Tip Velocity Research Articles

Rain erosion resistance of injection moulded and compression moulded polybutylene terephthalate PBT

Offshore wind turbine rotor diameters still increase. Blade tip velocities are up to 110 m/s, giving rise to more severe raindrop impact conditions and related erosion of the wind turbine blades. In the current work droplet impingement erosion tests were performed for injection moulded and compression moulded polybutylene terephthalate PBT. The measured incubation periods were compared to an extended and improved fatigue based erosion model.The developed erosion test set-up was based on a high water pressure nozzle system spraying water drops at a stationary PBT surface. Model results with thermoplastic materials simulating heavy rain conditions with a droplet size of 1.8 mm and an impact velocity of 120 m/s are shown. Model results with PBT materials simulating the used test conditions are shown and compared with the measured incubation periods. Although a reasonable similarity between test results and model calculations for the injection moulded PBT was found, the absolute value of the incubation period predicted by the model for compression moulded PBT differed substantially. This probably resulted from the lower confidence level of the S-N curve for the compression moulded PBT. The droplet impingement measurements and model predictions both showed a substantially higher incubation period for injection moulded PBT compared to compression moulded PBT.

Experimental study of flow characteristics around floodplain single groyne

This study investigated the flow around river’s floodplain single groynes. Two different compound channels with one and two symmetrical floodplains having widths of 1- and 2-times of the main channel width, respectively, were used. Both impermeable and permeable groynes with three different relative lengths (relative to the floodplain width) and having three different permeability values of 40, 60, and 80% were investigated. The 3D flow velocities were measured in the horizontal plane at 0.25 and 0.5 of floodplain water depth (hf), and in the vertical plane at the main channel’s centerline. Therefore, the flow velocities in the longitudinal, lateral, and vertical directions, and the flow water surfaces were measured and analyzed. The results showed that, as the groyne permeability increased up to 60%, a reduction of up to 30% to the maximum velocity and 22% to the tip velocity were observed. The permeable groyne length had limited influence on the flow structure. Both the groyne permeability and the length ratio had significant effects on the floodplain water depth. The scouring and the deposition activities resulting from impermeable groynes can be avoided, should the groyne length be kept below half of the floodplain width.

Flame propagation across a flexible obstacle in a square cross-section channel

Flame propagation across a single flexible fence-type obstacle was studied experimentally in a square cross-section channel, and compared to results obtained using similar blockage ratio (BR) rigid obstacles. The experiments were carried out with different BRs in premixed stoichiometric hydrogen-air mixtures, at initial conditions of 101 kPa and 298 K. High-speed Schlieren photography was employed to gain insight into the flame front structure and the flame tip velocity. Pressure transducers were used to measure the pressure at different axial positions near the obstacle. Flame propagation was found to be strongly influenced by the flow contraction of the unburned gas upstream of the obstacle, and the separated flow downstream of the obstacle. The most significant effect of the flexible obstacle, compared to the rigid obstacle, was observed for BRs above 0.71. The flame front evolution was dominated by the shear layer coming off the obstacle leading-edge and the vortex downstream from the obstacle. For the rigid obstacle BRs tested, the shear layer coming off the obstacle leading-edge reattached to the top of the obstacle, resulting in a vortex (i.e., recirculation-zone) downstream of the obstacle. For the high BR flexible obstacles (BR > 0.43), significant obstacle deformation (downstream tilt and vertical compression), and an associated decrease in BR, resulted in slightly lower flame tip velocities past the obstacle. The downstream obstacle tilt resulted in a different type of separated flow, compared to that observed in the rigid obstacle, where the shear layer didn't reattach to the top of the obstacle. The resulting vortex and strong shear layer confined the flame tip to the top part of the channel, delaying the consumption of the unburned gas immediately downstream of the obstacle. The deformation of the flexible obstacle reduced the peak pressure and the rate of pressure rise compared to that obtained with the rigid obstacles.

