Subcritical Velocity Research Articles

Nonlinear vibrations and static bifurcation of a hyperelastic pipe conveying fluid

This study investigates the free and forced nonlinear vibrations, along with the static bifurcation behavior, of a fluid transmission hyperelastic pipe supported by clamped ends. Both geometrical and material nonlinearities are taken into account. The mathematical model is grounded in Euler–Bernoulli beam theory, incorporating von Kármán nonlinearity to capture the complexities of the system. For the hyperelastic materials, the strain energy function proposed by Yeoh is employed. Considering that the lowest critical velocity of the fluid flow is associated with the first mode, after deriving the governing equation using Hamilton’s principle, Galerkin discretization is applied to obtain the reduced order model in the first mode. Analysis of static bifurcation and stability is performed and critical velocity values of fluid flow are determined. The analysis of free and forced vibrations of the hyperelastic pipe is conducted using the method of multiple time scales, specifically focusing on the sub-critical velocity range of fluid flow, which corresponds to the unbuckled state of the pipe. This approach allows for a comprehensive examination of how fluid flow velocity influences the frequency characteristics of free vibrations, as well as the frequency response in the vicinity of the main resonance. The results obtained from this study can significantly enhance our understanding of the design and application of hyperelastic pipes in various fluid transfer scenarios. By elucidating the dynamic behavior and critical parameters associated with these pipes, the findings can inform engineering practices and contribute to the optimization of systems that utilize hyperelastic materials for fluid conveyance.

Experimental study on the effects of branch tunnel ventilation on the smoke movement and temperature characteristics in bifurcated tunnel fires

A series of fire tests were conducted in a bifurcated tunnel model with branch tunnel ventilation. Three fire locations were considered. The characteristics of smoke movement and temperature profile under various fire source location scenarios were analyzed. The results indicate that when the fire source is not at the intersection, the ventilation airflow in the branch tunnel is diverted at the intersection before it is imposed on the fire source, which results in the actual velocity of ventilation air imposed on the fire source being less than the velocity of ventilation air in the branch tunnel. A new parameter, named the diversion coefficient, was introduced for convenient analysis. By substituting the diversion coefficient values into a classic maximum temperature rise prediction model for the single-line tunnel fires, good prediction results were observed. Moreover, a new dimensionless smoke temperature decay model was developed. The applicability of the model was validated using full-scale fire test data from previous research. The dimensionless temperature decay law of smoke was analyzed based on the newly established model. Results show that when the fire is positioned at the intersection, the decay coefficient of the smoke downstream of the fire decreases linearly as the ventilation rate increases, while decay coefficient of the smoke upstream of the fire decreases slowly at first and then increases with the increase of ventilation rate. When the fire source is not at the intersection, the branch tunnel ventilation conditions could be classified into three categories: sub-critical, critical, and super-critical velocity. Changes in the ventilation velocity within the branch tunnel have little influence on temperature decay process of smoke in the main tunnel under critical and sub-critical velocity conditions. However, under super-critical velocity conditions, the smoke temperature decreases rapidly after reaching the intersection. Furthermore, predictive models for the critical velocity of the branch tunnel under various fire locations were established based on theoretical analysis and experimental data. Within a specific range of heat release rate, the critical velocity is proportional to the cube root of the heat release rate. Compared to when the fire is located at the intersection, the critical velocity is reduced significantly when the fire is not in the intersection.

Dynamic Behavior and Double-Parameter Self-Adaptive Stability Control of a Gear Transmission System

