Numi absorber radioactive water system
(PART
II)
ABSTRACT
The goal of this project is
to size up the pumps and other components needed for the absorber radioactive
water system. The purpose of this report
is to describe the steps taken in the selection of the different components of
this water system.
INTRODUCTION
The Neutrinos at the Main
Injector Project will construct the entire infrastructure required to produce a
neutrino beam, which will be used to perform physics experiments. The final stage in the production of the
neutrino beam takes place in the absorber.
The beam absorber absorbs protons that did not interact in the target,
mesons that have not decayed and hadrons.
The core of the beam absorber
consists of a series of water-cooled aluminum plates. The heat load on these plates is considerable, ~70 kW at nominal
design conditions, since the particles filtered by it have high energies. It is crucial to avoid overheating the
plates because costly and time-consuming replacements would have to be
made. Therefore, a water-cooling system
had to be designed to maintain the absorber plates at an operational
temperature.
Given that the system
diagram was already designed, this project had the purpose of sizing components
of the system, all of which required engineering calculations. Other calculations on the system’s behavior
were also made.
SECTIONS
OF THE REPORT
This report has been
divided into several sections.
§
Pipes
§
Miter bends, elbows, and Tees
§
Pressure drop and flow rates for the absorber plates
§
Summary
The drawings shown below are
a rough sketch of the much more detailed NuMI Absorber Raw (Radio Active Water)
System (drawing number 8875.117-MD-363032).
Only the most important components of the system are shown. Additionally, the drawings show some of the
assumptions made on the length of the pipe and the quantity of elbows and
T’s. Please note that the left-side
diagram is called primary subsystem and right-side diagram is
called secondary subsystem throughout this report. Both systems intersect at the heat
exchanger, which is marked with a red dashed rectangle.
All pipe lengths were
estimated from the tunnel layouts. All
piping is 3”, schedule 10 for the primary subsystem and schedule 40 for the
secondary subsystem. However, the second
subsystem could also use schedule 10 piping.
Stainless steel pipes will be used, since it does not cause aluminum to
corrode. The water in the primary
subsystem will be filtered from ions but it will become radioactivated due to
the beam.
Figure 1. Basic schematic of the system and its two
subsystems.
To find the pressure drop across the different parts of the system,
it is necessary to first calculate what is the required flow rate of
water. Across the “de-ionizing bottle”
a flow of 10 gpm (gallons per minute) is required. The required flow rate across the absorber is not known. However, other physicists performed MARS
simulations and estimated the rate of heat going into the absorber to be 70
kW. Assuming all the heat is absorbed
by the water and that the water temperature increase will be from 100 to 110
degrees Fahrenheit, the rate of mass transfer across the absorber can be
calculated using the following equation:
qin = md C (T2
– T1 )
Where
qin à Rate of heat transfer
md à Rate of mass transfer
C à Heat capacity
(T2 – T1
) à Final minus initial water
temperatures
The rate of mass transfer can
be converted into volumetric flow rate with the following formula.
Vd = m v
Where
Vd à Volumetric flow rate
v à Specific volume
For the primary subsystem, the volumetric flow rate was
48.136gpm, which was rounded up to 50 gpm.
Therefore, adding 10 gpm of flow required across the de-ionizing bottle,
the required flow across the pumps is 60 gpm.
The flow rate for the secondary subsystem was considered to be the same.
PIPES
The most conservative way of performing this calculation is by
assuming that the flow through all the pipes in the system is 60 gpm. Detailed calculations, however, were
performed to find the pressure drops per pipe unit length according to the flow
in each pipe. The procedure to obtain
this is the same.
Using the following two
equations with the proper units, the Reynolds number is obtained.
Re = D Vel p / u
Vel = (V/dt) / A
Where
Re à Reynold’s number
D à Internal pipe diameter
Vel à Fluid velocity
p à Fluid density
u à Absolute viscosity
(V/dt) à Volumetric flow rate
A à Internal pipe area
Once the proper Reynolds
number is obtained the pressure drop can be computed from the following
formulas:
The S. E. Haaland approximation
to the Colebrook equation
f = (-1.8 Log(6.9/Re + (E/(3.7 D))^1.11))^-2
Where
f à Friction factor
Re à Reynolds number
Eà Roughness of the material
D à Diameter
HL = f L/D Vel^2/2g
P = p g HL
Where
HL à Head loss
f à Friction factor
L à Length of pipe
D à Pipe diameter
Vel à Fluid velocity
g à Acceleration of gravity
p à Density
P à Pressure drop
Regardless of the complexity of these calculations, the
pressure drop for the whole piping network of the primary subsystem resulted to
be less than 1 psi (pounds per square inch).
For the secondary subsystem a more significant 6 psi pressure drop in
piping was computed.
