i
ROTARY STEAM ENGINE:
Viability of the SpinDyne Shields Engine
Allgood, David
Bass, Brent
Buck, Jesse
Diaz, Christian
Ewa, Kenneth
Gillispie, Shane
Hargett, Michael
Hinson, Dylan
Labonte, Jonathan
Lawrence, Andre
Spruill, Franklin
MAE 435
Final Report
Dr. Sebastian Bawab
06 MAR 2014
ii
Table of Contents
Abstract……….…………………………………………………………………………….…..…1
Introduction…..……………………………………………….………………………………...…2
Methods….……………………………………………………………………………………...…4
Boiler/Heat Exchanger…………………………………………………………………….4
Engine…………………………………………………………………………….……….5
Combustion…………………..……………………………………………………………6
Condenser/Pump…………………………………………………………………..………7
Finite Element Analysis…………………………………………………………………...8
Results……………….…………………………………………………………..…………….…..9
Discussion…….…………………………………………………………………………………...9
References……….……………………………………………………………………………….11
Appendix……….………………………………………………………………………………...13
Figures…………………………………………………………………………...…….…13
Gantt Chart…...…………………………..………………………………………………19
Budget…...…………………………………………………………………………..…...20
Programs....……………………………………………………………………..………..21
Equations…………………………………………………………………………..……..33
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List of Figures
Figure 1. PV Diagram……………………………………………………………………………13
Figure 2. SpinDyne's Rotary Steam Engine.................................................................................. 13
Figure 3. Flow Chart of the Complete Engine System…..…..………..………………………....14
Figure 4a. Open Cell Metal Foam.................................................................................................14
Figure 4b. Closed Cell Metal Foam…….………………………….………...………………..…14
Figure 5. Results from Combustion Program………..…………………………………….…….15
Figure 6. Graphs of Combustion and Condenser Program…...…..……….……………………..15
Figure 7. Results of Condenser Program…………..……………………….……………………16
Figure 8. Combustion Results for Diesel…………..……………………….……………………16
Figure 9. Cost of Selected Fuels……….…………..……………………….……………………17
Figure 10. Engine Results……………….………..……………………….………..……………17
Figure 11. Engine Graphical Results………………..…………………….…………..…………18
Figure 12. Gantt Chart………………………………………………………………………..….19
Figure 13. Budget………………………………………………………………………...…..….20
1
ABSTRACT
SpinDyne has introduced a new design of a rotary steam engine that will be expected to
compete with the current efficiency and emission standards of the modern combustion engine.
Analysis of the engine must be done to determine if it is viable replacement for the combustion
engine. A thermodynamic analysis of the engine is ongoing, assuming the engine runs on an
ideal Rankine cycle for initial estimates, and a second analysis will be performed assuming nonideal conditions. A study of the combustor and the effect of various fuels on heat input were also
completed. A thermodynamic analysis of the condenser, pump, and heat exchangers will be
done. For a complete analysis, there will also be a finite element analysis done to determine
critical stress areas.
2
INTRODUCTION
The steam engine was invented in the 1700’s by James Watt. The engine cut fuel
consumption by 75% creating a practical solution to energy problems and has been used in
nearly every imaginable industry [1]. Steam engines use heat to convert the working fluid
(water) into steam where it is then converted from thermal energy to mechanical power. The
steam engine is a major contributor to the American Industrial Revolution. Steam powered ships
and cars were in existence during the early 1900s, however, this technology has not been directly
applied to vehicular propulsions since [2]. The first rotary steam powered machine was built in
1760, merely designed to pump water out of coal mines [3]. Following this invention, several
successive modifications and patents were made to improve its efficiency and design. In 1804,
the design of a high-pressure, non-condensing steam engines was introduced and used to power
the first amphibious vehicle [4]. This design broke the configuration of the steam engine into
individual modules with working components independent of one another; this particular
configuration has come to be the most widely acceptable method in steam engine design.
The internal combustion engine such as gasoline, diesel and gas turbine engines replaced
the steam engine in most industrial and automotive industries. The internal combustion engine
was a more compact method for providing motive force and was more user friendly than steam
engines of the time. Internal combustion engines require a specifically refined fuel and led to a
number of harmful emissions. Carbon emissions (carbon monoxide and carbon dioxide) from
internal combustion engines was among the leading causes of greenhouse gases from 1960-2008
[5]. Limiting carbon-based fuel usage by use of steam power is a plausible reality in personal
transportation. Already used in some power plants, steam powered engines use gaseous water
(steam) as the working fluid instead of carbon-based fuel [6]. This need for greater fuel
efficiencies and cleaner fuel options are driving the transportation industry in new directions.
The new direction could result in the resurgence of steam powered vehicles in the future. By out
fitting a rotary steam engine to operate on superheated steam instead of fossil fuels, it would help
reduce fuel consumption of nonrenewable resources and ultimately decreases harmful emissions.
Certain advances in material technology may make a modern steam engine feasible in today’s
environmentally conscious society. Decreasing the size, while increasing the efficiency, and
burning of cleaner fuels such as natural gas and bio-fuels could revolutionize the modern steam
engine [7][8]. To carry out a viability study of the SpinDyne rotary steam engine, analysis of the
following subsections were undertaken: the rotary steam engine itself, the boiler/heat exchanger,
the combustion and the condenser/pump.
In the past, the efficiency of the steam engine was limited by design type, manufacturing
capabilities, available fuel, lubrication requirements, and limited knowledge of material science
[9]. Some major concerns such as weight to power ratio, minimum component heat loss, and
temperature and pressure ranges need to be addressed. One of the problems with earlier design
was developing an engine case that behaved as an adiabatic component, without sacrificing the
weight to power ratio that results from adding heavier insulation around the case. A more
efficient thermal insulator such as aerogel [10] would be used.
A new approach will be introduced into our study whereby the engine would be treated as
a universal component within which all other components will be governed. Temperature,
3
pressure, and starting vane angle with corresponding cylindrical volume has been provided to us
as an initial starting point for which other values will be derived. Assuming the engine is treated
as an ideal isothermal and adiabatic system, a Matlab (Mathworks, Natick, MA) program will be
used to calculate all other initial values such as specific volume, enthalpy, and entropy. With
these values, using the laws of thermodynamics and the ideal gas law, a relationship between the
initial volume and final volume of the fluid in the system can be used to calculate desired values
at the final state. Finally, the end state computations can be used to calculate the required work,
torque, and horsepower. However, these calculations will need to be adjusted due to the
particular engine design. SpinDyne’s rotary steam engine operates on a two-cycle expansion
process per revolution, meaning that steam is injected into the expansion chamber, expanded,
and then exhausted four times per revolution [6]. This expansion allows for shaft power to be
created.
Another problem with older steam engines was the need for oil pumps to deliver oil to the
bearings without creating a need to separate the oil from the fluid. SpinDyne’s solution is to use
oil-less lubricant capable of operating at very high temperatures with little to no metal-to- metal
contact. Using gas foil bearings works ideally in this aspect [11]. All other moving components
within the engine will be coated with a newly discovered material known as BAM (BoronAluminum Magnesium). BAM has an extremely hard surface with an almost frictionless
characteristic that allows for a decrease in mechanical breakdown resulting from extended usage,
to optimize engine performance [12]. This material is a key piece that will allow modern day
steam engine to become reality.
