Design of a Heat Exchanger for Pebble Bed Reactor Applications.
By
Jesse Russell Schofield
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Adviser
Rensselaer Polytechnic Institute
Hartford, CT
April, 2010
© Copyright 2010
by
Jesse Schofield
All Rights Reserved
ii
Abstract
This project presents a novel heat exchanger design for application to Pebble Bed
Modular Reactors (PBMR) in nuclear power generation. The design incorporates a helium-helium transfer at high pressure (above 70 bar) and very high temperature (above
800 °C). A detailed description of a suitable set of operational characteristic equations
are presented. Common real world design conditions are evaluated and appropriate heat
exchanger materials are determined. An analytical work through is shown to develop a
set of design values for a successful shell and tube heat exchanger. The results are reflected on and advised as to where future work could lead in high temperature heat exchanger design.
iii
Table of Contents
Abstract
iii
List of Tables
v
List of Figures
vi
Nomenclature
vii
1.
Introduction
8
1.1
Statement of Problem
8
1.2
Literature Review
11
2.
3.
4.
Methodology
14
2.1
Procedure
14
2.2
Assumptions
14
2.3
Overall Heat Transfer
16
2.4
Shellside Coefficients
16
2.5
Tubeside Coefficients
20
2.6
LMTD Method
23
Results and Discussion
25
3.1
PBMR
25
3.2
Material Evaluation
25
3.3
Preliminary Evaluations
27
3.4
Tube Bundle Sizing
30
3.5
Shell Sizing
30
3.6
Heat Transfer Coefficients
31
3.7
Iterations and Stepwise Needs
32
Conclusions
35
4.1
Final Results
35
4.2
Future Work
37
5.
References
38
6.
Appendices
40
iv
List of Tables
Table 1: PBMR Plants
Table 2: Experimental Heat Exchanger Environmental Conditions
Table 3: Candidate Materials for Heat Exchanger
Table 4: Primary HTHX Design Properties
v
List of Figures
Figure 1: Pebble Bed Modular Reactor Pebbles
Figure 2: Pebble Bed Modular Reactor System
Figure 3: Heat Exchanger
Figure 4: Shell and Tube Heat Exchanger
Figure 5: HTR-10
Figure 6: Countercurrent Flow
Figure 7: Tube Layout Variations
Figure 8: Baffle Design
Figure 9: Visualized Baffle Function
Figure 10: Tube Bundle
Figure 11: High temperature Degradation
vi
Nomenclature
Sym-
P
Factor for LMTD Calculation
dim-less
bol
Description
Units
Pt
Tube Pitch
mm
A
General Area
m2
Prt
Tubeside Prandtl Number
dim-less
As
Shellside Area
m2
Prs
Shellside Prandtl Number
dim-less
Aof
Area of tube outside per unit length
m2/m
Q
General Heat Transfer Rate
W
Asr
Shellside Crossflow Area
m2
Qa
Estimated heat transfer of system
W
Aif
Area of tube inside per unit length
m2/m
Qs
Heat Transfer of Shellside
W
At
Tubeside Area
m2
Qt
Heat Transfer of Tubeside
W
Ao
General Estimated Area
m2
q
Heat Flux
W/m2
as
Shellside Crossflow Area
m2
R
Factor for LMTD Calculation
dim-less
B
Baffle Spacing
mm
Rb
Baffle Correction Factor
dim-less
C
Clearance
mm
rT
tube fouling correction
dim-less
Cs
Shellside Fluid Heat Capacity
kJ/K-kg
rS
shell fouling correction
dim-less
Ct
Tubeside Fluid Heat Capacity
kJ/K-kg
ReS
Shellside Reynolds Number
dim-less
cpt
specific heat of tubeside flow
kJ/kg-K
ReT
Tubeside Reynolds Number
dim-less
cps
specific heat of shellside flow
kJ/kg-K
ΔTlm
Log Mean Temperature Difference
K
Ds
Shell Inner Diameter
m
Tit
Same as T1
K
di
Tube Inner Diameter
mm
Tot
Same as T2
K
do
Tube Outer Diameter
mm
Tos
Same as t2
K
j
Colburn j-factor
dim-less
Tis
Same as t1
K
ktw
thermal conductivity of tube wall
W/m-K
Ti
Inlet Temperature
K
ks
thermal conductivity of material
W/m-K
To
Outlet Temperature
K
Ko
System Heat Transfer Coefficient
W/K-m2
U
General Heat Transfer Coef
W/K-m2
Lta
Length of individual tube
m
Uo
Heat Transfer Coefficient
W/K-m2
K
μ
Dynamic Viscosity
Kg/m-s
LMTD Log Mean Temperature Difference
MTD
Mean Temperature Difference
K
μs
Dynamic Viscosity
Kg/m-s
mdot s
massflow shellside fluid
kg/s
μ sw
Dynamic Wall Viscosity
Kg/m-s
mdot T
massflow of system
kg/s
ρ
Tube Wall Density
kg/m3
mdot t
massflow tubeside single tube
kg/s
ν
Kinematic Viscosity
m2/s
mdot o
massflow tubeside bundle
kg/s
αt
Tubeside Heat Transfer Coefficient W/K-m2
mdot r
massflow tubeside system
kg/s
αs
Shellside Heat Transfer Coefficient W/K-m2
Nb
Number of Baffles
N/A
δw
Ntt
Number of Tubes per bundle
N/A
vii
latent heat
kJ/kg
1. Introduction
1.1 Statement of Problem
The generation of electricity via nuclear reaction has been in service for over 54
years following the commissioning of Calder Hall, a 50 Megawatt (MWe) plant in England [NDA]. Heating of steam or similar thermofluids to transfer the heat of the reactor
has been done by conventional fission reaction designs. However, these old designs were
created before the aid of advanced computer simulation and highly specialized advanced
materials. A promising advancement of nuclear power generation is the Pebble Bed
Modular Reactor (PBMR). A PBMR utilizes fissible material encapsulated in pebbles
along with graphite and other compounds. Unlike many nuclear reactor designs, a
PBMR is inherently safe, because as the reactor temperature rises, the reactivity of the
pebble bed decreases. The setup creates a system where the maximum theoretical temperature would be 1140 °C and cannot progress higher [Koster]. This built in safety
helps assuage many fears that prior nuclear power plant disasters have created among the
general public. A schematic of the innovative PBMR fuel pebbles is shown in Figure 1.
Figure 1: Pebble Bed Modular Reactor Pebbles (PMBR)
The reactor thermal energy can readily be used by heating an inert gas such helium as it is pumped through the macro-porous pebble bed. The generation of power from
a nuclear reaction can only create electricity if the heat from the reactor is coupled with
an appropriate generator; in this case, a helium turbine. With classic designs, a heavyduty heat exchanger would be employed to transfer heat between two dissimilar fluids
and temper the flow out of the reactor. For a PBMR, a standard heat exchanger design is
8
not applicable due to the high pressure and extreme temperature environment the reactor
and turbine operate in. This project will serve as an exploration into what represents an
appropriate exchanger and where shortfalls and complications may arise for a PBMR
specific design. The goal of this project is to understand how the needs of a majority of
PBMR designs can be met by a simplified design. An example of a full PBMR system is
shown in Figure 2, this design incorporates recovery heat exchangers and two notable
intermediate heat exchangers where the red piping indicates.
Figure 2: Pebble Bed Modular Reactor System (NRC)
A heat exchanger, such as the basic three-dimensional one shown in Figure 3, is
a device used to transfer the heat of a thermo fluid stream to a colder thermo fluid
stream. The transfer is typically through an indirect process such as convection, or radiation if temperatures are very high, and while both streams are isolated in different states.
Heat exchangers vary from micrometer sizes to large industrial, some of the most durable are those used in power plants. A single-phase heat exchanger, or that which does not
cause a change of phase in either fluid stream, has been studied extensively for decades.
9
Figure 3: Heat Exchanger (AHR)
