fundamental approach to triga steady-state thermal- hydraulic chf analysis national organization of...
TRANSCRIPT
Fundamental Approach to TRIGA Steady-State Thermal-Hydraulic CHF Analysis
National Organization of Test, Research, and Training Reactors (TRTR) Meeting
Lincoln City, OregonSeptember 17-20, 2007
Earl E. Feldman
2
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
3
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
4
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.
Assume no mass exchange or heat transfer between adjacent subchannels, i.e, each subchannel behaves independently of its neighbors and can be analyzed separately.
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.
Subchannel
Fuel Rod
Fuel Rod Fuel Rod
Fuel Rod
5
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)
6
RELAP5 Thermal-Hydraulic Model for Current Analysis
Source Sink
ColdLeg
LowerReflectorCoolant(1 node)
HorizontalConnector
Fuel RodCoolant
(15 nodes)
UpperReflectorCoolant
(2 nodes)
ChimneyCoolant(1 node)
UpperReflector
FuelRod
LowerReflector
7
Representative TRIGA Generic Reactor Parameters(Not the Most Limiting Values for Safety Analysis)
Reactor
Parameter Hexagonal Pitch Rectangular Pitch
Fuel element 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
Inlet temperature, C (F) 25 (77) 30 (86)
Pressure (~mid-core), bars 1.68 1.80
Saturation temperature, C (F) 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
8
Axial Power Shape for Hottest Rod of Hexagonal Pitch TRIGA
0
0.2
0.4
0.6
0.8
1
0.2 0.4 0.6 0.8 1 1.2 1.4
Relative Power
Rel
ativ
e L
eng
th
9
Comparison of STAT and RELAP5 Results
STAT void detachment fraction is assumed to be zero.
RELAP5 fails to provide a stable (non-oscillatory) solution above 48 kW/rod.
Hexagonal Pitch TRIGA
0
20
40
60
80
100
120
140
0 10 20 30 40 50
Power Per Rod, kW
Ou
tlet
Co
ola
nt
Tem
per
atu
re,
C
STAT
RELAP5
Hexagonal Pitch TRIGA
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 10 20 30 40 50
Power Per Rod, kW
Flo
w R
ate
Per
Ro
d,
kg/s
RELAP5
STAT
10
Representative TRIGA CHF Parameters for the Limiting Channel (Step 2)
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.
Nominal Conditions CHF Conditions
Mixed-mean coolant temperature
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)
Pressure, bar ~1.8 ~1.8
11
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
12
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
13
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
4
V
15P
P54Pln57T
ft0.1Dif/D1090slope
ft0.1Dif/D48slope
V(slope)DD
D10890h
TThCHF
WBO
ee
e0.6e
ie
eBO
bwBO BO
14
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
15
Groeneveld K1 and K2 Factors
1986 K1 (hydraulic diameter, dh)
– 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.
After 1986 K1 (hydraulic diameter, dh)
mm25dfor570.K
mm25dmm3ford
8K
h1
h
21
h1
mm16dfor0.79K
mm16dmm2ford
8K
h1
h
31
h1
16
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 ) )
– For X slightly greater than 0, K4
increases rapidly with quality.This does not seem to affect thenear limiting CHF powers for thegeneric hexagonal pitch TRIGA.
Middle Node of Generic Hexagonal Pitch TRIGA
1.0
1.2
1.4
1.6
1.8
2.0
2.2
-0.2 0 0.2 0.4 0.6 0.8 1
Quality
K4
17
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.
