Fuel Economy of a Turbocharged, Single-Cylinder,Four-Stroke Engine

by

Colleen McCoy

Submitted to the Department of Mechanical Engineeringin Partial Fulfillment of the Requirements for the Degree of

Bachelor of Science in Mechanical Engineering

at the

Massachusetts Institute of Technology

June 2017

MASSACHUSETTS INSTITUTEOF TECHNOLOGY

JUL 2 5 2017

LIBRARIES

2017 Colleen McCoy. All rights reserved. ARCHIVES

Signature redactedSignature of Author: ..........................

C ertified by : ....................................

eparttnedft of Mechanical EngineeringMay 22, 2017

Signature redacted.Amos Winter

Assise fessor of Mechanical EngineeringThesis Supervisor

SignatureC ertified by : .....................................

The author hereby grants to MT permission toreproduce and to distribute publicly paper andelectronic copies of this thesis document inwhole or in part in any medium now known orhereafter created.

redacted

Rohit KarnikAssociate Professor of Mechanical Engineering

Undergraduate Officer

1

...

Fuel Economy of a Turbocharged, Single-Cylinder,Four-Stroke Engine

by

Colleen McCoy

Submitted to the Department of Mechanical Engineeringon May 22, 2017 in Partial Fulfillment of the

Requirements for the Degree of

Bachelor of Science in Mechanical Engineering

ABSTRACT

Agriculture is the main source of livelihood for a majority of India's population.However, despite the number of workers, the yield and the yield of principal crops in India ismuch lower than that in developed nations. One of the reasons for this is the lack of farmingmechanization in India. One of the common ways to run farming equipment is by using a single-cylinder, four-stroke diesel engine. Diesel engines can be turbocharged in order to make themmore efficient for less cost. A method has been found to turbocharge a single-cylinder dieselengine by adding an air capacitor to form a buffer between the intake and exhaust strokes. Thisthesis analyzes how the size and heat transfer of the air capacitor for this turbocharged dieselengine are correlated to engine performance and fuel economy. According to the modeledengine, a 3.0 liter capacitor had better peak power and fuel economy at high loads and speedsthan a 2.4 or 1.25 liter capacitor. Additionally, forced convection cooling on the capacitor usinga fan allowed the intake air density to increase, and the engine to have better fuel economy thanthe . However the peak power and fuel economy of the modeled naturally aspirated engine wasbetter than the turbocharged engine for speeds below 2500 rpm. The general trends from themodel were reflected in the experimental data. The forced convection increased cooling, andimproved the intake air density. However, it was difficult to make any confidentrecommendations about the fuel economy based on the experimental data.

Thesis Supervisor: Amos Winter

Tile: Assistant Professor of Mechanical Engineering

3

Table of ContentsABSTRACT .................................................................................................................................... 3

Acknowledgm ents ........................................................................................................................... 4

L ist o f F ig u res ................................................................................................................................. 7

L ist o f T ab le s .................................................................................................................................. 9

1. In tro d u ctio n ............................................................................................................................... 10

1. 1 Farm ing Power in India ..................................................................................................... 10

1.2 Fuel Econom y .................................................................................................................... 11

2. Background ............................................................................................................................... 13

2.1 Diesel Engines ................................................................................................................... 13

2.1.1 Fueling System ........................................................................................................... 14

2.2 Turbochargers .................................................................................................................... 14

2.2.1 Im provem ents for fuel economy and cost .................................................................. 15

2.2.2 Turbocharged Engine Use .......................................................................................... 16

2.3 Turbocharging a single-cylinder engine ............................................................................ 17

2.4 Goals of Research .............................................................................................................. 18

3. Computer M odeling .................................................................................................................. 19

3.1 Air Capacitor Size .............................................................................................................. 19

3.2 Tem perature Effects ........................................................................................................... 19

3.2.1 Air Capacitor Cooling Systems ................................................................................. 20

3.2.2 Forced Convection Cooling ....................................................................................... 24

3.3 Ricardo W AVE Engine M odels ......................................................................................... 25

3 .3 .1 C o o lin g ...................................................................................................................... 2 6

3.3.2 Density Gain ............................................................................................................. 27

3.3.3 Peak Power ................................................................................................................ 29

3.3.4 Fuel Consumption ..................................................................................................... 31

4. Experim ental Design ................................................................................................................. 35

4.1 Existing Setup ................................................................................................................... 35

4.2 Fuel Consumption M easurem ent ...................................................................................... 36

4.3 Experim ental Procedure .................................................................................................... 39

5. Results & Analysis .................................................................................................................... 41

5.1 Tem perature ...................................................................................................................... 41

5

5.2 Density Gain ...................................................................................................................... 43

5.3 Fuel Consum ption.............................................................................................................. 44

5.4 Error Analysis .................................................................................................................... 46

6. Conclusion & N ext Steps.......................................................................................................... 48

Appendices.................................................................................................................................... 50

Appendix A: Calculating the Air Temperature Drop due to Geometry or MaterialChange p .......................................................................................... 50

Appendix B: Forced Convection Heat Transfer M odel................................................. 53

Appendix C: Carbon Balancing Method for Fuel Consumption .................................. 55

Bibliography ................................................................................................................................. 56

6

List of Figures

Figure 1: Farm power and foodgrain yield in India from 1951-2010........................................... 11

Figure 2: Illustration of the diesel engine cycle from Encyclopedia Britannica [7]................. 13

Figure 3: Operation of a turbocharger, figure from LS 1 Tech [9]............................................ 15

Figure 4: Diagram of an experimental turbocharged single-cylinder diesel engine, using an aircapacitor to act as a buffer between the exhaust and intake strokes.......................................... 17

Figure 5: Graph of the modeled temperature drop in 6.5 inch, cylindrical, steel and aluminum aircapacitors, with volumes varying from 0.4-3.5 liters. ............................................................. 23

Figure 6: Temperature of the air exiting the small (1.25L) air capacitor for cases with forcedconvection cooling using a fan, natural convection, and a naturally aspirated baseline case....... 26

Figure 7: Graph of the density in the capacitor vs. speed for the small capacitor, the largecapacitor, and naturally aspirated cases ..................................................................................... 27

Figure 8: Maps of the percent air density gain compared to the naturally aspirated case for thelarge capacitor turbocharged case, for both natural and forced convection cases.................... 28

Figure 9. Bar graph of the intake air density increases for small, medium, and large capacitors,for natural and forced convection cases..................................................................................... 29

Figure 10: Brake power of the engine vs. speed, for an air-to-fuel ratio of 55......................... 30

Figure 11: Brake power of the engine vs. speed, for an air-to-fuel ratio of 19.......................... 30

Figure 12: Fuel economy map for the turbocharged engine with the medium air capacitor, withforced convection cooling............................................................................................................. 32

Figure 13: Brake-specific fuel consumption for the turbocharged engine with the mediumcapacitor for both forced and natural convection cooling, at high loads (air-fuel ratio of 25)..... 33

Figure 14: Bar graph of the percent improvement in BSFC for each case compared to naturallyaspirated for high loads (air-fuel ratio of 25) and high speeds (3500rpm). .............................. 34

Figure 15: Experimental setup. Panel A is the full setup with the engine, dynamometer,turbocharger, and air capacitor. Panel B is the turbocharged engine with the fan for forcedcon vection co olin g ........................................................................................................................ 3 5

Figure 16: Small, medium, and large air capacitors used for the experiment. ......................... 36

Figure 17: Graph of fuel consumption using carbon balancing vs. flowmeter measurements..... 39

7

Figure 18: Map of the non-dimensionalized temperature drop across the air capacitor............ 41

Figure 19: Map of percent density gain of the intake air over all loads and speeds for theturbocharged, medium capacitor case, with and without cooling............................................. 44

Figure 20: Comparison of the experimental and modeled BSFC for the medium capacitor no fancase, from 3000-3600rpm , and 6-7.6 kW of power...................................................................... 45

Figure 21: Experimental BSFC map for the medium capacitor, fan and no fan conditions......... 46

Figure 22: Block diagram of the fueling circuit and flowmeter placement............................... 48

8

List of Tables

Table 1: Overall heat transfer coefficients for three different sized capacitors using naturalconvection and forced convection models................................................................................. 24

Table 2: Capacitor diameter and lengths, and total buffer volume, including capacitor andm an ifo ld s....................................................................................................................................... 2 5

9

1. Introduction

1.1 Farming Power in India

Agriculture is the main source of livelihood for a majority of India's population.

