Blanchard and Spyridon (2014), LSU, AIAA Paper

American Institute of Aeronautics and Astronautics

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Preminary Investigation into Frozen Rocket Propellant’s Structural Capabilities

Clay M. Blanchard1 and Preston A. Spyridon2 Louisiana State Univerity, Mechanical Engineering, Baton Rouge, LA, 70803

This paper describes a preliminary investigation into the load-bearing capability of frozen propellants for full-scale and sub-scale launch vehicles over a wide range of temperatures. A novel launch vehicle concept has been proposed by LSU researchers (Baran, Anderson, and Auxt (2013)1) to reduce cost by using the benefits of modular construction equipped with a load-bearing solidified propellant column which retracts as it is consumed at one end; allowing for main-stage engines to be reused. A companion paper (McBride, Hollander, and Stewart (2014)2) presents a preliminary investigation of an end-burning, hybrid rocket-powered glider design. In this work we consider unconfined and confined columns to ensure functionality. An ANSYS numerical model is validated with analysis and compressive tests on an Instron machine for select materials. The confined configuration is a surrounding thin sleeve of higher strength material designed to improve load-bearing capabilities. The sleeve is limited by its hoop stress for which various materials and thicknesses are considered. Although buckling (elastic and inelastic) is considered for sufficiently slender columns, the focus of the investigation is on compression of non-slender columns where barreling determines ultimate compressive strength. A sub-scale rocket thrust stand has been designed for materials that are solid at ambient temperatures as well as various frozen materials at lower temperatures for further experimental investigation towards a full-scale launch vehicle.

Nomenclature a Inner Radius (thick

shell) E/1000 Tangent Modulus

(approx.) t Thickness (thin shell)

A Cross sectional area of cylinder

ET Space Shuttle External Tank

T Temperature

ANSYS Mechanical Analysis Software

FEA Finite Element Analysis u Displacement

ADPL ANSYS script-based commands

HTPB Hydtroxyl-Terminated Polybutadiene

UPGEOM Specific ANSYS command

APCP Aluminum Perchlorate Composite Propellant

KNSB Potassium Nitride-Sorbital

YP Yield Point

b Outer Radius (thick shell)

L Length of cylinder z Axial direction

C Core, Propellant L Liner, Confinement Material

ε Strain

CP Compression (ultimate) Point

LSU Louisiana State University

θ Circumferential direction

D, Dia. Cylinder diameter r Radial direction µ Coefficient of Friction DP Design Point R Radius (thin shell) ν Poisson's Ratio E Young's Modulus SSME Space Shuttle Main

Engine σ Stress

1 Undergraduate Research Assistant, Mechanical and Industrial Engineering, AIAA Student Member. 2 Undergraduate Research Assistant, Mechanical and Industrial Engineering, AIAA Student Member.


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I. Introduction PACE flight is becoming more prevalent across the world. Even commercial space flight is becoming more popular and more in demand. One of the biggest problems with spaceflight now is the cost. The aim for this

main project is to create an affordable access to space by using frozen rocket propellant and re-useable engines1. Refer to Reference 1 for more information. This novel technology create cheaper space flights as shown in Fig. 1.

The steps for the concept flight are labeled (a-h2) on Fig. 1 and are: (a) Pre launch Ops, (b) Retract Facility Shell, (c) Liftoff, (d) Aft module approaches forward module, (e) Aft and fwd module join, oxidizer tanks jettisoned, (f) Payload deployed, (g1) Nominal return-Integrated modular space plane return, (h1) If damage to rear module, it can be jettisoned and fwd module land by itself, (g2) Nominal return-safe landing, (h2) Emergency return.

The idea of the frozen propellant came from the notion that as a substance is cooled, it becomes more dense.

