Dimensionless Acceleration Research Articles

Numerical study on fluid flow pattern regulation and heat transfer characteristics in oval-pit spiral tube

Spiral tube heat exchangers are widely applied in daily industrial production. In order to improve the comprehensive heat transfer performance of the spiral heat exchanger to meet industrial production and policy demands, improvements to spiral heat exchangers are necessary. In this study, a new type of oval-pit spiral tube is proposed. Ansys Fluent software was used to develop the numerical models and simulate the heat exchange conditions in smooth spiral tube and oval-pit spiral tube. The development and evolution of secondary flow and heat transfer characteristics in spiral tube were analyzed by theoretical analysis, and the heat transfer mechanism was explored. The dimensionless temperature parameter Θ and dimensionless acceleration number Ω were defined to explore the influence of secondary flow on heat transfer characteristics, which provided a new approach for improving spiral heat exchangers. The results show that the secondary flow in the smooth spiral tube has a symmetric double-vortex structure, and it has an asymmetric double-vortex structure in the oval-pit spiral tube. Compared with smooth spiral tube, the local dimensionless temperature parameter Θ in oval-pit spiral tube fluctuates more sharply, the heat transfer non-uniformity is greater, and the local Nu number is higher. Additionally, the fluid in the oval-pit tube is fully developed at the smaller axial angle, and the flow and heat transfer stability are better. In the working range of inlet Reynolds number of 1000∼5000, compared with smooth spiral tube, the heat transfer coefficient of oval-pit spiral tube increases by 11.58∼44.73 %, the pressure drop increases by 33.56∼119.27 %, and the comprehensive heat transfer performance increases by 1.23∼14.65 %.

Two independent mechanisms with distinct laws for the generation of drag force on accelerating plates

Acceleration of objects in fluids widely exists in biological propulsions and contains rich unsteady fluid mechanisms. In this paper, the instantaneous drag force on accelerating normal flat plates (circular, elliptical, square, and rectangular plates) in a wide range of dimensionless acceleration (a*=16∼2) is measured, and the underlying mechanism for force generation is investigated. At first, we find that the drag force coefficient generally scales with the square root of a* when a*<1.0, coinciding with the scaling law given by Reijtenbagh et al. (PRL. 2023,130,174001). However, the drag force coefficient more linearly scales with a* rather than a* when a*>1.0, thereby indicating acceleration plays two distinct roles on the force generation depending on a*. Moreover, two scaling laws are built to quantitatively describe the two distinct roles of a* on the drag force generation. Based on fluid impulse, the drag force is largely contributed by the added mass of the accelerating plates (added mass force) and vorticity generation fed by the shear layer on the edge of the plates (vortex creation force). When a*<1.0, the vortex creation force scales with a* and almost contributes to the total drag force. When a*>1.0, the added mass force scaling with a* contributes to most of the drag force. Furthermore, the two force generation mechanisms associated with acceleration (a*) are independent, and a criterion based on the energy ratio is proposed to identify the transition of the two force generation mechanisms. The present results uncover the role of acceleration in force generation and explain the inconsistencies of using one quasi-steady model in describing the force on accelerating plates.

An Integrated C4-Spline Interpolation and Time-Free Global Optimization Methodology Applied to High-Speed Cam Motion Design

The optimal tuning of high-order motion parameters has emerged as a promising strategy for actively controlling the kinematics/dynamics of high-speed cam mechanisms. However, accomplishing this task remains challenging with current low-order interpolation or tuning methods. This study proposes an integrated high-order interpolation and tuning methodology for the optimal construction of high-speed motion curves. Initially, an explicit C4-spline interpolant (C4SI) is developed. This interpolant utilizes four-order continuous (C4) splines to synthesize a high-fidelity motion curve that satisfies the predefined motion constraints up to the fourth order, including dimensionless displacement, velocity, acceleration, jerk, and quirk. Concerning the reduction of motion peaks, a unique C4SI-based global kinematics optimization strategy is designed, using the definite integral of the motion curve (free of the time variable) as the objective function. This facile time-free optimization strategy could yield a simultaneous reduction in multiple motion peaks (up to five), which is currently inaccessible with conventional motion tuning strategies. Concerning the improvement of dynamic characteristics, the C4SI-based time-free global dynamics optimization of variable motion parameters is further performed. The results indicate that the optimized fourth-order motion curve offers minimal high-speed transmission error and residual vibration over the whole rise-dwell-return-dwell cycle, which outperforms the standard motion curves and other low-order counterparts.