However, despite the 263 million agricultural workers in the country, agricultural work in India

is far less productive than the numbers would suggest, and the yield of principal crops in India is

much lower than that in developed nations [1]. Only 15% of India's GDP comes from

agriculture, which is vastly disproportionate to the percentage of the country engaged in farming

[2]. A contributing to this issue is that farm mechanization is far less prevalent in developing

countries than in wealthier countries [1]. About 55% of the population of India works in

agriculture, compared to 2.4% of the U.S. population [1]. However, in India, only 40% of farm

work is mechanized, compared to 95% in the U.S [1]. Around 84% of the farms in India are

classified as "small and marginal" [3]. The small size and minimal revenue of these farms

means that many of these farmers cannot afford the productivity-increasing farming equipment

that larger farms are able to use. The lack of efficient farming equipment has a negative impact

on the yield of a farm, and it has been shown that the agricultural productivity of a farm is

correlated to the farm power available, as shown in Figure 1 [3].

10

3.5

3

2.5

1.5

1

05

0

1.92

+u-FoodgrainYield (T/ha)

1.38-*-Farn Power

(Kw/Ha).023 1.66

.872

. 5

1951 1961 1971 1981 1991 2001 2010

Figure 1: Farm power and foodgrain yield in India from 1951-2010.

One of the common ways to run farming equipment is by using a single-cylinder, four-

stroke diesel engine. The market size for small diesel engines in India alone is 1-1.2 million

units per year [4]. These engines run equipment such as tractors, generators, and irrigation

pumps, which are vital to the production levels of the farm. If farmers are able to get more

power out of these engines, they will be able to get more output from their farms, and therefore

increase their profit. There are many ways that farmers could increase their power output,

including using bigger engines, adding more cylinders to their engines, or modifying their

engines to be mechanically supercharged. However, these additions can be very expensive,

decreasing the value the farmers would gain by having extra farm power in the first place.

Therefore, being able to use a method to increase power and efficiency of their single-cylinder

engines while still keeping the cost down is paramount.

1.2 Fuel Economy

In addition to increasing power output of an engine, costs can be lowered by improving

the fuel economy. According to a 2014 study by USHA International, the second most important

11

priority for farmers buying diesel engines was achieving a higher fuel efficiency [4]. The

average cost of diesel fuel in India increased from Rs 5 per liter to Rs 34.84 per liter in the 17

years from 1990-2006, greatly increasing the operational costs of running diesel engines [5]. In

order to offset the rising costs of fuel, farmers could put in systems to improve the efficiency of

their diesel engines by reducing diesel consumption per hour of use as well as increasing output

from the engine [5]. In 2010, researchers at the Institute for Resource Analysis and Policy in

Hyderabad, India, and the Department of Agricultural Economics, Institute of Agricultural

Sciences at Banaras Hindu University, studied the effects of the rising price of diesel on farmers

using well irrigation. They found that in the eastern plain region of Uttar Pradesh, India, and in

south Bihar, India, the rising cost of diesel over the sixteen year study had increased the cost of

well irrigation by 18% and 32% respectively, even while accounting for a 7% yearly inflation

[5]. A 2002 survey published in Economic and Political Weekly found that the unanimous top

challenge to the farming operation of over 2,600 tube well owners in India, Pakistan, Nepal

Terai, and Bangladesh was "energy cost and availability" [6]. While the need for power for

electric wells also accounts for many of these responses, the need for more cost-effective energy

from diesel engines is plainly a pressing concern, especially given the dramatic rise in diesel

prices.

12

2. Background

2.1 Diesel Engines

Diesel engines are compression-ignition engines, where air is compressed in the

combustion chamber to a sufficiently high pressure and temperature to ignite diesel fuel which is

injected into the cylinder. The four strokes of the diesel engine cycle are as shown in Figure 2.

First is the intake stroke, where the intake valve opens and the cylinder expands to draw fresh air

into the combustion chamber. For a naturally-aspirated engine, this air is taken in at atmospheric

pressure. Second is the compression stroke, where both the intake and exhaust valves are closed,

and the piston rises, compressing the air, and thus raising the temperature. As the piston

approaches the top dead center of the stroke, a small amount of fuel is injected into the chamber,

igniting and causing the pressure and temperature to rise more rapidly to combust all of the fuel.

The third stroke is the power stroke, which starts when the piston is at top dead center, and

continues as the high-pressure gases push the piston down and force the crankshaft to turn. This

stroke provides the mechanical work to turn the crankshaft for the output of the engine. Finally,

the fourth stroke is the exhaust stroke, when the exhaust valve opens and allows the spent air-

fuel mixture to leaving the combustion chamber.

intake valve fuel Injector exhaust valve

.. . ~ .I , .................

intake compression power exhaust

Figure 2: Illustration of the diesel engine cycle from Encyclopedia Britannica [7].

13

2.1.1 Fueling System

The fueling system for a compression-ignition engine is different than that for a spark-

ignition engine. Air alone is inducted into the cylinder, and fuel is injected directly into the

combustion chamber as the air is compressed. The amount of fuel injected into the cylinder

controls the load of the engine. At full load, the mass of fuel injected is about 5 percent of the

mass of air in the cylinder [8]. Once the fuel has been injected, the amount of fuel combusted

depends on the mass of air within the cylinder. More combustion means more power from the

power stroke of the engine.

2.2 Turbochargers

The amount of air that is available to combust in the cylinder dictates the amount of

power that an engine can produce. If an engine can compress more air into the combustion

chamber, it will be able to bum more fuel and produce more power than a naturally-aspirated

engine. Engines can be turbocharged in order to increase the amount of air entering the

combustion chamber per cycle. A turbocharger includes two components: a turbine and a

compressor (Figure 3). The high pressure, high temperature air from the exhaust of the engine

powers the turbine. This turbine is coupled with the compressor, such that the exhaust stream

that powers the turbine also spins the compressor. The compressor is connected to the intake

stream so that the air coming into the engine is compressed, allowing more air to enter the

combustion chamber.

14

COMPRESSOR TURBINEINLET EXHAUST

7-

NRF!- TURBINECOMPRESSOR INLET

DISCHARGE IN LE

INTAKE EXHAUSTCHARGER MANIFOLD MANIFOLD

AIR COOLER

ENGINE

Figure 3: Operation of a turbocharger, figure from LS 1 Tech [9].

