1998-10 r.lo iaf98 modular cryogenic solid rocket propellant grains

9
1 IAF-98-S.3.10 Modular Dissected Cryogenic Solid-Rocket Propellant Grains Roger E.Lo, Berlin Univ. Techn., Aerospace Institute <Rog- [email protected]> Introduction The concept of cryogenic solid-rocket propellant (CSP-) grains - see (1) - is based on the idea that any conceivable chemical rocket propellant combination can be used as solid rocket propellant if the definition of solid propellants is not restricted to ambient temper- ature. Liquid bipropellants and tripropellants are thus transformed into solid propellants, so are hybrids, slur- ries and quasi-hybrids (i.e. solid mono- or bi- propellants with Hydrogen injection). Consider using frozen Oxygen (SOX) instead of Ammonium Perchlo- rate along with some solid hydrocarbon fuel (HC). What results is a solid propellant SOX/HC with an Isp roughly equal to the semicryogenic hybrid LOX/Polyethylene that in turn corresponds to the well known liquid combination LOX/Kerosene with an Isp of 300s (E, 68:1) that exceeds any conventional solid propellant. Consider a high energy solid grain using SOX/SH2. The first objection coming to mind against such a concept or similar ones is the danger of combus- tion instability up to detonation. Many quasi- homogeneous mixtures of cryogenic solid fuels and oxidizers might be very well behaved, but this is a concern for the majority of propellant combinations. The cure lies in transforming deflagration into boun- dary layer combustion by dissecting the grain into a number of homogeneous subunits. Imagine cylindrical elements with a central combustion channel of arbitrary shape. In hybrid propulsion, a solid fuel is consumed by having a fluid oxidizer flowing along its surface. The oxidizer source is o u t s i d e the combustion chamber. In the case of dissected solid propellant grains the source is a melting and/or evaporating solid oxidizer located inside the same combustion chamber. Therefore the arrangement can be called an "internal hybrid burner". Alternating layers of oxidizer and fuel yield multiple boundary layer combustion. Obviously, the leading element in such a stack needs to be an oxidizer rich gas generator module capable of self sustained burning. The concept of modular grains can be generalized to compounds of modules of any suitable shape and com- position. Elements can be 100% oxidizer or fuel as well as oxidizer- or fuel-rich gas generators. -------------------------------------------------------------------- Copyright : © 1998 by Roger E.Lo. Published by the American Inst.of Aeronautics and Astronautics, Inc. with permission. Released to IAF/IAA/AIAA to publish in all forms. CSPs combine the advantages of liquid and solid propulsion: high performance in terms of Isp and low structural mass per unit total weight. The scope of chemical propul- sion performance Chemical propulsion is based on chemical reactions that range from monopropellant decomposition to metal combustion. A widely used convention divides attaina- ble Isps into a high-energy and a low energy domain, with a narrow medium energy domain around 300 s in between (see Fig.1). * At the lower end, liquid monopropellants form the basis for hot gas AOC thrusters. * Conventional solid propellants are quasi- homogeneous mixtures of solid fuels, oxidizers and other constituents, stored in a container that later be- comes the combustion chamber. Defining as one in- dividual component every constituent that requires a separate container, such propellants are solid mono- propellants. Restriction to solid state at room temper- ature sets tight limits to the choice of suitable matters. As a result, even so called "high energy solid rocket propellants" are no more than medium energy on the absolute scale used in Fig.1. However, robust state- of-the-art solid propellants are low-energy. * Medium energy liquid bipropellants occupy the in- termediate realm, with storable hypergolics at the lower, semi-cryogenic combinations (e.g. LOX/hydrocarbon) at the upper end. * High energy (HE) liquid bipropellants include LOX/LH 2 the propellant combination marking the upper limit of chemical state-of-the-art propulsion with 391s at 68:1 E. To go beyond this mark would require using better oxidizers and/or fuels. Fluorine and ozone are known to yield higher Isps than Oxy- gen, but are not used because they are either too ag- gressive or too explosive. There are several metals that yield more combustion energy per unit mass of products than Hydrogen does. Using them in bipro- pellants requires slurries or gels that cause produc- tion, storage and feeding problems. However, slurry bipropellant combinations such as LOX/ Beryllium/ Hydrogen would perform close to the very limit of conventional chemical propulsion (1).

