Detachment Criterion Research Articles

Regular reflection to Mach reflection (RR–MR) transition in short wedges

Regular reflection (RR) to Mach reflection (MR) transitions ( ${\rm RR}\leftrightarrow {\rm MR}$ ) on long wedges in steady supersonic flows have been well studied and documented. However, in a short wedge where the wedge length is small, the transition prediction becomes really challenging owing to the interaction of the expansion fan emanating from the trailing edge of the wedge with the incident shock and the triple/reflection point. The extent of this interaction depends on the distance between the wedge trailing edge and the symmetry line (Ht). This distance is a geometric combination of the distance of the wedge leading edge from the symmetry line $(H)$ , the wedge angle ( $\theta$ ) and the wedge length $(w)$ . In the present study, we used the method of characteristics to model the complete wave interactions which accurately predicted shock curvatures and the reflection configurations for all ranges of the incoming flow Mach number. In the case of short wedges, the transition criterion strongly depends on the wedge length, which can be so adjusted even to eliminate the ${\rm RR}\rightarrow {\rm MR}$ transitions till the wedge angle reaches the no-reflection domain. Transition lines for both the detachment criterion and von Neumann criterion are also drawn to investigate the dual solution domain, and the reflection configurations were verified experimentally for the first time on short wedges. By using proper input configuration parameter ( $w/H$ ), various types of shifts in the dual solution domain for short wedges are studied and categorised into three types, namely Type I, Type II and Type III.

Research on ice shedding and broken conductor in tower-line system based on CR method

In cold climates, the damage to the transmission tower-line system is usually caused by ice shedding, broken conductors, and broken ground wires. To replicate the ice shedding and broken conductor scenarios more accurately and expeditiously within the transmission tower-line system, we have engineered a finite element computational program leveraging the co-rotational theory method, utilizing the C++ programming language. Additionally, we have orchestrated its visualization interface utilizing the QT and Visualization Toolkit (VTK) platforms. This program can accurately and rapidly simulate large displacement geometric nonlinear problems. An ice detachment criterion considering the resultant acceleration is proposed. Compared with previous judgment criteria, the criterion proposed in this article can adapt to the previous prediction accuracy and is more efficient in calculation. A finite element method for disconnection simulation of “node failure” was proposed, and its accuracy and computational efficiency were verified by comparison with experiments. By analyzing the coupling effect of disconnection and deicing in the tower line system, it is concluded that ground wires often have a stronger deicing effect than conductors. Although broken conductor will cause large-scale ice shedding from the span, the impact on the most dangerous point of the tower will be very small, this providing a theoretical basis for ice-covered broken conductor in the tower-line system. The simulation method proposed in this article also provides a new research idea for the simulation of ice shedding and broken conductor of tower-line systems.

Strong shock solutions in symmetric wedge flows: Unphysical or unstable?

This paper investigates the strong shock solutions in a supersonic wedge experimentally, analytically, and numerically. Experiments and computations are conducted on scaled-down models for the two types of shock reflection to be possible. The time-resolved schlieren observation of the flow evolution revealed that the shock formation is a highly dynamic transition of the starting shock from a strong Mach reflection (MR) to a weak regular reflection (RR) via a strong RR reflection over a constant shock wave angle for a wedge angle less than the detachment criterion angle for the shock transition. However, when the wedge angle is greater than the detachment criterion angle, the shock moves over the wedge with the MR structures of diminishing Mach stem height at a constant incident shock wave angle. These intermediate shock reflections are found to be unstable and oscillate at high amplitude and low frequencies to upstream pressure fluctuations. The nature of the intermediate shock reflection during the shock transition over the wedge has also been studied using an unsteady second-order two-dimensional compressible Navier–Stokes solver code with shear stress transport k-ω turbulence modeling. The computed flow parameters around the intermediate shock reflections confirmed that these are indeed strong shock reflections believed to be unphysical in steady wedge flows.