Picosecond x-ray radiography of microjets expanding from laser shock-loaded grooves

Material ejection upon the breakout of a shock wave at a rough surface is a key safety issue for various applications, including pyrotechnics and inertial confinement fusion. For a few years, we have used laser driven compression to investigate microjetting from calibrated grooves in the free surface of shock-loaded specimens. Fast transverse optical shadowgraphy, time-resolved measurements of planar surface and jet tip velocities, and post-shock analysis of some recovered material have provided data over ranges of small spatial and temporal scales, short loading pulses (ns-order), and extremely high strain rates. In the new experiment reported here, picosecond laser irradiation of a thin copper wire generates an ultrashort x-ray burst which is used to radiograph the microjets expanding from plane wedged-shape grooves in tin and copper samples shock-loaded by a longer, nanosecond laser pulse. Such ultrafast radiography provides estimates of the density gradients along the jets and of the total ejected mass at different times after shock breakout. Furthermore, it reveals regions of low density inside the samples deep beneath the grooves, associated with subsurface damage due to tension induced by the interaction of rarefaction waves. Thus, combining this x-ray probe with our former experimental techniques provides a more complete insight into the physics of microjetting at very high loading rates and the ballistic properties of the resulting ejecta.

Effect of thermal anisotropy on binary alloy dendrite growth

A numerical model to study the effect of thermal anisotropy on binary alloy dendrite growth is presented. The model is based on the volume averaged enthalpy method with explicit surface tension anisotropy for crystal orientation. Thermal anisotropy is incorporated using anisotropic thermal conductivity in the energy equation. This is done by splitting the anisotropic conductivity into two parts, equivalent isotropic conductivity and anisotropic departure source term, enabling the use of a conventional isotropic solver to model anisotropic heat transfer. The proposed model is applied to study the effect of thermal anisotropy ratio on tip velocity, aspect ratio and equivalent radius of an equiaxed grain growing in an undercooled binary alloy melt. It is found that the thermal energy stored in the grain during solidification plays an important role in interface evolution, and thus anisotropic conductivity in the solid affects the grain morphology. There is a consistent increase in the aspect ratio of grains with increase in thermal anisotropy ratio, although the grain volume remains almost invariant. Due to unequal growth rates of the perpendicular arms, severe distortion of the solid crystal is seen at higher thermal anisotropy ratios. The model is further extended to study the growth of multiple dendrites in order to simulate microstructure evolution with thermal anisotropy. It is observed that thermal anisotropy significantly affects the grain morphology at low grain density but has a smaller influence at high grain density as compared to other governing factors such as solute transport.

Mode I fracture in PMMA specimens with notches – Experimental and numerical studies

This paper shows the results of experimental and numerical investigation of fracture in PMMA (Polymethyl-methacrylate) plate specimens under mode I. Samples had two thicknesses (9.7 and 18 mm) and they were weakened by two types of edge-notches: rounded V-notch with radius 0.5 mm and U-notch with radius 10 mm. During tests, critical load value, fracture initiation point and fracture initiation angle were obtained. Additionally, the fracture process was recorded by a high-speed PHANTOM camera. Crack length growth and changes in crack tip velocity over time were analyzed. Stress and strain fields under the critical load value were calculated using Finite Element Method (FEM). Three-dimensional isoparametric elements were used and non-linearity of material and geometry was also included. A stress–strain criterion for notched specimens under tension was proposed.

Dynamic spray development of 2-methylfuran compared to ethanol and isooctane under ultra-high injection pressure

Understanding spray behaviors is key for the successful employment of high injection pressure systems and biofuels such as 2-methylfuran (MF) and ethanol (ETH) in modern direct-injection gasoline engines. In this present work, the MF spray characteristics in the near-field (up to 1.6 mm) and far-field (up to 48 mm) were experimentally investigated under ultra-high injection pressure of 30, 40 and 50 MPa compared to those of ETH and isooctane (ISO). The effects of injection pressure and fuel properties on the spray morphology, tip penetration and cone angle development have been analyzed. The results showed that MF had a unique spray tip structure with a bubble attached to a mushroom tip at 30 and 40 MPa. The formation of this mushroom tip and bubble was closely related and strongly influenced by the Weber number. Among the three fuels tested, MF presented the lowest spray tip velocity at both near-field and far-field due to its large density. Compared to ETH, MF and ISO always had wider macro cone angles due to their lower viscosity.

