Calculation Of Pressure Field Research Articles

Simulation Opportunities by a Three-dimensional Calculation of Injection Moulding based on the Finite Element Method

Abstract The simulation of injection moulding is essential to meet quality requirements and to increase the efficiency of the design process. In this paper a 3D-finite element model for the simulation of injection moulding is presented. The model's capability comprises the calculation of velocity, pressure and temperature fields as well as the prediction of the flow front position. The numerical approach is mainly based on the Galerkin formulation. Special emphasis is placed on the handling of polymer compressibility in order to enable a realistic simulation of the packing phase. The numerical efficiency has been largely enhanced through the employment of an automatic time step control. In order to demonstrate the code's capabilities and outline advantages and disadvantages over other simulation systems, the calculation results are compared to experimental data and to results obtained from other numerical models.

Modeling of linear pressure fields in sonochemical reactors considering an inhomogeneous density distribution of cavitation bubbles

Although a lot of experimental work was done on the investigation of chemical effects of power ultrasound, only very few efforts were directed towards engineering aspects, like optimum design and scale-up of sonochemical reactors. This paper deals with the calculation of acoustic fields and energy density distributions in sonochemical reactors with an inhomogeneous distribution of cavitation bubbles, which are a basis for the design of sonochemical reactors of various geometrical shapes. The time-dependent wave equation applied to a damped wave propagation represents the basis of our theory. A new model is presented for the numerical calculation of three-dimensional pressure fields in liquids taking into account an inhomogeneous distribution of wave parameters due to the presence of the cavitation bubbles. Compared to a single-phase fluid, gas bubbles in a liquid lead to a heavy change of phase velocity and sound attenuation. These changes are calculated for every time step and volume element of the reactor. Employing this technique, one should be able to calculate the pressure field in a sonochemical reactor with a sufficient accuracy which serves to predict the spatial distribution of cavitation events.

Compressible Narrow Groove Analysis—Part 2: Computation of Pressure Field in a Spherical Device Rotating in Either Direction

Compressible Narrow Groove Analysis, as derived in a companion paper (Pan, 1998), is a model implementation of Thin Film High-Resolution Modeling for gas films. This paper describes the numerical procedure to compute the pressure field in a centered spherical device, which has general design features originally intended for a high performance gas bearing gyroscope (Keating and Pan, 1968). The number of groove patterns is varied to bring out the significance of the local compressibility number. Increased local compressibility, associated with reduced number of groove patterns, causes successive degradation of the pressurization capacity until it is entirely suppressed at 32 groove patterns. Further study is made with reversed rotation to create a high vacuum state in the gas film concurrent with a large compressibility number. The evacuation operation (with reversed rotation) is relatively insensitive to the number of groove patterns, but is highly dependent on the accommodation coefficient. Experience in preparing these examples lends evidence to the robustness of Thin Film High-Resolution Modeling. Trouble free iterative computations are routinely performed for the local Knudsen number in excess of 109 and the effective local compressibility number larger than 100.

VIBRO–ACOUSTIC ANALYSIS AND IDENTIFICATION OF DEFECTS IN ROTATING MACHINERY, PART I: THEORETICAL MODEL

The objective of our work is the association of vibratory diagnosis knowledge with an acoustic part including frequential and spatial criteria for the identification of noise sources in rotating machinery. To control parameters for this difficult problem, one proceeds by stages and with confrontation of theoretical and experimental methods. This paper presents the theoretical modelling of a rotor on bearings system, with a simulation of several defects such as misalignment, imbalance and defective bearings. Pressure field calculations are performed with the help of an effective method based on modelling a structure by a set of point sources placed on the radiating surface.

Modeling of Three-Dimensional Linear Pressure Fields in Sonochemical Reactors with Homogeneous and Inhomogeneous Density Distributions of Cavitation Bubbles

A new model is presented for the numerical calculation of pressure fields in liquids with an inhomogeneous distribution of cavitation bubbles. To calculate the pressure field in a homogeneous single-phase fluid, the Helmholtz integral and the Kirchhoff integral are solved numerically. The Helmholtz integral equation and the Kirchhoff integral are used for the calculation of the acoustic field in a homogeneous fluid for all kinds of transducers of various shapes. The first term of the integral equation embodies a simple superposition of the pressure fields of several point sources, which serves to simulate a harmonic vibrating surface, while the Kirchhoff integral calculates the pressure field which emerges from the boundaries. With a new technique the three-dimensional time-independent pressure field is calculated gradually in the beam direction. With this procedure one is able to combine the Helmholtz integral with a wave propagation in liquids with inhomogeneous distributions of cavitation bubbles. Compared to a single-phase fluid, gas bubbles in a liquid lead to a heavy change of phase velocity and sound attenuation. These changes are determined and considered for every step in the beam direction. With this technique, one should be able to calculate the pressure field in a sonochemical reactor with a sufficient approximation which serves to predict the spatial distribution of cavitation events. These events are related to the yield of chemical reactions.

The calculation of the transient near and far field of a baffled piston using low sampling frequencies

A method is presented to calculate the near- and far-field transient radiation of acoustical transducers using low sampling frequencies. The method is based on the classical impulse response approach and on the fact that in practical use the spectrum of the excitation function of a transducer is band limited. This makes it possible to use a smoothed version of the impulse response function. A simple expression to calculate this smoothed function, for a rectangular or circular transducer, is derived. The proposed solution allows accurate computation of pressure fields and backscatter signals, while avoiding high sampling frequencies in the far field of the transducers. Several examples illustrate the accuracy of this new solution and its use for spectral analysis of simulated reflected signals.

