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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.
Swagelok Technology Summit
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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CFD – Application to Current System
Build the Geometry
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CFD – Application to Current System
Extract the Fluid volume
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CFD – Application to Current System
Create the Mesh: 3.2 million cells
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CFD – Application to Current System
Set Boundary Conditions
Solve
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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
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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
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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.
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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
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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
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Questions?