Bead milling disruption kinetics of microalgae: Process modeling, optimization and application to biomolecules recovery from Chlorella sorokiniana

Industrial development of microalgae biomass valorization relies on process optimization and controlled scale-up. Both need robust modeling: (i) for biomass production and (ii) for integrated processes in the downstream processing (DSP). Cell disruption and primary fractionation are key steps in DSP. In this study, a kinetic model, including microalgal cell size distribution, was developed for Chlorella sorokiniana disruption in continuous bead milling. Glass beads of 0.4 mm size at impeller tip velocity of 14 m.s−1 were used as optimal conditions for efficient cell disruption. These conditions allowed faster disruption of big cells than small ones. A modified expression of the Stress Number, including cell size effect, was then proposed and validated.Separation of starch, proteins and chlorophyll by mild centrifugation was studied as function of the disruption parameters. Low energy consumption conditions led to extreme comminution. An intermediate zone drew attention for allowing moderate energy consumption and efficient metabolites separation by centrifugation.

Comparison of macroscopic spray characteristics between biodiesel-pentanol blends and diesel

Spray characteristics of biodiesel-pentanol blends (with 0 v/v%, 10 v/v%, 20 v/v%, 30 v/v% and 40 v/v% pentanol) were investigated and compared with those of diesel in this work. Experiments under a variety of working conditions were carried out on a common-rail system and a constant volume chamber. High-speed Schlieren photography was used to capture the spray images. The analysis revealed that biodiesel and diesel showed the longest and the shortest spray tip penetration, the smallest and the largest spray cone angle, the smallest and the largest R (ratio between the liquid core area and the spray area), respectively. As the percentage of pentanol increased, the spray tip penetration of biodiesel-pentanol blends decreased, while the spray cone angle and R increased. BDP40 (60% biodiesel and 40% pentanol) showed similar spray characteristics as that of diesel. The comparison of tip velocities also showed that pentanol would reduce the initial axial momentum of injected fuels. Biodiesel showed the largest initial axial momentum while diesel owned the smallest one. Additionally, spray structures of blended fuels were more likely to fluctuate compared to biodiesel and diesel. The empirical equations of H-A model were used to verify the experimental results and showed great agreement between experimental results and predicts.

Shape transformation of a wake following the process zone at the tip of a propagating crack

A process zone containing a new phase often forms at the tip of a crack in a quasi-brittle solid. We study such a zone engendered by the propagating crack. We show that depending on the crack speed, V, this zone has two distinct configurations. If the crack tip velocity is small, the zone takes a concave shape. As soon as V exceeds a critical value, , the zone becomes convex. A metastable remnant, the wake, forms in its rear part. It is stretched backward over a great distance and exhibits a triangle configuration with the vertex angle decreasing with speed. The morphological zone transition and the wake shape is explained by competition of the velocity of a free, plane phase front and the crack tip speed.

Manipulation of individual superconducting vortices and stick-slip motion in periodic pinning arrays