Characterization of ultrasonic transducers by means of double-exposure holographic interferometry

Double-exposure holographic interferometry is applied to measure the surface displacements of ultrasonic transducers. Interferograms revealing detail surface displacements are produced using iron-doped lithium niobate crystals as the recording medium. Lead zirconate titanate disks poled in the longitudinal thickness mode possessing deposited, shaped electrodes are examined. Transducers with circular, strip, rectangular, and rosette electrode shapes are investigated. The displacement measurements reveal that the electrode “drags” the rest of the transducer surface. Thus the unmetallized portion of the transducer also contributes to the acoustic field. Pressure field calculations using the experimentally measured displacements are performed. It is shown that proper geometrical design of the electrode yields reduction of the sidelobes in the far field and smoothing of the maxima and minima in the near field, and improved focusing via reduced acoustic beam divergence. Most importantly, this work reveals that the unmetallized portion of the transducer contributes significantly to the displacement and to the resulting pressure fields.

Pressure field calculation methods for thin-layer viscous gas flows in the presence of discrete injection

Methods of solving nonlinear boundary problems describing the pressure distribution in multiply connected thin-layer viscous gas flows in the presence of discrete injection which make it possible to take completely into account the number, arrangement and dimensions of the injection holes and the relative motion of the surface bounding the layer are proposed. The results of calculations for a segmental and a closed annular layer are presented.

Efficient angular spectrum decomposition of acoustic sources. II. Results

For pt.I see ibid., vol.40, no.3, p.238-49 (1993). Results of angular spectrum computations are presented for three applications: general decomposition, pressure field calculation, and modeling of pulse-echo measurements. Wherever possible, analytical (exact) results are used as reference for the decomposition results. This permits the accuracy of the angular spectrum decomposition to be evaluated for specific choices of M and N where M is the number of samples across the maximum characteristic length, d, of the source region and N is the total number of samples along each side of the source decomposition plane, and for both sampling techniques. Based on the results for the three applications, guidelines for choosing M and N are presented in a graphical format.

Diffraction impulse response of rectangular transducers

A closed-form expression for the impulse velocity potential of rectangular pistonlike transducers, without any far field or paraxial approximation, is presented. The classical time-domain impulse response approach is used considering free-field, rigid baffle, and pressure release boundary conditions. Previous approaches to the rigid baffled rectangular piston require the use of superposition methods in order to find a general solution numerically. These must add or subtract, according to the field point location, the analytical expressions that were derived only for specific field points or geometrical regions. In this paper the complexity introduced by the geometrical discontinuities of rectangular apertures is analyzed. A new compacting methodology is proposed and applied to obtain a general solution for the impulse response. This new solution provides the value of the impulse response directly in the time domain, without requiring superposition methods. In addition, a closed-form solution for the pressure impulse response is also presented. This can be useful for physical insight and a qualitative analysis of transient and continuous wave pressure fields. Also included is a description of the temporal behavior of the impulse velocity potential and the pressure impulse response for field points in different regions. The proposed solution allows an efficient and accurate computation of pressure fields under realistic excitations. Several examples illustrate the use of this new solution in the computation of transient pressure waveforms, when wideband and relatively narrow-band excitation pulses are used. Three-dimensional plots of the peak amplitude of the transient pressure near field are presented, and certain characteristics are analyzed using the pressure impulse response.

Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers

A method for simulation of pulsed pressure fields from arbitrarily shaped, apodized and excited ultrasound transducers is suggested. It relies on the Tupholme-Stepanishen method for calculating pulsed pressure fields, and can also handle the continuous wave and pulse-echo case. The field is calculated by dividing the surface into small rectangles and then Summing their response. A fast calculation is obtained by using the far-field approximation. Examples of the accuracy of the approach and actual calculation times are given.

Airflow patterns for various approximations to velocity—pressure-gradient data

The effect of various ways of approximating velocity—pressure-gradient data on the computation of pressure fields in a grain bin is studied. The experimental data are also approximated by a cubic spline. The usual approximating formulas produce differing pressure patterns whenever the plenum pressure is sufficiently high to introduce velocities beyond the measured range.

Sound pressure near the focal area of an ultrasonic lens

A method of computing the pressure distribution of an ultrasonic single-surface lens is derived. The method is based on an impulse response method used in pressure field calculations of spherically curved ultrasonic transducers. By a simple transformation the lens is transformed into a curved transducer having the same focusing properties as the lens. The pressure distribution of this transducer is then computed using the rapid impulse response method. Expressions for focal point size and pressure gains are given. An example of the pressure distribution near the focal point of a lens is given pictorially.

Study on Cavitation Erosion

In this paper, authors conducted experimental investigations on cavitation damage to specimens of pure aluminum placed in a venturi type cavitation tunnel. The main object of experiments is to confirm the relation between damage intensity and flow velocity. Conclusions obtained are as follows: 1. Cavitation damage intensity is largely affected by flow velocity, for instance, the number of erosion pits varies with the 5th to 6th power of flow velocity. 2. Erosion pits are generated near the end of fixed-cavity. 3. Distribution of erosion pits are supposed to be caused by difference of initial radius of a collapsing bubble and oscillatory variation of length of fixed-cavity. Simplified equation of bubble radius is solved numerically. From the calculation of pressure field around a collapsing bubble, following results are obtained: 4. Maximum pressure on bubble wall varies with the 11th power flow velocity. 5. Maximum velocity of bubble wall varies with the 5th power of flow velocity. 6. On the assumption that damage intensity increases in proportion to impulse provided to the surface of specimens, these calculations show good agreement with experimental results.