2.2.1 Improvements for fuel economy and cost

Turbocharged engines have several advantages over naturally aspirated engines,

including increased fuel efficiency and power density and decreased cost [10]. Turbocharged

engines are more fuel efficient than similarly-rated naturally aspirated engines because they

experience less loss due from friction. This is because the turbocharger allows an engine with

fewer or smaller cylinders, and thus a smaller friction surface, to produce the similar power

levels as larger engines, but with higher power densities. Downsizing the engine by adding a

turbocharger typically reduces the weight of an engine by 10-15% for the same power output

[11]. Since the friction losses in small engines are significant compared to their low power

output, reducing the friction power is an important factor in improving fuel economy. A 2015

study by the Automotive Research Association of India compared the performance and

emissions of a two-cylinder naturally aspirated diesel engine, an upgraded two-cylinder

15

turbocharged, intercooled diesel engine of the same size, and a three-cylinder naturally aspirated

engine with similar power outputs. Their experiments found that the turbocharged and

intercooled engine power increased from 18.6 kW to 23 kW compared to the non-turbocharged

engine of the same size [11]. Turbocharging an engine to reach a certain power level also costs

less than adding a second cylinder. According to an original equipment manufacturer in India, a

turbocharger costs eighty percent less than adding a second cylinder [10].

2.2.2 Turbocharged Engine Use

Because of these advantages, turbocharging is widely used in commercially-available

engines. Today, most diesel engines are turbocharged due to the improved efficiency for the size

and cost [12]. However, despite its success in multi-cylinder engines, turbocharging is not used

in commercially-available single-cylinder engines. This is because of the phase mismatch

between the intake and exhaust strokes. Typically, turbocharged engines are designed with

multiple cylinders, each out of phase with the next, such that the exhaust stroke of one can power

the turbocharger to line up with the intake stroke of another. This method works for engines

with multiple cylinders, but runs into problems for single-cylinder engines, since the exhaust

stroke and intake stroke occur at different times. When the exhaust stroke powers the turbine

and the compressor, the intake valve is closed.

Another method to compress the intake air is supercharging, where the air compressor is

mechanically driven, rather than driven by the exhaust stream. Since supercharging does not rely

on the matching of exhaust and intake strokes, single-cylinder engines can be supercharged.

However, this is significantly more expensive than turbocharging and is inefficient for small

engines. Therefore, supercharging is not a good option for this application.

16

2.3 Turbocharging a single-cylinder engine

While turbocharged single-cylinder engines are not commercially available, a method has

been found to turbocharge a single-cylinder, four-stroke diesel engine by adding extra volume to

the intake manifold to smooth out the air flow between the exhaust and intake (Figure 4)

[10][13]. The added volume is subsequently referred to as an air capacitor. The air capacitor is

used to store and compress the air coming from the turbocharger, and then release it into the

combustion chamber during the intake stroke, creating a buffer between the exhaust and intake

strokes.

Intake Exhaustm*t Turbocharger

IntakeStream

ExhaustStream

AirCapacitor

Engine

Figure 4: Diagram of an experimental turbocharged single-cylinder diesel engine, using an aircapacitor to act as a buffer between the exhaust and intake strokes.

The added air capacitor increases the density of the intake air, successfully increasing the peak

power of the engine. Experiments have shown an intake density increase of 43%, and a power

increase of up to 29% for a cold start case, and up to 18% for a hot start case [14].

17

2.4 Goals of Research

The current experiment builds upon this study to determine the fuel economy of this

turbocharged, single-cylinder diesel engine. The goals of this thesis were to create a model to

analyze engine performance and fuel economy while varying air capacitor size and cooling, and

to run the physical experiment to compare the results with the model. The model was successful

at analyzing which air capacitors and cooling cases were better for different running cases.

However, there were significant errors in the experimental data collection, so the experimental

data provided mixed results. Many of the experimental errors were fixable, so future

experiments will address those errors.

18

3. Computer Modeling

3.1 Air Capacitor Size

Some important factors in the turbocharged engine performance include the air capacitor

size and cooling. The air capacitor size affects the intake air density and pressure drop, as well

as the fill time of the capacitor, so the capacitor must be small enough to minimize turbo lag, but

large enough not to experience a significant pressure drop during the intake stroke [14]. By

analyzing the pressure and volume of the capacitor and engine, it was found that the optimal air

capacitor volume to maintain the desired pressure throughout the intake stroke is about 5-6 times

the engine volume, or about 2.3 liters for a 0.4 liter engine [14].

3.2 Temperature Effects

The temperature of the intake air also affects engine performance. As the air is

compressed into the capacitor, the temperature increases due to the ideal gas law (Equation 3.1)

[15]. If the air inside the capacitor is cooled, the pressure inside the capacitor decreases,

allowing more air to enter, thus increasing the density of the air. The density of the air in the

capacitor due to the pressure and temperature is given in Equation 3.2. The change in density

due to the change in pressure in isotropic conditions is found by combining Equations 3.1 and

3.2 to get Equation 3.3. The higher the density of the intake air, the more fuel that can be burned

in the engine, and the more power that can be produced.

Y-1

(Pc\ Y

PO (3.1)

19

Pc (3.2)PC= RTC

Pc PC 1 (3.3)Po PO

The power is proportional to the density of the intake air, which, in turn depends on the

temperature of the intake air. Therefore, being able to cool the air in the air capacitor is

important in increasing the power density and thus fuel efficiency of the engine.

3.2.1 Air Capacitor Cooling Systems

In order for the cost-benefits from turbocharging the engine for better efficiency to pay

off, the construction of a capacitor and cooling system must be simple and cheap, yet effective.

While cooling mechanisms such as traditional intercoolers (cross flow heat exchangers which

work with larger turbochargers) or closed loop liquid cooling systems could be used to cool the

intake, these options are expensive, making them impractical for this application.

Some proposed ways to increase cooling of the air capacitor in cheaper ways included

changing the geometry of the capacitor to adjust wall thickness or surface area to volume ratio;

adjusting the material of the capacitor for a higher thermal conductivity; or adding fins. These

options were modeled in MATLAB to determine the approximate temperature drop due to the

changes in air capacitors.

The MATLAB model varied the air capacitor length and width and set the intake

pressure, temperature, and velocity (Appendix A). The convective heat transfer coefficient of

the air flowing through the capacitor was calculated using the Reynold's number and Nusselt

number (Equation 3.4) [15]. If the Reynold's number was less than 2300, the flow was laminar,

20

and the Nusselt number was calculated using Equation 3.5 [15]. If the Reynold's number was

greater than 2300, the flow was turbulent, and the Nusselt number was calculated using

Equations 3.6 and 3.7 [15]. The heat transfer coefficient was calculated using Equation 3.8 [15].

The convective heat transfer coefficient of the external air flowing across the capacitor was

calculated in a similar manner, using Equation 3.9 to calculate the Nusselt number [15].

(3.4)Re = p * v * Dc

P1

Nu = 3.66 +

D(0.66 ** Re *Pr)

(1 + 0.04* (D R *Pr) 2/3)

f = (0.79 log(Re) - 1.64)-2

N(* (Re - 1000) * Pr)Nu = ( 1/

(1 + 12.7 * * (Pr2 /3 - 1))

h= Nu * KairD

Nu = 0.664 * (Re'/2 * Pr'/3)

21

(3.5)

(3.6)

(3.7)

(3.8)

(3.9)

The thermal resistances of the capacitor from both convection and conduction were calculated,

and the total heat transfer found (Equations 3.10-3.14) [15]. The temperature drop across the

capacitor was then calculated using Equation 3.15.

