Group Assignment 2: Energy-Based Systems Modeling of an On Board Fuel
Processing Unit to Provide Hydrogen from Ammonia
Michael Huang, Zubin John, Bill Binder, Joel Toussaint
Task 1: Define goals and problem domain
As gas prices continue to rise above $4.00 a gallon, people are continuing to hurt at the
pump. A solution providing a more economical energy source to power vehicles is needed. In
order to meet this need our team is designing a power system for a fuel cell vehicle. This
involves the design of an on board fuel processing unit to provide fuel for a hydrogen fuel cell
vehicle based on ammonia. Ammonia would currently be valued at an energy price equivalent of
$2.00 a gallon of gasoline. This figure could stay reasonably low if animal waste collection and
other methods of ammonia production such as coal gasification are used as demand increases.
Ammonia is one of the most abundant commodities produced in the United States.
The
distribution network for ammonia is comparable to the distribution of gasoline (Thomas 2006).
The required initial investment may not be overwhelming to implement an ammonia
intermediated hydrogen fuel economy once an efficient on board processing unit can be
produced.
The primary goal of this project is to develop a design for this onboard ammonia
processing unit and simulate how it affects a generic drive train for an electric vehicle. A
simplified initial design will involve a liquid ammonia tank feeding into an ammonia cracker
which heats the ammonia with the help of a burner. The hydrogen that is produced from the
cracking process is then stored in an intermediate hydrogen storage tank. Some of the hydrogen
from this tank is sent to the burner to help in the cracking of ammonia. A larger portion of the
hydrogen in the tank flows into a Proton Exchange Membrane Fuel Cell (PEMFC) which
generates a current that is used to charge a battery. The battery powers a DC motor that is
connected to the generic drive train of an electric vehicle. The battery is also used to power the
burner and the ammonia cracker. Figure 1.1 shows a flow diagram that delineates an updated
framework of the design. Green coded processes involve chemical energy, orange processes
involve electrical energy, and blue coded processes involve mechanical energy. The energy
transferred between chemical processes is thermal energy.
1
Figure 1.1: Process for cracking ammonia to supply hydrogen for PEMFC to power a DC motor
The flow diagram shown above is used to build the model in Dymola. The main aim of
simulating this model is to understand the effects of using such a fuel processing method on the
attributes of a car like acceleration, fuel economy, top speed and production cost. Acceleration,
top speed and fuel economy are three important attributes that customers use to gauge the
performance of a car. Therefore, it is important that the design meets the customer requirements
since the primary aim of a company that sells this design will be to earn profits. As a result,
production cost is also an attribute that has to be considered since it directly affects the market
price of the design. Four different design variables are identified that directly affect these
attributes. The four design variables for this model are catalyst type, PEMFC size, resistance in
the motor circuit and EMF constant of the motor. The dependence of the attributes on the design
variables is illustrated with the help of an influence diagram as shown in Figure 1.2. The catalyst
that is used in the ammonia cracker significantly influences the cracking process. Changing the
catalyst affects the conversion ratio which relates the mass of ammonia that enters the system to
the mass of hydrogen that is produced after the cracking process. Numerically, this design
variable corresponds to the temperature at which hydrogen is produced during the cracking
process. For example, two possible catalysts, Nickel (Ni) and an alloy of Nickel (Ni) and
Ruthenium (Ru), can be compared. The conversion ratio when the Nickel alloy is used as a
2
catalyst is much higher because the same amount of hydrogen can be produced with a much
smaller mass of ammonia. When the Nickel alloy is used as a catalyst, the hydrogen that is
produced is at a much lower temperature. The hydrogen flows into the PEMFC which requires a
much lower temperature. A more detailed simulation model would incorporate a cooling phase
for the hydrogen; therefore, having a lower temperature at the end of the cracker is preferable
because it will improve the efficiency of the system. This variable will directly affect the fuel
economy of the car. The next design variable, PEMFC size, refers to the number of stacks
required to reach a certain voltage that can run the DC motor. The PEMFC controls the current
that is supplied to the battery which directly affects the top speed and the acceleration. The last
two design variables govern the behavior of the DC motor which is the Changes to the resistance
in the motor circuit and/or the EMF constant affect the top speed and the acceleration of the car.
These four design variables have to be optimized to reduce the production cost. Therefore,
simulations will be performed to address questions like “What is the top speed of the car?”,
“What is the mileage of the car?” and “How fast can the car accelerate from 0 to 60mph?” All
the experiments will be performed assuming that the car moves on a flat ground with traction.
Simulating this model will help to understand if such a design for a fuel cell vehicle is feasible. If
such an approach is feasible, then the simulation problem directly relates to the design problem
of creating a profitable design for an onboard fuel processing unit which uses ammonia as the
fuel.
Figure 1.2: Updated Influence diagram
3
Task 2: System and Simulation Specification
In order to create a model that approximates the behavior of the electric vehicle, the
entire system is divided into several functions that when put together will perform the desired
task of driving the electric vehicle using ammonia. Each function is of crucial importance for the
design of the vehicle. This is mainly the reason why each one of these functions is implemented
by modeling components which have the characteristics of each specific function. The
components of the electric vehicle system include a tank, an ammonia cracker, a burner, an
intermediate hydrogen storage tank, a Proton Exchange Membrane Fuel Stack (PEMFC), a high
voltage battery, a variable resistance, some controls and a simplified version of a drive train
system. The description of each component will be given in subsequent paragraphs.
The tank is the first component of the electric vehicle that has been modeled. It is
assumed to be the container that holds the ammonia fluid at a relatively high pressure namely
8.57bar in order to minimize the space it occupies in the vehicle. In real life experience, the
content of the tank would have been in a liquid state to allow better minimization of the occupied
space; however, the absence of proper media library renders the modeling of a two phase flow of
ammonia a much greater and unnecessary challenge for our project. It is sufficient to use an
equivalent volume of gaseous ammonia for the model. The pressure difference between the tank
and the next component, namely the cracker, is essential what drives the flow of the fluid in the
system. A valve has also been implemented in the tank model to regulate the flow of the fluid
with respect to the energy requirement of the system. It is to be noticed that the content of the
tank contains the required element that will be used as the fuel of the car itself and that at any
moment in time the content of the tank is at temperature much higher than -75 oC.
The next component in the system is the ammonia cracker. It is designed to receive the
flow of ammonia from the tank and break it down through some chemical reactions in order to
produce the fuel that will power the vehicle. It is modeled as a simple metal tube with an inner
coating of catalyst material. At high enough temperatures the ammonia will split into N2 and H2.
