Novel Design and Optimization of Vehicle's Natural Gas Fuel Tank
Novel Design and Optimization ofVehicle's Natural Gas Fuel Tank
A Thesis Presented to
The Faculty ofthe
Fritz J. and Dolores H. Russ College ofEngineering and Technology
Ohio University
In Partial Fulfillment
ofthe Requirement for the Degree
Master ofScience \
by , Shr-Hung Chen
March 1997
QHIO UN!VERSlrv LIBRARY Acknowledgments
I would like to thank my advisor, Dr. Bhavin V. Mehta, Assistant Professor of
Mechanical Engineering, for having given me the privilege of working on this problem.
Working on this thesis has been an invaluable experience and has greatly contributed to my knowledge and understanding ofthe subject.
I would also like to thank Dr. M. Khairul Alam, Professor of Mechanical
Engineering and Dr. Daniel Gulino, Associate Professor of Chemical Engineering of being on my thesis committee.
I dedicate this thesis to my parents who have been my source inspiration In pursuing my Master's degree. A special word ofthanks to my sister for her support. Table of Contents
Topic Page
List ofTable III
List ofFigure IV
1. Introduction 1
1-1 Introduction 1
1-2 Objective 1
1-3 Natural Gas Vehicles and High Pressure Storage Tanks 2
2. Literature Review 4
2-1 Natural Gas Vehicle 4
2-2 The Shape ofNatural Gas Storage Tanks 5
2-3 The Materials ofCompress Natural Gas Storage Tanks 6
3. Materials Consideration ofNatural Gas Storage Tanks 9
3-1 Introduction 9
3-2 Different Materials Considered 9
3-3 Aluminum-6061-T6 10
3-4 Steel-AISI-I040 16
3-5 Composite Material (Kevlar) 19
4. FEM Modeling and Design ofNatural Gas Storage Tanks 24
4-1 Introduction 24 ii Topic Page
4-2 Creation of3-D Model ofthe Tank Using Intergraph's CAD/CAM
System 24
4-3 Creation of3-D Model ofTank Using Patran3.0 36
5. Theory and FEM Analysis ofCylindrical Tank 38
5-1 Introduction 38
5-2 The Mathematical Model ofA Cylindrical Tank 38
5-2-1 Thin-Walled Cylindrical Pressure Vessels 38
5-2-2 Thick-Walled Cylindrical Pressure Vessels 41
5-3 FEM Analysis ofCylindrical Pressure Vessels 47
5-4 The Comparison ofTheoretic and FEM Analysis Result 52
6. FEM Analysis ofNoncylindrical Tanks and Optimization 55
6-1 Introduction 55
6-2 FEM Analysis ofNon-Cylindrical Model Considering 2 Materials 55
6-3 FEM Analysis Considering Kevlar Composite Material 70 .
6-4 Optimization 75
7. Conclusion and Discussion 79
7-1 Conclusion 79
7-2 Future Work and Recommendations 82
8. Bibliography 83 111 List ofTables
Table Title Page
3-1 Mechanical Properties ofMaterials 12
3-2 Designation system for aluminum alloys 13
3-3 Temper designation for alloys 14
3-4 The properties ofAluminum-6061-T6 15
3-5 SAE-AISI plain carbon steels 18
3-6 Properties ofKevlar Composite Material 22
4-1 3-D Modeling 26
4-2 The Dimensions Used in 3-D Modeling 27
5-1 The equation for the generalized Hook's Law 45
6-1 The Nodes and Tetrahedral Elements ofFinite Element Mesh 57
6-2 The Constrained Area 58
6-3 Model Versus Internal Pressure 59
6-4 The Maximum Stress Development with I/FEM and
Patran3.0 System 78
7-1 The Density and Yield Stress ofMaterials 81 iv List ofFigures
Figures Title Page 3-1 Comparison ofthe Yield Strength 20 3-2 The Structure ofKevlar 23 4-1 Square Shape 28 4-2 Cylindrical Shape 29 4-3 Cylindrical Shape with Two Hemispheric Ends 30 4-4 Square Shape with 4 Fins 31 4-5 Rounding Edge Square with 4 Fins 32 4-6 Rounding Square with 4 Fins and Hole Opening on Fins
(Thickness ofthe Wall is 0.5 in) 33
4-7 Rounding Square with 4 Fins and Hole Opening on Fins
(Thickness ofthe Wall is 0.7 in) 34
4-8 Rounding Square with 4 Fins and Hole Opening on Fins
(Thickness ofthe Wall is 1.0 in) 35
4-9 The Patran3.0 Finite Element Modeling
(Thickness ofthe Wall is 1 in) 37
5-1 Diagrams for analysis ofthin-walled cylindrical pressure
vessels 40
5-2 Diagrams for analysis ofthin-walled cylindrical pressure
vessels 40 v Figures Title Page
5-3 Diagrams for analysis ofthin-walled cylindrical pressure
vessels 41
5-4 Diagrams for analysis ofthick-walled cylindrical pressure
vessels 43
5-5 Diagrams for analysis ofthick-walled cylindrical pressure
vessels 43
5-6 The Constrained Area ofCylindrical Pressure Vessel 49
5-7 The Distribution ofStresses ofAluminum-6061-T6 Material
Model 50
5-8 The Distribution ofStresses of Steel-AISI-I040 Material Model 51
6-1 The Distribution ofStresses ofAluminum-6061-T6 Material
Model (Shape 1) 60
6-2 The Distribution ofStresses ofAluminum-6061-T6 Material
Model (Shape 3) 61
6-3 The Distribution ofStresses ofAluminum-6061-T6 Material
Model (Shape 4) 62
6-4 The Distribution of Stresses ofAluminum-6061-T6 Material
Model (Shape 5) 63
6-5 The Distribution ofStresses ofAluminum-6061-T6 Material
Model (Shape 6) 64 VI Figures Title Page
6-6 The Distribution of Stresses ofSteel-AISI-I040 Material Model
(Shape I) 65
6-7 The Distribution of Stresses ofSteel-AISI-I040 Material Model
(Shape 3) 66
6-8 The Distribution ofStresses ofSteel-AISI-I040 Material Model
(Shape 6) 67
6-9 The Distribution ofStresses ofSteel-AISI-I040 Material Model
(Shape 7) 67
6-10 The Distribution ofStresses ofSteel-AISI-I040 Material Model
(Shape 8) 68
6-11 The Distribution ofStresses ofSteel-AISI-I040 Material Model
under Patran3.0 Analysis (Shape 8) 72
6-12 The Model ofLaminate Material 73
6-13 The Distribution ofStresses ofKevlar Composite and Steel-
AISI-I040 Material Model under Patran3.0 Analysis (Shape 8) 74
6-14 The Gasoline Tank ofA Ford Escort 77 CHAPTERl Introduction
1-1 Introduction
The price of petroleum has become increasingly more expensive since the early
1970s. To fmd a new motor fuel for automobile use is an important challenge; natural gas is one of the most prospective of these fuels. Compared with gasoline, it is inexpensive and less polluting.