Study on the effectiveness of impact factor in underwater explosion model test

The dimensionless quantity is the invariant under the unit conversion, and the only choice to characterize the laws of physics. Aiming at the similarity law of underwater explosion model test, the deficiency of traditional impact factor and the similarity condition of single value of model test are analyzed by using dimensional analysis method and combining with domestic and foreign research. In view of the shortcomings of traditional impact factors, a new impact factor is derived from the perspective of single-value similarity based on the impact dynamic response characteristics of underwater explosion structures. Taking the midship cabin structure of a certain frigate as the prototype, the scale model tests are designed based on the traditional and new impact factors respectively. The effectiveness of the impact factors is evaluated from the aspects of structural damage characteristics, dimensionless deformation deflection, dimensionless velocity and dimensionless acceleration at the center of the structure. To account for the impact of structural characteristics, scale ratio, and proportional distance on the impact factor's effectiveness, various grillage, cabin, and hull girder model tests are conducted using ships of different tonnages as prototypes. The results of the model test, guided by the new impact factor, align well with the prototype test data. In contrast to the traditional impact factor, the model test exhibits greater precision for predicting structural responses, with a broad spectrum of potential applications.

Heat transfer of single-phase spray cooling on heated vibrating surfaces

Effective vibration control has potential to enhance convective heat transfer. However, the precise heat transfer mechanism of single-phase spray cooling under vibration remains elusive. This study aims to elucidate this mechanism by establishing a closed-loop system for vibrating surface spray cooling. Various vibration parameters, including vibration Reynolds number (Rev), dimensionless acceleration number (Ac), amplitude, and frequency, were investigated experimentally to determine their impact on heat transfer. The research findings demonstrate that the heat flux, heat transfer coefficient, cooling efficiency, and vibration enhancement factor all decrease with an increase in Rev and amplitude. At a heating power of 200 W and Rev of 4947, the spray cooling performance on the vibrating surface is inhibited by 22%. However, as the heating power increases, the inhibitory effects of Rev and amplitude on the spray cooling heat transfer performance are weakened. Conversely, the amplitude and frequency enhance the heat flux, heat transfer coefficient, cooling efficiency, and vibration enhancement factor. At a heating power of 200 W and an Ac of 3.6, the spray cooling heat transfer performance on the vibrating surface is enhanced by 17%. Finally, a dimensionless correlation equation and a Nusselt number (Nu) prediction model for single-phase spray cooling under vibrating conditions are derived and fitted with an error of ±13.2%.

Experimental study on the impulsively started motion of a close-to-neutral buoyancy freely decelerating sphere

An experimental study is presented that addresses the problem of a freely decelerating sphere in a still water tank. The diameter of the sphere was 0.04 m. Three different solid-to-fluid density ratios were considered: 0.78, 0.88, and 0.94. The submerged sphere was impulsively started upon being rammed by an actuator-mass system. Six initial velocities were considered: 0.91, 2.03, 2.54, 2.94, 3.29, and 3.78 m/s. The Reynolds number of the initial velocities based on the sphere diameter was 3.6 × 104, 8.1 × 104, 1.01 × 105, 1.17 × 105, 1.31 × 105, and 1.51 × 105 (subcritical). It was observed that both sphere dynamics and associated flow topology (identified via an optical system and a particle image velocimetry system, respectively) differed significantly from the case of an accelerating sphere. In the present case, a large vortex ring structure (both torus diameters of the order of the sphere's diameter) formed and attached to the sphere surface. This vortex ring followed the sphere motion all the way down the falling trajectory. From the data reduction standpoint, it was found that a suitably defined dimensionless acceleration parameter allowed for collapsing the kinematics variables of the sphere trajectory, namely, position, velocity, and acceleration, into a single ordinary differential equation.

