Axial Wavenumber Research Articles

Three-dimensional elastic Rayleigh–Taylor instability at the cylindrical interface

This paper presents a linear analysis of elastic Rayleigh–Taylor instability at both cylindrical column and cylindrical shell interfaces. By considering the rotational part of the disturbance flow field, an exact solution is derived, revealing that the most unstable mode is two-dimensional in the cross section. As the column radius decreases, the maximum growth rate increases, while the corresponding azimuthal wave number decreases incrementally until it reaches 1. Thinning the cylindrical shell is found to be a destabilizing effect, leading to an increase in both the cutoff wave number and the most unstable azimuthal wave number. The maximum growth rate usually increases as the shell becomes thinner, except in cases with small radii where feedthrough effects occur. For thin shells with small radii, the cutoff axial wave number is determined by the radius rather than the shell thickness. Comparisons between the growth rates derived from the potential flow theory and the exact solution show significant discrepancies in cylindrical shells, mainly due to substantial deviations in the cutoff wave number.

Modal and non-modal stability for Hagen–Poiseuille flow with non-ideal fluid

Modal and non-modal stability analyses are applied to Hagen–Poiseuille flow with a non-ideal fluid. The non-ideal fluid is defined as a fluid close to its vapor–liquid critical point. In this region, properties of the fluid deviate significantly from the assumptions of the ideal gas model. In this paper, the specific example of CO2 near the critical point is taken as a non-ideal fluid. We studied fluids at supercritical pressure and different wall temperatures so that the centerline temperatures can be lower, equal, and higher than the pseudo-critical temperature. Flow instability is characterized by the Reynolds number, and the product of the Prandtl and Eckert numbers. In modal stability analysis, we observe that there is no unstable mode in Hagen–Poiseuille flow with a non-ideal fluid. Regarding the growth rate, as the axial wavenumber increases, another mode becomes the least stable. The non-modal theory is employed to investigate the optimal response to harmonic external force and transient energy growth. The influence of axial and azimuthal wave numbers, Prandtl and Eckert numbers, and thermodynamic states are also taken into account. In this study, we identify an generalized inflection point in the transcritical base profile, causing the transcritical state to be the most unstable. In non-modal instability, we observe that the optimal response mainly occurs at time invariant axisymmetric disturbance. This suggests that the axisymmetric disturbance could potentially initiate the transition to turbulence.

Effects of cavity resonance and antenna resonance on mode transitions in helicon plasma

Mechanisms of cavity resonance and antenna resonance and their coupling effects on mode transitions in argon helicon plasma excited by a half-helical antenna (14 cm in length) were investigated in this paper. Cavity length was changed to distinguish the effects of cavity and antenna resonances in experiments. Plasma parameters under various discharge conditions, such as input power (0–2500 W), magnetic field (0–1000 G) and cavity length (10–42 cm) were measured. Characteristics of helicon discharges and mode transitions in cases of fixed and continuously changing cavity lengths were compared. The results show that multiple axial eigenmodes (at least five in the present work) were observed in both cases. In fixed-length cavities, the helicon discharge changes abruptly during mode transitions, while in changeable-length cavities, discharge features can change continuously (e.g. in a large range of density from 1.7 × 1012 to 1.3 × 1013 cm−3) without mode transition. Mode transitions also occur as the cavity length increases at fixed input power and magnetic field with periodical variations of plasma parameters. Cavity resonance plays a dominant role in the formation of standing helicon waves of eigenmodes and mode transitions, while antenna resonance significantly affects the transition from inductively coupled modes to helicon wave modes. Enhanced inter-coupling of cavity resonance and antenna resonance appears at specific axial wavelengths of eigenmodes. The threshold conditions for mode transitions were deduced and the overall transition path of wave modes and the corresponding density were predicted quantitatively, which shows that cavity resonance determines the transition path of wave modes, while antenna resonance gives the lower limit of the transition path. Characteristics of helicon discharge and mode transition are closely related to the axial wavenumber. Cavity and antenna resonances influence the helicon discharge and mode transition by determining the axial wavenumber of eigenmodes.