This paper proposes a new nonlinear transverse-torsional coupled model for single-stage gear transmission system, by taking transmission error, time-varying meshing stiffness, backlash, bearing clearances and the self-adaptive double-parameter control module into account. The nonlinear differential governing equation of system motion is derived and solved by applying variable step-size Runge–Kutta numerical integration method. The system’s nonlinear dynamic characteristics and stability are investigated systematically by a bifurcation diagram of the Poincaré map and parameter stability region. Firstly, the velocity bifurcation diagrams have shown that, under the same damping ratio and backlash and with the increase of control parameter [Formula: see text], the route to chaos in the subcritical velocity region is first experienced from crisis to periodic doubling, and to crisis again, but the route that reverts to periodic motion in the super-critical velocity region is not affected. Additionally, the backlash is found to be the key parameter to affect the route to chaos as well. With the increase of the backlash, the crisis becomes the unique route to chaos in sub-critical region no matter what the [Formula: see text] is, but the increase of [Formula: see text] could change the route that reverts to periodic motion from 3T-periodic attractor to 2T-periodic attractor. Secondly, with the increase of the control parameter [Formula: see text], the system starts to enter the chaotic motion and exit the chaos state at different critical points and through different routes. Besides, the unstable region could shrink dramatically and the route to crisis is suppressed as well with the increase of damping ratio. Thirdly, the motion stability region analysis established in full range of double-parameter and velocity provides a mathematical reference model and is stored in control module, which could be utilized to make the control module seek a nearest parameter set automatically that could make the motion stable again in the quickest way under unstable working condition. Finally, according to global motion stability diagram, the forbidden zones that cannot make the system motion stable by adjusting single control parameter are revealed, which has remarkable guiding value during the practical operation especially under the manual adjusting working condition.

Mechanics of ballistic impact with non-axisymmetric projectiles on thin aluminium targets. Part I: Failure mechanisms

The ballistic performance of thin aluminium targets under normal and oblique impacts with plate-like projectiles is investigated with emphasis on the local projectile-induced target response. Three projectiles of 5 mm thickness with decreasing bluntness were considered, with the ratio of the projectile’s equivalent diameter to the target’s thickness (deq/hT) within the range of 0 to 4.89. The obtained results suggest that defeat mechanisms, and target resistance measures were different from those observed in impact with equivalent axisymmetric projectiles, as a result of a high projectile’s cross-sectional aspect ratio. Projectiles with inclined nose sections inflicted a shear-dominant failure that was locally energetically expensive and depended on the product of length (LN) and half-angle (α) of the projectile’s nose. On the other hand, projectiles with blunt sections were associated with retardation of their penetration capacity due to dynamic effects, followed by a low-energy mechanism associated with membrane stretching and tensile failure of targets. A total of 48 experiments were performed at normal-impact conditions, to estimate the critical velocity of perforation/penetration and examine the real-time deformation patterns at sub-critical velocities, by employing the digital image correlation technique. Overall, the critical velocity showed a quadratic dependence on deq/hT, where the benefit of ballistic performance decreased with an increase in this ratio. The observed non-monotonic behaviour of the critical velocity with increasing impact obliquity in some cases and the distinction in failure mechanisms highlight the importance of the projectile’s geometrical parameters for the energy transfer mechanisms. Also, the lack of correlation between the critical velocity and the local work in the target defeat term suggests that the resultant energy transfer mechanisms considerably contributed to the dissipation of the projectile’s kinetic energy. Experimental data were utilised for calibrating the material model and separate experimental results for validating the numerical (finite-element) model. A total of 119 simulations were carried out for normal and oblique impact incidences to examine the role of the projectile’s (i) rotation, (ii) geometrical features, and (iii) obliquity on the target’s dynamic performance and induced defeat mechanisms. The conclusions of this study form the basis for considering the role of the projectile’s geometrical parameters on the energy transfer mechanisms in the target through statistical and semi-analytical approaches presented in the second part of this work.

Modeling of the Wind/Disk Outflow from Be Stars II: Formation of the Keplerian Disk

Computer modeling of the outflow from Be stars is performed. In our approach, processes of turbulence excitation and turbulent viscosity are added to the conventional model of the radiation driven winds. The objective of our study is to reproduce from the first principles the main features of the outflow from Be stars: a fast polar wind and a slow viscous Keplerian disk at the equator. At sub-critical velocity of rotation up to 0.999 of the critical velocity, our model reproduces the formation of the fast polar wind together with a slow highly turbulent outflow at the equatorial region. This outflow, however, does not reassemble a Keplerian disk. We link this to the absence of the angular moment transfer from the star to the disk. This process provides an increase of the angular momentum of the disk matter with radius. We consider a star with super critical rotation as the simplest way to supply the angular momentum to the disk. In this case, the star surface has a higher azimuthal speed than the matter at the inner edge of the disk. The angular momentum transfer becomes unavoidable. Already at rotation velocity 0.5% above the critical one, a quasi Keplerian disk at the equator is formed with size ∼10 stellar radius. At rotation 1% higher than the critical speed, the disk reaches ∼15 stellar radius. The main conclusion following from our work is that the conventional model of the radiation driven winds is able to reproduce the main features of the outflow from Be stars provided that the process of turbulence excitation and a process of angular momentum supply of the disk from the central source are added in to this model.

