The study of acoustic scattering from a single sound-permeable sphere

2018 ◽  
Vol 13 (4) ◽  
pp. 79-91 ◽  
Author(s):  
E.Sh. Nasibullaeva
Keyword(s):  
Speed Of Sound ◽  
Numerical Technique ◽  
Acoustic Scattering ◽  
Computer Time ◽  
Physical Parameters ◽  
Fast Method ◽  
Scattering Field ◽  
Permeable Sphere ◽  
Test Verification ◽  
Good Agreement

The paper presents a generalized mathematical model and numerical investigation of the problem of acoustic scattering from a single sound-permeable sphere during the passage of two types of waves - spherical from a monopole radiation source and a plane one. In solving the Helmholtz equation, a numerical technique based on the fast method of multipoles is used, which allows achieving high accuracy of the results obtained at the lowest cost of computer time. The calculations are compared with known experimental data and a good agreement is obtained. The formulas for calculating the main characteristic of the scattering field (the total scattering cross section) for a sound-permeable sphere are generalized. The effect on this characteristic of the physical parameters of media outside and inside the sphere, such as the density and speed of sound, is shown. A numerical parametric analysis of the pressure distribution around a single sound-permeable sphere for different values of the wave radius, density, and speed of sound of the outer and inner medium of the sphere is carried out. The obtained results will later be used for test verification calculations for the numerical solution of the generalized problem of acoustic scattering of a set of sound-permeable spheres (coaxial or arbitrarily located in space).

Investigation of scattering from soundproof single sphere under external influence

2017 ◽  
Vol 12 (1) ◽  
pp. 73-82 ◽  
Author(s):  
E.Sh. Nasibullayeva
Keyword(s):  
Numerical Technique ◽  
Spherical Wave ◽  
Complex Impedance ◽  
Computer Time ◽  
Fast Method ◽  
External Influence ◽  
Scattering Field ◽  
Total Scattering Cross Section ◽  
Single Sphere ◽  
Good Agreement

The scattering from a single soundproof sphere is investigated during the passage of two types of waves: a spherical wave from a monopole radiation source and a plane wave. In solving the Helmholtz equation, a numerical technique based on the fast method of multipoles is used, which allows achieving high accuracy of the results obtained, and also minimizing computer time. The calculations are compared with known experimental data and a good agreement is obtained. Formulas are obtained for the main characteristic of the scattering field (the total scattering cross-section) for a sphere with an arbitrary acoustic impedance. Its dependence on the main parameters of the ”sphere – environment“ system for two kinds of the incident field is shown. A numerical parametric analysis of the value of the potential on the surface of a sphere for different values of its radius, complex impedance, the type of external influence, etc.

Numerical simulation of acoustic scattering from coaxial sound-penetrable spheres

2019 ◽  
Vol 14 (2) ◽  
pp. 115-124
Author(s):  
E.Sh. Nasibullaeva
Keyword(s):  
Radiation Source ◽  
Numerical Study ◽  
Numerical Technique ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Computer Time ◽  
Fixed Number ◽  
Helmholtz Equations ◽  
Spherical Waves ◽  
Penetrable Spheres

This paper presents a generalisation of the mathematical model and numerical study of the acoustic scattering problem from multiple spheres in the case of spheres through which the wave passes and whose centers are located on the same axis (the case of sound-penetrable and coaxial spheres) under the action of spherical waves from a monopoly radiation source arbitrarily located in space. When solving the Helmholtz equations, a numerical technique based on the fast multipole method has been adapted for this task, which allows one to achieve high accuracy of the results obtained with minimal computer time. Comparison of the different approaches to truncation infinite series in the expansion showed the following: the result with a good degree of accuracy by a single calculation gives approach based on the truncation of all the rows with a fixed number in each expansion, and the result with a certain degree of accuracy gives an approach based on comparing two consecutive values of the sum of the series. A numerical parametric analysis of the pressure distribution inside and outside the spheres is carried out for various values of their radii, physical characteristics of the external and internal media, the number of spheres, the distances between the centers of the spheres, the frequency of exposure and the location of the monopole radiation source. It is shown that at certain values of the parameters, the appearance of zones of decrease or increase in pressure behind sound-penetrable spheres is possible. The obtained results will further allow to carry out test calculations to verify the general numerical algorithm for the case of a multitude of spheres arbitrarily located in space.

