Pressure Wave Model Research Articles

A real-time pressure wave model for knock prediction and control

This article develops a control-oriented real-time zero-dimensional knock pressure wave model for spark-ignited engines based on the reaction-based two-zone combustion model developed earlier. This knock pressure wave model is capable of predicting the in-cylinder pressure oscillations under knocking combustion in real-time and can be used for the model-based knock prediction and control. A pressure wave equation including the knock deadening behavior is proposed, simplified, and used to calculate the pressure perturbations generated by knock combustion. The boundary and initial conditions at knock onset are analyzed and the analytic solution of the pressure wave equation is obtained. The model is calibrated and validated over two engine operating conditions at knock limit. The chemical kinetic-based Arrhenius integral and the maximum amplitude of pressure oscillations are used as the evaluation methods for knock onset and intensity prediction, and the knock frequency is studied using a fast Fourier transform of the filtered in-cylinder pressure oscillations. The simulation results show that the proposed knock pressure wave model is able to predict the knock onset timing, frequency, and intensity accurately under two engine operating conditions. Furthermore, the knock characteristics associated with gas mixture properties at intake valve closing is analyzed based on the experimental data, and their effect to knock cycle-to-cycle variation is also studied for the proposed model.

Considerations for Choosing Sensitive Element Size for Needle and Fiber-Optic Hydrophones—Part I: Spatiotemporal Transfer Function and Graphical Guide

The spatiotemporal transfer function for a needle or reflectance-based fiber-optic hydrophone is modeled as separable into the product of two filters corresponding to frequency-dependent sensitivity and spatial averaging. The separable hydrophone transfer function model is verified numerically by comparison to a more general rigid piston spatiotemporal response model that does not assume separability. Spatial averaging effects are characterized by frequency-dependent "effective" sensitive element diameter, which can be more than double the geometrical sensitive element diameter. The transfer function is tested in simulation using a nonlinear focused pressure wave model based on Gaussian harmonic radial pressure distributions. The pressure wave model is validated by comparing to experimental hydrophone scans of nonlinear beams produced by three source transducers. An analytic form for the spatial averaging filter, applicable to Gaussian harmonic beams, is derived. A second analytic form for the spatial averaging filter, applicable to quadratic harmonic beams, is derived by extending the spatial averaging correction recommended by IEC 62127-1 Annex E to nonlinear signals with multiple harmonics. Both forms are applicable to all hydrophones (not just needle and fiber-optic hydrophones). Simulation analysis performed for a wide variety of transducer geometries indicates that the Gaussian spatial averaging filter formula is more accurate than the quadratic formula over a wider range of harmonics. Additional experimental validation is provided in Part II. Readers who are uninterested in hydrophone theory may skip the theoretical and experimental sections of this paper and proceed to the graphical guide for practical information to inform and support selection of hydrophone sensitive element size (but might be well advised to read the Introduction).

Needle hydrophone transfer function model for characterizing therapeutic transducers

A rigid piston model has been developed to predict needle hydrophone transfer functions. The model predicts that “effective” sensitive element diameter depends on the frequency and can exceed geometrical sensitive element diameter by a factor of up to 2.25. The model predicts harmonic distortion for hydrophone measurements of focused pressure waves, which were modeled using nonlinear plane wave theory for spectral characteristics and Gaussian radial pressure distributions. The pressure wave model was validated by comparing to hydrophone (sensitive element diameter: 85 microns) measurements performed in focal planes of source transducers (3.5 MHz, 64 mm diameter, 89 mm focus and 5 MHz, 19 mm diameter, 38 mm focus). Root mean squared difference (RMSD) between the model fit and measured relative strengths of the first four harmonics was 9% (3.5 MHz transducer) and 11% (5 MHz transducer) where Blackstock’s sigma parameter (JASA, 39, 1019–1026, 1966), which measures extent of nonlinearity, was optimized to fit the data. RMSD between model and measured half width half maxima was 10 ± 5%. Tone bursts from each transducer were measured using needle hydrophones (sensitive element diameters: 200, 400, 600, and 1000 microns). RMSD between model and measured harmonic distortion was 12 ± 4% for the first four harmonics.