Mechanics of ballistic impact with non-axisymmetric projectiles on thin aluminium targets. Part II: Energy considerations

In Part I of this study, the ballistic performance and failure mechanisms of a thin aluminium target impacted by plate-like, non-axisymmetric projectiles with three different geometries, were considered using the gas-gun experiments. Failure mechanisms of the target material were found to depend strongly on the projectile’s geometrical features. Also, the local target’s response was not a reliable predictor of the critical kinetic energy for perforation or penetration. In order to improve the prediction of ballistic performance of thin targets, a nonlocal target behaviour should also be accounted for. In this part of the study, the global target response is examined, and a heuristic approach is introduced for the energy balance. The approach involves a new factor that represents additional energy-dissipating mechanisms between the projectile’s critical energy and the local work in target defeat. The methodology is based on the identified strong correlation of the normalised impact-induced peak kinetic energy in the target, KE¯Tmax, and the normalised target impact-induced nonlocal internal energy, U¯TPL+KE, associated with plastic deformation and increase in kinetic energy. A physically-based semi-analytical formulation for KE¯Tmax is developed by decomposition of the contributions by the inclined and blunt projectile sections, succeeding statistical analysis of key projectile’s geometrical and impact parameters. The developed approach was assessed for 17 projectile geometries implementing a total of 119 finite-element simulations with experimentally validated numerical models at subcritical (50) and critical/supercritical (69) projectile velocities. The obtained predictions had an average absolute error of less than 6.5% for impact velocities at and above the ballistic limit, while at subcritical velocities a higher scatter was observed as a result of secondary interaction effects between the projectile and the target. Overall, the methodology yielded results for the ballistic limit with an error below 5%, improving the otherwise derived results nearly twofold. The method was proven to be a practical and accurate way to improve the projectile’s critical energy prediction for thin targets, and, even though developed for non-axisymmetric projectile cases, its framework is directly transferable to axisymmetric projectiles.

Two-layer model of the railway track: Analysis of the critical velocity and instability of two moving proximate masses

In this paper, the widely used two-layer model of the railway track is analysed with focus on the critical velocity and instability of moving masses. The model is assumed to be infinite with no changes in properties in the longitudinal direction. As far as the new demonstrations and conclusions: it is shown that in the undamped case, the onset of instability matches the critical velocity, and this is valid for one or more moving masses. However, in a damped case, the situation is more complicated. Instability of one moving mass occurs always in supercritical velocity range, but when two proximate masses are moving, then under certain conditions, the dynamic interaction between them together with the damping can shift the onset of instability into the subcritical velocity range. This newly derived negative effect has already been identified for Pasternak viscoelastic foundation in previous author's work. All results in this paper are presented in closed-form semi-analytical way for dimensionless parameters.The results presented are validated by eigenvalue expansion method on long finite model. For this purpose, vibration modes and orthogonality condition are derived. Modal equations are coupled and therefore rearrangement of the terms involved is introduced to save computational time. An excellent agreement between the results obtained on the infinite and finite models is achieved, which validates the newly derived formulas and the conclusions drawn from them.In order to simplify the expressions derived, continuous supports are implemented, because differences in behaviour would only be noticeable under high frequencies. This was checked by finite element analysis in commercial software. Unlike the more common usage of the two-layer model, shearing springs are added providing bases for further generalisations.

