Transcript TRIGA Thermal-Hydraulic Analysis

Fundamental Approach to
TRIGA Steady-State ThermalHydraulic CHF Analysis
National Organization of Test,
Research, and Training Reactors
(TRTR) Meeting
Lincoln City, Oregon
September 17-20, 2007
Earl E. Feldman
Outline
 Two-Step Process (Step 1: Flow; Step 2: CHF)
 Flow
– Coolant channel geometry of models
– Computer codes (STAT & RELAP5)
– Nodal structure of RELAP5 models used to determine flow
– List representative parameters for two generic TRIGA reactors -- a
hexagonal pitch TRIGA and a rectangular pitch TRIGA
– Compare STAT and RELAP5 flow results for a representative
hexagonal pitch TRIGA reactor
2
Outline (continued)
 Critical Heat Flux (CHF)
– Bernath correlation
– Groeneveld tables (1986, 1995, 2006)
– Hall and Mudawar (Purdue) outlet correlation
– PG-CHF (Czech Republic) correlations
– Compare CHF correlations for representative TRIGA reactor conditions
– Compare CHF power predictions for a representative hexagonal pitch
TRIGA reactor
 Suggested Approach to CHF
 Conclusions
3
Geometric Model for Calculation of Coolant Flow Rates (Step 1)
 The core flow area is divided into subchannels
defined by the cusps between adjacent fuel rods.
Fuel Rod
 Assume no mass exchange or heat transfer
between adjacent subchannels, i.e, each
subchannel behaves independently of its neighbors
and can be analyzed separately.
Fuel Rod
Subchannel
Fuel Rod
Fuel Rod
 Only potentially limiting subchannels need be
considered.
 Divide the length of the subchannel being analyzed
into a series of horizontal layers or nodes.
The 15-inch (0.381-m) heated length was divided
into 15 1-inch layers.
4
Codes Being Used for Thermal-Hydraulic Analysis
 STAT
– GA-developed code with fixed geometry of one subchannel.
– Custom made for TRIGA reactor hydraulics.
– Steady state only.
– No fuel rod temperature model
– Has 2 CHF correlations
• Bernath (1960)
• McAdams (1949)
 RELAP5-3D (Version 2.3)
– Current developer is the Idaho National Laboratory
– General transient thermal-hydraulic neutronics reactor code. No fixed
geometry. Uses a series of coolant nodes and junctions. Heat structures
attached to coolant nodes represent solid regions, such as fuel rods.
– Has 2 CHF correlation options
• 1986 Groeneveld table
• PG-CHF from the Czech Republic (~1994)
5
RELAP5 Thermal-Hydraulic Model for Current Analysis
Chimney
Coolant
(1 node)
Upper
Reflector
Coolant
(2 nodes)
Source
Fuel Rod
Coolant
(15 nodes)
Cold
Leg
Sink
Upper
Reflector
Fuel
Rod
Lower
Reflector
Horizontal
Connector
Lower
Reflector
Coolant
(1 node)
6
Representative TRIGA Generic Reactor Parameters
(Not the Most Limiting Values for Safety Analysis)
Reactor
Parameter
Hexagonal Pitch
Rectangular Pitch
Hexagonal
Rectangular conversion
Flow area per rod, cm2
5.464
5.532
Hydraulic diameter, mm
18.64
19.65
Rod (heated) diameter, mm
37.34
35.84
25 (77)
30 (86)
1.68
1.80
114.8 (238.6)
116.9 (242.4)