With a constant volume, this denseness means more fuel. Another main reason is that the frozen propellant should also be able to withstand the load of the trust. Without this solid state, the propellant would be useless in this concept. Figure 2 shows that when freezing the propellant, it can withstand the same load as some metals. The load bearing capabilities can be increased farther by wrapping an additional layer of material around the propellent to serve as a confining application to reinforce the propellent. Part (a) of the figure shows various materials’ strength (psi) as a function of temperature. It can be noticed that the metals are stronger than the propellants. Part (b) shows that by multiplying the strengths of materials by a given cross-sectional area (metals by thin outside shell of the ET, propellants by the entire cross-sectional area of the ET, the materials will be able to withstand a higher load as:

σ = F / A (eq. 1) and F =σ ⋅A (eq. 2)

S

Figure 1. Vehicle Flight Concept1. Flight concept from Pre-launch to nominal return. Stages (a)-(h2).

Figure 2. Mechanical Strength1. Frozen fluids and typical solids: (a) area basis, (b) total load.


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With an increase in cross sectional area, a given material can withstand a larger max load. The cross-sectional area of the thin shell is about 130 sq. in while the ET inside is about 86,000 sq. in.

II. Technical Goals This entire project deals with many problems, such as the ones described in the companion paper by McBride,

Hollander, and Stewart (2014)1). Our particular part of the main project deals with the solid-structural mechanics of the frozen propellant. The question that we were trying to answer was “does the propellant have sufficient strength to support the load during take off?” Through various experiments, research, and numerical modeling this question was answered. The goals for our research were to:

(1) Set up and validate models in ANSYS to predict various material’s mechanical properties

(2) Calculate and analyze the effects of hoop stress, strain, and displacement that are applied to a confining material by the core material under compression

There exist several material properties for materials in tensile loading but not so much with compression. What we were after were the properties of the materials in compression. We wanted to be able to predict the outcomes of various propellants when put under a compressive load. We wanted to understand the elastic and plastic properties of these materials so that they can be related to the compression that will be seen on the full-scale vehicle. Various mechanics of materials such as buckling, barreling, and confinement were analyzed.

A. Finite Element Modeling-Simple Verification The first part of this research deals with creating simple FEA models and validating them in ANSYS 15.0, an

engineering simulation software. Finite Element Analysis (FEA) is a way of approximating solutions by solving a system of ordinary differential equations numerically. The model is split into various finite elements so that many simpler equations can be used. With the boundary conditions known, the solver runs through various iterations until an approximate solution is derived.

A solid cylindrical of Structural Steel was created in ANSYS, L=0.2 m, D=0.15 m. The dimensions used were arbitrary. The mesh for this geometry used square elements. To verify simple calculations, a pressure of 100 Pa was placed on one side of the cylinder while the other was fixed. The normal stress of the cylinder should be 100 Pa. Fig. 3 shows a fairly uniform pressure distribution of 100Pa along the cylinder. The section of non-uniformity is created from end effects. Strain and deformation were also calculated by hand and compared to ANSYS solutions. These results were also exact.

This simple verification set us up for the more complicated problems such as buckling, barreling, and confinement.

B. FEA- Buckling Model The next case to analyze was the buckling effect. Buckling is a mathematical instability in static equilibrium.

Upon loading, a cylinder will deform laterally. This phenomenon is most prevalent in long, slender columns. In this case, the FEA solutions were compared to the Theorectical Euler buckling solutions.

The Euler formula predicts theoretical buckling critical loads, which are very conservative. This is because the theoretical results treat the column as a “perfect” column with no imperfections. In real life, the column will fail before the predicted Euler critical load, due to imperfections in the material. The critical load is the load at which buckling starts to occur. It is impossible for ANSYS to calculate a non-theoretical answer, or one that is more useful in real life applications. This is because in real life applications, the materials are non-linear. One thing that can be done to get a more approximate idea of the axial deformation of the cylinder is to set up a non-linear buckling system.

