13 Pressure Drop RCM4

Vienna, Austria, September 10-13, 2007

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Thermo-fluid dynamics and pressure drops in various geometrical configurations

M.R. Gartia, P.K. Vijayan D.S. Pilkhwal and D. Saha

Reactor Engineering DivisionBhabha Atomic Research Centre

Mumbai, India

4th RCM on the IAEA CRP on Natural Circulation Phenomena, Modelling and Reliability of Passive Safety Systems that Utilize Natural Circulation

Vienna, Austria, September 10-13, 2007 2

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Introduction

A large number of single-phase and two-phase flow pressure drop correlations can be found in literature. Important pressure drop relationships can be found in the IAEA technical document for “Thermohydraulic relationships for advanced water cooled reactors” (IAEA-TECDOC-1203).

Most of the pressure drop correlations are developed from data generated in forced circulation systems.

The mechanism of flow in natural circulation loop may be complex due to buoyancy effect and formation of secondary flows.

Therefore, there is a need to give a closer look to pressure drop phenomena under natural circulation, which is both complex and

important.


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Definition

Pressure drop is the difference in pressure between two points of interest in a fluid system. In general, pressure drop can be caused by resistance to flow, changes in elevation, density, flow area and flow direction .

It is customary to express the total pressure drop in a flowing system as the sum of its individual components such as distributed pressure loss due to friction, local pressure losses due to sudden variations of shape, flow area, direction, etc. and pressure losses due to acceleration and elevation.

An important factor affecting the pressure loss is the geometry.

Other factors are concerned with the fluid status, the flow nature, the flow pattern, the flow direction, flow type, flow paths and the operating conditions


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An important focus of this phenomenon is the geometric conditions that hinder the establishment of fully developed flow especially when the fluid in question is a mixture of steam, air and water. This complex thermo-fluid dynamic phenomenon warrants special attention.

Though in many systems like the primary system of a nuclear power plant, flow is mostly not fully developed, pressure drop relationships used in these systems are invariably those obtained for developed flow. This practice is also experimentally proved to be more than adequate in most of the cases. However, in some specific cases like containment internal geometry, it is necessary to consider thermo fluid dynamics in the developing region.

Normally the pressure loss inside a device depends on the nature of flow through the device and not on the nature of driving head causing the flow. However, under some circumstances, because of local effects, the pressure loss may get influenced by the nature of driving force.

Definition


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Scenario

In a flowing system there are two components of total pressure drop

1. Irreversible pressure drop 2. Reversible pressure drop

The irreversible pressure drop is called pressure loss. This is due to irreversible conversion of mechanical energy (the work of resistance force) into heat. This includes Friction loss and Local loss.

There are also reversible component of pressure drop such as elevation pressure drop and acceleration pressure drop.


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Scenario

Friction loss

Due to the viscosity (both molecular and turbulent) of real liquid and gases in motion, and results from momentum transfer between the molecules (in laminar flow) and between individual particles (in turbulent flow) of adjacent fluid layers moving at different velocities.

For two-phase flow, an additional frictional pressure drop may be due to the inter-phase friction between gas-liquid or steam-liquid phases.

Local losses

Caused by local disturbances of the flow; separation of flow from the walls; and formation of vortices and strong turbulence agitation of the flow


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Scenario

Acceleration pressure drop

Due to the energy spent in accelerating the molecules of the fluid. This reversible component of pressure drop is caused by a change in flow area or density.

Elevation pressure drop

Because of the work needs to be done against the gravity to raise the fluid molecules to a height. This reversible component of pressure drop is caused by the difference in elevation.


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Scenario

The pressure loss components are inseparable. However, for ease of calculation they are subdivided into components like local losses, frictional losses etc.

It is also assumed that the local losses are concentrated in one sectioned although they can occur virtually over a considerable length

Most of the pressure drop correlations reported in literature had been developed from steady state experimental data and mostly under adiabatic conditions.


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Hardware: where it occurs?

Channel type Vessel typeDistributed pressure drop - Feeder and tail pipe

- Bare bundle- Core and core bypasses- Surge line- Steam Generator (SG) tubes

Local pressure drop - Fuel bundle assembly- Various header connections- Valves and rupture disc locations

- Pump inlet, outlet and inside- Pressurizer and surge line connections

Safety system pressure drop

- Accumulator outlet line- ECCS header to water tube connection- Advanced fluidic device- Gravity Driven Water Pool (GDWP) to ECCS header connection

-Accumulator connections- ECCS connections

Geometries of interest to Nuclear Power Plants (NPPs) are only considered here.