MITER BENDS, ELBOWS AND TEES
The primary and secondary
subsystems were estimated to have 20 elbows and 4 tees each. The head losses for these elements were
calculated from the following formula.
HL = K Vel^2 / (2
g)
Where
Vel à Fluid velocity
G à
Acceleration of gravity
K = 60f à 90 degrees miter bends and
flow thru branch in Tees
K = 30f à standard elbows
The resulting pressure drop from these elements is equal to 0.5
psig. Miter bends are not used in
piping but they are used inside the absorber channels.
PRESSURE DROP AND FLOW RATES FOR THE ABSORBER PLATES
The NuMI absorber consists of a series of aluminum and steel
plates. The purpose of the absorber is
to remove particles other than neutrinos from the beam, that is protons that
did not interact in the target, mesons that have not decayed and hadrons. The aluminum plates receive most of the heat
load since the beam passes through them first.
The steel plates filter all the remaining particles and do not receive a
considerable heat load. As stated
previously, the heat transfer rate on the aluminum plates is 70 kW and the flow
rate for the absorber as a whole is 50 gpm.
An illustration of the absorber and two of the aluminum plates can be
observed in figures 2, 3, and 4. Please
note the differences between the two plates.
Figure
2. Absorber.
Figure 3. First of the water-cooled absorber’s aluminum plates.
Figure 4. Third of the water-cooled absorber’s aluminum
plates.
The channels in the absorber run in parallel. The flow in the inlet divides into sixteen
0.76” aluminum pipes. The flow in the outlet
pipes (16) converges into one.
Moreover, the channel configuration varies for the different plates,
same as the length of the aluminum pipe.
Since the channels in the plates are in parallel, the pressure drop for
all of them must be the same. It would
be conservative to calculate this pressure drop by just dividing the 50 gpm
flow by 16 and then computing the pressure drop across one channel. Nevertheless, a much more detailed
calculation was performed for the double purpose of computing the exact
pressure drop and the volumetric flow rate of water through each plate. This is useful to corroborate the proper
thermal performance of the absorber.
The channels inside the absorber were considered to have a
roughness slightly greater than commercial steel, while the aluminum pipe was
considered to have a roughness equal to that of commercial steel. The “elbows” (were flow changes direction)
inside the plates were considered 90 degree miter bends. The inlet and outlet manifolds were
considered a succession of Tees.
Appendix V shows in detail the formulas
that were combined to derive the equations used to calculate the flow rates
through each plate. If the appendix
takes a long time to load, try saving the file into your hard drive and then
open it with Adobe Acrobat. The
solutions to the equations obtained in appendix V were found with Excel. The spreadsheet solutions are available in
appendix VI.
The volumetric flow rates for each of the plates vary from 5.8
to 7 gallons per minute. This variation
is not something that may seriously disrupt the absorber’s performance. The pressure drop across the absorber plus
the pressure drop at the manifolds (the device needed to divide the flow) is
equal to 1.12 psi. The manifolds do not
add any considerable pressure drop.
Therefore, the pumps must be sized up according to the other branch of
the primary subsystem (the de-ionizing bottle branch) where the pressure drop
is greater. Additionally, the
pressure-regulating valve should be located on the branch that leads to the
absorber and not on the branch that leads to the de-ionizing bottle [the NuMI
Absorber Raw System drawing shows this valve in the wrong place].
SUMMARY
The following table summarizes the pressure drops for the
different components of the two subsystems.
An asterisk indicates that the pressure drop has been reasonably
assumed.
|
Component |
Primary
subsystem |
Secondary
subsystem |
|
Absorber plates, manifold, piping
and elbows (the whole absorber branch) Not considered for pump |
Less
than 2 psig |
N/a |
|
De-ionizing bottle |
15
psig |
N/a |
|
Pipe (in 20 ft, not considering
absorber branch in primary subsystem) |
0.05
psig |
6.02
psig |
|
Elbows and tees (Primary subsystem
10 and 4, secondary subsystem 20 and 3) |
0.36
psig |
0.5
psig |
|
Full Flow Filter |
5
psig* |
5
psig* |
|
Heat Exchangers |
5
psig* |
5
psig* X 2 |
|
Strainers 2 ½” strainer, max spheres 3/32” from
Hellan Strainer Catalog page 43 |
1
psig |
1
psig |
|
3 Way valve |
N/a |
5
psig* |
|
TOTALS
PRESSURE DROP |
26.41
psig |
27.52
psig |
|
TOTAL
HEAD LOSS Press Drop/((density)(gravity)) |
~61.5
feet |
~64
feet |
The head and flow requirements for the two pumps are almost the
same: 60 gpm @ 42-44 FT. Therefore the
same pump may be chosen for the two subsystems. A pump that operates at 1750 or less revolutions per minute would
be preferred to reduce noise. However,
pumps that operate at that speed have poor efficiencies at the specified flow
and head. Therefore, the following 3500
RPM closed coupled pump was chosen as the most suitable candidate [see graph
below].