To set up this system, an imperfection will be inputted into the system. This imperfection was a bent shape, which came from the linear buckling mode shapes, i.e., n=1,2,3,4. Basically, the mode shape was chosen, and with (ADPL) script commands the shape was introduced into the nonlinear buckling system before the solution was solved. When solved, this initial shape imperfection allows the cylinder to actually buckle. With this buckling, a better idea of the axial deformation, after the bifurcation point has occurred, was seen. When choosing a mode

Figure 3. ANSYS Simple Verification.


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shape, it is important to understand that different mode shapes have different critical forces. Generally speaking, the first or second mode usually has the lowest critical load. Therefore it is recommended that this mode shape be used for a conservative approach. If the column buckles, it will generally buckle at the first or second mode shape, so there is no point in analyzing higher mode shapes.

To recreate nonlinear buckling in ANSYS, various geometries with varying slenderness ratios were generated. The mesh was compiled of simple square elements An initial imperfection was inputted into the system with a specific (UPGEOM) command. Then, the system solved for the critical loads at the varying slenderness ratios. Figure 4 shows the 6 different FEA points on the curve which correspond to the varying slenderness ratios and critical load. These points fall directly on the theoretical elastic Euler solutions.

Different end conditons/constraint options such as fixed, pinned, and hinged were created so that more complicated buckling cases could be analyzed if need be. They were created with the remote displacement option with various degrees of freedom tuned off and on.

The buckling analysis was finally validated. As you can see, in Fig. 4, the Euler solutions only gave us intuition for slenderness ratios greater than around 40. For our scope, we were mostly interested in very low slenderness ratios. These ratios range from around 0.5 to 3. This is where barreling occurs. The next case that was analyzed was the barreling case.

C. FEA- Barreling Model Barreling is where the material bulges radially out from the center when under compression. This is also seen in

various metal forming applications with materials such as Aluminum. The reason that we were interested in barreling was because most launch vehicles have small slenderness ratios. Since our goal was to ultimately launch a column of solid propellant, a small ratio was needed.

The barreling model that was created was a Aluminum cylinder, L=12 mm, D=8 mm as shown in Figure 5. The Young’s Modulus, Poisson’s Ratio, and Yield strength used were 70,000 MPa, 0.35, and 140 MPa, respectively. This model also used a mesh with square elements. This model has the same parameters as the one used in the ANSYS compression tests by Inoue3. This particular model was set up with the same parameters because we wanted to validate our model with the results from Inoue. This barreling model was created without confinement. We will deal with confinement problems later in this paper.

For sake of computing time, a quarter cylinder was used to cut down on the number of mesh elements. To utilize the symmetry condition of this ¼ cylinder, symmetry was applied to two sides (sides that would be touching the rest of the cylinder). A thin flat plate was added to both sides of the cylinder to act as a compression platen. These plates were rigid and the material was Structural steel. The plates help us to understand the end effects, such those induced by friction. Frictional contact areas were used in order to create surfaces where the cylinder touched the plates. The coefficient of friction (µ) used was 0.15 for both sides. Frictional effects were irrelevant in for our scope at this time. They were only used in the model to allow barreling. If the ends were frictionless, there would be no “barrel” in the barreling effect. This makes sense because lubrication is used in real life applications to stop the barreling.

Figure 4. 2-D Buckling. This graph shows how the FEA solutions compare to the Elastic Euler theorectical solutions.

Figure 5. Barreling Shape in ANSYS. Shows how center bulges due to radial deformation.


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This model used numerous sub-steps. A fixed bottom was set and a remote displacement of the top plate was set to deflect 5mm. The model converged, a force-displacement graph was made.

This model was ran 3 times with varying displacements in order to compare the accuracy of FEA results. Each of these FEA curves overlapped. This overlap meant that the model was accurate. This data can be seen in Fig. 6. This data was compared to the experimental data from Figure 4 of T. Inoue’s paper3. The results of the comparison were great. Both curves fell on each other. The curves match all the way until the end of our test, which was 5 mm. These results validated our buckling model. Now, with a good working model, real experimental data was used for model validation.

