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Cryogenic Flow in Corrugated Pipes

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Presentation on theme: "Cryogenic Flow in Corrugated Pipes"— Presentation transcript:

1 Cryogenic Flow in Corrugated Pipes
2nd CASA Day: April 23, 2009 Patricio Rosen

2 Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work

3 Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work

4 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

5 Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work

6 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

7 Moody Diagram Experimental Results Moody Diagram Fully Turbulent
Colebrook Equation

8 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

9 Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work

10 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

11 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 :

12 Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work

13 CFD Navier Stokes f 8 Setting > = < : + f Discretization
@ P r = ~ z + f Discretization Velocity Pressure

14 Navier Stokes Re=2.13 Re=213 Re=2713 Re=676

15 Validation Several Corrugations (Re=213.5)

16 Forces at Wall Re=213 Re=2713 Pressure and Viscous Forces scale with Re in Laminar Regime and Skin Friction Dominates

17 Same Friction Factor as for Straight Pipes in Laminar Regime

18 Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work

19 CFD k-e Turbulence Model
Re=177 Re=843 Re=1.737e4 Re=3860

20 Several Periods Re=177 Re=847 Re=3860

21 At High Reynolds Numbers the Pressure Forces become Dominant

22 Friction Factor One Period Several Periods

23 Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work

24 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)

25 Outline Motivation Pipe Flow Preliminaries Fluid Flow Equations
CFD Navier Stokes CFD k-e Turbulence Model Conclusions Further work

26 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 ; + ` @

27 Thanks for your attention!

28 RANS

29 k-e Model Summary

30 FEM for Navier Stokes

31 Navier Stokes Weak Form


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