Since Modelica currently does not have a chemical reaction library or media’s that account for
changing mixtures, the cracker pipe must be discretized to follow a changing ideal mixture. The
discretized pipe is split into six segments with three pipes each allowing the flow of the three
different gases of the mixture. In between the segments an interface takes in the mixture
4
properties homogenizes the mixtures properties, calculates the chemical reaction, and then
redistributes the flow into the next pipe segment. Further detail of this process will be provided
in Task 4.
The hydrogen burner model followed the cracker. Its function is to generate the heat
required to sustain the reaction in the cracker. Once the reaction in the cracker had been started, a
fraction of the hydrogen generated is used by the burner. This process combines hydrogen with
oxygen to create water and energy. It is to be assumed that the water vapor created is dissipated
in the environment during this process. Currently, the cracker is just a simple annular tube
surrounding the cracker pipe where the combusted hydrogen heat up the cracker pipe through
convection. Some losses are taken into account via conduction and convection to the outside of
the burner. Before the hydrogen is generated in the hydrogen storage tank, a heating coil
preheats the ammonia cracker so when the flow is started almost no ammonia can reach the
PEMFC.
The intermediate hydrogen storage tank is used to help control the flow of hydrogen to
the PEFMC and the burner. It contains an inlet valve from the cracker and two outlet valves that
are connected to the PEMFC and to the hydrogen burner.
The PEMFC stack generates electrical power from the hydrogen received from the
intermediate hydrogen storage tank. Detailed modeling of the PEMFC is out of scope for this
project. However, in this project a simplified model had been used. The simplified version of the
PEMFC assumes that this component is a signal driven current source described by the following
equation:
𝐼=
𝐹Ṁ
𝑆
(2.1)
where I is the current, F is the Faraday constant, Ṁ is the molar flow rate of hydrogen gas, and S
is the number cells stacked in series to get a voltage higher than the battery voltage. It is assumed
that there is no electrical nor heat loss in this system. That is all the chemical energy of the
hydrogen flow rate is entirely converted into electricity. The main reason for the higher voltage
5
in the PEMFC is due to the fact that the higher this voltage the faster the battery will be able to
be charged by the PEMFC.
The battery has been modeled as a controlled voltage source in series with an internal
resistance. The battery had been given an initial capacity high enough to start the motion of the
vehicle once the switch is turned on in the vehicle. However, once the state of charge of the
battery reached a critical level, the PEMFC will power up and supply the current required by the
drive train and at the same time charge the battery. This process will continue until the state of
charge in the battery reached its maximum value then the battery will take over in powering the
system to modulate the cracker and PEMFC energy source to the motor. This provides a much
quicker current response to the motor. In a situation where a large acceleration is desired the
battery would initially provide most of the current and after a few seconds the PEMFC will catch
up and provide the energy to drive the load while at the same time recharging the battery.
Lastly a simplified version of a drive train has been modeled in this project. A simplified
drive train is modeled to evaluate the ammonia cracker and PEMFC combination. The drive
train involves an ideal DC motor, a simple gear, an ideal rolling wheel, a mass, and a drag force
model. The drive train is powered either by the battery or the PEMFC depending on the state of
charge in the battery. The current that these voltage and current sources output determine the
response of this system. It is assumed that the motor is rotating in its lubricated housing. This
creates a damping effect that depends on the relative angular velocity between the motor and its
housing. It is also assume that the total mass of the car, the driver and the ammonia tank is
represented by the one single mass present in this last subsystem. The drag force is modeled as a
quadratic relationship of the speed velocity of the car in the ambient air.
Task 3: Creating models in Dymola
The overall model contains an ammonia storage tank, ammonia cracker pipe, hydrogen
burner, intermediate hydrogen storage tank, PEMFC stack, battery, and a simplified drive train.
The primary focus of this system is the detailed modeling of the ammonia cracker. The electrical
and mechanical components such as the PEMFC and drive train are greatly simplified. Some
6
simplifications are made in the battery that does not take into account effects such as
polarization.
The first component, ammonia storage tank stores gaseous ammonia. In real life the
ammonia storage tank would store liquid ammonia and would have a proportionally smaller
volume based on their densities. Since we cannot model two phase flow of ammonia due to the
absence of a proper media library it will be sufficient to use a larger equivalent volume of
gaseous ammonia.
The tank is heated by the external environment in order to keep the
temperature above -75 oC where the model will break and to model what happens in real life.
The ammonia cracker is a simple metal tube with an inner coating of catalyst material.
At high enough temperatures the ammonia will split into N2 and H2. Since Modelica currently
does not have a chemical reaction library or media’s that account for changing mixtures, the
cracker pipe must be discretized to follow a changing ideal mixture. The discretized pipe is split
into six segments with three pipes each allowing the flow of the three different gases of the
mixture. In between the segments an interface takes in the mixture properties homogenizes the
mixtures properties, calculates the chemical reaction, and then redistributes the flow into the next
pipe segment. Further detail will be provided in Task 4.
The hydrogen burner uses a fraction of the hydrogen generated in the cracker to sustain
the reaction in the cracker. Currently the cracker is just a simple annular tube surrounding the
cracker pipe where hydrogen combusts heating the cracker pipe through convection. Some
losses are taken into account via conduction and convection to the outside of the burner. Before
the hydrogen is generated in the hydrogen storage tank, a heating coil preheats the ammonia
cracker so when the flow is started almost no ammonia can reach the PEMFC.
The intermediate hydrogen storage tank is used to help control the flow of hydrogen to
the PEFMC and burner. It contains an inlet valve from the cracker and two outlet valves to the
PEMFC and hydrogen burner.
The PEMFC stack generates electrical power from the hydrogen. Detailed modeling of
the PEMFC is out of scope for this project. The model used is simplified to a current source that
is described in the earlier task by equation 2.1. This means that a higher voltage battery will
charge slower and at the same time discharge faster requiring much more hydrogen in order to
stay charged. It is expected the PEMFC stack size will have the greatest effect on all three
attributes.
7
The battery modulates the cracker and PEMFC energy source to the motor.
This
provides a much quicker current response to the motor. In a situation where a large acceleration
is desired the battery would initially provide most of the current and after a few seconds the
PEMFC will catch up and provide most of the load and recharge the battery when the load is
decreased again.
A simplified drive train is modeled to evaluate the ammonia cracker and PEMFC
combination. The drive train involves an ideal DC motor, a simple gear, an ideal rolling wheel, a
mass, and a drag force model. Figure 3.1 shows the overall system’s model in Dymola.
step
system
defaults
g
Am?
startTime=6
variableResistor
clock
Mileage
startTime=2
const
>
k=0
Figure 3.1: Model of hydrogen fuel cell car with hydrogen stored in ammonia
8
Task 4: Verification of the individual modules
Module A: Ammonia Cracker and Burner
Cracker Segment: The cracker segment is modeled as 3 fluid pipes that contain nitrogen,
ammonia, and hydrogen. These pipes share an external heat port in parallel. On each end of the
pipe is a fluid port to connect to the segment interface. Figure 4.1 shows the cracker pipe
segment.
system
defaults
g
port_a1
port_b1
2
boundary3
boundary
H2_Pipe
m
boundary4
port_b2 boundary1
port_a2
2
m
boundary2
NH3_Pipe1
boundary5
port_a3
m
port_b3
thermalCondu?
