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Cryogenic Flow in Corrugated Pipes
2nd CASA Day: April 23, 2009 Patricio Rosen
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Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work
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Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work
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Motivation Corrugated Pipes/Hoses Portable Flexible
Several Application Areas LNG Transport Development of DTSE (Dual Tank Stirling Engine) Goal Describe and Predict Flow Behavior in Corrugated Hoses in an Efficient Way
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Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work
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Preliminaries P ¡ = : ¢ f ½ v 4 R Darcy Weisbach Equation
Straight Pipe Poiseuille Flow Non-straight Pipes? Roughness Actual Shape L R P 1 2 v z P 1 2 = : L f v z 4 R v z = 2 1 r R R e : = 4 v z f = 6 4 R e
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Moody Diagram Experimental Results Moody Diagram Fully Turbulent
Colebrook Equation
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LNG Composite Hose Moody Prediction Taking corrugation as roughnes
Measurements Water LNG f = . 4 5 f = . 5 8 Moody Diagram is a poor indicator for the friction factor Find a better Alternative (CFD) f = . 1 3
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Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work
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Set up saves lots of computation time
Fluid Flow Equations Assumptions Incompressible Flow Steady Flow Gravity negligible Isothermal Flow One-phase Cylindrical and Periodic Hose Fixed Wall No Swirl Cylindrical Symmetry Navier-Stokes v r = 1 @ P + h 2 i z Periodicity v ( R z ) ; = r L P + k Set up saves lots of computation time
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Analytic Expression for DFF
From continuity Rewrite z-momentum Using Divergence Theorem For Poiseuille Flow v r z = ( ) r ( v z ) = 1 P e + : P L : = i n o u t 1 j Z z d S @ v Pressure “Friction“ Skin “Friction“ f = 6 4 D v R e : P L = 8 v R 2 :
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Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work
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CFD Navier Stokes f 8 Setting > = < : + f Discretization
@ P r = ~ z + f Discretization Velocity Pressure
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Navier Stokes Re=2.13 Re=213 Re=2713 Re=676
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Validation Several Corrugations (Re=213.5)
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Forces at Wall Re=213 Re=2713 Pressure and Viscous Forces scale with Re in Laminar Regime and Skin Friction Dominates
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Same Friction Factor as for Straight Pipes in Laminar Regime
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Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work
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CFD k-e Turbulence Model
Re=177 Re=843 Re=1.737e4 Re=3860
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Several Periods Re=177 Re=847 Re=3860
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At High Reynolds Numbers the Pressure Forces become Dominant
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Friction Factor One Period Several Periods
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Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work
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Conclusions Correct Prediction of the Friction Factor Problem Solved?
(One phase, adiabatic flow) Problem Solved? Sensibility of Results (needs validation) Cryogenic Liquids not yet manageable Expensive computation time for dynamic flow computations 4 hours Computation (NS Example)
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Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work
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Towards a 1D Model v ( r ; ) = + ^ d z ( R v ) = ¡ 1 ½ P Z ^ r ; + ` º
: = 1 ( ) Z r ; d A i n o u t P ( z ) = 1 j Z d A d z ( R 2 v ) = 1 P Z ^ r ; + ` @
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Thanks for your attention!
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RANS
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k-e Model Summary
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FEM for Navier Stokes
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Navier Stokes Weak Form
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