Experimental investigation on vortex-induced force of a flexible pipe under oscillatory flow

In this paper, vortex-induced force (VIF) characteristics of a flexible pipe under oscillatory flow are experimentally investigated with different KC numbers ranging from 10 to 178, and reduced velocities from 4 to 7.9. The strain information caused by vortex-induced vibration (VIV) at different cross-sections on the flexible cylinder is measured in the model test. Combined with the modal superposition method and inverse analysis method for hydrodynamic force, the hydrodynamic forces on the flexible cylinder are inverted, including the excitation force in phase with velocity and added mass force in phase with acceleration. Then, through a least square method with forgetting factors, the excitation coefficients and added mass coefficients at each time step are identified. The results show that the VIV excitation coefficient of a flexible pipe under oscillatory flow has a significant “acceleration and deceleration” effect, that is, the excitation coefficients are mostly positive at the acceleration section of the oscillatory flow and negative at the deceleration section. This “acceleration and deceleration” effect also explains the response amplitude modulation feature of VIV under oscillatory flow. And this effect can be represented by the dimensionless acceleration parameter γ of the flow field, and the range of γ corresponding to the positive excitation coefficient is affected by the KC number and the maximum reduced velocity. In addition, the added mass coefficients present different time-varying features under oscillatory flow with different maximum reduced velocity. When the maximum reduced velocity is larger than 6.5, the time-varying trend of the added mass coefficient is opposite to that of the flow velocity. While when the maximum reduced velocity is smaller than 6.5, the added mass coefficient is maintained around 2.0 in VIV excitation region; and it is around 1.0 in the non-excited region which is close to the added mass coefficient of a cylinder in still water.

Incremental dynamic analysis of rigid blocks subjected to ground and floor motions and shake table protocol inputs

This paper reports the results of an extensive campaign of incremental dynamic analyses (IDA) of rigid rocking blocks under various loading histories, including real ground/floor motions and shake table testing protocol loading histories. Several block geometries are investigated considering various size and slenderness combinations representative of building contents, monumental elements, art objects, components of critical facilities, and other unanchored elements. The spectral response of the block to different loading histories is firstly assessed by highlighting the characteristics of the different seismic input sets. Dimensionless acceleration- and velocity-based parameters are considered as intensity measures, and the block rotation normalized considering the critical angle (i.e., dimensionless rocking amplitude) is assumed as an engineering demand parameter. The IDA curves are evaluated, and the dynamic response of the blocks is characterized in terms of: (a) type of loading history, (b) intensity measure, and (c) block geometry. New information and technical insights are presented regarding the assessment of seismic response of structural and nonstructural rocking systems. The dynamic response of the blocks subjected to the investigated protocols is found to be not always compatible with the capacities related to real ground/floor motions, often producing non-conservative estimations. The discrepancy identified between the block responses associated with the protocol inputs and real motions is found to be significantly affected by both block geometry and intensity measure.

DEM modelling of the influence of initial stress state on the discharge rate of spherical particles from a model silo

Formulation of a proper physical law describing the dynamics of discharge of granular solids has been undertaken by researchers for decades. A frequently expressed opinion is the existence of the free-fall arch region and independence of the discharge rate on pressure. The objective of this study was to explore the impact of dynamic particle–particle contact interactions in the vicinity of the orifice on the discharge flow rate from a model silo by means of DEM simulations with special attention paid to the impact of the bedding height and bottom pressure. The DEM simulations were performed with an assembly of spherical particles poured on a flat bottom of the cylindrical model silo with a height-to-diameter ratio of 1.14. The bottom pressure was changed by changing the height of the bedding deposit and depositing an additional layer of very dense particles on the top of the bedding of primary particles. The results indicate that the discharge rate was affected by both the orifice diameter and mean bottom pressure during storage. The correction coefficient derived from the integral of the dimensionless acceleration of particles along the dimensionless movement path allowed obtaining very good approximation of the discharge rate using the well known Beverloo equation in the entire range of change of the orifice size and bottom pressure.