2
N2_Pipe
G=3000
heatCapacitor
fixedHeatFlow
port_a
20
Q_flow =100000
Figure 4.1: Cracker pipe segment made of three pipes heated in parallel
Figure 4.2 shows a plot of the time response of specific enthalpy of the three pipes.
9E6
cracker_Segment.N2_Pipe.mediums[1].h
cracker_Segment.H2_Pipe.mediums[1].h
cracker_Segment.NH3_Pipe1.mediums[1].h
8E6
7E6
6E6
5E6
4E6
3E6
2E6
1E6
0E0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Figure 4.2: Specific enthalpy of N2, H2, and NH3. At the same temperature H2 has much higher
specific enthalpy.
9
Fluid Signal Processor and Segment Interface: The fluid signal processor and segment interface
takes in the three fluids from a cracker segment and homogenize fluid properties and calculates
the effects of the chemical reaction. Figure 4.3 shows the segment interface with the fluid signal
processor (which is just a signal input which reads signals as variables in equations; does not
have any models except for block interfaces).
system
specificEntha?
H2_Seg_in
temperature
boundary
m_flow
h
defaults
g
pressure
boundary3
m_flow
T
p
T
H2_Seg_out
p
ramp
const
duration=5
k=1
m
massFlow Rate
specificEntha?
NH3_Seg_in
temperature1
h
pressure1
boundary4
m_flow
T
boundary1
p
m_flow
T
fluid_Signal_Pro?
p
boundary3
NH3_Seg_?
boundary
m
T
m
massFlow Rate1
boundary1
boundary4
T
specificEntha?
N2_Seg_in
temperature2
boundary2
p
m_flow
h
T
m
pressure2
boundary5
m_flow
T
p
N2_Seg_out
m
boundary2
boundary5
T
m
massFlow Rate2
Figure 4.3: Shows the segment interface takes in fluid properties and processes them in the signal
fluid properties and outputs a new ideal mixture based on the chemical reaction
10
segment_Interface.fluid_Signal_Processor.T
600
400
200
0
0
1
2
3
4
5
6
7
8
9
10
6
7
8
9
10
segment_Interface.fluid_Signal_Processor.Eq
1.5
1.0
0.5
0.0
-0.5
0
1
2
3
4
5
Figure 4.4: As the temperature of the fluid rises the chemical equilibrium shifts towards the
nitrogen and hydrogen products
Hydrogen Burner: The hydrogen burner takes in a signal from a mass flow rate meter output and
converts this to heat in the following chemical reaction:
2𝐻2 + 𝑂2 → 2𝐻2 𝑂 + 572 kJ
(4.1)
Theoretically the hydrogen gives 129 kJ per gram of heat when burned. The flame temperature
can be set to any desirable value. The hydrogen flame heats the cracker pipe through convection.
A heat capacitor is used to model the specific heat capacity of the air and hydrogen mixture.
Heat losses to the outside of the burner are through a conductor model representing the outer
shell of the burner. This is assumed to be constructed out of an insulating material. The burner
converter is nothing more than a modified gain that converts a mass flow rate signal into a heat
input signal.
The hydrogen burner model also includes an initial heat source to preheat the pipes. This
represents a heating coil which would heat the system at startup. In later versions of the burner
11
this heat source will either be removed and initial hydrogen pressure in the hydrogen tank will be
used for startup or the heating coils will be modeled explicitly using a heating resistor. Figure
4.5 shows the burner model and the burner test.
fixedTempera?
K
T=293.15
const
heatCapacitor
const3
system
Cpt
defaults
g
max
k=0
k=Gd
max()
u
boundary1
port_b1
Gc
heatCapacitor
prescribedHe?
100
convection
ramp
thermalCondu?
thermalCondu?
burner?
prescribedHe?
G=3000
G=500
duration=5
step
boundary
10
m
heatCapacitor1
startTime=2
Figure 4.5: Burner model and burner test including startup preheating coil
pipe.mediums[1].T
1200
1000
800
600
400
200
0
0
1
2
3
4
5
6
7
8
9
10
Figure 4.6: Temperature profile of ammonia heated by hydrogen burner with ramped flow
The plot in Figure 4.6 shows the burner switching on at 2 seconds just as the coils are switched
off.
12
Burner Valve Control and Ammonia Storage Valve Control: The two storage tanks have PID
valve controllers. The controller for the hydrogen tank maintains the temperature in the cracker
even during rapid transients to keep the hydrogen pure and prevents the cracker pipe from
melting. The Ammonia tank valve controller receives feedback from the batteries state of charge
in order to keep up with the systems energy demands. The valve controls will be validated in the
full model validation since they cannot really be isolated since they require feedback.
Full Model Validation: The full model consists of an ammonia storage tank, an ammonia
cracker, a hydrogen burner, a PEMFC stack, a battery, a variable resistor (gas pedal), and a drive
train. Figure 4.7 shows the full model. Figure 4.8 shows the PEMFC and battery response to
acceleration
step
system
defaults
g
Am?
startTime=6
pulse
period=5
variableResistor
clock
Mileage
startTime=2
const
>
k=0
Figure 4.7: Full model of a hydrogen powered car with ammonia efficiently storing the hydrogen
13
simple_PEM.pin.i
1E4
finalSimpleHybridBatModel.P2.i
5E3
0E0
-5E3
-1E4
10
20
30
40
50
60
30
40
50
60
car.mass.v
60
40
20
0
-20
10
20
Figure 4.8: Current of PEMFC and battery with a pulsed variable resistor (gas pedal). Top graph
shows battery current (red) and PEMFC current (blue); bottom graph is velocity
Figure 4.8 demonstrates how the PEMFC and battery respond to the load from the motor. At the
beginning of an acceleration period the battery quickly ramps up current to the motor and after a
fraction of a second the PEMFC responds and takes most of the load. Basically for acceleration
lasting more than a second the PEMFC is able to respond in time to do most of the work. During
the periods when the resistance is increased greatly and the car decelerates the PEMFC recharges
the battery. The battery provides a fast response for initial acceleration and the PEMFC ensures
that the acceleration is sustained and keeps the battery charged.
