Combustion Cylinder Design for

Plasma Ignitor Testing

Submitted To:Dr. Smith

Submitted By:

Cody LesterMatt McHughLucas WareWill Young

Table of ContentsTable of Figures...........................................................................................................................................v

Table of Tables.............................................................................................................................................v

1 Introduction.........................................................................................................................................1

2 Methodology.......................................................................................................................................1

2.1 Maximum Temperatures and Pressures......................................................................................1

2.2 Stress Analysis.............................................................................................................................3

2.3 Viewing Port................................................................................................................................4

3 Results.................................................................................................................................................5

3.1 Maximum Temperatures and Pressures......................................................................................5

3.2 Stress Analysis.............................................................................................................................8

3.3 Viewing Port................................................................................................................................8

4 Design Properties................................................................................................................................9

Bibliography...............................................................................................................................................12

5 Appendix............................................................................................................................................13

5.1 Design Dimensions.....................................................................................................................13

5.2 Pipe Dimensions........................................................................................................................14

5.3 Flange Dimensions.....................................................................................................................15

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Table of FiguresFIGURE 1: CAD IMAGE OF FINAL DESIGN.............................................................................................................................9FIGURE 2: TESTING CONFIGURATION OF COMBUSTION CYLINDER AND VESSEL [7]......................................................................10

Table of TablesTABLE 1: KNOWN VARIABLES..............................................................................................................................................5TABLE 2: PRESSURE AND TEMPERATURE PRIOR TO COMBUSTION..............................................................................................6TABLE 3: AVAILABLE ENERGY FOR COMBUSTION OF VARIOUS FUELS..........................................................................................6TABLE 4: PEAK PRESSURE AND TEMPERATURES FOR VARIOUS COMPRESSION RATIOS....................................................................7TABLE 5: PEAK PRESSURE AND TEMPERATURES FOR VARIOUS COMPRESSION RATIOS....................................................................7TABLE 6: COMBUSTION CYLINDER DIMENSIONS.....................................................................................................................8TABLE 7: STRESSES PRESENT IN COMBUSTION CYLINDER..........................................................................................................8TABLE 8: NECESSARY THICKNESS OF VIEWING PORT GLASS USING ISP OPTICS............................................................................8TABLE 9: NECESSARY VIEWING GLASS THICKNESS USING ADVANCED GLASS INDUSTRIES................................................................9

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1 Introduction

The combustion chamber serves a testing compartment that must withstand the temperature and pressures from a combustion process. The main testing that will be performed is that of a plasma igniter, invented by Dr. James E. Smith. The plasma igniter is an ignition system that will compete with existing electric spark-based ignition systems. The plasma igniter allows for combustions takes place at a lower temperature and possibly a lower pressure than that from an electric spark-based igniter. The lower combustion temperature results in lower NOx emissions and easier control of the emissions stream. This system also allows for lean fuel mixtures which increases the fuel economy [1]. It permits all types of fuels to be used in the combustion at any compression ratio. The combustion chamber assists in the process by providing a controlled environment that is the same of each type of combustion being tested. The requirements of the chamber are to allow the user to inspect the combustion using sensors and visually as well. A visual inspection helps the user see that the flame is developing correctly. This combustion cylinder also accounts for the different pressures before, during, and after combustion.

2 Methodology

2.1 Maximum Temperatures and PressuresFuel combustion takes place at high pressures and temperatures. Modeling these combustions

inside of a rigid cylinder require strong materials to withstand these variables. In order to safely experiment with gasoline, diesel, natural gas, and other fuels, proper calculations of maximum pressures and temperatures are necessary.

A constant-volume heat addition experiment can be modeled after the second of four stages of the ideal Otto cycle. During the ignition phase of the cycle, an ideal environment for reciprocating engines is considered to have constant volume. The end of this stage experiences the highest pressure. This pressure is what is used to determine the maximum stresses experienced by the cylinder during combustion, ultimately leading to the selection of materials strong enough to withstand the stress.