Although some automobiles now run on compressed natural gas, storing sufficient gaseous fuel to accommodate the needs ofthe car is still a major problem. For a natural gas vehicle to travel as far as a gasoline vehicle (between 250 miles and 300 miles) without refueling, it must carry a very heavy high pressure natural gas storage. Many high-pressure tanks that meet the 300-mile distance requirements take up a lot of space and add weight to the vehicle. That is, few vehicles, such as mid-to-full-size pickup trucks, vans and heavy-duty vehicles, are large enough to provide sufficient storage space to install this equipment. Thus, developing a lighter tank which can store more high pressure natural gas is essential for natural gas vehicle's commercial success.
1-2 Objective
The objective of this research is to use I1FEM and Patran3.0 software to analyze eight shapes and three materials (Aluminum-6061-T6, Steel-AISI-I040 and Laminate
Composite material). The maximal stresses of these shapes and materials will be 2 compared to help fmd the best model and material for a compressed natural gas storage tank which can store at higher natural gas pressure.
Chapter 1 is an introduction to natural gas vehicles and the rationale for their development.
Chapter 2 is an overview of the literature pertaining to natural gas vehicles and high pressure storage tanks.
Chapter 3 evaluates materials used in natural gas storage tanks, the choices of three materials (Aluminum-6061-T6, Steel-AISI-I040 and laminate composite material), and discusses the properties ofthese materials.
Chapter 4 examines the designs of several models of high pressure vessels.
Intergraph's Engineering Modeling System (I/EMS) and MSC's Patran3.0 are used to develop 3-D fmite element models ofhigh pressure vessels.
Chapter 5 presents the mathematical models and results of the finite element analysis of a cylindrical vessel, and compares theoretical and fmite element analysis result.
Chapter 6 describes the fmite element analysis of non-cylindrical vessel models that were created by IIFEM and Patran3.0, and discusses optimization of natural gas storage tank models.
Chapter 7 presents conclusions and offers directions for future research.
1-3 Natural Gas Vehicles and High Pressure Storage Tanks
Natural gas is a widely available, inexpensive, efficient and clean burning fuel.
When used in automobile propulsion, natural gas is cheaper than the per gallon equivalent 3 of gasoline. Including compression costs, natural gas can be 25 percent to 50 percent cheaper than gasoline and costs as much as 50 percent less than such alternative fuels as methanol.
Natural gas bums cleaner than most alternative fuels. It produces only low levels ofpollutants, such as reactive organic gases, nitrogen oxide (NOx) and carbon monoxide
(CO), and produces virtually no particulates. Highly efficient, natural gas provides high engine thermal efficiency. Engine power can be increased by 40 percent with natural gas.
The fuel tank used by natural gas vehicle (GNV) is a high pressure storage tank.
In general, natural gas storage tank pressure is rated at 3000-psi to SOOO-psi. Tanks are most frequently composed of Steel-AISI-I040 or Aluminum-6061-T6. The purpose of this research is to find an optimal material and shape for storing high pressure natural gas. 4 CHAPTER 2 Literature Review
2-1 Natural Gas Vehicles
Many studies have been conducted on natural gas vehicles. Research has most frequently focused on the efficiency, pollution and economics ofnatural gas vehicles. In addition to investigating the advantages of natural gas vehicles, some university or research organizations have modified engine designs to improve the efficiency ofnatural gas vehicles.
Ecole Polytechnique de Montreal [1] has modified the design of a 364-ci engine with 12.7:1 compression ratio. The modification used 3.570-inch stroke crankshaft, installed new dome-shaped pistons, and rounded offthe combustion chamber edges. The modification increased engine power by 40 percent when natural gas is used, relative to the stock gasoline engine.
Duoba, McDowell and Ruiz [2] modified the fuel system ofnatural gas vehicle to improve its efficiency. The modifications are: first, the spark was uniformly advanced 6 degrees of crank angle. This was done to compensate for the slower burning of natural gas, compared to gasoline. Second, a special electronic box, Super Fix 1, was connected between the sensors and the computer, to avoid error codes caused by the lean operation and the different spark timing.
Brezonick [3] describes why the government considers the natural gas vehicle to be an alternative to the gasoline vehicle. Since 1990, natural gas augmentation of cars 5 has grown at a rapidly increasing pace. Because air pollution and problems of economy became very important government policy considerations, the federal government and a number of states have initiated new rules, programs and incentives to encourage the use ofalternative fuel (e.q. Natural Gas) vehicles.
2-2 Shapes ofNatural Gas Storage Tanks
In natural gas storage tanks, a form of high pressure tank, the shape and material are very important for storage under high pressure.
The ASME Code method [4] provides shape considerations for most noncircular pressure vessels and yields safe, economical designs for pressure vessel design. The
ASME Code method includes design rules for noncircular pressure vessels, for unreinforced and reinforced vessels. For unreinforced pressure vessels, the Code uses the stress distribution of a rigid frame with limitations. For reinforced vessels, each reinforcing frame is analyzed as a rigid frame, the plate panels between the frames are computed using small deflection plate bending theory.
Li [11] indicates how to optimize a high-pressure vessel. Li discusses sensitivity analysis for a fmite element model during shape optimization design for a pressure vessel.
Sensitivity analysis is an important part in structural analysis and optimization design for pressure vessels, especially for the shape optimization of those with complicated structures. Because the result from fmite element analysis is fully utilized in this method, the program is greatly simplified so that it becomes possible to carry out the shape optimization with comparatively more variables. 6 The theory ofpressure vessel calculation primarily uses three methods to analyze pressure vessels: small deflection analysis [4], large deflection analysis [5], and finite element analysis [6]. Small deflection analysis is very tedious and complex, and not suitable for use by the pressure vessel designer. For this reason, design formulas given in the ASME Code [4] are based on maximum stresses obtained from a frame analysis of the prismatic cross section ofthe vessel, combined with a small deflection plate analysis oflarge side panels.
Large deflection analysis [5] is an analysis method for deflections in excess of one-half of the thickness of the plate. The linear small deflection theory is no longer applicable because part ofthe load is carried by membrane tension. Ifmembrane tension is considered as part ofthe load carrying capacity of a plate, stresses for a given load are generally smaller, and stresses for a given deflection are generally greater than that considered in small deflection theory.
Finite element analysis [6]. can cover both small deflection analysis and large deflection analysis. It is an advanced computer technique for analysis of stress in a structure.
2-3 Materials ofCompressed Natural Gas Storage Tanks
Natural gas vehicle designers [8] prefer Aluminum-6061-T6 or Steel-AISI-I040 when building the storage tanks for natural gas vehicle. Aluminum is light weight and has excellent resistance to corrosion. Its use reduce the weight ofthe natural gas storage tank. Steel-AISI-I040 has higher strength than Aluminum-6061-T6. It can store more 7 gaseous fuel than can an aluminum tank, but it is much heavier and its corrosion resistant is inferior compared to an aluminum tank.
Besides steel and aluminum, the best material of gaseous tank is composite materials ([7],[8],[9]). Those include fiberglass wrapped aluminum [8], fiberglass wrapped steel [7] and Kevlar [7].
Fawley [8] indicates that the composite reinforced aluminum fuel tank weighs 50 percent less than existing steel natural gas storage tanks, reduces vehicle suspension overloading and alleviates installation handling problems. For example, a lOx 42 inch composite reinforced aluminum natural gas storage tank weighs 69 lbs, while the same size cylinder in steel weighs about 120 lbs.