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When gases and liquids or other fluids, including heterogenous ones (e.g. slurries) are frozen, the are transformed into a more or less cryogenic solid propellant CSP. Such solid propellant grains can thus include virtually any kind of chemical propellant combination. If necesssary, the constituents don't have to be mixed but can be chemically isolated from each other in what is called modular grains, e.g. as disk-stacks. These burn in multiple boundary layer combustion.

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Page 1: 1998-10 R.Lo IAF98 Modular Cryogenic Solid Rocket Propellant Grains

1

IAF-98-S.3.10

Modular Dissected Cryogenic Solid-Rocket Propellant Grains R o g e r E . L o , B e r l i n U n i v . T e c h n . , A e r o s p a c e I n s t i t u t e < R o g -

e r . L o @ T U - B e r l i n . d e >

Introduction The concept of cryogenic solid-rocket propellant

(CSP-) grains - see (1) - is based on the idea that any

conceivable chemical rocket propellant combination

can be used as solid rocket propellant if the definition

of solid propellants is not restricted to ambient temper-

ature. Liquid bipropellants and tripropellants are thus

transformed into solid propellants, so are hybrids, slur-

ries and quasi-hybrids (i.e. solid mono- or bi-

propellants with Hydrogen injection). Consider using

frozen Oxygen (SOX) instead of Ammonium Perchlo-

rate along with some solid hydrocarbon fuel (HC).

What results is a solid propellant SOX/HC with an Isp

roughly equal to the semicryogenic hybrid

LOX/Polyethylene that in turn corresponds to the well

known liquid combination LOX/Kerosene with an Isp

of 300s (E, 68:1) that exceeds any conventional solid

propellant.

Consider a high energy solid grain using

SOX/SH2. The first objection coming to mind against

such a concept or similar ones is the danger of combus-

tion instability up to detonation. Many quasi-

homogeneous mixtures of cryogenic solid fuels and

oxidizers might be very well behaved, but this is a

concern for the majority of propellant combinations.

The cure lies in transforming deflagration into boun-

dary layer combustion by dissecting the grain into a

number of homogeneous subunits. Imagine cylindrical

elements with a central combustion channel of arbitrary

shape. In hybrid propulsion, a solid fuel is consumed

by having a fluid oxidizer flowing along its surface.

The oxidizer source is o u t s i d e the combustion

chamber. In the case of dissected solid propellant

grains the source is a melting and/or evaporating solid

oxidizer located i n s i d e the same combustion

chamber. Therefore the arrangement can be called an

"internal hybrid burner". Alternating layers of oxidizer

and fuel yield multiple boundary layer combustion.

Obviously, the leading element in such a stack needs to

be an oxidizer rich gas generator module capable of

self sustained burning.

The concept of modular grains can be generalized to

compounds of modules of any suitable shape and com-

position. Elements can be 100% oxidizer or fuel as well

as oxidizer- or fuel-rich gas generators.

-------------------------------------------------------------------- Copyright: © 1998 by Roger E.Lo. Published by the American

Inst.of Aeronautics and Astronautics, Inc. with permission. Released

to IAF/IAA/AIAA to publish in all forms.

CSPs combine the advantages of liquid and solid

propulsion: high performance in terms of Isp and low

structural mass per unit total weight.

The scope of chemical propul-

sion performance Chemical propulsion is based on chemical reactions

that range from monopropellant decomposition to metal

combustion. A widely used convention divides attaina-

ble Isps into a high-energy and a low energy domain,

with a narrow medium energy domain around 300 s in

between (see Fig.1).

* At the lower end, liquid monopropellants form the

basis for hot gas AOC thrusters.

* Conventional solid propellants are quasi-

homogeneous mixtures of solid fuels, oxidizers and

other constituents, stored in a container that later be-

comes the combustion chamber. Defining as one in-

dividual component every constituent that requires a

separate container, such propellants are solid mono-

propellants. Restriction to solid state at room temper-

ature sets tight limits to the choice of suitable matters.

As a result, even so called "high energy solid rocket

propellants" are no more than medium energy on the

absolute scale used in Fig.1. However, robust state-

of-the-art solid propellants are low-energy.

* Medium energy liquid bipropellants occupy the in-

termediate realm, with storable hypergolics at the

lower, semi-cryogenic combinations (e.g.

LOX/hydrocarbon) at the upper end.