Among those designs, the shell and tube heat exchanger has been used across many industries as a well-developed means of transmitting heat successfully between two mediums. In its simplest form, a shell and tube heat exchanger represents its name directly,
with each stream traveling through its respective components. An elementary cutaway of
a one-pass shell, two pass tube, is demonstrated in Figure 4.
Figure 4: Shell and Tube Heat Exchanger (AHR)
10
The shell and tube has demonstrated itself to be a versatile heat exchanger that
can be specialized to fit a variety of needs, and even provide multiphase heat exchange
[Mukherjee]. This project will approach a unique design of a shell and tube heat exchanger for its use in extreme conditions for nuclear power generation.
For safety and replacement abilities, multiple heat exchangers are needed that
may also work in modular fashion and provide an ability to safely change out an improperly operating exchanger without a shutdown of the full gas flow. Therefore, this
report outlines the design of an appropriate heat exchanger design that is applicable for
most PBMR designs. With the additional consideration for modular and replaceable
needs, the scaling of any PBMR system is not important, only the design fluid characteristics such as temperature, pressure, viscosity, handling difficulties, etc. The overall
mass flow rates can be tempered by splitting the flow into more or fewer modular exchangers. Given the nature of the environment the reactor fluid operates in, the realities
of fouling or high temperature material degradation cannot be understood without experimental application and are therefore estimated to the best of the ability with existing
data.
1.2 Literature Review
The use of modular nuclear reactors is a developing field that provides economic
and logistical solutions for power generation at low cost and waste. In some designs, the
replacement of existing inefficient fossil fuel power plants with modular reactor systems,
in relatively smaller footprints, is a cutting-edge design approach in modern nonstandard nuclear power design. These small modular reactors use the principle of pebble
bed nuclear heat generation. The PBMR provides low maintenance and high reliability
with a very minor size, as compared to other counterpart designs. In most cases, the inert
fluid used for heat transfer from the nuclear reaction is helium in gas form. Helium is a
viable thermo-fluid, as its inertness prohibits it from absorbing any radioactive particles
after flowing through the pebble bed. In most practices, intermediate heat exchangers are
used to step-down the reactor helium outlet temperature and pressure to an appropriate
11
and exact level for turbine inlet specifications. Additionally, to create a more reliable
system, the heat exchanger incorporates a helium-helium transfer mechanism to allow a
safety buffer and prevent any conceivable problems such as debris or fouling from
reaching the turbine system. The design of heat exchangers for PBMRs is still relatively
new in nuclear power design. In many applications, a heat exchanger series is designed
to allow modular replacement and bypasses in the case of failure, along with a more
manageable system footprint.
A few experimental designs of PBMRs are being built or are operating in the
world. One of the most publicized PBMR plants is the HTR-PM being built in Shangdong Provence, China in 2009 to start initial operation in 2013. HTR-PM is a 250-MWe
reactor, which is a scaled up version of Tsianghua University's HTR-10 10-MWe reactor, shown in Figure 5, which has been in service since 2003 [Koster].
Figure 5: HTR-10 (NE&D)
Another notable design is the 117-Mwe plant in Koeberg, South Africa to be built by
Exelon Corporation if permitting issues can be resolved [Koster]. Including those mentioned, a few other PBMR related plants are listed to provide an idea of the history of
PBMR research:
12
Plant
Mwe
Year Built
Status
Arbeitsgemeinschaft Versuchsreaktor (AVR)
15
1966
Decommissioned
Thorium High Temperature Reactor (THTR-300)
300
1985
Decommissioned
High Temperature Reactor (HTR-10)
10
2003
Successful Demo Plant
Pebble bed Modules Reactor (HTR-PM)
250
2013
Still Constructing
Pebble Bed Modular Reactor Pty. Ltd
110
2012
Permitting Issues
MIT/INEEL
400
N/A
Design
Romawa B.V. (Neurus)
24
N/A
Design
Atoms Atomic Engine (AAE)
TBD
N/A
Design
Next Generation Nuclear Reactor (NGNR)
TBD
N/A
US Experimental Research
Table 1: PBMR Plants [Sunden], [Corrandini]
A pronounced limitation in the design of a high temperature heat exchanger for
this application is the lack of viable highly engineered materials. However, as with early
jet turbine designs, the continued funding into research and development aimed at creating materials to achieve specific goals, allows for inevitable approaches to the material
properties a heat exchanger requires. As of today, there are three notable categories of
materials that would be ideal for high temperature heat exchange; Nickel based alloys,
which have an ideal composition for helium flow but only moderate temperature resistance; Ferritic Steels, also good for helium application but similar temperature limit
problems; Carbon or Silicon Carbide composites, very high temperature resistance as
well as inertness to any irradiation [Sunden]. Therefore, the exact material is not as important as the characteristics an ideal material needs to have or can be expected to conform to. With a goal of a highly specialized material, a breakthrough superalloy could
one day conform to a wide range of desirable abilities such as high heat capacity, high
thermal diffusivity, ultra low coefficient of expansion and resistance to high temperature
oxidation. For practical purposes, currently existing materials are considered, but with a
caveat that the limits in materials are not as critical as the conceptual heat exchanger being able to achieve its performance as designed.
13
2. Methodology
2.1 Procedure
The project is primarily an analytical and theoretical evaluation. While data exists on a few experimental helium high temperature heat exchangers, the means of constructing a test case are unreasonable and also unnecessary. Assumptions will be made
on fouling, debris, and other actual-use considerations. The design process for a heat exchanger can be largely open-ended. Their application is ubiquitous across many industries, but commonly a design is used to fit a certain range of performance, and is essentially modified until the very specific characteristics are achieved.
The values used for the likely conditions seen in a PBMR application will be
based on existing experimental measurements along with various untested designs. The
values of critical interest pertain to the reactor helium outlet stream and the helium turbine inlet conditions. Less critical are the turbine exhaust stream inlet conditions, as they
define a bottom point for the cold fluid stream. The outlet conditions of the reactor helium flow are the least important, as they are commonly routed to auxiliary equipment or
flows and are conditioned before reentering the reactor.
2.2 Assumptions
A shell and tube heat exchanger is the preferred evaluated general design and it
will function as a fully evaluated trial design that can be formulated with reasonable assumptions about real-world variables that are unknown. The less complex geometry will