Conditions at room temperature will not produce the maximum pressure or temperature experienced at state 3 of the Otto cycle. Thus, the first step in the process is to calculate the variables at state 2 of the cycle, after the isentropic compression process. This will allow the simulation of the constant volume Otto cycle stage by setting the initial pressure and temperature of the cylinder prior to combustion to T2 and P2. The temperature can be found by Equation 1, which includes room

temperature T1, the ratio of specific volumes[ ν2

ν1 ], and the specific heat ratio of air k.

1

T1

T2=[ v2

v1 ]k−1 (Equation 1)

The specific volume ratio is also called the compression ratio r. Different compression ratios are recommended for combustion of different fuels. Gasoline is traditionally ignited under a 9:1 compression ratio, with diesel typically at 15:1. These ratios are used for each fuel throughout calculations as a maximum-minimum threshold to determine which one yields the highest pressure. The specific heat ratio of air at 298 K and 101.325 kPa is 1.4 [2]. Rearranging Equation 1 for T2 and inserting the compression ratio for the specific volume ratio yields Equation 2.

T 2=T 1

[ 1r ]

k−1 (Equation 2)

Approximations known as air-standard assumptions allow for easier analysis within complex gas power cycles [3]. These assumptions include that the working fluid is air, which continuously circulates in a closed loop, and always behaves as an ideal gas. Since the initial temperature to be set inside the cylinder is determined, this assumption allows for the pressure to be calculated using the ideal gas law. Equation 3 shows the original form of the ideal gas law equated to two separate states.

P1 ν1

RT 1=

P2 ν2

R T 2 (Equation 3)

R, the gas constant for air, can be cancelled because it is the same on both sides. After Equation 3 is rearranged for P2, the ratio of specific volumes can again be reduced to the compression ratio r. Equation 4 shows the reduced version of the ideal gas law used to find the initial pressure of the combustion cylinder.

P2=P1[ T2

T1 ]r (Equation 4)

After setting the initial conditions inside of the chamber, the ignition of the fuel takes place. Constant-volume heat addition is described in Equation 5.

q¿=u3−u2=cν (T 3−T 2 ) (Equation 5)

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The heat addition, qin, is calculated by multiplying the higher heating value of the fuel found in Table A-27 of Thermodynamics: An Engineering Approach with the mass of the fuel [4]. The mass of the fuel is determined by multiplying the fuel-air ratio with the mass of the air. Total mass of air is calculated by multiplying the density of air with the volume of the combustion chamber. Once q in is determined, the specific heat of air for each compression ratio is found through interpolation of values in Table A-2 of the textbook [2]. The interpolation uses the temperature at state 2 to find specific heat values. Equation 5 can be rearranged for T3. P3 is calculated by once again equating two states of the ideal gas law. Equation 6 shows this relationship.

P3=P2[ T3

T2 ][ ν2

ν3 ] (Equation 6)

The ratio of specific volumes can be reduced to 1 because the combustion is occurring in an isochoric process. The two parameters that control material selection, T3 and P3, have been calculated and a stress analysis is carried out.

2.2 Stress Analysis

The combustion cylinder will undergo stresses due to the internal reactions and pressure increase. In order to calculate these stresses, the cylinder is modeled after a thin-walled pressure vessel. The stress resulting from a pressurized cylinder can be categorized into three separate components. The radius of the element under consideration determines both radial and tangential stresses. Tangential stress, t, can be found by Equation 7. The inside of the cylinder is designated by ri and the outside by ro. Ambient pressure is given as po and the combustion pressure is signaled as pi.

σ t=pi ri

2−po ro2−ri

2r o2 ( po−pi )/r2

ro2−r i

2 (Equation 7)

Equation 8 shows the method of calculating radial stress, r.

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σ r=pi r i

2−po ro2+r i

2 ro2 ( po−pi ) /r2

ro2−ri

2 (Equation 8)

The longitudinal stress, l, is shown in Equation 9.