Brunswick Technical Group [9] developed a composite gaseous fuel tank that uses Brunswick composite. Its primary advantage lies in its weight savings over steel or aluminum-wrapped tanks as well as an increase in gaseous fuel capacity. The company asserts that the weight reduction of the Brunswick Composite can be as much as 70 percent over all-steel tanks, and from 30 percent to 50 percent over aluminum lined composite tanks. This can improves gaseous fuel capacity as a function of the thinner composite walls, which allows for as much as 15 percent more gas storage capacity with the same external volume.
Frank and Edward [7] use fiberglass wrapped aluminum, fiberglass wrapped steel and Kevlar to create the natural gas vehicle's gaseous tank for a 1991 Natural Gas
Vehicle Competition. The primary reason for using fiberglass to wrap the aluminum and steel is fiberglass not only adds to the strength ofthose two materials, can also reduce the 8 weight ofthe natural gas storage tank. Another, the Kevlar composite material is the best material for natural gas storage tanks, because it has higher strength and is lighter than fiberglass wrapped aluminum or steel. However, Kevlar is twice as expensive as fiberglass wrapped aluminum or steel. 9 CHAPTER 3 Materials Consideration For Natural Gas Storage Tanks
3-1 Introduction
In this chapter, natural gas storage tank design will be described following material considerations. In discussing materials, the chapter will describe the characteristics ofaluminum, steel and composite materials, including the mechanical and chemical properties of Aluminum-6061 T6, Steel-AISI-I040 and Kevlar composite material.
3-2 Different Materials Considered
Aluminum-6061-T6 and Steel-AISI-I040 are the most widely used materials in compressed natural gas storage tanks [8]. Steel-AISI-I040 is strong enough to store higher pressure (between 3000 psi to 3500 psi) natural gas, but its disadvantage is the heavy weight. Aluminum-6061-T6 is also commonly used in natural gas storage tanks.
This material is lighter than Steel-AISI-I040; its density is just one third of Steel-AISI
1040 (see Table 3-1). Its main disadvantage is that it is not strong enough to store higher pressure gas; thus Aluminum-6061-T6 is used in some natural gas storage tanks that don't store under high pressure (1000 psi to 1500 psi).
Some designers are beginning to consider composite materials, which can store more compressed natural gas than Steel-AISI-I040 does, and are lighter than Aluminum
6061-T6. Composite materials possess both advantages of Aluminum-6061-T6 and 10 Steel-AISI-1040, being strong and light. Although composite materials have so many advantages, they are more expensive than Aluminum-6061-T6 and Steel-AISI-I040.
Thus, they are not used widely in high pressure vessel.
3-3 Aluminum-6061-T6
Aluminum is the second most plentiful metal on earth. Until the late 1800s, aluminum wasn't used widely, because it was expensive and difficult to produce.
Development of electrical power and the Hall-Heroult process for electrically reducing
Al20 3 to liquid metal allowed aluminum to become one of the most widely used and an inexpensive engineering material. Applications of aluminum include beverage cans, household applications, chemical processing equipment, electrical power transmission equipment, automotive components, and aerospace parts and assemblies.
Aluminum's beneficial physical properties include light weight, excellent oxidation and corrosion resistance, high electrical conductivity, high thermal conductivity and nonmagnetic behavior. However, the disadvantages ofaluminum are low endurance, low melting temperature and low hardness.
Wrought aluminum alloys are designated by a four-digit number following the system adopted by the Aluminum Association in 1954 (see Table 3-2). Another, the temper designation indicates the treatment the alloy received while being processed into its present condition and associated properties. The temper ofan alloy is indicated by the letters 0, F, H or T followed by one or more numbers (see Table 3-3).
Aluminum-6061-T6 has better fabricating qualities in the quenched condition. It belongs to AI-Mg-Si (see Table 3-4) and age-hardenable alloys, so it has excellent 11 strength and mechanical properties(See Table 3-4) for use in canoes, railroad cars and natural gas storage tanks. 12
Table 3-1: Mechanical Properties ofMaterials [15]
Material Narne Alurninurn-6061-T6 Steel-AISI-I040
Elastic Modulus (psi) le+07 2.93e+07
Poisson 0.33 0.32
Shear Modulus (psi) 3.7594e+06 1.10985e+07
Density (pci) 0.098 0.284
Yield Stress (psi) 36000 64000 13
Table 3-2: Designation System for Aluminum Alloys [12]
Wrought Alloys lxxxx Commercially pure Al Not age-hardenable (>99% AI)
2xxxx AI-Cu and AI-Cu-Li Age-hardenable
3xxxx AI-Mn Not age-hardenable
4xxx AI-Si and AI-Mg-Si Age-hardenable ifmagnesium is present
5xxx AI-Mg Not age-hardenable
6xxx AI-Mg-Si Age-hardenable
7xxx AI-Mg-Zn Age-hardenable
8xxx AI-Li, So, Zr, or B Age-hardenable 14
Table 3-3: Temper Designations for Alloys [12]
F As-Fabricated (hot-worked, forged, cast, etc.)
0 Annealed (in the softest possible condition)
H Cold-Worked
W Solution-treated
T Age-Hardened
Tl cooled from the fabrication temperature and naturally aged
T2 cooled from the fabrication temperature, cold-worked, and naturally aged
T3 solution-treated, cold-worked, and naturally aged
T4 solution-treated and naturally aged
T5 cooled from the fabrication temperature and artificially aged
T6 solution-treated and artificially aged
T7 solution-treated, and stabilized by overaging
T8 solution-treated, cold-worked, and artificially aged
T9 solution-treated, artificially aged, and cold-worked
TIO cooled from the fabrication temperature, cold-worked, and artificially aged 15
Table 3-4: The Properties ofAluminum-6061-T6 [15]
Aluminum-6061-T6 composition
Cu Si Mg Cr Aluminum
0.25 0.6 1.0 0.25 Remainder
Physical properties
Densitytlb/in'') Electrical conductivity, Brinell hardness, 500 % lACS kg load, 10-mm ball
0.098 45 95
Mechanical properties
Yield strength, Tensile strength, Elongation, Endurance limit, 10001b/in2 10001b/in2 %in2in 10001b/in2
36 41 12 14 16 3-4 Steel-AISI-1040 Iron (Fe) is not a high-purity metal; rather, it contains chemical elements which have a large effect on its physical and mechanical properties. Steel is a malleable alloy of iron and carbon, and usually contains substantial quantities ofmanganese.
Steels are typically produced in two ways. One is produced by refining iron ore, another is produced by recycling scrap steel. Steels are based on iron-carbon alloys which include carbon steel and alloy steel. Carbon steel owes its distinctive properties chiefly to its carbon content. Alloy steel owes its distinctive properties chiefly to some element or elements other than carbon, or jointly to such other elements and carbon. The
SAE-AISI system is a numerical indexing system used to identify wrought carbon, alloy and stainless steels. The system is applied to semifmished forging, hot-rolled, cold- finished bar, wire rod, seamless tubular good, structural shape, plate, sheet, strip and welded tubing. The four numbers of SAE-AISI system designation are usually used to designate standard alloy and carbon steels specified to chemical composition ranges.
The SAE-AISI-system categorizes carbon steels into four groups (see Table 3-5).