Nonlinear electro-rheological instability of two moving cylindrical fluids: An innovative approach

The present article examines the nonlinear stability of two viscoelastic electrified cylindrical fluids immersed in permeable media. The current structure consists of two endless vertical cylinders containing two electrified fluids. An axial unchanged electric field (EF) is applied to the entire construction; additionally, the impact of the surface tension is reflected. The main driving force for understanding this challenge has increasing significance in atmospheric and oceanic dynamics. The viscous potential theory is employed to ease the mathematical processes. The fundamental hydrodynamic equations are combined with Maxwell's equations in the quasi-static approximation to set the boundary-value problem. The appropriate boundary conditions (BCs) are expressed in a nonlinear form; this nonlinearity is achieved by addressing the linearized controlling equations of the motion. The viscoelastic impacts are considered to illustrate how the BCs produce their contributions. Consequently, the equations of motion are tackled without the effects of viscoelasticity parameters. The interface displacement consequently interacts vertically along with the cylindrical axis. The Rayleigh Helmholtz–Duffing oscillator describes the propagation of the interface between the two fluids. The non-perturbative approach (NPA), based on the He's frequency formula, transforms the typical nonlinear differential equation (NDE) into a linear one. The non-dimensional analysis reveals a lot of dimensionless physical numerals. These non-dimensional physical characteristics can be utilized to study the fundamental character of the liquid movement. They are also used to reduce the quantity of variables that are needed to comprehend the framework. A quick explanation of NPA is also presented. The stability study reveals the real/complex coefficients of the NDE. The numerical simulations show that there is a consistent solution and that the increases in the axial EF, as well as axial wavenumber, stabilize the system. The obtained findings help to understand and explain diverse nonlinear progressions that have taken place in fluid mechanics. To show the impact of the different factors and the efficiency of the stability approach, diverse PolarPlot diagrams are graphed for both actual and hypothetical portions.

The wave mode transition of argon helicon plasma

In this paper, multiple wave modes and transitions of argon helicon plasma excited by a half right-helical antenna in a system without any reflection endplate are investigated experimentally and theoretically at increasing radio frequency (RF) powers and external magnetic fields. Experiments show that above a critical magnetic field strength and pressure (about 250 G and 0.3 Pa in this work), two to four distinct wave-coupled modes and transitions were observed at increasing RF powers and/or magnetic fields. Theoretical analysis based on the dispersion relationship shows that in a high magnetic field, the helicon wave of the lowest order of axial eigenmode is always excited first, then the higher-order axial or radial mode; hence, the plasma density increases after mode jumping. There are two mechanisms responsible for the wave mode transitions in the present system, i.e. axial and radial mode transitions due to the change of axial and radial wavenumbers from a lower eigenmode to a higher one. A higher plasma density and magnetic field are helpful for achieving more higher-order modes of helicon waves.

Shear flow effects in a 2D duct: Influence on wave propagation and direct impedance eduction

Impedance eduction of acoustic liners with flow is commonly performed under the assumption of a uniform velocity profile. In practice, the flow profile is not uniform and a significant mean flow shear is present close to the duct wall. The present paper aims to assess the validity of the uniform flow assumption, and more generally to study the effect of the mean flow shear on the impedance eduction process. This is particularly relevant when considering large ducts, high frequencies, high-order acoustic modes and flow velocities representative of aircraft engine nacelles. A numerical mode-matching model is used to compute the sound field in a 2D lined duct with different flow profiles. A detailed parametric study evaluates the influence of the mean flow shear on the axial wavenumbers of the acoustic modes and on the educed impedance. Various parameters are considered: the flow velocity profile (boundary layer thickness and mean Mach number), the direction of acoustic propagation relative to the flow, two different liner configurations and the presence of noise in the pressure data. A number of recommendations are given to achieve robust impedance eduction in large-duct facilities and at high-frequencies.

