scholarly journals The Evolutions in Time of Probability Density Functions of Polydispersed Fuel Spray—The Continuous Mathematical Model

2021 ◽  
Vol 11 (20) ◽  
pp. 9739
Author(s):  
Shlomo Hareli ◽  
Ophir Nave ◽  
Vladimir Gol’dshtein
Keyword(s):  
Mathematical Model ◽  
Combustion Process ◽  
Computation Time ◽  
Fuel Spray ◽  
Ignition Process ◽  
Experimental Distribution ◽  
Elegant Method ◽  
Short Period ◽  
The Right ◽  
The Mathematical Model

The dynamics of the particle size distribution (PSD) of polydispersed fuel spray is important in the evaluation of the combustion process. A better understanding of the dynamics can provide a tool for selecting a PSD that will more effectively meet the needs of the system. In this paper, we present an efficient and elegant method for evaluating the dynamics of the PSD. New insights into the behaviour of polydispersed fuel spray were obtained. A simplified theoretical model was applied to the experimental data and a known approximation of the polydispersed fuel spray. This model can be applied to any distribution, not necessarily an experimental distribution or approximation, and involves a time-dependent function of the PSD. Such simplified models are particularly helpful in qualitatively understanding the effects of various sub-processes. Our main results show that during the self-ignition process, the radii of the droplets decreased as expected, and the number of smaller droplets increased in inverse proportion to the radius. An important novel result (visualised by graphs) demonstrates that the mean radius of the droplets initially increases for a relatively short period of time, which is followed by the expected decrease. Our modified algorithm is superior to the well-known `parcel’ approach because it is much more compact; it permits analytical study because the right-hand sides of the mathematical model are smooth, and thus eliminates the need for a numerical algorithm to transition from one parcel to another. Moreover, the method can provide droplet radii resolution dynamics because it can use step functions that accurately describe the evolution of the radii of the droplets. The method explained herein can be applied to any approximation of the PSD, and involves a comparatively negligible computation time.

scholarly journals The Evolutions in Time of Probability Density Functions of Polydispersed Fuel Spray-The Continuous Mathematical

2021 ◽  
Author(s):  
Shlomo Hareli ◽  
OPhir Nave ◽  
Vladimir Gol'dshtein
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Combustion Process ◽  
The Self ◽  
Fuel Spray ◽  
Ignition Process ◽  
Simplified Models ◽  
Short Period ◽  
The Mean

Abstract The dynamics of the particle-size distribution of the polydispersed fuel spray are important for the evaluation of the combustion process. In this paper, we presented the particle-size distribution change in time which gives a new insight into the behavior of the droplets during the self-ignition process. Semenov was the first to shows that self-ignition in the homogeneous case can be qualitatively and even quantitatively described by simplified models \cite{first_Math_Semenov_1928}. A simplified model of the polydisperse spray is used for a study of combustion processes near the initial region. This model involves a time-dependent function of the particle-size distribution. Such simplified models are particularly helpful in understanding qualitatively the effect of various sub-processes. Our main results show that during the self-ignition process, the droplets' radii decrease as expected, and the number of smaller droplets increases in inverse proportion to the radius. An important novel result (visualized by graphs) demonstrates that the mean radius of the droplets, at first increases for a relatively short period of time, and that is then followed by the expected decrease. It means that the maximum of the mean radius is not located at the beginning of the process as expected. We only have a heuristic explanation of this phenomenon, but an analytic study is planned for the future. Our modified algorithm is superior to the well known `parcel' approach because it is much more compact, it permits an analytical study since the right-hand sides are smooth, and thus eliminates the need for a numerical algorithm transitioning from one parcel to another, The method explain herein can be applied to any approximation of the particle-size distribution, and it involves comparatively negligible computation time.

Influence of Imperfections in the Working Media on Diesel Engine Indicator Process: Part 2 — Results

1998 ◽  
Author(s):  
Stanislav N. Danov ◽  
Ashwani K. Gupta
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
High Pressures ◽  
Combustion Process ◽  
Ideal Gas ◽  
Working Medium ◽  
High Pressures And Temperatures ◽  
Specific Heat Capacities ◽  
Working Media ◽  
The Mathematical Model

Abstract In the companion Part 1 of this two-part series paper several improvements to the mathematical model of the energy conversion processes, taking place in a diesel engine cylinder, have been proposed. Analytical mathematical dependencies between thermal parameters (pressure, temperature, volume) and caloric parameters (internal energy, enthalpy, specific heat capacities) have been obtained. These equations have been used to provide an improved mathematical model of diesel engine indicator process. The model is based on the first law of thermodynamics, by taking into account imperfections in the working media which appear when working under high pressures and temperatures. The numerical solution of the simultaneous differential equations is obtained by Runge-Kutta type method. The results show that there are significant differences between the values calculated by equations for ideal gas and real gas under conditions of high pressures and temperatures. These equations are then used to solve the desired practical problem in two different two-stroke turbo-charged engines (8DKRN 74/160 and Sulzer-RLB66). The numerical experiments show that if the pressure is above 8 to 9 MPa, the working medium imperfections must be taken into consideration. The mathematical model presented here can also be used to model combustion process of other thermal engines, such as advanced gas turbine engines and rockets.