14
car.mass.v
60
40
20
0
0
10
20
30
40
50
60
40
50
60
ammonia_Storage.massFlowRate.m_flow
0.08
0.04
0.00
0
10
20
30
Figure 4.9: Ammonia mass flow rate in response to acceleration demand. Top graph is velocity;
bottom graph is mass flow rate
Module B: Ammonia Tank
The ammonia tank, Figure 4.10, is represented by the system below. The system consists
of a closed volume whose outlet is controlled by a valve that steps up. Also included is a signal
displaying the mass flow, used to calculate the miles/kg of ammonia used in the simulation. In
this scenario the valve starts open at 50% open. The tank starts at 8.57 bar and has a volume of
100m3. The system is tested according to Figure 4.11, which has a control for the valve on the
tank and a boundary for the ammonia to leak to.
15
integrator
volume
I
pressure
k=1
m_f low
V=NH3Volume
p
port_b1
valveCompre?
massFlow Rate
thermalCondu?
G=100
f ixedTempera?
K
T=293.15
Figure 4.10: Ammonia Tank
system
defaults
g
const
k=.5
boundary
Figure 4.11: Setup used for testing the Ammonia Tank. The Ammonia Tank is the maroon circle
with a straight outlet
16
The graphs below show the mass in the tank as the blue line and the pressure in the tank as the
red line in Figure 4.12. Both have an expected result of decreasing as time continues, but the
slope is decreasing in magnitude. The boundary is set at 1 bar and thus the two lines are not
approaching zero. The pressure is approaching 1 bar.
ammonia_Storage.volume.medium.p
9
8
7
6
5
4
3
0
200
400
600
800
1000
ammonia_Storage.volume.m
800
700
600
500
400
300
0
200
400
600
800
1000
Figure 4.12: Shows the mass and pressure of the ammonia in the tank with respect to time with
the valve 50% open
17
In order to make sure the system makes sense, Figure 4.13 shows the system with the
valve 75% open. When compared to Figure 4.12 it is clear that both the pressure and mass are
significantly lower, which is expected as the fluid is given a larger area to escape through.
ammonia_Storage.volume.medium.p
8
6
4
2
0
500
1000
ammonia_Storage.volume.m
700
600
500
400
300
200
100
0
500
1000
Figure 4.13: Shows the mass and pressure of the ammonia tank with the valve 75% open with
respect to time
18
The temperature of the ammonia in the tank decreases as ammonia flows out, and at low
pressures the model is unable to run since the ammonia reaches a temperature below -70 degrees
Celsius. A graph of the temperature is shown below in Figure 4.14. It is important for the model
that the temperature not be allowed to decrease to such a level as the simulation will stop. This
can be corrected by having the boundary pressure be higher, but since we are simulating how the
car will behave in real conditions this is not ideal. For this reason the volume is increased and the
valve is not allowed to open as much so that the simulations are not allowed to last sufficiently
long that the temperature falls to that low of a level. This is why a conductor is heating the tank,
in order to allow to the tank to be heated by the ambient while operating.
ammonia_Storage.volume.medium.T
-10
-20
-30
-40
-50
-60
-70
0
200
400
600
800
Figure 4.14: Shows the temperature of the ammonia in the tank with respect to time
19
1000
Module C: Hydrogen Tank
The hydrogen storage and testing scenario is shown below in Figure 4.15. The hydrogen
storage has a closed vessel as its primary component, with three valves that are controlled by
how open they are. The inlet valve is the valve coming from the cracker. The two outlets are to
the burner and to the PEM. This model, teal circle, was tested by having an inlet boundary with a
higher pressure than the outlets, shown on the right side of Figure 4.15.
system
InletValvePos
const
defaults
g
PEMValvePos
k=.2
HydrogenSto?
boundary
V=.1
InletValveInlet
InletValve
boundary2
PEMValve
PEMValveOutlet
BurnerValvePos
BurnerValve?
Figure 4.15: Shows the hydrogen storage tank on the left, with the testing circumstances shown
on the right where the hydrogen tank is represented by a teal circle
The below graphs, Figure 4.16, are of the pressure in the vessel as well as the mass of the
hydrogen in the vessel. The vessel has an initial volume of 0.1 m3 and pressure of 2 bar being fed
by a boundary with a pressure of 2 bar and the two outlets at 1 bar. The valves were all allowed
to be 20% open. The graphs are similar to the ammonia tanks response. This is expected since
the two are very similar and the same reasoning applies to both. As the tank loses mass for the
same volume, the pressure decreases.
20
2.2
hydrogen_Storage.HydrogenStorage.medium.p
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.00
0.018
0.01
0.02
0.03
0.02
0.03
hydrogen_Storage.HydrogenStorage.m
0.016
0.014
0.012
0.010
0.008
0.00
0.01
Figure 4.16: Shows the mass and pressure of the Hydrogen with respect to time with the valve
20% open
The graph below, Figure 4.17 is of the mass of the hydrogen with the valves at 40% open. As
would be expected since the tank is losing mass, the system’s time constant has lowered. This
21
makes sense since the fluid can escape more easily. Once again this is similar to the results
obtained for the ammonia tank.
0.018
hydrogen_Storage.HydrogenStorage.m
0.016
0.014
0.012
0.010
0.008
0.00
0.01
0.02
0.03
Figure 4.17: Shows the mass of the hydrogen with respect to time with the valve 40% open
Module D: Rechargeable Battery Model
In order to develop an accurate representation of the voltage drop seen across the battery
when a load is attached to it, a model had been created. This model includes a simple controlled
voltage source in series with a constant resistance namely the internal resistance of the battery as
depicted in Fig 4.18. It assumes that the characteristics of the battery remain the same for both
the charge and discharge cycles. The open voltage source is calculated using a non-linear
equation based on the State of Charge (SOC) of the battery. Equation 4.2 below was used to
compute the SOC.
22
Figure 4.18: Non-linear battery model
𝑡
∫ 𝑖𝑑𝑡
𝑆𝑂𝐶 = 100 (1 − 0
)
𝑄
(4.2)
where SOC represents the state of charge, Q is the battery capacity, i is the current flowing
𝑡
through the circuit, thus ∫0 𝑖𝑑𝑡 is the actual battery capacity.
The controlled voltage source is describes by equation 4.3 where E0 represents the battery
constant voltage, K is the polarization voltage (V), A is the exponential zone amplitude (V), B is
the exponential zone constant inverse (As)-1 and it is the actual capacity of the battery.
𝐸 = 𝐸0 − 𝐾
𝑄
+ 𝐴𝑒𝑥𝑝(−𝐵𝑖𝑡)
𝑄 − 𝑖𝑡
Figure 4.19 below is the Dymola model that has been created for the non-linear battery
23
(4.3)
Figure 4.19: Dymola model of the non linear battery
24
To test the validity of the model, a 337 V Nickel Metal-Hydrid battery with an initial
capacity of 1 Ah has been modeled with its characteristics. A resistive load of 1 Ohm had been
attached to it to take account of the voltage drop and current flowing through the circuit.