Investigation of acoustic scattering from a pair soundproof spheres under external influence

2019 ◽  
Vol 14 (1) ◽  
pp. 44-51 ◽  
Author(s):  
E.Sh. Nasibullaeva
Keyword(s):  
Mathematical Model ◽  
Radiation Source ◽  
Hard Spheres ◽  
Numerical Technique ◽  
Fast Multipole Method ◽  
Spherical Wave ◽  
Acoustic Scattering ◽  
Practical Interest ◽  
Computer Time ◽  
Helmholtz Equations

A mathematical model extension is presented and numerical studies were made for the problem of acoustic scattering from two soundproof spheres (the case of hard spheres) with an arbitrary acoustic impedance under the action a spherical wave from a monopole radiation source arbitrarily located in space. The case of two spheres is of practical interest, since, on the one hand, the scattered fields from the spheres interact with each other, and on the other hand, the interaction is simple enough for it to be studied in detail. When solving the Helmholtz equations, a numerical technique based on the fast multipole method is used, which allows to achieve high accuracy of the results obtained with minimal computer time. The testing of the algorithm was carried out on the basis of the known data (from the literature) of the response on the surface of one of the spheres in the case when the axis connecting the monopole radiation source and the center of the first sphere is perpendicular to the axis connecting the centers of the two spheres. The pressure distribution around the spheres is investigated for different values of the distance between the centers of the spheres and the arbitrary location of the monopole radiation source in space. It is shown that with certain parameters of the system, the presence of a second sphere can lead to the appearance of an increase or decrease zone of pressure. The obtained results will further allow generalizations of the mathematical model to the cases of acoustic scattering from a pair of sound-permeable spheres (cases of gas bubbles or liquid droplets) and many spheres (both coaxially and arbitrarily arranged in space), and can also be used for test calculations during verification numerical solution of these generalized problems.

scholarly journals Thermal ignition of a combustible over an inclined hot plate

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Salaika Parvin ◽  
Nepal Chandra Roy ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Mixed Convection ◽  
Convection Flow ◽  
Physical Parameters ◽  
Thermal Ignition ◽  
Mixed Convection Flow ◽  
Flow Properties ◽  
Continuous Transformation ◽  
Hot Plate ◽  
Ignition Characteristics ◽  
Good Agreement

AbstractIn this study, the ignition characteristics and the flow properties of the mixed convection flow are presented. Detailed formulations of the forced, natural and mixed convection problems have been discussed. In order to avoid inconvenient switch between the forced and natural convection we introduce a continuous transformation in the mixed convection. We make a comparison between these situations which reveal a good agreement. For mixed convection flow, the ignition distance is explicitly expressed as a function of the Prandtl number, reaction parameter and wall temperature. It has been observed that owing to the increase of the aforesaid parameters, the thermal ignition distance is reduced. Numerical results are illustrated for velocity, temperature, and concentration for different physical parameters. Furthermore, the development of combustion is presented by using streamlines, isotherms and isolines of fuel and oxidizer.

scholarly journals Couple stress fluid flow due to slow steady oscillations of a permeable sphere

2020 ◽  
Vol 9 (1) ◽  
pp. 352-360
Author(s):  
P. Aparna ◽  
P. Padmaja ◽  
N. Pothanna ◽  
J.V. Ramana Murthy
Keyword(s):  
Fluid Flow ◽  
Couple Stress ◽  
Bessel Functions ◽  
Pressure Field ◽  
Flow Region ◽  
Couple Stress Fluid ◽  
Physical Parameters ◽  
External Flows ◽  
Steady Oscillations ◽  
Permeable Sphere