This boiler/heat exchanger subcomponent of the steam generation cycle is the point
where the system absorbs heat from the combustion process and begins the phase change from
liquid water to steam. Previous research has shown that scaling on the heat exchanger tubes
caused by accumulation of combustion materials will decrease boiler efficiency and tube life
over long periods of time [13]. For this reason, the Lamont boiler will be used due to its’ vertical
construction which allows for reduced scaling. This particular boiler system was selected due to
its very high heat absorption rates, its relatively small size, and inexpensive and lightweight
tubing [14]. Failure to prevent heat loss in the boiler was a problem with older steam systems.
With improved knowledge in material science, heat loss in the boiler component can be reduced
using the aerogel thermal insulator without sacrificing overall boiler structure and size [15].The
incoming feed water is preheated using the exhaust gas exiting the boiler [16]. Increasing the
temperature of the feed water reduces the amount of energy required to generate steam, and
therefore, increasing the boiler efficiency. Once the steam is generated, before it gets to the
engine to begin the expansion phase, it passes through a series of heat exchangers that
continually heats the steam until the optimal superheated state is reached.
Currently, some power plants use steam as the working fluid instead of carbon-based
fuels [6]. However, power plant usage of steam engines required a combustion chamber to
produce the energy, or heat, needed to initiate the phase change from water into steam (the
combustion chamber used carbon-based fuels to generate the required energy, thereby limiting
the carbon emissions, not eliminating them) [6]. Research has been done on the combustion of
fuels, which allows for a vast knowledge of fuel properties. The rotary steam engine plans to be
powered by the combustion of a combination of different fuels simultaneously. The type of
4
useable fuels are liquid propane, gas, biomass derived gases (BDG), and various other liquid or
gaseous fuels. Each carbon-based fuel has a reaction that requires energy to initiate, termed the
heat of reaction. Also, energy is released along with the products, termed heat of combustion.
Most carbon-based fuels are exothermic and so if the energy released from the combustion is
greater than the energy required to initiate combustion, than they are effective in generating
positive net energy which comes out as heat. This heat will be used to generate steam.
Each gas has a different chemical makeup which allows specific fuels to burn hotter,
faster, and longer [17]. This along with many other fuel properties will allow for a certain fuel or
combination of fuels to be selected as the most efficient. A comprehensive Matlab program will
be created and used to model the combustion process. This program will be designed to test the
effectiveness of combined fuel versus a singular fuel to generate values of thermal energy input,
flame temperature, and fuel to air ratios. This program can then be directly applied to the steam
system allowing for instantaneous selection of the proper fuel. This type of optimization program
has been previously created and used in industry for power generation. Not only will the
programs decrease fuel consumption, which ultimately decreases overall cost, but will also
reduce the carbon footprint of the system as a whole [18]. The program will allow for the best
selection of fuel for the required need of the engine, thus improving the efficiency of the burner
and the engine simultaneously.
No steam engine cycle works without a condenser. The second law of thermodynamics
required all heat engines to reject heat in order to complete a full thermodynamic cycle. The
condenser serves this purpose by behaving as a continuous cycle, allowing the steam rejected
from the engine to be cooled and condensed before being pumped and re-introduced back to the
boiler. The operating pressure should be as low as possible; having the condenser operate in a
vacuum would be ideal, and would improve the thermal efficiency of the overall cycle [19]. The
amount of heat rejected can be determined from the enthalpies of the steam entering and exiting
the condenser [20].
The design of the condenser itself should accommodate the amount of heat that must flow
out of it. Calculating the heat transfer coefficients, the convection from the steam, and the heat
conduction through the condenser walls was used in certain Rankine cycle models to design
earlier condensers [21]. This design should also be optimized by balancing the heat transfer
surface area against the pressure drops caused by the larger area [22]. The use of special
materials, like metal foam, can be used to increase heat transfer, at the cost of higher-pressure
drops [23].
METHODS
Boiler/Heat Exchanger
Completed Method
The boiler converts incoming feed water to saturated steam. The super-heater further
heats the saturated steam to the temperature required for use in the engine. Beginning with an
ideal thermodynamic approach to the steam boiler and super-heater, modeled as a Rankine steam
cycle, the thermodynamic state of the incoming feed-water was identified. Determining the water
5
temperature (T) and pressure (P) allows for identifying the enthalpy (h), entropy (s) and specific
volume (v) of the incoming feed water from thermodynamic tables. Assuming the boiler to be
adiabatic with steady state flow and neglecting changes in kinetic and potential energy, and using
the first law of thermodynamics for a control volume, determine the exit state of the saturated
steam leaving the boiler was determined (1). Using the heat input from the burner and the first
law equation, the exit enthalpy was also found as well as the exit temperature by assuming
constant specific heat (Cp0) (2). Once exit temperature was known, the remaining
thermodynamic properties were found from saturated steam tables. By knowing the desired
temperature and pressure of the superheated steam for use in the engine, the amount of heat
needed was determined by applying the first law.
Proposed Method
Once ideal conditions are known, determining a reasonable thermal efficiency of the
boiler and superheater is next as well as using the calculated thermal efficiency to find the actual
thermodynamic properties of the saturated and superheated steam.
Engine
Completed Method
Using various assumptions such as reversible adiabatic, negligible kinetic and potential
energy, knowing initial thermodynamic state of the superheated steam entering the engine, and
the volume of each process—intake, expansion, exhaust—a Matlab code was created to simulate
the system (Prog.1). First, the steam entering the intake valve was modeled as a transient
process with isobaric and isothermal conditions. With such a simple assumption state one was
defined and all thermodynamic properties were obtained. As the valve closed the steam was
allowed to expand in a fixed volume. Assuming that there was steady pressure variations and
knowing the initial and final volume and the specific volume at each sub-state of expansion the
mass can be found. A while loop was used to collect and store all thermodynamic properties
using XSteam (Magnus Holmgren, www.x-eng.com) within a vector and the pressure decreased
and entropy stayed the same for each cycle. To end the while loop, state two and state one are
used to compare error of mass and if the mass error is less than the user specified error the loop
exits and state two is locked. As the now wet steam was allowed to exit through the exhaust, the
transient process again was assumed to be isobaric and isothermal. This will lock in state three
and now all thermodynamic properties were defined within the engine.
Once all properties were known the work of each process can be found. For the two
transient processes of the intake and exhaust, the work can be found using the known pressure
and volume difference for each given state. To find the work of the expansion process the substates are plotted on a Pressure vs. Specific Volume diagram and by finding the area under the
curve was calculated using the trapezoidal rule (Fig. 1). This area can be checked using the
internal energy difference between states one, two, and multiplying the now known mass. Once
all work can be found for each process and taking in account of the number of process happening
per revolution, the power can be found by summing all the total work per revolution and
multiplying by the design parameter for omega in revolution per second. This power can be
6
converted to horsepower so it can be comparable to other engines. If the shaft angular velocity is
known, then torque can be estimated. Finally, mass flow rate can be estimated using the total
mass entering at each intake process per revolution and multiplying by omega.
Since the Matlab code was written as a function a second code was allowed to utilize it
and vary parameters so horsepower and torque can be graphed and various other parameters
tabulated for a range of conditions.
