Cavity Detachment from a Wedge with Rounded Edges and the Surface Tension Effect

Cavity flow around a wedge with rounded edges was studied, taking into account the surface tension effect and the Brillouin–Villat criterion of cavity detachment. The liquid compressibility and viscosity were ignored. An analytical solution was obtained in parametric form by applying the integral hodograph method. This method gives the possibility of deriving analytical expressions for complex velocity and for potential, both defined in a parameter plane. An expression for the curvature of the cavity boundary was obtained analytically. By using the dynamic boundary condition on the cavity boundary, an integral equation in the velocity modulus was derived. The particular case of zero surface tension is a special case of the solution. The surface tension effect was computed over a wide range of the Weber number for various degrees of cavitation development. Numerical results are presented for the flow configuration, the drag force coefficient, and the position of cavity detachment. It was found that for each radius of the edges, there exists a critical Weber number, below which the iterative solution process fails to converge, so a steady flow solution cannot be computed. This critical Weber number increases as the radius of the edge decreases. As the edge radius tends to zero, the critical Weber number tends to infinity, or a steady cavity flow cannot be computed at any finite Weber number in the case of sharp wedge edges. This shows some limitations of the model based on the Brillouin–Villat criterion of cavity detachment.

Ground Displacements due to the Deformations of Shallow Tunnels with Arbitrary Cross Sections in Soft Ground

Nowadays, a huge number of shield-driven tunnels with noncircular cross sections are constructed in urban areas all around the world. However, the ground displacements associated with tunneling still form a difficult issue, especially for noncircular tunnels. In this study, an analytical solution is derived to estimate the ground displacements induced by the deformations of shallow noncircular tunnels in soft ground. First, a solution for the stresses and displacements around a deep tunnel in a full plane is formulated by imposing a specified convergence pattern over the cavity boundary. Subsequently, this solution is validated using finite element simulations in a case study of an elliptical tunnel with four different convergence patterns. Afterward, the solution in the full plane is extended to a half plane using the virtual image technique to estimate the ground displacements around shallow tunnels. The solution is also validated using finite element simulations.

The Non-Stationary Dynamic Analytical Solution of a Spherical/Cylindrical Cavity Expansion

A review of the pertinent literature related to the dynamic expansion of a spherical/cylindrical cavity shows that all the solutions with kinematic boundary conditions deal with a constant velocity at the cavity boundary. This paper develops a new general solution of the nonstationary dynamic problem of cavity expansion, which allows the application of time-dependent motion conditions at the cavity boundary. This solution can be used, for example, in the development of approximate approaches for projectiles penetrating with a non-constant velocity into different targets. Due to the complexity of the nonlinear nonstationary problem, an analytical solution of the problem may be developed if simplified constitutive relationships are used. In the present model, a simplified material model with a locked equation of state and a linear shear failure relationship is implemented. This solution may be applied to different materials such as concrete, soil, and rock. Special cases of the newly developed nonstationary solution are compared with different spherical and cylindrical cavity expansions solutions reported in the literature, and a good agreement is obtained. The capability of the present model is demonstrated in a following investigation of representative cases of cavity expansion with zero, constant, and variable acceleration of the cavity boundary. A significant difference in the stress variation for the different cases is shown. Along with the general solution which deals with an elastic–plastic region, a simplified solution which disregards the contribution of the elastic region is presented and the evaluation of the elastic region effect may be assessed.

Effect of a Boundary Layer on Cavity Flow

Cavity flow past an obstacle in the presence of an inflow vorticity is considered. The proposed approach to the solution of the problem is based on replacing the continuous vorticity with its discrete form in which the vorticity is concentrated along vortex lines coinciding with the streamlines. The flow between the streamlines is vortex free. The problem is to determine the shape of the streamlines and cavity boundary. The pressure on the cavity boundary is constant and equal to the vapour pressure of the liquid. The pressure is continuous across the streamlines. The theory of complex variables is used to determine the flow in the following subregions coupled via their boundary conditions: a flow in channels with curved walls, a cavity flow in a jet and an infinite flow along a curved wall. The numerical approach is based on the method of successive approximations. The numerical procedure is verified considering a body with a sharp edge, for which the point of cavity detachment is fixed. For smooth bodies, the cavity detachment is determined based on Brillouin’s criterion. It is found that the inflow vorticity delays the cavity detachment and reduces the cavity length. The results obtained are compared with experimental data.

