Compressible Flow Modeling Occurring in a Depressurization Process

Compressible Flow Modeling Occurring in a Depressurization Process Frédéric Viry 1, Vincent Bruyere 1, Thomas Paris 2, Patrick Namy 1 1 SIMTEC, 8 rue Duployé, Grenoble, 38100, France, +33 9 53 51 45 60 vincent.bruyere@simtecsolution.fr 2 CEA DAM, Valduc, Is-sur-Tille, 21120, France

SIMTEC www.simtecsolution.fr SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 2

SIMTEC www.simtecsolution.fr French company (founded in 2006) 4 Ph. D. Engineers SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 2

SIMTEC www.simtecsolution.fr French company (founded in 2006) 4 Ph. D. Engineers Experts in Modeling COMSOL Certified Consultants CFD Structural mechanics Electromagnetism Heat transfer Chemical engineering SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 2

SIMTEC www.simtecsolution.fr French company (founded in 2006) 4 Ph. D. Engineers Experts in Modeling COMSOL Certified Consultants CFD Structural mechanics Electromagnetism Heat transfer Chemical engineering Services Numerical modeling Custom-made training sessions Modeling assistance SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 2

Problem Statement SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 3

Problem Statement Gas particle High pressure tank (initially) Low pressure tank (initially) SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 3

Problem Statement Gas particle High pressure tank (initially) Low pressure tank (initially) Model the flow to: Study the sensitivity to the dimensions of the system; Understand the behavior of the gas flow, the time to reach the equilibrium; Coupling with others physics: e.g. chemistry, etc SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 3

The Flow Study and its Issues SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 4

The Flow Study and its Issues Navier-Stokes Equations (Mass and momentum balances) Energy balance Precise description of the movement! Constitutive law SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 4

The Flow Study and its Issues Navier-Stokes Equations (Mass and momentum balances) Energy balance Precise description of the movement! Constitutive law Turbulent flow : difficult to capture numerically SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 4

The Flow Study and its Issues Navier-Stokes Equations (Mass and momentum balances) Energy balance Precise description of the movement! Constitutive law Turbulent flow : difficult to capture numerically Shockwaves appearing at the sound speed : it breaks the continuity hypothesis! SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 4

Overview 5

Overview Model derived from an existing 1D approach A Simplified Model for Real Gas Expansion Between Two Reservoirs Connected by a Thin Tube, S. Charton, V.Blet et J. P. Corriou, 1995 5

Overview Model derived from an existing 1D approach A Simplified Model for Real Gas Expansion Between Two Reservoirs Connected by a Thin Tube, S. Charton, V.Blet et J. P. Corriou, 1995 Tanks as points Pipe modeled by a segment Location of the discontinuity given by a theoretical development No turbulences to handle Possibility to introduce the discontinuity 5

Gas Flow Within the Pipe 6

Gas Flow Within the Pipe Mass balance Mass variation 6

Gas Flow Within the Pipe Mass balance Mass variation Momentum balance Mass acceleration Friction forces (w/ viscosity) Pressure drop 6

Gas Flow Within the Pipe Mass balance Mass variation Momentum balance Mass acceleration Friction forces (w/ viscosity) Pressure drop Energy balance Internal energy variation Heat transfer by diffusion Friction forces work Pressure work 6

Tanks as Points 7

Tanks as Points Exterior Tank in 0D Junction with the pipe 7

Tanks as Points Exterior 0D means a spatial uniformity of: pressure, temperature and density! Tank in 0D Junction with the pipe 7

Tanks as Points Exterior 0D means a spatial uniformity of: pressure, temperature and density! Tank in 0D Junction with the pipe Mass Balance Mass variation Mass flow at the junction 7

Tanks as Points Exterior 0D means a spatial uniformity of: pressure, temperature and density! Tank in 0D Junction with the pipe Mass Balance Energy balance Mass variation Mass flow at the junction Internal energy variation Heat transfer by convection Transfer of Heat exchanges with kinetic energy the exterior 7

Tanks as Points Exterior 0D means a spatial uniformity of: pressure, temperature and density! Tank in 0D Junction with the pipe Mass Balance Energy balance Mass variation Mass flow at the junction Internal energy variation Constitutive law (ideal gas assumption) Heat transfer by convection Transfer of Heat exchanges with kinetic energy the exterior 7

