A mathematical model for predicting the maximum potential spotting distance from a crown fire

2012 ◽  
Vol 21 (5) ◽  
pp. 609 ◽  
Author(s):  
Frank A. Albini ◽  
Martin E. Alexander ◽  
Miguel G. Cruz
Keyword(s):  
Mathematical Model ◽  
Wind Speed ◽  
Lower Boundary ◽  
Cross Flow ◽  
Horizontal Distance ◽  
Crown Fire ◽  
Dimensional Model ◽  
Burning Particle ◽  
Fire Flame ◽  
Plume Flow

A mathematical model is presented for predicting the maximum potential spot fire distance from an active crown fire. This distance can be estimated from the height of the flame above the canopy top, wind speed at canopy-top height and final firebrand size (i.e. its residual size on alighting), represented by the diameter of a cylinder of woody char. The complete model system comprises several submodels or components: a model for the height and tilt angle of the wind-blown line-fire flame front, a simplified two-dimensional model of the wind-blown buoyant plume from the fire, an assumed logarithmic wind speed variation with height, and an empirically based model for the burning rate of a wooden cylinder in cross flow, which represents the firebrand. The trajectory of the burning particle is expressed analytically from where it leaves the lower boundary of the plume until it enters the canopy top. Adding the horizontal distance of this flight to that of the point where the particle can no longer be held aloft by the plume flow gives a spotting range that depends on the final diameter of the burning particle. Comparisons of model output with existing information on crown fire spotting distances has initially proved encouraging but further evaluation is warranted.

A MATHEMATICAL MODEL OF THE THERMAL MIXING PROCESSES IN CROSS-FLOW HEAT EXCHANGERS

1978 ◽  
Author(s):  
T. Fallows ◽  
C. R. Gane ◽  
R. C. Jones ◽  
J. Lis
Keyword(s):  
Mathematical Model ◽  
Heat Exchangers ◽  
Cross Flow ◽  
Mixing Processes ◽  
Thermal Mixing ◽  
Flow Heat

scholarly journals Analysis of Performance of the Wind-Driven Pulverizing Aerator Based on Average Wind Speeds in the Conditions of Góreckie Lake

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2796
Author(s):  
Andrzej Osuch ◽  
Ewa Osuch ◽  
Stanisław Podsiadłowski ◽  
Piotr Rybacki
Keyword(s):  
Mathematical Model ◽  
Wind Speed ◽  
Water Pump ◽  
Average Wind Speed ◽  
Flow Rates ◽  
Wind Speeds ◽  
Average Wind ◽  
Flow Through ◽  
Analysis Of Performance ◽  
Research Period

In the introduction to this paper, the characteristics of Góreckie lake and the construction and operation of the wind-driven pulverizing aerator are presented. The purpose of this manuscript is to determine the efficiency of the pulverizing aerator unit in the windy conditions of Góreckie Lake. The efficiency of the pulverization aerator depends on the wind conditions at the lake. It was necessary to conduct thorough research to determine the efficiency of water flow through the pulverization segment (water pump). It was necessary to determine the rotational speed of the paddle wheel, which depended on the average wind speed. Throughout the research period, measurements of hourly average wind speed were carried out. It was possible to determine the efficiency of the machine by developing a dedicated mathematical model. The latest method was used in the research, consisting of determining the theoretical volumetric flow rates of water in the pulverizing aerator unit, based on average hourly wind speeds. Pulverization efficiency under the conditions of Góreckie Lake was determined based on 6600 average wind speeds for spring, summer and autumn, 2018. Based on the model, the theoretical efficiency of the machine was calculated, which, under the conditions of Góreckie Lake, amounted to 75,000 m3 per year.

Design of Synchronous Machine Model Based on PRO/E and Dynamic Simulation

2012 ◽  
Vol 246-247 ◽  
pp. 1220-1225
Author(s):  
You Kun Zhong
Keyword(s):  
Mathematical Model ◽  
Dynamic Simulation ◽  
Three Dimensional ◽  
Transmission System ◽  
Synchronous Machine ◽  
Dimensional Model ◽  
Transmission Performance ◽  
Three Dimensional Model ◽  
Machine Model ◽  
Working Principle

With the increasing of the number of cars, people are also getting higher and higher demands on the performance of the car, and especially pay attention to the improvement and optimization of automobile transmission system. The transmission is a key part of automobile transmission system, and transmission performance and stability depend on the synchronous machine, so in order to make the vehicle transmission system with higher efficiency, it is necessary to study the synchronous machine. On the basis of elaborating synchronous machine working principle, the use of dynamics theory to establish mathematical model of synchronous machine system, and to carry out the simulation of synchronous machine three-dimensional model in PRO/E environment, then the use of virtual prototype technology to optimize the parameters of synchronous machine, thereby improving the performance of synchronous machine.