Combustion
Completed Method
A combination of fuels was combusted to create the energy that is used to power the
rotary steam engine (Fig. 2). The first step of the combustion analysis process was to select
which fuels were going to be used. The majority of the fuels selected were hydrocarbon-based
fuels; however the engine will run on almost anything. The type of useable fuels are liquid
propane, gas, kerosene, biomass derived gases (BDG), and various other liquid or gaseous fuels.
Each fuel has its individual chemical properties, which need to be documented prior to
performing a combustion analysis. These properties are the number of moles of hydrogen,
carbon, and oxygen, heating values (enthalpy of formation), flame (combustion or burning)
temperature, laminar burning velocity [17], gas constants, molar mass, and combustion
efficiency.
A Matlab program was created to model the combustion process. This program allows
the user to select specific quantities of a combination of different fuels (Prog. 2). The program
will intake known data (listed above) on each fuel and then simulate the combustion of these
fuels and return required quantities such as heat transfer, burning efficiency, and flame
temperature. If a combination of fuels is used the program will combine the fuels based on their
mass fraction and create 1 mole of a single fuel to analyze. Depending on the ratio of fuel to air
(FA), the program will run through a combination of for and if loops to test if the combustion is
burning with excess fuel, stoichiometric, or excess air conditions. Each time a test is satisfied,
the program, uses the Newton-Raphson method and a single equation involving the change in
enthalpy and solved constants to find the combustion temperature of each specific fuel [25].
The second Matlab program created was able to compute fuel usage in miles per gallon,
excluding mass of the vehicle, in this case a semi-truck and trailer, and the drag on the vehicle
(Prog. 3). In this ideal case, the miles per gallon were measured using the minimum and
maximum possible flame temperatures, ranged in increments of twenty-five Kelvin. The
minimum and maximum temperature were determined from the initial conditions given from
SpinDyne and the limits of the boiler, respectively.
Proposed Method
The program will be used to complete a cost feasibility study to determine which fuels
will be best for their engine. The cost feasibility study will consist of the prices per gallon of
each selected fuel and the data obtained from the Matlab program (Prog. 3). By comparing the
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miles per gallon of the fuels with the price per gallon of each fuel, we will determine the best
fuel.
Condenser/Pump
Completed Method
An injection pump was used to transfer the saturated fluid from the condenser to the preheater tubes so it can be reused to generate steam in the boiler. The saturated liquid from the
outflow of the condenser flows to a buffer tank. The tank is used to stage a specific volume of
fluid to ensure the pump does not run dry. From the buffer tank, the injection pump increases the
pressure of fluid and transfers it to the pre-heater tubes (Fig. 3).
A computer program was created using Matlab to model the injection pump performance.
The program is based on an ideal thermodynamic process that used known pump inflow
conditions to produce the pump work input with the desired pump outflow pressure. The ideal
process is assumed to be isentropic, with Steady-State Steady-Flow, single inflow/outflow, and
neglected changes in kinetic and potential energy. Given these assumptions the program used the
1st Law of Thermodynamics (1) to perform operations that solve for the pump work input.
Combining the 1st Law and 2nd Law of Thermodynamics (2), (3), the program performs
operations to solve for the pump efficiency. A sub program call to XSteam was used to obtain
values from the thermodynamic steam tables.
The program works by entering the pump inflow conditions, fluid temperature and
pressure, and the desired outflow pressure. The entered data is processed through XSteam to
obtain values for the enthalpies and specific volumes. The steam table values are then used in the
program to solve for the pump work and efficiency.
Proposed Method
Using the data produced by the performance model, a plot will be created to model the
pressure difference across the pump for several inflow/outflow conditions. The data will be
analyzed to have a better understanding of the pump performance, and compared to the fluid
pressure needed to provide continuous flow of the saturated fluid back to the pre-heater tubes
and boiler. From the analysis a consumer pump will be chosen based on performance criteria,
cost, and availability.
Once the injection pump analysis is complete we will assist in the condenser design based
on the condenser performance criteria. The use of special material called metal foam is being
considered for the condenser design [26]. There are two types of metal foams, an open cell metal
foam (Fig. 4a), and a closed cell metal foam (Fig. 4b). The final condenser design will be based
on the overall performance criteria, condenser size, cost, and availability. Using the design
proposed by SpinDyne in Fig 9, the dimensions and materials of the fins and tubing will be
determined, and used to find the heat transfer out of the condenser based on its design ,and adjust
the design to meet the needs of the engine.
8
Finite Element Analysis
Proposed Method
To carry out a Finite Element Analysis (FEA) of the rotor of SpinDyne’s steam engine,
Nastran/Patran (MSC Software Corporation, Newport Beach, CA) will used for modeling. First,
a geometric computer aided drafting (CAD) model that was designed and created by the
company was supplied. Using the CAD model supplied, in order for proper analysis, a
designated amount of finite element mesh seeds will be used on each surface so as to define the
amount of mesh elements needed [31]. The more mesh elements that a surface has increases the
accuracy of the analysis. After the mesh elements are generated and optimized, the material
properties such as, Elastic Modulus, Poisson’s Ratio, Density, and thickness, will be supplied to
the program.
Before beginning analysis, load cases will be defined, the first of which are the boundary
conditions as well as the calculated torque values ranging from 300 – 990 ft.lb. In order for the
geometric model to be considered as not floating in mid-air, there has to be one fixed point or
edge for proper analysis. With careful design and the specific generation of mesh elements, the
analysis will carried out to determine maximum stress and deflections under the supplied
conditions.
9
RESULTS
The results were simplified for the ideal case of a thermodynamic cycle powered by a
combustion process, meaning that most losses associated with an actual cycle were ignored. The
ideal cycle ran at four stages: stage one, condenser exit/pump inlet; stage two, pump exit/boiler
inlet; stage three, boiler exit/turbine inlet; and stage four: turbine exit/condenser inlet. The
program returns the Y ratio, the flame temperature (also the temperature out of the boiler), and
the Fuel-to-air ratio along with the heat into the boiler (Q high, on both a kJ/kmole and kJ/kg
basis), the mass flow rate (kg/s), the heat out of the condenser (Q low on kJ/kg basis) (Fig. 5,
Prog. 2). The Q high value was determined from the combustion process. The program also
returned two graphs, “Flame Temperature (Tp) versus Y ratio (Y/Ycc)” and “Mass Flow Rate
versus Y ratio (Y/Ycc) (Fig. 6).”
After using non adiabatic combustion equations to solve for the heat transfer from the
fuel to the working fluid. The mass flow rate of fuel was found from the ratio of heat transfer
from the water and from the fuel. Using this fuel consumption for the rotary steam engine was
found based on a range of entrance engine conditions. We performed an analysis on diesel and
the results were promising (Fig. 8). A cost analysis was done showing each fuel and their
respective price (Fig.9). We still are in the process of selecting the best fuel based on
performance, price, accessibility, and ease of transportation but diesel seems to be a front runner.
The engine model continues to improve with further iterations. For a single bore at
nominal entrance conditions of 800 psia and 718 F° we are creating 70.572 horsepower with
370.64 ft-lb of torque on a the four inch rotor design (Fig. 10). SpinDyne plans to use at least two
or three cores so the power and torque output with be proportional to numbers of cores used.