Tanks as Points Exterior 0D means a spatial uniformity of: pressure, temperature and density! Tank in 0D Junction with the pipe Mass Balance Energy balance Mass variation Mass flow at the junction Internal energy variation Constitutive law (ideal gas assumption) Heat transfer by convection Transfer of Heat exchanges with kinetic energy the exterior ODE interface 7

Handle the Discontinuity 8

Handle the Discontinuity Subsonic 8

Handle the Discontinuity Flow saturated to Mach 1 (second law of thermodynamics) Critical up Subsonic 8

Handle the Discontinuity Flow saturated to Mach 1 (second law of thermodynamics) Critical up Subsonic Sonic 8

Handle the Discontinuity Flow saturated to Mach 1 (second law of thermodynamics) Critical up Subsonic Sonic Critical down 8

Handle the Discontinuity Flow saturated to Mach 1 (second law of thermodynamics) Critical up Subsonic Sonic Critical down Conditions modified because of numerical issues 8

Handle the Discontinuity Flow saturated to Mach 1 (second law of thermodynamics) Critical up Subsonic Sonic Critical down Conditions modified because of numerical issues Events interface 8

Numerical Aspects 9

Numerical Aspects Space Discretization 9

Numerical Aspects Space Discretization Study of sensivity to the mesh At least homogeneous 1000 nodes Avoid numerical loss of mass during the discharge 9

Numerical Aspects Space Discretization Time Discretization Study of sensivity to the mesh At least homogeneous 1000 nodes Avoid numerical loss of mass during the discharge 9

Numerical Aspects Space Discretization Time Discretization Study of sensivity to the mesh Speed of sound reached very quickly At least homogeneous 1000 nodes Small timestep at the beginning of the simulation (about 10-7 s) Avoid numerical loss of mass during the discharge 9

Numerical Aspects Space Discretization Time Discretization Study of sensivity to the mesh Speed of sound reached very quickly At least homogeneous 1000 nodes Avoid numerical loss of mass during the discharge Small timestep at the beginning of the simulation (about 10-7 s) Gas less agitated after that: COMSOL chooses well its timestep automatically 9

Theoretical Validation SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 10

Theoretical Validation Theoretical results exist by neglecting the friction forces A. Lallemand, Ecoulements monodimensionnels des fluides compressibles, Techniques de l'ingénieur, 2014 SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 10

Theoretical Validation Theoretical results exist by neglecting the friction forces A. Lallemand, Ecoulements monodimensionnels des fluides compressibles, Techniques de l'ingénieur, 2014 The model respects the physics laws! SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 10

First Comparisons with Experiments SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 11

First Comparisons with Experiments The model does not reach the real equilibrium state SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 11

First Comparisons with Experiments Tracks to explain that Too reductive assumptions (e.g. ideal gas law...) The dimensions used to feed the model are not correct Some of the experimental results are not accurate enough The model does not reach the real equilibrium state A mix of them all SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 11

First Comparisons with Experiments Tracks to explain that Too reductive assumptions (e.g. ideal gas law...) The dimensions used to feed the model are not correct The model does not reach the real equilibrium state Some of the experimental results are not accurate enough Measurements of temperature A mix of them all SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 11

Simulation vs. (Corrected) Experimental SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 12

Simulation vs. (Corrected) Experimental Correction of the initial temperature in the tanks, regarding to the equilibrium SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 12

Simulation vs. (Corrected) Experimental Correction of the initial temperature in the tanks, regarding to the equilibrium The results of the model fits to the experiments in pressure! SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 12

Simulation vs. (Corrected) Experimental Correction of the initial temperature in the tanks, regarding to the equilibrium The results of the model fits to the experiments in pressure! Use of the model to detect experimental flaws SIMTEC INTRODUCTION FLOW MODELING VALIDATION CONCLUSIONS 12

Conclusions 13

Conclusions Numerical difficulties broken using a 1D approach General enough interfaces to implement it 13

Conclusions Numerical difficulties broken using a 1D approach General enough interfaces to implement it Validation of the model using theoretical and experimental results 13

Conclusions Numerical difficulties broken using a 1D approach General enough interfaces to implement it Validation of the model using theoretical and experimental results Some weaknesses on the thermal exchanges Inherent to the 0D simplification 13