We numerically examine the manipulation of vortices interacting with a moving trap representing a magnetic force tip translating across a superconducting sample containing a periodic array of pinning sites. As a function of the tip velocity and coupling strength, we find five distinct dynamic phases, including a decoupled regime where the vortices are dragged a short distance within a pinning site, an intermediate coupling regime where vortices in neighboring pinning sites exchange places, an intermediate trapping regime where individual vortices are dragged longer distances and exchange modes of vortices occur in the surrounding pins, an intermittent multiple trapping regime where the trap switches between capturing one or two vortices, and a strong couping regime in which the trap permanently captures and drags two vortices. In some regimes we observe the counterintuitive behavior that slow moving traps couple less strongly to vortices than faster moving traps; however, the fastest moving traps are generally decoupled. The different phases can be characterized by the distances the vortices are displaced and the force fluctuations exerted on the trap. We find different types of stick-slip motion depending on whether vortices are moving into and out of pinning sites, undergoing exchange, or performing correlated motion induced by vortices outside of the trap. Our results are general to the manipulation of other types of particle-based systems interacting with periodic trap arrays, such as colloidal particles or certain types of frictional systems.

On the phase field modeling of crack growth and analytical treatment on the parameters

A thermodynamically consistent phase field model for crack propagation is analyzed. The thermodynamic driving force for the crack propagation is derived based on the laws of thermodynamics. The Helmholtz free energy satisfies the thermodynamic equilibrium and instability conditions for the crack propagation. Analytical solutions for the Ginzburg–Landau equation including the surface profile and the estimation of the kinetic coefficient are found. It is shown how kinetic coefficient affects the local stress field. The local critical stress for the crack propagation is calibrated with the theoretical strength which gives the value of the crack surface width. The finite element method is utilized to solve the complete system of crack phase field and mechanics equations. The analytical expressions for the crack surface profile and the crack tip velocity are verified with the numerical solutions. It is shown that under mode I cracking and proper calibration of parameters, phase field models always agree with Griffith’s theory.

Study on the response of dendritic growth to periodic increase–decrease pressure in solidification via in situ observation using succinonitrile

A novel experimental apparatus for in situ observation of dendritic growth in directional solidification under dynamic pressure and thermal conditions was built, based on the principles of direct squeeze-casting, and the response of dendritic growth to an increase–hold–decrease pressure and a periodic increase–decrease pressure was investigated using succinonitrile. The results showed that, when continuous increase–hold–decrease pressure was applied, the dendrites underwent a growing and re-melting process where the dendritic re-melting phenomenon with fish-bone-like dendrites in the pressure decline stage was observed for the first time. When periodic increase–decrease pressure was applied, dendrites re-grew and were re-melted periodically owing to the change in effective undercooling, which is the difference between the equilibrium melting temperature under pressure TmP and the temperature at the dendrite tip Ttip, as expressed by ΔTeff=TmP-Ttip, whereas secondary dendrite arm spacing increased with the re-growth and re-melting cycle. The relationship of the velocity of the dendrite tip v with the effective undercooling ΔTeff and pressure change ΔP was derived and expressed as v=AΔTeff+BΔP2+C where the effective undercooling plays a primary role in determining the tip velocity.

Synchrotron tomographic quantification of the influence of Zn concentration on dendritic growth in Mg-Zn alloys

Dendritic microstructural evolution during the solidification of Mg-Zn alloys was investigated as a function of Zn concentration using in situ synchrotron X-ray tomography. We reveal that increasing Zn content from 25 wt% to 50 wt% causes a Dendrite Orientation Transition (DOT) from a six-fold snow-flake structure to a hyper-branched morphology and then back to a six-fold structure. This transition was attributed to changes in the anisotropy of the solid-liquid interfacial energy caused by the increase in Zn concentration. Further, doublon, triplon and quadruplon tip splitting mechanisms were shown to be active in the Mg-38 wt%Zn alloy, creating a hyper-branched structure. Using the synchrotron tomography datasets, we quantify, for the first time, the evolution of grain structures during the solidification of these alloys, including dendrite tip velocity in the mushy zone, solid fraction, and specific surface area. The results are also compared to existing models. The results demonstrate the complexity in dendritic pattern formation in hcp systems, providing critical input data for the microstructural models used for integrated computational materials engineering of Mg alloys.