σ l=p iri

2

ro2−r i

2 (Equation 9)

2.3 Viewing Port

Determining the thickness of the viewing port is an important step in the design process. First and foremost, it keeps the user safe. The material used for the viewing port allows for must account for the pressure forced on it. Determining this material also helps keep the integrity of the testing. If the glass would break, the testing results would be infected, thus causing incorrect results from the experiment. The viewing ports also have different diameters. One reason for this is due to the proximity to the actual combustion. Since the side view port will be close to the combustion, it has a smaller area for which the pressure to act on. This takes down some of the concern over breaking or shattering the glass.

Research for how to figure out the minimum thickness of the viewing port glass outputs two different equation. The first from ISP OPTICS [5]:

T=√ 1.1∗( P )∗R2∗SFMR (Equation 10)

Where:

SF = Safety Factor

MR= Rupture Modulus (PSI)

P =Pressure differential (PSI)

R=Unsupported radius for circular window (In)

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T= Thickness (In)

The safety factor being used in this equation is four, which is a modest value, sufficient for many applications. The unsupported radius is the radius of the viewing port that is not clamped between the caps of the chamber. The Rupture modulus, or flexure strength, differs between each type of material under consideration to be used. The pressure for this equation comes from the maximum pressure in the combustion chamber. See table 1 for the results.

The next equation that one uses for determining the minimum thickness for the view port material is from Advanced Glass Industries [6]:

T=R∗√ P∗0.75∗SFMR

(Equation 11)

The variables are the same as the previous equation, but there is a different constant. The constant of 0.75 accounts for the clamped edges that is found on the combustion chamber’s viewport design. Again the safety factor of four was applied to this equation. See Table 2 for the results.

The materials under consideration are Sapphire, Pyrex, and Fused Silica. These materials are commonly used in this type of application. They all allow for great transparency to visual inspection.

3 Results

3.1 Maximum Temperatures and Pressures

The ambient conditions and properties of the designed cylinder which will be used in later calculation are summarized below in Table 1.

Table 1: Known Variables

Room temperature (K) 298Room pressure (kPa) 101.325

Specific Heat Ratio of Air (298 K & 101.325 kPa) 1.4

Volume of Cylinder (m3) 0.00118

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Table 2 below summarizes the pressures and temperatures calculated prior to combustion based on various compression ratios.

Table 2: Pressure and Temperature Prior to Combustion

Compression Ratio (r)

T2

(K)P2

(kPa)

Density of Air

(kg/m3)

Mass of Air (kg)

cv

(kJ/kg-K)

7 649.0161 1544.7346 1.1847 0.00140 0.77578 684.6242 1862.2698 1.1847 0.00140 0.78439 717.6510 2196.1203 1.1847 0.00140 0.7922

10 748.5422 2545.1689 1.1847 0.00140 0.799511 777.6306 2908.4819 1.1847 0.00140 0.806412 805.1722 3285.2646 1.1847 0.00140 0.812813 831.3686 3674.8304 1.1847 0.00140 0.818814 856.3819 4076.5790 1.1847 0.00140 0.8244

Table 3 below represents the amount of energy available for combustion for various types of fuels.

Table 3: Available Energy for Combustion of Various Fuels

Fuel Mass of Fuel (kg)

Qin

(kJ)qin

(kJ/kg)

Methane 8.12785E-05 4.513 3228.514Propane 8.96104E-05 4.510 3226.153Octane 9.25881E-05 4.434 3171.755

Methanol 0.000215079 4.874 3486.241Ethanol 0.000155497 4.614 3300.194

Hydrogen 5.14037E-05 7.289 5213.986Gasoline 9.57475E-05 4.529 3239.577

Light Diesel 9.64186E-05 4.445 3179.517

Table 4 and 5 below shows the maximum pressures and temperatures that will be experienced in the combustion chamber which occurs at the time of combustion. These are shown for various combustion ratios.

