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POST CRITICAL HEAT FLUX HEAT TRANSFER
IN A VERTICAL TUBE INCLUDING SPACER GRID EFFECTS
by
EDWARD M. CLUSS, JR.
I
S.B., Massachusetts Institute of Technology
(1977)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREM4ENTS FOR THE
DEGREE OF
MASTER OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
(June 1978)
Signature of Author.
.
.-.
,aepartnentof Mechan
Certified by•.
Cerifi
Accepted by .
.
. .
.
1 Engineewng, June 2, 1978
A./I
.~~~
.
. .
~Thesis Supervisor
. . . . . . . .
Chairman, Department Committee on Graduate Students
iiiE
ARCHIVES
COW ; 7 ?D~I&
1
7A-
2
POST CRITICAL HEAT FLUX HEAT TRANSFER
IN A VERTICAL TUBE INCLUDING SPACER GRID EFFECTS
by
EDWARD M. CLUSS, JR.
Submitted to the Department of Mechanical Engineering
on June 2, 1978 in partial fulfillment of the requirements for the Degree of Master of Science.
ABSTRACT
Theoretical and experimental programs were conducted in order
to analyze the supplemental heat transfer, induced by a spacer grid,
during an upward post critical heat flux flow in a constant wall temperatyre pipe. A flooding rate of 1 in/sec, equivalent to 18, 720 lbm/hrft , was studied at atmospheric conditions, with hot wall temperatures
of 1000°F, 1100°F, 1200°F and 1300°F. Heat flux versus length data was
obtained and compared with theoretical predictions. A modified two
phase Dittus Boelter correlation was employed to obtain the steady-state
heat transfer coefficients. Both entrance and steady-state experimental
values correlated well with this model.
Results indicate that an increase in heat transfer does occur
at the spacer and is primarily a combination of two mechanisms:
(1) Increased flow velocity (caused by an area reduction at
the spacer) which increases vapor convection and droplet
heat transfer.
(2) Radiation to liquid deposited on the spacer.
The first contribution can be modeled as a multiplying factor of the
steady-state heat transfer level while the latter is a localized effect
occurring only at the spacer. The combination of both effects caused a
threefold heat transfer increase or greater at the spacer location for
the flows studied. Radiation, which is directly related to the hot
wall temperature, becomes the major contribution at higher temperatures.
Thesis Supervisor:
Title:
Peter Griffith
Professor of Mechanical Engineering
3
ACKNOWLEDGEMENTS
Financial support for this investigation was provided through
a research assistantship, funded by the Nuclear Regulatory Commission.
Some portions of the test apparatus were designed and built
during earlier heat transfer research by Thomas Smith and Paul Robershotte.
The latter also provided numerous suggestions germane to the
initial stages of this project.
Joseph "Tiny" Caloggero and Fred Johnson provided technical
advice and assisted in the mechanical construction of the experimental
apparatus.
Many thanks to Prudence Young, who typed the final and earlier
versions of this report, and to Dave Welland for his painstaking proofreading.
Helpful comments and friendship were always abundant from
the guys in my office, Mohamed Benchaita, Yin "Clem" Cheung, Joseph
Gonzalez-Rivas, and Baldeo Singh.
They made the Heat Transfer Lab an
interesting place to work.
Professor Griffith, my advisor, provided me with an abundance
of guidance and pertinent advice throughout the duratien of this project; but more importantly, always retained his optimism, sense of
humor, and patience when they were needed the most.
Last but never forgotten; special thanks go to my parents,
who have continually given me their love and support for all of my
endeavors.
To them I dedicate this, my final effort at M.I.T.
4
To My Mother,
Claire B. Cluss
And My Father,
Edward M. Cluss
5
TABLE OF CONTENTS
PAGE
TITLE PAGE . . . . . . . . . . . . . . . . . . . . . . . . ...
.·.·.·.·.·.·.
1
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
ACKNOWLEDGEMENTS . .....
TABLE OF CONTENTS
LIST OF FIGURES
. . . . . . . . . . . . . . . . 3
. . . . . . . . . . . . . . . . .. . . . . . 5
. . . . . . . .
. . . . . . .
.
. . . . . 7
LIST OF TABLES . . . . . . . . . . . . . . ·. ·. ·. ·. ·. ·. ·. .· .· ·. .··
9
10
NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . ... . ..........
14
CHAPTER I: INTRODUCTION . . . . . . . . . . . . . . . . . ... . ..........
1.1
Loss of Coolant Accident ................
.
............
14
1.2 Spacer Grid Effects ..................
15
1.3 Previous Experimentation . . . . . . . . . . . . . . . . 17
1.4 Objective of This Work . . . . . . . . . . . . . . . . . 19
CHAPTER II:
EXPERIMENTAL PROGRAM
. . . . . . . . . . . . . . . 20
2.1 APPARATUS . . . . . . . . . . . . . . . . . . . . . . .
2.1.1
2.1.2
2.1.3
2.1.4
Reactor Model . . . . . . . . . . .
Test Loop Description . . . . . . .
Test Section Components . . . . . .
System Monitoring and Control . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
20
20
21
25
29
2.2 EXPERIMENTAL PROCEDURE . . . . . . . . . . . . . . . .
31
2.3 DATA REDUCTION ....................
33
CHAPTER III:
THEORETICAL ANALYSIS . . . . . . . . . . . . . .
3.1 POST CHF HEAT TRANSFER ................
3.1.1
Forced Convection Heat Transfer to Vapor
.
..
3.1.2 Wall to Droplet Heat Transfer . . . . . . . . .
36
36
37
39
6
PAGE
3.2
SPACER GRID EFFECTS . . . . . . . . . . . . . . . . . .
43
3.2.1 Increased Flow Velocity . . . . . . . . . . . .
3.2.2 Wall to Spacer Radiation . . . . . . . . . .
44
46
. .
51
CHAPTER IV:
EXPERIMENTAL RESULTS AND COMPARISON TO THEORY
4.1
Experimental Heat Flux Results . . . . . . . . . . . .
51
4.2
Effective Heat Transfer Addition at Spacer . . . ....
57
CONCLUSIONS AND RECOMMENDATIONS . . . . . . . . . .
62
. . . . . .
62
5.2 Recommendations . . . . . . . . . . . . . . . . . . . .
63
CHAPTER V:
5.1
Conclusions . . . . . . . . . . . . . . .
65
REFERENCES .........................
APPENDIX A:
TEMPERATURE CONTROLLER . . . . . . . . . . . . . .
67
APPENDIX B:
EXPERIMENTAL DATA ...................
.
68
APPENDIX C:
THEORETICAL ANALYSIS COMPUTER PROGRAM . . . . . .
72
APPENDIX D:
THEORETICAL RESULTS . . . . . . . . . . . . . . .
82
APPENDIX E:
WATER AND VAPOR PROPERTIES . . . . . . . . . . . .
91
7
LIST OF FIGURES
PAGE
FIGURE
... .. . . . .
16
. . . . . .
18
1
PRESSURE HISTORY DURING BLOWDOWN . . .
2
TWO PHASE FLOW REGIMES . . . . . . . .