Dynamic interaction and instability of two moving proximate masses on a beam on a Pasternak viscoelastic foundation

The study analyzes the dynamic interaction of proximate masses using a new form of semi-analytical results for the moving mass problem developed by the author. This paper presents the results for a particular case of two moving masses of equal value acted upon by constant forces of equal values. The interaction level was demonstrated to be substantially high, making it impossible to superimpose the results obtained for one mass unless the masses were located at a significantly large distance apart. In the undamped case, the onset of instability occurred at the critical velocity, as with one moving mass; however, the onset of instability could be shifted significantly into the subcritical velocity range in the damped case. The critical distance between the moving masses was determined as the value at which the exponential increase in the amplitudes was severe. The implementation of dimensionless parameters revealed that this distance was slightly dependent on the damping. Moreover, the limiting moving mass ratio for such unexpected instability was derived.The results were validated by eigenmode expansion analysis on long finite beams, for which computational time savings were proposed by the rearrangement of the terms involved. Excellent agreement between the results was obtained, validating the new formulae. Furthermore, extension to more general cases and additional moving masses can easily be achieved.

Experimental Study of Sub-critical Velocity in Longitudinally Ventilated Tunnels

Experimental Study of Sub-critical Velocity in Longitudinally Ventilated Tunnels

Experimental and CFD analysis of MHD flow around smooth sphere and sphere with dimples in subcritical and critical regimes

An overview of previous researches related to the problem of flow around a bluff-body, using experimental and numerical methods, is presented in the paper. Experimental investigation was performed by a laser doppler anemometer, measuring velocity components of the water flow around a smooth sphere, and a sphere with dimples in square channels. Measurement results in subcritical velocity flow field, velocity fluctuation components, lift, drag and pressure coefficients, and 2-D Reynolds stress at quasi-stationary flow are conducted using 1-D laser doppler anemometer probe. The obtained experimental results are compared with numerical simulations, which are performed using the ANSYS-CFX software. For the numerical simulations of quasi-steady-state flow, k-? turbulent model was used, while for numerical simulation of unsteady fluid-flow and for the comparison of results related to the eddy structures, vortex shedding and Reynolds stresses, detached eddy simulation were used. Since the obtained results of experimental and numerical investigation of flow around smooth sphere and sphere with dimples showed good agreement, the considered flow problem was expanded by introducing the influence of a transverse magnetic field with a slight modification of the electrical conductivity of the working fluid. The other physical properties of the fluid remained the same, which also corresponds to realistically possible physical conditions. Numerical simulations were performed for three different values of Hartmann number and very small values of Reynolds magnetic number (inductionless approximation). Comparisons and analyzes of the results were made for the cases containing a magnetic field and those with an absence of a magnetic field.

Global linear analysis of a jet in cross-flow at low velocity ratios

The stability of the jet in cross-flow is investigated using a complete set-up including the flow inside the pipe. First, direct simulations were performed to find the critical velocity ratio as a function of the Reynolds number, keeping the boundary-layer displacement thickness fixed. At all Reynolds numbers investigated, there exists a steady regime at low velocity ratios. As the velocity ratio is increased, a bifurcation to a limit cycle composed of hairpin vortices is observed. The critical bulk velocity ratio is found at approximately for the Reynolds number , above which a global mode of the system becomes unstable. An impulse response analysis was performed and characteristics of the generated wave packets were analysed, which confirmed results of our global mode analysis. In order to study the sensitivity of this flow, we performed transient growth computations and also computed the optimal periodic forcing and its response. Even well below this stability limit, at , large transient growth ( in energy amplification) is possible and the resolvent norm of the linearized Navier–Stokes operator peaks above . This is accompanied with an extreme sensitivity of the spectrum to numerical details, making the computation of a few tens of eigenvalues close to the limit of what can be achieved with double precision arithmetic. We demonstrate that including the meshing of the jet pipe in the simulations does not change qualitatively the dynamics of the flow when compared to the simple Dirichlet boundary condition representing the jet velocity profile. This is in agreement with the recent experimental results of Klotz et al. (J. Fluid Mech., vol. 863, 2019, pp. 386–406) and in contrast to previous studies of Cambonie & Aider (Phys. Fluids, vol. 26, 2014, 084101). Our simulations also show that a small amount of noise at subcritical velocity ratios may trigger the shedding of hairpin vortices.