The input conditions for the condenser, at 7.25 psia and 178 degrees Fahrenheit, are not
covered for XSteam, and had to be computed by hand. The resulting heat rejection QL was 95.25
BTU/s. Assuming an isentropic process for the pump under these conditions, it was determined
that at least .39 HP was required to pump the water back to the boiler pressure. The pump
recommended by SpinDyne was determined to be insufficient for use in the system, as its
maximum operational temperature was much lower than 178 degrees calculated for the pump.
DISCUSSION
The purpose of this project is to conduct a viability study of SpinDyne's rotary steam
engine design. While the boiler, condenser, and combustion process will be important in the
system, the engine is the main point of focus. The engine will need to be capable of producing
power equivalent to that of a modern automobile using only dry steam.
While the preliminary results were not specifically engine based, it was necessary to
ensure certain engine parameters were theoretically realistic to obtain. One result obtained thus
far using numerical methods, was the flame temperature of fuel combustion. Depending on the
fuel used and controlling the fuel-to-air ratio, the ideal case can estimate the maximum flame
10
temperature which will be important for the heat transfer model of the heat exchangers inside
boiler.
There are possible issues with the condenser design itself. While the use of metal foam
would produce a greater heat transfer due to the increased area, one issue have been identified.
There is a possibility of the metal foam restricting the flow of the steam, and causing the system
to back up. This issue will have to be addressed before the condenser design can be finalized.
There are a few limitations to this project. One of the most important limiting factors of
the engine will be the slider that separates the two expansion chambers. If this slider fails, it will
interfere with the rotation of the rotor causing possible engine failure. Another limiting factor
will be the pump which will pump water from the condenser to the boiler. If the difference in
pressure is too great, there may not be a consumer available pump to do the required work. A
final limitation that will affect the project will be if the engine does not produce enough
theoretical power comparable to a modern automobile. This occurrence will prove that
SpinDyne's engine design is not viable.
In the future of this project, we will have a complete ideal model of the engine that will
be capable of estimating maximum power output based on the calculated thermodynamic
properties. With these ideal maximums, we will be able to estimate actual operating conditions
required to drive the system cycle. If the engine does not expand the dry steam to a stage of
small amounts of wet steam, the engine timing will be adjusted and if that does not solve the
issue an additional means of expansion may need to be investigated. After all possibilities that
will be considered, a condenser, pump, heat exchangers, and boiler dimensions will be obtained.
Finally a final report stating our findings and recommendations will be constructed and presented
to SpinDyne at the conclusion of the project.
11
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04844
J. Wang, M. Wang, M. Li, J. Xia, and Y. Dai. (2013, Apr.). Multi-objective optimization
design of condenser in an organic Rankine cycle for low grade waste heat
recovery using evolutionary algorithm. International Communications in Heat
and Mass Transfer [Online].45, pp. 47-54. Available:
http://www.sciencedirect.com.proxy.lib.odu.edu/science/article/pii/S07351933130
00845
M. Odabaee and K. Hooman.(2011. Aug.). Application of metal foams in air-cooled
condensers for geothermal power plants: An optimization study. International
Communications in Heat and Mass Transfer[Online]. 38, pp. 838-843.Available:
http://www.sciencedirect.com.proxy.lib.odu.edu/science/article/pii/S07351933110
0073X
http://www.sciencedirect.com.proxy.lib.odu.edu/science/article/pii/019689049490
0361
2012, pp. 6 17-671.
A. Taylor, “ME Power Systems Theory and Design”, 2013,
http://www.mem.odu.edu/faculty_staff/taylor/mae411/handout1.pdf
A. Hernadez, “Combined Flow and Heat Transfer of Characterization of Open Cell
Aluminum Foils’” University of Puerto Rico, Mayaquez Campus, Puerto Rico,
2005.
C. H. Lee, K. C. Jiang, P. Jin, and P. D. Prewett, "Design and fabrication of a micro
Wankel engine using MEMS technology," Microelectronic Engineering, vol. 73–
74, pp. 529-534, 6// 2004.
13
APPENDIX
Figures
Figure 1. PV Diagram
Figure 2. SpinDyne's Rotary Steam Engine
14
Figure 3. Flow Chart of the complete Engine System