3
SCHEMATIC OF EXPERIMENTAL APPARATUS
. .
22
4
ENTIRE APPARATUS . . . . . . . . . . . . . . . . . . . .
23
5
LOWER PORTION OF APPARATUS . . . . . . . . . . . . . . .
23
6
ELECTRIC PREHEATER . . . . . . . . . . . . . . . . . . .
23
7
PIPE CONNECTOR . . . . . . . . . . . .
8
PIPE WITHOUT COPPER BLOCK
9
PIPE WITH COPPER BLOCK . . . . . . . . . . . . . . . .
..
. . . . . . .
I . . .
...
. . . . . . . . . .. . . . . .
. .
23
24
24
10
TEST SECTION WIRING . . . . . . . . . .
. . . .
24
11
ENVIRONMENT CHAMBER, CONTROLLER CLOCKS, AND VARIACS . .
24
12
. I .26
EXPERIMENTAL SPACER . . . . . . . . . . . . . ....
13
DETAILS OF 1-7/8 INCH COPPER BLOCK
14
MOUNTING OF THERMOCOUPLES . . . . . . .
15
EFFECT OF ENTRANCE CONFIGURATION ON LOCAL STANTON NUMBER
40
16
TEST SECTION INLET CONFIGURATION . . . . . . . . . . . .
41
17
SPACER IDEALIZATION . . . . . . . . . . . . . . . . . .
48
18
VIEW FACTOR, F, FOR DIRECT RADIATION BETWEEN
ADJACENT PERPENDICULAR RECTANGLES . . . . . . . . .
49
19
COMPARISON OF DATA AT 1 IN/SEC AND 1000°F TO THEORY . .
52
20
COMPARISON OF DATA AT 1 IN/SEC AND 1100°F TO THEORY . .
53
21
COMPARISON OF DATA AT 1 IN/SEC AND 1200°F TO THEORY . .
54
22
COMPARISON OF DATA AT 1 IN/SEC AND 1300°F TO THEORY . .
55
, . . . . . . . . .
. . , . . ,.
28
30
8
PAGE
FIGURE
23
THEORETICAL NONDIMENSIONAL HEAT TRANSFER COEFFICIENT . . 58
24
SUPPLEMENTAL HEAT TRANSFER AT SPACER . . . . . . . . . . 59
25
THEORETICAL BREAKDOWN OF HEAT TRANSFER AT SPACER . . . . 61
26
WALL TEMPERATURE CONTROLLER CIRCUIT DIAGRAM . . . . . .
67
9
LIST OF TABLES
TABLE
PAGE
1
EXPERIMENTAL PROCEDURE .
32
2
SYSTEM PROPERTIES .................
91
10
NOMENCLATURE
SYMBOL
DEFINITION
A
Area
Cp
Specific Heat
E
Energy
F
Geometric View Factor
G
Mass Flux
H, h
Enthalpy
Hfg
K
Heat of Vapor
m
Mass Flow Rate
Nu
Nusselt Number
P
Perimeter, Power
Pr
Prandtl Number
q
Heat Transfer
R
Resistance
Re
Reynold's Number
St
Stanton Number
T
Temperature
t
Time
V
Velocity, Voltage
X
Quality
Thermal Conductivity
11
Greek Symbols
DEFINITION
a
Void Fraction
Radiating Fraction of Wall
at
At
Time Difference
S
Effectiveness, Emmisivity
p
Density
a
Stefan-Boltzman Constant
1J
Viscosity
12
SUBSCRIPTS
DEFINITION
Cu
Copper
d
Droplet
DB
Dittus-Boelter
DS
Droplets at Spacer
eq
Equilibrium
exp
Experimental
f
Liquid
G
Gross
g9
Vapor
homo
Homogeneous
in
Inlet
L
Loss
out
Outlet
PRE
Preheater
RS
Radiation at Spacer
S
Spacer, Saturation
sat
Saturation
SS
Stainless Steel
t
Total
v, ap
Vapor
vs
Vapor at Spacer
w
Wall
x
Local, Distance
13
SUBSCRIPTS
DEFINITION
1
Perpendicular or Deposition
00
Steady-State
14
CHAPTER I:
INTRODUCTION
Man's ever increasing demand for energy coupled with dwindling
fossil fuel supplies has produced a sharp increase in the cost of conventional power production and has necessitated a switch to alternate
but still reliable energy sources,
Consequently, following the second
World War, the nuclear power industry experienced extensive growth, with
the hopes of providing a cheaper and cleaner method of power production.
Recently, fears coupling nuclear energy with nuclear weapons and anxiety
over a large scale reactor accident have drastically reduced the industry's rate of expansion.
It has become increasingly more apparent that
the design and construction of only the safest and most reliable reactors will be acceptable to the majority of the population.
This concern
and controversy has demanded that both commercial reactor producers and
the Nuclear Regulatory Commission (responsible for the licensing of
nuclear reactors) be extremely cautious and only apply the most conservative reactor design schemes when safety and long term reliability is
the question.
To insure this reactor dependability, emergency systems
are built to handle the most extreme types of accidents.
One such hypo-
thetical crisis is the "loss of coolant accident" or LOCA.
1.1
LOSS OF COOLANT ACCIDENT
The hypothetical loss of coolant accident is a problem highly
unlikely to occur but is of great interest as a limiting design case.
During this accident, a double guillotine break occurs in the main pipes
15
of the primary loop causing a rapid depletion of the reactor coolant
and extreme depressurization of the reactor core.
Figure 1,obtained
from Hsu (1), shows that inapproximately 30 seconds the pressure can
drop from 2300 psig to nearly 50 psig. This subcooled depressurization
period isknown as the Blowdown stage and has been modeled extensively
by Bdrnard (2).
As the rate of pressure drop decreases, the remaining flow
may experience several flow reversals, and flashing of liquid into vapor
occurs.
Due to the high void and low coolant flowrate, dryout occurs
on the fuel rod surfaces and the critical heat flux condition isreached.
Figure 1 also shows that at approximately 10 seconds after the main
pipe's rupture, the emergency cooling system (ECCS) is initiated and
water ispumped into the reactor core.
When the rising pool of water
(traveling typically at 1 in/sec) inthe lower plenum reaches the drted
out fuel rods, water isboiled and this resulting two phase flow aids in
slowly cooling the upper portions of the rods and their structural supports.
Eventually the rising pool of water quenches the fuel rods and a
quench front propogates upward.
1.2 SPACER GRID EFFECTS
An observation made by Bjornard (2)and other investigators
is that there are discrete locations ahead of the quench front where a
limited amount of rewetting has already occurred. These positions correspond to the orientation of fuel rod structural supports, known as
spacer grids. Apparently, due to mechanical constrictions and distur-
16
in
w
0
co
lGO
0
0
0
N
n
I-Q
A_1-CD
v 0~ Cc:
w
CD
Cr
0
o
o
o
0
0
9a
(6!sd) aJnsaJd
. >=j
_n>
,..'h-=
3Q
*
LU
CN
0
17
bances, a beneficial effect which aids in the cooling process has been
encountered.