Group I steels have the lowest carbon content (less than 0.15 percent) and is selected when enhanced cold formability or drawability is required. Group I steels have relatively low tensile values. Group IT steels contain 0.15 percent to 0.30 percent carbon and less than about 0.75 percent manganese. This group has increased strength and hardness and reduced cold formability compared with the lowest carbon group. Group ill have medium carbon content (0.30 percent to 0.55 percent), and are suitable for a wide variety of automotive applications. Group N steels are high-carbon steels (0.55 percent to less 17 than approximately 1.0 percent carbon), and are used for applications where the higher carbon is needed to improve wear characteristics.
Steel-AISI-I040 is a carbon group ill steel. The steel is used widely for certain types of cold-formed parts. In nearly all cases, the parts cold formed from Steel-AISI-
1040 are annealed, normalized, or quenched and tempered prior to use. The higher carbon grades of the steels are frequently cold drawn to specified mechanical properties for use without heat treatment for some applications. 18
Table 3-5: SAE-AISI Plain Carbon Steels [14]
Group I SAE-AISI 1005, 1006, 1008, 1010, 1012, 1013
Group II SAE-AISI 1015,1016,1017,1018,1019,1020,1021,1022,
1023, 1025, 1026, 1029, 1513, 1522, 1524, 1526, 1527
SAE-AISI 1030, 1035, 1037, 1038, 1039, 1040, 1042, 1043,
Group III 1044, 1045, 1046, 1049, 1050, 1053, 1536, 1541, 1548, 1551,
1552
Group IV SAE-AISI 1055, 1059, 1060, 1065, 1069, 1070, 1074, 1075,
1078, 1080, 1085, 1086, 1090, 1095, 1561, 1566 19 3-5 Composite Material (Kevlar)
A composite material is produced when two or more materials are joined to give a combination ofproperties not found in the original materials. Most composite materials
developed thus far have been fabricated to improve mechanical and chemical properties
such as strength, stiffness, toughness, weight, high-temperature performance, corrosion resistance, hardness or conductivity. The strengthening mechanism strongly depends on the geometry of the reinforcement. Other characteristics, based on the shapes of the materials, can be placed into three categories: particulate, fiber, and laminar composites.
A particulate composite is a composite whose reinforcement may be classified as particles. The type of particle, such as ceramic, metal, or inorganic particles, produce reinforcing effects in metallic matrices by different strengthening mechanisms. In general, particles are not very effective in improving fracture resistance. Particulate composites are designed to produce unusual combinations of properties rather than to improve strength.
Fibrous composites provide improved strength, fatigue resistance, stiffness and strength-to-weight ratio by incorporating strength and stiffness. The matrix of the material transmits force to the fibers. Because of their small cross-sectional dimensions, fibers are not directly usable in engineering applications. They can carry most of the applied force, and the strength of the fibrous composite can be high at both room temperature and elevated temperatures (see Figure 3-1). 20
150~()()() . Borsic fiber-reinforced aluminum composite (50% boron fibers)
.~ I()() ~ ()()( ) c...... c: 7075-T6
5()J)()()
()
Figure 3-1: Comparison of the yield strength of dispersion strengthened sintered aluminum powder (SAP) composite with that of two conventional two-phase high-strength aluminum alloys. The composite as benefits above 300 DC. A fiber reinforced aluminum composite is shown for comparison. [13] 21 Laminar composite materials include thin coatings, thicker protective surfaces, claddings, bimetallics, laminates, and a host of other applications. Laminating can improve the properties of materials or combine several materials into one, such as corrosion resistance, while retaining low cost, high strength, light weight, superior wear or abrasion resistance, and the other important characteristics, including unusual thermal expansion characteristics and improved appearance.
Kevlar is an aramid fiber composite. Kevlar's chemical structure is of aromatic polymers strengthened by a backbone containing benzene rings (see Figure 3-2). Kevlar has excellent strength and stiffness, and has superior specific strength and specific modulus (see Table 3-6) but can't be used in high temperature situations because of its low density. In addition, Kevlar is too expensive for casual use. In industry, Kevlar is usually used in laminar composites like Arall (Kevlar aluminum laminate). Thus, this research will focus on laminate composite (2 sheets Kevlar with 1 sheet Steel-AISI-I 040) 22
Table 3-6: Properties ofKevlar Composite Material
Material Kevlar
3 Density (lb/in ) 0.0362
Tensile Strength (ksi) 650
Modulus ofElasticity (x 106 psi) 18.0
Melting Temperature (OC) 500
Specific Modulus (x 107 in) 34.7
Specific Strength (x 106 in) 10.1 23
H 0 H -c-()-~-N-()-i-c-()-~-N-()-I-I II I
o H 0 H H 0 H I II I -()-~-N -()-i-C-()-~-N -()-i---- o H 0 H
Figure 3-2: The structure of Kevlar. (The fibers are joined by secondary bonds between oxygen and hydrogen atoms on adjoining chains.) [13] 24 CHAPTER 4 FEM Modeling and Design ofNatural Gas Storage Tanks
4-1 Introduction
The software used in the fmite element modeling of the compressed natural gas storage tank were Intergraph's Finite Element Modeling (I/FEM) and Patran3.0. I/FEM was the modeling and fmite element analysis for the tank under the consideration of isotropic material as Aluminum-6061-T6 and Steel-AISI-I040. This was done mainly in order to compare the maximum stress and stress's distributions of the several different shapes. Another package, Patran3.0, was used to model the tank under the consideration of laminate composite materials. In Patran3.0, it was easier to assign the material properties oflaminate composite materials and analyze them.
4-2 Creation of3-D Model ofThe Tank Using Intergraph's
CAD/CAM System
I/FEM, Intergraph's Finite Element Modeler, a finite element package used in mesh generation and fmite element analysis, was used for structure stress analysis ofthe natural gas storage tank. I/EMS (Intergraph's Engineering Modeling System) 3-D modeling system was used from within I/FEM for the purpose ofcreating the 3-D Model. 25 A 3-D solid model of the tank was created on an Intergraph Microstation using
Intergraph's Engineering Modeling Software(IIEMS). The following steps were used in creation ofthe 3-D model for analysis:
1) Geometry creation;
2) Assigning the material mechanical character and properties on the solid
model;
3) Setting pressure inside the solid model;
4) Assign boundary condition on the model; and
5) Auto-meshing on the 3-D model;
The 3-D model was created in eight different shapes on I1EMS (see Tables 4-1 and 4-2). Shapes included a square (see Figure 4-1), cylinder (see Figure 4-2), cylinder with hemispheric ends (see Figure 4-3), square with 4 fms (see Figure 4-4), rounding- edged square with 4 fms (see Figure 4-5) and rounding edge square with 4 fins and hole openings on fins (see Figures 4-6, 4-7, 4-8). Shapes 6, 7 and 8 are the same type of geometry, but their wall thickness are different at 0.5, 0.7 and 1.0 inches, respectively 26
Table 4-1: 3-D Modeling
Shape 1 Shape 2 (Square) (Cylinder
I / I ! t H /'1 V L w f
Shape 3 Shape 4 C linder with Bemis heric Ends S uare with 4 Fins R ~------r-
L
Shape 5 Shapes 6, 7, 8 (Rounding Edge Square with 4 (Rounding Edge Square with 4 Fin, and hole Fins o enin on each fin ~ ~i 11 .••:.!.1 I~ H H .. j.- 1_ 1- 27
Table 4-2: The Dimensions Used in 3-D Modeling
Shape No. Shape Shape Shape Shape Shape Shape Shape Shape 1 2 3 4 5 6 7 8 High 12 in 12 in 12 in 12 in 12 in 12 in ( H) Width 12 in 12 in 12 in 12 in 12 in 12 in (W) Length 10 in 20 in 15 in 10 in lOin lOin 10 in 10 in (L) Radius 5in 5in (R) Thickness 0.5 in 0.5 in 0.5 in 0.5 in 0.5 in 0.5 in 0.7 in 1.0 in ( t ) Thickness 0.25in 0.25in 0.25in 0.25in O.2Sin of Fin ( t2 ) Radius of 0.2 in 0.2 in 0.2 in 0.2 in Rounding Edge Fillet (r) Radius of 0.5 in 0.5 in 0.5 in hole (r2 ) 28
Figure 4-1: Square Shape 29
~ \
Figure 4-2: Cylindrical Shape 30
Figure 4-3: Cylindrical Shape with Two Hemispheric Ends 31
Figure 4-4: Square Shape with 4 Fins 32
Figure 4-5: Rounding Edge Square with 4 Fins 33
Figure 4-6: Rounding Square with 4 Fins and a Hole Opening on Fins (Thickness ofthe Wall is 0.5 in) 34
Figure 4-7: Rounding Square with 4 Fins and a Hole Opening on Fins (Thickness ofthe Wall is 0.7 in) 35
Figure 4-8: Rounding Square with 4 Fins and a Hole Opening on Fins (Thickness ofthe Wall is 1 in) 36 4-3 Creation of3-D Models ofThe Tank Using Patran3.0
Patran3.0 is a fmite element package developed by MSC Engineering. Patran3.0 provides several finite element analysis packages, including FEM, ADVANCEDFEM and ABAQUS. In this research, then ADVANCEDFEM (advanced finite element analysis) analysis package is used to analyze the structural stresses oflaminate composite material gaseous tank.