allow less potential for obstruction and contamination in the event of debris leaving the
reactor area and being transported by the reactor helium into the exchanger. In consideration to its application, the exchanger will allow for simple inspection or cleaning. The
heat exchanger will be operating with helium at least 773 K. As further verification of
the application, the simplified geometry requirement will lend itself as a better candidate
for a successful operation and more effective service life.
14
To establish realistic assumptions on the transfer of heat within the exchanger
and the inherently safe operation, all flows should be designed to be laminar. In the interest of simplifying calculation, the assumption of laminar flow will also be applied to
entrance lengths and inlet or outlet areas where even a verified laminar flow has the potential to enter a turbulent regime. A flow that is considered turbulent or transitional
would have dramatically higher heat transfer rate, but also largely unknown rates without accurate experimental measurements. For general flow through tubes, transitional
flow regime will be assumed, essentially creating a large design margin, as the heat
transfer rate will be assumed much lower than it likely would be.
The shell and tube heat exchanger is designed to be countercurrent flow shown in
figure 6, meaning the two fluid streams flow in an opposing manner. This setup allows
the hottest flow entering the shell area to transfer heat to the colder tubeside flow, and
essentially continue transfer as each stream approaches each other's temperature, the
tubeside rising and the shellside temperature declining. This function is much more effective and found in most shell and tube heat exchangers [Lewin]. The heat exchanger
will be considered an isolated system with only the inlet and outlet fluid streams being of
interest. The shell itself will be considered adiabatic and perfectly insulated, so no heat
loss to surroundings or work from surroundings will be factored into transfer equations
for this design. This assumption is commonly incorporated into analytical evaluations
and referred to as assuming temperature invariance [Ravagnani].
Figure 6: countercurrent flow (PBMR)
15
2.3 Overall Heat Transfer [Edwards]
The performance of a heat exchanger can be generalized by an overall equation
of transmitted heat in Watts, represented by Q, and based on input and output temperatures, Ti and To in Kelvin, as shown in equation 2. The other variables used were the heat
transfer area, A in square meters and the heat transfer correlation, U in W/K-m2, the heat
transfer area and the change in temperature:
Ti To
QUA
[2]
In the case of a shell and tube heat exchanger, there are two distinct fluid streams
exchanging heat with one another. For the shell side, the heat exchange is calculated in
 in kg/s, specific heat capacity,
equation 3 with stream specific variables for massflow, m
C in J/K-kg and inlet and outlet temperatures.
QS  m S C S Tis  Tos 
[3]
For application to the tubeside heat transfer, the exchange is calculated in equation 4 with the opposite stream specific qualities, as well as a swapped temperature difference as the tubeside flow is warmer at the outlet.
 T CT Tot  Tit 
QT  m
[4]
Realistically, while both exchanges are based on separate variables, the two are
coupled together, and through a conservation of energy and neglecting losses in the system, only one total heat exchange can occur within the exchanger before each stream
leaves it. An example of the intricate coupling of the two flows is shown in an example
shell and tube heat exchanger in figure 7. Given the relationship between the two
streams, a much more detailed evaluation is needed to create an accurate representation
of the heat exchange between surfaces.
2.4 Shellside Coefficients
In the case of the shellside heat domain, the area, As in square meters, in equation
5 can be determined by using the outer individual tube surface area per unit length, Aof in
m2/m, the length of each tube, Lta and the number of tubes overall, Ntt.
A
A
s
ofL
taN
tt
16
[5]
To maintain the assumption about laminar or transitional flows, it is important to
verify that the flow within the shell regime has an appropriate Reynolds number below
10000, the limit between turbulent and transitional flow. The calculation of the Reynolds
number in equation 6 uses the massflow per heat exchanger, m S in kg/s, the outer diameter of the tubes the flow surrounds, do in m, the viscosity of the fluid  S in kg-m/s, and a
corrected area, Asr in m2.
s
dom
sAsr
[6]
Ds CB
PT
[7]
Re
S
Asr 
Asr , expanded further in equation 7 is a representation of the cross flow area the
shellside flow experiences. It is dependent on the configuration of the tube bundle based
on the shell diameter Ds in m, the tube clearance, C in mm, the baffle spacing B in mm
and the tube pitch, PT in mm. To help maintain a low Reynolds number, the area should
be as large as possible within constraints. This can be helped by keeping a large baffle
spacing and shell inner diameter. But it can also be helped by keeping a low tube pitch,
Pt which is a function of the tube outer diameter, do and clearance as shown in equation
8.
P
T do C
[8]
To aid in keeping a low tube pitch, various tube layouts, such as those shown in
figure 8, may be used. But for this application, a square pitch is required as it provides
easier access for inspection and cleaning and the lowest pressure drop [Edwards].
17
Figure 8: Tube Layout Variations (Thome)
An additional consideration of shell design is its ratio of tube length to diameter.
A general guideline is to maintain a ratio of 1:5 to 1:15 shell diameter to tube length to
provide adequate shellside flow and heat exchange [Edwards].
The initial stream temperatures will be based on experimental data discussed in
the results section. The critical characteristic for the shellside heat transfer is its heat
transfer coefficient. There are multiple methods for this determination, but the most
practical methods used today are the Kern or the Bell-Delaware. In common practice for
analytical research, most heat exchange coefficients are estimated using literature tables
rather than calculating them from the correlations provided by both methods [Ravagnani].
In this project, the Bell-Delaware method will be used, as it allows for the inclusion of baffles within the shell, provides a more accurate value, and no literature tables
exist to provide correlating specific values. The Kern method does not incorporate baffle
correction factors, and would not yield as accurate values [TFD-HE14]. The BellDelaware method formulated the following relationship in equation 9 for the calculation
of shellside heat transfer coefficients. The critical characteristics needed for finding the
heat transfer coefficient for the shellside flow, αs in W/K-m2 are the massflow, m S in
18
kg/s, over the shellside area, As in m2, the specific heat of the fluid flow, cp,s in W/kg-K,
the colburn j-factor (dimensionless), the fluid viscosities in the bulk of the fluid,  S in
kg/m-s, the wall temperature viscosity,  SW in kg/m-s, and the fluid conductivity, ks
W/m-K[Guo].