Thermodynamic Properties of the Inverse Evershed Flow at Its Downflow Points

Abstract We used spectropolarimetric observations of a sunspot in the active region NOAA 11809 in the Ca ii line at 854.2 nm taken with the SpectroPolarimeter for Optical and Infrared Regions at the Dunn Solar Telescope to infer thermodynamic parameters along 100 super-penumbral fibrils that harbor the inverse Evershed flow. The fibrils were identified in line-of-sight (LOS) velocity and line–core intensity maps. The chromospheric LOS velocity abruptly decreases from 3 to 15 km s−1 to zero at the inner footpoints of the fibrils that are located from the mid penumbra to about 1.4 spot radii. The spectra often show multiple absorption components, indicating spatially or vertically unresolved structures. Synthetic spectra with a 100% fill factor of a flow channel in the upper atmosphere yield strongly asymmetric profiles but no multiple separate components. The line–core intensity always peaks slightly closer to the umbra than the LOS velocity. Using the CAlcium Inversion using a Spectral ARchive code, we find that the fibrils make an angle of 30°–60° to the local vertical away from the umbra. The temperature near the downflow points is enhanced by 200 K at log and up to 2000 K at log τ ∼ (−6) compared to the quiet Sun, without any signature in the low photosphere. Our results are consistent with a critical, i.e., sonic, or supersonic siphon flow along super-penumbral flux tubes in which accelerating plasma abruptly attains subcritical velocity through a standing shock in or near the penumbra.

Internal Gravity Waves Generated by an Oscillating Source of Perturbations Moving with Subcritical Velocity

This paper considers the problem of constructing far-field asymptotics of internal gravity waves generated by an oscillating local source of perturbations moving in a stratified flow of finite depth. The velocity of the perturbation source does not exceed the maximum group velocity of an individual wave mode. The wave pattern consists of waves of two types: annular and wedge-shaped. Solutions expressed in terms of the Hankel function are obtained for the asymptotics of annular waves. The asymptotics of wedge-shaped waves are expressed in terms of the Airy function and its derivative.

Critical assessment of the nanofiltration for reusing brackish effluent from an anaerobic membrane bioreactor

In this study, a saline effluent from an anaerobic membrane bioreactor was treated by nanofiltration in order to allow its agricultural reuse. Short-term tests were conducted to investigate membrane fouling and selective rejection of ions and emerging organic contaminants (EOCs). The study has been conducted with a negatively charged commercial thin-film composite membrane (DK, GE Osmonics). The effect of operating pressure (5–20 bar) and cross-flow velocity (0.12–0.37 m/s) on membrane performance have been researched. Dimensional analysis of steady permeate flux indicated that the gel layer or the polarization layer can be completely removed at critical cross-flow velocity. At a sub-critical velocity, membrane autopsies by scanning electron microscopy (SEM) and energy dispersive X-Ray spectroscopy revealed a complex mixture of organic matter, phosphates and colloidal silica over the membranes surface. Since the rejection of monovalent cations (76–88%) was lower than that of multivalent cations (above 96%), the treated effluent was characterized by a very high levels of sodium adsorption ratio and ammonium. In addition, moderate rejection of low molecular weight EOCs (clofibric acid and caffeine) was observed. Therefore, the treated effluent did not achieve enough quality to be reused for agricultural irrigation. © 2017 American Institute of Chemical Engineers Environ Prog, 37: 383–390, 2018

Internal Gravitational Waves Excited by an Oscillating Source of Perturbations Moving with Subcritical Velocity

Internal Gravitational Waves Excited by an Oscillating Source of Perturbations Moving with Subcritical Velocity

The varying densification strain in a multi-layer aluminum corrugate structure: Direct impact testing and layer-wise numerical modelling