Synthesis of trigonometric motion programs with lower motion characteristics

Abstract. Motion characteristics are dimensionless peak values of velocity, acceleration, jerk, and acceleration multiplied by velocity of a motion program. In general, these peak values of synthesized motion programs should be as low as possible. Some trigonometric motion programs are widely used because they have a good compromise of all motion characteristics. A property in common for trigonometric motion programs is that their acceleration functions can be expressed as a qualitative shape of a sinusoidal function. The interval of the sinusoidal function is divided into several zones having different linear slopes. The acceleration function can be easily shaped by specifying presented phase angle function to synthesize desired motion programs. To improve the kinematic quantities of trigonometric motion programs, this paper addresses an alternative phase angle function to obtain synthesized motion programs with simultaneous reduction in all the motion characteristics. The synthesis process and results are illustrated by examples.

Numerical evaluation of virtual mass force coefficient of single solid particles in acceleration

• Single solid sphere in acceleration is numerically simulated based on the vorticity-stream function formulation. • Particle acceleration changes significantly the surrounding flow field and the stress tensor on the particle surface. • Virtual mass force coefficient is evaluated from the numerical simulation. • A correlation of total drag coefficient with the Reynolds number and acceleration number is proposed for tentative use in particulate flow simulation. Virtual mass force is an indispensable component in the momentum balance involved with dispersed particles in a multiphase system. In this work the accelerating motion of a single solid particle is mathematically formulated and solved using the vorticity-stream function formulation in an orthogonal curvilinear coordinate system. The total drag coefficient was evaluated from the numerical simulation in a range of the Reynolds number ( Re ) from 10 to 200 and the dimensionless acceleration ( A ) between −2.0 to 2.0. The simulation demonstrates that the total drag is heavily correlated with A , and large deceleration even drops the drag force to a negative value. It is found that the value of virtual mass force coefficient ( C V ) of a spherical particle is a variable in a wide range and difficult to be correlated with A and Re. However, the total drag coefficient ( C DV ) is successfully correlated as a function of Re and A , and it increases as A is increased. The proposed correlation of total drag coefficient may be used for simulation of solid–liquid flow with better accuracy.

DETERMINATION OF WAVE SLAMMING LOADS ON HIGH-SPEED CATAMARANS BY HYDROELASTIC SEGMENTED MODEL EXPERIMENTS

A 2.5m hydroelastic segmented catamaran model has been developed based on the 112m INCAT wave-piercer catamaran to simulate the vibration response during the measurement of dynamic slam loads in head seas. Towing tank tests were performed in regular seas to measure the dynamic slam loads acting on the centre bow and vertical bending moments acting in the demihulls of the catamaran model as a function of wave frequency and wave height to establish the operational loads acting on the full-scale 112m INCAT catamaran vessel. Peak slam forces measured on the bow of the model are found to approach the weight of the model, this being similar to the findings of full-scale vessel trials. A review of the motions of the hydroelastic segmented catamaran model found that the heave and pitch motions give a good indication of slamming severity in terms of the dimensionless heave and pitch accelerations. The dynamic wave slam forces are closely related to the relative motion between the bow and the incident wave profile.

Precursor nuclei on the bottom of a vibrating container: The onset of granular self-assembly crystallization

Kinetic energy is transferred through collisions to the millimeter particles that are in contact with the base of a vertically vibrated 3D container. In the early stages of a vibrational annealing process where the dimensionless acceleration is kept constant, the spontaneous appearance and disappearance of unstable clusters of ordered particles near the bottom surface of the container is observed. In later stages of this vibrational annealing process, the precursor nuclei stabilize becoming stable crystal seeds which resembles a thermal phase transition. Molecular Dynamics simulations based on these experimental observations are used to study the unstable–stable transition. The Ornstein–Zernike equation using the Percus–Yevick closure is applied to the stages before and after the observation of the stable crystal seeds in order to extract the effective potentials associated with the phase transition. Both the radial distribution function and the effective potentials show a clear correspondence of the spatial correlation as the crystallization phase begins to appear.