2
/
3

s



m
k
s
s




j
c
0
.
36
S ip
,
s



 
A
c
s
p
s




sw

0
.
14
[Guo]
[9]
The Prandtl number, or a dimensionless quantity that compares the momentum
diffusivity to thermal diffusivity for the flow can be calculated with equation 10.
Pr
s
cp,ts
ks
[10]
By comparing this to equation 9, the coefficient already incorporates the inverse
of the Prandtl number. The j factor is a correlation from the findings of Chilton and Colburn, as a dimensionless value that adds a correction factor to the exchanger based on
empirical data [TFD-HE14]. The Colburn factor in equation 11 is based on the Reynolds
number and the tube arrangement, a square tube layout as decided in the assumptions.
The constants within the equation are provided by empirical calculation from testing on
various tube arrangements and their corresponding colburn correction factor [Ravagnani].
1
.
45
0
.
519
1

0
.
14

Re



1
.
33

0
.
388



j
0
.
321
Re
i


P
/
d
T
o


[11]
As previously mentioned in tube pitch discussion, baffle spacing is an important
variable in the exchanger. In many heat exchangers, baffles, as seen in figure 9, are employed to encourage more complex circulation throughout and around the tube bundle
[Costa]. However, baffles also create complex geometry that would prevent an exchanger corresponding to a simple design and one less likely to experience high temperature
expansion issues. Baffles cannot be eliminated entirely given the high-pressure gas flow
in the exchanger. Using Tubular Exchanger Manufacturers Association (TEMA) standards, baffles are suggested to secure the tube bundle and limit the impact of highpressure flow induced vibration or similar effects that could create decay in the tube materials strength through cycle fatigue [Lewin].
19
Figure 9: Visualized Baffle Function (AHR)
Therefore, only limited baffles below 25% of the shell diameter will be used. A
more realistic display of how baffles interact with the tube bundle is shown in figure 10,
where 80% baffles are placed in position as the bundle is assembled. The maximum
spacing of baffles, B in m, which helps maintain a large cross flow area, is defined by
equation 13, based on the tube outer diameter.
B74do0.75
[12]
Figure 10: Baffle Design (ACP Coils)
2.5 Tubeside Coefficients
The heat transfer surface for tubeside heat exchange, in equation 14, is similar to that of
the shellside but incorporates the tube inner diameter per unit length, Aif in m2/m instead.
A
T A
ifL
taN
tt
[13]
Additionally, to maintain the laminar or transitional flow assumption, the Reynolds number needs to be evaluated for the tube bundle. Equation 14 shows the dimen-
20
 in kg/s, the tube inner
sionless number for a single tube using the mass flow per tube, m
diameter, di in m, and the fluid viscosity, T in kg/m-s.
Re
t 
t
dim
t Atr
[14]
The mass flow is differentiated between the overall global flow, the flow per exchanger and the flow per tube as shown in equation 15, the massflow per bundle is defined as m o and the massflow for the entire reactor flow is defined as m R .
 
R
m
m
1
.15
t  o 
m
N
6
N
tt
tt
[15]
To establish the tubeside coefficient of heat transfer, the Prandtl number is calculated
first using equation 16 and incorporating the tubeside specific heat, cp,t in kJ/kg-K, the
tubeside viscosity, T in kg/m-s and the fluid conductivity, ktw in W/m-K.
Prt 
c p ,t  t
[16]
k tw
Using the Bell-Delaware method, the heat transfer coefficient in respect to
tubeside exchange,  T in W/kg-m2, can be determined with equation 17. Similar to the
shellside coefficient, the formula incorporates the Prandtl number of the fluid flow, as
well as the fluid density,  t , the dynamic and kinematic fluid viscosities, T in kg/m-s
and  T in m2/s, and the tube wall conductivity, ktw in W/m-K [Guo].

 0
k


d
.
3
tw
t
t
i




0
.
023
Pr
T
t


d
i
t 
0
.
8
[Guo]
[17]
A completely assembled two-pass tube bundle is shown in figure 11, along with
3 baffles, it is ready for placement within a heat exchanger shell.
21
Figure 11: Tube Bundle (ACP Coils)
While both of the coefficients are determined for each stream in isolation, the
reality of the exchange is that no matter how effective one stream may be to exchange
heat, it is ultimately limited by the least effective of each streams, along with a few select correction factors.
The Bell-Delaware method and the work by Dittus-Boelter provides an accurate
representation of the total system heat transfer coefficient, Ko in W/K-m2, and can be
determined in equation 18 by combining equations 9 and 17, as well as applying tube
and shell effectiveness factors, rt and rs respectfully in K-m2/W, heat exchanger material
properties such as wall thickness,  W in m, and wall thermal conductivity ktw in W/m-k
[Guo].
 1
Ko  
 T
 do

 di

d
  rT  o

 di
  w  do
 

k
tw

 di

1 
  rs 

S 

1
W/K-m2
[18]
The overall heat exchange for the system, Q in Watts, can now be represented in
equation 19, with the surface area, the overall heat transfer coefficient and a specialized
temperature difference, Tlm in K, known as a log mean temperature difference (LMTD).
QAK
Tlm
o
[19]
The LMTD, shown in equation 20, represents a system value which combines
both streams into a proportional value of the differences in fluid stream temperatures.
22
Tlm  LMTD 
Tit T is   Tot T os 
 T T is
ln  it
 Tot T os



[20]
As a secondary representation of the heat exchanger, as well as a verification of
the comparable performance, the log mean temperature can be used for finding LMTD
factors. The LMTD originates from experimental measurements of relative calculations
for heat exchangers, it therefore is much more appropriate for use in estimating the
qualities of an exchanger than calculating exact values.
2.6 LMTD Method [Thome]
In a generalized shell and tube system, with known passes, experimental data has
yielded correlations between the broad stream temperature data and the corresponding
performance. While not detailed like the Bell-Delaware and other supporting flow equations, it works as an acceptable basis to estimate the geometric sizing that would be
needed for the heat exchanger. Using the log mean temperature difference found in
equation 20, two other dimensionless parameters shown in equations 21 and 22 are
needed. The thermal effectiveness, P, and the heat capacity ratio of the exchanger, R
[Ponce-Ortega].
P
Tis T os
Tit T os
[21]
R
Tit T ot
Tis T os
[22]
Using reference charts with LMTD, R and P, the temperatures can indicate an F-factor,
or an empirical correction factor for determining the best number of shell and tube passes and its relative effectiveness [Thome]. The LMTD empirical charts are shown in Appendix 6. With an F factor, a global heat transfer, QA in Watts, shown in equation 23 can
be used to calculate a rough heat exchange system by converting the LMTD into a mean
temperature difference (MTD) [Lewin]. The equation incorporates an estimated surface
area, Ao, in m2, and an estimated heat transfer coefficient, Uo in W/K-m2.
LMTD

Q
U
A
F
A
o
o
23
[23]
The value for the heat transfer coefficient is not as sophisticated as the BellDelaware correlations, but by rearranging equation 23 it can calculate the needed area
for a desired heat transfer rate. Using an estimated heat transfer rate as well as an LMTD
and F-factor, a desired surface area value can be determined, as shown in the rearranged
version of equation 24.
Q
Q
A
 A  A
o