scholarly journals Sound propagation in a lined nozzle with shear and bias flows

2018 ◽  
Vol 18 (1) ◽  
pp. 3-48
Author(s):  
LMBC Campos ◽  
C Legendre
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Boundary Layers ◽  
Lower Boundary ◽  
Cross Flow ◽  
Core Flow ◽  
The Core ◽  
Wide Range ◽  
Bias Flow ◽  
Number Formula

In this study, the propagation of waves in a two-dimensional parallel-sided nozzle is considered allowing for the combination of: (a) distinct impedances of the upper and lower walls; (b) upper and lower boundary layers with different thicknesses with linear shear velocity profiles matched to a uniform core flow; and (c) a uniform cross-flow as a bias flow out of one and into the other porous acoustic liner. The model involves an “acoustic triple deck” consisting of third-order non-sinusoidal non-plane acoustic-shear waves in the upper and lower boundary layers coupled to convected plane sinusoidal acoustic waves in the uniform core flow. The acoustic modes are determined from a dispersion relation corresponding to the vanishing of an 8 × 8 matrix determinant, and the waveforms are combinations of two acoustic and two sets of three acoustic-shear waves. The eigenvalues are calculated and the waveforms are plotted for a wide range of values of the four parameters of the problem, namely: (i/ii) the core and bias flow Mach numbers; (iii) the impedances at the two walls; and (iv) the thicknesses of the two boundary layers relative to each other and the core flow. It is shown that all three main physical phenomena considered in this model can have a significant effect on the wave field: (c) a bias or cross-flow even with small Mach number [Formula: see text] relative to the mean flow Mach number [Formula: see text] can modify the waveforms; (b) the possibly dissimilar impedances of the lined walls can absorb (or amplify) waves more or less depending on the reactance and inductance; (a) the exchange of the wave energy with the shear flow is also important, since for the same stream velocity, a thin boundary layer has higher vorticity, and lower vorticity corresponds to a thicker boundary layer. The combination of all these three effects (a–c) leads to a large set of different waveforms in the duct that are plotted for a wide range of the parameters (i–iv) of the problem.

scholarly journals Interpolation of Boundary Condition at Time-Interval of Unknown Lenghth for the Problem of Convective Diffusion in a Three-Layered Water Filter

2019 ◽  
pp. 25-28
Author(s):  
Olha Chernukha ◽  
Yurii Bilushchak
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Boundary Condition ◽  
Boundary Value Problem ◽  
Convective Diffusion ◽  
Lower Boundary ◽  
Time Interval ◽  
Water Filter ◽  
The Right

On the basis of mathematical model of convectivediffusion in a three-layered filter it is formulated a contactinitial-boundary value problem for description of mass transferof pollution accompanying the sorption processes. It is proposedthe algorithm for establishing the estimation of values of soughtfunction (concentration of pollution) at the lower boundary of thefilter on the basis of the interpolation of experimental data. It istaken into account that the right end of the interpolation segmentis unknown. It is determined the exact solutions of contact-initialboundaryvalue problems of mass transfer with provision forboth diffusive and convective mechanisms of transfer as well assorption processes, which is based on integral transformationsover space variables in the contacting regions. Is it designedsoftware and established regularities of convective diffusionprocess in the three-layered filter.

Side wind and tank speed influence on lateral displacement of the projectile

2021 ◽  
pp. 24-29
Author(s):  
M. Sorokatiy ◽  
M. Voytovych ◽  
L. Velychko ◽  
O. Moskalova
Keyword(s):  
Mathematical Model ◽  
Wind Speed ◽  
Lateral Displacement ◽  
Longitudinal Section ◽  
Projectile Velocity ◽  
Air Density ◽  
Dimensionless Coefficient ◽  
Air Resistance ◽  
The Difference ◽  
Firing Distance

This article indicates the scope of the formula for determining the magnitude of the lateral displacement of the projectile under the action of crosswind, which is used in the compilation of firing tables. This formula is valid under the following conditions: the force of frontal air resistance to the motion of the projectile is proportional to the its velocity squared; wind speed components are much smaller than the horizontal component of projectile velocity; the projectile velocity projections on the Oy and Oz axes are much smaller than the projections on the Ox axis; the dimensionless coefficient of resistance and the magnitude of the crosswind are constant values. However, in reality, the force of frontal air resistance to the motion of the projectile is only sometimes proportional to the its velocity squared; the projectile velocity projections on the Oz axis may be are much smaller than the projections on the Ox axis and may even be greater than it; the coefficient of resistance is depends on the value of the Makh number, so it can be considered constant only when shooting at short distances. The authors propose a mathematical model for determining the magnitude of the lateral displacement of the projectile under the action of crosswinds. It is believed that the force of the crosswind on the projectile depends on the following factors: air density; the maximum area of the longitudinal section of the projectile; the difference between the value of the lateral component of the wind speed and the speed of the lateral displacement of the projectile, which is raised to a certain power. The magnitude of the values of the lateral displacement of the projectile under the action of the crosswind when shooting at short distances, determined based on the proposed mathematical model, slightly differ from the values of the lateral displacement specified in the firing tables. However, with increasing firing distance, the difference between these values is constantly increasing and the value of the lateral displacement of the projectile determined theoretically is much larger than indicated in the firing tables. In addition, in this research the influence of the tank velocity on the value of the projectile lateral displacement taking into account the action of the crosswind is studied.