Two results, therefore, seem likely.
Spacer grids may
cause local fuel rod rewetting shortly before the neighboring region
quenches, and secondly, the heat transfer may be enhanced at these discrete locations both before and after quenching occurs.
1.3
PREVIOUS EXPERIMENTATION
A great deal of effort and money has been expended to obtain
a better understanding of the flow regimes encountered during a LOCA
and their corresponding modes of heat transfer.
When dryout occurs on
the surface of the fuel rods, there is a departure from nucleate boiling.
This regime, known as post critical heat flux (or post CHF), is
characterized by a violent increase in wall temperature and rapid decrease in the associated heat transfer coefficient.
Possible flow re-
gimes that are experienced include inverted annular flow film boiling
and dispersed flow film boiling.
fractions.
The latter occurs at higher void
These flow regimes are shown in Figure 2 along with the
flow situations encountered prior to CHF.
Experimental and theoretical research has been carried on at
MIT for several years.
Smith (3)studied heat transfer and void frac-
tion during upflow while Robershotte (4)performed similar heat transfer
experimentation and some associated modeling for the downflow situation.
An analytical program was developed by Kaufmann (5)to model heat transfer in inverted annular and dispersed flow film boiling during upflow.
Bjrnard (2)developed a computer program package which models the entire
18
DISPERSED FLOW
FILM BOILING
INVERTED ANNULAR
FILM BOILING
TRANSITION BOILING
NUCLEATE BOILING
SINGLE PHASE LIQUID
NOT TO SCALE
FIGURE 2:
TWO PHASE FLOW REGIMES
19
blowdown stage. Currently, Singh (6)is studying the flow reversal
phenomenon, characteristic of the saturated depressurization period
following blowdown, and the thermal hydraulics of gravity - feed reflood
is being investigated by Cheung
7).
Gonzalez-Rivas (8)recently con-
cluded a void fraction and carryover transient analysis.
1,4 OBJECTIVE OF THIS WORK
Virtually no prior experimentation and only minor modeling
efforts have been conducted that are directly related to spacer grid
effects encountered during the reflood period. As a result, both an experimental and analytical program were developed to investigate this
problem, Specifically, upflow will be considered with flow parameters
typical of those occurring during reflood. The models employed allow
one to make reasonable estimations of the added heat transfer effect
of spacer grids during a steady-state, upflow, post critical heat flux
situation.
20
CHAPTER II:
EXPERIMENTAL PROGRAM
2.1 APPARATUS
Equipment employed during this investigation was a combination of that used by Smith (3), Robershotte (4), and additions or alterations performed by the current experimenter.
Elaborate efforts
were made to insure that the apparatus accurately represents the actual
physical situation experienced ina reactor core during a LOCA.
2,1.1
Reactor Model
The reactor core consists of a bundle of fuel rods and
control rods ina spacer grid assemblage which provides structural support. When boiling occurs low in the bundle during reflood the resulting two phase flow moves vertically past the rod bundle. This flow, external to the rods was experimentally modeled as a two phase internal
flow in a tube by matching the external flow's hydraulic diameter, mass
flux and Reynolds number.
At the discrete spacer grid locations, a flow constriction is
incurred and droplet interference isencountered. This external flow
behavior was also transformed to a corresponding internal model which
accounted for the flow area reduction.
The entire experimental system was responsible for providing
the correct inlet flow conditions to a constant wall temperature section, which included the spacer model.
21
2.1.2 Test Loop Description
A schematic of the entire experimental apparatus is shown
in Figure 3 and photographs are presented in Figures 4 and 5. At the
start of a cycle, water left a reservoir tank and proceeded, via copper
tubing, to a 10 gallon per minute capacity centrifugal pump.
Due to the
pump's over production, most of the liquid was immediately recycled around it through a bypass valve.
The water continuing forward passed
through a Fulflo SSHP-2416 filter and was then monitored with a float
type flowmeter (Tube #FP-1/2-27-6-10/55, Float #GUSVT-40T60).
Fine ad-
justments of the flow rate were made by valves located at either end of
the flowmeter.
Water next entered a shell and tube 40 psi steam preheater in
order that the liquid subcooling be reduced.
A recirculating valve was
employed during start up operations in order that thermal time constants
be reduced in the main test section.
During steady state operation,
however, all of the liquid traveled past the recirculating valve and
through the four-way valve, advancing towards the electric preheater.
The electric preheater, a 3/8 inch 304 stainless steel pipe (.675 inch
O.D., .493 inch I.D.) was heated with a direct current generator capable
of producing 45 KW of power.
Although a fraction of this power output
was required, the cables connecting the preheater and generator were
water cooled.
A photograph of the electric preheater appears in Figure
6. Voltage was measured directly across the electric preheater; whereas
current measurements were obtained from the voltage drop across a cali-
') ,
0z
9
I
F
hiac
w
I-.
4
w
I
!i
hi
4
I-
CD
a_I
a
Li
I-
0
LiX
LLI
X
'-
0
tL
<
CC
/-
LL
13Li
'-U
hi
IC
L.L
i-)
2
'I
I.JAl
c.
U.
C-)
I) E
IL
Li.
,_
CY~
!,
cchc
0c
23
Figure 4.
Figure 6.
Entire Apparatus
Electric Preheater
Figure 5.
Lower Portion of Apparatus
Figure 7.
Pp
onco
24
Figure 8.
Figure 10.
Pipe Without Copper Block
Test Section Wiring
Figure 9.
Figure 11.
Pipe with Copper Block
Environment Chamber, Controller Clocks, and Variacs
25
brated NBS shunt resistor located on the generator console. Teflon
disks (1/16 inch thick) inserted ina specially produced pipe connector
shown in Figure 7, electrically insulated the preheater from the neighboring test loop elements. Constant monitoring of the preheater's power
level and temperature were required to guard against pipe burnout and
rupturing since this was a constant heat flux mode of heat transfer.
The low quality steam produced in the electric preheater then
entered the main test section, wall temperature of which was controlled
and set at a constant temperature, Heat, added to maintain the fixed
wall temperature, was measured and recorded inorder that heat flux versus length data could be obtained. A more complete explanation of the
components involved in this process will be presented in the next two
sections. Steam, exiting from the main test section, re-entered the
copper tubing network and was desuperheated and subcooled ina condenser. Liquid produced inthe condenser, returned to the system reservoir
and awaited further recycling.
2.1.3 Test Section Components
The test section consisted of a 304 stainless steel pipe
with a "spacer" internally welded to it. All instrumentation and related components were located along a 22 inch stretch of the pipe; however, a short entrance length and longer exiting one increased the pipe's
overall length to 34 inches.
The spacer, shown inFigure 12, was welded
at the 11-1/4 inch mark along this 22 inch stretch, inorder that a
steady-state flow could be established both before the spacer and downstream of t. Figure 17, in Chapter 3, illustrates the spacer with a
26
J
-
!
