Normal Component Of Particle Velocity Research Articles

МОДЕЛЮВАННЯ ДВОФАЗНОГО ПОТОКУ ПРИ ХОЛОДНОМУ ГАЗОДИНАМІЧНОМУ НАПИЛЮВАННІ

The one-dimensional gas-dynamic model for calculation of acceleration and heating of particles which takes into account space from the nozzle outlet to the substrate has been improved. One cycle of particle acceleration by a gas flow can be divided into three parts: mixing a gas flow with powder; particle movement and acceleration in the divergent part of the nozzle; the movement of gas-powder flow from nozzle outlet to substrate. It is known that cold spray coating formation depends on the normal component of particle velocity towards the surface to be sprayed. Each material obtains its value of the critical velocity when the coating formation process starts. At particle velocities above critical, they adhere to the substrate and form coating due to plastic deformation of particles, and at velocities below critical value surface erosion or spraying with low efficiency is observed. One of the features of the process of cold gas-dynamic spraying is a relatively small distance between the nozzle outlet and the deposited surface, which leads to the occurrence of the reverse flow of the gas stream (bow shock) reflected from the substrate. The reflected flow significantly inhibits the trajectory of particles of sprayed powder which need to be investigated. Impact temperature and velocity of aluminum and nickel particles with size 25 microns with a substrate for SK-20 supersonic nozzle of DIMET-405 low-pressure cold spraying machine has been calculated. Although the one-dimensional isentropic gas-dynamic model, which is usually used to calculate flow parameters, describes flow only along the axis of the nozzle, excluding heat transfer with nozzle and friction loss on the inner walls, which leads to overestimated results of calculations, its utilization allows to optimize the geometry of the nozzle channel and develop a technological process of the spraying process. Mathematical modeling of two-phase flow dynamics of the cold spraying process was performed using the MATLAB software. Comparison of simulation results with experimental data to determine the flow velocity and temperature showed that the theoretical calculations differ from the experimental ones by no more than 10 %.

Waves at a fluid-solid interface: Explicit versus implicit formulation of boundary conditions using a discontinuous Galerkin method.

An accurate solution of the wave equation at a fluid-solid interface requires a correct implementation of the boundary condition. Boundary conditions at fluid-solid interface require continuity of the normal component of particle velocity and traction, whereas the tangential components vanish. A main challenge is to model interface waves, namely, the Scholte and leaky Rayleigh waves. This study uses a nodal discontinuous Galerkin (dG) finite-element method with the medium discretized using an unstructured uniform triangular meshes. The natural boundary conditions in the dG method are implemented by (1) using an explicit upwind numerical flux and (2) by using an implicit penalty flux and setting the modulus of rigidity of the acoustic medium to zero. The accuracy of these methods is evaluated by comparing the numerical solutions with analytical ones, with source and receiver at and away from the interface. The study shows that the solutions obtained from the explicit and implicit boundary conditions provide the correct results. The stability of the dG scheme is determined by the numerical flux, which also implements the boundary conditions by unifying the numerical solution at shared edges of the elements in an energy stable manner.

A theoretical model for prediction of deposition efficiency in cold spraying

The deposition behavior of a spray particle stream with a particle size distribution was theoretically examined for cold spraying in terms of deposition efficiency as a function of particle parameters and spray angle. The theoretical relation was established between the deposition efficiency and spray angle. The experiments were conducted by measuring deposition efficiency at different driving gas conditions and different spray angles using gas-atomized copper powder. It was found that the theoretically estimated results agreed reasonably well with the experimental ones. Based on the theoretical model and experimental results, it was revealed that the distribution of particle velocity resulting from particle size distribution influences significantly the deposition efficiency in cold spraying. It was necessary for the majority of particles to achieve a velocity higher than the critical velocity in order to improve the deposition efficiency. The normal component of particle velocity contributed to the deposition of the particle under the off-nomal spray condition. The deposition efficiency of sprayed particles decreased owing to the decrease of the normal velocity component as spray was performed at off-normal angle.

Application of the PE method to up‐slope sound propagation

The wide‐angle PE method is applied to the prediction of sound propagation in a range‐dependent environment. The finite‐difference model treats the sloping ground by a staircase approximation. The method allows impedance and slope angle variations to be taken into account. The implementation of sloping interfaces in one‐way PE models introduces a fundamental problem of energy conservation. This is generated at the lower boundary condition. The ground is assumed to be a locally reacting surface where the ground impedance is defined as the ratio of pressure to the normal component of particle velocity at the surface. The staircase PE method approximates the normal at the slope surface with the vertical component at the stair‐step surface. A numerical correction can be included. Using a scale model facility [K. B. Rasmussen, 3617–3620 (1994)], a series of measurements is carried out. The results are compared with the PE calculations. The magnitude of the error due to the interface condition is evaluated.

The rotated parabolic equation and sloping ocean bottoms

A new approach for solving problems involving sloping ocean bottoms with the parabolic equation (PE) method is presented. In most implementations of the PE, range-dependent environments have been approximated as a sequence of range-independent regions. The PE, which has one range derivative, does not conserve both pressure and the normal component of particle velocity across boundaries between regions. For problems involving sloping ocean bottoms, this can lead to large errors for slopes of only a few degrees. The rotated PE, which marches parallel to the ocean bottom and has two normal derivatives, handles sloping interfaces properly. A benchmark solution for an upslope problem is presented to demonstrate the accuracy of the rotated PE.