(3.10)log (.)Rcylinder = 2T * kmetai * L

Rend cap -

Rconvection - (

ro - ri(27w * kmetai * (r 2

- D 2 )

1

h* (2rowL + 2w(r0 2 - D 2 3)

1+ (hi * (2ri7L + 2w(ri2 - D 2 ))

1Rtotai = Rconvection +

Rcylinder Rend cap

(Ti - TO)Rtotai

(3.13)

(3.14)

(3.15)Tdrop =

(V * Pout * Cp,air)

Since the heat transfer from a surface increases with area, the temperature drops for

capacitors with increasing surface area to volume ratio were calculated to determine if varying

22

(3.11)

(3.12)

the capacitor geometry would significantly change the temperature drop. Heat transfer also

increases with increasing thermal conductivity, so the results were also calculated for metals with

two different thermal conductivities - steel and aluminum - which have approximate thermal

conductivities of 50 and 205 W/mK respectively. The modeled results for a 6.5 inch-long

capacitor with volumes varying between 0.4-3.5L are shown in Figure 5. Neither the increased

surface area for the material for the capacitors significantly changed the temperature drop. The

maximum temperature drop was calculated to be 2.2 K, which only corresponds to a 1% increase

in density over the no heat transfer case, according to Equations 3.1-3.3. Since this corresponds

to a mere 1% engine power increase, to first order approximation, these adjustments are

negligible. Increasing the capacitor length and volume by a factor of six only drops the

temperature by another 2 K. Therefore, if keeping the air capacitor within the size limitations of

the engine, neither the surface area to volume ratio nor the capacitor material have a significant

effect on cooling, and were not explored further.

2.4

22.2 -

0

S2-

i 1.8 -

E

1.6

1.4

* Atmi capac citor*Aluminum capacitorl

0.1 0.2 0.3 0.4 0.5 - 0.6Capacitor radius over length [-]

Figure 5: Graph of the modeled temperature drop in 6.5 inch, cylindrical, steel andaluminum air capacitors, with volumes varying from 0.4-3.5 liters.

23

3.2.2 Forced Convection Cooling

Another way to increase the cooling is by forced air convection over the capacitor.

A MATLAB model was used to calculate the overall heat transfer coefficient due to the forced

convection from a small fan. The measured wind velocity from the fan was used to calculate the

Reynold's number. In all cases, it was found that the Pr > 0.5 and Re > 1 A4, so the Nusselt

number was calculated according to Equation 3.16 [15].

Nu = 1.15 * Re'/2 * Pr/3 (3.16)

Once the overall Nusselt numbers were found, the overall heat transfer coefficients were

calculated using Equation 3.8.

The overall heat transfer coefficients from three air capacitors of increasing volume are shown in

Table 1. The forced convection increased the heat transfer coefficient by a factor of 5-6.

Therefore, forced convection is a much more viable and effective method of cooling than geometry

or material change or fin addition.

Overall Heat Transfer Coefficient [W/m 2K]

Capacitor Volume Natural Convection Forced convection

0.4 L 8.5 48.5

1.1 L 8.5 42.3

1.7 L 7.0 42.3

Table 1: Overall heat transfer coefficients for three different sized capacitors usingnatural convection and forced convection models.

24

3.3 Ricardo WAVE Engine Models

The cooling of the air capacitor and fuel economy of the engine were modeled using

Ricardo WAVE. Seven different cases were tested in the model, accounting for both air

capacitor size and natural vs. forced convection over the capacitor, as well as a naturally

aspirated baseline case, as shown in Table 2.

Diameter Length Total buffer volume(inches) (inches) (liters)

Small capacitor 3.8 4.25 1.25

Medium capacitor 5.0 4.25 2.5

Large capacitor 5.0 6.25 3.0

Table 2: Capacitor diameter and lengths, and total buffer volume, including capacitor andmanifolds.

The model was set to run across the much of the operating conditions of the real engine, with the

speeds swept from 1500-3600 rpm and the air-fuel ratio, which controls the loading, swept from

19-60. This allowed the model to collect enough data to create maps for the fuel economy across

the range of the engine. The naturally aspirated case was modeled using simple ducts connecting

the ambient air pressure, density, and temperature to the intake. The turbocharger was modeled

using a turbine and compressor connected between the exhaust and intake strokes. The air

capacitor was created by adding a duct of the dimensions shown in Table 2 in between the

compressor and the cylinder and setting the heat transfer rate of that duct to the calculated values

in Table 1. All seven models were run for 200 cycles or until convergence conditions were

reached. The Ricardo model was able to produce data for many different engine parameters,

with the important parameters for this test being intake temperature, pressure, and density, and

brake-specific fuel consumption (BSFC).

25

3.3.1 Cooling

The Ricardo WAVE model demonstrated consistent cooling for the capacitors with

forced convection versus natural convection. For all capacitors, fan or no fan, the addition of the

turbocharger and the air capacitor increased the temperature of the intake air. However, there

was a temperature drop in the air capacitor between the forced convection cooling and natural

convection cooling cases. Figure 6 shows the temperature at the exit of the air capacitor for the

small air capacitor at high loads.

320Small capacitor,Fan

~'315 - ___Small capacitor,..No fanZ - Naturally AspiratedQ-310 -

S 305 -

E-300

2951500 2000 2500 3000 3500

Speed [RPM]

Figure 6: Temperature of the air exiting the small (1.25L) air capacitor for cases with forced

convection cooling using a fan, natural convection, and a naturally aspirated baseline case.

For the small capacitor, the forced convection caused a temperature drop in the air capacitor of

up to 17 K at high loads and speeds, and 4 K at low loads and speeds. For the large capacitor,

the modeled temperature drop was 14 K and 4 K respectively. This temperature drop is

significant because it corresponds to a density increase by the ideal gas law.

26

3.3.2 Density Gain

As discussed in section 3.2, as more air is compressed into the capacitor, the temperature

of the air increases, as described by the idea gas law. When the air is cooled, the pressure

decreases, and the density increases. The density of the intake air affects the output power of the

engine by allowing more fuel to be combusted. The modeled density increase was greater for the

forced convection cases, as predicted, due to the temperature drop. As shown in Figure 7, the

density of the air exiting the capacitor increased with the engine speed for the turbocharged

cases, and was higher for the forced convection cooling cases than for the natural convection

cases.

1.35

ET 1.3

.0

a1.25CL

~1.2

S1.15C

1.1 L_1500 2000 2500 3000 3500

Speed [RPM]

Figure 7: Graph of the density in the capacitor vs. speed for the small capacitor, the large

capacitor, and naturally aspirated cases.

27

m- p Fan-+- Small capactor, Fan

H Small capactor, No fan-0- Large capacitor, Fan

- -*-Large capacitor, No fanI- Naturally Aspirated Baseline

-. ... .

As shown in the air density maps in Figure 8, air density gain increased with both load and speed

for the turbocharged cases, and was slightly higher across all loads and speeds for the forced

convection case compared to the natural convection case.

Large Capcitor

00 2000 2500 3000 3500Speed [RPM]

19

8

7

6

5

4

3

2

1

15

O Large Capacitor,Forced Convection9

8

7

6

5

4

3

2

1

2000 2500 3000Speed IRPM]

Figure 8: Maps of the percent air density gain compared to the naturally aspirated case for

the large capacitor turbocharged case, for both natural and forced convection cases.

In all three capacitor sizes, the forced convection provided a boost in air density (Figure 9). For

the small capacitor, the natural convection case showed a density increase of 7.3%, and the

forced convection case had a density increase of 13.1%; for the medium capacitor, the natural

convection density increase was 9.9% and the forced convection was 11.3%; and for the large

capacitor, the natural convection density increase was 8.1% and the forced convection was

11.3%.

28

00

0

a)

cuM.

12

11

10

9

8

7

6

5

4

3

01

C:

3500

14

'0 =No Fan

12 Fan

C,

10 -

8Z

6 --0a)

C4

C

0 0Small Capacitor Medium Capacitor Large Capacitor

Figure 9. Bar graph of the intake air density increases for small, medium, and largecapacitors, for natural and forced convection cases.

