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The Modeling of the Gas Dynamics Processes in Internal Combustion Engines

Domenii publicaţii > Stiinte ingineresti + Tipuri publicaţii > Carte

Autori: V. A. Soloiu, N. Buzbuchi, M. Dinescu

Editorial: 1999.

Rezumat:

In this book are presented the results of the mathematical modeling, computer simulation and experiments on the fluid flow in the Internal Combustion Engine and the turbulent kinetic energy characteristics that result from this type of motion.

1. The book mathematical support conceived and developed to describe the gas dynamics phenomenon and wave’s propagation for low Mach numbers was consisted of the mathematical modeling of the second order partial differential non-linear system of equations that govern the flow and the solution of this system for a 2 and 4 stroke engine configuration. The modeling and the integration of the system of fundamental differential equations that govern the unsteady flow phenomenon were made by algorithms, techniques, computer programmes developed and optimised by the authors.

The convection phenomenon (hyperbolic partial differential equation system), wave’s diffusion (parabolic partial differential equation system) and pressure corrections have been studied independently, and coupled in the final stage in an original multidimensional mathematical model regarding Mach, Courant-Friedrichs-Leroy and Peclet criteria.

The family of explicit higher order numerical schemes developed for this purpose is new in the literature, showing closed performances compared with those proposed by Leonard and Causon.

To improve the stability and convergence of the numerical solutions some implicit optimised numerical schemes with a large area of application without the danger of instabilities for large Courant and Peclet numbers have been developed.

The pressure correction derived from Navier-Stokes equations imposed the development of a Patankar type mathematical model based on the control volume integration technique.

The fluid movement determined by computer simulations showed a good agreement with the results presented in the listed papers: Gosman, Watkins, Blair, El Tahry, both through the position and the amplitude of the tumble motion and the recirculation regions.

2. The experimental technique employed for fluid flow simulations was consisted of a modern compression-expansion machine, a powerful Laser in back-scattered light configuration for LDV and sophisticated data acquisition facilities. The experiments of this section have been developed by the first author in 1994 in IC Engines Lab, Rits University, Japan under the supervising of Prof. dr. K. Nishiwaki.

For the separation of the tumble from the squish motion and the independent study an installation for the rapid compression machine based on a special experimental cylinder was designed and developed by the first author. In the same time, a photographic study of the flow allowed to find the optimum position and configuration of the intake and exhaust windows to obtain a maximum diameter tumble motion.

The experimental results for the turbulent kinetic energy laid between the theoretical results obtained by Morel and Monsour for low intake turbulence intensity and those obtained by Kido’s model for medium and high turbulence intensity at the beginning of the intake stroke.

The authors tried to bring a contribution to the understanding of the generation and the development of unsteady flows and wave’s propagation in the Internal Combustion Engine, through the mathematical modeling of the fundamental equations that govern the flow and experimental studies.

Volume I

The Mathematical Modeling of Unsteady Flows in IC Engines
Part I

1. INTRODUCTION 15

2. REAL FLUID FUNDAMENTAL EQUATIONS FOR
THE IC ENGINE 17
2.1. Introduction 17
2.2. Momentum equations (Navier-Stokes equations) 17
2.3. Continuity equation (The fluid mass conservation) 24
2.4. Energy conservation equation 25
2.5. Complete Navier-Stokes conservative equations 28
References 31

3. COORDINATION TRANSFORMATIONS AND DISCRETISATION
GRIDS 33
3.1. Introduction 33
3.2. General transformation of equations 34
3.3. Metrics 38
3.4. Elastic grids 40
3.5. Coordinates systems adapted to the flow field 43
3.6. Active grids 46
References 49

4. HYPOTHESIS FOR INTEGRATION OF EQUATIONS
THAT DESCRIBE THE UNSTEADY FLOW THE IC ENGINES 50
4.1. Introduction 50
4.2. Equations that govern the flow 50
4.3. Employed hypothesis 51
4.4. Navier-Stokes advection term integration 52
4.5. The numerical integration scheme 54
4.6. Results 55
4.7. The study of convergence and consistence of
numerical solution 59
4.8. Conclusions 61
References 61

