Swagelok Technology Summit © Swagelok Company, 2005 CFD Prediction of Liquid Flow through a...

Swagelok Technology Summit

© Swagelok Company, 2005

CFD Prediction of Liquid Flow through a 12-Position Modular Sampling System

Tony Bougebrayel, PE, PhD

Engineering Analyst

Swagelok Co.



AGENDA

• How is the driving pressure consumed?• Why do liquids require more driving pressure?• Predicting driving pressure for a conventional system• What is CFD?• CFD application to a 12-position modular system• Results: CFD vs. Actual• Conclusion



How is the driving pressure consumed?

Momentum LossMomentum Loss::

Pipe size reductionPipe size reduction

Control Control ComponentsComponents (valves, filters, check (valves, filters, check valves, meters, gages…)valves, meters, gages…)

Entry and exit effects (velocity profile)Entry and exit effects (velocity profile)

Contraction/ExpansionContraction/Expansion

DirectionalDirectional Changes (elbows, Ts..) Changes (elbows, Ts..)

Potential EnergyPotential Energy: Height: Height

Viscous LossesViscous Losses: Boundary Layer formation: Boundary Layer formation

Turbulent EnergyTurbulent Energy

Modular systems experience Momentum, Viscous, and Turbulent losses



Driving Liquids

Flow in a straight pipe

f values taken for smooth pipes flowing at 104 and 105 Re

fα Re,ε(Re = U d/)

↑ Re ↓ f↑ P↑

↑ Re ↑ f↓ P↑ 10x increase in yields 71%

increase in P 10x increase in yields in

580% increase in P

Darcy’s equation: P = .000216 x f x x L x Q2 / d5

¤

¤

Density is dominant in straight pipes



Piezometric pressure gradientViscous termsMomentum

terms

Local acceleration

2

2

2

2

2

2ˆ

z

u

y

u

x

u

x

p

z

uw

y

uv

x

uu

t

u

Navier-Stokes Equations (Incompressible, Laminar, in 3D Cartesian Coordinates)

Driving Liquids

For Non-Uniform Geometry

Both Density and Viscosity affect 2nd order terms



Conventional System: Predicting Driving Pressure

Bernoulli’s Equation (mechanical energy along a streamline)

z1 + 144 p1/1 + v12/2g = z2 + 144 p2/2 + v2

2/2g + hLPotential Pressure Kinetic TotalEnergy Energy Energy Head Loss

Where, hL = K v2 / 2g

Ki = f L / D (Ki: Flow Resistance)

Ktotal = Ki

L / D: Equivalent pipe length for non-pipes i.e. valves, fittings

Fitting L/DGlobe Valve 340

Lift Check Valve 600

Ball Valve 6

Tee- Branch flow 60

Elbow- 90 60

Bend r/D = 20 50

Flow resistance approach in systems design



Q, ml/min 300 OD 1/4"

Pipe friction, f 0.0308Wall

Thickness0.065

Non-Pipe friction, f_T 0.0379

Component Quantity Ki f*Ki K

90-Elbow 20 60 2.27 45.4

Check Valves 1 600 22.71 22.7

Globe Valves 8 500 18.93 151.4

90-Bends, r/d=8 20 24 .91 18.2

Flow-thru-branch 6 60 2.27 13.6

Pipe, inch 120 30.8

K_total 282.1

h, in 265.8

P, psi 9.6

Courtesy of Exxon MobilK values are empirical

Conventional System: Predicting Driving Pressure



Pressure Required for a MPC

Flow Flow

Empirical Approach (Cv or K): Cv = 29.9 d2 / k1/2

(1/Cv-total)2 = Σ (1/Cv-i)2

Testing

CFD

Cv-1

Cv-5

Cv-4

Cv-3

Cv-2Cv-total < Cv-i



What is CFD?A numerical approach to solving the Governing flow equations over any Geometry and Flow conditions

CFD is used to solve the general form of the flow equations



CFD – The Governing Equations

pdy [p+(p/x)dx]dyC.V.

(u/y)dx|y

(u/y)dx|y+dy

w

External Forces

F= d(MU)/dt = u(u/x)dxdy + v(u/y)dxdy

Differential Control Volume

dx

dy

1

xy

[u+ (u/x)dx]2dy

[u+(u/y)dy][v+(v/y)dy]dx

u2dyC.V.