While all cases showed an increase in air density as predicted, the increase was rather small

compared to previous experiments. Some possible sources of error include the model not

converging, the mesh size being too large, or the model not being able to accurately portray a

turbocharger under pulsating conditions.

3.3.3 Peak Power

As the air density increases, the power from the combustion in the engine can also

increase. However, this power increase only occurs at speeds above 2500rpm, as shown in

Figures 10 and 11. This is because the turbocharger stalls at lower speeds, due to too low of

mass airflow, and does not adequately fill the capacitor to provide the added benefits for

combustion. However, for higher speeds, the turbocharger and air capacitor provide a boost in

29

peak power. Across all cases for all loads, the peak power benefits from turbocharging only

began when the modeled engine was running above 2500rpm.

2.4

2.2-

2-

0

13-

mD

1

1.6

1.4

1.2'-1500 2000 2500 3000 3500

Speed [RPM]

Figure 10: Brake power of the engine vs. speed, for an air-to-fuel ratio of 55.

10

L..0)

0a-0)CuL..m

4L1500 2000 2500 3000 3500

Speed [RPM]

Figure 11: Brake power of the engine vs. speed, for an air-to-fuel ratio of 19.

30

Small capactor,FanSmall capacitor,No fanLarge capactor,FanLarge capacitor,No fanNaturallyAspirated

Small capactor,FanSmall capacitor,No fanLarge capactor,FanLarge capacitor,No fanNaturallyAspirated

-

9

7

6

For high air-to-fuel ratios, or low power, the peak power for the engine occurred below the

crossing point, and the naturally-aspirated peak power was 15% greater than the turbocharged,

small capacitor, forced convection case, and 6% greater than for the turbocharged, large

capacitor, natural convection case. For loads close to the engine maximum, the large capacitor

provided a 15% power increase over naturally aspirated, and the small capacitor provided an

11% power increase. However, the same possible sources of modeling error as stated in section

3.3.2 above apply.

3.3.4 Fuel Consumption

The fuel consumption of an engine is calculated using BSFC to measure how efficiently the

engine is actually using the fuel that is supplied. The amount of fuel combusted in the engine

controls the power of the engine. Therefore, lower air-fuel ratios (~19-40) cause higher engine

power, and higher air-fuel ratios (~40-60) cause lower engine power. A fuel consumption map

gives useful information for the best operating conditions for the engine.

Figure 12 is the fuel economy map from the Ricardo WAVE model for the turbocharged

engine with the medium capacitor under forced convection cooling conditions.

31

10 600

9 550

8 500

6- 4000

5 350 CO

4 300

3 250

2 2001500 2000 2500 3000 3500

Speed [RPM]Figure 12: Fuel economy map for the turbocharged engine with the medium air capacitor,with forced convection cooling.

As expected, the model gives that the engine will operate most fuel-efficiently at high

speeds and high loads, or low speeds and low loads. The fuel maps for the naturally aspirated

and all of the turbocharged cases are similar in form.

To compare the fuel economy for the fan, no fan, and naturally aspirated cases, the BSFC

for each case at high loads is graphed in Figure 13. As shown, the BSFC for the naturally

aspirated case was below both turbocharged cases for speeds below about 2500rpm. This trend

was consistent across all loads for both the medium and large capacitors, where the fuel economy

for the naturally-aspirated case was better for speeds below 2500, but the turbocharged cases

were better for speeds above 2500rpm. This is expected, since the turbocharger is not powered

at low RPM.

32

280 T

- Medium capactor, Fan

270. - Medium capactor, No fan- Naturally Aspirated

F26o

>250

240-

2300-

2201500 2000 2500 3000 3500

Speed [RPM]

Figure 13: Brake-specific fuel consumption for the turbocharged engine with the mediumcapacitor for both forced and natural convection cooling, at high loads (air-fuel ratio of25).

For all capacitor sizes, across all speeds and loads, the fuel economy of the case with the fan

was slightly better than that of the case without the fan. However, this increase was less than

0.5% for almost all cases, so the benefit was less than the benefit over the naturally aspirated

case. At 3600rpm, the turbocharger with the medium capacitor provided a 3.1% fuel

consumption benefit over naturally aspirated for the fan case and 2.8% benefit for the no fan

case. Figure 14 show the percent improvement in BSFC for each size capacitor for high loads

(air-fuel ratio of 25) at 3600rpm.

Additionally, the size of the capacitor affected the fuel economy. The large capacitor had

the best fuel economy throughout all of the turbocharged cases, and the small capacitor had the

worst.

33

2.5No fanFan

2

c -

CID 1 .5 -

0<

.

.-

Uc/) z 0.5-

01Small Capacitor Medium Capacitor Large Capacitor

Figure 14: Bar graph of the percent improvement in BSFC for each case compared to

naturally aspirated for high loads (air-fuel ratio of 25) and high speeds (3500rpm).

As shown, for each case, the turbocharger provided a fuel economy benefit at high loads and

speeds, with the forced convection version providing a slight increase over the natural

convection case. The large capacitor had the best fuel economy at high loads and speeds, and the

small capacitor had the worst.

34

4. Experimental Design

4.1 Existing Setup

This experiment was built on an existing experimental engine setup. The diesel engine

selected was a Kholer KD440. The engine is a four-stroke, single cylinder engine with a swept

volume of 0.44 L [16]. It was selected for this experiment because it is a commonly-used engine

and is able to be easily fitted with a turbocharger. The engine was coupled with a Taylor

Dynamometer to allow for load control and measurement [17]. The air capacitor was added

between the turbocharger and the intake valve using (Figure 15A). The cooling due to forced

convection over the air capacitor was produced using a standard 12" diameter desk fan blowing

over the capacitor (Figure 15B).

Turbocharger ;N

Figure 15: Experimental setup. Panel A is the full setup with the engine, dynamometer,turbocharger, and air capacitor. Panel B is the turbocharged engine with the fan for forcedconvection cooling.

35

The experiment was run for seven cases: naturally aspirated; turbocharged with a 1.25 liter

capacitor, with and without cooling, turbocharged with a 2.5 liter capacitor, with and without

cooling; and turbocharged with a 3.1 liter capacitor, with and without cooling. The air capacitors

were made out of steel in varying sizes and shapes, as shown in Figure 16.

Figure 16: Small, medium, and large air capacitors used for the experiment.

The engine was fitted with sensors for temperature and pressure at several different points, and

sensors for exhaust emissions.

4.2 Fuel Consumption Measurement

The fuel economy was measured using a chemical balance for the combustion of the

intake air and fuel and the exhaust emissions. This carbon balancing method assumes that since

combustion occurs just between the air and the diesel fuel, all of the carbon atoms in the engine

exhaust came from the fuel being injected into the combustion chamber. By measuring the

amount of carbon in the exhaust, a chemical balance of the combustion equation can be used to

36

determine the amount of diesel fuel being used. A Testo 350 combustion & emission analyzer

was used to measure the exhaust emissions from the engine for this balance [18].

The chemical composition of diesel fuel is given by C12H23. Assuming no unburned fuel

in the exhaust emissions, the chemical balance of combustion between air and diesel fuel is given

in Equation 4.1[8]. The additional terms for CO, NOx, and 02 were added because the

experimental setup includes these sensors. These additions are only expected to affect the results

by <1%.