AbstractThe study of oscillating flow of a Couple Stress fluid past a permeable sphere is considered. Analytical solution for the flow field in terms of stream function is obtained using modified Bessel functions. The formula for Drag acting on the sphere due external flow is evaluated. Pressure field for the flow region past and inside the sphere is obtained. Effects of physical parameters like couple stress parameter, permeability, frequency and geometric parameters on the drag due to internal and external flows are represented graphically. It is observed that the drag for viscous fluid flow will be less than the case of couple-stress fluid flow and hence couple stress fluids offer resistance for flow.

EQUATION OF STATE FOR HOT GLUON PLASMA WITH EFFECTIVE TWO LOOPS

2001 ◽  
Vol 16 (27) ◽  
pp. 1751-1759 ◽  
Author(s):  
XIN WANG ◽  
JIARONG LI ◽  
JUEPING LIU
Keyword(s):  
Equation Of State ◽  
Gluon Plasma ◽  
Physical Parameters ◽  
Finite Width ◽  
Debye Screening ◽  
Debye Mass ◽  
Analytical Results ◽  
Good Agreement ◽  
Hard Thermal Loops

We present analytical results for the equation of state for hot gluon plasma obtained with an effective perturbation based on hard thermal loops resummation theory. The effective two-loop results depend on Debye screening and finite width of gluons as physical parameters. Considering next-to-leading Debye mass and finite width effects, we find the equation of state to be in good agreement with recent lattice results for T≳2T c .

Linear iterative refinement method for the rapid simulation of borehole nuclear measurements: Part I — Vertical wells

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. E9-E29 ◽  
Author(s):  
Alberto Mendoza ◽  
Carlos Torres-Verdín ◽  
Bill Preeg
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Numerical Technique ◽  
Integral Form ◽  
Computer Time ◽  
Iterative Refinement ◽  
Detector Response ◽  
Layer By Layer ◽  
Response Factors ◽  
Refinement Method

As a result of its high numerical accuracy and versatility to include complex tool configurations and arbitrary spatial distributions of material properties, the Monte Carlo method is the foremost numerical technique used to simulate borehole nuclear measurements. Although recent advances in computer technology have considerably reduced the computer time required by Monte Carlo simulations of borehole nuclear measurements, the efficiency of the method is still not sufficient for estimation of layer-by-layer properties or combined quantitative interpretation with other borehole measurements. We develop and successfully test a new linear iterative refinement method to simulate nuclear borehole measurements accurately and rapidly. The approximation stems from Monte Carlo-derived geometric response factors, referred to as flux sensitivity functions (FSFs), for specific density and neutron-tool configurations. Our procedure first invokes the integral representation of Boltzmann’s transport equation to describe the detector response from the flux of particles emitted by the radioactive source. Subsequently, we use theMonte Carlo N-particle (MCNP) code to calculate the associated detector response function and the particle flux included in the integral form of Boltzmann’s equation. The linear iterative refinement method accounts for variations of the response functions attributable to local perturbations when numerically simulating neutron and density porosity logs. We quantify variations in the FSFs of neutron and density measurements from borehole environmental effects and spatial variations of formation properties. Simulations performed with the new approximations yield errors in the simulated value of density of less than [Formula: see text] with respect to Monte Carlo-simulated logs. Moreover, for the case of radial geometric factor of density, we observe a maximum shift of [Formula: see text] at 90% of the total sensitivity as a result of realistic variations of formation density. For radial variation of neutron properties (migration length), the maximum change in the radial length of investigation is [Formula: see text]. Neutron porosity values simulated with the new approximation differ by less than 10% from Monte Carlo simulations. The approximations enable the simulation of borehole nuclear measurements in seconds of CPU time compared to several hours with MCNP.