Mathematical Modeling of Steppe Fires

2020 ◽  
pp. 48-62 ◽  
Author(s):  
Valeriy Afanasievich Perminov
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Wind Speed ◽  
Vegetation Cover ◽  
Meteorological Conditions ◽  
Condensed Phases ◽  
Pyrolysis Products ◽  
Rate Of Spread ◽  
The Mathematical Model ◽  
Steppe Fires

The chapter presents a mathematical model of the initiation and spread of the steppe fire. The mathematical model is based on the laws of mechanics of multiphase reacting media. The main physicochemical processes describing the drying, pyrolysis, and combustion of gaseous and condensed pyrolysis products are taken into account. As a result of the numerical solution, the distributions of the velocity, temperature, and concentration fields of the components of the gas and condensed phases were determined. The dependence of the rate of spread of the steppe fire on the main parameters of the state of vegetation cover and wind speed was studied. The mathematical model presented in the chapter can be used to predict the spread of steppe fires for various types of steppe vegetation and meteorological conditions, as well as for preventive measures.

scholarly journals Preliminary Design of a Wind Driven Vessel Dedicated to Hydrogen Production

2017 ◽  
Author(s):  
Jean-Christophe Gilloteaux ◽  
Aurélien Babarit
Keyword(s):  
Mathematical Model ◽  
Wind Speed ◽  
High Performance ◽  
Turbine Disk ◽  
Preliminary Design ◽  
Aerodynamic Coefficients ◽  
Ship Hulls ◽  
Water Turbine ◽  
Existing Data ◽  
Innovative Concept

An innovative concept of harnessing wind energy is presented. The concept consists of a wind driven ship equipped with a hydro-generator that converts the kinetic energy of the water flow into electricity. The electricity is then converted into hydrogen by electrolysis. In the present study the use of a Flettner rotor is considered to propel the ship. A mathematical model of the hydrogen producing ship is developed based on existing data for high performance ship hulls and aerodynamic coefficients of existing Flettner rotors. The design is optimized with respect to the axial induction velocity through the water turbine disk. Results indicate that a 22m long vessel could produce 200 kW while a 80 m long vessel is able to generate 1 MW of mechanical power both for a true wind speed of 8 m/s.

Mathematical Modelling and Field Measurements of Nitrogen Oxides in Metropolitan Areas

1992 ◽  
Vol 3 (2) ◽  
pp. 133-147
Author(s):  
M.M. Elkotb ◽  
O.M.F. Elbahar ◽  
T.A. Abdou Ahmed ◽  
T.W. Abou-Arab
Keyword(s):  
Mathematical Model ◽  
Wind Speed ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Field Measurements ◽  
Mass Conservation ◽  
Eddy Diffusivity ◽  
Solution Procedure ◽  
Pollutant Emissions ◽  
Motor Vehicles

A mathematical model for the prediction of pollutant emissions from motor vehicles is presented. The model is based on the numerical solution of the three-dimensional equation representing the mass conservation of dilute diffusing species. The variation of wind speed and eddy diffusivity with height is taken into consideration. The three-dimensional diffusion equation is solved numerically. The numerical procedure involves the discretization of the partial differential equation using the finite volume approach. The resulting set of discretization equation is solved iteratively using a fully implicit solution procedure. Furthermore, field measurements of the concentrations of nitrogen oxide in the downtown area of Cairo were conducted. For this purpose, a mobile air pollution laboratory fitted with gas analyzers, particulate matter sampler and equipment for the measurement of wind speed and direction has been used. This laboratory is also fitted with data recording and monitoring facility. The mathematical model is tested by comparing the computed pollutant concentrations with the experimental data obtained from the field measurements in the Cairo Metropolitan Area.

A mathematical model for the fluidelastic mechanism exciting vibrations in a system of blunt bodies placed in cross flow of liquid

2012 ◽  
Vol 59 (6) ◽  
pp. 462-467
Author(s):  
S. M. Kaplunov ◽  
N. G. Val’es ◽  
N. A. Chentsova ◽  
V. Yu. Fursov
Keyword(s):  
Mathematical Model ◽  
Cross Flow ◽  
Blunt Bodies
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