Inlet K-loss
3.58
1.672
Exit K-loss
3.0
0.6
Reactor power, MW
2.0
1.0
Number of rods
100
90
Radial power factor (hot. rod)
1.5
1.565
Power of hottest rod, kW
30.0
17.4
Fuel element pitch
Inlet temperature, C (F)
Pressure (~mid-core), bars
Saturation temperature, C (F)
7
Axial Power Shape for Hottest Rod of Hexagonal Pitch TRIGA
Relative Length
1
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Relative Power
8
Comparison of STAT and RELAP5 Results
 STAT void
detachment
fraction is
assumed to
be zero.
Flow Rate Per Rod, kg/s
Hexagonal Pitch TRIGA
0.14
0.12
0.10
0.08
0.06
0.04
RELAP5
STAT
0.02
0.00
0
20
30
40
50
Power Per Rod, kW
Hexagonal Pitch TRIGA
140
Outlet Coolant
Temperature, C
 RELAP5 fails
to provide a
stable (nonoscillatory)
solution
above 48
kW/rod.
10
120
100
80
60
40
20
STAT
RELAP5
0
0
10
20
30
40
50
Power Per Rod, kW
9
Representative TRIGA CHF Parameters for the Limiting
Channel (Step 2)
Nominal Conditions
CHF Conditions
Less than boiling
Less than or at boiling
Mass flux, kg/m2-s
~100
~300
Velocity, cm/s (ft/s)
~10 (~1/3)
~30 (~1)
~1.8
~1.8
Mixed-mean coolant
temperature
Pressure, bar
 Difficulty: Much of the published CHF measurements is
focused on power reactors, which operate at high pressures
and flow rates. However, TRIGA reactors operate at low
pressures and at low (natural-convective) flow rates.
10
CHF Correlations Considered
 Bernath (1960) – Used in STAT code along with McAdams (1949)
(STAT results indicate that for TRIGA reactors the Bernath correlation predicts
lower CHF values than does the McAdams correlation.)
 1986 Groeneveld Table – RELAP5 option
 1995 Groeneveld Table – Not available in RELAP5
 2006 Groeneveld Table – Not available in RELAP5
 Hall and Mudawar (Purdue) – Proprietary 1998 collection of world’s CHF data in
water. Has a simple correlation for subcooled boiling.
for quality < −0.05 and G>300 kg/m2-s
 PG-CHF (Czech Republic, ~1994) – RELAP5 rod-bundle option, 4 flavors
11
Bernath Correlation (1960)
 Based on low pressure subcooled measured data
– 1956 Columbia University data
• Annulus formed by 27.4-mm (1.08-inch) diameter heater inside an
unheated tube
• 14 tests with approximate ranges of 2 to 4 bar, 80 to 110° C, 1800
to 9000 kg/m2-s (6 to 30 ft/s), and dh = 10.6 to 14.7 mm
– 1949 McAdams data – 0.25” heater inside 0.77” tube (dh = 13.2 mm)
 Checked by Bernath against several sets of independently measured
data covering a wide range of parameters
 Applicable to subcooled boiling; Limited applicability to low-pressure bulk
boiling
12
Bernath CHF Correlation
 CHF = CHF, pound centigrade
units per hr-ft2
(1 p.c.u. = 1.8 Btu)
 film coefficient at CHF,
p.c.u./hr-ft2-C
 TWBO = wall temperature at
CHF, C
 Tb = bulk coolant temperature,
C
 De = hydraulic diameter, ft
 Di = diameter of the heated
surface = heat perimeter / π, ft
(In STAT code, diameter of
fuel rod)
 P = pressure, psia
 V = coolant velocity, ft/s