According to Kirchhoff’s laws for electric circuit, the electric current that flows through the
circuit is given by the ratio of the voltage and the sum of the resistance present in the circuit. In
our case, the computed resistance in the circuit is equal to 1.0046 Ohm thus the current will be
approximately 335 A. For such a circuit the time it will take for the battery to discharged
assuming the current stays constant is given by equation 4.4.
𝑡=
𝑄
𝑖
(4.4)
where Q is the rated capacity of the battery, t is the time of discharged and i is the current
intensity. Therefore, it is expected that the battery will last approximately 10.74 s before running
out of charge as shown in figure 4.20.
25
Figure 4.20: Displays the simulated plot of the current flowing through the load
According to figure 4.20 above the battery took 10.872 s to drop to a zero Amp. This
value corresponds almost exactly to the time interval computed above. The discrepancy between
the two results is due to the exponential drop seen above right before the end of life of the
battery. The state of charge of the battery is also shown in the figure above. One can notice that
it is linearly decreasing as the resistor is being powered by the battery up to the moment in time
where the voltage across the load is zero. This linear behavior of the SOC discharge agrees well
with the model prediction given by Equation 4.2 above and the expected behavior of battery
when discharging through a purely resistive load as shown in figure 4.21.
.
Figure 4.21: Testing circuit for the battery
26
In order to verify the behavior of the battery when connected to the PEM cell a signal
voltage had been attached in parallel with the battery. The signal voltage represents the behavior
of the PEM cell and is powered by a pulse which varies from zero to 340V for a period of 10
seconds. The pulse had been set to a start time of 5 s to record the behavior of the battery when
the PEM is not charging. It is expected that the battery will go through a series of charging and
discharging cycles as the voltage of the PEM is varying. Figure 4.22 below shows that when the
voltage across the battery is zero the SOC abruptly dropped to zero. However, when The PEM
voltage is 340 V the battery is slowly charging until the value reached the SOC becomes 100%.
The SOC remains at this value as long as the voltage across it is higher than its nominal voltage.
Once the voltage of the PEM across the battery is null all the current flows through the internal
resistance until the SOC becomes zero.
Figure 4.22: Correlation between the SOC and the voltage across the battery
Module E: Drive Train
A DC Motor has an electrical source input of a DC voltage. The relevant output would be
the angular velocity of the motor. A model of a DC Motor can be seen in Figure 4.23. The source
comes from p1 and the negative part of the source connects to n1. The voltage goes through a
resistor and then an inductor in series before being connected to the emf, the electromotive force,
which converts electrical energy to mechanical energy. Support1 is necessary because the motor
27
has to rotate relative to something. In reality the motor rotates in its housing. This is why the
damper is connecting the mechanical output of the emf to the other end of the emf that connects
to support1. The motor is rotating in its housing which is lubricated, and thus a damping effect is
created and relies upon the relative angular velocity of the motor to its housing. The rotor has its
own inertia that is taken into account with the inertia, J1. This can then be connected to
flange_b2 which would be the output of the motor.
support1
p1
resistor
inductor
R=R1
L=L1
flange_b2
k=K1
inertia
n1
emf
J=J1
d=B1
damper
Figure 4.23: Shows the model for an electric DC motor
In order to test the DC Motor Model, a 12V DC battery is connected to the model from
Figure 1 but no additional mechanical load is placed, which can be seen in Figure 4.24. This
would simulate the motor running without anything connected to it, which is why flange_b2 is
not connected to anything. Since the housing is assumed to not move, support1 is fixed. The
negative side of the voltage source is grounded in order to specify the voltage as the voltage
source provides only a relative voltage.
28
f ixed
ground
Figure 4.24: Shows DC Motor with Battery Model
With a voltage source attached it was possible to simulate the model in action. Table 1
shows the parameters used to initially test the DC motor model.
Table 1: Shows the initial parameters for the DC Motor Model
Voltage,
Armature
Armature
Torque
v (V)
Resistance,
Inductance,
Constant,
R (Ohms)
L (mH)
(N*m/Amp)
0.05
10
0.3
120
Rotor Inertia, J Viscous
K (kg*m2)
Coefficient,
Friction
B
(N*m*s/rad)
0.2
0.3
Some of the important values of interest are the motor’s angular velocity, the motor’s
current, and the motor’s angular acceleration. A plot of these over time is shown in Figure 4.25,
shown below.
29
dC_Motor.inertia.w [rad/s]
2000
dC_Motor.inertia.a [rad/s2]
dC_Motor.resistor.i [A]
1500
1000
500
0
-500
0
1
2
Figure 4.25: Shows a plot of the motor's angular velocity, angular acceleration, and current as a
function of time
It is interesting to note that the inertia’s angular velocity and the motor’s current approach
the same value in steady state. The reason for this can be seen from the equation for Torque:
Τload = Kί – Jώ – Bω
(4.5)
where Τload is the torque load, K is the torque constant parameter that was specified to be 0.3
N*m/Amp, ί is the motor current, J is the rotor’s inertia parameter that was specified to be 0.2
kg*m2, B is the Viscous Friction Coefficient parameter that was specified to be 0.3 N*m*s/rad,
ω is the angular velocity of the rotor, and ώ is the derivative of angular velocity of the rotor.
In steady state, the derivative of angular velocity is zero since there is no angular
acceleration in steady state. Also, the torque load is zero since the motor is not attached to any
load. This only leaves the current and angular velocity terms, however K and B are both 0.3 and
therefore cancel out to leave the current equal to the angular velocity in steady state. If K were to
be 0.6 instead of 0.3, then the current would have to be half of the angular velocity’s steady state
value. Figure 4.26 shows the case where K is 0.6, thus proving the relationship as the value of the
current is approximately half of the angular velocity. The other equation that governs the DC
motor is that of the electrical side:
30
di
v = Rί +L dL +Kω
(4.6)
where v is the source voltage, R is the armature resistance, and L is the armature inductance.
From this equation, if the resistance were increased, the angular velocity would decrease. Even
though the current will also decrease as a result of the increased resistance, the angular velocity
should still suffer. This also makes physical sense as the resistance transforms electrical power
into heat, thus wasting power that could have been transformed to mechanical work. This is
shown in Figure 4.27. Figure 4.27 shows the current and angular velocity when the resistance is
increased to 0.1 Ohms. It is clear that the system does not oscillate as much, so the resistance
helps to dampen the response.
dC_Motor.inertia.w [rad/s]
800
dC_Motor.resistor.i [A]
600
400
200
0
-200
-400
0
1
2
Figure 1.26: Shows the DC motor with K= 0.6.
