A Differential Equation of the First Law of Thermodynamics for Modeling the Indicator Process of a Diesel Engine

1997 ◽  
Author(s):  
Stanislav N. Danov
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
High Pressure And Temperature ◽  
First Law Of Thermodynamics ◽  
Ideal Gases ◽  
Working Medium ◽  
Engine Cylinder ◽  
Computing Procedure ◽  
The Mathematical Model ◽  
Good Agreement

Abstract Several improvements to the mathematical model of the indicator process taking place at a diesel engine cylinder are proposed. The thermodynamic behavior of working medium is described by the equation of state, valid for real gases. Mathematical dependencies between thermal parameters (P, T, v) and caloric parameters (u, h, cv, cp) have been obtained. An improved mathematical model, based on the first law of thermodynamics, has been developed, taking into account working medium imperfections. The numerical solution of the simultaneous differential equations is made by a method of Runge-Kutta type. The computing procedure is iterative. Calculations in respect to the caloric parameters (u, h, cv and cp) for various gases under pressure up to 25 MPa and temperature up to 3000°C have been carried out. The results show, that there are significant differences between the values, calculated by equations for ideal gases, and the proposed equations for real gases under high pressure and temperature. Actual applied problems for two-stroke turbocharged engines Sulzer-RLB66 and 8DKRN 74/160 have been solved. The comparison between the experimental data and numerical results show very good agreement. The numerical experiments show that if the pressure is above 8–9 MPa, the working medium imperfections must be taken into consideration.

Influence of Imperfections in Working Media on Diesel Engine Indicator Process

2000 ◽  
Vol 123 (1) ◽  
pp. 231-239 ◽  
Author(s):  
S. N. Danov ◽  
A. K. Gupta
Keyword(s):  
Mathematical Model ◽  
High Pressure ◽  
Diesel Engine ◽  
High Pressures ◽  
Ideal Gas ◽  
Working Medium ◽  
Engine Cylinder ◽  
Specific Heat Capacities ◽  
Working Media ◽  
The Mathematical Model

Several improvements to the mathematical model for the indicator process in a diesel engine cylinder are proposed. The thermodynamic behavior of working media is described by the equation of state valid for real gases. 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 applied to the various products encountered during the burning of fuel and the gas mixture as a whole in the engine cylinder under conditions of high pressures. An improved mathematical model, based on the first law of thermodynamics, has been developed by taking into account imperfections in the working media that appear under high pressures. The numerical solution of the simultaneous differential equations is obtained by Runge–Kutta-type method. The mathematical model is then used to solve the desired practical problems in two different two-stroke turbo-charged engines: 8DKRN 74/160 and Sulzer-RLB66. Significant differences between the values calculated using ideal gas behavior and the real gas at high-pressure conditions have been found. The numerical experiments show that if the pressure is above 8 to 9 MPa, the imperfections in working medium must be taken into consideration. The results obtained from the mathematical dependencies of the caloric parameters can also be used to model energy conversion and combustion processes in other thermal machines such as advanced gas turbine engines with high-pressure ratios.

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.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

scholarly journals Computer Simulation of the King's Cross Fire: Effect of Radiative Heat Transfer on Fire Spread

1991 ◽  
Vol 205 (3) ◽  
pp. 201-208 ◽  
Author(s):  
W M G Malalasekera ◽  
F Lockwood
Keyword(s):  
Mathematical Model ◽  
Radiative Heat ◽  
Health And Safety ◽  
Fire Spread ◽  
Future Research ◽  
Full Description ◽  
Department Of Health ◽  
Underground Fire ◽  
The Mathematical Model ◽  
Good Agreement

A mathematical model has been applied to simulate model experiments of the 1987 King's Cross underground fire by the Department of Health and Safety Executive. The predicted growth of the fire is compared with the experimental data and in particular the predicted and measured times to ‘flashover’ are compared. The comparisons show exceptional agreement which, in part, may be fortuitous due to the need to facilitate the prediction of the early stages of the growth with the aid of an experimentally estimated fire strength. The good agreement nonetheless is also due to the full description of the radiation transfer which is a feature of the mathematical model. It is concluded that the flashover phenomenon that occurred at King's Cross was thermal radiation driven and that future research should be devoted to modelling the details of fire spread across a combustible surface.

The Onset of Tear Propagation at Slits in Stressed Uncoated Plain Weave Fabrics

1999 ◽  
Vol 66 (4) ◽  
pp. 926-933 ◽  
Author(s):  
T. A. Godfrey ◽  
J. N. Rossettos
Keyword(s):  
Mathematical Model ◽  
Micromechanical Model ◽  
Crucial Aspect ◽  
Damage Site ◽  
Plain Weave ◽  
Actual Configuration ◽  
Tear Propagation ◽  
The Mathematical Model ◽  
Frictional Slip ◽  
Good Agreement

A simple micromechanical model is developed to predict the onset of tear propagation at slit-like damage sites (i.e., a series of consecutive aligned yarn breaks) in biaxially stressed plain weave fabrics under increasing loading. A crucial aspect of the model is the treatment of the frictional slip of yarns near the damage site. Although the actual configuration of slipping regions is complex, the onset of tear propagation in large slits (i.e., more than, say, 35 breaks) is dominated by slip occurring on the first few intact yarns adjacent to the breaks. The assumptions in the mathematical model were motivated by both experimental observations and calculations for key configurations. Analytical results obtained for this simple model exhibit good agreement with experimental results, which are presented for a variety of fabrics with initial slits of 35 and 45 breaks.