Floquet-based analysis on three-dimensional non-axisymmetric instabilities in oscillatory-driven Taylor–Couette flows and their low-frequency asymptotic behavior using Wentzel–Kramers–Brillouin method

This paper revisits the linear stability analysis of oscillatory-driven flows between two oscillating cylinders against non-axisymmetric disturbances. This study is motivated by the lack of a sufficiently reliable theoretical analysis giving insight into the experimentally observed spiral-like non-axisymmetric patterns when the cylinders are counter-oscillating. A new generalized time-dependent algebraic eigenvalue problem is constructed from the linearized set of the three-dimensional Navier–Stokes equations around the purely azimuthal basic state. Numerical evaluation of the critical eigenvalues combining both Floquet theory and spectral method reveals the existence of frequency ranges where this basic state becomes unstable against three-dimensional non-axisymmetric disturbances before it does so for two-dimensional axisymmetric ones. Indeed, as the oscillation frequency of the cylinders increases, the azimuthal wave number of the critical eigensolution is found to change from 0 to 2 to 1 and then back to 0. The primary bifurcation exchange between two instability modes with different azimuthal wave numbers occurs via different types of codimension-2 bifurcation points giving rise to discontinuities in the critical axial wave number where reversing and non-reversing non-axisymmetric Taylor vortex flows are identified. In addition, by extending our numerical calculations to the co-oscillating case, we show that the axisymmetric disturbances are the most unstable confirming thus existing experimental findings. Furthermore, a Wentzel–Kramers–Brillouin (WKB) analysis is performed to shed light on the asymptotic behavior of these time-dependent flows in the low-frequency limit when the cylinders are slowly oscillating.

Quantum mechanical approach to plasma waves with helical wavefront

Plasma waves with helical wavefront are studied theoretically from the quantum mechanical viewpoint and are shown to produce a spinning motion of a charged macroparticle in a complex plasma. The electrostatic helical perturbations are described by the wave function for a Laguerre–Gaussian beam mode with the radial/angular mode numbers n/l. The interaction and the transfer of angular momentum from the wave to a particle are analyzed by the method of second quantization with the help of the Feynman diagram. Laguerre function, instead of the Born approximation, is introduced to describe plasma waves with helical wavefront. A pair of dust particles in a complex plasma exchange a quasiparticle (virtual plasmon) resulting in the acquisition of angular momentum, which makes a dust particle spin in motion with rotational frequency Ωϕ. The resonance condition ω−kvz−lΩϕ=0 and the conservation of angular momentum IdΩϕ=lℏ determine the rotational frequency, where ω and k are frequency and axial wave number of the helical wave, and vz and Id are axial velocity and the moment of inertia of a dust particle.

Non-axisymmetric modes in ultrathin annular liquid films coating a cylindrical fiber

This paper presents a detailed analysis of the three-dimensional stability properties of an annular liquid film coating a cylindrical fiber in the presence of van der Waals (vdW) interactions, whose influence depends on the wettability of the solid by the liquid. Under wetting conditions, vdW interactions can stabilize a uniform annular film when its thickness is smaller than a critical value that depends only on the fiber radius, the Hamaker constant, and the surface tension coefficient [Quéré et al., Science 249(4974), 1256–1260 (1990)]. In contrast, under non-wetting conditions, both surface tension and vdW forces contribute to destabilize the interface, and non-axisymmetric modes may become dominant depending on the thickness of the film and the relative strength of the surface tension and vdW forces. We perform temporal stability analyses of both the Stokes and lubrication equations of motion, allowing us to reveal the dominant azimuthal mode, as well as the optimal axial wavenumber and the corresponding temporal growth rate, as a function of the relevant governing parameters.

Generalized hydrodynamic coefficients of twin connected circular cylinders in finite water depth

In this work the generalized hydrodynamic coefficients of connected twin circular cylinders are studied. Firstly, a matched boundary element method with eigen-function expansion is applied to study the generalized hydrodynamic coefficients of floating and submerged tunnels with twin horizontal cylinders in finite water depth. By numerical examination it is found that gap resonance problem can be neglected for the submerged floating tunnels with a certain submergence depth, and the axial wave number play an important role for the added mass. Then, analytic solutions are derived for the high frequency approximations of the generalized added masses of twin connected cylinders by the eigenfunction expansion in the polar coordinate system with aid of their images about the x-axis in the infinite fluid domain. The high frequency approximations of generalized added masses decrease with increasing vibration wave number. When T/a and B/a are larger than 3 (where T is the cylinder submergence, B is the spacing distance between the twin cylinders and a is the radius of the cross-section of the cylinder), the hydrodynamic interference between the two cylinders can be neglected and the generalized added mass coefficients of connected twin cylinders can be derived from these of single isolated cylinders.