31
3
dC_Motor.inertia.w [rad/s]
1000
dC_Motor.resistor.i [A]
800
600
400
200
0
-200
0
1
2
Figure 4.27: Shows the DC motor with a resistance of 0.1 Ohms
Inductance is a property that induces a magnetic field and a voltage in the opposite
direction of the voltage driving the inductance. This causes the second order nature of the
response. Figure 4.28 shows the response of the DC motor with the inductance increased to 100
mH. The time constant is clearly increased since it takes much longer for the system to settle to
steady state. The overall shapes of the curves are equivalent to the original system, indicating the
inductance does not change the relationships, but does change the time constant.
32
dC_Motor.inertia.w [rad/s]
600
dC_Motor.resistor.i [A]
500
400
300
200
100
0
-100
0.0
2.5
5.0
Figure 4.28: Shows the DC motor with an inductance of 100 mH
The inertia is the other form of energy storage. This means that an increase in the
inertia’s value will most likely mimic the effect of an increase in the inductance for the
determination of the time constant of the system, however since the inertia is the mass being
accelerated, an increase in the inertia will most likely reduce the apparent effects of the second
order system. Figure 4.29 shows the simulation with the inertia increased to 2 kg*m2, the same
magnitude change as the inductance, and therefore the same time constant. Figure 4.29 shows
that the inertia’s angular velocity appears first order as expected, but the motor’s current still
experiences a second order response as it has a large maxima before lowering down to the steady
state value. Once again, since the damping and torque constant have not been changed, the
current and angular velocity still approach the same value in steady state.
33
dC_Motor.inertia.w [rad/s]
2000
dC_Motor.resistor.i [A]
1500
1000
500
0
-500
0.0
2.5
5.0
Figure 4.29: Shows the DC motor with an inertia of 2 kg*m2
The viscous friction is also responsible for removing energy from the system, much like
the resistance. This means that it can help reduce the second order nature of the response. Unlike
the resistance however, the damping is an effect that is not in the electrical circuit. The viscous
friction coefficient was also one of the parameters that affected how the current and angular
velocity act relative to one another in the steady state. Thus, an increase in the damping will
reduce the angular velocity’s steady state value. Since the speed is reduced, according to
equation 2 the current will also rise. Figure 4.30 shows the motor with a viscous friction
coefficient of 3 N*m*s/rad, an increase of one magnitude, so it is expected that the angular
velocity will be one tenth the current in the steady state, as shown in Figure 4.30. Figure 4.30
also shows that the second order response has been removed and the time constant has been
reduced as well.
The final parameter of interest is the source voltage. Since the voltage is the input to the
linear system, an increase in voltage should merely be a proportional increase in the output
34
parameters, current and angular velocity. Figure 4.30 shows the motor with the voltage increased
to 240 V. Figure 4.31 shows that the entire curve has been amplified by a factor of 2, the same
increase of the voltage. The time constant has not been changed and the second order nature of
the curves has not been changed, merely the amplitude.
dC_Motor.inertia.w [rad/s]
2000
dC_Motor.resistor.i [A]
1500
1000
500
0
-500
0.0
0.5
Figure 4.30: Shows the DC motor with a viscous friction coefficient of 3 N*m*s/rad
35
1.0
dC_Motor.inertia.w [rad/s]
2500
dC_Motor.resistor.i [A]
2000
1500
1000
500
0
-500
0
1
2
3
Figure 4.31: Shows the DC motor with a voltage of 240 V
The DC motor will power a car by using a gear system. This gear system will turn a
wheel to accelerate a mass which is being subject to air drag. Figure 4.32 shows the model of the
car. The model begins the same as a battery attaches to a grounded motor, however a load is
applied this time. In this case the rotational energy from the motor runs an ideal gear, which in
turn runs an ideal rolling wheel. The wheel causes the mass to translate but that translation is
damped by air drag.
36
fixed
idealGear
idealRollingW?
mass
m=m1
ratio=Ratio
ground
f
force
Figure 4.32: Model of a DC motor running a car which is subject to drag
The air drag uses the speed of the mass to determine how much force is being supplied by the
drag. The equation for this is:
Fdrag = 0.5*Cd*A*ρ*v2
(4.7)
where Fdrag is the drag force, Cd is the drag coefficient, A is the frontal area of the car, ρ is the air
density, and v is the speed of the car. This drag acts in the opposite direction of motion so it is
always slowing down the car. Table 2 shows the initial parameters used to simulate the car,
whose speed and the motor’s torque can be seen in Figure 4.33 below.
37
Table 2: Shows parameters used for the car simulation
Note: the DC Motor parameters are used in all car simulations
Gear
Wheel
Mass, m Drag
Ratio
Radius,
(kg)
Air
Frontal
Coefficient, Density,
r (m)
ρ
Cd
Area,
A
(m2)
(kg/m3)
5
0.332
1500
0.32
1.29
mass.v
25
2.2
dC_Motor.support1.tau
600
20
15
400
10
200
5
0
0
-5
0
10
20
30
0
10
20
30
Figure 4.33: Shows the car's speed and torque output from the motor
The maximum speed the car reaches is 22.3 m/s and the maximum torque is 625.6 N*m.
In order to verify that the drag is acting in the correct direction, Figure 4.34 shows the simulation
where the drag has been removed. The car now has a maximum speed of 22.8 m/s and the
maximum torque is 625.6 N*m. Even though the speed did increase when the drag was removed,
the torque did not change significantly. This is due to the fact that when the torque is its
maximum, at time equal to 0.6 seconds, the drag has not had a significant effect on the car. The
torque does have a significantly lower steady state value as the motor provides the energy that
the drag would otherwise be removing.
38
mass.v
25
dC_Motor.support1.tau
600
20
15
400
10
200
5
0
0
-5
0
10
20
30
0
10
20
30
Figure 4.34: Shows the car's speed and torque output from the motor without drag
It is clear from both figures that the motor is struggling to provide enough torque when
the car is just starting, with the torque peaking very early and then decreasing to its steady state
value. The gear ratio allows for the motor’s torque to be amplified when being applied to the
wheel, however this effect limits the maximum speed that the car can go. Figure 4.35 shows the
effect of a gear ratio of 1. The car’s maximum speed is now 51.2 m/s and the maximum torque
from the motor is now 710.5 N*m. In this case the car is accelerating much more quickly and to
a higher overall speed. This made the drag slightly more significant for determining the
maximum value of torque, but the higher steady state speed led to a much higher steady state
torque, as the speed increases the overall energy taken out by drag is a function of the square of
the speed, so the motor has to work extremely hard to counter the drag force. Lowering the gear
ratio did not change the overall shape of the curves, however it did greatly affect the time
constant as the time to steady state is approximately 125 seconds as compared to 25 seconds, five
times as large, the same factor the gear ratio was changed.