A-0 2 + B-N2 + C-C12H2 3 D-O 2 + E-CO +F-CO2 + G-NO 2 + H-NO +I-N 2 + J-H20 (4.1)

The mass flow of air can be calculated using the intake temperature and pressure, and the engine

volume and speed (Equation 4.2). Using this equation and the facts that the composition of air is

78% nitrogen and 21% oxygen, with the other 1% assumed to be mostly-inert gases such as

Argon, the amount of nitrogen and oxygen atoms entering the combustion chamber can be

calculated [19].

. Pi * * Ve (4.2)

2Tj * R

Therefore, A and B from Equation 4.1 are known, and the only unknown in the left side of

Equation 4.1 is C, the number of molecules of diesel. The emissions sensors can measure the

amount of 02, CO, NO 2, and NO in the exhaust, thus determining D, E, G, and H from Equation

4.1. The remaining variables, C, F, J, and I, are determined by completing the chemical balance,

as shown in Equations 4.3-4.6. Solving the equations for the number of diesel molecules, C,

37

gives the amount of fuel flow going to the engine, and thus the fuel consumption. The

MATLAB code for this calculation is given in Appendix C.

Oxygen: 2-A = 2-D + E + 2-F + 2-G + H + J (4.3)

Carbon: 12-C = E + F (4.4)

Nitrogen: 2-B = G + H + 2-I (4.5)

Hydrogen: 23-C = 2J (4.6)

A study by the EPA in 1979 compared the accuracy of fuel consumption measurements using a flow

meter vs. the carbon balancing method, and found that the two methods are linearly related, as shown in

Figure 17, with the flow meter measuring just 3.2 0.4% higher than the carbon balancing [20]. This

means that the carbon balancing is a valid method for determining steady-state fuel economy.

38

*

2

+

* 2 :F*** 3 *

5*23

2

* 8S

$

* *

*

V5. 105.00 115.00 .125.00 135.00130.(0

Fuel Flow Measurements (cc/km)

Figure 17: Graph of fuel consumption using carbon balancing vs. flowmeter measurements.

4.3 Experimental Procedure

The experimental procedure is given below:

1. Start turbocharger oil pump and dynamometer water cooling.

2. Zero the torque sensor

39

I..C..0 +

1 Io .00 +

.9

120.0 4

t

ii1;.o0 +LO

0I

.0

14I10.VO +

*2

+

* *

2

C15. 00

*

+

* *

+

*

*

100.00 +

* *

*

4.

* *

0

2

9!".. Of:O +

L00.00 1-0.00 120.00

155. C0 +

3. Turn on the engine at no load and run until it warms up and reaches steady state, then

shut off the engine by increasing load until the engine stalls.

4. Start exhaust emissions sensors and connect them to the dynamometer software.

5. Start the engine at no load and wait until the emissions sensors reach steady state (<40s).

6. Log the load, temperature, pressure, and emissions readings.

7. Increase speed by 300rpm and wait until emissions sensors have reaches steady state

(<40s).

8. Log the load, temperature, pressure, and emissions readings.

9. Repeat steps 7-8 until reaching max speed.

10. Increase load by 700-800W and repeat steps 6-9 until the engine stalls. For high loads,

run the engine only at higher speeds.

40

5. Results & Analysis

5.1 Temperature

Since the density of the intake air depends on temperature, the temperature drop across the

capacitor due to forced convection cooling gave an indication of how much adding the fan would

affect the engine performance. However, the temperature inside the testing room increased as

the engine was running. Therefore, comparing the absolute value of the temperatures across the

capacitor did not give accurate results. To compensate for this, the temperature drop across the

capacitor was non-dimensionalized with the testing room temperature (Equation 5.1).

__- - - Tcompressor Tintake (5.1)

Tcompressor Tamb

The non-dimensionalized temperature drop across the medium capacitor is given in Figure 18.

As shown, the average temperature drop across the capacitor is greater for the case with the fanat lower loads.

12 12 10%Med Capacitor, Medium Capacitor,

0 No Fan WFan10 108 8

a) 6 6

0 ~CO0 U

m2 2

0 t0 -z

2000 2500 3000 3500 2000 2500 3000 3500Speed [RPM] Speed [RPM]

Figure 18: Map of the non-dimensionalized temperature drop across the air capacitor.

41

However, significant error is expected, because of the proximity of the intake temperature

sensor to the engine block. As the engine kept running, the engine block heated up, so the

measurements for the intake temperature increased dramatically and were dominated by the

temperature of the engine block.

Another way to quantify the amount that the fan helped with the cooling is to calculate the

overall heat transfer coefficient of the capacitor. Treating the air capacitor and the surrounding

air as a heat exchanger, Equations 5.2-5.7 are used to calculate the heat transfer coefficient, h

[15].

Q = hAATLMTD (5.2)

AT2 - AT1 (5.3)ATLMTD

n(2)AT1,

AT1 = Tcompressor - Tamb (5.4)

AT2 = Tintake - Tamb (5.5)

Q = marcp(Tcompressor - Tintake) (5.6)

Vengine (5.7)Pintake r rpm- 2

air intkae R

42

However, due to the inaccuracy of the intake temperature measurements, as discussed

above, these calculations do not give reasonable results with the data collected, and must be

recalculated with more accurate temperature readings.

5.2 Density Gain

The intake air density gain due to the turbocharger and air capacitor is an important

indicator of performance. The density of the air was calculated from the intake temperature and

pressure using the ideal gas law using Equations 5.8-5.9. The density gain of the turbocharged

intake air over the naturally aspirated intake was calculated using Equations 5.10-5.11, and was

converted to a percent increasing using Equation 5.12.

PV = MRT

M PDensity = RT

V RT

(5.8)

(5.9)

Density Gain = Turbocharged DensityNaturally Aspirated Density

Pintake/TintakeR

Pamb/TambR

Pintake intakeR PintakeTamb

Pamb ambR TintakePamb

Percent Density Gain = (PintakeTamb i) * 100

T intakekanm

43

(5.10)

(5.11)

(5.12)

Using Equation 5.12 with the measured intake temperature and pressure, a map of the intake air

density gain was created for the turbocharged engine using the medium capacitor, both for the

case with forced convection using a fan, and for the no fan case (Figure 19). As shown, the

density gain is between 0-32% across the spectrum for both cases, with the density gain

increasing for higher speeds. The maximum density increase was 32% for both cases, and

despite the cooling from the fan.

12 12 304 Medium Capacitor, No fan 1 Medium Capacitor, Fan

10 -10-

8- 8I20 c

6 -:60

CL 15 10"a) C

4 -4

102 2

50 01500 2000 2500 3000 3500 1500 2000 2500 3000 3500

Speed [RPM] Speed [RPM]

Figure 19: Map of percent density gain of the intake air over all loads and speeds for theturbocharged, medium capacitor case, with and without cooling.

However, due to the intake temperature measurement error discussed in section 5.1, these density

gains are expected to have considerable error.

5.3 Fuel Consumption

The fuel consumption of the engine, calculated using the carbon balancing method described

in section 4.2, was mapped across all loads and speeds from the experimental data. For sections

44

of high load and speed, the experimental data matched the modeled data well, as shown in Figure

20. While it was not exact, the general range of BSFC and trends remained the same.

7.5 [Experiment -MediumCapacitor, No Fan

6

Mediumr, No Fan

3200 3400 3600Speed [RPM]

7-

.5

6 -3000 3100 3200 3300 3400 3500

Speed [RPM]

Figure 20: Comparison of the experimental and modeled BSFC for the medium capacitorno fan case, from 3000-3600rpm, and 6-7.6 kW of power.

However, for other sections of the maps, especially at higher BSFC, the experimental fuel

economy increases to over 7 times the modeled BSFC. As shown in Figure 21, the same trend as

was found in the model, with the BSFC highest at low loads and high speeds, remained, but the

BSFC increased exponentially in many places.