uvdx

Change in Momentum

The flow equations are based on the conservation laws



0

z

w

y

v

x

u

t

Continuity equation

Local acceleration

2

2

2

2

2

2ˆ

z

u

y

u

x

u

x

p

z

uw

y

uv

x

uu

t

u

2

2

2

2

2

2ˆ

z

v

y

v

x

v

y

p

z

vw

y

vv

x

vu

t

v

Inertia terms Piezometric pressure gradient Viscous terms

2

2

2

2

2

2ˆ

z

w

y

w

x

w

z

p

z

ww

y

wv

x

wu

t

w

Navier-Stokes Equations for an Incompressible, Laminar flow

CFD – The Governing Equations

The N.S. eqs. are highly elliptical and impossible to solve manually



011

1

i

ii

ii yxx

yy

ii

ii

i xx

yy

x

yy

1

1'

Solve: y + y = 0 (1st order PDE)

for 0 x 1

From Taylor’s:

Plug into (1):

For a structured grid: x = Xi+1 - Xi

x

x

j

y

i

y

y1 y2 y3 y4

0 1

(Eq. 2): Discretized, Algebraic Equation

-yi + (1+ x )yi+1 = 0 (3)

Apply equation (3) to the 1-D grid at nodes 1,2,3:

-y1 + (1+ x )y2 = 0 (i=1) (4)

-y2 + (1+ x )y3 = 0 (i=2) (5)

-y3 + (1+ x )y4 = 0 (i=3) (6)

Equations 4, 5, & 6 are 3 equations with 4 unknowns

The B.C. y1=1 completes the system of equations

XXNNXX11 Discrete Discrete

DomainDomain

CFD – How does it Work?

Convert the PDE into an Algebraic equation



Next, we write the system of equations in a matrix form: [A]{y}={0}

1 0 0 0

-1 (1+ x ) 0 0

0 -1 (1+ x ) 0

0 0 -1 (1+ x )

y1 = 0 (BC)

y2 = 0 (4)

y3 = 0 (5)

y4 = 0 (6)

• To solve, is to find [A]-1

• Much CFD work revolves around optimizing the inversion process

What is CFD?

0.35

0.45

0.55

0.65

0.75

0.85

0.95

0 0.2 0.4 0.6 0.8 1

x

y

4 pts. PredictionActual8 pts. Prediction

Accuracy is grid dependent



CFD – Application to Current System

Toggle Shut-off

Pneumatic Shut-off

Toggle Shut-off

Pneumatic Switching Valve

Toggle Shut-off

Check Valve

Pressure

PressureSwitching Valve

PneumaticShut-off

ManualShut-off

Flow Flow




Build the Geometry




Extract the Fluid volume




Create the Mesh: 3.2 million cells




Set Boundary Conditions

Solve



Results

Pressure required to drive 300 cc/min through the 12-position system, psi

Pressure required to drive liquid samples through modular systems are in line with available pressure

MPC

Tested

MPC

CFD PredictionsConventional Calculated

Water 15.6 16.9 9.6

Diesel 17.9 15.1 10.8

Gasoline 12.5 11.7 7.1



Results: CFD vs. Actual

GASOLINE

100

150

200

250

300

350

0 2 4 6 8 10 12 14

Delta p, psi

Flo

w R

ate,

cc/

min

Tested

CFD Predicted

WATER

50

100

150

200

250

300

0 2 4 6 8 10 12 14

Delta P, psi

Flo

w R

ate,

cc/

min

Tested

CFD Predicted

DIESEL

50

100

150

200

250

300

0 2 4 6 8 10 12 14

Delta P, psi

Flo

w R

ate

, cc

/min

Tested

CFD Predicted

CFD predictions are very accurate when fluid characteristics are known



Results: Density vs. Viscosity

SG , cP

Water @ 65 F 1 1

Diesel Fuel #2 @ 100 F

.85 1.69

Unleaded Gasoline

.73 .47

Actual Test Data

0

50

100

150

200

250

300

350

0 5 10 15

Delta P, psi

Flo

w R

ate

, cc

/min

Water @ 70 F

Diesel Fuel #2 @ 70 F

Unleaded Gasoline @ 70 F

Viscosity effects are more prominent than density effects in modular systems

Testing conducted by Colorado Engineering Experiment Station Inc.



SG = /, cSt

Water @ 65 F 1 1

Diesel Fuel #2 @ 100 F .85 2

Unleaded Gasoline .73 .64

The Kinematic viscosity compares relatively well to pressure

ΔPfluid/ΔPwater ≈ (fluid/water)0.5

Pressure to Drive 300 ml/min

Water

Diesel

Gasoline

0.15

0.35

0.55

0.75

0.95

1.15

1.35

1.55

10 11 12 13 14 15 16 17 18 19

Pressure (psi)

Kin

emat

ic V

isco

sity

(cSt

)^.5

Results: Density vs. Viscosity



Conclusion

• Reasonable pressure required to drive typical liquid samples through NeSSITM systems

• CFD can be employed to accurately predict flow under different conditions

• The Kinematic viscosity of the liquid sample is a good indicator of its pressure requirement



Questions?

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