* High energy (HE) liquid bipropellants include

LOX/LH2 the propellant combination marking the

upper limit of chemical state-of-the-art propulsion

with 391s at 68:1 E. To go beyond this mark would

require using better oxidizers and/or fuels. Fluorine

and ozone are known to yield higher Isps than Oxy-

gen, but are not used because they are either too ag-

gressive or too explosive. There are several metals

that yield more combustion energy per unit mass of

products than Hydrogen does. Using them in bipro-

pellants requires slurries or gels that cause produc-

tion, storage and feeding problems. However, slurry

bipropellant combinations such as LOX/ Beryllium/

Hydrogen would perform close to the very limit of

conventional chemical propulsion (1).

Page 2: 1998-10 R.Lo IAF98 Modular Cryogenic Solid Rocket Propellant Grains

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Fig.1: Isp range of chemical propulsion

* Hybrids are liquid/solid bipropellants. Isp-

performance covers a broad range from low- to high-

energy. Hypergolic combinations such as

HNO3/Amine-fuel (not shown in Fig.1) are found at

the lower end. Semi-cryogenic hybrids include envi-

ronmentally benign, medium energy combinations

(e.g. LOX/Polyethylene, PE, not shown). The solid

fuel in regular hybrids lends itself for adding metals.

Among others, the formation of the Oxides and Fluo-

rides of Beryllium, Lithium, Boron, and Aluminum

yields the highest known mass-specific heats of for-

mation. Powders of these metals can be mixed with

solid fuels or can be introduced as hydrides if such

exist in solid state. Thus, regular hybrids cover a

broad range on the scale of Isps.

Metal combustion does not make much sense without

molecular weight reduction. This can be achieved by

an excess of Hydrogen. Metal-rich solid propellants

used for Hydrogen heating are a special category of

bipropellants and were dubbed "Quasi-hybrids" (2).

Using extra Hydrogen in addition to some other fuel,

one obtains three component combinations also

called tripropellants. Hybrids with highly metalized

fuel grain are excellent means for heating excess Hy-

drogen (3) and were called tribrids. Most of the met-

als in question can easily reduce H2O under combus-

tion chamber conditions. Hence it can be demonstrat-

ed that the combustion products at maximum Isp mix-

ture ratios are free of Hydrogen combustion products

even in very complex mixtures (4)(5). Using liquid

Ozone rather than LOX and BeH2 rather than Be

(both are endothermic compounds) one obtains prob-

ably the highest known Isp of conventional chemical

propellants.

* The concept of modular dissected cryogenic solid-

rocket propellant grains (CSPs) provides a means for,

in principle, realizing a l l propellant combinations

as solid propellant motors. This includes, under cer-

tain provisions, propellants that are hypergolic liquids

at ambient temperature. If Hydrogen is to be used,

temperatures well below 14K (25R) are required.

This kind of cryogenic solids is the main subject of

investigations at Berlin University of Technology's

Aerospace Institute (6)(7)(8).

Super High Energy Propellants (SHEPs) employ

metastable chemical species. Known examples are

atomic Hydrogen and other atomic species, free radi-

cals and excited species. If storable, they could push

the upper limit of chemical propulsion by a factor of 4

to 5 beyond the bounds shown in Fig.1. Matrix isola-

tion is one method of storing SHEPs. In the case of

some of the more sensitive species it is believed that

matrix isolation needs extremely low temperatures

along with strong magnetic fields. Cryogenic solids are

being studied at USAF in the High Energy Density

Matter Program, which considers solid Hydrogen

Page 3: 1998-10 R.Lo IAF98 Modular Cryogenic Solid Rocket Propellant Grains

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doped with SHEPs and burned in hybrid manner with

liquid Oxygen, see (10). Such elements could easily be

included in the modular CSPs suggested in this article.

Special cryogenic high energy

propellants S O X / S H 2

CSPs are much colder than liquids and hence con-

tain less energy resulting in lower Isp performance.

However, a more detailed calculation shows that the

missing heats of liquefaction are small compared with

the overall heat content and therefor the differences are

small. Fig.2 shows the situation for SOX/SH2: even

when subcooled to 2K (3,6R), the difference to

LOX/LH2 performance is only 0,5%!

3760

3770

3780

3790

3800

3810

3820

3830

Liqui d Soli d, 14 K Soli d, 2K

Frozen Fl ow

Equil ibrium Fl ow

Fig.2: Mass specific impulse [m/sec] of O2/H2 propel-

lants at optimum mixture ratio, standard 68:1 equili-

brium expansion (7)

The following

Tab.1 contains further data about SOX/SH2 Isps

as function of mixture ratio. As Fig.3 shows, the opti-

mum mixture ratio is where one is used to find it when

Oxygen and Hydrogen are liquid.