45

7.5 Model -Capacito

7

3. 5

63000

420

400

380

360

340

320

300

280

LL0C-

12 - - -- 12 - - 800

O Medium Capacitor, F Medium Capcitor,

No Fan I Fan 70010- 10

8 60098- -8

500)

a 6 6 UL-e 400 CO

4 4 300

2 - 2 2002000 2500 3000 3500 2000 2500 3000 3500

Speed [RPM] Speed [RPM]

Figure 21: Experimental BSFC map for the medium capacitor, fan and no fan conditions.

This indicates a severe problem with either the emissions sensors or the carbon balancing

method. Therefore, it is difficult to make concrete conclusions about the fuel economy from the

experimental data, since major errors have been found.

5.4 Error Analysis

There are several possible sources of error in the data. First, the torque measurement

may have been slightly off due to some drifting of the sensor. This could have happened due to

the temperature rise in the room from the engine running, which could have changed the

resistance in the sensor, causing the reading to drift. Some of the discrepancy also could have

been explained by the vibration in the engine itself. In addition, as discussed in section 5.1, the

temperature measurements at the intake were taken very close to the engine body. Therefore, as

the engine heated up, the temperature readings could have been overpowered by the temperature

of the body itself, rather than just the intake air. In the future, the intake temperature sensor

46

could be placed in a different location, further from the engine body, or with insulation between

the sensor and the engine body. In addition, the ambient temperature in the testing room

increased as the engine was running, so each testing case did not start at the same temperature.

This could be mitigated by having the test in a temperature-controlled room. The starting

temperature of the room and the engine affected the data. Since the tests were run concurrently,

the first test was run in a cold start condition and the rest were run with a hot start. This

temperature difference at the beginning affected the readings throughout the test. The

differences in starting conditions for each test could be mitigated by allowing the engine and the

room to completely cool in between each test for a cold start, or by running hot start cases at the

same temperature for all test runs. To collect consistent data that could be directly compared

more easily, all tests could be carefully controlled so that each was run at the same loads and

speeds for all cases.

47

6. Conclusion & Next Steps

This thesis shows that the size and heat transfer of the air capacitor for a single-cylinder,

turbocharged diesel engine are correlated to engine performance and fuel economy. According

to the model, the large capacitor had the best peak power and fuel economy at high loads and

speeds. However the peak power and fuel economy of the modeled naturally aspirated engine

was better than the turbocharged engine for speeds below 2500 rpm. The general trends from the

model were reflected in the experimental data. The forced convection increased cooling, and

improved the intake air density. However, it was difficult to make any confident

recommendations about the fuel economy based on the experimental data.

A next step would be to measure the fuel consumption using flow meters, to compare the

results with the fuel consumption found using carbon balancing. A proposed method to do this

would be to place two flow meters on the fuel lines leaving from and returning to the tank.

Figure 22 shows a block diagram of the proposed experimental setup for the fueling circuit.

Fuel Fuel Injection Injector Injected FuelTank Filter Pump

Return Line

Injector Leak-off Line

Figure 22: Block diagram of the fueling circuit and flowmeter placement.

The first flowmeter is placed on the fuel line directly after the fuel leaves the tank, to measure

the total amount of fuel going into the fuel filter, and thus the entire system. The second

flowmeter is placed on a line connecting the injector leak-off line and the return tubes coming

48

from the fuel filter and the injection pump. The fuel flow measure in the return lines would be

subtracted from the total fuel flow coming from the tank, to be able to measure the amount of

fuel being injected into the combustion chamber. This method would hopefully allow the fuel

consumption to be measured more accurately.

49

Appendices

Appendix A: Calculating the Air Temperature Drop due to Geometry or MaterialChange of the Air Capacitor

This is the code described in section 3.2.1 to calculate the temperature drop across the air capacitordue to the change of surface area to volume ratio or thermal conductivity.

%calculating the h values from the air capacitor resistances

%parameters to vary:L all = 0.0254*[4.25, 4.25, 6.25]; %capacitor lengths in [m]

V all = 0.001*[0.4, 1.1, 1.7]; %capacitor volumes in [mA3]

t = 0.0254*0.125; %[m] thickness of the metal wall of the capacitor converted

from inches to metersK = 50; %Thermal conductivity of steel and aluminum in w/mk

T i = 380; %temperature of the air inside the capacitor[K]T_o = 300; %Ambient air temperature [K]Vdot = .0067; %volume flow rate of air [m^3/s]R = 287; %gass costant for aitKair = 0.027; %conductivity of air in w/mkuair = 2*10^(-5); %viscosity of airCpair = 1000; %specific heat of airPr= Cpair * uair/Kair; %prandlt number of airVmove = 0.5; %velocity of tractor/wind speed in [m/s]

%set up variables to calculateT_drop nofin = []; %temperature drop without fins [K]

T_drop fin = []; %temperature drop with fins [K]

TotalSAwithoutfins = []; %total surface area without fins [m^2}

Total SA over-volume = []; %total surface area divided by volume [1/m]

Radiusoverlength = []; %non-dimensionalR_tot = []; %total resistance due to convection and conduction

Q_tot = []; %total heat transfer across the capacitorh_overall = [];

%iterate through all the capacitors to find temperature drops

for AC number = 1:length(L all)L = L all(ACnumber);V = V all(ACnumber);A = V/L; %cross sectional area of capacitorr i = sqrt(A/3.14); %inner radius of capacitor [m]r o = r i+t; %outer radius of the capacitor [m]

d = 0.03302; %diameter of tubing hole on the capacitor [m]Perimeter = 2*r o*3.14; %Perimeter of capacitor [m]D = 4*A/Perimeter; %Hydraulic diameter of capacitor [m]

Vin = Vdot/A; %velocity of air [m/s]SAtot= 3.14*D*L + 2*3.14*(ro^2-d^2); %total outer surface area of

capacitor [m^2]

%calculating h of air flowing through the capacitorPin = 1.8*10^5; %pressure of air inside cap

pin = Pin/(R*T i); %density of air inside [kg/m^3]

50

Re = pin*Vin*D/uair; %reynolds number of air flowing through the pipe

if (Re<=2300)Nu=3.66+(0.065*(D/L)*Re*Pr)/(l+.04*((D/L)*Re*Pr)^(2/3));flow = 'laminar'

endif(Re>2300)

f=(0.79*log(Re)-1.64)^(-2);Nu=( (f/8) * (Re-1000) *Pr) / (1+12.7* ( (f/8)^(.5)) *((Pr^ (2/3)

)-l));flow = 'turbulent'

end

h i= Nu*Kair/D; %convective heat transfer coefficient for air inside

capacitor

%calculating h of air flowing around the capacitor, treat it as

laminar flow over a plate

Pout = 1*10^5; %pressure of air outside

pout = Pout/(R*T o); %density of air outside[kg /M^3

Re = pout*Vmove*L/uair; %reynolds number of air flowing outside the

pipeNu=0.664* (Re^ (1/2) )*(Pr" (1/3));

h o= Nu*Kair/L; %convective heat transfer coefficient for air outside

capacitor

%calculating the thermal resistance of the capacitor

R_cyl = log(ro/ri)/(2*pi*K*L); %resistance of cyldindrical wall

[k/wiR cap = (r o-r i)/(2*K*pi*(r i^2-d^2)); %resistance of end caps [k/w]

R convo = 1/(ho*(2*ro*pi*L+2*pi*(r-i^2-d^2))); %resistance due to

convection of air outside [k/w]