Validation of the pressure wave model in the aspect of special structures endurance

Abstract The article presents results of the research on the validation of impact wave in the aspect of special structures’ endurance. Impact waves have been examined according to numerical and analytical methods. In order to verify the results obtained, a workstation for experimental research had been prepared. Before conducting the experiment, approximate pressure value had been checked empirically. The pressure had been measured using sensors for free wave measurements. The topic of the paper is empirical examination of the phenomenon of explosion in the aspect of the free wave pressure. Due to a difficulty of the issue, it was necessary to conduct complex examination of the phenomenon for various charges. The paper examines cases of spherical charge explosions with a balanced mass of 1 kg TNT.

Linear stability analysis for severe slugging in air–water systems considering different mitigation mechanisms

This work presents a numerical study of the effects of mechanisms such as gas injection, choking and different boundary conditions on the stability of the stationary state for two-phase flows in vertical and catenary pipeline–riser systems. Numerical linear stability analysis is performed to a suitable mathematical model for the two-phase flows in a pipeline–riser system. The mathematical model considers the continuity equations for the liquid and gas phases and a simplified momentum equation for the mixture, neglecting inertia (NPW – no pressure wave model). A drift flux correlation, evaluated in local conditions, is utilized as a closure law. Gas injection and a choke valve are added, respectively, at the riser bottom and top. The extended model is applied to air–water pipeline–riser systems reported in the literature. Numerical linear stability analysis results are compared with experimental and numerical results reported in the literature with excellent agreement.

Numerical Modeling and Simulation of Pressure Wave in Combination Electronic Unit Pump High Pressure Pipeline

High pressure (HP) fuel pipeline is one of the major components of Combination Electronic Unit Pump (CEUP) diesel fuel injection system and has significant contribution in building up of high pressure required during fuel injection cycle. A MATLAB numerical model of pressure wave inside HP fuel pipeline of CEUP system using damped wave equation has been developed in MATLAB to study and simulate pressure wave propagation through fuel pipeline at various operating conditions of diesel engine. Finite Difference method has been applied to model and simulate pressure equation at various equidistant locations of fuel pipeline. Dynamic variations of fuel properties as a function of varying pressure have also been incorporated. The MATLAB model has been validated by comparing simulated pressures with those of experimentally validated AMESim numerical model of CEUP fuel injection system. Quantitative comparisons were also done using Root Mean Square Error (RMSE) and Index of Agreement (IA). Results show that MATLAB numerical model is quite accurate especially at low cam rotational speeds and low cam angles.

238 集中系モデルによる水中圧力波の解析

A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effects in the propagation medium. In the previous papers, a concentrated mass model was proposed to analyze a nonlinear pressure wave phenomenon in air. In this paper, we apply the model to pressure wave in water. When an ultrasonic pressure wave propagates in water, the wave often changes to a shock wave in shorter distance than low-frequency wave. And, when water contains air bubbles, speed of sound decrease significantly by bubbles. The purpose of this study is to establish a practical analytical model to analyze these phenomenon. To confirm the validity of the proposed the model of supersonic pressure wave, we compare the experimental result of supersonic pressure wave by Burox et al. with the numerical results obtained by the concentrated mass model. Furthermore we perform experiments of water containing air bubbles, and compare the experimental result with numerical result obtained by the concentrated mass model.

Numerical simulation of the porous filter properties for the internal arc mollifying effects

A mathematical model and numerical experiments of pressure wave impacts with a porous medium are presented to simulate the valve burst out of a medium voltage switchgear and to evaluate the protection filter efficiency. A simplified one-dimensional gas flow model in porous medium with variable porosity is used. To solve numerically the governing equations, we employed the numerical method presented in Rochette et al. (2005) [18] to take into account the non-conservative term P(∂ ϕ/∂ x). Three sets of test are performed to study several filter prototypes. The objective is to provide a filter which does not produce a high reflected wave and cools enough the ejected hot gas. We first consider filters with variable porosity and simulate the interaction with an incident pressure wave, then we consider two types of granular material to characterize their incidence on the flow and finally, we simulate two different fluid flows (air and SF6) going through the porous medium.