D. Lab Experiment Compression Testing In this lab experiment, the goal was to get compression data from Aluminum 6063 samples. This data was used

to compare the FEA barreling model further. Once this FEA model was completely set up, many other materials could be analyzed through FEA. This model predicted what would happen to the materials upon compression.

A few Aluminum 6063 samples were machined in the LSU machine shop. Since the LSU Instron machine is only used for tension tests, there was not a compression platen. Needing a platen for the testing, one was manufactured at the machine shop. This platen was made out of 1018 mild carbon steel. The plate was ¾’’ thick with a 8’’ diameter. This experiment used an Instron tensile/compression testing machine, 50,000 lbf max. force.

Three compression tests were executed. The first test had technical difficulties. The second test was compressed until a trapezoidal shape was noticed. This shape was due to shear forces. The test was soon stopped. The third test ran flawlessly, with no mishaps. Pre/post test pictures of the second and third specimen are in Fig. 7; data in Table 1.

(a) (b) (c)

Figure 7. Compression Test Specimens, (Before and After). Part (a) shows specimen #2 (circled in red, on left) and #3 (boxed in red, on right) prior to testing. Part (b) shows deformation after compression of Aluminum sample #2. Part (c) shows deformation after compression of Aluminum sample #3.

Figure 6. Force as a function of displacement. This figure compares FEA solutions (Blue) and Experimental data from T. Inoue3.

Specimen #2 Specime #3 Initial Length, mm 18.491 12.009

Final Length, mm 10.274 3.607

Length Change, mm -8.217 -8.402

Initial Dia., mm 9.177 9.983

Final Dia., mm 12.065, 13.005 14.892

Dia. Change, mm 2.888, 3.828 4.909

Table 1. Compression measurements, initial and final.

Figure 8. Stress as a function of strain. This figure shows both experimental lab compresson tests. Solid blue line is specimen #2. Orange-dashed is specimen #3.


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Because different size specimens were used, a Stress-Strain curve was derived from the Instron output data of force vs deformation. This curve helped us easily compare the two compression tests because even though the two specimens had different Force-Displacement curves, the Stress-Strain curves were the same for a given material.

Figure 8 shows the Stress-Strain curves for the last two specimens tested. The blue solid line shows how run #2 was stopped during compression where as the orange-dashed line shows a larger deformation.

Since the FEA characteristic curve for Aluminum was very similar to the experimental curves, it was now safe to say that our barreling model was now validated. Even though the FEA used pure Al, and the experiments used 6063 Al, this FEA model shows accurate estimates of the deformation due to a given load. With this accurate FEM model, compression predictions for other materials at large-scale operations, such as the scale of the ET, were solved and analyzed.

E. FEA-Full Scale Model The reason that the full scale model was created is because it gives us insight to how a real world frozen column

would react under compression. We want to be able to see what happens when the force of 3-SSME acts on the solid coulumn. This is why we want to use the ET for the geometry, so that it can be compared the the Space Shuttle’s thrust and size. The results from the Hydrogen and Methane predictions below and future predictions will help us determine if the propellant is strong and stiff enough without some sort of confinement.

To set up the full scale models, the only thing that changes from the model used above was the geometry. An ET sized cylinder was created in ANSYS, with D=27.5 ft, L=82.5 ft. The material used was solid Hydrogen and Methane. Two cases of Methane were ran. The difference was the temperature of the frozen material. The mesh included square elements. The needed material properties for the three cases can be seen in Table 2. The Tangent Moduli for these cases were all estimated. This estimation was that the Tangent Modulus is equal to the Yield Strength divided by 1000.

The three FEA cases were ran and solutions can be seen below. The solid hydrogen deformed about 35 ft. The results of the force vs displacement curve can be seen in Fig. 9. These results make sense when compared to Fig. 2. When Hydrogen at 3.6 R and a cross-sectional area the size of the ET are used, the max load is small compared to other propellants. At the end of the Force vs Displacement curve in Fig. 9, where the line starts to change rapidly (at a displacement between 30 and 35ft), is where the solution started not to converge. This non-convergance means that the solutions at those points are not accurate. This explains the erratic behavior in the figure.