O/F Ispvac,E Isp,E vg.density vol. spec. Isp, E

1,00 3374 3167 0,146 461

2,00 3857 3617 0,207 748

3,00 4034 3766 0,262 987

4,00 4093 3804 0,312 1186

5,00 4091 3787 0,357 1353

6,00 4053 3734 0,399 1488

7,00 3980 3649 0,436 1593

8,00 3858 3529 0,471 1663

9,00 3714 3400 0,504 1712

10,00 3366 3117 0,533 1750

Tab.1: Theoretical performance of SOX/SH2 propel-

lants at 68:1 equilibrium expansion (9)

1 2 3 4 5 6 7 8 9

3300

3400

3500

3600

3700

3800

3900

F

Is

p [

m/s

]O/F

E

Fig.3: Mass-specific impulse of SOx/SH2 as function

of O/F mass ratio at 68:1 equilibrium expansion (7)

In general, the density of solids is higher than the one

of liquids. This is also true for Oxygen and Hydrogen

(see Fig.5). As a consequence, the slight Isp reduction

found for CSPs is more than offset when volume spe-

cific Isps are compared (see Fig.6).

C S P s i n s t e a d o f s l u r r i e s

Frozen Hydrogen provides for easy mixing with denser

materials. There is no danger of separation as with

slurries. Propellants of the type O2/Al/H2 or O2/Mg/H2

can therefor be used as monopropellants (defined as

explained above), by using solid Oxygen elements

along with frozen Hydrogen / metal suspensions.

In the following Tab. 2 are shown results of calcu-

lations with such propellants. The amount of metal in

the fuel was chosen between 45 to 90%. However, the

ratio of Oxygen to Aluminum was always kept in equi-

valence according to the formation of Al2O3 due to the

earlier demonstration in (3)(4)(5) that this is optimal. It

should be noted that the exhaust products near the Isp

maximum around 60 - 65% Al (corresponding to a

molar ratio of about 8, see Fig.4) are exclusively made

up of solid Al2O3 and molecular Hydrogen. There is no

H2O in the equilibrium at all, hence the term "Chemi-

cal heating of Hydrogen" (as opposed to nuclear heat-

ing, for instance).

Page 4: 1998-10 R.Lo IAF98 Modular Cryogenic Solid Rocket Propellant Grains

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As can be seen in Fig.1 and Tab. 2, there is only a

small gain compared with the metal-free system. Now

how about density? Fig.5 shows average specific pro-

pellant masses over mixture ratio, Fig.6 the correspond-

ing volume specific Isps (i.e. Isp times specific mass).

%AL

in fuel

%H2

in fuel

Mass ratio

H2/Al

Molar ratio

H2/Al

O/F

[kg SOX /

kg fuel]

Isp,E

[m/s]

Ispvac ,E

[m/s]

vol. spec.

Isp E

Avg. prop.

density

[g|cc]

90,00 10,00 0,11 1,50 0,80 3011 3308 2416 0,8028

81,80 18,20 0,22 3,00 0,73 3472 3801 1864 0,5365

75,00 25,00 0,33 4,50 0,67 3728 4077 1541 0,4136

69,23 30,77 0,44 6,00 0,62 3837 4160 1344 0,3425

64,29 35,71 0,56 7,50 0,57 3872 4172 1147 0,2962

60,00 40,00 0,67 9,00 0,53 3861 4145 1017 0,2636

56,25 43,75 0,78 10,50 0,50 3822 4095 915 0,2395

52,94 47,06 0,89 12,00 0,47 3774 4038 833 0,2209

50,00 50,00 1,00 13,50 0,45 3722 3978 767 0,2061

47,37 52,63 1,11 15,00 0,42 3670 3918 712 0,1941

45,00 55,00 1,22 16,50 0,40 3616 3859 666 0,1841

Tab. 2: Theoretical performance of SOX/(SH2+Al) CSPs with equiv. ratio of SOX/Al. (9)

Mol H2/Al

Isp,va

c,E [m

/s]

2000

2500

3000

3500

4000

4500

0 2 4 6 8 10 12 14 16 18

I_sp_v ac_E

I_sp_E

Fig.4: Isp (E, 68:1) of SOX/(SH2+Al) CSPs with

equiv. ratio SOX/Al; (9)