5. THE STUDY OF WAVES PROPAGATION 63
5.1. Navier-Stokes advection term integration through higher
order numerical schemes and control volume method 63
5.1.1. Introduction 63
5.1.2. First order numerical scheme analysis 63
5.1.3. The development of higher order numerical
schemes 66
5.1.4. Results 69
5.1.5. Generalization. The development of a
higher order numerical scheme with variable
integration step 73
5.1.6. Results 74
5.1.7. Conclusions 76
5.2. Waves diffusion. The Navier-Stokes diffusion term analysis 76
5.2.1. The consistence of the proposed numerical scheme 79
5.2.2. The accuracy improvement of the proposed
numerical scheme 81
5.2.3. The grid optimum refinement and the ratio of
accuracy/ computing time for the Navier-Stokes
diffusion term 81
5.2.4. Conclusions 85
5.3. The construction and the study of an implicit numerical
scheme 86
5.3.1. Introduction 86
5.3.2. The finite difference of the parabolic differential
equation that corresponds to the diffusion term
of the momentum equation 86
5.4. The solving of the partial differential parabolic equation
system 89
5.4.1. The flow field boundary conditions 91
References 91

6. THE CALCULUS OF THE PRESSURE FIELD 94
6.1. Introduction 94
6.2. The grid for the flow field 94
6.3. The control volume equations 94
6.4. The boundary conditions of the flow 99
References 100

7. THE SOLVING OF THE MULTIDIMENSIONAL MATHEMATIC
MODEL 101
7.1. The turbulence modeling 101
7.1.1. k- model 107
7.1.2. Reynolds Stress Model 127
7.1.3 Large Eddy Simulation 129
7.2. Other mathematical models for simulation of unsteady
gas dynamic flow in IC Engines 134
7.3. The solving of the proposed mathematical model 135
7.4. The grid 138
7.5. The CPU time 140
7.6. The solver algorithm 140
7.7. The boundary conditions at the walls 140
References 141

8. THE NUMERICAL SIMULATION OF THE UNSTEADY FLOW
RESULTS AND CONCLUSIONS 145
8.1. The two stroke engine 145
8.2. The four stroke engine 146
References 149

The Experimental Investigation of Unsteady Flows
in IC Engines
Part II

9. APPLIED EXPERIMENTAL TECHNIQUES FOR FLOW
INVESTIGATION IN IC ENGINES 152
9.1. Techniques for local pressure and velocity measurements 152
9.2. Techniques for velocity and turbulence measurements 154
9.2.1 Hot wire anemometer 154
9.2.1.1. Transducer design 155
9.2.1.2. The measurement methodology 157
9.2.1.3. Constant current method 159
9.2.1.4. Constant temperature method 163
9.2.1.5. Fluid temperature compensation 165
9.2.1.6. The design of the probes 167
9.2.2. Ionization techniques – electric sparks 169
9.2.3. Propeller anemometer 173
9.3. Optical methods for flow investigation 175
9.3.1. Shadows technique 177
9.3.2. Schlieren technique 178
9.3.3. Interferometer technique 181
9.3.4. Laser-Doppler-Anemometer (LDA) 185
9.3.5. Optical methods for vector and scalar fields in
unsteady flow measurements 200
9.3.5.1. Particle Image Velocimetry (PIV) 204
9.3.5.2. Phase-Doppler Anemometer ((PDA) 215
9.3.5.3. Laser-Induced Fluorescence
Techniques (LIF) 217
References 217

10. EXPERIMENTAL FACILITIES – LDV 222
10.1. Introduction 222
10.2. Technical characteristics of Laser system with Ar+ ion 223
10.3. The fringes distance determination for the measurement
volume 226
10.4. The directional sensitivity 227
10.5. Data sampling principals 227
10.6. Signal post-processing 229
10.7. The experiment parameters 230
10.8. The setting of the Laser installation 231
References 235

11. THE EXPERIMENTAL SIMULATION OF THE FLUID
COMPRESSION-EXPANSION IN THE IC ENGINE
FOR TUMBLE MOTION GENERATION 236
11.1. The rapid compression-expansion machine 236
11.2. The separation of tumble motion from swirl motion 237
11.2.1. The optimum solenoid valve determination 240
11.3. The estimation of the new compression ratio 240
11.4. The calculus of the gas exchange time 242
11.5. The design of the rapid compression machine cylinder 244
11.6. The optimization of the number and position of the intake
and exhaust pipes 244
11.6.1 Results 246
11.7. The particles admission installation for the air flow 251
11.8. The types of pressure sensors and relays, for dead center
signal and solenoid valve operation 251
11.9. Conclusions 253
References 253

12. THE AMPLIFICATION AND THE DUMPING OF THE
TURBULENCE GENERATED IN THE RAPID COMPRESSION – EXPANSION MACHINE 255
12.1. Introduction 255
12.2. The equation that corresponds to 256
12.3. The experimental results of the turbulence kinetic
energy measurement 257
12.4. Experiment conclusions 259
References 259

Cuvinte cheie: Unsteady Fluid Dynamics, Internal Combustion Engines, Tumble Motion, CFD

URL: www.ad-astra.ro/soloiu