Electron- and proton-scale nested magnetic cavities: Manifestation of kinetic theta-pinch equilibrium in space plasmas

<p>Magnetic cavities, sometimes referred to as magnetic holes, are ubiquitous in space and astrophysical plasmas characterized by localized regions with depressed magnetic field strength, strongly anisotropic particle distributions, and enhanced plasma pressure. Typical cavity sizes range from fluid to ion and sub-ion kinetic scales, with recent observations also identifying nested cavities that may indicate cross-scale energy cascades. Although heavily investigated in space, magnetic cavities have analogs in laboratory plasmas, the classical theta-pinches. Here, we develop an equilibrium solution of the Vlasov-Maxwell equations in cylindrical coordinates (in similar format to theta-pinch models), to reconstruct the cross-scale profiles of magnetic cavities observed by the four-spacecraft MMS mission. The kinetic model uses input parameters derived from single-spacecraft measurements to successfully reproduce signatures of magnetic cavities from all observing spacecraft. The reconstructed profiles demonstrate that near the electron-scale cavity boundary, the decoupled electron and proton motions generate a radial electric field that contributes to electron vortex formation that has been previously attributed mostly to diamagnetic effects. At larger scales, the diminishing electric field implies that diamagnetic motion is solely responsible for proton vortices.</p>

Dynamics of a spherical enclosure in a liquid during ultrasonic cavitation

The paper investigates the process of pulsation of a spherical cavity (bubble) in a liquid under the influence of a source of ultrasonic vibrations. The pulsation of a spherical cavity is described by the Kirkwood-Bethe equations, which are one of the most accurate mathematical models of pulsation processes at an arbitrary velocity of the cavity boundary. The Kirkwood-Bethe equations are essentially non-linear, therefore, to construct solutions and parametric analysis of the bubble collapse process under the influence of ultrasound, a numerical algorithm based on the Runge-Kutta method in the Felberg modification of the 4-5th order with an adaptive selection of the integration step in time has been developed and implemented. The proposed algorithm makes it possible to fully describe the process of cavitation pulsations, to carry out comprehensive parametric studies, and to evaluate the influence of various process parameters on the intensity of cavitation. As an example, the results of calculating the process of pulsation of the cavitation pocket in water are given and the influence of the amplitude of ultrasonic vibrations and the initial radius on the process of cavitation of a single bubble is estimated.

Nanotherapeutics for neurosurgically-applied drug delivery

Despite multimodal treatment, the median survival of Glioblastoma multiforme (GBM) remains less than 15 months, in considerable part due to diffusely infiltrative disease. Better treatment methods are necessary to eradicate residual tumour burden remaining beyond the resection cavity boundary. Based on an increasing understanding of GBM intra-tumour heterogeneity, the capability to deliver multiple therapeutic moieties from single formulations is clinically-relevant. It is hypothesised that incorporating drug-loaded polymer pro-drugs, which are capable of transcytotic ‘hopping’, into a biodegradable microparticulate paste will lead to efficacious local delivery. Here we report the formulation of numerous self-assembling cytocompatible nanoparticles, based on different linear and branched polymeric architectures. The polymers were synthesised by ring opening polymerisation with organic catalysts, leading to controlled reaction kinetics and greater potential biomedical applicability. We demonstrated that copolymerisation of a monomer with functional capability enabled the successful conjugation of doxorubicin to the polymer chain. We hypothesised that polymers with a greater degree of branching over traditional linear structures would lead to greater drug loading, and successfully tested this hypothesis through the encapsulation of olaparib. We will discuss strategies to incorporate: i) pH-sensitive linkers to the polymeric backbone, which would allow controlled drug release in acidic microenvironments; ii) multiple combined chemotherapeutics, including doxorubicin and olaparib. Future work will assess the efficacy of the polymer pro-drugs against primary GBM lines derived from the invasive margin and safety/efficacy using orthotopic syngeneic allografts. This is the first study incorporating polymer pro-drugs of this type into an existing localised micro-scale delivery system for GBM therapies.

3D simulations of planet trapping at disc–cavity boundaries

Inward migration of low-mass planets and embryos of giant planets can be stopped at the disc–cavity boundaries due to co-orbital corotation torque. We performed the first global three-dimensional (3D) simulations of planet migration at the disc–cavity boundary, and have shown that the boundary is a robust trap for low-mass planets and embryos. A protoplanetary disc may have several such trapping regions at various distances from the star, such as at the edge of the stellar magnetosphere, the inner edge of the dead zone, the dust-sublimation radius and the snow lines. Corotation traps located at different distances from a star, and moving outward during the disc dispersal phase, may possibly explain the observed homogeneous distribution of low-mass planets with distance from their host stars.

Experimental research of cavity geometry behind high-speed bodies in water

At high speed launching of bodies via smoothbore throwing facility into water, a stabilization of bodies was experimentally achieved due to periodical interactions of body contour with the cavity boundaries. If the body contours are not exceeding produced cavity boundary, drag force localized mostly at nose part of a body, which calls “cavitator”. Based on this, it will be rational to take into consideration cavity shape when designing contours of bodies.

Numerical Study of the Influence of Insect Grille on Airflow in Ventilated Facade Constructions

This article discusses a numerical model to evaluate the influence of inlet/outlet insect grilles in naturally ventilated facades. Two models were created for this comparison. The difference between these models is in inlet and outlet openings. One model is fitted with insect grilles and the other one without insect grilles. Both models are three dimensional vertical ventilated cavity. Boundary conditions fit to summer season. In particular, the influence of insect grilles on airflow velocity and air temperature in the cavity are evaluated. The main goal of this work is to show the effect of openings size and geometry to functionality of natural ventilated constructions.