121086420

0,0

0,2

0,4

0,6

0,8

1,0

Avg

. Pro

p. D

ensi

ty [

g/c

c]

Mass Ratio: Ox./total Fuel

SOX/SH2

LOX/LH2

45% Al

75% Al

90% Al

Fig.5: Average propellant density of O2/H2 propellants

in solid and liquid state (9)

121086420

0

1000

2000

3000

Isp

,vol [k

g/s

,m2]

Mass ratio O/(H2±Al)

SOX/(SH2+Al)

SOX/SH2

LOX/LH2

Fig.6: Volume-specific impulse of SOX/(H2±Al) as

function of O/F mass ratio at 68:1 equil. expansion; (9)

0,90,80,70,60,50,4

0

1000

2000

3000

Mass ratio O/(H2+Al)

Isp

,vo

l [k

g/s

,m2

]

45

60

50

75

90 % Al

Fig.7: Volume-specific impulse of SOX/(SH2 +Al) as

function of O/F mass ratio at 68:1, equil. expansion;

Page 5: 1998-10 R.Lo IAF98 Modular Cryogenic Solid Rocket Propellant Grains

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Oxygen in equivalence to Aluminum. %Al refer to fuel

composition; (9)

Fig.7 shows the aluminized part in more detail. Density

and hence Isp,vol skyrocket within a small O/F range,

because in comparison with Hydrogen, Aluminum

needs ten times less Oxygen for combustion.

The effect of more and more metal combustion is to

replace more and more Oxygen, rather than Hydrogen.

It takes 8kg Oxygen for burning 1kg of Hydrogen, but

less than 0,9 kg for 1kg of Aluminum. Compared on a

constant total impulse basis, it would therefor take

quite aluminum rich fuel mixtures in SOX/(SH2+Al)

propellants if the average density of SOX/SH2 were to

be equaled.

Thus the heating of Hydrogen by metal-combustion

rather than Hydrogen-combustion is a process with

much higher efficiency in terms of propellant mass

consumption. As Tab. 3 shows, several metals release

more than twice as much energy per unit Oxygen as

Hydrogen does. Ironically, this is exactly the reason,

why metal-combustion used in thermal Hydrogen pro-

pulsion is not a very good means for improving average

propellant density.

Prod.

(solid)

Hf

[Mj/kg]

A-wght

metal

M-

wght

prod.

MJ/kg-

metal

MJ/kg

O2

BeO 23,948 9,013 25,013 66,462 37,439

Li2O 19,971 6,94 29,88 42,992 37,296

B2O3 18,338 10,82 69,64 59,014 26,606

Al2O3 16,412 26,98 101,96 31,012 34,862

MgO 14,947 24,32 40,32 24,780 37,666

H2O g 13,431 1,008 18,016 120,029 15,124

Tab. 3: Energy released by the formation of oxides

S O X / f r o z e n H y d r o c a r b o n s

Obvious candidates for improving on the density Isp of

SOX/SH2 are hydrocarbon fuels. The following data

(Tab. 4) show SOX with frozen Kerosene as an exam-

ple.

LOX/RP1

SOX/SRP1

O/F Isp

68:1,E

avg. spec.

mass

vol. spec.

Isp E

Isp

68:1,E

avg. spec.

mass

vol. spec.

Isp E

1,00 2015 0,924 1863 1884 0,976 1838

2,00 2844 0,989 2812 2771 1,046 2899

2,50 2944 1,009 2970 2898 1,068 3094

3,00 2908 1,024 2979 2876 1,085 3121

4,00 2765 1,047 2895 2737 1,110 3038

5,00 2637 1,063 2803 2609 1,127 2941

6,00 2522 1,074 2709 2492 1,140 2840

7,00 2414 1,083 2615 2382 1,150 2738

8,00 2314 1,090 2522 2279 1,157 2637

9,00 2221 1,096 2433 2185 1,163 2542

10,00 2136 1,100 2350 2099 1,168 2453

Tab. 4: Isps and average densities of Oxygen/Kerosene in liquid and solid state;

based in part on extrapolated values by (9)

Page 6: 1998-10 R.Lo IAF98 Modular Cryogenic Solid Rocket Propellant Grains

6

2000

2200

2400

2600

2800

3000

3200

0,0 2,0 4,0 6,0 8,0 10,0

MR [-]

I_sp

[m

/s]