The 3-D solid model of the laminate composite material (2 sheets of Kevlar with
sheet of Steel-AISI-I040) was created on the Patran3.0 analysis software. The development of 3-D model lies in the creation of points, lines, surfaces and solids. The following steps were used in creating the 3-D models:
1) Geometry creation;
a) The creation ofgrids
b) Lines connecting these grids
c) Connecting line to line into faces
d) Extruding the faces into solids.
2) To set boundary conditions (pressure and constrained side);
3) To assign the laminate composite (2 sheets of Kevlar with Steel-AISI-I040)
material properties;
4) To create a fmite element mesh; and
5) To assign the material properties on element property.
The creation of 3-D model results in shape 8 (see Figure 4-9). The purpose is to compare the maximum storable pressure on shape 8. 37
Figure 4-9: ThePatran3.0 Finite Element Model (Thickness ofthe Wall is 1 in) 38 CHAPTER 5
Theory and FEM Analysis of Cylindrical Tank
5-1 Introduction
In this charter, mathematical models used to describe the cylindrical tank will be discussed, and compared with their FEM analysis results. This will be accomplished in three steps:
1) The mathematical model ofthin-wall and thick-walled cylindrical tanks;
2) FEM analysis ofcylindrical tanks; and
3) The comparison oftheory and FEM analysis.
5-2 The Mathematical Model ofA Cylindrical Tank
The cylindrical shape is widely used for pressure vessels in industry. Second only to the sphere, the cylinder is the best shape for high pressure vessels. This section will present the mathematical model for cylindrical pressure vessels. The content includes the mathematical model for thin-walled and thick-walled cylindrical pressure vessels.
5-2-1 Thin-Walled Cylindrical Pressure Vessels
The ideal shape of thin-walled cylindrical pressure vessel is considered with the exception of the junctures with ends, and the walls act as a membrane. That means no bending ofthe walls. 39 The analysis of pressure vessels will begin by considering a cylindrical pressure vessel such as a boiler. A segment is isolated from this vessel by passing two planes perpendicular to the axis ofthe cylinder and one additional longitudinal plane through the
same axis. The hoop stress is a}, and the longitudinal stress is a 2 • The hoop stress and longitudinal stress, multiplied by the respective areas on which they act, maintain the element ofthe cylinder in equilibrium against the internal pressure (see Figure 5-1).
The internal pressure in excess of the external pressure is defined as p psi. The internal radius ofthe cylinder is r. The thickness ofthe wall is t. The cylindrical segment onto the diametral plane is AI. The area of both longitudinal cuts is 2A. On the Z coordinate, the total forces of action on the cylindrical segment are shown in Figure 5-2.
Thus,
pAl = a} (2A) (5.1)
Al == 2r Llx (5.2) and A=tLlx (5.3) so (5.4) and (5.5)
We can obtain the hoop stress
pr a}=- (5.6) t 40
r
r
Figure 5-1 Figure 5-2
The other component ofnormal stress, a ,is longitudinal stress (see Figure 5-3). 2
By passing a section through the vessel perpendicular to its axis, the force caused by the
2 internal pressure is p1r r , and the force developed by the longitudinal stress (j2 in the walls is 0'2[nCr + 1)2 - ;rr2]. By equating these two force we get;
(5.7)
Thus, (5.8)
However, t is the thickness of the cylindrical wall, and this development is restricted to thin-walled vessel. This means that t is very small, so it can be set at t 2 ~ O. The longitudinal stress is thus
pr o: =- (5.9) 2 2t 41
y
z I
Figure 5-3
5-2-2 Thick-Walled Cylindrical Pressure Vessels
Consideration of a thick-walled cylindrical pressure vessel under internal and external pressure is related to the thin-walled cylindrical pressure vessel, and using the mathematical theory of elasticity to solve the problem. The equilibrium conditions are related to the element deformation using Hook's law. Then the governing differential equation is solved by the prescribed boundary conditions.
The dimensions of the long cylinder with axially restrained ends are shown in a cross-section in Figure 5-4. The inside radius of the cylindrical vessel is r., and the outside radius is '0. The internal pressure ofthe cylindrical vessel is Pi , and the external pressure is Po. a, is the normal radial stress acting on the infinitesimal element at a 42 distance r from the center ofthe cylinder, and both normal tangential stress acting on the other two faces of the element are at. These stresses, normal tangential stress at' are equal. Other normal tangential stresses are similar to the hoop stresses in thick-walled cylinder. Moreover, the axial stresses ax on the two faces of the element are equal and opposite normal to the Y-Z plane (see Figure 5-5).