Oblique stability of circularly polarized MHD waves

1990 ◽  
Vol 43 (2) ◽  
pp. 257-268 ◽  
Author(s):  
E. Mjølhus ◽  
T. Hada
Keyword(s):  
Mathematical Model ◽  
Finite Amplitude ◽  
Mhd Waves ◽  
Circularly Polarized ◽  
Right Hand ◽  
Wave Trains ◽  
The Stability ◽  
The Right ◽  
The Mathematical Model ◽  
Dnls Equation

The stability of finite-amplitude weakly dispersive circularly polarized MHD wave trains with respect to oblique modulations is investigated. The mathematical model is a multi-dimensional extension of the DNLS equation. We have found that the right-hand-polarized wave, which is stable with respect to parallel modulations, is unstable with respect to certain oblique modulations for most primary wavenumbers.

Computations of Three-Dimensional Gas-Turbine Combustion Chamber Flows

1979 ◽  
Vol 101 (3) ◽  
pp. 326-336 ◽  
Author(s):  
M. A. Serag-Eldin ◽  
D. B. Spalding
Keyword(s):  
Mathematical Model ◽  
Turbulent Flows ◽  
Combustion Process ◽  
Three Dimensional ◽  
Solution Algorithm ◽  
Physical Models ◽  
Turbulence Energy ◽  
Experimental Conditions ◽  
Diffusion Controlled ◽  
The Mathematical Model

The paper presents a mathematical model for three-dimensional, swirling, recirculating, turbulent flows inside can combustors. The present model is restricted to single-phase, diffusion-controlled combustion, with negligible radiation heat-transfer; however, the introduction of other available physical models can remove these restrictions. The mathematical model comprises differential equations for: continuity, momentum, stagnation enthalpy, concentration, turbulence energy, its dissipation rate, and the mean square of concentration fluctuations. The simultaneous solution of these equations by means of a finite-difference solution algorithm yields the values of the variables at all internal grid nodes. The prediction procedure, composed of the mathematical model and its solution algorithm, is applied to predict the fields of variables within a representative can combustor; the results are compared with corresponding measurements. The predicted results give the same trends as the measured ones, but the quantitative agreement is not always acceptable; this is attributed to the combustion process not being truly diffusion-controlled for the experimental conditions investigated.

Study on the Dynamic Models of Systems Biology from the View of Engineering

2012 ◽  
Vol 220-223 ◽  
pp. 952-957
Author(s):  
Chen Liu ◽  
Xiao Yan Liu
Keyword(s):  
Mathematical Model ◽  
Systems Biology ◽  
Dynamic Process ◽  
Biological System ◽  
Dynamic Models ◽  
Model Parameters ◽  
State Variables ◽  
Biochemical Pathway ◽  
The Right ◽  
The Mathematical Model

From the view of engineering, based on expatiating the features of systems biology, the paper discusses the workflows and the research emphasis of systems biology. It also explains how to model and analyze the dynamic process of signal transmitting network for a biological system by an example. Based on the complexity and uncertainty of the mathematical model, the right methods are chosen to realize the effective estimation of state variables and model parameters for the biochemical pathway.

The Effect of Leakage on Railroad Brake Pipe Steady State Behavior

1988 ◽  
Vol 110 (3) ◽  
pp. 329-335 ◽  
Author(s):  
K. Abdol-Hamid ◽  
D. E. Limbert ◽  
G. A. Chapman
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Transmission Lines ◽  
Computation Time ◽  
State Behavior ◽  
Implicit Finite Difference Scheme ◽  
Inlet Flow Rate ◽  
Model Equations ◽  
The Mathematical Model ◽  
Steady State Behavior

A mathematical model for pneumatic transmission lines containing leakage is developed. This model is used to show the effect of leakage size and distribution on the steady state behavior of the brake pipe on a train brake system. The model equations are solved using the implicit finite difference scheme without neglecting any terms. The model is presented in a nonlinear continuous network form, consisting of N sections. Each of the network sections represents one car and may contain one leakage. A computer program was developed to solve the model equations. This program is capable of simulating a train with cars of various lengths and takes a minimum amount of computation time as compared with previous methods. Through analysis and experimentation, the authors have demonstrated that pressure gradient and inlet flow rate are very sensitive to leakage locations as compared with leakage size. The results, generated by the mathematical model, are compared with the experimental data of two different brake pipe set-ups having different dimensions.