Along with the force vs displacement data from the compression test, the double barreling effect can be seen in Fig. 10. This picture gives us a representative picture of how Hydrogen may actually perform under the load of 3-SSME. With the load of 3-SSME applied, Hydrogen displaced about 14.67 ft.

Figure 9. Force as a function of displacement. This graph shows a full scale, ET-sized, solid Hydrogen compression test in FEA.

Hydrogen Methane Case #1

Methane Case #2

Temperature, R 3.6 26 126 Young’s Modulus, psi 46,002 446,842 302,404 Poisson’s Ratio 0.239 0.390 0.305 Yield Strength, psi 14.31 208.45 19.91 Tangent Modulus, psi 0.01431 0.2085 0.01991

Table 2. Material properties for Hydrogen and Methane.

Figure 10. Full Scale Solid Hydrogen(3.6R) Barreling shape..This figure represents what the displacement would look like with the force of 3-SSME. The color represents the plastic strain. It was used to help distinguish the double barreling shape.


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In both of the Methane cases, the cylinder was deformed about 12 ft. The diffences in the two Methane cases can

be noticed in the figures below. The lower temperature Methane, at 26 R (not shown) was a lot stronger than at 126 R (Figures 11 and 12). Both of these Methane cases show that it is a lot stronger than Hydrogen. In Fig (12L) the full scale deformation was calculated from the slope of the curve. The full scale deformation occurs at a force equivalent to 3-SSMEs thrust. For Methane at 126 R, the full scale deformation is only 0.0049 ft (shown in Fig. 12), and at 26 R it is 0.0033 ft, both of which are still in the elastic region. Methane at 126 R approaches the yield point shown in Fig. 12, with the load of 3-SSME. Even with the weaker of the Methanes being in the elastic region, we would make it even stronger by cooling the Methane more, which is the case of the first Methane. This means that with a ET sized column of frozen Methane, and a force from 3-SSMEs, the column only moves 0.0049 and 0.0033 ft in the axial direction. This is also shown in the results of the ANSYS model presented in Fig. 13. In that figure there are no significant barreling features observed in the column shape. This is very good. It means that most likely, Methane will not need confinement.

These Hydrogen and Methane predictions were just the start of the many predictions to come. There may be a point where a given propellant will need to be stronger. There are numerous ways to do this such as alloying the material. Presence of impurities will impede dislocation movement in the slip planes. Another way to reinforce the material could be to add confinement via a thin shell. The next topic discuses the movement towards modeling FEA confinement.

F. Confinement Effects When a given material is too weak to support the

load, a confinement may be added in order to reinforce the solid cylinder.

An FEA model is in the process of being set up to analyze the stresses of the cylinder with added confinement. Although the model is not complete, other things have been done in order to set up this model. So far, a cylinder with an outer shell was created. Surface contact areas were defined between the outside of the cylinder and the inside of the thin shell. This contact could add frictional or frictionless effects. No tests have been run on the model yet. This solid cylinder plus thin shell can be seen in Fig. 14.

Figure 11. Full Scale Solid CH4, T=126 R.. This figure shows the deformation characteristic curve of Solid Methane at 126 R.

Figure 13. Full Scale Solid Methane (126R) Barreling shape.. This figure represents what the displacement would look like with the force of 3-SSME. The color distribution represents the plastic strain.

Figure 12. Full Scale Solid CH4, T=126R.. This figure shows the deformation due to full scale load of 3-SSME.

Figure 14. ANSYS Model with confinement. This figure shows a solid propellant brown), with an outer confinement shell(green).