BARCBARCBARCBARCSingle Phase Pressure Drop: flow

under transition regime• In many transients, the flow may change from laminar to turbulent, or vice versa, necessitating a switch of correlations.

• Numerical calculations, often encounter convergence problems when such switching takes place due to the discontinuity in the friction factor values predicted by the laminar flow and turbulent flow equations.

• Well established correlations for friction factor do not exist in transition region.

Few ways:

1.Calculate both fTURBULENT and fLAMINAR. If fT > fL then f = fT. This procedure, however, causes the switch over from laminar to turbulent flow equation at Re1100.

2. f = (fT)4000 for 2000 Re 4000 where (fT)4000 is the friction factor calculated by the turbulent flow equation at Re = 4000.


BARCBARCBARCBARCSingle Phase Pressure Drop: flow

under diabatic condition

fNON-ISOTHERMAL = fISOTHERMAL* F

1. F in terms of temperature correction:

F=1+ C Tf ;

Tf is the temperature drop in the laminar layer (q”/h). Constant C = 0.001-0.0025

2. F in terms of viscosity ratio:

F = ( bulk / wall )- 0.28

fNON-ISOTHERMAL = fISOTHERMAL with properties evaluated at film temperature

Tfilm = 0.4 (Twall - Tbulk) + Tbulk


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Two-phase

Two-phase pressure drop relationships- adiabatic Empirical correlation based on the homogeneous model Empirical correlation based on the two-phase friction multiplier concept Direct empirical models Flow pattern specific models

Void fraction relationships

Slip ratio models K- models Correlations based on drift flux models


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Models using interfacial friction

Another form of two-phase pressure drop correlations are that uses interfacial friction models. The two-fluid model used in many of the advanced system codes require correlations for interfacial friction in addition to wall friction.

Flow under diabatic condition

The correlations discussed so far are applicable to adiabatic two-phase flow. The effect of heat flux on two phase pressure drop has been studied by Leung and Groeneveld (1991), Tarasova (1966) and Koehler and Kastner (1988).

Two-phase


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Assessment of two-phase pressure drop correlationsThe table given below gives the assessment of pressure drop correlations by various authors and their recommendation.

Authors Categories No. of correlations

tested

No. of data

points

Recommended correlation

Weisman-Choe (1976)

Homogeneous model

--- --- McAdams (1942) and Dukler et al. (1964)

Idsinga et al. (1977)

Homogeneous model

18 3500 Owens (1961) and Cicchitti (1960)

Beattie-Whalley (1982)

Homogeneous model

12 13500 Beattie and Whalley (1982)

Dukler et al. (1964) Multiplier concept

5 9000 Lockhart and Martinelli (1949)

Idsinga et al. (1977)

Multiplier concept

14 3500 Baroczy (1966) and Thom (1964)

Friedel (1980) Multiplier concept

14 12868 Chisholm (1973) and Lombardi-Pedrocchi (1972)

Two-phase


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Snoek-Leung (1989)

---- 9 1217 Friedel (1979)

Vijayan et al. (2000) --- 14 424 Lockhart and Martinelli (1949) with Chexal et al. (1996) for

void fraction.

Weisman-Choe (1976)

Flow pattern specific

11 Separated flow: Agrawal et al. (1973) and Hoogendoorn (1959)

10 Homogeneous flow : McAdams (1942), Dukler et al. (1964) and Chisholm (1968)

7 Intermittent flow: Dukler (1964), Lockhart-Martinelli (1949) and Hughmark (1965)

6 Annular flow: Dukler (1964) and Lockhart- Martinelli (1949)

Two-phase


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Mandhane et al. (1977)

Flow pattern specific

14 10500 Bubbly: Chenoweth and Martin (1956)

Stratified: Agrawal et al. (1973)

Stratified wavy: Dukler et al (1964)

Slug: Mandhane et al. (1974)

Annular, annular mist: Chenoweth and Martin

(1956)

Dispersed bubble : Mandhane et al. (1974)

Two-phase


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Natural and Forced Circulation Pressure Drop

For forced circulation loops, the driving force is the head developed by the pump which is generally far greater than the buoyancy driving head.