An enhanced composting process with bioaugmentation: Mathematical modelling and process optimization

2021 ◽  
pp. 0734242X2110337
Author(s):  
Tea Sokač ◽  
Anita Šalić ◽  
Dajana Kučić Grgić ◽  
Monika Šabić Runjavec ◽  
Marijana Vidaković ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Model Simulation ◽  
Process Conditions ◽  
Air Flow Rate ◽  
Optimal Process ◽  
Composting Process ◽  
Different Types ◽  
Adiabatic Reactor ◽  
The Mathematical Model ◽  
Good Agreement

In this paper, two different types of biowaste composting processes were carried out – composting without and with bioaugmentation. All experiments were performed in an adiabatic reactor for 14 days. Composting enhanced with bioaugmentation was the better choice because the thermophilic phase was achieved earlier, making the composting time shorter. Additionally, a higher conversion of substrate (amount of substrate consumed) was also noticed in the process enhanced by bioaugmentation. A mathematical model was developed and process parameters were estimated in order to optimize the composting process. Based on good agreement between experimental data and the mathematical model simulation results, a three-level-four-factor Box-Behnken experimental design was employed to define the optimal process conditions for further studies. It was found that the air flow rate and the mass fraction of the substrate have the most significant effect on the composting process. An improvement of the composting process was achieved after altering the mentioned variables, resulting in shorter composting time and higher conversion of the substrate.

KINEMATIC WAVE EQUATIONS FOR MOVABLE RIVERBEDS

2021 ◽  
pp. 43-54
Author(s):  
A. N. Krutov ◽  
◽  
S. Ya. Shkol’nikov ◽  
Keyword(s):  
Mathematical Model ◽  
Numerical Method ◽  
Wave Equations ◽  
Simple Wave ◽  
Kinematic Wave ◽  
Calculation Results ◽  
Self Similar ◽  
Similar Solutions ◽  
The Mathematical Model ◽  
Good Agreement

The mathematical model of kinematic wave, that is widely used in hydrological calculations, is generalized to compute processes in deformable channels. Self-similar solutions to the kinematic wave equations, namely, the discontinuous wave of increase and the “simple” wave of decrease are generalized. A numerical method is proposed for solving the kinematic wave equations for deformable channels. The comparison of calculation results with self-similar solutions revealed a good agreement.

Experimental and Theoretical Investigation of Performance of a Solar Chimney Model Part II: Model Development and Validation

2021 ◽  
Vol 5 (2) ◽  
Author(s):  
Ibrahim A Abuashe ◽  
Bashir H Arebi ◽  
Essaied M Shuia
Keyword(s):  
Mathematical Model ◽  
Power Output ◽  
Model Development ◽  
Geometrical Parameters ◽  
Balance Equations ◽  
Solar Chimney ◽  
And Performance ◽  
Development And Validation ◽  
The Mathematical Model ◽  
Good Agreement

A mathematical model based on the momentum, continuity and energy balance equations was developed to simulate the behavior of the air flow inside the solar chimney system. The model can estimate the power output and performance of solar chimney systems. The developed mathematical model is validated by the experimental data that were collected from small pilot solar chimney; (experiment was presented in part I). Good agreement was obtained between the experimental results and that from the mathematical model. The model can be used to analyze the solar chimney systems and to determine the effect of geometrical parameters such as chimney height and collector diameter on the power output and the efficiency of the system

Experimental Validation of a Dynamic Model for Flexible Link Mechanisms

2001 ◽  
Author(s):  
R. Caracciolo ◽  
A. Gasparetto ◽  
A. Trevisani
Keyword(s):  
Mathematical Model ◽  
Experimental Validation ◽  
Numerical Results ◽  
Test Case ◽  
Planar Mechanisms ◽  
Transient Period ◽  
Element Approach ◽  
Multi Body ◽  
The Mathematical Model ◽  
Good Agreement

Abstract This paper presents an experimental validation of a finite element approach for the dynamic analysis of flexible multi-body planar mechanisms. The mathematical model employed accounts for mechanism geometric and inertial non-linearities and considers coupling effects among rigid-body and elastic motion. A flexible five-bar linkage actuated by two electric motors is employed as a test case. Experimentally determined link absolute deformations are compared with the numerical results obtained simulating the system dynamic behavior through the mathematical model. The experimental and numerical results are in good agreement especially after the very first transient period.

Deregulation of p53-dependent microRNAs: the results of mathematical modeling

2017 ◽  
Vol 12 (1) ◽  
pp. 151-175 ◽  
Author(s):  
О.Ф. Воропаева ◽  
O.F. Voropaeva
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Numerical Analysis ◽  
Neurodegenerative Disease ◽  
Numerical Investigation ◽  
Tumor Markers ◽  
Critical Properties ◽  
Laboratory Studies ◽  
The Mathematical Model ◽  
Good Agreement

The mathematical model of the dynamics of the tumor markers network p53–Mdm2–microRNA for microRNA class with a direct positive connection with p53 was formulated. Numerical investigation of the microRNA functioning in conditions of the deregulation of p53 and p53–Mdm2-network was carried out. The deregulation of microRNA in detail was studied. The situations in which p53, its inhibitor Mdm2 and microRNAs exhibit critical properties for the patient's status and can be identified as diagnostic markers of cancer and neurodegenerative disease were studied. The results of numerical analysis are in good agreement with the data of clinical and laboratory studies of known microRNAs.

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