x
Figure 5-4 Figure 5-5
The forces acting on the element are obtained by multiplying the stresses by their respective areas, neglecting the weight ofthe element. Stress a, acts on area 1x rdo and the a, + dar acts on 1x (r + dr)d¢. Both normal tangential stresses at act on the
1 element's two faces which are dr x l , and both CYt are inclined "2d¢ to the line perpendicular to OA. Then, L F = o. Thus, 43 drjJ O"r(1 x rd¢) +2 x (O"( x 2)(1 x dr) - (rr, +dO"r)[(r +dr)d¢ = 0,(5.10)
Which can be simplified to
(5.11)
From Figure 5-4, the strain Cr ofthe element in the radial direction is
(u+du) - u du C = (5.12) r dr dr
Strain ct ofthe element in the tangential direction is
21C(r + u) - 2;rr u (5.13) ct = 2w r
From the generalized Hook's law (see Table 5-1), one obtains
(5.14)
(5.15)
(5.16)
However, in the thick-walled cylindrical vessel with axially restrained deformation, strain e, =o. So,
(5.17) 44 And then, the Eq.(5.17) can be substituted into the Eq.(5.14) and Eq.(5.15), obtaining Eq.(5.18) and Eq.(5.19)
crE -- = (1 - v)a - va (5.18) 1+ v r t
ctE -- = (1- v)a - va (5.19) 1+ v t r 45
Table 5-1: The equations for the generalized Hook's law for isotropic
linearly elastic materials for use with Cartesian coordinates
_ T xy r xy G
r.. r; = G 46 Solving Eq.(5.18) and Eq.(5.19), one obtains
(5.20)
(5.21 )
From Eq.(5.12) and Eq.(5.13), the radial and tangential stresses are
E du u a, = (1+ v)(1- 2v) [(1- v) dr + v;] (5.22)
and (5.23)
By substituting these values into Eq.(5.11) and simplifying, the following differential equation is obtained:
2 diu du r -+r--u=O (5.24) dr ' dr
Since Eq.(5.24) is an Euler-Cauchy equation, the corresponding general solution is
(5.25)
The internal and external pressures are equal to the radial stresses acting on the elements at the respective radius. Therefore,
(5.26)
(5.27) 47
In this case, consider internal pressure only, so that means to set Pi =-1-= 0, and Po = 0 .
Then Eq.(5.25) can be substituted into the expression for o; given by Eq.(5.22) and
Eq.(5.23), obtaining
E C2 (j (r) = -p = [C - (1- 2v)-] (5.28) r i i (1 + v)( 1- 2 v) 1 r 2 i and (5.29)
Solving equations Eq.(5.28) and Eq.(5.29) for constants C, and C2,
(5.30)
and (5.31 )
Moreover, Eq.(5.25) and its derivative, together with the constants C, and C2 given by
Eq.(5.30) and Eq.(5.31), are substituted into Eq.(5.22) and Eq.(5.23). This obtains the general equations for the radial and tangential stresses at any point ofan elastic cylinder: radial stress: (5.32)
2 2 and tangential stress: at = fir; 2 (l + \ ) (5.33) - ro ri r
5-3 FEM Analysis of Cylindrical Pressure Vessels
I1FEM, a finite element analysis software package, was used in mesh generation and finite element analysis for cylindrical pressure vessel in this research. The 3-D model 48 of the cylindrical pressure vessel was created by IlEMS, and was analyzed by I1FEM software.
The finite element mesh command ofI/FEM is "Automesh". The mesh was made up of2080 nodes and 6173 tetrahedral elements. All nodes at the face "A" (see Figure 5-
6) were constrained. The face "A" is on the plane ofthe symmetry ofthe halfcylindrical shape. The materials simulated in the 3-D finite element model are aluminum-6061-T6 and Steel-AISI-I040 (see Table 3-1). The load of internal pressure applied to area "B"
(see Figure 5-6) is 1000 psi for Aluminum-6061-T6 and 2000 psi for Steel-AISI-I040.
After applying the boundary and loading conditions, the 3-D finite element model was analyzed to evaluate the distribution of stresses. From the plot for distribution of stresses from I/FEM, one can see the maximum stress area and minimum stress area, and the values ofthese stresses (see Figures 5-7 and 5-8). 49
/~ (Constrained Area) / / A~· //
Figure 5-6 50
Figure 5-7: The Distribution of Stresses of Aluminum-6061-T6 Material
Model 51
-
Figure 5-8: The Distribution of Stresses of Steel-AISI-I040 Material
Model 52 5-4 Comparison ofTheoretical and FEM Analysis Result
In this case, the outside radius of the cylindrical shape is 5 in. The thickness of the wall is 0.5 in. The internal pressure is 1000 psi for Aluminum-6061-T6 material. As defined by thin-walled pressure vessel theory, p = 1000 psi, r = 4.5 in, t = 0.5 in .
The hoop stress and longitudinal stress follow by direct application of Eq.(5.6) and
Eq.(5.9):
pr 1000 x 4.5 hoop stress: a = - = = 9000 (psi) 1 t 0.5
pr 1000 x 4.5 longitudinal stress: 0"2 =2t = 2 x 0.5 =4500 (psi)
Consideration ofthe thick-walled cylindrical pressure vessel theory, the thickness
• of the wall is 10 percent of the outside radius of the cylindrical shape, so ro = 1.lri
Using Eq.(5.33) for at :
The maximum normal tangential stress:
; and Pi = 1000 (psi); so (at) r=/j = 10523 (psi)
The minimum normal tangential stress: 53
and Pi = 1000 (psi); so (at) r=J;) = 9523 (psi)
The average hoop stress is (at) avg = 10046 (psi)
From the result of the finite element analysis of the cylindrical pressure vessel
(Aluminum-6061-T6) I/FEM, the maximum stress developed in the cylindrical pressure vessel was 12270 psi. The hoop stress showed in thin-walled pressure vessel theory was
9000 psi, and the hoop stress showed in thick-walled pressure vessel theory was from
10523 psi to 9523 psi. Average hoop stress was 10046 psi. In this case, the outside radius ofthe cylindrical pressure vessel is 5 in, and the thickness ofits wall is 0.5 in. This case is a thick-walled pressure vessel. As seen in the above description, the value of maximum stress of finite element analysis approaches the values used in thick-walled pressure vessel theory. Therefore, the results ofthe finite element model ofthe pressure vessel within I/FEM demonstrate the validity of the model developed, and conformed well with results obtained by thick-walled pressure vessel theory.
Moreover, the distribution of stresses of Steel-AISI-I040 of cylindrical pressure vessel show that a maximum value of 24580 psi and a minimum value of 1691 psi. The internal pressure of Steel-AISI-1040 material model is 2000 psi, and its maximum stress approaches double the value of maximum stress of the Aluminum-6061-T6 material model. That means the result of FEM analysis of Steel-AISI-1040 material model is 54 correct. In addition, the distribution of stresses of Aluminum-6061-T6 material model and Steel-AISI-I040 material model appeared to be similar. Therefore, the main influence on stress disposal and the maximum stress depends on the figure ofthe vessel's model. 55 CHAPTER 6 FEM Analysis ofNon-Cylindrical Tanks and Optimization
6-1 Introduction
This chapter will describe the FEM analysis result of non-cylindrical model derived from I/FEM and Patran3.0. The material consideration of fmite element model includes Aluminum-6061-T6, Steel-AISI-1040 and Laminate Composite Material.
Moreover, the chapter will present the optimizing consideration of natural gas storage tank's designing, which includes the material and geometric models.
6-2 FEM Analysis of Non-Cylindrical Model Considering 2
Materials
In this research six different models of pressure vessels for Aluminum-6061-T6 and Steel-AISI-1040 materials were built. One is a cylindrical model which was described in Chapter 5. The 3-D model of the non-cylindrical shapes created using
IlEMS was brought up within I/FEM for the purpose of the analysis. I/FEM, a finite element package used in mesh generation and fmite element analysis, was used for stress analysis ofthe 3-D models.