CHF  h BO Tw BO  Tb
h BO

 De 
  (slope) V
 10890
 De  Di 
slope  48 /De
0.6
if De  0.1 ft
slope  90  10 /De
TWBO
if De  0.1ft
 P  V
 
 57 ln P  54 
 P  15  4
13
1986, 1995, and 2006 Groeneveld CHF Look-Up Tables
 CHFtable is a function of:
– pressure (kPa)
– mass flux (kg/m2-s)
– quality – Negative values are used to represent subcooled conditions
 Based on water flowing inside an 8 mm diameter tube that is heated from
the periphery
 Linear interpolation used for values between table entries
 Multiplicative factors for other geometries and conditions
– CHFbundle = CHFtable × K1 × K2 × K3 × K4 × K5 × K6 × K7
– 1986 has 6 factors.
– Factors have changed after 1986. Later ones have 7 factors.
– Some of the newer factors are tentative or not well defined
– Most factors should be close to 1.0
14
Groeneveld K1 and K2 Factors
 1986 K1 (hydraulic diameter, dh)
 8 
K1   
 dh 
K1  0.79
1
3
for 2 mm  d h  16 mm
for d h  16 mm
 After 1986 K1 (hydraulic diameter, dh)
 8 
K1   
 dh 
K1  0.57
1
2
for 3 mm  d h  25 mm
for d h  25 mm
– For dh = 18.64 mm (hexagonal pitch TRIGA):
• 1986 => K1=0.79
• After 1986 => K1=0.66
– After 1986 / 1986 = 0.83
 For K2 (rod bundle factor)
– After 1986 a tentative new relationship was suggested.
– The 1986 relationship will be assumed to apply to all years.
– It is K2 = min[ 0.8, 0.8 × exp(-0.5 × quality(1/3) ]
– Therefore, K2 = 0.8 for subcooled regions and less for bulk boiling
regions.
15
Groeneveld K4 Factors
 For K4 (heated length factor)
– It appears that it has not been changed between 1986 and 2006.
– The following is based on the RELAP5 source code:
• X = quality
• L = heated distance from channel inlet to middle of node
• D = heated diameter (i.e., 4 × flow area / heated perimeter)
• ρf and ρg are the densities of saturated liquid and vapor, respectively.
• If X < 0, X = 0
• If L/D < 5, L/D = 5
• α = X / (X + ρg (1 − X) / ρf )
• K4 = exp( D/L × exp( 2 × α ) )
2.2
2.0
1.8
K4
– For X slightly greater than 0, K4
increases rapidly with quality.
This does not seem to affect the
near limiting CHF powers for the
generic hexagonal pitch TRIGA.
Middle Node of Generic Hexagonal Pitch TRIGA
1.6
1.4
1.2
1.0
-0.2
0
0.2
0.4
0.6
0.8
1
Quality
16
Errors Associated with 2006 Groeneveld Table*
 For the region of the table of interest for TRIGA reactors, the CHF values
are not a result of direct measurement. These regions, Groeneveld*
states, “represent calculated values based on selected prediction
methods …”
 In addition, Groeneveld* uses smoothing methods to eliminate
discontinuities that are a result of scatter in the measured data. The paper
provides RMS errors between the measured data and the smoothed
entries in the table. For the direct substitution method being used in the
current analysis, negative qualities in the measured regions of the table
have an RMS error of 14.74%. Positive quality regions have much higher
RMS errors.
* D.C. Groeneveld, J.Q. Shan, A.Z. Vasić, L.K.H. Leung, A. Durmayaz, J.
Yang, S.C. Cheng, and A. Tanase, “The 2006 CHF look-up table,”
Nuclear Engineering and Design 237 (2007) 1909-1922.
17
Hall & Mudawar (Purdue) CHF Outlet Correlation
G D