Finite element solution to the parabolic wave equation

In seeking more ways to predict underwater sound fields, the underwater acoustical parabolic wave equation is solved using the finite element (FE) method. The mathematical theory for the finite element method in an N-medium case is discussed, when the conditions of continuity of pressure and continuity of the normal component of particle velocity are perfectly satisfied at each interface. Several propagation examples for horizontal and irregular interfaces are presented to demonstrate the capability of this effective FE method.

Spherically symmetrical acoustic propagation across a fluid/fluid boundary

The problem of determining the spherically symmetrical field generated by an acoustic point source at the center of a fluid sphere that itself is immersed in a second fluid medium is discussed. A method of solving for the field in the internal and external fluid regions is introduced, based on finite Hankel transforms. These transforms and their inverses are constructed in such a way that the boundary conditions (continuity of pressure and normal component of particle velocity) at the spherical interface are satisfied. In particular, the inverse transforms are integrals; that is, there is a continuum of radial wavenumbers. This contrasts with the more usual formalism, involving a Fourier–Bessel series taken over a discrete distribution of radial wavenumbers. The latter type of inversion formula is suitable only for problems involving relatively simple boundary conditions (e.g., Dirichlet or Neumann). Using the new technique, an exact analytical solution is given for the acoustic field in both the sphere and the surrounding fluid.

Boundary element analysis of sound fields around enclosures with circular apertures.

This paper is concerned with the application of the Boundary Element Method (BEM) to the three-dimensional analysis of each distribution of sound pressure levels around two kinds of boxlike enclosure models with circular apertures through which sound is radiated. In these analyses, triangular boundary elements are used and it is assumed that the sound pressure and the normal component of particle velocity on an element are constant. Several mesh models with different numbers of elements are used in order to examine the convergence of the numerical solution. The sound-pressure-level distributions calculated are compared with those measured in detail through a sound visualization method using three color-light-emitting diodes. For both cases of pure tone and 1/3 octave band noise, the calculated results agree fairly well with the measured ones. these results show that the complicated sound fields around such enclosures can be estimated with a high accuracy by using BEM.

Spherically symmetric acoustic propagation across a fluid/fluid boundary

The problem of determining the spherically symmetrical field generated by an acoustic point source at the center of a fluid sphere that itself is immersed in a second fluid medium is discussed. A method of solving for the field in the internal and external fluid regions is introduced, based on finite Hankel transforms. These transforms and their inverses are constructed in such a way that the boundary conditions (continuity of pressure and normal component of particle velocity) at the spherical interface are satisfied. In particular, the inverse transforms are integrals; that is, there is a continuum of radial wavenumbers. This contrasts with the more usual formalism, involving a Fourier–Bessel series taken over a discrete distribution of radial wavenumbers. The latter type of inversion formula is suitable only for problems involving relatively simple boundary conditions (e.g., Dirichlet or Neumann). Using the new technique, an exact analytical solution is given for the acoustic field in both the sphere and the surrounding fluid.

Reflection of sound at an interface, taking into account mass and heat transport across it

With the aid of an equation which was derived by Meinhold-Heerlein in 1973, five boundary conditions are given for a two-phase system. These boundary conditions include the two of classical acoustics, namely, steadiness of pressure and of the normal component of particle velocity across the interface. They permit a calculation of coefficients of reflection and transmission which obtain the classical acoustic coefficients as leading terms. Moreover, three transformation coefficients are given, describing the movement of the interface and the propagation of heat waves in the liquid and vapour. The time-averaged energy dissipation is calculated.

A finite-difference treatment of interface conditions for the parabolic wave equation: The horizontal interface

An elegant finite-difference technique applicable to the parabolic wave equation is developed to handle the boundary conditions at the interface between two media with different sound speeds and densities. Continuity of pressure and continuity of the normal component of particle velocity are preserved at the interface. The method is designed to be implicit and is unconditionally stable. A complete mathematical treatment for the case of a horizontal interface is described.

A finite-difference treatment of interface conditions for the parabolic wave equation: The irregular interface

A finite-difference solution to the parabolic wave equation is extended to treat an irregular interface. Interface conditions are developed to preserve continuity of pressure and continuity of the normal component of particle velocity at the boundary between media having different sound speeds and densities. A complete mathematical treatment for the case of an irregular interface is presented. To demonstrate the method, numerical results are obtained for sound propagation from deep to shallow water.

Absorption by Sound-Absorbent Spheres

The absorption of a plane wave of sound by a sphere is computed. The calculations are based on the assumption that the complex ratio of sound pressure at a point on the sphere's surface to the normal component of particle velocity is a constant independent of the direction of incidence (“normal impedance assumption”). Absorption measurements were made on hair felt-covered spheres placed in a reverberation room, and were compared with the computed absorption by means of the reverberation room statistics appropriate for spheres. The theory and measurements both show that absorbent spheres can have absorption coefficients greater than unity. The discrepancies between theoretical and experimental coefficients seem to indicate that the normal impedance assumption is not valid for the hair felt used in the experiments.

Absorption by sound-absorbent spheres

The absorption of a plane wave of sound by a sphere is computed. The calculations are based on the assumption that the complex ratio of sound pressure at a point on the sphere's surface to the normal component of particle velocity is a constant independent of the direction of incidence (“normal impedance assumption”). Absorption measurements were made on hair felt‐covered spheres placed in a reverberation room, and were compared with the computed absorption by means of the reverberation room statistics appropriate for spheres. The theory and measurements both show that absorbent spheres can have absorption coefficients greater than unity. The discrepancies between theoretical and experimental coefficients seem to indicate that the normal impedance assumption is not valid for the hair felt used in the experiments.