Semi-Analytical Model of a Helicon Plasma Thruster

This article is devoted to the presentation of a semianalytical model of a helicon plasma thruster based on: 1) a 0-D global source model (GSM) for the simulation of the plasma source; 2) a monodimensional acceleration model for the plasma expansion and thrust production in the magnetic nozzle; and 3) a detachment criterion for the identification of the location in the nozzle where the plasma separates from the magnetic field lines. The developed GSM permits the simulation of magnetic topologies provided for radial cusps in the source region. Three different acceleration models presented in the literature have been implemented and employed for component 2) of the full thruster model. Two detachment criteria have also been considered for component 3). A comparison between the characteristics and the results of the different models employed has been carried out. Finally, the results obtained by all the combinations of acceleration models and detachment criteria presented have been compared against the solutions of a numerical fluid code and experimental thrust measurements. A maximum relative deviation between the results of the acceleration models of 3% was found, while a thrust variation of up to 20%–30% was recorded by changing the detachment criteria. A maximum relative error between the model’s predictions and the experimental measurements of 25% was obtained.

Bubble formation from sub-millimeter orifices under variable gas flow conditions

We provide an experimental investigation on the mechanism of the bubble formation from sub-millimeter orifices under variable gas flow conditions VGFC. The effect of influential parameters including the volumetric gas flow rate Q, the orifice diameter dor, and the volume of the gas reservoir Vc upstream of the orifice are investigated in detail. We found that, by enlarging Vc,q increases. This affects various aspects of bubble formation dynamics such as the bubble base expansion, the apparent contact angle at the three-phase contact point, and the bubble detachment criterion. The effect of Vc is best presented by its dimensionless group, the capacitance number Nc. The minimum Nc from which the influence of the gas reservoir becomes important depends on the orifice size. Moreover, a significant increase in Vc leads to a change in the bubbling regime towards multiple bubble formation.

Energetic criterion for adhesion in viscoelastic contacts with non-entropic surface interaction

We suggest a detachment criterion for a viscoelastic elastomer contact based on Griffith's idea about the energy balance at an infinitesimal advancement of the boundary of an adhesive crack. At the moment of detachment of a surface element at the boundary of an adhesive contact, there is some quick (instant) relaxation of stored elastic energy which can be expressed in terms of the creep function of the material. We argue that it is only this "instant part" of stored energy which is available for doing work of adhesion and thus it is only this part of energy relaxation that must be used in Griffith's energy balance. The described idea has several restrictions. Firstly, in this pure form, it is only valid for adhesive forces having an infinitely small range of action (which we call the JKR-limit). Secondly, it is only applicable to non-entropic (energetic) interfaces, which detach "at once" and do not possess their own kinetics of detachment.

Effect of the Size of Particles on Their Adhesion in Composite Polypropylene/SiO2

The effect of particle size on the mechanical characteristics of biaxially oriented composite polypropylene/SiO2 is studied. The material is oriented in plane by squeezing two lead-tin alloy plates with the composite film being placed between them. Deformation is defined by the composition of the plates. This makes it possible to obtain the material with low degrees of orientation. The oriented composite preserves plasticity typical of the polypropylene matrix. After biaxial orientation of the unfilled PP, the yield point decreases by approximately 40% upon subsequent stretching. A reduction in the size of particles changes their adhesion behavior during stretching. Coarse particles with a size of about 20 µm separate from PP during stretching. On the contrary, nanoparticles with sizes of 200 and 500 nm do not separate even under plastic deformation of the composite. As a result, nanoparticles reinforce the thermoplastic the same way as carbon black nanoparticles reinforce rubber. The energy detachment criterion explaining an increase in the detachment stress with decreasing particle size is derived.

Peridynamic modelling of clay erosion

Experimental observations of the erosion of clays indicate a high degree of coupling between the hydro-chemical processes in the clay–water system and the mechanics of erosion. In contrast with the volume of experimental work and the significance of swelling clay erosion in many geotechnical engineering problems, limited advances have been made with the predictive modelling of this phenomenon. The critical erosion step, missing in existing models, is the particles’ detachment from the moving boundary of the expanding clay – a discontinuous process. This paper presents, for the first time, a non-local formulation for clay erosion, which brings together clay swelling, particle detachment and detached particle transport, into a single modelling tool. The detachment criterion, an essential element of the integrated erosion model, is first tested against a series of experimental benchmarks to show the excellent agreement between calculated and experimental results. The integrated erosion model is subsequently validated by comparison with experimental data for the behaviour of compacted bentonite under several eroding environments. The results: (a) show clearly the capacity of the model to capture concurrently the free swelling of clay, the detachment of clay particles and the transport of detached particles in the eroding environment; and (b) support strongly the applicability of the model to account for the hydro-chemical conditions (composition and velocity) of the eroding environment. The proposed multi-physics non-local formulation, successfully validated for hydro-chemical effects on clay erosion, provides a robust framework for incorporating a wide set of additional couplings.

