to pronounced flow oscillations due to coupling between separated shear layers and standing acoustic waves. Experimental investigation of acoustically coupled shear layers was conducted using digital particle image velocimetry in conjunction with unsteady pressure measurements. Global instantaneous and time-averaged flow images, as well as turbulence statistics, were evaluated to provide insight into the flow physics during flow tone generation. The emphasis was on the acoustic response of the resonator during the first and second hydrodynamic modes of the shear layer oscillation. Onset of the locked-on resonant states was characterized in terms of the acoustic pressure amplitude and the quality factor of the corresponding spectral peak. In addition, visco-thermal acoustic damping and patterns of generated acoustic power were calculated using a semi-empirical approach.     

Non-linear dynamics of a slender beam carrying a lumped mass with principal parametric and internal resonances

The non-linear behaviour of a slender beam carrying a lumped mass subjected to principal parametric base excitation is investigated. The dimension of the beam–mass system and the position of the attached mass are so adjusted that the system exhibits 3 : 1 internal resonance. Multi-mode discretization of the governing equation which retains the cubic non-linearities of geometrical and inertial type is carried out using Galerkin’s method. The method of multiple scales is used to reduce the second-order temporal differential equation to a set of first-order differential equations which is then solved numerically to obtain the steady-state response and the stability of the system. The linear first-order perturbation results show new zones of instability due to the presence of internal resonance. For low amplitude of excitation and damping Hopf bifurcations are observed in the trivial steady-state response. The multi-branched non-trivial response curves show turning point, pitch-fork and Hopf bifurcations. Cascade of period and torus doubling, crises as well as the Shilnikov mechanism for chaos are observed. This is the first natural physical system exhibiting a countable infinity of horseshoes in a neighbourhood of the homoclinic orbit.     

Wavelet decomposition method decoupled boiling/evaporation oscillation mechanisms over two to three timescales: A study for a microchannel with pin fin structure

Boiling/evaporation heat transfer in a microchannel with pin fin structure was performed with water as the working fluid. Simultaneous measurements of various parameters were performed. The chip wall temperatures were measured by a high spatial-time resolution IR image system, having a sensitivity of 0.02 °C. The flow pattern variations synchronously changed wall temperatures due to ultra-small Bi number. The wavelet decomposition method successfully identified the noise signal and decoupled various temperature oscillations with different amplitudes and frequencies. Three types of temperature oscillations were identified according to heat flux q and mass flux G. The first type of oscillation occurred at q/G < 0.62 kJ/kg. The approximation coefficient of wavelet decomposition decided the dominant cycle period which was ∼3 times of the fluid residence time in the microchannel, behaving the density wave oscillation characteristic. The detail coefficients of wavelet decomposition decided the dominant cycle period, which matched the flow pattern transition determined value well, representing the flow pattern transition induced oscillation. For the second type of oscillation, the wavelet decomposition decoupled the three oscillation mechanisms. The pressure drop oscillation caused the temperature oscillation amplitudes of 5–10 °C and cycle periods of 10–15 s. The density wave oscillation and flow pattern transition induced oscillation are embedded with both the pressure rise and decrease stages of the pressure drop oscillation. The third type of oscillation happened at q/G > 1.13 kJ/kg, having the density wave oscillation coupled with the varied liquid film evaporation induced oscillation. The liquid island, retention bubble induced nucleation sites and cone-shape two-phase developing region are unique features of microchannel boiling with pin fin structure. This study illustrated that pressure drop oscillation and density wave oscillation, usually happened in large size channels, also take place in microchannels. The flow pattern transition and varied liquid film evaporation induced oscillations are specific to microchannel boiling/evaporation flow.     