39
mass.v
60
dC_Motor.support1.tau
800
50
600
40
400
30
20
200
10
0
0
-10
-200
0
40
80
120
160
0
40
80
120
160
Figure 4.35: Shows the car simulation with a gear ratio of 1
The mass of the system is where a majority of the energy is being stored. This means
that adjusting the mass will most likely change the time constant. That is why reducing the mass
of race vehicles is so important, it allows for cars to get to their top speed much more quickly
than the more massive cars. Figure 4.36 shows the car simulation with a mass of 300 kg. The
max speed does not change as it is still 22.3 m/s but the maximum torque changed to 507.9 N*m.
This decrease in the maximum torque is due to the decreased amount of effort to move a less
massive object. Once again, the curves have not changed their shape, but the time constant has
been changed by a factor of five in the other direction. The car’s top speed does not change with
a decrease in mass because in steady state the torque from the motor is only countering the drag
on the car, which does not depend on the mass of the car.
mass.v
25
dC_Motor.support1.tau
600
500
20
400
15
300
10
200
5
100
0
0
-100
-5
0.0
2.5
5.0
0.0
2.5
Figure 4.36: Shows the velocity of the car and the torque from the motor for a mass of 300 kg
40
5.0
All of the factors in equation 3 will affect the drag, which affects the steady state torque
and the top speed of the car. Changing a parameter for the drag will allow the car to reach a
higher speed, which is a squared factor in drag. This is shown in Figure 4.37, where the frontal
area has been double to 4.4 m2. The higher frontal area reduces the max speed to 21.8 m/s with
the torque remaining at 625.6 N*m since the drag is still not a significant factor when the torque
is at its max. The steady state torque has almost doubled. Since the frontal area was doubled but
the maximum speed was reduced because of this the torque necessary to counter the drag in
steady state is not quite doubled. Similar effects would occur if the other drag parameters were
changed by the same factor.
dC_Motor.support1.tau
mass.v
25
600
20
15
400
10
200
5
0
0
-5
0
10
20
30
0
10
20
30
Figure 4.37: Shows the car's velocity and torque from the motor with a frontal area of 4.4 m2
Module F: Proton Exchange Membrane Fuel Cell (PEMFC)
The PEMFC is modeled as a current source based on the incoming flowrate of hydrogen
and the number of stacks in series. The voltage of each stack is approximately 72 volts. Later
verisions will take into account a limited current density at this voltage. The PEMFC also
includes a limiter of the current for when the load does not require the additional current. This
represents hydrogen not being used when the current is low.
41
system
defaults
g
const1
pin
const
const
k=99.99
product
k=1000*9648?
k=95
m_flow
port_a
const2
massFlow Rate
boundary
boundary
k=0
m
const3
sw itch1
division
division1
pin_n
integrator
k=.72
const1
ground
I
k=1
k=300
Figure 4.38: PEMFC model and test setup
simple_PEM.pin.i
-210
-220
-230
-240
-250
-260
0
1
2
3
4
5
6
7
8
9
10
Figure 4.39: Amperage of PEMFC calculated from mass flow rate of hydrogen. The more stacks
in series the lower the current and higher the voltage.
42
Task 5: Experimentation and Interpretation
Effect of PEMFC Voltage on Top Speed and Acceleration: As the voltage of the PEMFC a
higher voltage battery can be used. It is assumed that the voltage of the PEMFC is just above the
voltage of the battery so that the PEMFC can charge the battery. When the system's voltage is
higher the current to the motor is increased which affects acceleration and top speed.
Four
system voltages will be tested: 200 V, 300 V, 400 V, and 500 V PEMFC stacks each with a
comparable battery voltage.
Figures 5.1-5.4 show the velocity profiles for each voltage
respectively.
car.mass.v
40
30
20
10
0
0
10
20
30
40
50
60
Figure 5.1: Velocity profile of 1500 kg car with 200 V PEM stack. 0-60 mph is about 8.9
seconds. Top speed is about 46 m/s
43
car.mass.v
70
60
50
40
30
20
10
0
-10
0
10
20
30
40
50
60
Figure 5.2: Velocity profile of 1500 kg car with 300 V PEM stack. 0-60 mph is about 5.9
seconds. Top speed is about 60 m/s
car.mass.v
80
70
60
50
40
30
20
10
0
-10
0
10
20
30
40
50
60
Figure 5.3: Velocity profile of 1500 kg car with 400 V PEM stack. 0-60 mph is roughly in 4.2
seconds. Top speed is about 74 m/s
44
car.mass.v
80
60
40
20
0
0
10
20
30
40
50
60
Figure 5.4: Velocity profile of 1500 kg car with 500 V PEM stack. 0-60 mph is roughly in 3.6
seconds. Top speed is about 89 m/s
Clearly the system at 500 V is able to provide much more power to the motor than at 200 V.
Both acceleration and top speed of the 500 V PEMFC and battery are double that of the 200 V
system.
Effect of Cracker Catalyst Material on Mileage: A superior catalyst material is able to assist the
dissociation of ammonia at a faster rate and at lower temperatures. Four catalyst materials are
tested in this experiment: Pure nickel, Ni + Pt, Ni + Pd, and Ni + Ru. Figure 5.5 shows the
mileage of the car with different cracker catalyst materials.
45
Figure 5.5: Mileage in meters per kilogram of ammonia for different catalyst materials at steady
state
The Ni + Ru catalyst is the best performing catalyst which allows for operation of the cracker at
far lower temperatures around 200 K lower than the normal Ni catalyst. The mileage of the Ni +
Ru catalyst is 5.26% higher than the nickel catalyst.
Effect of Resistance of Motor Circuit and EMF constant on acceleration and top speed: The next
set of experiments illustrate the behavior of the model when the motor constants are varied. As
listed earlier, the resistance in the motor circuit and the EMF constant are two of the design
variables that affect the attributes of the model. The experiments focus on observing the effect of
changing motor constants on the torque of the motor and the time constant. Shown below are two
equations, 5.1 and 5.2, that will help to understand these changes. Equation 5.1 can be used to
calculate the torque of the motor while equation 5.2 can be used to calculate the maximum
angular speed of the motor or the speed of the motor at steady state.
𝜏= (
𝑅𝑏 − 𝑘 2
𝑘𝑉
)𝜔 +
𝑅
𝑅
46
(5.1)
where R is the resistance in the motor circuit, b is the damping coefficient, k is the EMF constant,
V is the voltage across the terminals of the motor and 𝜔 is the angular speed of the motor.
