Pressure Drop

L.K.H. LeungThermalhydraulics Branch

Chalk River Laboratories, AECL

UNENE Thermalhydraulics Course

Pg 2

Outline• Background

• Conservation equations

• Single-phase pressure gradient

• Onset of significant void

• Two-phase pressure gradient

• Summary

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Introduction

• A pumped system is often employed for flow mediums circulation and transportation

• All piping components in the flow system reduce the system pressure

• Pressure reduction can be minimized but is not always feasible

• Pump capacity must be matched properly with the system requirements

• For design calculations, the pump size has a large impact on the system cost.

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Applications

• General applications:− Optimize pump capacity requirement− Optimize pump energy requirement

• CANDU nuclear reactor applications:− Determine coolant-flow rate in primary circuit− Determine local conditions in bundles and subchannels− Determine flow rate across parallel interconnected

subchannels in fuel bundles

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CANDU Applications

Partial Setup of Nodes In Subchannel Code - ASSERT

Outlet Header

Inlet Header

CANDU Fuel Channel

Pg 6

Conservation Equations

• Mass-balance (continuity) equation• Momentum-balance equation• Energy-balance equation• Cases:

− Steady-state flow in channel of uniform flow area in axial direction

• Assumptions− Negligible variation of fluid properties over the control volume− Homogeneous or separated flow

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Force-Momentum Balance within a Control Volume

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Basic Equations for Homogeneous-Flow Assumption

( )

+

+

−=−

θρ+

++τ=−

θρ+

ρ+τ=−

ρρ

ρ−+ρ=

ρ

δθρ+δ+δτ=

δ+−

ρ−

ρ

∫∫∫∫

gaf

Hl)ax1(

gax2

w

HH

2w

lg

gala

H

A HA mS wA

dzdP

dzdP

dzdP

dzdP

singdzdG

AS

dzdP

singGdzd

AS

dzdP

)x1(x1

dAzsingdAzuGdzddSzdAz

dzdPPP

Pg 9

Basic Equations for Separated-Flow Assumption

( )

( )

+

+

−=−

θρα−+αρ+

++τ=−

θρα−+αρ+α+α−+τ=−

ρα−+αρ=ρ

δθρ+δ++δτ=

δ+−

ρα−−

ρα

∫∫∫∫

gaf

lgl)1(

2)ax1(g

2ax2

w

lgggllw

lgtp

A tpA ggllS wA

dzdP

dzdP

dzdP

dzdP

sing))1((dzdG

AS

dzdP

sing))1((uGuG)1(dzd

AS

dzdP

)1(

dAzsingdAzuGuGdzddSzdAz

dzdPPP

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Pressure Gradients• Friction

− Between fluid and channel wall− Primarily affected by tube diameter, velocity gradient and viscosity

• Acceleration− Change in fluid momentum between locations− Significant in channel with varying flow area and fluid temperature

• Gravity− Change in hydrostatic head− Only in vertical channel

• Others− Flow blockages: valves, orifices, bundle junction, appendages, etc.− Change in flow direction: elbows, etc.− Change in flow area: sudden contraction, sudden expansion, etc.

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SP Pressure-Drop Equations

• Friction

• Acceleration

• Gravity

• Form

lhyfricsp

GDLfP

ρ2

2,

∆=∆

laccsp GP υ∆=∆ 2.,

zgP bgsp ∆=∆ θρ sin,

llocallocalsp

GKPρ2

2, =∆

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Single-Phase Friction Factor

• Tubes− Colebrook-White equation

• Bundles− Based on hydraulic-equivalent diameter approach with the

tube-based equation− Correction for geometry effect (differences between tubes and

bundles)− Correction for eccentricity effect (differences between

concentric and eccentricity bundles) in crept channels− Correction for channel shape effect (converging and

diverging channels) in crept channels− Correction for surface heating effect

+−=

Re51.2

7.3/log21

tube

tube

tube fD

fε

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Bundle Correction Factor

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Eccentricity Effect

• More fluid tends to flow in the open region (less resistance)

• Non-uniform velocity distribution

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Eccentricity Correction Factor

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Single-Phase Loss Coefficients

• Sudden contraction− Based on flow-area ratio

• Sudden expansion− Based on flow-area ratio

• Bends− Based on angle

• Junction and appendages in bundles− Based on data obtained with production bundles− Correction for eccentricity effect

KAAcontf

o.