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As mentioned in part C. of the paper, when a solid propellent becomes load bearing the propellent will begin to deform in a barrel-like shape. This can be minimized by adding a confining cylindrical material of a certain thickenss around the solid propellent that will in turn increase its load carring capabilities. To obtain the results needed and to gain further insight into the required thickness of the confining material, thick shell and thin shell versions of the equations for stress and strain were reviewed. Thin shell equations can be used to predict stresses when the ratio of the radius to thickness is over 10. From stress and strain, displacement was found. Similar equations were found to describe the stress, strain, and displacement of the propellant material.

An approximate method involves assuming the propellant repsonds only to the applied load and deforms. This deformation is then matched by the confining material. This was the method used here for a first calculation. A more accurate method would be to simultaneously consider propellant being loaded by the applied load and the confining material. This is planned for future work.

In the first part of the calculation, as the rocket flies, the propellant (designated here as “core (C)”) is primarily loaded in the axial direction as illustrated in the left hand side (a) of Fig. 15. This will primarily develop an axial stress (eq. 3) and associated strains (eqs. 4-6) in all three directions (axial, circumferential , and radial). The most relevant variable for confinement is the radial strain. This is converted to radial displacement by multiplying strain by the radius of the propellant’s original cylindrical shape (eq. 7). This represents the propellant (core) pushing radially out because of the applied load.

σ z,C =Fz,CAC

(eq. 3)

εz,C =σ z,C

EC

(eq. 4)

εθ ,C = −νCεz,C (eq. 5)

εr,C = −νCεz,C (eq. 6)

ur,C = εr,CRC (eq. 7)

In the second part of this approximate method, the displacement of the confining material (referred to here as “liner (L)”) is assumed to be equivalent to that of a separate hypothetical hydrostatic problem as illustrated in the right hand side (b) of Fig. 15. This part of the analysis assumes only a 2-D plane stress situation. In this part, the loading can be represented as a internal pressure pushing outward on the confinement layer of a selected material and a selected thickness. A pressure (P) was chosen. The confining material is primarily loaded in the radial direction by pressure and will develop stresses (eqs. 8-9 assuming thin shell, and eqs. 10-13 assuming thick shell) and associated strains (eqs. 14-15) in two directions (radial and circumferential); hoop stress on the inner radius being the most significant. This pressure was iterated until the confinement material is displaced (eq. 16) the same amount as calculated before (propellant pushing out). If the hoop stress exceeds the maximum designed stress, failure could result. Values of thickness were selected until a safety factor of 1.2 (ultimate over max allowable) was obtained (eq. 18).

Thin shell equations for liner stress (in terms of inner radius (R) and thickness (t)):

σ r,L,thin = −P (eq. 8)

σθ ,L,thin =PRt

(eq. 9)

(a) (b) Figure 15. Approximate analytical model of confinement. This figure shows an inital solid propellant core (black) undergoing deformation (red) and shows an initial outer confinement liner (blue) radially deformed (green).


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Thick shell equations for liner stress (in terms of inner radius (a=R) and outer radius (b=R+t):

σ r,L,thin (a) =a2

b2 − a2"

#$

%

&'P

1− b2

a2"

#$

%

&' (eq. 10)

σϑ ,L,thin (a) =a2

b2 − a2"

#$

%

&'P

1+ b2

a2"

#$

%

&' (eq. 11)

σ r,L,thin (b) = 0 (eq. 12)

σϑ ,L,thin (b) =a2

b2 − a2"

#$

%

&'P

1+ b2

b2"

#$

%

&' (eq. 13)

Strains:

εr,L =σ r,L−νLσθ ,L( )

EL

(eq. 14)

εθ ,L =σ θ ,L−νLσ r,L( )

EL

(eq. 15)

Displacement:

ur,L = εr,Lt (eq. 16)

Factor of safety of 1.2 is equivalent to:

σθ ,L (a)σY ,L

=11.2

= 0.833 (eq. 17)

Table 3 shows the results of these calculation for thirteen cases of propellant (core) materials from the companinon LSU paper2. These were considered at various temperatures representative of possible states of propellant. Liner materials under consideration for confinement were lightweight metals such as Aluminum alloys common in aerospace vehicles, and various common fiber reinforced polymers such as Kevlar 49. These two liner materials were used in these representative calculations and were assumed to be at the same temperature as the core.