Effect of the wall temperature on Mach stem transformation in pseudo-steady shock wave reflections

Pseudo-steady shock wave reflections on a compression ramp are recognized as a significant phenomenon in the shock dynamics field. Several investigations have been performed on this phenomenon by shock tube experiments, combined with numerical and theoretical analyses. In addition to the availability of numerous reliable and accurate data on shock reflection patterns in the form of regular reflection, double-Mach reflection, transitional-Mach reflection, and single-Mach reflection, several transitional criteria such as detachment criterion and mechanical-equilibrium criterion are also established. However, none of the research focuses on the influence of the wall temperature on Mach stem transformation in pseudo-steady shock wave reflections. In order to articulate the role played by the wall temperature, a two-dimensional numerical simulation is performed by resolving the unsteady Reynolds-averaged Navier-Stokes equations to investigate the transformation of the Mach stem. Shear-stress transport k-ω turbulence model and third-order Monotonic Upwind Scheme for Conservation Laws scheme are explored to accurately capture various shock structures. Numerical results are initially validated with experimental data in the open literature and it is evident that there is an excellent match between the present simulation and the actual structure. Subsequently, the grid resolution and time step independence analyses are considered to better resolve the shock reflection configuration. Large-scale negative and positive heat fluxes are imposed on the ramp wall, which can simulate the cooling and heating ramps respectively. A new Mach stem transformation that illustrates significant differences in physical structure evolutions caused by the variation of the wall temperature is numerically captured for the first time. The mechanism of wall temperature effects on the transformation of the Mach stem is clearly expounded with the purpose of profound understanding for pseudo-steady shock wave reflections.

Evaluation and optimization of a shock load de-icing method for transmission lines with combined ice failure criteria

A mechanical de-icing process for overhead transmission lines using shock load is investigated numerically by finite element analysis, where a combination of three validated ice failure criteria is implemented, namely- the maximum bending strain criterion, the tensile detachment criterion and the shear detachment criterion. A total of 25 numerical scenarios are established and the ice shedding ratio and dynamic response of overhead lines are studied. The goal is to assess the relative importance of the leading parameters that affect the efficiency of the shock-load deicing method and the corresponding transient effects. The parameters under study include: the shock load characteristics (amplitude, time history and applied location along the span), the ice accretion characteristics (equivalent thickness and eccentricity ratio), and the line profile (height difference of span suspension points and adjacent spans). The study leads to suggestions to improve the de-icing efficiency of the shock-load method and reduce the adverse transient effects on the line components. The modeling approach used in this study provides a cost-effective tool and helpful reference for design, evaluation and optimization of a variety of mechanical de-icing methods, devices and procedures.

Cluster of the Kendall-type adhesive microcontacts as a simple model for load sharing in bioinspired fibrillar adhesives

The problem of multiple adhesive contact is considered for an elastic substrate modeled as a transversely isotropic elastic half-space. It is assumed that a large number of the Kendall-type microcontacts are formed between the substrate and circular rigid (i.e., nondeformable) and frictionless micropads, which are interconnected between themselves, thereby establishing a load sharing. The effect of microcontacts interaction is accounted for in the formulation of the detachment criterion for each individual microcontact. A number of different asymptotic models are presented for the case of dilute clusters of microcontacts with their accuracy tested against a special case of two-spot contact, for which an analytical solution is available. The pull-off force has been estimated and the effects of the array size and the microcontact spacing are studied. It is shown that the flexibility of the micropads fixation, which is similar to that observed in mushroom-shaped fibrils, significantly increases the pull-off force. The novelty of the presented approach is its ability to separate different effects in the multi-scale contact problem, which allows one to distinguish between different mathematical models developed for bioinspired fibrillar adhesives.