The fmite element mesh was created by the "Automesh" command ofI/FEM. The nodes and tetrahedral elements offmite element mesh are shown in Table 6-1. All nodes at the face "A" (see Table 6-2), which is the face on the plane ofthe symmetry ofthe half 56 model, were constrained. The following material properties were used to represent the shapes 1,3,4,5 and 6 (see Tables 4-1 and 4-2) is Aluminum-6061-T6 (see Table 3-1), and represented by the shapes 1, 3, 6, 7 and 8 (see Tables 4-1 and 4-2) is Steel-AISI-I040
(see Table 3-1). The load of internal pressure was applied to the inside face of the models; resulting values ofload are shown in Table 6-3.
After the boundary and load conditions are applied, those 3-D fmite element models can be analyzed. The stress distribution of I/FEM will be shown by several different colors to represent different magnitude of the stress's value, and the value of maximum and minimum stress (see Figures 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 6-7, 6-8, 6-9 and
6-10). 57
Table 6-1: The Nodes and Tetrahedral Elements ofFinite Element Mesh
Material Aluminum-6061-T6
Shape No. Total Number ofNodes Total Number of Tetrahedral Elements Shape 1 1933 5615
Shape 3 2069 6198
Shape 4 2720 8338
Shape 5 2749 8489
Shape 6 2733 8378
Material Steel-AISI-I040
Shape No. Total Number ofNodes Total Number of Tetrahedral Elements Shape 1 1933 5615
Shape 3 2069 6198
Shape 6 2733 8378
Shape 7 2482 7587
Shape 8 1966 6059 58
Table 6-2: The Constrained Area
Sha e 3 /
.--. --... A
V.,,'
Sha e4 Sha e 5
Sha e 6 t=0.5); Sha e 7 t=0.7) Sha e 8 (t=I.0) 59 Table 6-3·• M 0 de I V ersus Internal Pressure
Aluminum-6061-T6
Internal Pressure (psi)
1000 Shape 1,3,4,5,6
Steel-AISI-I040
Internal Pressure (psi) Shape No.
Shape 1
4000
5000
8000 60
- -....._.,
Figure 6-1: The Distribution of Stresses ofAluminum-ono l-T6 Material
M:odel (Shape 1) 61
Figure 6-2: TIle Distribution of Stresses ofAluminum-6061-T6 Material
Model (Shape 3) 62
f~~~ -..• '.-: ";t - :~ -~A l~. ;.< -~1 ~ r~ ; UN! T
Figure 6-3: The Distribution of Stresses ofAluminum-oflol-To Material
Model (Shape 4) 63
Figure 6-4: The Distribution of Stresses ofAluminum-6061-T6 Material
Model (Shape 5) 64
-==
Figure 6-5: TIle Distribution of Stresses ofAluminum-6061-T6 Material
Model (Shape 6) 65
-,- -.~ }:~ -M MIN : IJ NIT
Figure 6-6: TIle Distribution ofStresses ofSteel-AISI-I040 Material Model
(Shape 1) 66
-_.-
Figure 6-7: TIle Distribution of Stresses of Steel-AISI-I040 Material Model
(Shape 3) 67
-
Figure 6-8: The Distribution of Stresses ofSteel-AISI-I040 Material Model
(Shape 6) 68
-
Figure 6 ...9: TIle Distribution of Stresses ofSteel-AISI-I040 Material Model
(Shape 7) 69
-
Figure 6-10: The Distribution ofStresses ofSteel-AISI-l040 Material
Model (Shape 8) 70 6-3 FEM Analysis ofModel Considering Kevlar Composite
Material
The 3-D model ofthe Kevlar composite material was created by Patran3.0 system, and brought up within P3/ADVANCED_FEM for the purpose of mesh generation and stress analysis. The Kevlar composite material model is for shape 8 (see Tables 4-1 and
4-2).
The fmite element model ofthe Kevlar composite material constructed using a total of 57 solids was made of 2213 nodes and 1520 Hexagonal 8 nodes isoparametric elements.
Before Analyzing the Kevlar composite material model, the Steel-AISI-1040 material was loaded and the same boundary conditions and internal pressures obtained as in the I1FEM analysis was used. The purpose is to compare the analysis results between I1FEM system and Patran3.0. Figures 6-10 and 6-11 show that the maximum stresses of the I1FEM analysis is 61970 psi, and ofthe Patran3.0 analysis is 61672 psi. Moreover, the stress's distributions of the I1FEM and Patran3.0 analysis are similar. Thus, the results of the finite element model of shape 8 within Patran3.0 analysis system was conformed well with results obtained for I/FEM and prove the validity ofthe model.
In the next case, the chosen material was a constructed laminate composite that includes 2 sheets of Kevlar composite material and 1 sheet Steel-AISI-1040. The thickness ofeach sheet of Kevlar is 0.1 in, and the thickness ofSteel-AISI-1040 is 0.7 in
(see Figure 6-12). Moreover, the specific strength ofKevlar is 1.01x108 in (see Table 3
6). The specific strength ofthe Kevlar is important characteristic: 71 Yield Strength Specific Strength = D' · ensity
7 5 The Yield Strength is 1.01 X 10 x 0.0362 = 3.66 x 10 • The properties of the laminar composite material parallel to the lamellae are estimated from the rule of mixture. The
Yield Strength oflaminate material is: 64000xO.7 + 366000xO.3 = 154600 (psi).
After the boundary condition and load internal pressure of 15000 psi is applied, the fmite element model can be analyzed. The stress distribution of Patran3.0 fmite element models show that its stress values and stress appearance are similar to those found by the I/FEM system (see Figure 6-13). 72
Figure 6-11: The Distribution of Stresses ofSteel-AISI-1040 Material
Model under Patran3.0 Analysis (Shape 8) 73
Kevlar CDIUP0 site Material
0.15 in
Figure 6-12: The Model ofLaminate Material (2 Sheets Kevlar Composite
Material with 1 Sheet Steel-AISI-I040) 74
Figure 6-13: The Distribution ofStresses ofKevlar Composite and Steel
AISI-I040 Laminate Material Model under Patran3.0 Analysis
(Shape 8) 75 6-4 Optimization
In this research, the guiding ideas of the natural gas storage tank's design are to reduce the weight ofthe natural gas storage tank, storing higher pressure gas in a tank and choosing the best geometric model to fit in the space available inside or under the
automobile. Therefore, the optimization of a natural gas storage tank's design needs to
follow the above ideas ofdesigning to choose the material and modeling.
For the material selection, Aluminum-6061-T6 is a light metal that can reduce the
weight of natural gas storage tank, hut its Yield Strength is just 36000 psi. The Yield
Strength is too low to load higher pressure gas. Steel-AISI-1040 has high Yield Strength
(64000 psi), and load higher pressure gas than Aluminum-6061-T6, hut its density is
greater than Aluminum-6061-T6 by nearly three times (see Table 3-1). It is too heavy for a natural gas storage tank in automobile use. Although some natural gas vehicle's designers use Steel-AISI-1040 to build their gaseous fuel tank, it can be used efficiently only in larger size cars or trucks.