U


U
F
LMTD
MTD
o
o
[24]
The surface area value is useful in beginning design of the heat exchange geometries with reasonable accuracy before iteration and adjusting the values.
24
3. Results and Discussion
3.1 PBMR
To set the goals of the desired operational guidelines for a heat exchanger working intermediately between a PBMR and a helium turbine, both components were researched. For PBMRs, the data from table 1 such as South Africa's Koeberg as well as
hypothetical designs like MIT's INEEL [Hechanova]. Units like Russia's 286-MWe GTMHR, a helium gas turbine using a different heat transfer source were also researched.
The various operating values of these designs demonstrate the realistic operational characteristics an exchanger would see. To design for possible next generation reactor designs as well as state-of-the-art efficient helium turbines, hypothetical data was also included. Ultimately, the ranges the exchanger would need to function in are shown in table 2.
System Property
Range
Reactor Outlet Temp
750-950 K
Reactor Inlet Temp
280-520 K
Reactor Mass Flowrate
120-320 kg/s
Reactor Helium Pressure
70-90 bar
Turbine Inlet Temp
800-890 K
Turbine Outlet Temp
480-500 K
Table 2: Experimental Heat Exchanger Environmental Conditions [Dardour] [Sunden]
3.2 Material Evaluation
With the general limits of the design based on experimental data established, the
next step is to recognize the limitations of materials that may be used for the heat exchanger. Given that this is a theoretical evaluation and design, the assumptions that
would be made to corrosion, expansion and high temperature phenomena in service such
as scaling, spalling, pitting or oxidation will be neglected. Many of the common fouling
problems can be eliminated with the helium fluid combined with an inert material. The
largest issue for degradation would come from the quality and uniformity of the microstructure of a material and its behavior in thermal cycling, along with any tendency to
25
fracture or other mechanisms of creating particle debris [Sunden]. An example of degradation problems for high temperature ferritic steel is shown in figure 12, along with the
performance of an optimized coated sample of the same material. The degradation has
fully advanced on the upper coupons to catastrophic failure.
Figure 12: High temperature Degradation (AHR)
Numerous characteristics are important to evaluate the possible candidate materials for heat exchangers; the density of a material is needed as an indicator of the problems that may be seen from cyclic expansion, as a more dense material will create compressibility effects. The melting point is important to verify the exchanger can easily
handle possible maximum condition of 1140 K [Koster]. The coefficient of thermal expansion is important, as the expansion can be dramatic for such a high temperature application. The lower the expansion coefficient, the longer the service life and fewer rate
of failure as components expand in different lengths during warm up or cool down.
Thermal conductivity is the most critical quality of a viable material for a heat exchanger. The conductivity is a direct indication of its ability to effectively transmit heat between two fluid streams. The specific heat value is desired to be as low as possible, as it
indicates the materials ability to rise in temperature with less applied heat. The materials
evaluated for the heat exchanger are shown in table 3.
26
Material
Density (kg/m3)
Melting Point (K)
Thermal Expansion (10^-6 m/m-K)
Thermal Conductivity (W/m-K)
Specific Heat (kJ/kg-K)
SiC
3100
2173
4.02
77.5
0.67
Hastelloy
8890
1598
11.2
9.8
0.427
Inconel
8470
1625
15.9
25.7
0.597
Waspaloy
8250
1603
15.4
22.7
0.58
High
Chromium
Steel
7850
1698
11.6
16
0.48
Graphite
2230
3948
3.2
82
0.71
Table 3: Candidate Materials for Heat Exchanger [Sunden][Hurley]
The material chosen for this design is the specialized Silicon Carbide (SiC). It
stands out as one of the best materials due to the fact that it is actually a ceramic while
others are superalloys. In comparison on the chart, the SiC is a good candidate; it has a
very low coefficient of thermal expansion, which will allow the least amount of adjustment within the tube bundle and system. It has a phenomenal thermal conductivity due
to its ceramic properties, whose structure also allows for natural thermal shock resistance
[Sunden]. One of the best features of the Silicon Carbide is that it is also inert, so like the
helium, it is a perfect application to the reactor system, as stray particles of the pebbles
that may be irradiated would be mitigated by the heat exchanger material’s resistance
toowad absorbing radiation and transmitting it into the turbine helium stream. Table 3
does show that performance from graphite may seem better than the other material
choices. And while exact material is not as critical, as mentioned previously, the SiC is
already made in standardized pipe size forms. Graphite is largely an unproven material
for use in complex forms and the high stress environment of the exchanger. The current
state of development with SiC allows enough options to likely create the structures, and
a perfect medium to create a highly efficient device. A data sheet on the specific composition can be found in Appendix 4.
3.3 Preliminary Evaluations
To narrow the limits of the heat exchanger, the LMTD method can be used to
estimate the geometry. Knowing the temperatures the heat exchanger will be exposed to,
the LMTD can be calculated using equation 20. In this case, the temperatures chosen
27
were a tubeside flow with temperatures of inlet 610K and outlet 820K and shellside flow
with temperatures of inlet 950 K and outlet 650K.
Tlm  LMTD 
950  610  820  650  76.36m 2
 950  610 
ln 

 650  820 
To be able to use the LMTD method correlation charts, the non-dimensional characteristics R and P are found with equations 21 and 22.
R
T1 T 2
 1.43
t 2 t 1
P
t 2 t 1
 0.62
T1 t 1
Using the LMTD chart on Appendix 6, the F factor is found to be 0.7. Due to the
arrangement of the charts, the convergence of the R and P values with a correction Ffactor also indicates the ideal passes for achieving the performance [Lewin]. In this case,
a two-shell pass, four-tube pass construction will stand to meet the heat transfer necessary for the application.
To find the heat rate, the turbine stream (tubeside) is focused on. The heat rate
for the turbine stream is more critical because it is needed to achieve the ideal inlet properties for power generation in the helium turbine. The turbine stream heat rate is found
using equation 3.
 o Ct Tot  Tit   25082kW
Qt  m
The mass flow for the heat transfer on either side is differentiated from the total
mass flow for the entire PBMR system. Using a total flow of 120 kg/s, the flow per heat
exchanger with a 15% margin is 23 kg/s. This is found using equation 15.
 


1
.
15
m

1
.
15
(
120
)

m
 R


23
kg
/
s
o
6
6
Using the known properties, all that is needed is a generalized assumption of the
heat transfer coefficient to find the estimated surface area needs. This value is only a
rough figure, in this case 600 W/K-m2, which has been found as a good approximation
for high-pressure helium applications by previous heat exchange research [Salimpour,
28
Thome]. Applying the known values into equation 26, the useful surface area is estimated as:
Ao 
QT
QT

 782.1m 2
U o F LMTD  U o MTD 
A surface area of 782.1 m2 will correspond to the tube bundle’s heat transfer area, and it
can be considered the rough estimate of the interior area of the entire tube bundle. To
verify this will satisfy the heat transfer from the reactor stream, the same procedure can
be used to ensure that the area for the shellside flow is similar to that of the tubeside
flow using equations 4 and 26.
 S C S Tis  Tos   35831kW
QS  m
Ao 
QS
QS