II
el
a
Li
Cc
-CL
en
1-
X:
Lii
0_
I
00%
ii
0
mu
_
owk
CD
Lii
§_Lr-m
K~~~~~~~~~~~~~~~~~c
'
ll
0
z
0
LL
27
portion of the stainless steel pipe wall,
Direct contact conduction heating from hot copper blocks supplied the test section with the required heat flux spikes along its
length. The copper blocks were made from 4 inch diameter cylindrical
copper, which was cut into 120 ° sectors and held tightly against the
stainless steel pipe with hose clamps. Copper block heights of 7/8
inch, 1-7/8 inch, and 2-7/8 inch were employed with gaps averaging 1/8
inch between neighboring blocks. Holes were drilled and reamed radially into the blocks, 1 inch apart vertically and separated by 40° cir-
cumferentially.
Figures 8 and 9 show the stainless steel pipe before
and after mounting a copper block. Details of a 1-7/8 inch block are
illustrated in Figure 13,
Pressed into the radially drilled holes and supplying heat to
the copper blocks were 1/4 inch diameter, 1-1/2 inch long, Hotwatt AC
resistance cartridge heaters. Each heater was capable of delivering up
to 120 watts individually and 198 heaters were uniformly distributed
over the 22 inch length, Voltage supplied to the cartridge heaters originated from 10 variable transformers (Variacs), each with a 140 volt/
10 amp power potential.
A total of 10 copper blocks (30 sections) were
used such that there was a one to one correspondence between blocks and
variacs, This enabled the power delivered to each block to be independently determined and ten individual heat flux spikes established.
Since
more experimental accuracy isdesired at the spacer, shorter copper
blocks were located nearby. Hence, there were two 7/8 inch length blocks
used by the spacer and four each of the larger two sizes elsewhere.
28
4'
__
IA
r
_
r
rl-A
0a
['7/8"
L
0
L
a
0
COPPER
r
STAINLESS
PIPE
STEEL
- ----
FIGURE 13:
DETAILS OF 1-7/8 INCH COPPER BLOCK
29
This assortment, including gaps, accounted for the 22 inch total length.
Surrounding the block assemblage and blanket of asbestos insulation was
an aluminum environment chamber with pyrex windows. This box was filled
with nitrogen and served to reduce oxidation of the copper blocks.
2.1.4System Monitoring and Control
Instrumentation was primarily concerned with monitoring
and establishing a constant wall temperature in the test section. Temperature readings were obtained using chromel-alumel thermocouples throughout the entire assemblage. At the test section, a total of 30 thermocouples were employed, 3 each at 10 different axial positions. The locations were chosen such that each thermocouple corresponded to one of
the 30 copper block pieces. Grooves were cut into the stainless inorder
to recess the thermocouples inside of the pipe wall, as shown in Figure
14, and insulation was packed on top to insure accurate readings. All
30 thermocouples were monitored and of these, 10 also served as the initial link inthe closed loop constant wall temperature controller.
Ten temperature controller circuits (one per block) each compared a different block's thermocouple output to a reference voltage
which was set to correspond to the desired wall temperature. A comparator turned a power relay on ifthe temperature measured was 10°F below
the reference point and turned the power relay off if the temperature
measured was 10O°F above it. The power relay performed two tasks. One,
itdetermined whether current could flow through a Variac and hence if
power would be delivered to the block, and two, it turned a sweep hand
cr
-j
0_
C)
t3
C-,
C
w
I-
.0
0
CE
CD
6-4
I--
2i
U-
31
clock on and off which measured the duration of power flow. A circuit
diagram of this controller, originally designed by Robershotte (4), is
presented inAppendix, A, Figure 26. Photographs of the electrical
connections between the test section and terminal blocks; and the environment chamber, controller clocks, and Variacs are shown in Figures
10 and 11.
Due to the comparitor's hysterisis and the Variac's voltage
setting, a duty cycle resulted which required a 20 minute total run
time for proper averaging.
Since the voltage level of a Variac was kept
constant during any given run, the total energy transferred to a block
is simply:
E = PAt
(2.1)
where P isthe constant power delivered to the cartridge heaters when
the variac ison and At isthe time recorded on the clock. The gross
heat flux then for a 20 minute run is:
(q/A) G = E/At(20)
(2.2)
where At isthe inside area of the tube.
2.2 EXPERIMENTAL PROCEDURE
A standard procedure was followed for each individual run executed with the apparatus. A cursory description of the steps involved
will be presented here and a tabular form may be consulted in Table 1.
Initially, a desired wall temperature was chosen and the corresponding controller reference voltage set. Estimates of the test section
32
TABLE 1
EXPERIMENTAL PROCEDURE
I. Initial Preparation
1) Choose desired wall temperature and set corresponding
controller reference voltage
2) Estimate test section power requirements and set Variac
voltage level
3) Calculate required amount of preheating
4) Reset clocks
II. Start Up Operations
1) Open condenser and cooler water valves
2) Bleed nitrogen into environment chamber
3) Open recirculation and steam valves
4) Turn pump and test section power on
5) Check thermocouples and flowrate
6) When test section obtains desired temperature, close
recirculating valve and turn electric preheater on.
III.
Steady-State and Shutdown Procedure
1) Turn clocks on
2) Monitor and record flow rate, preheater power level,
and temperatures
3) Shut down system and turn off clocks after 20 minutes
4) Record elapsed time on clocks, Variac voltages, cartridge
resistances, etc.
33
power requirements were made and Variacs turned to the proper voltage
levels.
Also calculations pertinent to the flow's quality (and hence
Reynolds Number) were made inorder to determine the required amount of
preheating.
During start up operations, the generator cable coolant and
condenser water were allowed to flow and nitrogen was bled into the environment chamber.
Next the recirculation valve and steam valve were
opened; and the pump and test section power turned on, The flow rate
was established while the thermocouples were being monitored.
Once the
test section obtained its desired temperature, the recirculating valve
was closed and the electric preheater turned on.
After the entire system reached steady-state, the clocks were
turned on the the run was begun.
During the following 20 minutes, the
flowrate, preheater power level, and temperatures were monitored and adjusted accordingly.
When the run was completed, the time elapsed on
each clock was recorded; and resistance measurements of the cartridge
heaters conducted, testing for burnouts, Also the flowrate, wall temperature, variac settings, preheater power level and observations were
noted for data reduction and further analysis.
2.3 DATA REDUCTION
The total average power to each block isequal to the rate of
energy dissipation in the cartridge heaters. The total resistance of n
parallel heaters ina given block isRt, where:
n
1 =
Rt :
li
=1 Ri
(2.3)
34
The gross heat transfer rate, then, isdependent on this resistance, a
Variac's voltage setting, and the ratio of time on to the total run
time.
G=
trun
V2 ) ( ton F
{T
) (3.412)
trun
~~~~~~~(2.4)
(2.4)
where 3.412 isa conversion factor from Watts to Btu/hr.
Not all of this gross energy transfer directly heats the test
section.