The buoyancy being the driving head, natural circulation flows are characterized by low driving head and consequent low mass flux.

Due to buoyancy effect and presence of secondary flows, the velocity profile in a heated pipe may get modified which also depends on the orientation of the pipe (horizontal, vertical upward or downward).

The secondary flow may, in turn, affect the friction factor for the pipe, as the friction factor is mainly dependent upon the velocity gradient.


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Natural and Forced Circulation Pressure Drop

Forced Circulation Natural Circulation

Driving head Large Small

Secondary flow Negligible effect Could be significant

Transition from laminar to turbulent flow

Occurs at higher Reynolds number (Re)

Occurs at lower Re due to secondary flow

Pressure drop correlations at low mass flux

Accuracy need not be high

High accuracy required

Transient Relatively fast Sluggish

Flow Relatively high Low

Stratification Not a concern Commonly encountered

Instabilities Less potent High potential

CHF Relatively higher Relatively lower


BARCBARCBARCBARC Pressure Drop under Low Mass Flux, Low Pressure Conditions

• For a natural circulation loop during start-up, the flow builds up virtually from zero flow condition. Hence the friction factor and loss coefficient correlations should be accurate at very low mass flux.

• Natural circulation loops are particularly susceptible to instabilities at low pressure conditions. These flow instabilities may be characterized by repetitive flow reversals.

• There is a need to assess the existing correlation in terms of its applicability for natural circulation loop.


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0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

Presure = 21 bar

Mass flux = 558 kg/m2-s Pipe ID = 26.64 mm

Pre

ssu

re d

rop

- k

g/c

m2

Quality

Calculated (Chisholm Model) Measureed

Comparison of measured and calculated pressure drop in a vertical pipe with diabatic flow

Pressure Drop at Low Mass Flux


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0.0 0.4 0.8 1.2 1.6 2.00.0

0.4

0.8

1.2

1.6

2.0 Presure = 21 - 72 bar

Mass flux = 40 - 2000 kg/m2-s

heat flux = 55 - 65.2 W/m2

Pipe ID = 26.64 mm

+10%

+20%+3

0%

-10%

-30%

-20%

P meas=

P cal

Experimental data

Pca

l - b

ar

Pmeas

- bar

Comparison of measured and predicted pressure drop using CNEN (1973) correlation for vertical upward diabatic flow in a tube

Pressure Drop at Low Mass Flux


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Single Phase Natural Circulation

The generalized flow correlation for single-phase loops (Vijayan, 1992) is given by,

r

effmss L

DGrC

Re rpC 2 and br 31

where p and b are given by the friction factor correlation of the form

bpf Re

5.0

1768.0Re

G

mss N

Gr

364.0

96.1Re

G

mss N

Gr

Laminar flow (p=64, b=1)

Turbulent flow (p=0.316, b=0.25) with Blasius correlation

Depending on the value of p and b, the flow correlation is given as

pr

hTrm

CA

HgQDGr

3

20

3

Modified Grashoff number

i

N

ibb

eff

r

tG

ad

l

D

LN

121Geometrical parameter


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106 107 108 109 1010 1011 1012102

103

104

105

6 mm loop 11 mm loop 23.2 mm loop 26.9 mm loop VHHC orientation

f = 0.184 / Re0.2

Blasius correlation

f = 0.316 / Re0.25

f = 55.92 / Re0.9501

f = 64 / Re

Re ss

Grm / N

G

Effect of friction factor on steady state flow rate in a single-phase natural circulation loop as predicted by generalized flow correlation

Generalized Correlation


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Flow dependency on power

0.0 0.5 1.0 1.5 2.0 2.50.000

0.025

0.050

0.075

0.100

Flo

w (

kg/s

)

Power (kW)

Experimental data

Blasius correlation (f = 0.316 Re-0.25)

f = 0.184 Re-0.2

Effect of friction factor on steady state flow rate in a single-phase natural circulation loop

b

Gbr

br

brhT

ss CpN

ADQHg

pW

3

122

02


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Two Phase Natural Circulation

5.0

1768.0Re

G

mss N

Gr

364.0

96.1Re

G

mss N

Gr

A generalized flow correlation of the same form as that of single-phase has been developed (Gartia et al. (2006)) to estimate the steady state flow rate in two-phase natural circulation loops which is given by,

rGmss NGrCRe

Where Ress= Steady State Reynolds Number ; Grm = Modified Grashof Number NG = Geometric Parameter