 1117m 2
U o F LMTD  U o MTD 
The helium flow entering and exiting is at roughly the same pressure on either
side, but at different temperatures. Using the chart in Appendix 1, the viscosity for each
connection can be calculated:
si  4.2 , so 5.14, ti  5.32, to  4.53(all in kg/m-s multiplied by 106)
Given the subtle change from inlet to outlet viscosities for each, the calculation
will be simplified by using a bulk dynamic viscosity value, which is an average of the
connections, at  b  4.8  10 6 kg / m  s .
To verify the flow on the tubeside is remaining below turbulent flow, a preliminary tube inner diameter is chosen. Common pipe sizing is indicated in Appendix 5. To
try a possible size, a 10-gage tube is evaluated, with a 31.75 mm outer diameter and an
inner diameter of 24.74 mm and evaluated with equation 14.
Re t 
d i m t
1
 164308
 10000
 t Atr
N tt Lt
With two unknown values remaining, to create a more coherent design, the two will be
chosen to be realistic. With the number of tubes about 300, the length of each individual
tube will have to be 27.83 meters (remembering that in the bundle they will be folded for
U-tube construction with multiple passes). This is a reasonable amount for an extremely
29
high duty tube bundle. It is important to note that the diameter of the tube is irrelevant
for calculating the Reynolds number as the radius cancels out, making the viscosity and
mass flow the truly critical aspects of the non-dimensional number. Calculating the
Prandtl number with equation 16:
Prt 
c p ,t  t
kt
 3.0e  3
The very low Prandtl number indicates that the ratio of the diffusion rate thermally is
much larger than that viscously, as expected for helium as a high temperature gas.
3.4 Tube Bundle Sizing
A general surface area needed for the tubes is known, and the more detailed heat
exchanger properties can be calculated. Given the rough surface area value, the size of
the tube bundle needs to be formulated in order to work towards the shellside variables.
Using the chosen piping sizes given in the previous section of a 10-gage pipe with 31.75
OD and 24.74 ID, a bundle size can be worked out. With the assumption of a square
pitch tube layout, along with the chosen sizing, the tube bundle geometry can be calculated to be fit into a shell as:
Di  d o N tt / 1.5  1.391m [Thome]
Knowing the sizing of the tube bundle, the shell can now be designed to fit and its properties may be calculated.
3.5 Shell Sizing
Using the geometry found for the tube bundle, and the suggested shell diameter to tube
bundle length ratios given in section 5.1, the shell can be constructed as 1.4 m in diameter and about 6.96 m in length.
Calculating the shell properties, the same bulk viscosity is used. The calculation
of the Colburn J factor in equation 11, that will be needed for the heat transfer coefficient, results in a correction of 0.01. Additionally, the cross flow area of the shell is
needed from equation 5.
30
As  Aof Lta N tt  832.35m 2
In order to calculate the Reynolds number for the flow through the shell, the area defined
in equation 7 is needed, as the exterior pipe area does not represent the area value that
influences the Reynolds correlation. Because a square tube layout was chosen previous-
do, meaning that the clearance value will be
ly, the tube pitch can be given as PT 1.25
25% of the outer diameter.
Asr 
Ds CB
 1.94m 2
PT
Verifying the Reynolds number of the shellside flow from equation 6 is below 10000:
Re S 
Ds m s
 9379
 s Asr
And to draw a comparison to the tubeside Prandtl number, the shellside correlation is
determined using equation 10. It will also be incorporated inversely in the overall
shellside heat transfer coefficient
Prs 
c p ,t  s
ks
 2.69e  3
The value of 2.7e-3 indicates that similar to the tubeside flow, the thermal diffusion is
also much greater than the viscous diffusion.
3.6 Heat Transfer Coefficients
Now that nearly all of the detailed characteristics of the flows are calculated, the specific
heat transfer coefficients for each stream are determined using equations 9 and 17.
2/3
 k s


 c p  s




k  d
 T  0.023 tw  t t i
di  t



 m
 S  ji c p , s 0.36 s
 As
 s 


  sw 
0.14
 674.85
0.8
Prt
0.3
 774.41
As discussed previously, the system heat transfer coefficient is a combination of both
values along with a few correction factors as the two streams are intimately tied together.
31
To calculate the overall system heat transfer coefficient, correction factors for the tubes
rT and for the shell rS are used. Given the assumptions about neglecting high temperature
oxidation effects, and the use of helium on a ceramic construction, both fouling factors
will likely be smaller than 1x10^-6 and for practical purposes, essentially zero when factored into the system heat exchange coefficient from equation 18.
 1
Ko  
 T
 do