Numerical investigation of flow around a square cylinder in accelerated flow

To investigate the flow field evolution and resultant aerodynamic characteristics of a square cylinder during flow acceleration, large-eddy simulations were undertaken to simulate flow with a dimensionless acceleration rate ap of 0.0048. The adopted ap resembles that is likely to be experienced during a severe downburst wind storm. The tested incidence angle α ranges from 0° to 45° and the time-dependent Reynolds number Re [Re = U(t)D/v, where U(t) is the time-dependent inflow velocity and D and v are the cylinder length and the kinematic viscosity, respectively] varies from 0 to 5 × 104 throughout the simulation. Results revealed that the flow around a square cylinder in accelerated flow evolves through three distinct temporal flow phases: namely, Phase I (Ia and Ib) where no vortex shedding (the instantaneous lift force through this period is zero) is observed, Phase II, where periodic vortex shedding and associated lift force oscillations are initiated and enhanced, and Phase III where stable vortex shedding occurs. Phase I can be further broken down into Phase Ia, which is characterized by laminar shear layer separation and the existence of steady recirculation vortices in the near wake region, and Phase Ib (only present at α = 0° and 45°) which is distinguished by the presence of quasi-steady recirculation vortices behind the cylinder. Aside from the variation of flow patterns, the transient lift and drag coefficients and the wind pressure distributions, as well as the spatial evolution of three-dimensional flow structures and pressure distributions, are also elucidated in detail.

Light-powered self-excited motion of a liquid crystal elastomer rotator

Self-excited motions have the advantages of directly harvesting energy from the environment, autonomy, and portability of the equipment, and consequently, the development of a wealth of new self-excited motion modes can greatly expand the application of active machines. In this paper, a rotator capable of self-excited movement is proposed, which consists of a liquid crystal elastomer (LCE) bar and a regular bar with an axle. Based on the dynamic LCE model, through theoretical modeling and numerical calculation, it is found that the LCE rotator has three motion modes, namely static mode, oscillation mode and rotation mode. The detailed dynamical process reveals the mechanism of self-excited oscillation and rotation. In this paper, the effects of parameters such as light intensity, damping coefficient, dimensionless gravitational acceleration, length ratio, illumination region and initial angular velocity on the self-excited oscillation and rotation are further studied systematically, and the corresponding limit cycles are given by various cases. The results show that the light intensity, damping coefficient and length ratio have important influence on the motion mode, while the initial angular velocity does not affect the motion mode. The influence of various parameters including light intensity and illumination region on the amplitude and frequency of self-excited oscillation is also studied. It is found that the amplitude mainly depends on light intensity and damping. This study can deepen people's understanding of non-equilibrium self-excited motions and provide promising applications in the fields of energy harvest, power generation, monitoring, soft robotics, medical devices and micro–nano-devices.

Particle acceleration and pressure gradient in a solitary wave traveling over a horizontal bed

This study presents experimental data on the hydrodynamic features of a nonlinear solitary wave of height H0 = 2.9 cm propagating over a horizontal bed in otherwise still water depth h0 = 8.0 cm. High-speed particle image velocimetry is used to quantify the local and convective particle accelerations and pressure gradients under the solitary wave. It is found that the magnitudes of the horizontal and vertical particle local accelerations are invariably larger than their convective counterparts, highlighting the important contribution of local acceleration to the pressure gradient in a solitary wave. The dimensionless pressure gradient in the horizontal direction is favorable, zero, and adverse for time before, at, and after the wave crest passes the section of interest. The dimensionless adverse pressure gradient exhibits a maximum for the dimensionless time T[=t(g/h0)1/2, where g is the gravitational acceleration and t is the time with respect to the crest passing the section] = 1.39, at which the dimensionless local acceleration has a negative maximum. Subsequently, flow reversal takes place above the bed surface. The relationship is elucidated between flow reversal at the bed surface and the evolution of the adverse pressure gradient in the near-bed zone, where uniform horizontal/free stream velocity exists.