Cellular automaton modeling for dendritic growth during laser beam welding solidification process

A modified non-equilibrium cellular automaton (CA) model is proposed to simulate the dendrite growth along the fusion boundary under transient conditions during the solidification process of laser beam welding (LBW) pool. The main non-equilibrium solidification effects, including solute trapping, deviation of the liquidus line slope, and kinetic undercooling, are taken into consideration in this modified CA model. The evolution of dendrite morphology, concentration field, and velocity field was investigated. Four growth periods, i.e., the initial stable period, the instability period, the competitive growth period, and the short-term stable period, were observed during the solidification process of LBW pool. The dendrite growth patterns were different in these periods due to the transient solidification conditions. The solute distribution predicted by this modified CA model showed similar trends to that predicted by the previous phase field model. The dendrite tip velocity was significantly influenced by the thermal undercooling and constitutional undercooling in the LBW pool, and the tip velocity field can be divided into three stages, i.e., the planar growth stage, competitive stage, and short-term steady growth stage. In addition, further comparison between the simulated dendrite morphology and experimental dendrite morphology was performed. Results showed that the simulated morphology of dendrites agreed well with the experimental results. In particular, the primary dendrite arm spacing predicted by this model was in good agreement with that obtained from experiments.

New insight on physical meaning of fracture criteria for growing cracks

Because plastic unloading is inevitable during crack growth in elastic plastic materials, the J integral is not applicable anymore, and several path-independent integrals are thus proposed by different authors to overcome this limitation. In this paper, we start from the crack tip energy flux. We first derive two important formulas and then find that these path-independent integrals are in fact identical to each other and consistent with the crack tip energy flux. That is, the crack tip energy flux is more essential for growing cracks in elastic plastic materials. In addition, a force such as crack tip parameter, which is conjugated to crack tip velocity, is proposed by us on the perspective that crack tip energy flux can be considered as the power dissipated by crack tip due to crack growth. This parameter is proved to be the absolute value of the projection of the crack tip configurational force vector into the direction of the nominal crack growth direction, and thus, this parameter is the thermodynamic crack driving force. Moreover, this parameter can represent crack tip stress and displacement fields of growing cracks, and thus, a fracture criterion based on this parameter is proposed. The critical value of this parameter corresponds to the rate of energy dissipated in the fracture process zone per unit crack extension.

Concomitant sensing and actuation for piezoelectric microrobots

Sensor fabrication for microrobots is challenging due to their small size and low mass. As a potential solution, we present a technique for estimating the velocity of piezoelectric bending bimorph actuators, a popular choice for driving such microscale devices, that requires simple electronics and no additional mechanical components. Our approach relies on the insight that motion of the actuators causes varying strains on the surface on the piezoelectric material, which via the direct piezoelectric effect, results in a current proportional to the actuator velocity. We propose that the actuator be electrically approximated as a parallel combination of a frequency and voltage dependent resistor and capacitor, and a velocity proportional current source. We develop an experimental procedure to measure these quantities, and are able to experimentally determine the actuator tip velocity to within 10% accuracy over a range of voltages (25–200 V) and frequencies (1–2000 Hz, well beyond actuator resonance). We successfully apply this sensing methodology to two microrobots, the RoboBee and the Harvard Ambulatory MicroRobot (HAMR), to estimate the wing and limb motion respectively. We further use sensor feedback to close the loop on HAMR’s leg phase and obtain desired leg trajectories near transmission resonance. The proposed sensor methodology is generic and can be applied to piezoelectric actuators of different geometries and configurations for uses in microrobotic applications.