Figure 4a. Open Cell Metal Foam
Figure 4b. Closed Cell Metal Foam
15
Figure 5. Results from Combustion Program
Figure 6. Graphs of Combustion and Condenser Program
16
Figure 7. Results of Condenser Program
Flame Temperature versus Miles per Gallon (Ideal)
12
11.8
11.6
MPG
11.4
11.2
11
10.8
10.6
10.4
800
850
900
950
1000
1050
1100
1150
Flame Temperature, Tp Fahrenheit
Figure 8. Combustion Results for Diesel
1200
1250
17
Results:
UNITS:
NG (Methane)
Propane
Gasoline(Octane)
Ethanol
Biodiesel(20%)B2
Diesel
Price
$/Gallon or GGE
2.05
2.96
3.45
3.04
4.02
3.91
Figure 9. Cost of Selected Fuels
Figure 10. Engine Results
18
Figure 11. Engine Graphical Results
19
Figure 12. Gantt Chart
20
Costs
Labor
Total Workers = 11
Finite Element Analysis Program
Microsoft Office
MATLAB Program
Contingency
Total:
Days - From Sept 3rd
Completed
Total
Budget
Estimated days Est. hours Est. Pay Damage
22
8
$25/hour $4400/person
days/person hours/day
$48,400
$4,000
$400
$100
$500
$53,400
Final Report Budget Analysis
September
October November December
27
31
27
31
27
31
30
31
Labor Per Group
Engine
Combustion Heat Exchangers Pump
# Workers
3
2
3
3
Total per Group$13200
8800
13200 13200
January February
March
31
28
31
28
April
5
31
0
14
Rotary Steam Engine Status as of March 5th, 2014
80.71748879
36000
40500
75.84269663
60.00%
182
78.11158798
36400
40900
1.009876543
400
52877.75061
53000
0.968992248
100
90
81%
80
76%
78%
% Actually Spent:
% Work Completed:
70
Percent
% To have been spent:
Spent Labor:
Total Expenses:
% Actually Spent:
Tasks Completed:
Actual Days
% Work Completed:
Earned Labor:
Earned Expenses:
CPI (Cost Performance Index)
CV (Cost Variance)
FCAC (Forecasted Cost at Completion
FCAC (Forecasted Cost at Completion
TCPI (To-Complete Performance Index)
60
50
40
30
20
10
0
% To have been spent:
Figure 13. Budget
Total
180
223
21
Program 1. Engine Analysis
%
Assumputions
%
Constant rpm, Steady pressure variations
%
mass is constant->m1=m2, rev. adiabatic -> s1 constant
% Engine Parameters: P1 = 800 psia, T1 = 718.2ºF, V1 = .0013715 ft3
%
V2 = 0.074867 ft3 rpm = 1000 rpm
%Ve = 0.000144675926 ft3
%Common input:
%
SteamEngine(800,.0013715,.074867,.25,2)
%P1 - Steam pressure entering intake
%V1 - Volume of steam at beginning of expansion (intake closed)
%V2 - Volume of steam at end of expansion (exhaust about to open)
%Pdiv - Pressure division difference (P1 - Pdiv = P1a) [0.1<Pdiv<1.3]
%
a big Pdiv will be unsteady expansion but
%
a small Pdiv will create longer processor times and
%
may create additional error
%error - the precent error of the initial mass and final mass
function [Total_Hp Torque P1 Pm mdot T T2] = SteamEngine(P1,V1,V2,Pdiv,error)
global omega
omega = 1000;
T = XSteamUS('Tsat_p',P1) + 200;%
Uses pressure to find saturation
%
temperature and adds a number for
%
superheated conditions
[Pm vm hm um Hp mdot T2] = Expansion(P1,T,V1,V2,Pdiv,error);
%
Work for Transient process-%
assuming Pave is small between Pi and P1 then Pi = P1
Work = P1*V1*195.2378;% Psia-ft3 \\ 1 Psi-ft3 = 195.2378 Joules ->
J/transient-rev
Total = Work*4; %
Joules/rev
TotalPower = Total*omega/60; %
J/rev * Rev/min * min/sec = J/sec = Watt
Hp2 = TotalPower/745.699872; % Watt * 1 Hp/745.699872 Watt -> Hp/core
%
Work for Exhausting process
Ve = 0.000144675926; % ft3---Hardcorded Last 10 degrees differential Volume
Work = Pm(length(Pm))*Ve*195.2378;
Total = Work*4; %
Joules/rev
TotalPower = Total*omega/60;
Hp3 = TotalPower/745.699872;
Total_Hp = Hp + Hp2 + Hp3;
%
Torque ratio 1:1
Torque = Total_Hp*5252/omega; %
end
5252 is conversersion factor for Hp and rpm
%
Assumptions: negiable kinetic and potential energy
function [Pm vm hm um Hp mdot T2] = Expansion(P1,T1,V1,V2,Pdiv,error)
global omega
% [...]m - desinates expansion values
h1 = XSteamUS('h_pT',P1,T1);
s1 = XSteamUS('s_pT',P1,T1);
v1 = XSteamUS('v_pT',P1,T1);
u1 = XSteamUS('u_pT',P1,T1);
Cp = XSteamUS('Cp_ps',P1,s1);
22
Cv = XSteamUS('Cv_ps',P1,s1);
m1 = V1/v1;
hm(1) = h1; vm(1) = v1; um(1) = u1;
Tm(1) = T1; Pm(1) = P1;
i = 2; itr = 0; ea = 100;
while error < ea & itr < 10000
hm(i) = XSteamUS('h_ps',P1-Pdiv,s1);
vm(i) = XSteamUS('v_ps',P1-Pdiv,s1);
um(i) = XSteamUS('u_ps',P1-Pdiv,s1);
Tm(i) = XSteamUS('T_ps',P1-Pdiv,s1);
m2 = V2/vm(i);
ea = abs(m2 - m1)/m1 * 100;
P1 = P1 - Pdiv;
Pm(i) = P1;
i = i + 1;
itr = itr + 1;
end
n = Cp/Cv;
const = Pm(1)*vm(1)^n; %PV^n = const -> const/V^n = P
Pp = const./vm.^n;
hold on
plot(vm,Pm)
plot(vm,Pp,'r--')
xlabel('Volume (ft3)');
ylabel('Pressure (Psi)');
legend('Adiabtic Expansion Process','Polytropic Expansion Process')
hold off
T2 = Tm(length(Tm))
P2 = Pm(length(Pm))
m2
m1
ea
X = XSteamUS('vx_ps',P2,s1)
%Mass flow rate
mdot = m2*4*omega/60; %
lbm/massEnter-rev * mass-Enter * rev/min * min/sec