Some energy is lost to the environment and thermal capacitance
effects may occur in the stainless steel pipe or copper blocks.
qG
= qnet + qL + [(lnCp)
SS
+ (Cp)
]dT
Cu
(2.5)
Due to the cyclis nature of the heating process and steady state conditions; however,
t
I
=0~~~
~dT
(2.6)
This reduces Equation 2.5 to:
qnet
qG-
qL
(2.7)
Heat losses to the environment were measured before each run and deducted from the calculated gross heat transfer, yielding the net heat
transferred to the test section.
Knowing qnet' an experimental heat
transfer coefficient could be obtained with A = At.
35
hexp
=
(q/A)net.
T
- T
wall - sat
(2.8)
)(
Itis also necessary to know the entering equilibrium quality
and hence, also the entering enthalpy to the test section. Since the
fluid temperature entering the preheater, Ten t, was known, the amount
of superheat enthalpy was calculated from an energy balance at the
electric preheater
Hin = (Tin - Tsat)
qPRE
(2.9)
m
The difference intemperature between Tin and Ta t in Equation 2.9
represents the amount of enthalpy required to eliminate the subcooled
liquid. The equilibrium quality entering the test section is then,
(X )
eq in
=
H.
(2.10)
in
Hfg
The inlet equilibrium quality can not be calculated for subsequent
blocks using
(itl)
Xeq
(i+l)
= qnet
(i)
+Xeq
(2.11)
(I)(Hfg)
which isan energy balance performed on each test section increment.
36
CHAPTER II I:
THEORETICAL ANALYSIS
3.1
POST CHF HEAT TRANSFER
During an analysis dealing with a two phase flow, proper iden-
tification must be made of the equivalent single phase properties.
In
this investigation, an effective equilibrium vapor Reynolds Number is
applied which incorporates the mass flux, quality, and void fraction:
Re = GD Xeq
(3.1)
a v
The vapor flow isconsidered turbulent when Rev > 3000.
Inthe dis-
persed flow region, a isapproximately equal to 1.0, indicating that
the void fraction may be neglected when testing for turbulence. Thus,
turbulent flow occurs when
GD X
eq > 3000
(3.2)
v
The total heat flux inthis situation is the result of two contributions.
(q/A) = (q/A)v + (q/A)d
(3.3)
The first term, (q/A)v, represents wall to vapor forced convection heat
transfer; while (q/A) d is the wall to droplet mode of heat transfer.
37
3.1.1
Forced Convection Heat Transfer to Vapor
Dittus-Boelter (9)correlated data for a forced convec-
tion single phase flow ina pipe and established an empirical equation
for a heat transfer coefficient.
Inthis two phase study, the single
phase Reynolds Number used by Dittus-Boelter is replaced by the effective Reynolds Number in Equation 3.1 yielding:
.8
hDB = (.023) D
Kv (Re)v
.4
(Pr) v
(3.4)
Since thermal equilibrium is not insured, this heat addition can either
increase the quality or superheat the existing vapor.
If no superheat-
ing occurs (typical of higher mass velocities), and equilibrium model
may be employed,
(q/A)v = hDB (Twall
-
Tsat)
Vapor properties are evaluated at the saturation temperature.
(3.5)
During
lower mass velocities, however, a model which assumes only superheating ismore accurate.
Inthis case, vapor properties are calculated
at the actual vapor temperature.
(q/A)v = hDB (Twall - Tva p )
(3.6)
Equation 3.5 is known as the "Equilibrium Model" or "Dougall-Rohsenow
Limit", while Equation 3.6 is called the "Fixed Vapor Fraction Model" or
38
"Fixed Gx Model". The present investigation utilizes the latter model,
since flows with mass velocities typically encountered during reflood
ina reactor have been modeled more successfully with this formulation
(4). This decision, however, is not of great consequence, since use of
the equilibrium model would only slightly alter the primary results being sought.
The vapor temperature is found by performing a control volume
heat balance on a test section increment. Heat entering the vapor is
simply,
qv
=
x ) Cp (Tout
Tin)
(3.7)
The mean value of the inlet and outlet temperatures is the vapor temperature;
Tvap = ()
Tin + Tout)
(3.8)
This scheme, which calculates Tvap, isan iterative one, since the
vapor properties used to evaluate Equation 3.4 for the heat transfer
coefficient are dependent on this temperature.
It is necessary to
first estimate the vapor temperature, then evaluate the vapor properties, calculate the heat transfer coefficient, and apply Equation 3.6.
Next, an energy balance isconducted with Equations 3.7 and 3.8 yielding an updated approximation for the actual vapor temperature. Only a
few iterations are required with this method and convergence is quickly
obtained.
39
The method of evaluating the wall to vapor heat transfer
assumes a fully-developed flow.
Since a development length will be ex-
perienced, entrance effects must be accounted for. Figure 15, reproduced from ESDU (1968) (10), gives plots of three entrance effects based
on different entrance configurations,
This figure shows the ratio of
the local Stanton Number to the fully developed value, where
Stx = Nu
RePr
= h D
(3.9)
k-0ePr
The actual heat transfer coefficient compared to its fully-developed
value is proportional to the corresponding Nusselt numbers, and hence,
also to the Stanton quantities.
hx
h
=
NUx
Rii
= Stx
St
(3.10)
-
Apparatus utilized in this research (see Chapter II)used an electrically insulating pipe coupler, which behaves like an orifice to the
flow.
A short calming distance of four inches is then encountered
followed by a jump in temperature at the heated section, as illustrated
in Figure 16. Although none of the entrance configurations exactly
match this situation, cases 2 and 3 provide a range in which the anticipated entrance effects should lie.
3.1.2 Wall to Droplet Heat Transfer
The second and less pronounced mode of heat transfer in
tin
An
0
CX
Or
0
z
-J
U
C,
J
C-
0
0
p-
X
I-Q
LL
0
CD
LU
LU
U0
FU
LLJ
LL
LU
FJ
u
LL
I-
LU
-
LU
_
4:
Olor
cn (1)
_
41
i
w
L
IU)
L
0
14
L
0z
C
I-L3.
C
Cl) w0.
(..)
C,)
4
L
c
I-LU
w
-mj
z wi
w
.J
C(
!-ILAJ
C,)
(./3
I-
C,-)
F-
LI
I-
t~O
LU
U-
n
U
42
Equation 3.3 is the wall to droplet heat transfer term, (q/A)d.
An
elusive quantity to obtain despite recently intensified research programs,
this contribution is due to droplet evaporization upon entering the vapor
boundary layer. A single droplet analysis was performed by Ganic (11),
resulting in an expression for the wall to droplet heat flux term;
(q/A)d
=
(l-a) pf Hfg V1 e
(3.11)
where a is the void fraction, pf, the liquid density, Hfg, the heat of
vaporization, V
the perpendicular or deposition velocity, and
the effectiveness or percentage of drop evaporization.
,
Due to the single
droplet model, this expression has a high void requirement.
If the void
were to significantly decrease, droplets colliding with other droplets
would begin reducing the actual droplet and wall interaction.
Hence,
the major restriction placed on Equation 3.11 is that it not be applied
when voids are less than 98%. A second limitation is that there be
enough vapor to ensure a turbulent dispersed flow.