CHF  0.0722 G hfg 
 ρf σ 
2
Symbol
0.312
 ρf 
 
ρ 
 g
Variable
0.644
0.724


 ρf 
1  0.900  
x0 
ρ 


 g


Minimum
Maximum
D
Hydraulic Diameter, mm
0.25
15.0
G
Mass Flux, kg/s-m2
300
30,000
1
2000
-1.00
-0.05
Pressure, bar
x0
Quality
hfg
Latent heat of vaporization
σ
Surface tension
ρf
Density of saturated liquid
ρg
Density of saturated vapor
18
PG-CHF (Czech Republic) CHF Data
 One of 2 CHF options built into RELAP5. (The other is Groeneveld 1986.)
 Based on three separate experimental databases – one for tubes, one for
rod bundles, and one for annuli.
 For each geometry there are four PG-CHF forms called: “Basic,” “Flux,”
“Geometry,” and “Power” (It appears RELAP5 produces obviously
erroneous results for the “Basic,” “Flux,” and “Geometry” forms.)
 Rod bundle database
– 153 test geometries
– 7,616 total points
 Data ranges for rod bundles:
– Pressure: 2.8 to 187.3 bar (TRIGA ~1.8 bar)
– Mass flux: 34.1 to 7478 kg/m2-s
– Quality: subcooled to 100% steam
– Heated length: 0.4 to 7.0 m (TRIGA 0.381 m)
– Fuel rod diameter: 5 to 19.05 mm (TRIGA ~37 mm)
19
CHF vs. Coolant Quality for 8 mm Diameter Tube
1.8 bar, 300 kg/m2-s
2
kW/m
Critical Heat Flux,
1.8 bar, 300 kg/m2-s, 8 mm Diameter Tube
8000
7000
6000
5000
4000
3000
2000
1000
0
-0.20
11.5 C
Subcooled Boiling
Purdue (outlet)
1986 Groeneveld
1995 Groeneveld
2006 Groeneveld
Bernath
Bulk Boiling
-0.15
-0.10
-0.05
0.00
38.0 C
64.4 C
90.8 C
116.9 C
0.05
Coolant Quality
0.10
116.9 C
0.15
0.20
116.9 C
Coolant Temperature
20
CHF vs. Temperature for 19.65 mm Diameter Tube
1.8 bar, 300 kg/m2-s (Rectangular Pitch TRIGA)
1.8 bar, 300 kg/m2-s, 19.65 mm Diameter Tube
Purdue (outlet)
1986 Groeneveld
1995 Groeneveld
2006 Groeneveld
Bernath
2
5000
kW/m
Critical Heat Flux,
6000
4000
3000
2000
1000
0
0.00
20.00
40.00
60.00
80.00
100.00
120.00
Coolant Temperature, C
21
CHF Ratios for Hexagonal Pitch TRIGA Evaluated at Nominal
Power, where Highest Power Rod is 30kW
 CHR Ratio = local CHF prediction / local heat flux
 Thermal-hydraulics code is shown in parentheses
Directly
from STAT
Heated Axial Location,
Inches
16
Hexagonal Pitch TRIGA
1.05
1.06
1.06
1.07
1.07
1.08
1.09
1.10
1.12
1.14
1.18
1.22
1.22
1.22
1.22
14
12
10
8
6
4
2
0
1
Directly from
RELAP5
2
3
Bernath (STAT)
Bernath (RELAP)
2006 Groeneveld (RELAP)
1986 Groeneveld (RELAP)
K4 Groeneveld Factor
8
7
6
5
4
(1
Corresponds
to
30
kW/rod)
CHF Ratio
22
PG-CHF CHF Ratios for Hexagonal Pitch TRIGA Evaluated
at Nominal Power, where Highest Power Rod is 30kW
 RELAP5 flow except for Bernath, which uses STAT flow
PG-CHF, Basic, Geometry, Flux, & Power (RELAP)
Heated Axial Location,
Inches
16
14
Power
12
1986 Groeneveld (RELAP)
10
8
Geometry & Flux
6
4
Basic
2
Bernath (STAT)
0
1
2
3
4
5
CHF Ratio
6
7
8
23
CHF Power Prediction of Hexagonal Pitch TRIGA Based
on Groeneveld 2006 Table
Power of Hottest Rod, kW
Groeneveld 2006 CHF Correlation
90
Dashed implies linear extrapolation.
80
CHF Power Based on RELAP5 Conditions
70
60 CHF Power at Equilibrium*
RELAP5/
50
62.1 kW/rod
Groeneveld CHF,
40
RELAP5 quit here. 68.9 kW/rod, if
30
the flow is as
RELAP5 Conditions
20
projected
10
*Equilibrium is achieved by adjusting the channel power until it equals the CHF power.
0
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
Flow of Hottest Rod, kg/s
24
CHF Power Prediction of Hexagonal Pitch TRIGA Based
on Bernath (1960) Correlation
Power of Hottest Rod, kW
Bernath (1960) CHF Correlation
80
70
Dashed implies linear extrapolation.
CHF Power Based on RELAP5 Conditions
60
50
40
30
20
10
CHF Power at Equilibrium*
STAT
RELAP5/Bernath
CHF, 50.6 kW/rod
RELAP5 Conditions
STAT/Bernath CHF, 37.1 kW/rod
*Equilibrium is achieved by adjusting the channel power until it equals the CHF power.
0
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Flow of Hottest Rod, kg/s
25
