pressure drop presentation lknl

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

Pg 3

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.

Pg 4

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

Pg 5

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

Pg 7

Force-Momentum Balance within a Control Volume

Pg 8

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

Pg 10

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.

Pg 11

SP Pressure-Drop Equations

• Friction

• Acceleration

• Gravity

• Form

lhyfricsp

GDLfP

ρ2

2,

∆=∆

laccsp GP υ∆=∆ 2.,

zgP bgsp ∆=∆ θρ sin,

llocallocalsp

GKPρ2

2, =∆

Pg 12

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

Pg 13

Bundle Correction Factor

Pg 14

Eccentricity Effect

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

• Non-uniform velocity distribution

Pg 15

Eccentricity Correction Factor

Pg 16

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

Pg 17

Single-Phase Pressure Distribution over a Square-Edged Orifice

Pg 18

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

Pg 21

Single-Phase Pressure Distributions over Aligned and Misaligned Bundles

Pg 22

Water Pressure Drop Test Station

Pg 23

Water Pressure Drop Test Results

400000 600000 800000200000

24

23

22

25

Reynolds Number

Pg 24

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

Pg 25

Hydraulic Characterization Test

DP-7 DP-1

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

InnerProbe

DP-4

Outer Probe Reference

Flow

Outer Probe

Inner Probe

Pg 26

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

Pg 27

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.

Pg 28

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

Pg 29

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

Pg 30

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 −=

Pg 31

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=∆

−−

Pg 32

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)

Pg 33

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−

Pg 34

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

Pg 36

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

Pg 42

Two-Phase Pressure Distributions over Aligned and Misaligned Bundles

Pg 43

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

Pg 44

Axial Power Profile in Water Tests

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

0

0.5

1

1.5

2Coolant Flow

Pg 45

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

Pg 46

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%

Pg 48

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

Pg 49