Computational Fluid Dynamic (CFD)
Analysis of Gas and Liquid Flow
Through a Modular Sample System
Tony Y. Bougebrayel, PE, PhD
John J. Wawrowski
Swagelok
Solon, Ohio
IFPAC 2003
Scottsdale, Az
January 21-24, 2003
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Agenda
Objective
Cv, K Factor
CFD Background
MPC - CFD Model Description, Procedure
Results
Conclusions
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Objectives
Evaluate the flow capacity (Cv) for a threeposition Swagelok MPC substrate flow component
Investigate the effects of using different surfacemount components on the total system Cv
Determine an analytical method for predicting the
total system Cv
Investigate the effect of the fluid type on the
pressure drop through a substrate flow component
Determine the pressure required to flow a liquid
sample through a Swagelok MPC system
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Cv and K Factors
The Cv Approach
The K Approach
What causes Cv and K and how are they
determined?
How do they relate to the MPC?
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The Cv Approach
Cv: Flow capacity (component)
For Newtonian Liquids:
Through control components: q = N1 * Fp * Cv * (Δp / Gf)1/2 (ISA 75.01)
Through straight pipes: Δp = .000216 f L  Q2 / d5
(Darcy’s)
For Gases:
Through control components:
q = N7 * Fp * Cv * p1 * Y * [x / (Gg T1 Z)]1/2
(ISA 75.01)
For Low pressure drop: 1.0 < Y < 2/3, (p1 2p2) and Y = 1 – x / (3Fk xt)
For high pressure flow (choked flow, p1>2p2):
Y= 2/3, xt=.5 and q = N7 * Fp * Cv * p1*.471*[1 / T1 Z)]1/2
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The K Approach
K-Factor: Resistance to flow (system)
Head loss through a pipe, valve, or fitting:
hL = K v2 / 2g
where: K = f L / D (Darcy’s)
Bernoulli’s equation (mechanical energy):
z1 + 144 p1/1 + v12/2g = z2 + 144 p2/2 + v22/2g + hL
Potential
Energy
Pressure
Kinetic
Total
Energy
Energy
Head Loss
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The Make-up of Cv and K
Changes in the flow direction (turns)
Changes in the geometry (expansion, contraction, flow
obstacles)
Geometry size
Weight of the fluid (density effects)
Velocity of approach (entry and exit velocity)
Friction between the fluid and solid as well as within the
fluid layers (viscosity effects)
Elevation (1psi is about 27.8 inches of water head)
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The Make-up of Cv and K —
Order of Importance
1. Transition: A sharp 90-degree turn costs the flow more
energy (pressure) than the frictional losses or pipe
reduction losses (i.e. losses due to a short 90 deg. turn
are four times greater than losses due to a half size
reduction in the pipe diameter)
2. Pipe Size: Pipe size reduction has a 5-power effect on
the flow where the frictional losses are at 1st order
3. Friction: The frictional losses are of greater relative
importance in smaller components (frictional losses
decrease with the increase in flow velocity or pipe
diameter)
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How are Cv and K determined?
Testing (ISA 75.02)
Empirical values (macroscopic approach)
CFD (microscopic approach)
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Computational Fluid Dynamics —
Background
CFD History
How it works
Swagelok’s Effort
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CFD History
Scientific community (space research and power
production)
Current Status and Applications
Challenges
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How Does CFD Work?
Geometry
Mesh
Boundary Conditions
Solution Method
Post Processing
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Geometry
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Geometry
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Mesh – External Volume
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Mesh – Internal Volume
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Boundary Conditions
Mass Flow Rate
Pressure
Velocity
Inlet-Vent
Inlet-fan
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Solution Method
Coupled/Segregated
Laminar/Turbulent
K-, RSM, k-, LES,…
Compressible/Incompressible
Steady State/Transient
Set the Boundary Conditions
Initialize the Solution
Solve
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Post Processing
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Post Processing
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Post Processing
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Swagelok’s Effort
Swagelok gained in-house CFD capabilities in
1997
The majority of applications revolve around
finding/optimizing Cv and Heat transfer analysis
Swagelok tool box: Fluent®, Floworks®, and
Pipeflow®
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MPC – CFD Model
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MPC - CFD Model
Model: Turbulent, Steady State, Segregated, Implicit
Geometry: 3D with symmetry about the center plane
Viscous Model: Standard k- turbulence model
Medium: Water, Air and some Hydrocarbons
Boundary Conditions:
Inlet: Mass Flow Rate (300 ml/min)
Outlet: Atmospheric pressure
Mesh: Hybrid, 120k order
Convergence Criteria: Conservation of mass, Y+
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Results
Cv of a three-position system
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Results
Predicted Cv: 0.040
Tested Cv: 0.045
Flow Direction
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Results
Cv changes based on surface-mount components
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Results
Total system Cv: 1/Cvtotal 2 = Σ (1/Cvi)2
Cv1
Cv2
Cv3
Cv4
Cv5
Cv6
Cv7
Flow Direction
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Results - Effects of fluid type on required driving pressure

For liquids with similar kinematic viscosities (υ = μ/ρ):
ΔPfluid / ΔPwater = (1/SGfluid) x (mass flow rate of fluid/mass flow rate of water)2

For liquids with different kinematic viscosity (i.e. motor oil):
ΔPfluid / ΔPwater = (υfluid / υwater).5
Viscosity vs. Pressure Drop Correlation
Benzene
Water
Ethylene-Glycol
Ethyl Alcohol
(C2H6O2)
(C2H5OH)
Delta P total
Kinematic
Viscosity
Ethylene-Glycol
(C2H6O2)
Ethyl Alcohol
(C2H5OH)
Water
Benzene
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Results – Pressure drop on 3 position assembly
Media
Density
(kg/m3)
Kinematic
Viscosity
(m2/s)
P
(psi)
Air
1.2
1.5 x 10-5
0.003
Ethyl Alcohol
790
1.5 x 10-6
1.14
Benzene
875
6.7 x 10-7
1.22
Ethylene-Glycol
1,111
1.4 x 10-5
2.74
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Results
Total Presssure Required, psig
Pressure Required to drive 300 ml/min through
Swagelok's MPC (3-position assembly)
30
25
20
15
10
5
0
Benzene
Water
Ethylene-Glycol
(C2H6O2)
Ethyl Alcohol
(C2H5OH)
Air
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Conclusions
A valid model for predicting flow capacity of
a Swagelok MPC system
The surface-mount component has the
largest effect on total system Cv
Developed a valid equation for predicting
pressure to drive liquids
Based on kinematic viscosity
MPC requires minimal driving pressure
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