Dissipative Instability of Magnetohydrodynamic Sausage Waves in a Compressional Cylindrical Plasma: Effect of Flow Shear and Viscosity Shear

The shear flow influences the stability of magnetohydrodynamic (MHD) waves. In the presence of a dissipation mechanism, flow shear may induce an MHD wave instability below the threshold of the Kelvin–Helmholtz instability, which is called dissipative instability. This phenomenon is also called negative energy wave instability because it is closely related to the backward wave, which has negative wave energy. Considering viscosity as a dissipation mechanism, we derive an analytical dispersion relation for the slow sausage modes in a straight cylinder with a discontinuous boundary. It is assumed that the steady flow is inside and dynamic and bulk viscosities are outside the circular flux tube under photospheric condition. When the two viscosities are weak, it is found that for the slow surface mode, the growth rate is proportional to the axial wavenumber and flow shear, consistent within the incompressible limit. For a slow body mode, the growth rate has a peak at a certain axial wavenumber, and its order of magnitude is similar to surface mode. The linear relationship between the growth rate and the dynamic viscosity established in the incompressible limit develops nonlinearly when the flow shear and/or the two viscosities are sufficiently strong.

Axial wavenumber-merging design method for finite-length liners

The Cremer concept via the classical entire-mode merging fails in most cases to achieve the optimal design for finite liners, whose efficient design remains unsolved. To this end, based on not only the simple- but also the cross-modal power analyses, the axial wavenumber(kx*)-merging design method (AWMDM) is proposed herein, merging the imaginary part Im(kx*) and modulating the real part Re(▵kx*)=2πq/L*. It is found for a not-too-short finite liner of length L* that, the AWMDM of q = 1 and 2 can almost capture the globally optimal and suboptimal solutions, respectively, while the Cremer concept is a particular case of the AWMDM at q = 0. The physical mechanism to optimize a finite liner is further revealed: 1) the simple-modal power shows purely exponential attenuation and can be minimized directly by merging Im(kx*); 2) under the premise of merging Im(kx*), the total cross-modal power exhibits a periodic oscillation, and just reaches the first/second trough at the liner exit when one/two (q = 1 or 2) complete oscillation(s) occur(s) within L* by modulating Re(kx*), and thus can be minimized. However, the Cremer concept is based on the infinite-length assumption and considers only a single simple-modal power, so that 1) it cannot capture the inlet effect of the total power in a finite liner; 2) the unexpected cross-modal power has an oscillating period tending to be infinite and thus cannot reach the trough at the exit, which result in its limitation. Generally, the AWMDM of q = 1 and q = 0 exhibit the optimality at lower and higher Helmholtz number scopes respectively, and the valid scope of q = 1 is significantly expanded with the increases in both the length L* and the circumferential mode.

Stability characteristics of the spiral Poiseuille flow induced by inner or outer wall rotation

