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**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