On decomposition of the fundamental solution of the Helmholtz equation over solutions of iterative parabolic equations

2021 ◽  
pp. 1-14
Author(s):  
Pavel S. Petrov ◽  
Matthias Ehrhardt ◽  
Mikhail Trofimov
Keyword(s):  
Fundamental Solution ◽  
Point Source ◽  
Helmholtz Equation ◽  
Parabolic Equations ◽  
Initial Conditions ◽  
Source Model ◽  
Wide Angle ◽  
Practical Applications ◽  
Correct Point ◽  
Insight Into

Recently, it was shown that the solution of the Helmholtz equation can be approximated by a series over the solutions of iterative parabolic equations (IPEs). An expansion of the fundamental solution of the Helmholtz equation over solutions of IPEs is considered. It is shown that the resulting Taylor-like series can be easily transformed into a Padé-type approximation. In practical propagation problems such iterative Padé approximations exhibit improved wide-angle capabilities and faster convergence to the solution of the Helmholtz equation in comparison to Taylor-like expansion over IPEs solutions. A Gaussian smoothing of the expansion terms gives insight into the derivation of initial conditions consistent for IPEs, which can be used for point source simulation. A correct point source model consistent with the wide-angle one-way propagation equations is important in many practical applications of the parabolic equations theory.

Application of Inverse Analysis to Determine the Parameters of the Weighted Multi Point Source Model for the Prediction of Heat Flux From Flames

2015 ◽  
Author(s):  
R. B. Miguel ◽  
F. H. R. França ◽  
I. M. Machado ◽  
F. M. Pereira ◽  
P. R. Pagot
Keyword(s):  
Heat Flux ◽  
Point Source ◽  
Inverse Analysis ◽  
Radiant Heat ◽  
Source Model ◽  
Point Sources ◽  
Multiple Sources ◽  
Practical Applications ◽  
Extremal Optimization ◽  
Computational Resources

Thermal radiation is responsible for a substantial portion of the heat transfer from a flame. Radiative characteristics of jet fires are usually expressed through the use of the fraction of heat radiated. Detailed flame simulations provide useful information but may be prohibitive for practical applications due to the significant computational resources that are required. The weighted-multi-point-source model uses point sources with different weights to simulate the contribution of each portion of the flame. This method can give good predictions of the radiant heat flux both in the near and far fields. While previous studies used the trial-and-error approach to determine the weights of the sources, this paper proposes a method to obtain the weight of each source by inverse analysis. In the analysis, the experimental measured radiation heat flux distribution is the input data, while the weights of the sources and the fraction of heat radiated are the sought parameters. The inverse problem is formulated as an optimization problem, which is solved by the generalized extremal optimization. As will be shown in the paper, the inverse method is capable of recovering the weights of the sources that lead to results with more accuracy than the single source model or the multiple sources model with the commonly employed linear variation in the weights.

Particle motion with air resistance

2012 ◽  
Vol 8 (1) ◽  
pp. 1-15
Author(s):  
Gy. Sitkei
Keyword(s):  
Basic Equation ◽  
Initial Conditions ◽  
Equation Of Motion ◽  
Terminal Velocity ◽  
Dimensionless Form ◽  
Wood Industry ◽  
Acceptable Error ◽  
General Validity ◽  
Practical Applications ◽  
Air Resistance

Motion of particles with air resistance (e.g. horizontal and inclined throwing) plays an important role in many technological processes in agriculture, wood industry and several other fields. Although, the basic equation of motion of this problem is well known, however, the solutions for practical applications are not sufficient. In this article working diagrams were developed for quick estimation of the throwing distance and the terminal velocity. Approximate solution procedures are presented in closed form with acceptable error. The working diagrams provide with arbitrary initial conditions in dimensionless form of general validity.

Market Opportunity Analysis in Thailand: Case of Individual Power Sources by Thermoelectric-Generator Technology for Portable Electronics

2019 ◽  
Vol 16 (03) ◽  
pp. 1950027
Author(s):  
Surapree Maolikul ◽  
Thira Chavarnakul ◽  
Somchai Kiatgamolchai
Keyword(s):  
Thermoelectric Generator ◽  
Electrical Power ◽  
Technology Commercialization ◽  
Market Opportunity ◽  
Business Research ◽  
Power Sources ◽  
Practical Applications ◽  
Portable Electronics ◽  
Decision Factors ◽  
Insight Into

Thermoelectrics, an energy-conversion technology, has been developed for its potential to support portable electronics with an innovative power source. Primarily focusing on the metropolitan market in Thailand, the study, thus, aimed at the market insight into portable electronics users’ characteristics and opinions of thermoelectric-generator (TEG) technology commercialization. The business research was conducted to analyze their behaviors for power-supply lacking problems, encountering heat or cold sources, purchasing decision for a TEG-based charger and key decision factors. For practical applications, an innovative TEG-based charger should be more flexible by harnessing various heat or cold sources from ambient situations to generate electrical power.