/

.= −

0 5 1

3 4

KAAf

oexp. = −

1

2

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Single-Phase Pressure Distribution over a Square-Edged Orifice

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Fuel String Pressure Drop

• Part of the overall pressure drop between headers• Separated into single-phase and two-phase regions• Pressure-drop components

− Friction− Bundle junction, spacers, buttons, and bearing pad planes− Acceleration− End fittings

• Simplified evaluation approach for bundles− Combined friction and form losses into a bundle loss

coefficient

lappendagejunction

hy

BundleBundle

lBundleBundlesp

GKKDLfGKP

ρρ 22

22,

++==∆

Pg 19

Appendages in a CANDU Fuel Bundle

Pg 20

Bundle Junction Alignment

Aligned Bundles Misaligned Bundles

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Single-Phase Pressure Distributions over Aligned and Misaligned Bundles

Pg 22

Water Pressure Drop Test Station

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Water Pressure Drop Test Results

400000 600000 800000200000

24

23

22

25

Reynolds Number

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Freon Pressure Drop Test Station Inlet Temperature (RTD)Inlet Pressure (Pressure Transmitter)

Outlet Temperature (RTD)Outlet Pressure (Pressure

Transmitter)

Fillerbundle

CANFLEX ACR bundles

CANFLEX Mk-IVbundles

YDG AE HO F CB

Fillerbundle

Flow

∆P measurement ∆P measurement

∆P measurementMixed bundle

junction

#12#10#9 #11#8

DP-10 DP-11DP-12

DP-13DP-15DP-14

Centre-line of Bundle C

YB CH A D

#13

DP-16

#7#6

DP-8 (Interface junction pressure drop)

DP-9

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Hydraulic Characterization Test

DP-7 DP-1

DP-2DP-3DP-5DP-6

InnerProbe

DP-4

Outer Probe Reference

Flow

Outer Probe

Inner Probe

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Freon Pressure Drop Test Results

0

1

2

3

4

5

0 100 200 300 400 500 600 700 800Axial Distance (mm)

Dim

ensi

onle

ss P

ress

ure

Dro

p

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Misaligned Junction Signatures

4

6

8

10

12

14

16

18

20

-30 30 90 150 210 270 330 390Misalignment Angle (Degrees)

Two-phase (x = 13%)Single-phase (x = 0%)

37-Rod Bundle

Sutradhar, Proc. 6th Int. Conf. on CANDU Fuel, Niagara Falls, Canada, September 26-30, 1999.

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Onset of Significant Void (OSV)

• Determined from axial pressure distributions along the full-scale bundle simulator in reference and aged channels

• A linear relation over the single-phase region in uncrept channel and a parabolic equation over the two-phase region

• The intersecting point of these two equations is considered as the OSV

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Axial Pressure Distribution

10900

11000

11100

11200

11300

11400

11500

11600

11700

-1 0 1 2 3 4 5 6 7

Axial Distance (m)

Pres

sure

(kPa

)

OSV point

End of heated length

Start of heated length

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OSV Correlations

• Saha-Zuber correlation for tubes− Peclet number (G D Cp / k) < 70,000

− Peclet number ≥ 70,000

• Modified Saha-Zuber correlation for bundles− Update empirical coefficients using full-scale bundle data− Proprietary information

fgf

pfHkCDq

0022.0xOSV −=

fgHGq154xOSV −=

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TP Frictional Pressure Drop

• The two-phase frictional pressure drop is calculated with

liquidphaseglesinasflowtotalonbasedP

channeltheinliquidphaseglesinonlyonbasedP

Reafwhere)x1(

PPorPP

LO,f2LO

L,f2L

bb2a

2L

2LO

LO,f2LOTP,fL,f

2LTP,f

−∆−φ

−∆−φ

=−φ=φ

∆φ=∆∆φ=∆

−−

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Two-Phase Multiplier

• Two-phase multipliers, φ2L or φ2

LO, are empirical factors based on experimental data

• Expressed in the form of graphs or correlations (large uncertainty due to scatter among data)