Analytical and Experimental Simulation of Loose Pedestal Dynamic Effects on a Rotating Machine Vibrational Response

1991 ◽  
Author(s):  
Pavel Goldman ◽  
Agnes Muszynska
Keyword(s):  
Excitation Frequency ◽  
Experimental Studies ◽  
Experimental Simulation ◽  
Physical Parameters ◽  
Vibrational Response ◽  
Rotating Machine ◽  
Qualitative Pattern ◽  
The Impact ◽  
Good Agreement ◽  
Periodic Changes

Abstract This report presents experimental, analytical, and numerical results describing vibrational phenomena in a rotating machine with one loose pedestal. The loose-pedestal machine rotor vibrations represent unbalance-related excited vibrations of synchronous and fractional subsynchronous regimes. In this study the loose-pedestal machine is first simulated by a simple vibrating beam excited by a shaker mounted on it. The shaker simulates an unbalanced machine rotor. The beam occasionally enters in contact with the foundation. The excited vibrations are modified by impacting occurrences, and by periodic changes in system stiffness. A new model of the impact has been developed. The results of analytical and experimental studies stand in a good agreement. They illustrate the existence of the synchronous regime and several subsynchronous fractional regimes in various excitation frequency ranges. The analysis adequately predicts the occurrence of these regimes and determines the physical parameters affecting them. The analytical and experimental results are then compared with the responses of experimental rotor rig with one bearing pedestal looseness. They show the same qualitative pattern.

scholarly journals Contact angle of water on iron ore fines: Measurement and analysis

2015 ◽  
Vol 51 (1) ◽  
pp. 33-40 ◽  
Author(s):  
X.B. Huang ◽  
X X.W. ◽  
J.J. Song ◽  
C.G. Bai ◽  
R.D. Zhang ◽  
...  
Keyword(s):  
Contact Angle ◽  
Iron Ore ◽  
Contact Angles ◽  
Physical Parameters ◽  
Iron Ores ◽  
New Model ◽  
Pressure Method ◽  
Measurement And Analysis ◽  
Iron Ore Fines ◽  
Good Agreement

The relative contact angle (?RCA) for seven iron ore fines was measured by using Washburn Osmotic Pressure method under laboratory conditions. By choosing cyclohexane as the reference that can perfectly wet iron ore particles, the relative contact angles were measured and varied from 57? to 73?. With the volume % of goethite (?G) as the variable, a new model for relative contact angle was developed. The expected relative contact angle for pure goethite is about 56?, while that for goethite free samples is about 77?. Physical properties, such as surface morphology (SMI) and pore volume (Vpore) can influence the relative contact angle. The ?G can be expressed as a function of SMI and VPore. Thus, we inferred that the relative contact angle is a function of ?G for the iron ores used. The measured relative contact angles were found to be in good agreement (Radj 2 >0.97) with the calculated ones based on the research from Iveson, et al. (2004). Comparing with the model developed by Iveson et al.(2004), the new model for contact angle proposed in this paper is similar, but more detailed with two meaningful physical parameters. The modification of physicochemical properties on iron ores would be another topic in the further study on granulation.

Determination of the limits of stable combustion at high supersonic flow velocities in a channel

2010 ◽  
Vol 3 (2) ◽  
pp. 47-60
Author(s):  
Alexey V. Starov
Keyword(s):  
Paper Analysis ◽  
Measurement Methods ◽  
Experimental Results ◽  
Physical Parameters ◽  
Supersonic Speed ◽  
Combustion Limits ◽  
Criterial Description ◽  
Selection Of ◽  
Good Agreement

In this paper, analysis of existing methods application of criterial description of ignition conditions and combustion break-out for summarizing of experimental results is carried out. Experimental results are obtained at investigations of hydrogen combustion in combustor with high supersonic speed of airflow. For these conditions selection of several criterions was substantiated and they have a good agreement with new experimental results. At the same time complexity of determination of experimental physical parameters, which are included in criterions, do not allow confidently to apply them for prediction of steady-state combustion limits. Therefore further accumulation of experimental data and development of measurement methods are necessary for accurate criterions obtaining.

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