pressure drop presentation lknl
TRANSCRIPT
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