= lbm/s
%Polytropic Work (Bad model approximation)
%Polytropic_Work = ( Pm(length(Pm))*V2 - Pm(1)*V1)/(1-n);
%Polytropic_work = m2*Polytropic_Work*195.2378; % 1 Psi-ft3 = 195.2378 Joules
% Adiabtic_Work = m2*trapz(vm,Pm)*195.2378; %trapizodial rule checks!
Work_check = (um(1)-um(length(um)))*m2*1.055056*1000; % J/expansion-rev
Total = Work_check*4; % Based on four total expansions a rev-> J/rev
Power = Total*omega/60; %
J/rev * Rev/min * min/sec = J/sec = Watt
Hp = Power/745.699872; %
Watt * 1 Hp/745.699872 Watt -> Hp/core
end
Program 2. Combustion and Condenser Program
%% SpinDyne Viability Initial Program
%% Computing Q high - Heat into the boiler
clear;clc
23
format shortg
%naturalgas
%fill in
%gasoline
%fill in
%diesel,
%fill in
%n-butane,
%Hrpl -2622800
%Hrpg -2644200
%Mfuel=58;
%propane, C3H8
%Hrpl -2016900
%Hrpg -2032800
%Mfuel=44;
%ethalalcohol,
%Hrpl -814460
%Hrpg -851840
%Mfuel=32;
%hydrogen
%Methane
%Hrpl 0
%Hrpg -797570
%Mfuel=16;
Tr = 298.16; % Kelvin
j = 1;
y=1;
n=0;
% while i<=3
%
if j == 1
%
mc(j) = input('Enter Moles of Carbon: ');
%
mh(j) = input('Enter Moles of Hydrogen: ');
%
mo(j) = input('Enter Moles of oxygen: ');
%
HrpFuel(j)= input('Enter The enthalpy of combustion value as a
gaseous negative #: ');
%
Mfuel(j) = input('Enter The molar mass of the fuel: ');
%
Molfrac(j) = input('Enter The mole fraction of the fuel: ');
%
elseif j == 2
%
mc(j) = input('Enter Moles of Carbon: ');
%
mh(j) = input('Enter Moles of Hydrogen: ');
%
mo(j) = input('Enter Moles of oxygen: ');
%
HrpFuel(j)= input('Enter The enthalpy of combustion value as a
gaseous negative #: ');
%
Mfuel(j) = input('Enter The molar mass of the fuel: ');
%
Molfrac(j) = input('Enter The mole fraction of the fuel: ');
%
elseif j == 3
%
mc(j) = input('Enter Moles of Carbon: ');
%
mh(j) = input('Enter Moles of Hydrogen: ');
%
mo(j) = input('Enter Moles of oxygen: ');
%
HrpFuel(j)= input('Enter The enthalpy of combustion value as a
gaseous negative #: ');
%
Mfuel(j) = input('Enter The molar mass of the fuel: ');
24
%
%
%
%
%
%
%
%
%
%
%
% end
Molfrac(j) = input('Enter The mole fraction of the fuel: ');
end
if i <=3
another=input ('Would you like to enter another fuel? y/n :');
if another == y
i=y;
elseif another == n
i=4;
end
end
j = j+1;
mc(1) = 3;
mh(1) = 8;
mo(1) = 0;
HrpFuel(1) = -2032800;
Mfuel(1) = 44;
Molfrac(1) = 1;
Mair = 28.97;
% Given combustion efficiency
Combeff = .95;
% Calculate Q high
%for l=1:3
Qhmol = abs(Combeff*HrpFuel(1)/1000) % kJ/kmol
Qh = Qhmol/Mfuel(1) % kJ/kg
%end
%% Combustion Process
Hrp = HrpFuel(1);
mc = mc(1);
mh = mh(1);
mo = mo(1);
% constants
CO2A1 = 56835; CO2A2 = 93048;
CO2B1 = 66.27; CO2B2 = 68.58;
CO2C1 = -11634.0; CO2C2 = -16979.0;
COA1 = 299180; COA2 = 309070;
COB1 = 37.85; COB2 = 39.29;
COC1 = -4571.9; COC2 = -6201.9;
H2OA1 = 88923; H2OA2 = 154670;
H2OB1 = 49.36; H2OB2 = 60.43;
H2OC1 = -7940.8; H2OC2 = -19212.0;
O2A1 = 43388; O2A2 = 127010;
O2B1 = 42.27; O2B2 = 46.25;
O2C1 = -6635.4; O2C2 = -18798.0;
N2A1 = 31317; N2A2 = 44639;
N2B1 = 37.46; N2B2 = 39.32;
N2C1 = -4559.3; N2C2 = -6753.4;
% Hrp(Tr) = [hco+1/2ho2-hco2]
25
HrpTr=282800;
% Equation: hT = A + BT + Cln(T)
hTrH2O=H2OA1+H2OB1*Tr+H2OC1*log(Tr);
hTrN2=N2A1+N2B1*Tr+N2C1*log(Tr);
hTrCO=COA1+COB1*Tr+COC1*log(Tr);
hTrCO2=CO2A1+CO2B1*Tr+CO2C1*log(Tr);
hTrO2=O2A1+O2B1*Tr+O2C1*log(Tr);
% Y ratio
Ycc = mc+mh/4+mo/2;
Ymin = Ycc-mc/2;
Yrat = Ymin/Ycc;
Tp1 = Tr+1;
tol = 1.e-6;
max = 100;
% Y=Yrat*Ycc;
% N1 = 2*(Ycc-Y);
% N2 = 2*(Y-Ymin);
% N3 = Mh/2;
% N4 = 3.76*Y;
% fn='Hrp+N1*(HrpTr+COA1+COB1*Tp+COC1*log(Tp)hTrCO)+N2*(CO2A1+CO2B1*Tp+CO2C1*log(Tp)hTrCO2)+N3*(H2OA1+H2OB1*Tp+H2OC1*log(Tp)hTrH2O)+N4*(N2A1+N2B1*Tp+N2C1*log(Tp)-hTrN2)';
%
gn='N1*(COB1*Tp+COC1)/Tp+N2*(CO2B1*Tp+CO2C1)/Tp+N3*(H2OB1*Tp+H2OC1)/Tp+N4*(N2
B1*Tp+N2C1)/Tp';
disp('
Y ratio
Flame Temperaute(K)
f(FA)')
Tp=Tp1;
n=0;
j=1;
%This program utilizes XSteam to find the inlet and outlet enthalpies of
%steam, and uses it to calulate Ql.Credit for XSteam goes to Magnus Holgrem
%of www.x-eng.com
for i=j:1:14
%
if Yrat==.68
%
Y=Yrat*Ycc;
%
fn='Hrp+N1*(HrpTr+COA2+COB2*Tp+COC2*log(Tp)hTrCO)+N2*(CO2A2+CO2B2*Tp+CO2C2*log(Tp)hTrCO2)+N3*(H2OA2+H2OB2*Tp+H2OC2*log(Tp)hTrH2O)+N4*(N2A2+N2B2*Tp+N2C2*log(Tp)-hTrN2)';
%
gn='N1*(COB2*Tp+COC2)/Tp+N2*(CO2B2*Tp+CO2C2)/Tp+N3*(H2OB2*Tp+H2OC2)/Tp+N4*(N2
B2*Tp+N2C2)/Tp';
%
N1 = 2*(Ycc-Y);
%
N2 = 2*(Y-Ymin);
%
N3 = Mh/2;
%
N4 = 3.76*Y;
%
while abs(eval(fn)) > 1.e-6 %Newton-Raphson
%
Tp=Tp1;g1=eval(gn);
%
Tp=Tp1;f1=eval(fn);
%
Tp2=Tp1-f1/g1;
%
[Tp1,Tp2];
26
%
%
%
%
%
%
%
%
%
Tp1=Tp2;
Tp=Tp1;
n=n+1;
f=eval(fn);
[n f];
end
T(j)=Tp;
j=j+1;
Yrat = .8;
if Yrat==Ymin/Ycc
for Yrat=Ymin/Ycc:.1:.9
Y=Yrat*Ycc;