Model properties relevant to laser ablation of moderately absorbing polymers

A set of polymers including biopolymers and polymers from renewable resources are studied, with attention paid to their capability to form a foamy surface layer by laser irradiation. A model of laser-induced pressure wave is discussed, with its tensile tail giving rise to a fast and dense nucleation of cavities that can expand to microbubbles when filled with ablation gas. The intensity of the pressure wave has a maximum for an absorption coefficient of ∼1000 cm−1. Polyvinyl acetate, studied as a prototype polymer experimentally and by modeling, allows discussing the role of the viscosity drop in the dynamics of the laser-induced cavitations. In the Zeldovich frequency factor, a T (temperature) and P (pressure) dependent model of viscosity, and a T-dependent model of surface tension are introduced. It is further suggested that the well-known free-volume nanoholes existing in the material before the irradiation can constitute the nuclei of importance and that their concentration is one of the factors controlling the pre-exponential factor in the nucleation rate law.

Modeling the dynamics of one laser pulse surface nanofoaming of biopolymers

Self standing films of biopolymers like gelatine, collagen, and chitosan irradiated with single nanosecond or femtosecond laser pulse easily yield on their surface, a nanofoam layer, formed by a cavitation and bubble growth mechanism. The laser foams have interesting properties that challenge the molecular features of the natural extracellular matrix and which make them good candidates for fabrication of artificial matrix (having nanoscopic fibers, large availability of cell adhesion sites, permeability to fluids due to the open cell structure). As part of the mechanistic study, the dynamics of the process has been measured in the nanosecond timescale by recording the optical transmission of the films at 632.8 nm during and after the foaming laser pulse. A rapid drop 100→0% taking place within the first 100 ns supports the cavitation mechanism as described by the previous negative pressure wave model. As modeled a strong pressure rise (∼several thousands of bar) first takes place in the absorption volume due to pressure confinement and finite sound velocity, and then upon relaxation after some delay equal to the pressure transit time gives rise to a rarefaction wave (negative pressure) in which nucleation and bubble growth are very fast.

A mathematical model and numerical simulation of pressure wave in horizontal gas-liquid bubbly flow*

Abstract By using an ensemble-averaged two-fluid model, with valid closure conditions of interfacial momentum exchange due to virtual mass force, viscous shear stress and drag force, a model for pressure wave propagation in a horizontal gas-liquid bubbly flow is proposed. According to the small perturbation theory and solvable condition of one-order linear uniform equations, a dispersion equation of pressure wave is induced. The pressure wave speed calculated from the model is compared and in good agreement with existing data. According to the dispersion equation, the propagation and attenuation of pressure wave are investigated systemically. The factors affecting pressure wave, such as void fraction, pressure, wall shear stress, perturbation frequency, virtual mass force and drag force, are analyzed. The result shows that the decrease in system pressure, the increase in void fraction and the existence of wall shear stress, will cause a decrease in pressure wave speed and an increase in the attenuation co...

Study of Rotational Noise Reduction for Axial Flow Fan. (Analysis and Estimation of Secondary Fan-Noise Component).

Rotational noise is one of the main sources of noise emitted by a fan. This type of noise has discrete frequency components, and is so severe that many methods have been developed for its reduction. There have been few studies on rotational noise, however, to clarify the generation mechanism and determine concrete methods for noise reduction. In the present study the spacings of the blades were changed and comparisons were made with a fan having equally spaced blades. The discrete frequency components were found to be suppressed in the fan with unequally spaced blades and the noise tended to become white noise if the blade spacing and blade setting angles were properly chosen. The instantaneous pressure change on the shroud due to blade passing was examined since it is closely related to the discrete frequency components of noise. By decomposing the measured pressure change in terms of a Fourier series the characteristics of rotational noise were analyzed and compared with simulation results obtained using a pressure wave model. The prediction of the rotational noise emitted by axial fans with unequally spaced blades is presented and found to agree well with the experimental results.