Analysis of thrust-induced sail plane coning and attitude motion of electric sail

This paper investigates the dynamic characteristics of thrust-induced sail plane coning and attitude motion of an electric solar wind sail (E-sail) by considering high-order modes of flexible elastic tethers. The tethers of the E-sail are assumed elastic and discretized into inter-connected 2-noded tensile elements using the nodal position finite element method, while the central spacecraft and the remote units are simplified as lumped masses. The E-sail is assumed in the heliocentric ecliptic orbital plane at a distance of 1 au from the Sun. The influences of the propulsive force models and the initial E-sail orientation on the dynamic characteristics of the sail plane coning and attitude motion of E-sail are analyzed. The current work derives an analytic expression of the coning motion frequency under the assumption of small coning angle. Through parametric analyses, the current work shows that the magnitude of the propulsive force significantly influences the increment magnitude of the E-sail's orbital radius while has little effect on the angles of sail and thrust angles and the E-sail spin rate. The parametric analyses also show that the initial E-sail orientation significantly influences the thrust vector and the variation of sail angle. Finally, the relationships of the sail and thrust angles, as well as the dimensionless acceleration of the E-sail, are given in polynomial expressions by curve-fitting of simulation results of E-sails with the consideration of coning motion. The relationships are compared with the previous results of E-sails without including coning motion. It shows the coning motion has negligible effect on the macro dynamic behaviors of E-sail.

Dynamics of Two-liquid System at Rotation and Vibration with Equal Frequencies

The impact of vibrations on the dynamics of a system of two immiscible liquids filling a rotating container is studied experimentally. A horizontal cylindrical container is rotating at a rate sufficient for the liquids, whose densities are not equal, to become steadily distributed in the form of core and annulus. The vibrational motion of the container has a frequency virtually equal to that of rotation. It is demonstrated that at the coincidence of the frequencies the container’s oscillations lead to the transformation of the centrifugal field. As a result, the column of light liquid is shifted steadily in the rotating frame of reference. With the increase in the amplitude of vibrational forcing, in a threshold manner the liquid–liquid interface loses its axial symmetry, and a centrifugal wave emerges on it. The threshold of wave onset is determined by the dimensionless vibrational acceleration. The obtained results demonstrate a possibility to apply vibrations for the positioning of a liquid core in a rotating container and for the control of its dynamics.

Velocity scaling and breakup criteria for jets formed due to acceleration and deceleration process

A study of velocity scaling and breakup criteria for jets formed as a result of an acceleration and deceleration process is presented. The process is characterized by five dimensionless numbers: Weber number, Ohnesorge number, Bond number, and dimensionless acceleration and deceleration times.

Heat flux correlation models for spray evaporative cooling of vibrating surfaces in the nucleate boiling region

New empirical correlation models are constructed to characterise heat transfer associated with spray evaporative cooling of vibrating surfaces - a process involving complex two-phase physics well beyond current numerical simulation capabilities. The proposed correlation models, which account for dynamic, rather than just static surface conditions as in existing models, are constructed using dimensional analysis involving the Generalized Buckingham Π-Theorem. Experimentally-measured spray evaporative cooling data is used to fit the model using the Vibrational Reynolds number and a dimensionless acceleration number which better correlate the influence of surface frequency and amplitude in the nucleate boiling regime. Different coolant flow-rates through a full-cone spray nozzle are used to cool a flat circular test-piece acting as a horizontal surface. The test-piece surface is excited by a shaker through a range of low and high vibration frequencies and amplitudes. The results show that surface dynamic effects certainly influence nucleate boiling, but they also show that surface vibration does not have the same effect for all excess temperatures - dynamic effects can either increase or decrease heat transfer depending on the heat transfer mechanism. These new models are important for thermal management in several areas, particularly involving batteries, power electronics, and electrical machines in automotive and aerospace applications.