In this paper we reveal, that the stability behavior of the spiral Poiseuille flow in an annular gap with rotating inner or outer cylinder exhibits a striking similarity at low and intermediate rotation rates, while both cases differ significantly at higher rotation rates. Based on the work of Vasanta Ram (2019) we formulate the flow problem by means of the inner swirl parameter (Si), the outer swirl parameter (So) and the curvature parameter (ϵ). Six different values of the curvature parameter {0.005; 0.025; 0.111; 0.25; 0.333; 0.785} and a swirl range of 10−5<Si;So<105 are investigated. We reveal that for the rotating outer cylinder case three characteristic jumps of the critical axial and azimuthal wavenumbers can be identified. Similar features can be identified for the inner rotation case. Based on this, we define three regimes delimited for both the rotating inner and rotating outer cylinder which enables us to perform a systematic comparison. The first regime transition occurs at low values of the swirl parameter (Si; So>10−4) and is accompanied by a rapid decrease of the critical Reynolds number. Our computations reveal that this regime transition does not occur for a small curvature parameter of ϵ= {0.005; 0.025} in the outer rotation case. The second wavenumber jump occurs at higher swirl parameters of around Si>2.5 and So>1.6. While the critical Reynoldsnumber decreases monotonously in the inner cylinder rotating case, we show that in the case of rotating outer cylinder a rapid increase of Rec is observed as So increases further. To gain an insight into the mechanisms involved that induce such wavenumber jumps, a detailed comparative study on the associated Reynolds shear stress distributions is performed. For larger ϵ it is shown that the distributions of the Reynolds shear stresses change significantly over the first jump exhibiting similar features for both flow cases, leading to the conclusion that in both cases the same centrifugal instability is triggered here. Instead, the distributions of the Reynolds shear stresses before and after the second jump are fundamentally different for inner and outer rotation. While the Reynolds shear stresses spread over the whole gap height for the inner rotation case, they are nonzero only close to a small regime near the inner cylinder for the outer rotation case at high rotation rates. Overall, analyzing the shear stresses, we reveal that a similar instability arises in the Spiral Poiseuille flow with inner and outer cylinder rotation at intermediate swirls, but at higher swirl outer rotation seems to give rise to an instability associated with a critical layer that is inherently different to the inner rotation case.

Nearly Perfect Transmission of Lamé Modes in a Rectangular Beam with Part and Through-Thickness Vertical Cracks.

The guided waves in the uniform waveguide of rectangular cross-section exhibit complicated propagation and scattering characteristics due to the diversity of vibration modes. This paper focuses on the mode conversion of the lowest Lamé mode at a part-through or through-thickness crack. Firstly, the Floquet periodicity boundary condition is applied to derive the dispersion curves in the rectangular beam, which relates the axial wavenumber to the frequency. On this basis, the frequency domain analysis is conducted to investigate the interaction between the fundamental longitudinal mode in the vicinity of the first Lamé frequency and a part-through or through-thickness vertical or inclined crack. Finally, the nearly perfect transmission frequency is evaluated by extracting displacement and stress harmonic fields throughout the cross-section. It is shown that this frequency originates from the first Lamé frequency, increases with the crack depth, and decreases with the crack width. Between them, the crack depth plays a major role in the frequency variation. In addition, the nearly perfect transmission frequency is negligibly affected by the beam thickness, and such a phenomenon is not observed for inclined cracks. The nearly perfect transmission may have potential applications in the quantitative evaluation of crack size.

Free Vibration Characteristics Analysis of Metal-Rubber Cylindrical Shells Based on Viscoelastic Theory

The cylindrical shell made of metal rubber has a strong ability to reduce and absorb vibration, which widens its application in the industrial field. Therefore, it is of great significance to study the vibration characteristics of metal-rubber cylindrical shells (MRCSs). However, there is relatively little research on this aspect. Based on this, the dynamic properties of MRCS are investigated in this paper based on viscoelastic theory, the Rayleigh–Ritz method, and the Gram–Schmidt orthogonal polynomials. The correctness of the proposed model was verified by comparison with the literature and experimental verification. The results show that the preloading state and boundary conditions have significant effects on the natural frequency and modal loss factor of MRCS. The effect of the Pasternak elastic foundation on the natural frequency and modal loss factor of MRCS varies with the change of the axial half wave number m. The effect of the Pasternak elastic foundation on higher-order vibrations is similar to that of the artificial spring technique.

How tidal waves interact with convective vortices in rapidly rotating planets and stars