 di

d
  rT  o

 di
 w
 
 w
 do

 di

1 
  rs 

S 

1
 360.61
Now that the system heat transfer coefficient is known, and the log mean temperature difference has been evaluated, the heat exchanger design can be represented in a
global heat exchange equation.
Q  AK o Tlm  740.6  360.61  76.36  20388.7kW
In other words, given the streams temperatures, and taking an external view of the exchanger, it provides a heat rate of 20388.7 kW.
3.7 Iterations and Stepwise Needs
As shown in the aforementioned methodology equations, many are not solved in
isolation but rather with components found from each other such as; the shellside reynolds number (eq 6); the shellside effective area (eq 7); the shellside heat transfer coefficient (eq 9); the colburn j-factor (eq 11); the tubeside Reynold’s number (eq 14); the
tubeside heat transfer coefficient (eq 17); the total system heat transfer coefficient (eq
18); and the overall heat exchange (eq 19). The values demonstrated in the worked out
example were a successful case, but in an evaluation, when a value such as the calculated Reynolds number exceeds the limits, the next step is to move back in calculations and
start with modified values. The work throughout calculation of this design can be viewed
as trial and error if results begin to come out beyond prescribed limits. Unfortunately,
since many of the equations are related so closely, modifying a variable can subsequently change a multitude of heat exchanger properties. In higher-level design of standard
industrial shell and tube heat exchangers, an algorithm is commonly used to iterate the
process and automatically produce a convergence of a set of heat exchanger properties
[Munoz]. In this project, an iterative system could not be applied, as its focus was to re-
32
flect on the general and successful design rather than produce the most optimized heat
exchanger.
In working out the heat exchanger, a semi-iterative process was followed, by
hand calculation using the equations defined in previous sections. The most successful
heat exchanger's characteristics are summarized in Table 4. A more detailed display of
the results can be found in Appendix 7.
Description
Shellside Pressure
Shellside Inlet T
Shellside Outlet T
Tubeside Pressure
Tubeside Inlet T
Tubeside Outlet T
Log Mean Temperature Difference
LMTD R Value
LMTD P Value
LMTD F Factor
Area Needed
Tubeside Area Needed
Estimated Length
Number of Tubes
Tube ID
Tube OD
Tubeside Reynolds Number
Tubeside Prandtl Number
Shell Diameter
Shell Length
Shellside Reynolds Number
Shellside Prandtl Number
Shellside Heat Tranfer Coefficient
Tubeside Heat Tranfer Coefficient
System Heat Transfer Coefficient
System Heat Rate
Symbol
Ps
t1
t2
Pt
T1
T2
LMTD
R
P
F
Ao
At
Lof
Ntt
di
do
Ret
Prt
Ds
Lds
Res
Prs
alpha s
alpha t
Ko
Qg
Units
bar
K
K
bar
K
K
K
N/A
N/A
N/A
m2
m2
m
tubes
mm
mm
N/A
N/A
m
m
N/A
N/A
W/K-m2
W/K-m2
W/K-m2
W
Value
70
610
820
950
650
0.7
25
250
24.74
31.75
Calculated
70
610
820
70
950
650
76.36
1.43
0.62
0.7
782.10
1117.28
27.83
300
0.02
0.03
19.68
0.00
1.39
6.96
9379.44
0.00
674.85
774.41
360.61
20388740.46
Table 4: Primary HTHX Design Properties
Along with the design margin of 15% on the massflow, there is a secondary design margin due to the shellside input temperature. Any adjust on the input helium temperature for the turbine side will lead to a better performing heat exchanger. The turbine
helium return temperature can be variable based on the post processing uses of the ex33
hausting flow. A common use in creating a successful turbine flow is to use precoolers
before the entry into the heat exchanger to reach a desired outlet condition from the
shellside helium flow which is piped directly into the high pressure turbine inlet [Dardour].
To calculate the performance of the heat exchanger, an excel sheet was used. The
excel chart with applicable equations could determine the shell and tube characteristics
much faster than hand calculation. In Appendix 7, the column labeled value indicates
whether the metric was input into the sheet, or calculated in the right hand side column.
In the select results, it can be seen that most of the bottom half of the results are the results of equation outputs using the chosen variables for the heat exchanger.
34
4. Conclusions
4.1 Final Results
The most significant result about the final heat exchanger design is its size. The
exchanger is enormous compared to many industrial shell and tube exchangers which
generally are below 10 meters in length and 1 m in diameter and less than 150 tubes
[Edwards]. But this design is near 7 meters in length and has a girth of nearly 2 m along
with the packed tubes. This is expected given the large mass flow rate through the exchanger system, as well as the high temperature change that occurs within the process.
The important aspect of the heat exchanger design was that the tubeside heat
transfer area required was larger than the required shellside area. With this relationship,
a satisfying tubeside area would certainly results in a larger shellside area seeing as the
tubes have a larger outer diameter. With the shellside area needs surpassed, the turbine
side flow will easily experience enough heat transfer to achieve the desired outlet temperature of 820 K.
While the design is analytically sound, it is important to determine if it is realistic
with other shell and tube exchanger designs, especially high temperature or helium applications. From research into the GT-MHR and the PBMR, a design margin is expected
with both commonly utilizing the so-called “free heat” from the turbine exhaust helium
for other applications as the heat exchanger can handle a lower inlet turbine helium flow
temperature [Dardour].
Many studies in the algorithm development acknowledge the problems of making many design characteristic decisions such as tube sizing, and layouts “a priori”, leading to the convergence of a design and geometry solution which is acceptable, but could
result in other successful design solely on the initial inputs [Ravagnani]. For this reason,
even the most advanced algorithms can typically only stand to improve a conceivable
heat exchanger design by slight modification, making them only somewhat more effective than the analytical process that was used in this project, but much faster.
The use of non-finned tubes is also favored in high temperature helium applications [Sunden]. For this design, internal or external fins would have dramatically increased the tube surface area, likely allowing a smaller tube size that still achieves the
35
surface area requirements of both fluid flows. The use of tube fins, internal or external is
seen as too problematic with the tendency for debris generation from the temperature
regime they are operating in.
One of the most unexpected results of the design was the requirement for multiple passes on both the tube and shell side to achieve the operating level after the determination of the LMTD F-factor. It was expected that a single shell pass, two tube pass
exchanger would likely satisfy the exchange needs, particularly combined with the multiple modular exchangers in parallel [PBMR]. One possible way to reduce the extra
passes construction would be to add baffles larger than those at tube bundle support levels such as 25%. Adding large baffles can increase the shellside heat transfer rate and
therefore reduce the pass needs. However, the addition of larger baffles also results in
more turbulent flow, and much larger pressure drops, which are of critical interest for the
shellside outlet flow, which connects directly to the high pressure turbine and demands a
specific pressure and temperature.
The most challenging aspect of converging on a solution was determining the
most realistic heat transfer coefficient to use during the LMTD estimating process to
move into more details geometry calculations. Trial runs were typically done using 700750 W/K-m2 [Lewin]. But eventually it became clear that such a high value, while mentioned as being achievable in high-pressure helium-to-helium heat exchange was possible, was unlikely in this application. A more reasonable initial guess of a heat transfer
coefficient of 600 W/K-m2 could yield a solution that could result in a similar analytical
heat exchange using the detailed Bell-Delaware equations.
The use of ceramics like SiC is also favored in the design of smaller scale helium
heat exchange. It has been employed for many chemical processing applications, which
has allowed the extensive production and research funding that this design and other future power generation designs can benefit from [Sunden]. However, the assumption that
SiC can be constructed in shapes beyond standard tube sizes is a strong requirement for