18
Hall & Mudawar (Purdue) CHF Outlet Correlation
0
0.724
g
f
0.644
g
f
0.312
f
2
fg xρ
ρ0.9001
ρ
ρ
σρ
DGhG0.0722CHF
Symbol Variable Minimum Maximum
D Hydraulic Diameter, mm 0.25 15.0
G Mass Flux, kg/s-m2 300 30,000
Pressure, bar 1 2000
x0 Quality -1.00 -0.05
hfg Latent heat of vaporization
σ Surface tension
ρf Density of saturated liquid
ρg Density of saturated vapor
19
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)
20
CHF vs. Coolant Quality for 8 mm Diameter Tube1.8 bar, 300 kg/m2-s
1.8 bar, 300 kg/m2-s, 8 mm Diameter Tube
010002000300040005000600070008000
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
Coolant Quality
Cri
tica
l H
eat
Flu
x,
kW/m
2
Purdue (outlet)
1986 Groeneveld
1995 Groeneveld
2006 Groeneveld
Bernath
Subcooled Boiling Bulk Boiling
11.5 C 38.0 C 64.4 C 90.8 C 116.9 C 116.9 C 116.9 C
Coolant Temperature
21
CHF vs. Temperature for 19.65 mm Diameter Tube1.8 bar, 300 kg/m2-s (Rectangular Pitch TRIGA)
1.8 bar, 300 kg/m2-s, 19.65 mm Diameter Tube
0
1000
2000
3000
4000
5000
6000
0.00 20.00 40.00 60.00 80.00 100.00 120.00
Coolant Temperature, C
Cri
tica
l H
eat
Flu
x,
kW/m
2
Purdue (outlet)
1986 Groeneveld
1995 Groeneveld
2006 Groeneveld
Bernath
22
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
Hexagonal Pitch TRIGA
1.051.061.061.071.071.081.091.101.121.141.181.221.221.221.22
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8CHF Ratio
Hea
ted
Axi
al L
oca
tio
n,
Inch
es
Bernath (STAT)Bernath (RELAP)2006 Groeneveld (RELAP)1986 Groeneveld (RELAP)K4 Groeneveld Factor
Directly from RELAP5
Directly from STAT
(1 Corresponds to 30 kW/rod)
23
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)
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8CHF Ratio
Hea
ted
Axi
al L
oca
tio
n,
Inch
es
Bernath (STAT)Basic
Geometry & Flux
Power
1986 Groeneveld (RELAP)
24
CHF Power Prediction of Hexagonal Pitch TRIGA Based on Groeneveld 2006 Table
Groeneveld 2006 CHF Correlation
0
10
20
30
40
50
60
70
80
90
0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
Flow of Hottest Rod, kg/s
Po
wer
of
Ho
ttes
t R
od
, kW CHF Power Based on RELAP5 Conditions
CHF Power at Equilibrium*
RELAP5 Conditions
RELAP5/Groeneveld CHF, 68.9 kW/rod, if the flow is as projected
Dashed implies linear extrapolation.
*Equilibrium is achieved by adjusting the channel power until it equals the CHF power.
62.1 kW/rod
RELAP5 quit here.
25
CHF Power Prediction of Hexagonal Pitch TRIGA Based on Bernath (1960) Correlation
Bernath (1960) CHF Correlation
0
10
20
30
40
50
60
70
80
0.06 0.08 0.1 0.12 0.14 0.16 0.18
Flow of Hottest Rod, kg/s
Po
wer
of
Ho
ttes
t R
od
, kW
RELAP5 Conditions
CHF Power at Equilibrium*
CHF Power Based on RELAP5 Conditions
RELAP5/Bernath CHF, 50.6 kW/rod
Dashed implies linear extrapolation.
*Equilibrium is achieved by adjusting the channel power until it equals the CHF power.
STAT
STAT/Bernath CHF, 37.1 kW/rod
26
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.
Purdue CHF Correlation (CHF Power = Channel Power)
10
20
30
40
50
60
70
0.06 0.08 0.1 0.12 0.14 0.16 0.18
Flow of Hottest Rod, kg/s
Po
wer
of
Ho
ttes
t R
od
, kW
RELAP5
RELAP5 Extrapolated
CHF Power at Equilibrium RELAP5/Purdue CHF, 50.6 kW/rod, if the flow is as projected
27
CHF Power Prediction of Hexagonal Pitch TRIGA Based on PG-CHF (~1994) Correlations
PG-CHF CHF Correlation (CHF Power = Channel Power)
0
25
50
75
100
125
150
0.05 0.1 0.15 0.2 0.25 0.3 0.35
Flow of Hottest Rod, kg/s
Po
wer
of
Ho
ttes
t R
od
, kW
RELAP5
RELAP5 Extrapolated
Basic, 124.4 kW*
Geometry, 129.7 kW* Flux & Power, 128.7 kW*
*RELAP5/PG-CHF kW/rod, if the RELAP5 flow is as projected
28
Summary of CHF Results for Hexagonal Pitch TRIGA
CHF Power = Channel Power
0
25
50
75
100
125
150
0.05 0.1 0.15 0.2 0.25 0.3 0.35
Flow of Hottest Rod, kg/s
Po
wer
of
Ho
ttes
t R
od
, kW
RELAP5 Flow
STAT Flow
Extrapolated RELAP5 Flow
Purdue CHF (50.6 kW)*
Bernath CHF (50.6 kW)*
Groeneveld 2006 CHF (68.9 kW)*
Flux & Power PG-CHF CHF (128.7 kW)*
*Power at Intersection with Extrapolated RELAP5 Flow
G=549 kg/s-m2
Xexit = 0
G=183 kg/s-m2
Maximum Calculated RELAP5 Flow, 0.1394 kg/sB – RELAP5/Bernath & B - Purdue
B – Groeneveld 2006
A
B – Flux & Power PG-CHF
A
29
Summary of CHF Results for Hexagonal Pitch TRIGA (continued)
Flow CHF CorrelationRod CHF Power, kW CHF Ratio*
A** B+ C++ A** B+ C++
STAT Bernath 37.1 52.5 1.24 1.75
RELAP5
Bernath 49.6 50.6 57.5 1.65 1.69 1.92
Purdue 48.9 50.6 1.63 1.69
Groeneveld 2006 62.1 68.9 71.9 2.07 2.30 2.40
Groeneveld 1986 100.3 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.
30
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.
31
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.