Core Liner Loading Margin Thick-ness

# Material T (R)

E,C (psi)

ν ,C

Material E,L (psi)

ν ,L

Cond., Dia. (in)

σθ,L(a)/ σY,L

t,L (in)

1 H2 10 39,942 0.25 Al-2024-T4 12,638,888 0.33 DP, 331 0.8286 9.5 2 H2 10 39,942 0.25 Kevlar 49 17,984,681 0.36 DP, 331 0.8404 5 3 CH4 144 281,228 0.31 Al-2024-T4 11,783,333 0.33 DP, 331 0.85577 2.2 4 CH4 144 281,228 0.31 Kevlar 49 17,984,681 0.36 DP, 331 0.8296 1.1 5 CH4 26 446,841 0.39 Kevlar 49 12,527,777 0.33 DP, 331 0.8123 0.75 6 CH4 144 281,228 0.31 Kevlar 49 11,783,333 0.33 YP, 2 0.8389 0.0033 7 CH4 26 446,841 0.39 Kevlar 49 12,527,777 0.33 CP, 2 0.8497 0.0090 8 KNSB 540 850,000 0.30 Kevlar 49 10,600,000 0.33 YP, 2 0.8433 0.065 9 KNSB 540 850,000 0.30 Kevlar 49 10,600,000 0.33 CP, 2 0.8229 0.09

10 APCP/ HTPB 540 435 0.50 Kevlar 49 10,600,000 0.33 YP, 2 0.8256 5

11 APCP/ HTPB 540 435 0.50 Kevlar 49 10,600,000 0.33 CP, 2 0.8510 6

12 Paraffin 540 30,023 0.30 Kevlar 49 10,600,000 0.33 YP, 2 0.8392 0.2 13 Paraffin 540 30,023 0.30 Kevlar 49 10,600,000 0.33 CP, 2 0.8471 0.26

Table 3. Results of calculations of the approximate confinement model.


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Temperature variation of Young’s Modulus and Poisson’s ratio was included if available, otherwise assumed to be constant at lower temperatures (in the absence of data). Loading conditions that were considered included: some design point (DP) conditions at full scale (D=331 in =27.5 ft) from the companion paper2, as well as yield point (YP) and compression point (CP) conditions at a laboratory scale (D=2in) representative of testing goals of potential propellant materials in future research. The target of the ratio of hoop stress to ultimate stress (from eq. 17) used in these calculations is shown. Finally the resulting required thickness of the liner material to provide confinement is presented.

As was shown in Section E, the design point for Hydrogen is that the yield point is exceeded and the propellant core undergoes plastic deformation. No accounting of plastic behavior was taken here. Still, assuming elastic behavior throughout, Hydrogen requires nearly a 10 in thick Aluminum liner (case 1) if confinement alone was to reduce radial displacement. As a point of reference, the Space Shuttle External Tank skin was approximately 0.125 in thick. Kevlar (case 2), though still a substantial thickness, does cut the required thickenss nearly in half. As was summarized in Section E, one way to remedy the insufficient strength of an unconfined pure Hydrogen column is a combination of alloying and confinement.

Methane was shown in Section E to have sufficient strength as an unconfined column at a relatively hight temperature (144 R) compared to its melting temperature (162 R) to be close to but above its yield point and remain intact at its design point. Aluminum liner thickness (case 3) is still rather large but Kevlar (case 4) is found to be more and more viable to provide added load bearing if necessary. The reduction in liner thickness is significant compared to Hydrogen primarily because of significanty higher Young’s modulus of Methane which reduces the amount of strain for a given level of stress. This also continues at colder temperatures for Methane (case 5). At laboratory scale, a very modest Kevlar sleeve thickness can be used for the lower yield point (case 6) loading as well as for a larger compressive ultimate point (case 7).