fn='Hrp+N1*(HrpTr+COA2+COB2*Tp+COC2*log(Tp)hTrCO)+N2*(CO2A2+CO2B2*Tp+CO2C2*log(Tp)hTrCO2)+N3*(H2OA2+H2OB2*Tp+H2OC2*log(Tp)hTrH2O)+N4*(N2A2+N2B2*Tp+N2C2*log(Tp)-hTrN2)';
gn='N1*(COB2*Tp+COC2)/Tp+N2*(CO2B2*Tp+CO2C2)/Tp+N3*(H2OB2*Tp+H2OC2)/Tp+N4*(N2
B2*Tp+N2C2)/Tp';
N1 = 2*(Ycc-Y);
N2 = 2*(Y-Ymin);
N3 = mh/2;
N4 = 3.76*Y;
while abs(eval(fn)) > 1.e-6 %Newton-Raphson
Tp=Tp1;g1=eval(gn);
Tp=Tp1;f1=eval(fn);
Tp2=Tp1-f1/g1;
[Tp1,Tp2];
Tp1=Tp2;
Tp=Tp1;
n=n+1;
f=eval(fn);
[n f];
end
T(j)=Tp;
fa(j) = 1/(4.76*Yrat)*(Mfuel/Mair);
%This program utilizes XSteam to find the inlet and outlet
enthalpies of
%steam, and uses it to calulate Ql.Credit for XSteam goes to
Magnus Holgrem
%of www.x-eng.com
P3=800*0.06894775729;% convert kpsi to psi to bar
T3=Tp-273.15; % convert from Kelvin to Celsius
h3=XSteam('h_pt',P3,T3);
s3=XSteam('s_pt',P3,T3);
P4=5*0.06894775729;s4=s3;
h4=XSteam('h_ps',P4,s4);
wt=h3-h4;
P1=P4;
h1=XSteam('hL_p',P1,0);
s1=XSteam('sL_p',P1);
s2=s1;
%h2=h3-Qh
h2=XSteam('h_ps',800,s2);
qL(j)=h1-h4;
wp=h1-h2;
wn(j)=wt-wp;
27
qh(j)=wn(j)-qL(j);
m(j) = Qh/qh(j);
QL(j) = qL(j)*m(j);
Wn(j) = wn(j)*m(j);
fprintf('\t%4.10f
\t%4.10f
j=j+1;
\t%4.10f \n',Yrat,T(j),fa(j))
end
Yrat=1;
elseif Yrat == 1
Y=Ycc;
fn='Hrp+N1*(HrpTr+COA2+COB2*Tp+COC2*log(Tp)hTrCO)+N2*(CO2A2+CO2B2*Tp+CO2C2*log(Tp)hTrCO2)+N3*(H2OA2+H2OB2*Tp+H2OC2*log(Tp)hTrH2O)+N4*(N2A2+N2B2*Tp+N2C2*log(Tp)-hTrN2)';
gn='N1*(COB2*Tp+COC2)/Tp+N2*(CO2B2*Tp+CO2C2)/Tp+N3*(H2OB2*Tp+H2OC2)/Tp+N4*(N2
B2*Tp+N2C2)/Tp';
N1 = 0;
N2 = mc;
N3 = mh/2;
N4 = 3.76*Y;
while abs(eval(fn)) > 1.e-6 %Newton-Raphson
Tp=Tp1;g1=eval(gn);
Tp=Tp1;f1=eval(fn);
Tp2=Tp1-f1/g1;
[Tp1,Tp2];
Tp1=Tp2;
Tp=Tp1;
n=n+1;
f=eval(fn);
[n f];
end
T(j)=Tp;
fa(j) = 1/(4.76*Yrat)*(Mfuel/Mair);
%This program utilizes XSteam to find the inlet and outlet enthalpies
of
%steam, and uses it to calulate Ql.Credit for XSteam goes to Magnus
Holgrem
%of www.x-eng.com
P3=800*0.06894775729;T3=Tp-273.15;
h3=XSteam('h_pt',P3,T3);
s3=XSteam('s_pt',P3,T3);
P4=5*0.06894775729;s4=s3;
h4=XSteam('h_ps',P4,s4);
wt=h3-h4;
P1=P4;
h1=XSteam('hL_p',P1,0);
s1=XSteam('sL_p',P1);
s2=s1;
%h2=h3-Qh
h2=XSteam('h_ps',800,s2);
qL(j)=h1-h4;
wp=h1-h2;
wn(j)=wt-wp;
qh(j)=wn(j)-qL(j);
m(j) = Qh/qh(j);
QL(j) = qL(j)*m(j);
28
Wn(j) = wn(j)*m(j);
fprintf('\t%4.10f
\t%4.10f
\t%4.10f \n',Yrat,T(j),fa(j))
j=j+1;
Yrat = 1.1;
elseif Yrat == 1.1
for Yrat = 1.1:.1:2
Y=Yrat*Ycc;
fn='Hrp+N1*(HrpTr+COA2+COB2*Tp+COC2*log(Tp)hTrCO)+N2*(CO2A2+CO2B2*Tp+CO2C2*log(Tp)hTrCO2)+N3*(H2OA2+H2OB2*Tp+H2OC2*log(Tp)hTrH2O)+N4*(N2A2+N2B2*Tp+N2C2*log(Tp)-hTrN2)+N5*(O2A2+O2B2*Tp+O2C2*log(Tp)hTrO2)';
gn='N1*(COB2*Tp+COC2)/Tp+N2*(CO2B2*Tp+CO2C2)/Tp+N3*(H2OB2*Tp+H2OC2)/Tp+N4*(N2
B2*Tp+N2C2)/Tp+N5*(O2B2*Tp+O2C2)/Tp';
N1 = 0;
N2 = mc;
N3 = mh/2;
N4 = 3.76*Y;
N5 = Y-Ycc;
while abs(eval(fn)) > 1.e-6 %Newton-Raphson
Tp=Tp1;g1=eval(gn);
Tp=Tp1;f1=eval(fn);
Tp2=Tp1-f1/g1;
[Tp1,Tp2];
Tp1=Tp2;
Tp=Tp1;
n=n+1;
f=eval(fn);
[n f];
end
T(j)=Tp;
fa(j)=1/(4.76*Yrat)*(Mfuel/Mair);
%This program utilizes XSteam to find the inlet and outlet
enthalpies of
%steam, and uses it to calulate Ql.Credit for XSteam goes to
Magnus Holgrem
%of www.x-eng.com
P3=800*0.06894775729;T3=Tp-273.15;
h3=XSteam('h_pt',P3,T3);
s3=XSteam('s_pt',P3,T3);
P4=5*0.06894775729;s4=s3;
h4=XSteam('h_ps',P4,s4);
wt=h3-h4;
P1=P4;
h1=XSteam('hL_p',P1,0);
s1=XSteam('sL_p',P1);
s2=s1;
%h2=h3-Qh
h2=XSteam('h_ps',800,s2);
qL(j)=h1-h4;
wp=h1-h2;
wn(j)=wt-wp;
qh(j)=wn(j)-qL(j);
m(j) = Qh/qh(j);
QL(j) = qL(j)*m(j);
Wn(j) = wn(j)*m(j);
29
fprintf('\t%4.10f
j=j+1;
\t%4.10f
\t%4.10f \n',Yrat,T(j),fa(j))
end
end
end
Yrat = [Ymin/Ycc .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0]';
T=[T]';
f=[f]';
m=[m]';
QL=QL';
Wn=Wn';
flow_values = [Yrat m QL Wn]
figure(1)
plot(Yrat, T)
xlabel('Y/Ycc');
%axis([.68 2 1700 2700])
ylabel('Tp - Adiabatic Flame Temp')
grid on
title('Tp vs Y/Ycc')
%xlswrite('Propulsionsystemshw3.xls',YratvsT,'Tp vs f','C1');
figure(2)
plot(Yrat, m)
xlabel('Y/Ycc');
ylabel('mass flow rate, kg/s');
grid on
title('Mass Flow Rate vs Y/Ycc');
Program 3. Combustion Corrections and Adjustments
%% corrections
%
%
%
%
%
P = 800 psi
T2 = 718 F
Flame Temperature 800:1400
Y is fixed at Ycc
Combustion Equation is written on the basis of "each one kmol of fuel
clear;clc
format shortg
%gasoline C8H18
%Hrpl -5047800
%Hrpg -5089100
%Mfuel=114
%roe = 703.00 kg/m^3
%Diesel, C12H23
%roe = 832.00 kg/m^3
%Biodiesel B20,Later
%fill in
%Propane, C3H8
30
%Hrpl -2016900
%Hrpg -2032800
%Mfuel=44;
%Ethalalcohol, C2H5OH
%Hrpl -814460
%Hrpg -851840
%Mfuel=32;
%Methane/Natural Gas CH4
%Hrpl 0
%Hrpg -797570
%Mfuel=16;
Tr = 298.16; % Kelvin
j = 1;
y=1;
n=0;
% while i<=3
%
if j == 1
%
mc(j) = input('Enter Moles of Carbon: ');
%
mh(j) = input('Enter Moles of Hydrogen: ');
%
mo(j) = input('Enter Moles of oxygen: ');
%
HrpFuel(j)= input('Enter The enthalpy of combustion value as a