The Kevlar composite is the best choice for the natural gas storage tank. The advantages of Kevlar are its low density and high strength, but its price much is expensive compared to Aluminum-6061-T6 and Steel-AISI-1040, so Kevlar is usually
3 used in laminate material for economic effect. The density ofKevlar is just 0.0362 Ib/in , lower than the density of Aluminum-6061-T6 (0.098 Ib/irr'), The yield Strength of
Kevlar is 366000 psi, nearly 6 times ofthe Yield Strength of Steel-AISI-1040. However, we choose 2 sheets of Kevlar (the thickness of each sheet is 0.15 in) material with one sheet ofSteel-AISI-1040 (thickness of0.7 in) to be laminate material for economic effect 76 in this research. From the rule of mixture, the density of the laminate material is
0.0362 x 0.3+ 0.284 x 0.7 = 0.209, and the combined yield stress is 154600 psi (see previous section). The density is lower than Steel-AISI-1040, while the Yield Strength is nearly 2.5 times higher.
The modeling considerations ofnatural gas storage tank include first three simple models which are square (Shape 1), cylinder (Shape 2) and cylinder with two hemispheric ends (Shape 3) to compare their stress distribution and maximum stress. From the Table
6-4, shape 3 has the lowest value ofmaximum stress.
However, the real model of gasoline tank of automobile is a complicated shape, like that in Figure 6-14. The shape ofthe gasoline tank is not smooth like shape 3, and in order to enforce the structure of the tank and reduce the stress effect on the corner, one needs to design non-cylindrical tanks. Shape 4 has four fms inside the square, and shape
5 is designed as a rounding edge square with 4 fms. From Table 4-6, the maximum stress ofShape 4 is 16940 psi, and the maximum stress of Shape 5 is 14400 psi. The maximum stress was decreased from 35010 psi (Shape 1) to 14400 psi (Shape 5) under the same internal pressure. Moreover, considering the flux ofnatural gas, shape 6 was created with an opening hole on the each fm. Because the radius of the hole is only 0.5 in, the maximum stress increased only 14400 psi to 14710 psi. Shapes 7 and 8 increase the thickness of the wall from 0.5 in (Shape 6) to 0.7 in and 1.0 in. The purpose is to increase the loading of internal pressure. Therefore, model using the Steel-AISI-I040 material (see Table 6-4), internal pressure increasing from 4000 psi (Shape 6) to 5000 psi
(Shape 7) and 8000 psi (Shape 8) 77
VAPOR VALVES OVERFLOW HOSE
FILLER NECK HOSE
FUEL TANK
Figure 6-14: The Gasoline Tank ofA Ford Escort [16] 78 Table 6-4: The Maximum Stress Development With I/FEM and Patran3.0's System
The System of Finite Element Analysis : I1FEM Material Aluminum 6061-T6 Shape Choice Shape 1,2,3,4,7,8 Yield Stress 36000 psi Shape No. Inner Force (psi) Max. pressure (psi) Min. pressure (psi) Shape 1 1000 35010 860.0 Shape 2 1000 12270 860.2 Shape 3 1000 8750 2124.0 Shape 4 1000 16940 412.1 Shape 5 1000 14400 678.7 Shape 6 1000 14710 632.2 Material Steel-AISI-I040 Shape Choice Shape 1, 2, 3,4,6, 7, 8, Yield Stress 64000 psi Shape No. Inner Force (psi) Max. pressure (psi) Min. pressure (psi) Shape 1 2000 70690 1731 Shape 2 2000 24580 1691 Shape 3 2000 17490 4256 Shape 6 4000 59520 2596 Shape 7 5000 59570 1534 Shape 8 8000 61970 1141 The System ofFinite Element Analysis: Patran3.0
Material Laminate Material (2 Sheets ofKevlar with Steel-AISI-l 040) Shape Choice Shape 8 Yield Stress 154600 psi Shape No. Inner Force (psi) Max. pressure (psi) Min. pressure (psi) Shape 8 15000 130854 10860 79 CHAPTER 7 Conclusion and Discussion
7-1 Conclusion
The following are conclusions to the research on material selection, 3-D solid modeling and finite element analysis ofthe natural gas storage tank:
1. The principles of material selection for Natural Gas Vehicle's gaseous fuel tank are
light weight and high strength. This research selected three materials for natural gas
storage tank. There are Alnumimum-6061-T6, Steel-AISI-I040 and Laminate
Composite material (Kevlar with Steel-AISI-I040). Aluminum-6061-T6 and Steel
AISI-I040 are the most popularly used in natural gas storage tank. Kevlar is a new
composite material used in natural gas storage tanks. It has low density and high
strength, but it is more expensive than above two material, so it usually used in
laminate material with other metal material. From the comparison (see Table 7-1),
the Yield Stress of laminate composite material is higher than Aluminum-606I-T6
and Steel-AISI-I040. Although the density of the laminate composite material is
higher than Aluminum-6061-T6 in this research, its Yield Stress is 4.30 times the
Yield Stress of Aluminum-6061-T6. Therefore, the laminate composite material
(Kevlar with Steel-AISI-I040) is preferred to Aluminum-6061-T6 and Steel-AISI-
1040 for Natural Gas Vehicle's fuel tank. 80 2. The 3-D solid model of the natural gas storage tank was created 8 different shapes.
The analysis results of Shape 2, cylindrical shape created by I/EMS and analyzed by
VFEM, was confirmed by theoretical result ofthin-walled and thick-walled cylindrical
vessel to prove that the 3-D finite element models under the VFEM system were
correct. Shape 8 was analyzed by I/FEM and Patran3.0 under the same material and
pressure. Similar results of stress distributions, confirmed the correctness of 3-D
finite element models between I/FEM system and Patran3.0.
3. From the stress distributions results of the 8 models, one can observe that the
maximum stress of Shape 3 was the lowest value among the all models. Moreover,
the maximum stress occurred on the border of Shape I, on the edge of Shapes 2 and
3, and near the hole and border in Shapes 6, 7 and 8. From the magnitude of the
maximum stress of different models, the rounding edge and placing fins inside the
model can reduce the maximum stress in the model significantly. The holes are
needed on the fins for gas flow and homogeneity of the tank. The holes do create a
stress concentration, and the maximum stress was observed higher. Optimization of
the number and size ofholes will be very critical. The rounding ofedges, placing fins
and having holes opening in the fins are important considerations in the design of
high pressure natural gas storage tanks. 81
Table 7-1: The Density and Yield Stress of Aluminum-6061-T6, Steel-AISI-I040, Kevlar Composite Material and Laminate Composite Material..
Material Aluminim- Steel-AISI- Kevlar Laminate Composite
6061-T6 1040 (Kevlar with Steel-AISI-I040)
Density 0.098 0.284 0.0362 0.209
3 (lb/in )
Yield Stress 36,000 64,000 366,000 154,600
(psi) 82 7-2 Future Work and Recommendations
In this study, the stress effects of internal pressure were considered in the design of natural gas storage tanks. However, in the actual design of natural gas vehicle tank, one has to consider the influence of fluid and thermotics on gaseous tank during motion.
That means the fluid-structural dynamic analysis and thermotic analysis will be important for future work.
Another major problem of natural gas vehicle has that the driving distance is not like that in a gasoline vehicle. Ifthe natural gas vehicle is to be driven 250-350 miles like gasoline vehicle, it must store approximately 25000 psi ofcompressed natural gas. Thus, finding a material which can load this high pressure (25000 psi) without increasing the weight of tank, or the size of the tank has to be researched. Currently, the last design
(model 8), can withstand 15,000 psi, which would give an average distance of 150 miles.
Before prototype, vibrational analysis of the tank with gas filled in, and mounted on the chase should also be performed. 83 CHAPTER 8 Bibliography
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