𝜔𝑚𝑎𝑥 =
𝑘2
𝑘𝑉
− 𝑅𝑏
(5.2)
Figure 5.6 shows the base case when the k, b and R are 1 Nm/A, 0.3 and 0.125 Ω. The velocity
of the car and the angular speed of the motor are plotted. The maximum speed of the car is 60
m/s.
car.mass.v [m/s]
250
car.dC_Motor.inertia.w [rad/s]
200
150
100
50
0
-50
0
50
100
Figure 5.6: Base case (k = 1; R = 0.125; b = 0.3)
The value of k is decreased to 0.1 while holding the R and b constant. Figure 5.7 shows the
resulting behavior of the model. The top speed is reduced to 32.7m/s while the time constant is
much larger which indicates the acceleration of the car is much lower as compared to the base
case.
47
car.mass.v [m/s]
120
car.dC_Motor.inertia.w [rad/s]
100
80
60
40
20
0
-20
0
100
200
300
400
Figure 5.7: Experiment (k = 0.1; R = 0.125; b = 0.3)
Next, the value of k is increased to 2 while holding the other parameters constant. Figure 5.8
shows the result. The top speed is reduced to 39.6m/s while the time constant is reduced
significantly which implies that the car accelerates much faster as compared to the base case.
This behavior can be explained using equation 5.2. The quadratic expression in the denominator
aids this kind of behavior.
car.mass.v [m/s]
200
car.dC_Motor.inertia.w [rad/s]
150
100
50
0
-50
0
20
40
60
Figure 5.8: Experiment (k = 2; R = 0.125; b = 0.3)
For each of the experiments discussed above, the motor torque can be plotted against time with
sole purpose of observing if there is a stall torque that affects the motor. Figure 5.9 shows the
behavior of the model for the base case when k is 1. The maximum torque for this scenario is
48
2218 Nm. The abnormality at t = 2 seconds just indicates the time at which the PEMFC starts
charging the battery.
car.mass.v [m/s]
2500
car.dC_Motor.support1.tau [N.m]
2000
1500
1000
500
0
-500
0
4
8
12
16
Figure 5.9: Base case (k = 1; R = 0.125; b = 0.3)
Figure 5.10 shows the torque plot for the first experiment when the value of k is reduced to 0.1.
In this case the plot suggests that there is stalling to a certain extent because the slope of the
graph is close to 0. Even after the PEMFC starts supplying current, the torque falls very slowly
implying that the speed of the motor is increasing very slowly. This is substantiated by the fact
stated earlier that the time constant for this case is small; as a result, the acceleration is slow. The
stall torque in this case is 25 Nm.
car.mass.v [m/s]
30
car.dC_Motor.support1.tau [N.m]
25
20
15
10
5
0
-5
0
4
8
12
Figure 5.10: Experiment (k = 0.1; R = 0.125; b = 0.3)
49
16
Likewise, the torque plot for second experiment where k is increased to 2 is plotted in Figure
5.11. The maximum torque in this case is 4346 Nm. The torque in the motor falls off quickly
because the angular speed of the motor increases quickly. The time constant for this case is much
smaller as compared to the base case which indicates that the car will reach its top speed quickly.
This behavior can be further substantiated using equation 5.1. An increase in the value of k will
increase the value of the torque.
car.mass.v [m/s]
5000
car.dC_Motor.support1.tau [N.m]
4000
3000
2000
1000
0
-1000
0
4
8
12
16
Figure 5.11: Experiment (k = 0.1; R = 0.125; b = 0.3)
The next experiment involves changing the resistance in the motor circuit. The resistance is
doubled to 0.25 Ω while k and b are held at 1 and 0.3 respectively. Figures 5.12 and 5.13 show
the results of this experiment for different time periods.
car.mass.v [m/s]
1200
car.dC_Motor.support1.tau [N.m]
1000
800
600
400
200
0
-200
0
4
8
12
Figure 5.12: Experiment (k = 1; R = 0.25; b = 0.3)
50
16
car.mass.v [m/s]
1200
car.dC_Motor.support1.tau [N.m]
1000
800
600
400
200
0
-200
0
50
100
Figure 5.13: Experiment (k = 1; R = 0.25; b = 0.3)
The maximum velocity reached in this case is 48.4 m/s which is lower that the velocity of the car
in the base case. Likewise, the maximum torque for this case is 1118 Nm which is again lower
than the base case. Equation 5.1 delineates this fact; as R is increased, the value of the torque
goes down.
Task 6: Lessons learned
One of the biggest lessons we learned was how only a few of our possible variables affect
our parameters. Initially the tanks volume and pressure were to be considered as variables to
possibly affect mpg, acceleration, and/or top speed. During the experimental stage we found this
not to be as significant as we had originally hoped. Even more surprising was the fact that the
length and diameter of the ammonia cracker also did not change these parameters significantly.
This was surprising as we thought changing the applicable volume and surface area for the
ammonia to be heated would greatly affect the system, but unless extreme values were chosen
these effects were minimal. We concluded that it was thanks to the controls that regulated the
valves that decided how much ammonia was being input and how much hydrogen was burning
to fuel the reaction. If the volume flow rate was too large these controls could just reduce the
flow of ammonia or increase the amount of hydrogen burning. Reducing the input kept the
system approximately the same. In addition, even if a larger input of ammonia was present, this
51
cracked more hydrogen and therefore made more available to the burner to keep the temperature
high. This helped us focus on what parts were actually useful for optimizing our system with
mpg, acceleration, and top speed in mind.
This is how we decided on our new design variables of the number of PEM’s in a stack,
the catalyst material, the motor’s stall torque, and the motor’s maximum angular velocity. The
number of PEM’s in a stack determines the voltage of the system which was found to be very
significant in our design parameters. The catalyst material determines what temperature the
cracking process occurs efficiently at. Due to this, the cracker can operate at a lower temperature
with similar hydrogen production, and since less would be necessary for the burner, more is
available for the PEM, and therefore the motor will receive more current. Finally, the motor is
the part of the system that actually translates electrical forces into mechanical. Due to this,
variations in the motor characteristics have a particularly powerful effect on the performance of
the vehicle and this was proven in some of the experiments that took place.
In our experimentation we learned what was actually affecting our system and to what
extent. This greatly improved our level of knowledge of the system and would affect decisions
on how we would do the project if we were to do it again. If we were to do the system again, we
would most likely put more attention to the motor, whereas until now we just treated it as some
constant that was almost irrelevant since it was not initially part of the focus of our project,
merely a means to translate our hydrogen fuel cell into a meaningful model of a car. In addition,
the experimentation revealed some issues with the cracker that were previously unknown.
Therefore, recreating the cracker with the idea of keeping it more robust would be one of the first
priorities of the new system.
References
1.
George Thomas and George Parks, "Potential Roles of Ammonia in a Hydrogen Fuel
Economy", United States Department of Energy (2006)
52