Context. The dissipation of tidal inertial waves in planetary and stellar convective regions is one of the key mechanisms that drive the evolution of star–planet and planet–moon systems. This dissipation is particularly efficient for young low-mass stars and gaseous giant planets, which are rapid rotators. In this context, the interaction between tidal inertial waves and turbulent convective flows must be modelled in a realistic and robust way. In the state-of-the-art simulations, the friction applied by convection on tidal waves is commonly modeled as an effective eddy viscosity. This approach may be valid when the characteristic length scales of convective eddies are smaller than those of the tidal waves. However, it becomes highly questionable in the case where tidal waves interact with potentially stable large-scale vortices such as those observed at the poles of Jupiter and Saturn. The large-scale vortices are potentially triggered by convection in rapidly-rotating bodies in which the Coriolis acceleration forms the flow in columnar vortical structures along the direction of the rotation axis. Aims. We investigate the complex interactions between a tidal inertial wave and a columnar convective vortex. Methods. We used a quasi-geostrophic semi-analytical model of a convective columnar vortex, which is validated by numerical simulations. First, we carried out linear stability analysis using both numerical and asymptotic Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) methods. We then conducted linear numerical simulations of the interactions between a convective columnar vortex and an incoming tidal inertial wave. Results. The vortex we consider is found to be centrifugally stable in the range –Ωp ≤ Ω0 ≤ 3.62Ωp and unstable outside this range, where Ω0 is the local rotation rate of the vortex at its center and Ωp is the global planetary (stellar) rotation rate. From the linear stability analysis, we find that this vortex is prone to centrifugal instability with perturbations with azimuthal wavenumbers m = {0,1, 2}, which potentially correspond to eccentricity, obliquity, and asynchronous tides, respectively. The modes with m &gt; 2 are found to be neutral or stable. The WKBJ analysis provides analytic expressions of the dispersion relations for neutral and unstable modes when the axial (vertical) wavenumber is sufficiently large. We verify that in the unstable regime, an incoming tidal inertial wave triggers the growth of the most unstable mode of the vortex. This would lead to turbulent dissipation. For stable convective columns, the wave-vortex interaction leads to the mixing of momentum for tidal inertial waves while it creates a low-velocity region around the vortex core and a new wave-like perturbation in the form of a progressive wave radiating in the far field. The emission of this secondary wave is the strongest when the wavelength of the incoming wave is close to the characteristic size (radius) of the vortex. Incoming tidal waves can also experience complex angular momentum exchanges locally at critical layers of stable vortices. Conclusions. The interaction between tidal inertial waves and large-scale coherent convective vortices in rapidly-rotating planets (stars) leads to turbulent dissipation in the unstable regime and complex behaviors such as mixing of momentum and radiation of new waves in the far field or wave-vortex angular momentum exchanges in the stable regime. These phenomena cannot be modeled using a simple effective eddy viscosity.

Impedance eduction experiments covering higher frequencies based on the multimodal straightforward method

The multimodal straightforward method is developed further, validated and applied experimentally. The trust-region algorithm is introduced to reduce the eduction time, a flow duct setup with a cross section of 51 × 51 mm2 is built for the impedance eduction, and several single- and multi-layer perforated liners are tested from 0.5 kHz up to 6.0 kHz at two average Mach numbers under several types of modal sound sources. It is validated that, this method, by utilizing a diagonal microphone array and improving Prony’s algorithm, enables the automatic match between axial and transverse wavenumbers, and thus realizes the full decomposition to three-dimension multimodal sound fields. By introducing the trust-region algorithm, it can educe the impedance with a good consistency and a higher time efficiency. Generally, this method is applicable to the practical impedance eduction in multimodal aeroacoustic environments on a real flow duct, with the upper frequency extended from 3.0 to 6.0 kHz covering the main frequency range of aeroengine fan noises. For multilayer liners, the educed impedance spectrum is considerably flatter than the prediction by an existing impedance model in some cases especially near the antiresonance, and the grazing flow magnifies such a flatting trend accompanied by more evident predicting deviations. The spectra of educed impedance and transmission loss show that the multilayer liner possesses more resonant frequencies within the concerned range and broadband absorption potentials if well designed.

Response analyses on the drill-string channel for logging while drilling telemetry