R_conv i = 1/(h i*(2*ri*pi*L+2*pi*(r-i^2-d^2))); %resistance due to

convection of air inside [k/w]

R cond tot = 1/(l/R cyl+1/R cap); %total resistance due to conduction

R tot(AC_number) = R convo+R convi+R cond tot; %total resistance

due to both conduction and convection

Q_tot(ACnumber) = (Ti -To)./Rtot(ACnumber); %total heat transfer

T_dropnofin(ACnumber) = Qtot(ACnumber)./(Vdot*pout*Cpair);

%Temperature drop due through the capacitor

h overall(AC number) = 1/R tot(AC number);

Total SA without fins(AC number) = SAtot;

TotalSA over volume(AC number) = SAtot/V;

Radius over length(ACnumber) = r o/L;

end

figure;plot(Radius overlength,Tl,'bo')

hold on

51

xlabel('Capacitor radiusylabel('Temperature dropset(gca,'fontsize',18);box on;

over length [-]', 'fontsize',18)[K]', 'fontsize',18)

12=legend('Steel capactitor','Aluminum capacitor');set(12,'Fontsize',12)

52

Appendix B: Forced Convection Heat Transfer Model

This is the code described in section 3.2.2 to calculate the overall heat transfer coefficient of the

air capacitor. The code outputs the heat transfer coefficient for three capacitors for natural

convection conditions, as well as forced convection conditions due to the wind from a fan.

%Finding the h value from forced convection over a cylinder

%capacitor geometry for each of the three capacitors

L = 0.0254*[4.25, 4.25, 6.25]; %Capacitor length (converted from inches to

meters) [m]D = 0.0254 * [3.8, 5.0, 5.0]; %Outer diameter of the Air Capacitor (converted

from inches to meters) [m]

%inside and outside temperatures [K]

T i = 380;T o = 300;

%Go through each capacitor to find the h value:

h = []; %set up h

Fanspeed = [1];for ACnumber = 1:length(L) %go through all capacitors

AC numberfor Fanspeed = 1:length(Fanspeed) %find h for all three

each capacitor%Reynold's number:

p air = 1.2; %density of air at ~300K [kg/m^3]

V air = [4.8]; %Measured velocity of the air from the

u air = 2*10^(-5); %viscosity of air [kg/ms]

Re = pair*V air(Fan speed)*D(ACnumber)/uair;

fan speeds for

fan [m/s]

%Prandtl number

Cp air = 1000; %specific heat of air [J/kgK]

K air = 0.027; %conductivity of air [w/mk]

Pr= Cp air * u air/K air; %prandlt number of air

%Nusselt number

if Pr > 0.5 & Re > 10A4

disp('Pr > 0.5 & Re > 10^4') %display in which case Nu will fall

Nu = 1.15*Re^(1/2)*PrA(1/3);elseif Re < 10^4 & Pr >= 0.5

disp('Re < 10^'4 & Pr >= 0.5')%display in which case Nu will fall

Nu = 0.3 + (0.62*ReA(1/2)*PrA(1/3))/(1+(0.4/Pr)A(2 /3 ))A(1/ 4 );

elseif 2.0*10A4 < Re & Re < 4.0*10^5

disp('2.0*10^4 < Re & Re < 4.0*10A5')%display in which case Nu

will fallNu = 0.3 +

((0.62*ReA (1/2)*PrA (1/3))/(1+(0.4/Pr)A (2/3) )^ (1/4))*(1+(Re/282000)A (1/2

elseif 4.0*10^5<Re & Re<5.0*10A6

disp(1 4.0*10A5<Re & Re<5.0*10^6')%display which case Nu will fall

underNu = 0.3 +

((0.62*Re^(1/2)*PrA(1/3))/(l+(0.4/Pr)^(2/3))A (1/4))*(+(Re/282000)A(5/8))A(4 /

5);

53

elseif Re*Pr < 0.2

disp('Re*Pr < 0.2')%display which case Nu will fall under

Nu = 1/(0.8237-(log(Re*Pr))^(1/2));else

disp('No Nu value found')

end

%find the h value from Nu = h*L/kh(AC number,Fanspeed+1) = Nu*Kair/D(ACnumber);

%find the Nu value for natural convection on the surface of a

horizontal cylinder%to be able to compare

V amb = 0.5; %velocity of ambient air

Re nc = p-air*Vamb*L(ACnumber)/uair; %reynolds number of air

flowing outside the pipeNu nc=0.664*(Re nc^(1/2))*(Pr^(1/

3 ));

h nc= Nunc*Kair/L(ACnumber); %convective heat transfer coefficient

for air outside capacitor

%set the first column of h to be the natural convection h value

h(ACnumber, 1) = h nc;

endend

54

Appendix C: Carbon Balancing Method for Fuel Consumption

This is the code described in section 4.2 to calculate the fuel consumption using the carbonbalancing method.

%data inputfile='filename.csv'; %file input

speed = dlmread(file,',', [31 52 0 52]); %speed in rpm

power = dlmread(file,',',[31 66 0 66]); %power in kw

NO=dlmread(file,',',[31 305 0 305]); % Nitrogin monmxide concentration in PPM

N02=dlmread(file,',', [31 302 0 302]); % Nitrogen dioxide concentration in PPM

NOx=dlmread(file,',', [31 304 0 304]); %total Nitrogen oxides concentration in

PPMCO= dlmread(file,',',[31 196 0 196]); %Carbon monoxide in PPM

C02= dlmread(file,',', [31 192 0 192]); %Carbon dioxide in percent

02=dlmread(file,',',[31 306 0 306]); % Oxygin in percent

Pintake=dlmread(file,',', [31 110 0 110]); %intake pressure (PSI) Pressure

Input#6PintakePa=(LNEPintake+14.5)*6894.76;

Tintake=dlmread(file,',',[31 258 0 258]); %intaake temp (f)

TintakeK=convtemp(Tintake, 'f', 'k');%intaake temp (k)Tcomp=dlmread(file,',',[31 255 0 255]); %compressor temp (f)

TcompK=convtemp(Tcomp, 'f', 'k') ;%compressor temp (k)

TambF = dlmread(file,',',[31 319 0 319]); %ambient air temperature, deg F

TambK = convtemp(TambF, 'f', 'k'); %ambient air temperature, K

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Calculations

AirMassFlow=((PintakePa.*speed*Veng/2)./(TintakeK*R)); %estimated mass flow

(kg/s) based on intake temp and pressure

02burnt=21-02; %Percent 02 that is burnt in the exhaust by volume

02burntPPM=O2burnt*10000*32/29;02ExPPM=02*10000*32/29;CO2ppm=CO2*10000*44.1/29;N2exPPM=79*10000*28/29-NO-NO2;H20ppm=O2burntPPM*2-CO2ppm*2-CO-NO-2*NO2;ExhaustGasWeight-18*H20ppm+N2exPPM*28+NO*30+NO2*46+0

2 ExPPM*3 2 +CO* 2 8 +4 4 *CO2ppm

; %exhaust gas molecular wight

CarbonWeight=((12)*CO+(12)*CO2ppm); %Percent Carbon in exhaust

CarbonMassPercent=(CarbonWeight./ExhaustGasWeight);%Percent Carbon in exhaust

fuelMassPerc'ent=CarbonMassPercent*13.7/12; %Percent of exhaust that is burnt

fuelFuelMassFlow=AirMassFlow./(1-fuelMassPercent)-AirMassFlow; %kg/min

FuelMassFlow=FuelMassFlow*1000; %g/min

FuelEconomy=FuelMassFlow*60./power; %g/kWhr

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

55

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