the ceramic material performance of this heat exchanger. It was common to find advanced silicon carbide distributors offering tubes of standardized dimensions such as
those used in lower level less complicated shell and tube design processes, such as those
defined by Thome. But to create an exchanger, if the ceramic can not be constructed in
36
other complex shapes, the shell, brackets and more importantly the baffles will need to
be constructed out of dissimilar materials. The implications of mixing materials within
the exchanger would likely be prohibitive. The mechanics of materials with different expansion rates and chemical behavior could dramatically shorten the service time of such
an exchanger and lead to a high rate of failure as the non ceramic tubes perform under
the same conditions within a high pressure container.
4.2 Future Work
To expand the work this project has done, a direct application could be to apply
an advanced algorithm to the current calculations. With an algorithm, such as a genetic
algorithm (GA), the convergence of a solution would be much quicker than the stepwise
analytical calculations [Munoz]. It would allow design runs to also operate nearly autonomously while evaluating certain characteristics, such as applicable tube sizes, and optimizing the geometry while verifying it to be the most efficient choice. This would be
advisable if the use of shell and tube heat exchangers were to enter into common application and real world data was available to directly compare with these analytical predictions.
Further research into PBMR heat exchangers could also approach design using alternative estimation techniques. In this project, LMTD was used, but some heat exchanger design methods prefer to incorporate the ε-NTU method [Ponce-Ortega]. Similar to the LMTD method, it provides a way to estimate the performance of a shell and
tube exchanger. But unlike the LMTD, it relies on a relative value of net thermal units
(NTU), along with an efficiency correction factor.
One regime of this heat exchanger that was not evaluated was the velocity gradient
within the exchanger. Given the assumptions of more unified qualities, it is understood
that in actual operation, tubes will not always see uniform flow, and shellside flow will
likely have low and high velocity areas. Additional research and experimental testing of
high temperature heat exchangers could provide a perspective on the significance of velocity flows and their effects on localized convection. More importantly, velocity research could result in modified baffle or shell design optimized for high-pressure helium
flows rather than the integration of standard shell and tube design used in this project.
37
5. References
[Thome] Thome, John. “Wolverine Tube Heat Transfer Data Book” Wolverine Tube, Inc. Vol
III. Lausanne, Switzerland. 2009
[Ponce-Ortega] Ponce-Ortega, J.M. “Design and optimization of multipass heat exchangers”
Chemical Engineering and Processing 47 (2008): 906–913.
[Costa] Costa, Andre´. “Design optimization of shell-and-tube heat exchangers” Applied Thermal Engineering 28 (2008): 1798–1805.
[Muñoz] Muñoz, Juan. “COMSOL and MATLAB® Integration to Optimize Heat Exchangers
Using Genetic Algorithms Technique” Proceedings of the COMSOL Conference (2008).
[Fakheri] Fakheri, A. “Efficiency and Effectiveness of Heat Exchanger Series” ASME: Journal
of Heat Transfer 130 (2008).
[Ravagnan] Ravagnani, M. “A MINLP MODEL FOR THE RIGOROUS DESIGN OF SHELL
AND TUBE HEAT EXCHANGERS USING THE TEMA STANDARDS” Chemical Engineering Research and Design 85 (2007): 1423-1435.
[Edwards] Edwards, J.E. “MNL 032A- Rating of Shell and Tube Heat Exchangers” P & I Design
LTD. Teeside, UK. 29 August 2008.
[Salimpour] Salimpour. “Heat transfer coefficients of shell and coiled tube heat exchangers” Experimental Thermal and Fluid Science 33 (2009): 203–207.
[Guo] Guo, J. “The application of field synergy number in shell-and-tube heat exchanger optimization design” Applied Energy 86 (2009): 2079–2087.
[Sunden] Sunden, Bengt. “High Temperature Heat Exchangers (HTHE)” Enhanced, Compact
and Ultra-Compact Heat Exchangers. 29. CHE2005. 226-238
[Hurle] Hurley, John. “TESTING OF A VERY HIGH-TEMPERATURE HEAT EXCHANGER
FOR IFCC POWER SYSTEMS” University of North Dakota, Energy & Environmental Research Center. (2008).
[Hechanova] Hechanova, A. “IV.G.4 High Temperature Heat Exchanger Project*” DOE Hydrogen Program (2005).
[Dardour] Dardour, S. “Utilisation of waste heat from GT–MHR and PBMR reactors for nuclear
desalination” Desalination 205 (2007): 254–268.
[Corrandini] Corrandini, M. “ADVANCED NUCLEAR ENERGY SYSTEMS: HEAT
TRANSFER ISSUES and TRENDS” Rohsenow Symposium on Future Trends in Heat
Transfer: MIT. (2003).
[Kragh] Kragh, Helge (1999). Quantum Generations: A History of Physics in the Twentieth Century. Princeton NJ: Princeton University Press. pp. 286
38
[Peterson] Peterson, Helge. “The Properties of Helium” Danish Atomic Energy Commission. Riso Report 224. Copenhagen. September 1970.
[Koster] Koster, A. Nuclear Engineering and Design, Volume 222, Issues 2-3, Pages 231-245.
June 2003
Figures:
[NDA] Nuclear Decommissioning Authority website http://www.nda.gov.uk/
[PBMR] Pebble Bed Modular Reactor Company website http://www.pbmr.co.za/
[NRC] Nuclear Regulatory Committee website
http://www.nrc.gov/reactors/advanced/pbmr.html
[AHR] Advanced Heat Recovery website
http://advancedheatrecovery.com/HeatExchangerProbs.html
[NE&D]. Nuclear Engineering and Design, Volume 218, Issues 1-3, October 2002, Pages 25-32
Zongxin Wu, Dengcai Lin, Daxin Zhong
[ACPCoils] Heat Exchanger Material Supplier website
http://acpcoils.com/products_heatcraft_tube.htm
39
6. Appendices
Density and Dynam ic Viscosity of Helium
16
Density or Viscosity*10^5
14
12
10
Density at 70bar
Density at 80bar
8
Density at 90bar
Dynamic Viscosity*10^5
6
4
2
0
0
200
400
600
800
1000
1200
Tem perature (K)
Appendix 1: Helium Properties [Data from Peterson]
40
1400
Appendix 2: Moody Chart [Data from Peterson]
41
Appendix 3: Heat Exchanger Construction
42
Appendix 4: SiC Alloy Properties
43
Pipe
Size
1/4"
3/8 "
1/2 "
5/8 "
3/4 "
7/8 "
1"
1 1/4 "
2"
Outer
Diameter
Gage
mm
Wall
Inner Di-
thickness
ameter
mm
mm
6.35
22
0.711
4.928
6.35
24
0.559
5.232
9.525
18
1.245
7.035
9.525
20
0.889
7.747
9.525
22
0.711
8.103
12.7
18
1.245
10.21
12.7
20
0.889
10.922
15.875
16
1.651
12.573
15.875
18
1.245
13.385
15.875
20
0.889
14.097
19.05
12
2.769
13.512
19.05
14
2.108
14.834
19.05
16
1.651
15.748
19.05
18
1.245
16.56
19.05
20
0.889
17.272
22.225
14
2.108
18.009
22.225
16
1.651
18.923
22.225
18
1.245
19.735
22.225
20
0.889
20.447
25.4
12
2.769
19.862
25.4
14
2.108
21.184
25.4
16
1.651
22.098
25.4
18
1.245
22.91
31.75
10
3.404
24.942
31.75
12
2.769
26.212
31.75
14
2.108
27.534
31.75
16
1.651
28.448
50.8
12
2.769
45.262
50.8
14
2.108
46.584
Appendix 5: Common Pipe Size Specifications
44
Appendix 6: LMTD Correction Factor
45
Description
Shellside Pressure
Shellside Inlet T
Shellside Inlet viscosity
Shellside Outlet T
Shellside Outlet viscosity
Tubeside Pressure
Tubeside Inlet T
Tubeside Inlet viscosity
Tubeside Outlet T
Tubeside Outlet viscosity
Log Mean Temperature Difference
LMTD R Value
LMTD P Value
LMTD F Factor
Shellside Massflow
Shellside Specific Heat Capacity
Shellside heat rate
Symbol
Ps
t1
mu s1
t2
mu s2
Pt
T1
mu t1
T2
mu t2
LMTD
R
P
F
mdots
cps
Q
Units
bar
K
kg/m-s
K
kg/m-s
bar
K
kg/m-s
K
kg/m-s
K
N/A
N/A
N/A
kg/s
kJ/K-kg
W
Value
70
610
Assumed Heat Transfer
Uo
W/K-m2
600
Area Needed
Massflow Tubeside
Tubeside Specific Heat Capacity
Tubeside possible heat rate
Tubeside Area Needed
Estimated Length
Number of Tubes
Tube ID
Tube OD
Calculated Inner Area
Calculated Outer Area
Tube wall resistance
Tubeside Reynolds Number
Tubeside Prandtl Number
Shell Diameter
Shell Length
Diameter to Length Ratio
Shellside Area
Ao
mdott
cpt
Q
At
Lof
Ntt
di
do
m2
Shellside Effective Area
Shellside Reynolds Number
Shellside Prandtl Number
Shellside Colburn Factor
Helium Density
Aes
Res
Prs
j
rho
kg/m3
Shellside Heat Tranfer Coefficient
alpha s
W/K-m2
674.85
Tubeside Heat Tranfer Coefficient
alpha t
W/K-m2
774.41
Ko
Ag
Qg
W/K-m2
360.61
740.46
20388740.46
System Heat Transfer Coefficient
System Area
System Heat Rate
kg/s
kJ/K-kg
W
m2
m
tubes
mm
mm
m2
m2
kw
Ret
Prt
Ds
Lds
N/A
As
820
950
650
0.7
120
5193
120
5193
25
250
24.74
31.75
468.705874
50.2499696
77.5
N/A
N/A
m
m
N/A
m2
m2
N/A
N/A
0.1787
m2
W
Appendix 7: Sample Excel Chart Readout
46
Calculated
70.00
610.00
3.27E-005
820.00
4.02E-005
70.00
950.00
4.46E-005
650.00
3.42E-005
76.36
1.43
0.62
0.70
120.00
5193.00
25082190.00
600.00
782.10
120.00
5193.00
35831700.00
1117.28
27.83
300.00
0.02
0.03
648.57
832.35
77.50
19.68
2.99E-003
1.39148819
6.96
0.20
832.35
1.94
9379.44
2.69E-003
0.10
0.18