Flexible multibody dynamics modelling of point-absorber wave energy converters

Abstract As an inexhaustible and environmentally-friendly energy resource, ocean wave power, which is extracted from ocean waves through WECs (wave energy converters), is highly valued by coastal countries. Compared to other types of WECs, point-absorber WECs, the main body of which can be fixed on a platform (e.g. ship), save on installation costs and therefore have concentrated significant interest among researchers and technology developers. In the development of point-absorber WECs, it is crucial to develop a reliable structural model to accurately predict the structural dynamic responses of WECs subjected to wave loadings. In this work, a FMBD (flexible multibody dynamics) model, which is a combination of MBD (multibody dynamics) and FEA (finite element analysis), has been developed for point-absorber WECs. The FMBD model has been applied to the structural modelling of the NOTC (National Ocean Technology Centre) 10 kW multiple-point-absorber WEC. The floater arm tip displacement and velocity obtained from the FMBD model are validated against the values obtained from an analytical model, which is also developed in this work. The results from the FMBD model show reasonable agreement with those from the analytical model, with a relative difference of 10.1% at the maximum value of the floater arm tip displacement. The FMBD model is further used to calculate the stress distributions, fatigue life, deformations, modal frequencies and modal shapes of the structure. The results indicate that WECs are prone to experience fatigue failure, with the shortest fatigue life (2 years) observed in the floater arm. The FMBD model developed in this work is demonstrated to be capable of accurately modelling point-absorber WECs, providing valuable information for designers to further optimise the structure and assess the reliability of WECs.

Rate and State Friction Relation for Nanoscale Contacts: Thermally Activated Prandtl-Tomlinson Model with Chemical Aging

Rate and state friction (RSF) laws are widely used empirical relationships that describe macroscale to microscale frictional behavior. They entail a linear combination of the direct effect (the increase of friction with sliding velocity due to the reduced influence of thermal excitations) and the evolution effect (the change in friction with changes in contact "state," such as the real contact area or the degree of interfacial chemical bonds). Recent atomic force microscope (AFM) experiments and simulations found that nanoscale single-asperity amorphous silica-silica contacts exhibit logarithmic aging (increasing friction with time) over several decades of contact time, due to the formation of interfacial chemical bonds. Here we establish a physically based RSF relation for such contacts by combining the thermally activated Prandtl-Tomlinson (PTT) model with an evolution effect based on the physics of chemical aging. This thermally activated Prandtl-Tomlinson model with chemical aging (PTTCA), like the PTT model, uses the loading point velocity for describing the direct effect, not the tip velocity (as in conventional RSF laws). Also, in the PTTCA model, the combination of the evolution and direct effects may be nonlinear. We present AFM data consistent with the PTTCA model whereby in aging tests, for a given hold time, static friction increases with the logarithm of the loading point velocity. Kinetic friction also increases with the logarithm of the loading point velocity at sufficiently high velocities, but at a different increasing rate. The discrepancy between the rates of increase of static and kinetic friction with velocity arises from the fact that appreciable aging during static contact changes the energy landscape. Our approach extends the PTT model, originally used for crystalline substrates, to amorphous materials. It also establishes how conventional RSF laws can be modified for nanoscale single-asperity contacts to provide a physically based friction relation for nanoscale contacts that exhibit chemical bond-induced aging, as well as other aging mechanisms with similar physical characteristics.

Dynamic crack propagation in wood fibre composites analysed by high speed photography and a dynamic phase field model

Using an experimental setup, with a high-speed camera to track crack tip velocity, dynamic fracture is studied in wood fibre polylactic acid (PLA) composite and pure PLA. The experiments are analysed quantitatively in terms of the relation between energy release rate and crack tip velocity, and qualitatively in terms of branching occurrence and fracture surface appearance. Branching occurs frequently in PLA specimens but not in wood fibre composite specimens, in spite of high energy release rates. Scanning electron microscopy images of the fracture surfaces show that the fracture surfaces in wood fibre composite materials are rugged and uneven compared to PLA, whose surfaces are smoother.The experimental results are compared to numerical results, obtained using a dynamic phase field finite element model. Simulations correlate well with experiments with respect to the relation between energy release rate and crack tip velocity. For PLA, the simulations also predict branching correctly, but for wood fibre composites, the simulations slightly over-predict the amount of branching and point to a need for further development of fracture models in order to better capture the constitutive behaviour of these heterogeneous materials.