Laminar flow (p=64, b=1)

Turbulent flow (p=0.316, b=0.25) with Blasius correlation

For density variation, pm

tp hv

1


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Generalized Correlation

Effect of friction factor on steady state flow rate in two-phase natural circulation loops

105 106 107 108 109 1010 1011 1012 1013 1014 1015

102

103

104

105

Turbulent flow equation( C=1.96, r=0.364)

-25%

+25%

Laminar flow equation( C=0.1768, r=0.5)

Re ss

Grm/ N

G

Generalized correlation

Ress

=C [Grm/N

G]r

Apsara loop (ID:1/2") Apsara loop (ID:3/4") Apsara loop (ID:1")


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0 100 200 300 400 5000

1

2

3

4

5

6Pressure=50 bar

Tfeed

=250oC

Mas

s F

low

Rat

e (k

g/s

)

Power (kW)

RELAP5/Mod 3.2 (Two-Fluid Model) Experimental data (ITL) Generalized correlation with Blassius model Generalized correlation with Colebrook model

Variation of friction factor on two phase flow prediction

Effect of friction factor on steady state flow rate in a two-phase natural circulation loop as predicted by the generalized flow correlation

b

Gbr

lb

rbrtpr

ss N

ADQHg

pW

3

12

2


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0 10 20 30 40 50 60 70 80

0.08

0.12

0.16

0.20Colebrook Model for single-phase friction factor

Pressure = 20 barT

sub = 4K

Mas

s fl

ow

rat

e (k

g/s

)

Power(kW)

Homogeneous Lockhart-Martinelli Martinelli-Nelson Chisholm-Laird Sekoguchi

Effect of two-phase friction factor multiplier on steady state flow rate in a two-phase natural circulation loop using the generalized correlation

Effect of Friction Factor Multiplier


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Effect of pressure on steady state flow rate in a two-phase natural circulation loop

Effect of Pressure

10 20 30 40 50 60 700.0

0.4

0.8

1.2

1.6

2.0

2.4Single-phase friction factor used

Experimental : f = 0.569 / Re0.30457

Theoretical : Colebrook Model

Power = 30 kWT

sub = 2 K

Mas

s fl

ow

rat

e (k

g/s

)

Pressure (bar)

Homogenous model Lockhart-Martinelli model Martinelli-Nelson model Chisholm-Laird model Sekoguchi model Experimental data (HPNCL)


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Effect of friction factor on stability

Effect of friction factor on stability in a single-phase natural circulation loop

0 1 2 3 4 5 6 7 8 9 1010-7

100

107

1014

1021

1028

1035

Lt=7.23m, L

t/D=267.29, HHHC Orientation

Stable

Stable

Un

sta

ble

Gr m

Stm

Turbulent flow (p=0.184, b=0.2) Turbulent flow (p=0.316, b=0.25)


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Effect of friction factor on stability

Effect of two-phase friction factor multiplier on the stability of a two-phase natural circulation loop

0 5 10 15 20 25 30 350

20

40

60

80

100

120T

sub= 4K Homogenous model

Lockhart-Martinelli model Martinelli-Nelson model Chisholm-Laird model Sekoguchi model Threshold of Instability

[Furutera (1986)]

Stable

Unstable

Po

wer

(kW

)

Pressure (bar)


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Effect of large flow areas on pressure drops

Although large diameter pipes, large manifolds are used in natural circulation system, still there is no valid correlation for such geometry.

Simpson et al. (1977) compared six pressure drop correlations with data from large diameter (127 and 216 mm) horizontal pipes.

None of the pressure gradient correlations studied predicted the measure pressure drops adequately. In particular, measured pressure gradients for stratified flow differed by an order of magnitude from those predicted by the various correlations.

In view of this, the validity of the existing empirical correlations needs to be checked. However, this is not unique to only natural circulation system.


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Concluding Remarks

Within the range of parameter studied so far, relationships for forced circulation as given in TECDOC-1203 were found to be adequate for natural circulation and stability of natural circulation.

More accurate prediction capability is required at low mass flux and for large area flow paths. However, this issue is not unique to only natural circulation systems.

Applicability of existing correlations to natural circulation needs to be assessed covering wider range of parameters.

Documents

13 Pressure Drop RCM4