Adhesive Strength of Contacts of Rough Spheres

The adhesive contact between a parabolic indenter with superimposed roughness and an elastic half space is studied in the JKR-limit (infinitely small range of action of adhesive forces) using the boundary element method with mesh-dependent detachment criterion suggested in 2015. Three types of superimposed roughness are considered: one- and two-dimensional waviness and randomly rough roughness. It is shown that in the case of regular waviness, the character of adhesion is governed by the Johnson adhesion parameter. For our randomly rough surfaces a new adhesion parameter has been identified numerically, which uniquely determines the adhesive strength of the contact.

Adhesive contact between a rigid body of arbitrary shape and a thin elastic coating

Application of the principle of energy balance to a rigid indenter in contact with a thin elastic layer on a flat rigid substrate provides a very simple derivation of the detachment criterion which earlier has been obtained by much more complicated asymptotic analysis. The simple criterion is additionally confirmed by the fully three-dimensional simulations of contact with a coated rigid substrate using the recently developed formulation of the boundary element method for coated media. The found detachment criterion is applied to contact of indenters of various shape. In the case of flat-ended indenters, the adhesive strength occurs to be proportional to the area of the face of the indenter (independently of the shape). The asymptotic criterion is also used for calculation of the adhesion strength of indenters having arbitrary shape and is illustrated with a case study of a contact of a rough indenter with a coated substrate.

A theoretical and computational study of the vibration excitation on the transition criteria of shock wave reflections

In this paper, we study the vibration excitation on the reflection of shock waves in hypersonic flows by using analytical and computational approaches. First, a theoretical approach is established to solve the shock relations which are further applied to develop the shock polar analytical method for high-temperature air. Then, a comparative investigation using calorically perfect gas model and thermally perfect gas model considering vibration excitation indicates an obvious change to the overall profile of the shock polar. The post-shock pressure increases within the strong branch of the shock polar while decreases within the weak branch due to vibration excitation of air molecules. A more notable phenomenon is the increase in the maximum deflection angle of the shock polar which can significantly influence the detachment criterion of shock reflection transition in high-temperature air flows. The shock polar analysis of shock reflection shows that the vibration excitation result in an obvious increase to the detachment criterion while a slight increase to the von Neumann criterion. A series of computations are conducted to confirm the above analytical findings on the shock reflection considering the vibration excitation. A slight difference of transition criterion between the theory and computations is found to be caused by the existence of the expansion fan which is an inherent flow structure. The proposed shock polar analytical method is proved to be an effective but simple approach for the study of shock wave reflections in hypersonic flows.

Interface‐based crystal particle autoselection via membrane crystallization: From scaling to process control

Accurate crystallization control is an essential aspect for chemical engineering and separation processes. Herein, we demonstrated the novelty of membrane crystallization (MCr) on the interfacial based‐crystal particle autoselection aimed for nucleation regulation and process control. With the proposed model based on a van der Waals‐friction‐hydrodynamic force field and classical nucleation theory, the motion mechanisms of heterogeneously induced nucleation were illustrated. The defined particle detachment criterion K revealed the control mechanism of the crystal particle motion behavior: temporary adherence, detachment, and perpetual adherence (scaling) at the membrane interface. For the first time, the function region of MCr (nucleation detection, scaling control, and crystallization regulation) was systematically illustrated and validated with the directly observed laboratory demonstration. These findings also demonstrate the potential applications of the uniform size distribution, morphology modified particle manufacture, and in situ nucleation detection. © 2018 American Institute of Chemical Engineers AIChE J, 65: 723–733, 2019

Adhesive contact of rough brushes.

The adhesive contact between a rough brush-like structure and an elastic half-space is numerically simulated using the fast Fourier transform (FFT)-based boundary element method and the mesh-dependent detachment criterion of Pohrt and Popov. The problem is of interest in light of the discussion of the role of contact splitting in the adhesion strength of gecko feet and structured biomimetic materials. For rigid brushes, the contact splitting does not enhance adhesion even if all pillars of the brush are positioned at the same height. Introducing statistical scatter of height leads to a further decrease of the maximum adhesive strength. At the same time, the pull-off force becomes dependent on the previously applied compression force and disappears completely at some critical roughness. For roughness with a subcritical value, the pressure dependence of the pull-off force qualitatively follows the known theory of Fuller and Tabor with moderate modification due to finite size effect of the brush.