gaseous negative #: ');
%
Mfuel(j) = input('Enter The molar mass of the fuel: ');
%
Molfrac(j) = input('Enter The mole fraction of the fuel: ');
%
elseif j == 2
%
mc(j) = input('Enter Moles of Carbon: ');
%
mh(j) = input('Enter Moles of Hydrogen: ');
%
mo(j) = input('Enter Moles of oxygen: ');
%
HrpFuel(j)= input('Enter The enthalpy of combustion value as a
gaseous negative #: ');
%
Mfuel(j) = input('Enter The molar mass of the fuel: ');
%
Molfrac(j) = input('Enter The mole fraction of the fuel: ');
%
elseif j == 3
%
mc(j) = input('Enter Moles of Carbon: ');
%
mh(j) = input('Enter Moles of Hydrogen: ');
%
mo(j) = input('Enter Moles of oxygen: ');
%
HrpFuel(j)= input('Enter The enthalpy of combustion value as a
gaseous negative #: ');
%
Mfuel(j) = input('Enter The molar mass of the fuel: ');
%
Molfrac(j) = input('Enter The mole fraction of the fuel: ');
%
end
%
if i <=3
%
another=input ('Would you like to enter another fuel? y/n :');
%
if another == y
%
i=y;
%
elseif another == n
%
i=4;
%
end
%
end
%
j = j+1;
% end
mc(1) = 12;
31
mh(1) = 26;
mo(1) = 0;
HrpFuel(1) = -7310000;
Mfuel(1) = 170.336;
Molfrac(1) = 1;
roe(1) = 832;
%Ethalalcohol, C2H5OH
%Hrpl -814460
%Hrpg -851840
%Mfuel=32;
Mair = 28.97;
% Given combustion efficiency
Combeff = .95;
% Combustion Process
Hrp = HrpFuel(1);
mc = mc(1);
mh = mh(1);
mo = mo(1);
roe = roe(1);
% constants
CO2A1 = 56835; CO2A2 = 93048;
CO2B1 = 66.27; CO2B2 = 68.58;
CO2C1 = -11634.0; CO2C2 = -16979.0;
COA1 = 299180; COA2 = 309070;
COB1 = 37.85; COB2 = 39.29;
COC1 = -4571.9; COC2 = -6201.9;
H2OA1 = 88923; H2OA2 = 154670;
H2OB1 = 49.36; H2OB2 = 60.43;
H2OC1 = -7940.8; H2OC2 = -19212.0;
O2A1 = 43388; O2A2 = 127010;
O2B1 = 42.27; O2B2 = 46.25;
O2C1 = -6635.4; O2C2 = -18798.0;
N2A1 = 31317; N2A2 = 44639;
N2B1 = 37.46; N2B2 = 39.32;
N2C1 = -4559.3; N2C2 = -6753.4;
% Hrp(Tr) = [hco+1/2ho2-hco2]
HrpTr=282800;
% Equation: hT = A + BT + Cln(T)
hTrH2O=H2OA1+H2OB1*Tr+H2OC1*log(Tr);
hTrN2=N2A1+N2B1*Tr+N2C1*log(Tr);
hTrCO=COA1+COB1*Tr+COC1*log(Tr);
hTrCO2=CO2A1+CO2B1*Tr+CO2C1*log(Tr);
hTrO2=O2A1+O2B1*Tr+O2C1*log(Tr);
% Y ratio
% Assuming Y = Ycc
32
Ycc = mc+mh/4+mo/2;
% Heat transfer needed to heat up the water/steam using SteamTab program
% (55.158 bar)
h2 = 3139.16; % based off of initial conditions and steam tables
h1 = 344.016; % based off of estimate of temperature of 178 F
mw = 0.052213; % based off of mass flow rate from the engine
Qdotw = mw*(h2-h1) % kW
i=1;
j=1;
for T = 700:25:925 % 1200 Farenheit = 922.0389 Kelvin, the max temp of the
boiler
hTpCO2(i) = CO2A1 + CO2B1*T + CO2C1*log(T);
hTpH2O(i) = H2OA1 + H2OB1*T + H2OC1*log(T);
hTpO2(i) = O2A1 + O2B1*T + O2C1*log(T);
hTpN2(i) = N2A1 + N2B1*T + N2C1*log(T);
%Y(j)=(-Hrp-Mc*(hTpCO2(i)-hTrCO2)-Mh/2*(hTpH2O(i)-hTrH2O)+15.5*(hTpO2(i)hTrO2))/((hTpO2(i)-hTrO2)+3.76*(hTpN2(i)-hTrN2));
Qf1(i) = Ycc*((hTpO2(i)-hTrO2)+3.76*(hTpN2(i)-hTrN2));
Qf2(i) = (-Hrp-mc*(hTpCO2(i)-hTrCO2)-mh/2*(hTpH2O(i)hTrH2O)+Ycc*(hTpO2(i)-hTrO2));
Qf(i) = Qf1(i)-Qf2(i);
mf(i) = abs(Qdotw/Qf(i)); % kg/kmol-s -> fuel is based on 1 kmol of fuel,
so kmol/s
mfnew(i) = mf(i)*Mfuel; % kg/s
%f1(j) = 1/(4.76*Ycc)*(142/28.97);
i = i+1;
j=j+1;
end
T = ([700,725,750,775,800,825,850,875,900,925]-273.15)*(9/5)+32;
mflow = (mfnew./roe).*(264.172*3600);
mpg = 55./mflow % 55 mph/ (gallons/hr) -> miles per gallon
figure(1)
plot(T, mpg)
grid on
title('Flame Temperature versus Miles per Gallon (Ideal)')
xlabel('Flame Temperature, Tp Fahrenheit')
ylabel('MPG')
Wdotnet = [61.246, 65.910,
70.572,75.232,79.891,83.258,87.916,92.572,97.226,101.88,106.53,111.17,115.82,
120.46,123.82,128.46,133.10,137.74,
142.37,147.00,151.63,156.25,160.88,165.50,170.12,174.12,179.34,183.95,188.56]
.*(745.699872/1000);
Wdotnet'
th_eff = Wdotnet./Qdotw;
th_eff'
for i = 1:1:10
denom = abs(mf(i)*Hrp);
com_eff = Wdotnet./denom;
com_eff'
i=i+1;
end
33
Equations:
1st Law of Thermodynamics, where h2 – h1 = v (P2 – P1)
2nd Law of Thermodynamics
1.
2.
wp = h2 – h1
s2s = s1
3.
wp =
4.
Specific enthalpy
5.
Specific internal energy
6.
Specific Volume
7.
Using the relationship between volume and specific volume
8.
Conservation of Mass equation ṁ = mė + mi, Mass/Volume/Specific volume relation =
9.
Idea gas (v1 )
10.
Steady state, uniform flow
v(P2−P1)
np
Pump Work Input, where efficiency = np = ( h2s – h1) / (h2 – h1)
k−1
v
2
h−hfg
hg − hf
v − v1
v2 − v1
=
Qin + ∑ mi (hi +
=
hsat − hf
u − u1
u2 − u1
=
hg − hf
=
usat − u1
u2 − u 1
vsat − v1
v2 − v1
V1
V2
P2
Vi
2
1
+ gzi ) = ∑ė m (ui +
Wout
12.
S=(rc)2µNP
13.
µNP≥1.7(10−6)
14.
ƒ=2π2µNPrc
15.
s=πpsrc33µl'(1+1.5ϵ2)
16.
∆T=2πJρCpWNƒr3µl'(1+1.5ϵ2)πρrc3
17.
h2 - h1 = Cp0(T2-T1).
Vi
2
1
+ gzi ) + Wout
(ui − hi ) , ignoring potential and kinetic energy.
v
= v1
P1
11.
=
,
2
V
v