To fully understand Equation 3.11, each term must be individually defined. The most common definition employed for the void fraction
during upflow is the homogeneous model, where the liquid velocity is
assumed equal to the vapor velocity due to the interfacial drag force.
ahomo
Cthomo
p=
1 +(X
Pf
+
l
(193,12)
3P
43
Liquid density and heat of vaporization are determined by the system's
temperature and pressure, The deposition velocity was determined to be
a function of vapor velocity and vapor Reynolds Number by Liu (12).
-.125
V1 = .0289) Vv (Re)v
(3.13)
Effectiveness, , perhaps the most difficult value to pinpoint, was investigated extensively by Kendall (13). Although lengthy empirical expressions were obtained, a constant value assigned to the effectiveness
still seems adequate.
: .004
(3.14)
Considering Equation 3.11 once more, we see that the strongest influence
on the wall to droplet heat flux is the void fraction. Hence, within
the correlation's limitations, the wall to droplet heat transfer contribution will substantially increase inmagnitude, as the liquid fraction
rises or the void fraction is lowered.
3.2 SPACER GRID EFFECTS
Numerous causes of increases in total heat transfer at a spacer
grid seem likely.
Effective area reductions which constrict the flow,
increase the flow velocity for a short distance and create an entrance
effect at the spacer. This would tend to increase both the wall to
vapor convection and wall to droplet conduction. Droplets inpacting
the spacer form a saturated liquid boundary layer, which may desuperheat
44
the vapor, provide some fin cooling, splash drops onto the hot pipe wall
downstream, and furnish the hot wall with an available radiation sink.
The desuperheating effect isminor since vapor superheating isminimal.
Droplet splashing and fin effects cannot be measured and quantified in
this investigation but are not considered as major modes of heat transfer, The remaining mechanisms mentioned include increased velocity
vapor convection, increased velocity droplet conduction, and wall to
spacer radiation.
(q/A)s = (q/A)v s + (q/A)D S + (q/A)R S
(3.15)
These individual contributions will now be examined ingreater detail.
3.2.1
Increased Flow Velocity
Based on mass continuity, the increased mass flux and
flow velocity, due to area reduction at the spacer, can be determined:
*= ms
s
(3.16a)
GA = GsA s
(3.16b)
Gs
(3.16c)
G(A )
As
The mass flux at the spacer isthen related to the upstream and downstream mass flux simply by the area ratio. Also, since the flow density isassumed to remain constant, we have:
V = V(A )
s
As
(3.17)
45
Due to the increased mass flux, decreased flow area, and also a changed
hydraulic diameter, the vapor Reynolds Number must be modified at the
spacer location.
(Re) = G D X
(3.18)
Pv
The hydraulic diameter, D s, is obtained by considering the actual flow
area and the wetted perimeter;
Ds
= 4As
P
(3.19)
These alterations are now substituted into Equations 3.4, 3.6, 3.11
and 3.13, yielding the governing relationships required for determining
the vapor convection and droplet conduction heat transfer contributions
at a spacer grid.
(hDB)s
= (.023) K (Re) s
Ds
.8
.4
(Pr)v
(q/A)v s = (hDB)s (Twall
Tvap)
(3.20a)
(3,20b)
-.125
(Vl)s
= (,0289) V s (Re)s
(q/A)Ds = (1-a) Pf Hfg (V1) s
(3.21a)
(3,21b)
46
3.2.2 Wall to Spacer Radiation
Droplets moving with the vapor flow collide with the
spacer grid and become entrained on its surface. Newly formed droplets
splash off the rear of the spacer as the liquid boundary layer builds
up and periodically erupts. At all times, however, the spacer iswetted
by the liquid and remains at the saturation temperature. Due to the
large magnitude in temperature difference between the fuel rods and
spacer grids during the CHF period and the low flooding rates typically
encountered inreflood, a very significant portion of the overall heat
transfer experienced at the spacer isexpected to be radiation induced.
An important step in quantitatively analyzing the radiation
contribution is to properly understand the geometry. Reviewing Figure
8 in Chapter II,the configuration presented is simply a thick cross
bounded by a circular wall. Only the pipe wall section not incontact
with the spacer, Aw , isable to radiate energy. For this gray body
radiation, the governing net heat transfer equation developed by Hottel
(14) is,
qwf
Aw
'wf
4
(Tw
-
Tf4)
(3.22)
where the subscripts w and f denote wall and liquid respectively, temperatures are measured indegrees Rankine, wf is the gray body effective view factor, and a is the Stefan-Boltzman constant,
0.1713 x 10 8 Btu
ft hr R(3.23)
47
Assuming nonrefracting surfaces encompassing a nonabsorbing medium,
11
wf_
~Ff
Where
w
1
1 + Af
+ (-)w-
-1)
(.4
isthe emissivity of the hot oxidized stainless steel wall,
cf is the emissivity of the saturated liquid, and Fwf is the geometric
viewfactor from the radiating wall to the spacer. To obtain Ff,
Figure 8 is idealized by straightening the curved surface as illustrated
inFigure 17. Due to symmetry, only one quarter of this configuration
need be considered inorder to evaluate F.
The following relation-
ships may then be derived.
A3F3
FWf
= A1 F13 + A2 F23
=
F3 wf= U
2(w) F 13
=/
~~13
w
F 12 + F13
=
(3.25a)
F13
1
1
FWf = V2 (1 - F12 )
(3.25b)
(3.25c)
(3.25d)
The remaining view factor introduced, F12, may be calculated using a
chart reprinted from Hottel inRohsenow (15), which gives the view factor for direct radiation between adjacent rectangles in perpendicular
planes.
This chart isreproduced inFigure 18.
Since the radiation heat flux at the spacer must be based on
the entire pipe area, the fraction of wall area seen by the spacer of
48
I I
2,L
3, W
FIGURE 17:
SPACER IDEALIZATION
49
I
II
I
I
III
SI .I
Z1)
OD
.
-~~~
0
~ M.~~~~~~~~~~~~~,
--
00
4--'0I.
0~~~~.
~-0
:
-
° · °
--
_ Ce:N
_ __
° °
°
oo
°w
°
-
egO°N@O
N.
-
-
u) 0
~
E
0'
C~~~~~~~~~~~~~~~~~~~~~~~
L-
0
E-0.I
:,U
''~~~~~~~~~~~~~~~~a
Ij-
o
-4
C>
___
o
0
6
'A
6
6
ci
U
0
14
6
0
In
cl-i
0
N\
c
c;
*:I
0(30j
)
-
6660O
0
-
U')
0
0
I-
LiiJ
S-
50
the total area must be defined.
aO Aw
(3.26)
Substituting this relationship into Equation 3.22 yields an expression
for the radiation heat flux experienced at the spacer.
4
4
~3wf a (Tw4 _ Ts4 )
(q/A)s =
(3.27)
In this investigation, the following values were appropriate,
B = .801
(3.28a)
Et
.96
(3.28b)
= .94
w
F12 = 29
F12
(3.28c)
Fwf
wf = 1.0
(3.28e)
=
e
(3.28d)
Substituting into Equation 3.24 yields,
T=
'^f
.92
(3.29)
51
CHAPTER IV:
EXPERIMENTAL RESULTS AND COMPARISON TO THEORY
4.1
EXPERIMENTAL HEAT FLUX RESULTS
Tests were conducted at a mass flux of 18, 720 lbm/hr-ft 2,
which isequivalent to a flooding rate of 1 in/sec. The test section
wall temperatures included 1000°F, 1100°F, 1200°F and 1300°F while the
system pressure was kept at atmospheric.