The remaining three pairs of cases (8-13) consist of three potential room temperature propellants considered for near-term future research in this area: Potassium Nitrate-Sorbitol (KNSB) solid propellant common in amateur rocketry, Ammonium Composite Rubber-based solid propellant (APCP/HTPB) common in amateur rocketry and experimental university rocketry research, and Paraffin wax solid fuel common in experimental university hybrid rocketry research. Of the three, the APCP/HTPB has a very low Young’s modulus consistent with its rubber-based composition. Without adding aluminum particles to the propellant (aluminizing), this common propellant would not be a realistic candidate. Paraffin is a significantly stiffer material which may require a significant amount of confinement unless it has addatives mixed in to increase strength or increase its diameter to reduce the stress. However, the confinement required is not excessive. KNSB has the highest Young’s modulus and would require the least amount of confinement and would represent a reasonably thin liner if required.

G. Sub-Scale Rocketry A sub-scale model (D=2 in) of a paraffin propellant column was run. The goal for this project is to eventually be

able to launch small-scale rockets and glide them to landing. In order to move forward with this research, an independent study course, ME 4903 was created where some preliminary studies were made. Another objective was to develop the ability to predict loads an to be able to assess the extent of barreling if it were to occur. Figures 16 and 17 show the elastic response of an unconfined Paraffin column for a design point case from the companion LSU study2 and show no evidence of barreling.

Figure 16. FEA sub-scale model. This figure shows the force vs displacement for paraffin wax2.

Figure 17. FEA sub-scale model(zoom-in). This figure shows the deformation of paraffin due to a 250lbf force2.


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The objectives of ME 4903 independent study course also included developing concepts for a small rocket thrust stand. This stand should be able to test rockets anywhere from 10 lbf to 250 lbf. The stand will be a vertical test stand, with the thrust poining away from the ground. This stand will eventually help advance the frozen propellant concept into experimental demonstrations of proof of concept with the goal of bringing about affordable access to space.

III. Conclusion An FEA analysis capability was developed using ANSYS, validated with experiments performed at LSU, and

the numerical model was used to analyze full-scale and sub-scale elastic and plastic response of unconfined propellant material including buckling and barreling. The ability to include confinement in the numerical model was shown to be possible. Independent approximate confinement calculations were made for many cases that predicted the thickness of confining liner material to minimize radial displacement of propellant core material. Hydrogen was shown to require alloying and confinement for the full-scale design point considered in this concept. Methane was shown to have sufficient strength for the full-scale design point considered in this concept. Paraffin was shown to have sufficient strength for the sub-scale design point concept considered in the companion LSU study2.

Acknowledgments This work was supported by the Louisiana Space Consortium and the National Aeronautics and Space

Administration through a LURA LaSPACE/NASA grant under the parent award number NNX10AI40H with Dr. John Wefel as the project manager Ms. Diane DeTroye as the NASA COTR. Clay Blanchard would also like to acknowledge the Department of Mechanical and Industrial Engineering of Louisiana State University for the Independent Topics course ME 4903 under which the paraffin research was performed.

References 1Baran, Anderson, and Auxt (2013), “An In-Line Reuseable Launch Vehicle Concept Using Confined Load-Bearing Frozen Propellants,” AIAA 2013-3921. 2McBride, Hollander, and Stewart (2014), “Preliminary Investigation of a Modular, Reusable, End-Burning, Hybrid Rocket-Powered Glider,” AIAA Region IV Student Conference, Albuquerque, NM, April 24-26, 2014. 3T. Inoue, Z. Horita, H. Somekawa, K. Ogawa (2008) “Effect of initial grain sizes on hardness variation and strain distribution of pure aluminum severely deformed by compression tests,” Acta Materialia 56, 2008, 6291–6303.

Documents

Blanchard and Spyridon (2014), LSU, AIAA Paper