Downhole acoustic telemetry (DAT), using a long drill string with periodical structures as the channel, is a prospective technology for improving the transmission rate of logging while drilling (LWD) data. Previous studies only focused on the acoustic property of a free drill string and neglected the coupling between pipes and fluid-filled boreholes. In addition to the drill-string waves, a series of fluid waves are recorded in the DAT channel, which has not been investigated yet. Unpredictable channel characteristics result in lower transmission rates and stability than expected. Therefore, a more realistic channel model is needed considering the fluid-filled borehole. In this paper, we propose a hybrid modeling method to investigate the response characteristics of the DAT channel. By combining the axial wavenumbers and excitation functions of mode waves in radially layered LWD structures, the channel model is approximated to the 1-D propagation, which considers transmission, reflection, and interconversion of the drill-string and fluid waves. The proposed 1-D approximation has been well validated by comparing the 2-D finite-difference modeling. It is revealed that the transmitted and converted fluid waves interfere with the drill-string wave, which characterizes the DAT channel as a particular coherent multi-path channel. When a fluid-filled borehole surrounds the drill string, the channel responses exhibit considerable delay as well as strong frequency selectivity in amplitude and phase. These new findings suggest that the complexity of the channel response has been underestimated in the past, and therefore channel measurements on the ground are unreliable. To address these channel characteristics, we apply a non-coherent demodulation strategy. The transmission rate for synthetic data reaches 15 bps in a 94.5 m long channel, indicating that the acoustic telemetry is promising to break the low-speed limitation of mud-pulse telemetry.

Free vibration characteristics of cord-reinforced air spring with winding formation under preload conditions

A precise transfer matrix was employed to analyze the free vibration characteristics of a cord-reinforced air spring with winding formation under preload conditions. The air spring was abstracted as a rotary combined shell structure with variable winding trajectory characteristics. The rotary structure, which consisted of cylindrical and toroidal shells, was analyzed for its shell pre-stress under preload conditions. The shell pre-stress was combined with the theory of thin shells to create the rotary shell vibration control equations under preload effect. The Helmholtz equation was used to analyze the influence of sound pressure inside shells under the fluid–structure coupling boundary conditions. The rotary shell transfer matrix was derived from the variable winding trajectory equation, geometrical equation, and physical equation of shells. Under the continuous conditions of state vector between the cylindrical and toroidal shells, the shells were combined into a rotary combined shell structure to obtain its total free vibration equation. The shell boundary conditions were considered to solve the natural frequency of the air spring. The calculation results were compared with the prototype test and simulation results to verify the effectiveness and accuracy of the theoretical model. On this basis, we explored the influence of axial half wave number, circumferential wave number, geometrical structure, and material characteristics on the free vibration characteristics of the air spring. The research findings would provide important and significant guidance for the structural design of cord-reinforced air springs with winding formation.

Generalized hydrodynamic coefficients of a circular SFT in finite water depth

In this work, a numerical model is developed for calculating the generalized hydrodynamic coefficients of a horizontal vibrating cylinder representative of a submerged floating tunnel in finite water depth. In this model, the whole computational domain is divided into three sub-domains and the velocity potential for describing the fluid motion in each sub-domain is solved separately using different approaches. In the inner domain bounding the cylinder, a simple Green function is utilized to form a boundary integral equation, which is solved by the boundary element method (BEM), and the technique of eigenfunction expansion is applied in the outer domains away from the cylinder. The eigenfunctions in the outer domains indicate that there exists a critical vibration frequency below which no propagating wave can be generated and thus the radiation damping is zero. Characteristics of the generalized hydrodynamic coefficient in a wider range of the submergence depth, the vibration frequency and the axial wavenumber are explored. It is found that the generalized hydrodynamic coefficients in the vicinity of the critical vibration frequency experience abrupt changes, characterised by a ‘sharp peak’ profile. Generally, the generalized (horizontal and vertical) added mass increases firstly with the vibration frequency to its maximum value at the critical frequency, and then decreases with the further increase in the vibration frequency. However, behaviours are rather different in terms of the vertical added mass if the cylinder is fully submerged; a discontinuity at the critical frequency is observed, and the value jumps from positive to negative here. Afterwards the vertical added mass starts to increase quickly and becomes positive again with the further increase of the vibration frequency. This phenomenon of discontinuity may be associated with the fact that the radiation force changes its direction suddenly at the critical frequency; from being ‘out-of-phase’ to ‘in-phase’ with the cylinder motion. In addition, semi-analytical solutions are derived for approximating the generalized added mass in a high frequency range, which suggests that the generalized added mass decreases with the axial wavenumber, and with the presence of free surface, especially when the axial wavenumber is small. While for a deeply submerged cylinder, the effect of the free surface is negligible and then further simplified solutions are provided.