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

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

Tony Bougebrayel, PE, PhD

Engineering Analyst

Swagelok Co.

- 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

- Momentum Loss:
Pipe size reduction

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

Entry and exit effects (velocity profile)

Contraction/Expansion

Directional Changes (elbows, Ts..)

- Potential Energy: Height
- Viscous Losses: Boundary Layer formation
- Turbulent Energy

Modular systems experience Momentum, Viscous, and Turbulent losses

- Flow in a straight pipe

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

- fαRe,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

¤

¤

Density is dominant in straight pipes

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

Viscous terms

Local

acceleration

Momentum terms

Piezometric pressure gradient

Driving Liquids

- For Non-Uniform Geometry

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

Both Density and Viscosity affect 2nd order terms

Bernoulli’s Equation (mechanical energy along a streamline)

z1 + 144 p1/1 + v12/2g = z2 + 144 p2/2 + v22/2g + hL

Potential 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

Flow resistance approach in systems design

K values are empirical

Courtesy of Exxon Mobil

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-5

Cv-4

Cv-3

Cv-total < Cv-i

Cv-2

Cv-1

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

Differential Control Volume

1

dy

y

dx

x

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

u2dy

C.V.

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

(u/y)dx|y+dy

uvdx

pdy

[p+(p/x)dx]dy

C.V.

w

(u/y)dx|y

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

External Forces

Change in Momentum

The flow equations are based on the conservation laws

Continuity equation

Navier-Stokes Equations for an Incompressible, Laminar flow

Local

acceleration

Viscous terms

Inertia terms

Piezometric pressure gradient

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

X1

Discrete Domain

XN

x = Xi+1 - Xi

For a structured grid:

CFD – How does it Work?

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

for 0 x 1

From Taylor’s:

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

Plug into (1):

(Eq. 2): Discretized, Algebraic Equation

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

y2

y1

y3

y4

-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

y

y

x

0

1

j

i

x

Convert the PDE into an Algebraic equation

What is CFD?

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

y1= 0 (BC)

y2= 0(4)

y3= 0 (5)

y4= 0 (6)

1 0 0 0

-1(1+ x ) 0 0

0 -1 (1+ x ) 0

0 0 -1 (1+ x )

- To solve, is to find [A]-1
- Much CFD work revolves around optimizing the inversion process

Accuracy is grid dependent

Check Valve

Switching Valve

Pressure

Pressure

Toggle Shut-off

Pneumatic Switching Valve

Pneumatic Shut-off

ManualShut-off

PneumaticShut-off

Toggle Shut-off

Toggle Shut-off

Flow

Flow

Build the Geometry

Extract the Fluid volume

Create the Mesh: 3.2 million cells

- Set Boundary Conditions
- Solve

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

CFD predictions are very accurate when fluid characteristics are known

Viscosity effects are more prominent than density effects in modular systems

Testing conducted by Colorado Engineering Experiment Station Inc.

Results: Density vs. Viscosity

ΔPfluid/ΔPwater≈ (fluid/water)0.5

The Kinematic viscosity compares relatively well to pressure

- 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