Parametric instabilities of the radial motions of non-linearly viscoelastic shells under pulsating pressures

This paper treats the classical problem of radial motions of cylindrical and spherical shells under pulsating pressures. The novelty in this work is that the shells are taken to be non-linearly viscoelastic (of strain-rate type). It is remarkable that this classical problem, which does not treat the loss of stability to non-radial motions (but which is essential for such treatments), has such a rich dynamics due to the often neglected effects of non-linear material response, to the role of prestress under the action of the mean pressure, and to the different effects of pressure on cylindrical and spherical shells. The study of radial motions near primary resonance (when the frequency of the pulsating pressure is near the natural frequency about an equilibrium state under a constant pressure) gives formulas ensuring that the motions are of hardening or softening type depending on the constitutive functions and whether the constant mean pressure is compressive or inflational. The method of multiple scales gives asymptotic formulas for the principal parametric instability regions (Mathieu tongues) and for the stable and unstable motions at twice the forcing frequency, which closely agree with those obtained by numerical continuation methods. The dependence of frequency on amplitude and the form of instability regions are critically influenced by deviations (even very slight deviations) of material response from that of linearly viscoelastic shells, by the constant mean pressure, and by the type of shell. This paper exhibits the rich diversity of postcritical periodic motions.     

An investigation into flow mode transition and pressure fluctuations for fluidized dense-phase pneumatic conveying of fine powders

This paper presents the results of an ongoing investigation into the fluctuations of pressure signals due to solids–gas flows for dense-phase pneumatic conveying of fine powders. Pressure signals were obtained from pressure transducers installed along different locations of a pipeline for the fluidized dense-phase pneumatic conveying of fly ash (median particle diameter 30 μm; particle density 2300 kg/m³; loose-poured bulk density 700 kg/m³) and white powder (median particle diameter 55 μm; particle density 1600 kg/m³; loose-poured bulk density 620 kg/m³) from dilute to fluidized dense-phase. Standard deviation and Shannon entropy were employed to investigate the pressure signal fluctuations. It was found that there is an increase in the values of Shannon entropy and standard deviation for both of the products along the flow direction through the straight pipe sections. However, both the Shannon entropy and standard deviation values tend to decrease after the flow through bend(s). This result could be attributed to the deceleration of particles while flowing through the bends, resulting in dampened particle fluctuation and turbulence. Lower values of Shannon entropy in the early parts of the pipeline could be due to the non-suspension nature of flow (dense-phase), i.e., there is a higher probability that the particles are concentrated toward the bottom of pipe, compared with dilute-phase or suspension flow (high velocity), where the particles could be expected to be distributed homogenously throughout the pipe bore (as the flow is in suspension). Changes in straight-pipe pneumatic conveying characteristics along the flow direction also indicate a change in the flow regime along the flow.     

Evolution of three-dimensional cavitation following water entry of an inclined cylinder

The water entry of an inclined cylinder is firstly studied experimentally for low Froude number. The cylinder is 50 mm in diameter and 200 mm in length, with a moderate length to diameter ratio. As it is submerged below the water surface, the cavity is fully three-dimensional. Due to the rotation of the cylinder caused by the initial inclined impact, the cavity evolution is quite complicated and a new phenomenon is revealed. The cylinder moves along a curved trajectory in water, which greatly affects the evolution of the cavities. The cavity breaks up into two sub-cavities, and finally collapses because of hydrostatic pressure.     

Flow tones in a pipeline-cavity system: effect of pipe asymmetry

Flow tones in a pipeline-cavity system are characterized in terms of unsteady pressure within the cavity and along the pipe. The reference case corresponds to equal lengths of pipe connected to the inlet and outlet ends of the cavity. Varying degrees of asymmetry of this pipe arrangement are investigated. The asymmetry is achieved by an extension of variable length, which is added to the pipe at the cavity outlet. An extension length as small as a few percent of the acoustic wavelength of the resonant mode can yield a substantial reduction in the pressure amplitude of the flow tone. This amplitude decrease occurs in a similar fashion within both the cavity and the pipe resonator, which indicates that it is a global phenomenon. Furthermore, the decrease of pressure amplitude is closely correlated with a decrease of the Q (quality)-factor of the predominant spectral component of pressure. At a sufficiently large value of extension length, however, the overall form of the pressure spectrum recovers to the form that exists at zero length of the extension.Further insight is provided by variation of the inflow velocity at selected values of extension length. Irrespective of its value, both the magnitude and frequency of the peak pressure exhibit a sequence of resonant-like states. Moreover, the maximum attainable magnitude of the peak pressure decreases with increasing extension length.