I_sp_vac_E

I_sp_E

Fig.8: Standard Isp 68:1, E and Isp,vac.

of SOX/SRP1 (9)

Boundary layer combustion in

solid propulsion The concept of dissected solid-rocket propellant

grains is based on the idea that the degree of separation

is a perfect means for controlling the rate of propellant

consumption in solid rockets. Example: consider a

cylindrical grain of SOX followed by a cylindrical

grain of hydrocarbon, both with a central combustion

channel (not necessarily of circular shape). Without

other means, this 2-piece "Internal Hybrid" arrange-

ment would not be able to sustain combustion. As the

degree of dissection is increased by increasing the

number of alternating oxidizer and fuel elements, the

regression velocity attainable after ignition would, to a

certain degree, approach the value expected for a mix-

ture of the two reactants. Dissected grains offer a new

degree of freedom for controlling combustion rate, that

may not have been required with conventional propel-

lants ("Sandwich grains") but might be essential for

cryogenic solids.

Fig.9 shows a motor with modular CSP grain de-

sign. (All dimensions in this figure are arbitrary). The

grain is a stack of alternating oxidizer- and fuel ele-

ments. The cross section of the central combustion

channel can have any shape and change along the grain.

Gasgenerator ModuleIgniter- and sustainermodule

Fuel Element

Oxidizer Element

Fig.9: Solid rocket motor using a modular CSP grain in

disk-stack design

The concept of modular dissected solid-rocket pro-

pellant grains is based on the idea that for any solid

propellant combination there exist subcritical mixture

ratios that do not require separation for well behaved

combustion. Propellant elements with such mixture

ratios

offer a further degree of freedom for obtaining a

desired value of regression rate (combustion veloci-

ty)

offer themselves as modules for ignition as well as

for sustaining and enhancing combustion (not nec-

essarily using the same propellants as the bulk of

the modular grain composite).

The element at the front end of the stack in Fig.9 is

formed by such a fuel rich gas generator composition,

capable of self-sustained burning. It serves as igniter

and sustainer (of course, the arrangement of oxidizing

and reducing elements might just as well be the other

way round). If required, there is another self sustained

burner at the end, serving as what with hybrids is called

"turbulator". In between, there is the dissected stack

with multiple boundary layer combustion.

There are many more geometrical solutions other

than sandwiches, e.g. wedge shaped arrangements or

cigarette burners. A "mixedness parameter" has been

defined for their characterization, see (6).

To ensure proper operation, they are all subject to

the following boundary conditions and requirements

concerning their operational parameters:

1. The time average over-all mixture ratio (= "tank

mixture ratio") determines the overall equivalence

ratio. It is defined as

O/ F to t 1

t c

(O / F)xmax

t0

c

t dt M oxMfu

where

tc : cut-off time (i.e.: c = combustion duration)

(O/F)xmax : instantaneous over-all mixture ratio

Mox : Total amount of oxidizer present in ele-

ments and gas generators

Mfu : Total amount of fuel present in elements

and gas generators

xmax: rear edge of grain, maximum value of the co-

ordinate of linear length x

Desired condition: O/ F tot

= some specific value

2. Instantaneous over-all mixture ratio, i.e. O/F ratio

of gases passing rear edge of grain (of course relat-

ing to the composition of their sources before com-

bustion)

(O/F)xmax(t) = mfox(t) / mffu(t)

Page 7: 1998-10 R.Lo IAF98 Modular Cryogenic Solid Rocket Propellant Grains

7

where

mf: mass flows with

mfox(t) =

i

i1

n ox

A i (t )r i i

i1

ngg

mf ox,gg (t)

and

mffu(t) = ditto

where

nox , nfu , ngg: number of respective oxidizer-, fuel-

or gas generator elements

i: number of individual elements (e.g. number 1 =

gg, 2, 4, 6 = oxidizer, 3, 5, 7 = fuel)

i: specific mass of element i

Ai(t): combustion surface area of element i at time t

r i : average regression velocity (= combustion rate

per unit area) between linear co-ordinate xi,o (front

edge of element i) and xi,e (rear edge)

mfox,gg(t), mffu,gg(t): mass flow contribution of gas

generator i at time t according to its primary com-

position

Desired condition: the instantaneous (O/F) over-all

mixture ratio should at all times be as close to the

desired value as possible:

1

t c

(O / F)xma x

t0

t c

(t )dt = (O/F)tot

3. The average regression velocity of element i ex-

tending between xi,o (front edge) and xi,e (rear

edge)

r i =

1

x i ,e x i,0

ri (x)dx

x i ,0

x i ,e

where

ri(x): local regression velocity of element i, that

must satisfy the basic hybrid heat balance

ri(x) = q (x) / (i•hi)

where

q (x): local heat flow per unit area

hi : specific heat of sublimation of element i

Desired condition:

ri(xi,e) = ri+1(xi,o)

i.e. adjacent elements should keep a smooth common

edge. This desire should actually by quite easy to

meet, because

• steps do not normally form in hybrids since they en-

hance regression of protruding material

• regression velocities can be matched by either ma-

nipulating the lengths of individual elements or

their total number.

Performance of cryogenic solid

rockets

A general feasibility study of Cryogenic Solid

Boosters (CSBs) sponsored by the German Aerospace

Research Center DLR (2) was finished in 1996. The

basic assumption was that the above concepts are feasi-

ble and it aimed at identifying specific problem areas

and their possible solutions. Boosters were investigated

with solid Hydrogen (SH2) and Oxygen (SOX) as a

sample propellant combination. As a result, no insur-

mountable problems were found in the areas of cooling

equipment and its operation during fabrication and

launch operations; neither were there problems with

thrust to weight ratio of uncooled but insulated CSBs

that leave their terrestrial cooling equipment at the

launch pad. The pressure variation of the melting points

of SOX (and its allotropic modifications) and of SH2

appeared manageable.

Precautions will be necessary with respect to me-

chanical stability and the influence of off-design condi-

tions. While many frozen liquids are quite sturdy (see

(11)) special supporting and enclosing measures are

suggested (see (12)).

On the other hand, under specific assumptions, very

substantial performance gains were calculated for

ARIANE V and the US-STS if the conventional solid

boosters were replaced by cryogenic ones (SOX/SH2).

As is shown in

Tab.5, the lift-off mass of the boosters of both space

transportation systems could be cut down to about 2/3

of their present mass.

As was already pointed out in the section on Isp-

calculations, the use of metalized SOX/(Al,SH2) solid

propellants does not really improve on the metal-free

combination. A just slightly lesser mass would have to

be bought by using about 60% of Aluminum in the fuel

(see Tab.6). Whether such amounts could be burned

with sufficient efficiency, must be doubted.

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8

STS-SRB STS-SRB

CSP-

Ersatz

ARIANE

5-EAP

ARIANE

5-EAP

CSP-

Ersatz

Isp [m/s] 2634,9 3438,52 2678,13 3438,52

pc [bar] 62,4 20 ~30 20

pc/pe - 66 ~77 66

O/F 2,3 5 ~2,3 5

M-prop [Mg] 504 349,525 237 167,870

Itot [MNs] 1320 1320 634,7 634,7

cut-off time [s] 124 120 130 130

Thrust [kN] 11500 5300

M-tank [Mg] 91,000 54,411 38,000 26,207

Lift-off [Mg] 595 403,936 275 194,077

Tab.5: STS and ARIANE V boosters compared with

their CSP-Ersatz; after (7)

The results were optimized for best mixture ratio of

SOX/SH and for optimum chamber pressures chosen,

see Fig.10

400

410

420

430

440

450

460

470

480

490

500

0 20 40 60 80 100 120

Chamber pressure [bar]

ST

S-S

RB

ma

ss

[M

g]

Fig.10: Mass of SOX/SH2 SRB-Ersatz Boosters at opt.

O/F over chamber pressure (7)

Aluminum addition does not replace Hydrogen, ra-

ther, it replaces Oxygen. This can be seen in the follow-

ing example series of results, refering to ARIANE V

EAPs: the non-metalized EAP-booster uses 32340 kg

of SH2 and 132590kg of SOX. The weight minimized

metalized booster of same total impulse burns 67150kg

Aluminum with 60470kg of Oxygen (less than half the

previous amount!), heating but not oxidizing 37300kg

of Hydrogen (15% more!).

%Al Mp [t] Vp[m3]

90,00 210,9 262,8

81,80 182,9 340,7

75,00 170,3 412,0

69,23 165,5 472,5

64,29 164,0 553,8

60,00 164,5 624,2

56,25 166,2 694,1

52,94 168,3 762,0

50,00 170,6 828,0

47,37 173,0 891,8

45,00 175,6 954,1

0,00 164,9 521,0

Tab.6: Propellant mass and volume of boosters of

ARIANE V size (Itot ~635 MNs) with SOX/(Al,SH2)

cryo-solid propellants

Feasibility demonstration Ongoing work aims at the experimental demonstra-

tion of the feasibility of cryogenic solid grain combus-

tion and is considered as the second step in a four step

procedure leading to the acquisition of the technology

of modular, dissected solid propellant grains.