• Depends mainly on quality and pressure• Mass-flux effect primarily observed at low flows (flow-

regime dependent)• Surface heating has a strong impact (near-wall effect)

on two-phase multiplier in tubes and annuli, but not in bundles (compensating effect)

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Homogeneous Two-Phase Multiplier

• The simplest form

Beattie)patternflow(f

.aletDukler)x1(x

.aletCicchitti)x1(x

.aletMcAdamx1x1

x1f

f

TP

l

la

g

gaTPTP

lagaTP

l

a

g

a

TP

b

TP

l

g

gla

TP

l

l

TP2LO

−=µ

ρµ−

+ρ

µρ=µ

µ−+µ=µ

µ−

+µ

=µ

µµ

ρ

ρ−ρ+=

ρρ

=φ−

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TP Multiplier in Separated FlowMartinelli and Nelson Graph

Pg 35

Friedel Correlation

• Complex formulation• Based on over 25,000 data points• Uncertainty: ±26%, ±32% and ±25% for single-

component upward, horizontal and downward flow• Recommended by many studies

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Surface-Heating Effect

• Changes in near-wall velocity gradient due to bubble formation, hence two-phase pressure drop

• Sharp variations due to liquid-film thinning, liquid-surface contact or vapour-surface contact

• Depends strongly on critical heat flux

Pg 37

Effect of Surface Heating

Water Flow Helium Flow

Pg 38

Two-Phase Multipliers in Pre- and Post-Dryout Regions

Pg 39

Corresponding Surface-Temperature Variations

Pg 40

Local Pressure Drop

• Two-phase local pressure drop is calculated with

multiplierphasetwousHomongeneo

x1

PP

g

gla

2local,LO

SP,local2

local,LOTP,local

−

ρ

ρ−ρ+=φ

∆φ=∆

Pg 41

Two-Phase Pressure Distribution over a Square-Edged Orifice

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Two-Phase Pressure Distributions over Aligned and Misaligned Bundles

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High Pressure Water Test Station

P4

Tout

P2

P3P1

dP1

Tin

Coolant Flow

dP2 dP13 dP3 dP14 dP4 dP5 dP7 dP8 dP9 dP10 dP11

dP12

dP6

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Axial Power Profile in Water Tests

Axial Distance (m)0 1 2 3 4 5 6

0

0.5

1

1.5

2Coolant Flow

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1-1 2 3 4 5 6 7

109

Axial Distance (m)0

108

107

106

105

104

103

110Axial Flow Tube Diameter Variation

Flow Direction

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Onset of Significant Void

0

10

20

30

40

50

60

70

80

90

0 2000 4000 6000 8000

Power (kW)

Pres

sure

Dro

p (P

a)

1.4 mm BP, 5.1% Crept Channel

DP8

DP9

DP10

DP11

DP12

DP13

Dimmick et al., Proc. 6th Int. Conf. on CANDU Fuel, Niagara Falls, Canada, September 26-30, 1999

Pg 47

Pressure Gradient Along Flow Channel

Dimmick et al., Proc. 6th Int. Conf. on CANDU Fuel, Niagara Falls, Canada, September 26-30, 1999

350

300

250

200

150

100

50

0

400

2 3 4 5 6 7 8 9 111 12 13 1410Pressure Tap

Test ConditionsMass Flow Rate: 19 kg/sOutlet Pressure: 10.5 MPaInlet Temperature: 285 C

5.1% Crept Channel1.4 mm Bearing Pads Two-phase

Power: 5700 kWOutlet Quality: 2%

Single-phasePower: 2700 kWOutlet Quality: -10%

Two-phasePower: 6500 kWOutlet Quality: 5%

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Summary

• Pressure drop is one of the main thermal-hydraulics parameters in flow re-circulation systems

• Pressure drop depends on flow conditions, flow regimes, and surface heating

• Four main components in the overall pressure drop: friction, acceleration, gravity, and form

• Two-phase pressure drops due to friction and local disturbances are expressed in terms of two-phase multipliers

• A large number of correlations are available for two-phase multiplier; uncertainty remains high due to large scatter among data

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