Tony Y. Bougebrayel, PE, PhD 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

Agenda Objective Cv, K Factor CFD Background MPC - CFD Model Description, Procedure Results Conclusions

Objectives Evaluate the flow capacity (Cv) for a three-position Swagelok MPC substrate flow component Investigate the effects of using different surface-mount 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

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?

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

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 Pressure Kinetic Total Energy Energy Energy Head Loss

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)

The Make-up of Cv and K — Order of Importance 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) Pipe Size: Pipe size reduction has a 5-power effect on the flow where the frictional losses are at 1st order Friction: The frictional losses are of greater relative importance in smaller components (frictional losses decrease with the increase in flow velocity or pipe diameter)

How are Cv and K determined? Testing (ISA 75.02) Empirical values (macroscopic approach) CFD (microscopic approach)

Computational Fluid Dynamics —Background CFD History How it works Swagelok’s Effort

CFD History Scientific community (space research and power production) Current Status and Applications Challenges

How Does CFD Work? Geometry Mesh Boundary Conditions Solution Method Post Processing

Geometry

Geometry

Mesh – External Volume

Mesh – Internal Volume

Boundary Conditions Mass Flow Rate Pressure Velocity Inlet-Vent Inlet-fan

Solution Method Coupled/Segregated Laminar/Turbulent K-, RSM, k-, LES,… Compressible/Incompressible Steady State/Transient Set the Boundary Conditions Initialize the Solution Solve

Post Processing

Post Processing

Post Processing

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®

MPC – CFD Model

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+

Results Cv of a three-position system

Results Predicted Cv: 0.040 Tested Cv: 0.045 Flow Direction

Results Cv changes based on surface-mount components

Results Total system Cv: 1/Cvtotal 2 = Σ (1/Cvi)2 Cv1 Cv2 Cv3 Cv4 Cv5 Flow Direction

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

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

Results

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 Visit Swagelok at Booth 51