An aluminum (1050 H14) multi-layer corrugated structure composed of brazed 16 trapezoidal zig-zig fin layers was direct impact tested above the critical velocities for shock formation using a modified Split Hopkinson Pressure Bar. The experimentally measured stress-time histories of the cylindrical test samples in the direct impact tests were verified with the simulations implemented in the explicit finite element code of LS–DYNA. The quasi-static experimental and simulation deformation of the corrugated samples proceeded with the discrete, non-contiguous bands of crushed fin layers, while the dynamic crushing started from the proximal impact end and proceeded with a sequential and in-planar manner, showing shock type deformation characteristic. The experimental and numerical crushing stresses and the numerically determined densification strains of the fin layers increased with increasing impact velocity above the critical velocities. When the numerically determined densification strain at a specific velocity above the critical velocities was incorporated, the rigid-perfectly-plastic-locking idealized model resulted in peak stresses similar to the experimental and simulation mean crushing stresses. However, the model underestimated the experimental and simulation peak stresses below 200m s−1. It was proposed, while the micro inertial effects were responsible for the increase of the crushing stresses at and below subcritical velocities, the shock deformation became dominant above the critical velocities.

Three-dimensional problem of disturbing an ice cover by a dipole moving in fluid

The three-dimensional problem of disturbing an ice cover by a dipole which begins to move uniformly and rectilinearly along a horizontal in the fluid initially at rest is considered. It is shown that a steady-state ice perturbation is established in the co-moving coordinate system when the dipole moves during a long time. Analytic expressions for the deviation of the fluid-ice interface from the equilibrium position are obtained. Examples of the numerical investigation of ice-cover perturbations are given for subcritical dipole velocities.

Influence of the Longitudinal and Lateral Suspension Damping on the Vibration Behaviour in the Railway Vehicles

Abstract The paper focuses on the influence of the longitudinal and lateral suspension damping in correlation with the velocity upon the vibration behaviour of the railway vehicles while moving on a tangent track. The numerical simulations are developed based on a linear model of a 17-degree of freedom vehicle that allows the evaluation of the dynamic behaviour of the vehicle in a sub-critical velocity. Based on the response frequency functions of the vehicle in a harmonic and in a random behaviour, a series of basic properties of the stable behaviour of the forced lateral vibrations has been made evident, as well as the opportunities to lower the level of the carbody vibrations by changing the suspension damping.

INFLUENCE OF GROUPING OF THE BRIDGE PIERS ON SCOUR

Influence of grouping of the bridge piers on scour of the ground surface is investigated. Experimental research results of influence of bridge pier as three-row much pile grillage, which is placed behind of prismatic pier, on a form and depths local and global scours are presented. It is set that at the flow around single and group of bridge piers on a hard and erosion surface are generated the large-scale horseshoe vortical systems in junction region of surfaces of piers with a bottom, the intensive vortical tubes in shear layers on sides of the bluff bodies, wake vortices behind piers and jets between the close located piers. In plane axial symmetry of pier, the scour profile consists of two slopes of deposition of sand. An overhead slope has a less angle of slope and appears operating on the particles of sand of the horseshoe vortex, arising up at separation of boundary layer from the overhead frontal edge of opening of scour. The bottom slope of deposition of sand is conditioned by the action of the horseshoe vortex, which is engendered by a flow, directed to the erosion bottom along the forehand of pier. Grouping of bridge piers decreases on (10…15) % the scour depth near-by prismatic pier for subcritical velocities. For critical velocities the scour depth does not depend on grouping of piers, and for supercritical velocities the scour depth before prismatic pier increases on (15…20) %.

Flow past a self-oscillating airfoil with two degrees of freedom: measurements and simulations

The paper focuses on investigation of the unsteady subsonic airflow past an elastically supported airfoil for subcritical flow velocities and during the onset of the flutter instability. A physical model of the NACA0015 airfoil has been designed and manufactured, allowing motion with two degrees of freedom: pitching (rotation about the elastic axis) and plunging (vertical motion). The structural mass and stiffness matrix can be tuned to certain extent, so that the natural frequencies of the two modes approach as needed. The model was placed in the measuring section of the wind tunnel in the aerodynamic laboratory of the Institute of Thermomechanics in Nový Knin, and subjected to low Mach number airflow up to the flow velocities when self-oscillation reach amplitudes dangerous for the structural integrity of the model. The motion of the airfoil was registered by a high-speed camera, with synchronous measurement of the mechanic vibration and discrete pressure sensors on the surface of the airfoil. The results of the measurements are presented together with numerical simulation results, based on a finite volume CFD model of airflow past a vibrating airfoil.