Numerous attempts were made
to obtain data at both higher flooding rates and greater Reynolds Num-
ber values (Re
v > 5000). Unfortunately, all of these efforts were
thwarted by an inlet quench problem. Further comments with regard to
this will be made in Chapter V. Heat flux results obtained from the
successful runs are plotted along with the corresponding theoretical
curves in Figures 19, 20, 21 and 22.
Several
ortions of these curves first deserve identifica-
tion. The shaded region at the start of each plot represents the range
of anticipated entrance effects as predicted by cases 2 and 3 in Figure
15. This did indeed compare reasonably well with experimental values.
Flat portions of the curves indicate steady-state values which were
obtained both upstream and downstream of the spacer.
The effect of
the spacer itself is clearly recognizable by the sudden combination of
step increase and step decrease in the predicted heat flux at the 101/2 inch and 12 inch marks respectively. These figures strongly infer
that there isa very noticeable enhancement of heat transfer experienced at the spacer location.
52
0
N
LJ
>
FC
F-
==.
0
0o
C
o
<C
I
-
Li.
C
Z:
g
L
L)
C
_
L
z AS:-
CD
AL
n~~
0
(0
0
0
0
N
(j .~q/n4) :_01 x V/0
0
53
\
LU
IC)
LL
C)
o
0
,CD
I-I
z
r-
O
CM
Z:
:
ICL.
C-,
-
0
(Z; J4L/n4lg)
01 x V/)
54
)
of
J
C.
0I
o.
0
()
C
C
Lo
z
Z
Wr-
L.)
L
cn
T-
._
LU
0
au_
:
LL.
0
(lJ4
U)
0
(+J4ng
*0
No
£-0 X l
-
0_O
55
O
N
n,'
CI
ILL
C),
o0
C)
o~Z~~~CY
emLU
C
h
<
OL
LU
FF
0 CD Z<
z
<
J
4
tm
CD
C-M
CM
r,
CD
Ii
OL
cc
((;
4J'/n4l)
e-o x V/
56
Although the experimental data straddles the theoretical
model, the magnitude of its scatter isat first alarming. The major
cause of this behavior isdue to copper block temperature differences,
creating an axial heat transfer not accounted for in the model.
More
specifically, the test section wall temperature iscontrolled to be at
a constant level along its length. Heat flux spikes, however, vary
significantly from block to block. This results indifferences incopper block temperatures which act as the driving potentials causing the
heat flux spikes. Due to this temperature variance, heat is convected
across the 1/8 inch gap from one block to another. This effect is
felt most strongly at the spacer where the net heat flux is considerably
greater than the fully-developed value. Accordingly, heat is transferred directly to the neighboring cooler blocks. Figures 19 and 20
exemplifying this situation, both indicate a negative net heat transfer
immediately downstream of the spacer. What this all indicates is simply
that the experimental heat fluxes at the spacer should be decreased
enough inorder that the neighboring values be increased to at least
the fully-developed value, such that the total energy transferred remains constant.
Since the two blocks at the spacer are only one half
as thick as the adjacent ones, the high experimental heat flux results
obtained at the spacer should be decreased a distance equal to twice
the increase inmagnitude of the lower values.
The primary inpetus of this investigation is the specific
determination of the spacer grid's effect. With this goal inmind, a
57
more detailed analysis of the effect will now be considered.
4.2 EFFECTIVE HEAT TRANSFER ADDITION AT SPACER
A local heat transfer coefficient can be determined similar
to the experimental heat transfer coefficient given in Equation 2.8.
h
= (q/A)x
(4.1)
(Twall - Tsat)
When a flow reaches steady-state, this parameter also obtains a constant value given by h. The ratio hx to h yields a nondimensional
heat transfer coefficient magnitude.
hx
(q/A)
(4.2)
When Figures 19 through 22 are replotted inthis fashion, they completely coincide except at the spacer. Figure 23 indicates that a three
fold increase inthe local heat transfer coefficient isexperienced at
this location.
This effect iscaused by the radiation mode of heat
transfer, which is heavily dependent on temperature and is localized
at the spacer.
The magnitude of increase inheat transfer caused by the
spacer can also be obtained by integrating the heat flux curves.
In
this process, the valleys mmediately before and after the high spacer
heat flux values are accounted for, such that the previously ignored
problem of thermal interaction between adjacent blocks isvirtually
eliminated.
These integrated values are plotted inFigure 24 along
58
CD
I--
LU
Z
L)_
N
C##j~C
r{,?)
LU
Ln
I-
C
oD=
,cS
LU
CD
uI-
LL
ZZi
Z
0~4
0
ci
cC
(z
C
Ldo U--L
t
Cq/
It3
a
/"4
u~r
59
no
0
-
V- . M
LL
c
L)
0o0J ..
iJV
F
cJ
LU
-
0
I
0 i
CC
LI
LJ
CD
CL
a)~~V
I
I
I
(0
I
C3j
(Jt/n~Ei) _0 x s o0
I
0
60
with a theoretical curve obtained from the model presented inChapter
III.
Although this model underestimates the experimental findings,
the correlation between the two ismuch better than indicated earlier
by the heat flux curves. As the wall temperature increases, the model
seems to predict a greater percentage of the experimentally determined
spacer heat transfer.
This trend isdirectly caused by the increasing
importance of wall to spacer radiation at higher temperatures, which
iseasily accounted for. To make this concept clearer, the total
energy transferred at the spacer, based on the theoretical model, is
broken down between the three heat transfer modes by percentage and
plotted inFigure 25. At lower temperatures, the radiation effect is
not much greater than the droplet contribution; however, radiation becomes the primary mode of heat transfer beyond 1400°F.
Several reasons for the model's underpredictions seem plausible. A disturbance caused by the flow's constriction at the spacer may
induce an entrance effect at the spacer and slightly downstream of it.
This, however, would not effect the radiation contribution, and therefore isconsistent with the trend illustrated in Figure 24. A second
consideration isthe exceptionally high temperature of copper blocks
located at the spacer.
Not only is heat transferred axially, but an
increased radial heat loss isexperienced which isgreater than that
measured during heat loss tests.
In summary, we see that there are
reasons why the actual heat transfer at the spacer isgreater than what
the model predicts but also less than what experimental results may
have us believe.
61
0
0
to
LU
C-)
IL:
*
ClI-
LU
woU-
V)
OD..LUJ
Cj
Z
CD~
0o
0
(0
(%)
(%)S
*
l
0
N
39VLN333
3 39VIN3383d
JO
0
LU-
62
CHAPTER V:
CONCLUSIONS AND RECOMMENDATIONS
5.1
CONCLUSIONS
The goal of this investigation was to determine the extent of
spacer induced heat transfer enhancement during a post critical heat
flux situation.