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Table 4: Peak Pressure and Temperatures for Various Compression Ratios

7:1 Compression

Ratio

8:1 Compression

Ratio

9:1 Compression

Ratio

10:1 Compression

Ratio

FuelT3

(K)P3

(kPa)T3

(K)P3

(kPa)T3

(K)P3

(kPa)T3

(K)P3

(kPa)

Methane 4811.04 11450.84 4801.29 13060.16 4793.13 14667.70 4786.49 16274.87Propane 4808.00 11443.59 4798.28 13051.98 4790.15 14658.58 4783.54 16264.83

Octane 4737.87 11276.68 4728.92 12863.30 4721.48 14448.44 4715.50 16033.49Methanol 5143.29 12241.63 5129.92 13954.07 5118.47 15663.29 5108.83 17370.89

Ethanol 4903.45 11670.78 4892.69 13308.78 4883.61 14944.60 4876.14 16579.70Hydrogen 7370.60 17542.90 7332.96 19946.65 7299.47 22337.48 7269.75 24718.36

Gasoline 4825.30 11484.78 4815.40 13098.54 4807.10 14710.44 4800.33 16321.91Light Diesel 4747.87 11300.50 4738.82 12890.22 4731.28 14478.43 4725.21 16066.50

Table 5: Peak Pressure and Temperatures for Various Compression Ratios

11:1 Compression

Ratio

12:1 Compression

Ratio

13:1 Compression

Ratio

14:1 Compression

Ratio

FuelT3

(K)P3

(kPa)T3

(K)P3

(kPa)T3

(K)P3

(kPa)T3

(K)P3

(kPa)

Methane 4781.05 17882.00 4777.12 19491.61 4774.23 21103.15 4772.69 22719.11Propane 4778.12 17871.05 4774.21 19479.76 4771.35 21090.41 4769.82 22705.48

Octane 4710.67 17618.76 4707.29 19206.69 4704.91 20796.75 4703.84 22391.37Methanol 5100.63 19077.31 5094.19 20785.33 5088.99 22494.43 5085.32 24207.32

Ethanol 4869.93 18214.45 4865.30 19851.42 4861.77 21490.10 4859.64 23133.02Hydrogen 7243.07 27090.42 7219.79 29458.19 7199.02 31821.22 7181.14 34183.90

Gasoline 4794.77 17933.31 4790.73 19547.14 4787.74 21162.87 4786.11 22782.99Light Diesel 4720.29 17654.76 4716.84 19245.65 4714.39 20838.65 4713.25 22436.19

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3.2 Stress Analysis

The dimensions of the designed cylinder are shown below in Table 6.

Table 6: Combustion Cylinder Dimensions

Cylinder dimensions (in)di 3.827

do 4.501

length 6

ri 1.9135

ro 2.2505

Using these dimensions as well as the formulas described earlier, the stresses present in the cylinder are summarized below in Table 7.

Table 7: Stresses Present in Combustion Cylinder

Stressesr

(in)σt

(psi)σr

(psi)σl

(psi)1.9135 33276.98 15048.61 9167.232.2505 29658.74 11430.36 9167.23

3.3 Viewing Port

Using the formulas discussed earlier, the minimum viewing port glass thickness is summarized below in Table 8 and Table 9.

Table 8: Necessary Thickness of Viewing Port Glass Using ISP Optics

SF MR P Rbottom Rside Tbottom Tside

Sapphire 4 65,000 3510.9285 1.035 0.69 0.5046 0.3364Pyrex 4 2,400 3510.9285 1.035 0.69 2.6259 1.7506Silica 4 7000 3510.9285 1.035 0.69 1.5375 1.0250

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Table 9: Necessary Viewing Glass Thickness Using Advanced Glass Industries

SF MR P Rbottom Rside Tbottom Tside

Sapphire 4 65,000 3510.9285 1.035 0.69 0.4166 0.2778

Pyrex 4 2,400 3510.9285 1.035 0.69 2.1682 1.4455Silica 4 7000 3510.9285 1.035 0.69 1.2696 0.8464

4 Design Properties

The designed system is completely ready to be built. After extensive analysis, the combustion cylinder will withstand both the pressure and temperature is may be subject to. This is a critical step in the progression of proving the worth of the plasma igniter. If this testing proves to be as successful as it is thought to be, the plasma igniter could revolutionize the internal combustion engine industry. The final designed combustion cylinder can be seen below in Figure 1 and appendix 5.1.