Summary As a conclusion, the concept of Modular Dis-

sected Cryogenic Solid Rocket Propellants opens a

whole area of new chemical propulsion research and

development. Chemical propellant combinations of the

highest known values of Isp can be used in solid rocket

motors because deflagration is replaced by boundary

layer combustion in an arangement that was dubbed

"multilayer internal hybrid combustion".

The concept was accepted as "potentially revolu-

tionizing propulsion technology" at the recent Ad-

vanced Propulsion Workshop of the IAA (Jan.1998 at

El Segundo, Cal., see 3). In the framework of the APW

a web site was established for describing and discuss-

ing the concept in public (http://www.aero.org/apw/).

Page 9: 1998-10 R.Lo IAF98 Modular Cryogenic Solid Rocket Propellant Grains

9

Literature

(1) R.E.Lo, , DFVLR-Stuttgart: "Technical Feasibili-

ty of Chemical Propulsion Systems with very high

Performance", Proceedings of the XVIIIth Astro-

nautical Congress, Belgrade, 25.-29.9.1967, pp.

121-132

(2) R.E.Lo, DFVLR-Lampoldshausen: "Quasihybrid

Rocket Propulsion Systems (Quasihybride Rake-

tenantriebe)", Raumfahrtforschung, Heft 4, April

1970, in German.

(3) R.E.Lo, DFVLR-Stuttgart: "Chemical Heating of

Hydrogen by Tribrid Combustion (Chemische

Wasserstoffaufheizung durch tribride Verbren-

nung)", DGLR-Symposion 'Chemical Rocket En-

gines', 21.March,1967 Munich, Chemie-

Ingenieur-Technik (1967) 39, Heft 15, S. 923-

927, in German

(4) R.E.Lo, DFVLR-Lampoldshausen: "Chemical

Heating of Hydrogen by Aluminum Combustion

with Oxygen or FLOX (Chemische Wasserstof-

faufheizung durch Verbrennung von Aluminium

mit Sauerstoff oder FLOX)", DLR-Mitt. 70-03

(Feb. 1970), in German

(5) R.E.Lo, DFVLR-Lampoldshausen: "Theoretical

Performance of the Rocket Propellant Combina-

tion F2,02/LiH,Al/H2 and Simpler Subsystems

(Theoretische Leistungen des Raketentreibstoff-

systems F2,02/LiH,Al/H2 und einfacherer Teil-

systeme)", DLR-Mitt. 69-21 (Dez.1969), in Ger-

man

(6) R.E.Lo, Berlin Univ.Techn.: "A Novel Kind of

Solid Rocket Propellant", Aerospace Science and

Technology, Elsevier, 1998

(7) B.Voslamber, M.Voslamber.R.Lo, Berlin Un-

iv.Techn: "Feasibility Study on Cryogenic Solid

Rocket Boosters", DARA Project 50TT 9631, Fi-

nal Report 2/1997 (in German)

(8) D.Froning, Jr.,Roger E. Lo: „Possible Revolutions

in Rocket Propulsion", 49th

Int. Astronautical

Congress, Melbourne, Austr., Oct.02.1998, Ses-

sion IAA.3.3., Co-operation and Competition in

Advanced Propulsion, IAA-98-IAA.3.303

(9) Calc. by H.Adirim, ILR/ Berlin Univ.Techn,

Jul.1998

(10) P.G.Carrick, Phillips Lab, Edwards AFB: "Theo-

retical Performance of High Energy Density

Cryogenic Solid Rocket Propellants", AIAA-95-

2892, 31st AIAA Joint Propulsion Conf., San Di-

ego Jul.1995

(11) W.F.Staylor, NASA-Langley R.C.: "Frozen Pro-

pellant - A Booster Concept?", Astronau-

tics&Aeronautics, Sept.1997, p.56-59

(12) R.E.Lo, N.Eisenreich: "Modulare und kryogene

Feststofftreibsätze - eine neue Klasse chemischer

Raketenantriebe" Deutscher Luft- und Raum-

fahrtkongress, Bremen 5.-8.Okt.1998