Figure 5. Graph of the 5”-1 ¼” pump series.
The pump shown above is relatively inexpensive. Also, it can be ordered in “all iron”, since
this material avoids copper bearing materials.
Copper bearing materials should not be used in a system with aluminum
components. The most important
technical data of this pump is that it gives the required head at the required
flow rate. The 4 9/16” impeller (second
curve from top to bottom) can be used to have a little extra flow through each
of the system’s parts. However, this
same impeller can be trimmed down to 4 ½” to give an output closer to the exact
requirements of the system. In both
cases a motor of 2 horsepower (or higher) that operates at 3500 rpm is
required.
NET POSITIVE SUCTION HEAD
In order to function
properly, all centrifugal pumps require a certain absolute pressure on their
suction side. This is called “net
positive suction head required” (NPSH required). The system, however, can give a certain amount of NPSH; this term
is called NPSH available. In theory the
NPSHavailable has to be more than or equal to NPSHrequired. In practice it is better to apply a safety
margin. Therefore, (1.5)NPSHavailable has to be more
than or equal to NPSHrequired.
(1.5) NPSHavailable > or = NPSHrequired
From the graph NPSHrequired= 8 ft. From Burks Pumps Catalog section 11 page 11
the following equation is obtained:
NPSHavailable
= (Barometric pressure (min - psia) + Gauge pressure (pressure in expansion
tank - psig) –Vapor Pressure (max)*(2.31/ specific gravity) + static
head – pipe loss
The last two terms from the last equation are negligible, thus
they are ignored. All the other terms
in the equation above can be obtained from books, with the exception of gauge
pressure. Gauge Pressure is the
pressure at which the expansion tank will be set. Solving the equality and the equality above for water
temperatures of 150 and 200 degrees Fahrenheit give a Gauge Pressure of –4 and
3.5 psig respectively. Temperatures as
high as 200 are not expected, therefore the system could even operate at a
vacuum pressure! This is not good for
the pumps, since any leaks in the system could make air come inside the pipes
and into the pumps, which reduces pump life and efficiency. Therefore, the recommended pressure for the
expansion tank is 10 psig.
The expansion tank is a
pressure vessel that is required to stabilize the system by providing an “air
cushion” for water expansion. It also
maintains the pumps operating at a safe pressure. As previously stated, the recommended pressure for the expansion
tank is 10 psig. However, ventilation
of the tank is necessary to avoid flammable concentrations of hydrogen, which
may be created during the absorber operation.
As a consequence, the inlet valve of the pressure vessel would be set at
12 psig and the outlet pressure would be 8 psig. These settings are more than enough to ensure proper ventilation
and pressure.
The capacity of the expansion tank is determined by equating
10% of the expansion tank’s volume with the expected liquid expansion. The liquid expansion is computed from the
volume of water in the system (pipes, heat exchanger, full flow filter, etc)
and the expected temperature fluctuation.
The following formulas were used for this calculation:
V = L A + other elements(water in heat
exchanger, full flow filter, de-ionizing bottle, and absorber)
m@60 F = m@140
F
m =V/v
Where
Và Volume
Là length of pipe
Aà Cross sectional area of the pipe
mà Mass
Và Volume
và Specific volume
By using these formulas the expected expansion of the primary
subsystem is calculated to be 4.94 gallons.
Therefore, the expansion tank’s capacity of the primary subsystem should
be 50 gallons. The expected water
expansion of the secondary subsystem is equal to 6.84 gallons. The expansion tank from the secondary system
should be at least 70 gallons in capacity.
Another important component of the expansion tank is the
pressure relief valve. The tank design
pressure will be 100 psig. The relief
valve should open at any pressure in the range of 20 to 70 psig. However the flow capacity of it is
determined with the following equation.
Qa = 0.029 Wc
Where
Qa à Flow capacity in cubic feet per minute of
free air
Wc à Water capacity of the container in pounds
The water capacity in pounds of the pressure vessel can be obtained
from its volume and the formulas shown before.
Using the proper units, the required flow capacity of the relief valve
is equal to 12.1 cubic feet per minute.
The two heat exchangers of the system are expected to exchange
70 kW but 200 kW will be used for the specification to allow some safety
margin. The heat exchanger that links
the two systems will be a plate and frame heat exchanger. Plate and frame heat exchangers exchange
heat more effectively, but they can only be used with clean fluids. The heat exchanger in the secondary
subsystem will be a shell and tube heat exchanger. It is not as effective as the other, but it can handle fluids
such as pond water easily. The
specifications for the plate-and-frame and shell-and-tube heat exchangers are
shown in appendix VII and
appendix VIII respectively.