Analysis of Coal With Coal-Mule and Biomass Co-Combustion in Slurry Form/Analiza Współspalania Węgla Z Mułem Węglowym I Biomasą W Postaci Zawiesiny

2014 ◽  
Vol 59 (2) ◽  
pp. 347-366 ◽  
Author(s):  
Agnieszka Kijo-Kleczkowska
Keyword(s):  
Mathematical Model ◽  
Mass Loss ◽  
Fluidized Bed ◽  
Combustion Process ◽  
Environment Protection ◽  
Technical Application ◽  
Depth Analysis ◽  
Combustion Technology ◽  
The Mathematical Model

Abstract Combustion technology of coal-water fuels creates a number of new possibilities to organize the combustion process fulfilling contemporary requirements e. g in the environment protection. Therefore an in-depth analysis is necessary to examine the technical application of coal as energy fuel in the form of suspension. The paper undertakes the complex research of the coal with coal-mule and biomass co-combustion. The mathematical model enables the prognosis for change of the surface and the centre temperatures and a mass loss of the fuel during combustion in air and in the fluidized bed.

scholarly journals DEVELOPMENT OF AN AUTOMATED DIAGNOSTICS AND CONTROL SYSTEM FOR BIOGAS COMBUSTION PROCESSES

2017 ◽  
Vol 7 (4) ◽  
pp. 15-19
Author(s):  
Oxana Zhirnova
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Combustion Process ◽  
Research Process ◽  
Energy Performance ◽  
Pilot Studies ◽  
Complex Process ◽  
Combustion Processes ◽  
And Control ◽  
The Mathematical Model

The article shows the ecological and economic efficiency of biogas. Depending on the complexity of the tasks, the mathematical model could describe the research process with varying degrees of accuracy. Thus, numerical simulation should be combined with experimental research to compare and assess the validity of the model. Below is presented, a mathematical model of combustion of biogas. Then, based on the results of pilot studies to validate the mathematical model, a numerical simulation of the combustion of biogas. Process for the combustion of biogas is a complex process of their heterogeneous and homogenous combustion. The model of combustion process of extreme management not good can improve energy performance by maintaining the optimum cop value. Proved by simulation model of extreme management efficiency in changing signal assignments, the maintenance efficiency of the boiler is on a level with the specified accuracy.

Study on Torsion-Eliminating Performance of Laterally Interconnected Air Suspension

2014 ◽  
Vol 596 ◽  
pp. 17-21 ◽  
Author(s):  
Zhong Xing Li ◽  
Long Yu Ju ◽  
Hong Jiang ◽  
Xing Xu
Keyword(s):  
Mathematical Model ◽  
Test Bench ◽  
The Body ◽  
Body Parts ◽  
Full Vehicle ◽  
Air Suspension ◽  
Spring Force ◽  
Working Principle ◽  
The Right ◽  
The Mathematical Model

Laterally interconnected air suspension combines the right and left air springs with pneumatic pipes, which can protect the auto-body parts from fatigue damage and increase the service life of vehicles. The mathematical model of full vehicle with laterally interconnected air suspension was established based on the analysis of its working principle, and a test bench was built. The simulation and experimental results show that, laterally interconnected air suspension can reduce the peak of dynamic body torsion load effectively, especially for steady state conditions, in which the body torsion load caused by the spring force can be nearly eliminated.

Effects of antiarrhythmic drug therapy on atrioventricular nodal function during atrial fibrillation in humans*

EP Europace ◽  
2005 ◽  
Vol 7 (s2) ◽  
pp. S71-S82 ◽  
Author(s):  
Laurence Mangin ◽  
Alain Vinet ◽  
Pierre Pagé ◽  
Leon Glass
Keyword(s):  
Atrial Fibrillation ◽  
Mathematical Model ◽  
Drug Effects ◽  
Surgical Patients ◽  
Ventricular Rate ◽  
Av Node ◽  
Physiological Basis ◽  
The Mean ◽  
The Right ◽  
The Mathematical Model

Abstract Aims To assess the effects of metoprolol and amiodarone on atrial and ventricular activity during atrial fibrillation (AF) in post-surgical patients, and to develop and use a mathematical model of the atrioventricular (AV) node during AF that incorporates parameters describing the properties of the AV node to evaluate the physiological basis of the drug effects. Methods and results Ten post-surgical patients were evaluated where three received no medical therapy, three received metoprolol, three received amiodarone, and one received both metoprolol and amiodarone. The medications led to increases of 37–310 ms in the mean VV interval in treated patients, but much smaller changes in the mean AA intervals in the right and left atria. The mathematical model incorporating a random influence of the concealed conduction parameter was capable of reproducing the histograms of the VV intervals based on the input from the right atrium by systematically searching parameter space. Conclusions Changes in the ventricular rate are mainly due to the alteration in the AV nodal properties rather than changes in the atrial rhythm. The medications can display differential effects on the physiological properties of the AV node, and therefore the mathematical model may help to identify novel pharmacological targets.

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