In this vein both experimental and theoretical programs
were designed to quantitatively analyze the magnitude of this effect.
Wall temperature was varied in increments of 100 degrees between 1000°F
and 1300°F. The mass flux equaled 18,720 lbm/hr-ft 2 , which is equivalent to a 1 in/sec flooding rate,
The "Fixed Vapor Fraction Model" predicted entrance and steadystate heat transfer levels consistent with experimental values.
Where
discrepancies at the spacer due to experimental scatter occurred, an
integration scheme was applied which accounted for a heat transfer interaction not included in the theoretical model.
Results indicate that
for the flows considered, an increase of at least three times the net
heat transfered at the spacer may be expected.
This supplemental energy
from the hot wall at the spacer is primarily due to:
(1) Higher vapor velocities which increase the vapor convection and droplet conduction.
(2) Wall to saturated liquid (entrained on the spacer)
radiation.
The first effect is independent of wall temperature and depends simply
on the steady-state flow. The magnitude at the spacer will be a constant multiple (with respect to temperature) of the steady-state value.
63
The second effect, radiation, isonly dependent on wall temperature
and provides extra heat transfer localized at the spacer. When the
wall temperature exceeds 1400°F, the radiation effect dominated in the
low Reynolds Number (Re
v = 4800), low flooding rate (1in/sec) situation.
One final consideration concerns an entrance effect at the
spacer.
Similar to the initial portion of the test section, a rise in
heat transfer may result from unsteady flow behavior. Assuming this
to be the case, the theoretical model incorporated in this analysis
will underpredict the vapor convection and droplet conduction.
The
radiation contribution, however, will not be affected since it is independent of the vapor flow.
5.2 RECOMMENDATIONS
Several suggestions seem inorder with regard to future
spacer grid analysis; inparticular, construction of the experimental
apparatus.
In this study, thin copper heating blocks were used at the
spacer in hopes of obtaining a more sensitive measurement. Since the
cartridge heaters were inserted radially, a large block diameter was
required.
This tended to greatly aggravate the inter-block heat trans-
fer problem, which was the primary cause of data scatter.
Inthe future,
one heating block should be employed at the spacer with a thickness of
approximately two inches and all block diameters throughout the test
section should be minimized.
Inaddition, thermocouples could be
mounted on the copper blocks inorder to determine any remaining thermal
64
interaction between blocks and to more accurately account for individual block heat losses to the environment.
A second recommendation pertains to the test section inlet.
Liquid leaving the electric preheater was able to wet the unheated pipe
wall previous to the test section. Upon entering the heated section,
the first block received full responsibility of maintaining a vapor
blanket on the pipe wall.
This tended to be an unstable situation
since liquid constantly rewetted the start of the test section, violently
pulling the wall tempeature out of the post critical heat flux region
before the controller mechanism could have an effect.
During downflow
studies, the flow can be funneled into the test section, mechanically
providing an artificial dry starting length as the flow isexpanding.
This cannot be applied to the upflow situation since the gravitational
force would tend to form a pool of water between the funnel and test
section wall.
What isrequired isa totally different approach, one
which can insure that the post CHF state of the test section inlet flow
ismaintained.
65
REFERENCES
1. Hsu, Y.Y. and Sullivan, H., "Thermal-Hydraulic Aspects of PWR
Safety Research", Thermal and Hydraulic Aspects of Nuclear Reactor
Safety, Vol. 1, 1977.
2. Bjrnard, T.A., "Blowdown Heat Transfer in a Pressurized Water Reactor", PH.D. Thesis, Massachusetts Institute of Technology, August
1977.
3. Smith, T.A., "Heat Transfer and Carry Over of Low Pressure Water in
a Heated Vertical Tube", Masters Thesis, Massachusetts Institute
of Technology, January 1976.
4. Robershotte, P., "Downflow Post Critical Heat Flux Heat Transfer
of Low Pressure Water", Masters Thesis, Massachusetts Institute
of Technology, July 1977.
5. Kaufman, J.M., "Post Critical Heat Flux Heat Transfer to Water in
a Vertical Tube", Masters Thesis, Massachusetts Institute of
Technology, September 1976.
6. Singh, B., Current Research at the Mechanical Engineering Heat
Transfer Lab, Massachusetts Institute of Technology.
7. Cheung, Y., Current Research at the Mechanical Engineering Heat
Transfer Lab, Massachusetts Institute of Technology.
8. Gonzalez-Rivas, J.I., "Carry-Over Predictions from the Upper Plenum
of a Pressurized Water Reactor Based on a First Order Void Fraction
Analysis", Masters Thesis, Massachusetts Institute of Technology,
May 1978.
9. Dittus, F.W. and Boelter, L.M.K., University of California Pub.
Eng. 3, 443, 1930.
10,
11.
ESDU (1968), "Forced Convective Heat Transfer in Circular Tubes",
Part III: Further Data for Turbulent Flow. Item No. 68007,
(251-259 Regent St., London WR 7AD).
Ganid, E.N. and Rohsenow, W.M., "Post Critical Heat Flux Heat
Transfer", MIT Report No. 82672-97, June 1976.
66
12. Liu, B.Y.H. and Ilori, T.A., "Inertial Deposition of Aerosol Particles in Turbulent Pipe Flow". Presented at the ASME Symposium
on Flow Studies in Air and Water Pollution. Atlanta Georgia,
20-22 June 1973.
13.
Kendall, G., "Heat Transfer to Impacting Drops and Post Critical
Heat Flux Dispersed Flow", Ph.D. Thesis, Massachusetts Institute
of Technology, March 1977.
14. Hottel, H.C. "Radiation", Chapter IV of Heat Transmission, by
W.H. McAdams, McGraw-Hill, 1954.
15.
Rohsenow, W.M. and Choi, H.Y., Heat Mass and Momentum Transfer,
Prentice-Hall Inc., 1961.
67
APPENDIX A: TEMPERATURE CONTROLLER
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68
APPENDIX B
EXPERIMENTAL DATA
RUN
Twa 1I
1
2a
2b
3a
3b
4
1000°F
1100°F
1100°F
1200°F
1200°F
1300°F
(Rev)inlet
4300
4800
4950
4850
5000
4725
Flow = 18,720 lbm/hr-ft2, PRESS = 0 psig
69
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APPENDIX C
THEORETICAL ANALYSIS
COMPUTER PROGRAM
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APPENDIX D
THEORETICAL RESULTS
RUN
Twall
1
2
3
4
1OO0° F
1100°F
1200°F
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(Rev)inlet
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91
APPENDIX E:
WATER AND VAPOR PROPERTIES
TABLE 2:
SYSTEM PROPERTIES
WATER
L 60
(CP)L = 1
1bi/ft3
Btu/lbm°F
STEAM
Pv
= .04559 - .00003958 x Tvap
Kv
=
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00747 + 0000551 x Tva
p
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.48 Btu/lbm°F
Prv = (CP)V x V
Kv
Ibm/ft3
Btu/Hr,ft
1bm/hr-ft
F