CHF Power Prediction of Hexagonal Pitch TRIGA Based
on Purdue (Outlet) Correlation
 Not valid because at CHF conditions the mass fluxes, G, is less than 300
kg/s-m2 and the quality, X, is greater than -0.05. For a CHF power of 50.6
kW, G is 265 kg/s-m2 and X is -0.02 at the limiting axial location.
Power of Hottest Rod, kW
Purdue CHF Correlation (CHF Power = Channel Power)
70
RELAP5 Extrapolated
60
50
40
CHF Power at Equilibrium
RELAP5/
Purdue CHF, 50.6
kW/rod, if the flow
is as projected
30
20
10
0.06
RELAP5
0.08
0.1
0.12
0.14
0.16
0.18
Flow of Hottest Rod, kg/s
26
CHF Power Prediction of Hexagonal Pitch TRIGA Based
on PG-CHF (~1994) Correlations
Power of Hottest Rod, kW
PG-CHF CHF Correlation (CHF Power = Channel Power)
150
Geometry, 129.7 kW*
Flux & Power, 128.7 kW*
125
Basic, 124.4 kW*
100
75
RELAP5 Extrapolated
50
RELAP5
25
*RELAP5/PG-CHF kW/rod, if the RELAP5 flow is as projected
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Flow of Hottest Rod, kg/s
27
Summary of CHF Results for Hexagonal Pitch TRIGA
CHF Power = Channel Power
B – Flux & Power PG-CHF
Power of Hottest Rod, kW
150
Flux & Power PG-CHF CHF (128.7 kW)*
Extrapolated RELAP5 Flow
125
A
Xexit = 0
100
B – Groeneveld 2006
Groeneveld
2006 CHF
(68.9 kW)*
75
Purdue CHF (50.6 kW)*
Bernath CHF (50.6 kW)*
50
B – RELAP5/Bernath & B - Purdue
STAT Flow
Maximum Calculated RELAP5 Flow, 0.1394 kg/s
25
*Power at Intersection with
Extrapolated RELAP5 Flow
RELAP5 Flow
0
0.05
0.1
G=183 kg/s-m2
A
0.15
0.2
0.25
Flow of Hottest Rod, kg/s
0.3
0.35
G=549 kg/s-m2
28
Summary of CHF Results for Hexagonal Pitch TRIGA (continued)
Flow
STAT
CHF Correlation
Rod CHF Power, kW
A**
Bernath
B+
C++
37.1
52.5
57.5
Bernath
49.6
50.6
Purdue
48.9
50.6
Groeneveld 2006
62.1
68.9
RELAP5 Groeneveld 1986
71.9
CHF Ratio*
B+
C++
1.24
1.75
1.65
1.69
1.92
1.63
1.69
2.07
2.30
A**
100.3
2.40
3.30
PG-CHF, Basic
105.9
124.4
3.53
4.15
PG-CHF, Geometry
108.9
129.7
3.63
4.32
PG-CHF, Power or Flux
109.2
128.7
3.64
4.29
*1.0 corresponds to 30 kW for the highest power rod and 2.0 MW for the reactor.
**A (RELAP5 Flow): CHF curve at maximum calculated flow per rod (0.1394 kg/s, thin vertical
black line A-A in the previous figure), where RELAP5 flow begins to oscillate.
+B (Extrapolated RELAP5 Flow): Intersection of a CHF correlation curve and a reactor flow
curve, as shown on the previous figure.
++C (Not Recommended): CHF based on calculated reactor power and flow at 30 kW/rod.
29
Suggested Approach to CHF
 Use the 2006 Groeneveld CHF table, with K1 (the newer one), K2, and K4, as
provided above.
 Evaluate the CHF table at the power that produces CHF, i.e., CHF power =
channel power.
 Use RELAP5, or other suitable code, to predict flow. If flow extrapolation is
needed, be conservative.
 NUREG-1537, Part 1, Appendix 14.1, page 5 recommends minimum CHF ratios
of at least 2.0 for reactors with engineered cooling systems. TRIGA reactors with
natural-convective primary flow do not have engineered cooling systems. A
minimum CHF ratio is under discussion.
30
Conclusions
 Flow Rate:
– For the hexagonal pitch TRIGA reactor, the RELAP5 flow rate predictions are
greater than the STAT predictions, especially at power levels approaching CHF
conditions.
 CHF
– There is substantial uncertainty in the data. Correlation predictions differ greatly.
– The 2006 Groeneveld table, with K1, K2, and K4 as outlined above, is judged to
be the best choice for TRIGA reactors.
 For the hexagonal pitch TRIGA reactor:
– The proposed 2006 Groeneveld CHF and RELAP5 flow combination (column A
of the previous table) predicts 62.1 kW/rod.
– The traditional method of using the STAT code with the Bernath CHF correlation
predicts 37.1 kW
– Thus, in this example, the proposed method predicts the CHF power to be 67%,
i.e., (62.1/37.1 – 1) × 100%, greater.
31