Improving Techniques in Statically Equivalent Serial Chain Modeling for Center of Mass Estimation

2014 ◽  
Author(s):  
Bingjue Li ◽  
Andrew P. Murray ◽  
David H. Myszka
Keyword(s):  
Center Of Mass ◽  
Original System ◽  
Rigid Bodies ◽  
Joint Angles ◽  
Practical Applications ◽  
Serial Chain ◽  
System Of Rigid Bodies ◽  
Final Development ◽  
Data Error ◽  
Insight Into

Any articulated system of rigid bodies defines a Statically Equivalent Serial Chain (SESC). The SESC is a virtual chain that terminates at the center of mass (CoM) of the original system of bodies. A SESC may be generated experimentally without knowing the mass, CoM, or length of each link in the system given that its joint angles and overall CoM may be measured. This paper presents three developments toward recognizing the SESC as a practical modeling technique. Two of the three developments improve utilizing the technique in practical applications where the arrangement of the joints impacts the derivation of the SESC. The final development provides insight into the number of poses needed to create a usable SESC in the presence of data collection errors. First, modifications to a matrix necessary in computing the SESC are proposed. Second, the problem of generating a SESC experimentally when the system of bodies includes a mass fixed in the ground frame are presented and a remedy is proposed for humanoid-like systems. Third, an investigation of the error of the experimental SESC versus the number of data readings collected in the presence of errors in joint readings and CoM data is conducted. By conducting the method on three different systems with various levels of data error, a general form of the function for estimating the error of the experimental SESC is proposed.

scholarly journals Laminar Burning Velocities of Hydrogen-Blended Methane–Air and Natural Gas–Air Mixtures, Calculated from the Early Stage of p(t) Records in a Spherical Vessel

Energies ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 7556
Author(s):  
Maria Mitu ◽  
Domnina Razus ◽  
Volkmar Schroeder
Keyword(s):  
Natural Gas ◽  
Initial Conditions ◽  
Numerical Study ◽  
Early Stage ◽  
Linear Trend ◽  
Burning Velocity ◽  
Pressure Rise ◽  
Spherical Vessel ◽  
Practical Applications ◽  
Hydrogen Addition

The flammable hydrogen-blended methane–air and natural gas–air mixtures raise specific safety and environmental issues in the industry and transportation; therefore, their explosion characteristics such as the explosion limits, explosion pressures, and rates of pressure rise have significant importance from a safety point of view. At the same time, the laminar burning velocities are the most useful parameters for practical applications and in basic studies for the validation of reaction mechanisms and modeling turbulent combustion. In the present study, an experimental and numerical study of the effect of hydrogen addition on the laminar burning velocity (LBV) of methane–air and natural gas–air mixtures was conducted, using mixtures with equivalence ratios within 0.90 and 1.30 and various hydrogen fractions rH within 0.0 and 0.5. The experiments were performed in a 14 L spherical vessel with central ignition at ambient initial conditions. The LBVs were calculated from p(t) data, determined in accordance with EN 15967, by using only the early stage of flame propagation. The results show that hydrogen addition determines an increase in LBV for all examined binary flammable mixtures. The LBV variation versus the fraction of added hydrogen, rH, follows a linear trend only at moderate hydrogen fractions. The further increase in rH results in a stronger variation in LBV, as shown by both experimental and computed LBVs. Hydrogen addition significantly changes the thermal diffusivity of flammable CH4–air or NG–air mixtures, the rate of heat release, and the concentration of active radical species in the flame front and contribute, thus, to LBV variation.

scholarly journals Tunable Fluid-Type Metasurface for Wide-Angle and Multifrequency Water-Air Acoustic Transmission

Research ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhandong Huang ◽  
Shengdong Zhao ◽  
Yiyuan Zhang ◽  
Zheren Cai ◽  
Zheng Li ◽  
...  
Keyword(s):  
Incident Angle ◽  
Acoustic Energy ◽  
Wide Angle ◽  
Acoustic Metamaterials ◽  
Fluid Type ◽  
Acoustic Transmission ◽  
Interface Instability ◽  
Practical Applications ◽  
Air Interface ◽  
Transmission Enhancement

Efficient acoustic communication across the water-air interface remains a great challenge owing to the extreme acoustic impedance mismatch. Few present acoustic metamaterials can be constructed on the free air-water interface for enhancing the acoustic transmission because of the interface instability. Previous strategies overcoming this difficulty were limited in practical usage, as well as the wide-angle and multifrequency acoustic transmission. Here, we report a simple and practical way to obtain the wide-angle and multifrequency water-air acoustic transmission with a tunable fluid-type acoustic metasurface (FAM). The FAM has a transmission enhancement of acoustic energy over 200 times, with a thickness less than the wavelength in water by three orders of magnitude. The FAM can work at an almost arbitrary water-to-air incident angle, and the operating frequencies can be flexibly adjusted. Multifrequency transmissions can be obtained with multilayer FAMs. In experiments, the FAM is demonstrated to be stable enough for practical applications and has the transmission enhancement of over 20 dB for wide frequencies. The transmission enhancement of music signal across the water-air interface was performed to demonstrate the applications in acoustic communications. The FAM will benefit various applications in hydroacoustics and oceanography.

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