SIMULATION OF FRACTURE USING A MESH-DEPENDENT FRACTURE CRITERION IN THE DISCRETE ELEMENT METHOD

Recently, Pohrt and Popov have shown that for simulation of adhesive contacts a mesh dependent detachment criterion must be used to obtain the mesh-independent macroscopic behavior of the system. The same principle should be also applicable for the simulation of fracture processes in any method using finite discretization. In particular, in the Discrete Element Methods (DEM) the detachment criterion of particles should depend on the particle size. In the present paper, we analyze how the mesh dependent detachment criterion has to be introduced to guarantee the macroscopic invariance of mechanical behavior of a material. We find that it is possible to formulate the criterion which describes fracture both in tensile and shear experiments correctly.

RR–MR transition of a Type V shock interaction in inviscid double-wedge flow with high-temperature gas effects

The transition between regular reflection (RR) and Mach reflection (MR) of a Type V shock–shock interaction on a double-wedge geometry with non-equilibrium high-temperature gas effects is investigated theoretically and numerically. A modified shock polar method that involves thermochemical non-equilibrium processes is applied to calculate the theoretical critical angles of transition based on the detachment criterion and the von Neumann criterion. Two-dimensional inviscid numerical simulations are performed correspondingly to reveal the interactive wave patterns, the transition processes, and the critical transition angles. The theoretical and numerical results of the critical transition angles are compared, which shows evident disagreement, indicating that the transition mechanism between RR and MR of a Type V shock interaction is beyond the admissible scope of the classical theory. Numerical results show that the collisions of triple points of the Type V interaction cause the transition instead. Compared with the frozen counterpart, it is found that the high-temperature gas effects lead to a larger critical transition angle and a larger hysteresis interval.

Strength of adhesive contacts: Influence of contact geometry and material gradients

The strength of an adhesive contact between two bodies can strongly depend on the macroscopic and microscopic shape of the surfaces. In the past, the influence of roughness has been investigated thoroughly. However, even in the presence of perfectly smooth surfaces, geometry can come into play in form of the macroscopic shape of the contacting region. Here we present numerical and experimental results for contacts of rigid punches with flat but oddly shaped face contacting a soft, adhesive counterpart. When it is carefully pulled off, we find that in contrast to circular shapes, detachment occurs not instantaneously but detachment fronts start at pointed corners and travel inwards, until the final configuration is reached which for macroscopically isotropic shapes is almost circular. For elongated indenters, the final shape resembles the original one with rounded corners. We describe the influence of the shape of the stamp both experimentally and numerically.Numerical simulations are performed using a new formulation of the boundary element method for simulation of adhesive contacts suggested by Pohrt and Popov. It is based on a local, mesh dependent detachment criterion which is derived from the Griffith principle of balance of released elastic energy and the work of adhesion. The validation of the suggested method is made both by comparison with known analytical solutions and with experiments. The method is applied for simulating the detachment of flat-ended indenters with square, triangle or rectangular shape of cross-section as well as shapes with various kinds of faults and to “brushes”. The method is extended for describing power-law gradient media.

Numerical and experimental investigation of oblique shock wave reflection off a water wedge

Shock wave interaction with solid wedges has been an area of much research in past decades, but so far very few results have been obtained for shock wave reflection off liquid wedges. In this study, numerical simulations are performed using the inviscid Euler equations and the stiffened gas equation of state to study the transition angles, reflection patterns and triple point trajectory angles of shock reflection off solid and water wedges. Experiments using an inclined shock tube are also performed and schlieren photography results are compared to simulations. Results show that the transition angles for the water wedge cases are within 5.3 % and 9.2 %, for simulations and experiments respectively, compared to results obtained with the theoretical detachment criterion for solid surfaces. Triple point trajectory angles are measured and compared with analytic solutions, agreement within $1.3^{\circ }$ is shown for the water wedge cases. The transmitted wave in the water observed in the simulation is quantitatively studied, and two different scenarios are found. For low incident shock Mach numbers, $M_{s}=1.2$ and 2, no shock wave is formed in the water but a precursor wave is induced ahead of the incident shock wave and passes the information from the water back into the air. For high incident shock Mach numbers, $M_{s}=3$ and 4, precursor waves no longer appear but instead a shock wave is formed in the water and attached to the Mach stem at every instant. The temperature field in the water is measured in the simulation. For strong incident shock waves, e.g. $M_{s}=4$, the temperature increment in the water is up to 7.3 K.