Figure 1: CAD Image of Final Design

As seen from Figure 1, this design includes 2 viewing ports, a main body, and a removable insert. The main body of the cylinder is 4.5in schedule 80 steel pipe described in appendix 5.2. One viewing port should be located on the bottom, creating and upward depiction of the combustion as

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well as one located on the side, viewing the exact point of ignition. The two viewing ports will be connected to the body of the cylinder with class 300 level weld neck flanges explained in appendix 5.3. The glass and approved gasket should be recessed into the first half of the flange and secured tightly by bolting the second half of the flange over top. The connection point for the ignitor will be recessed into the cylinder and will be able to be inserted and removed with a class 300 blind flange.

Also, there are locations for connecting pressure and temperature measurement devices, input location for fuel and air, the plasma igniter, and an exhaust location.

The next steps involved with the chamber include construction and then testing can begin. Outlined in this report are the design considerations in which the combustion chamber will be built. After construction, a possible testing configuration can be seen below in Figure 2.

Figure 2: Testing Configuration of Combustion Cylinder and Vessel [7]

As can be seen in Figure 2, a few other pieces will be needed in conjunction with the combustion cylinder. First, a fuel source must be selected and connected to the cylinder through one of the openings and will be controlled using a flow meter. Air will be pumped into the cylinder also and can also be controlled using a flow meter. Using the flow meters, the fuel/air ratio can be varied to the user’s preference. Also, a fan can be seen inside the combustion cylinder. This is placed inside to ensure constant and consistent mixture of the fuel and air for proper combustion.

The temperature will be measured during combustion using a fast response thermocouple. Pressure will be monitored during combustion using a piezoelectric pressure sensor or something similar. Finally, the exhaust gases should be collected and analyzed.

In conclusion the testing for this device can begin as soon as construction is complete. The authors are very confident in the integrity and safety of the designed combustion cylinder. The

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maximum stress occurs on the inner surface at a value of roughly 33300 psi. Stainless steels have yield stresses of 50000 psi up to 450000 psi confirming the safety of the design. Additionally, the glass should be thick enough as well. The side viewport will have a thickness of .34 inches while the bottom viewport will be .51 inches thick.

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Bibliography

[1] "The Next Gen Ignition System," PLASMA IGNITER, LLC, [Online]. Available: http://www.plasma-igniter.com/wp-content/uploads/2016/08/The-Next-Gen-Ignition-System.pdf. [Accessed 20 November 2016].

[2] Y. A. Cengel and M. A. Boles, "Table A-2," in Thermodynamics: An Engineering Approach, 7th ed., McGraw-Hill, 2011, p. 1024.

[3] Y. A. Cengel and M. A. Boles, "9-3: Air Standard Assumptions," in Thermodynamics: An Engineering Approach, 7th ed., McGraw-Hill, 2011, p. 1024.

[4] Y. A. Cengel and M. A. Boles, "Table A-27," in Thermodynamics: An Engineering Approach, 7th ed., McGraw-Hill, 2011, p. 1024.

[5] "DESIGN OF PRESSURE WINDOW," IPS OPTICS, [Online]. Available: http://www.ispoptics.com/articles/8/DESIGN%20OF%20PRESSURE%20WINDOW. [Accessed 20 November 2016].

[6] "PRESSURE WINDOW DESIGN," Advanced Glass Industries, [Online]. Available: http://www.advancedglass.net/pdfdocs/PressureWindows.pdf. [Accessed 20 November 2016].

[7] F. A. J. Pertl, "Prospects of Lean Ignition With the Quarter Wave Coaxial Cavity Igniter," 2008.

[8] Y. A. Cengel and M. A. Boles, "Table A-17," in Thermodynamics: An Engineering Approach, 7th ed., McGraw-Hill, 2011, p. 1024.

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5 Appendix

5.1 Design Dimensions

13

5.2 Pipe Dimensions

14

5.3 Flange Dimensions

15

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