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Naminosuke Kubota Propellants and Explosives Thermochemical Aspects of Combustion Second, Completely Revised and Extended Edition... Preface to the First Edition Propellants and explosiv

Naminosuke Kubota

Propellants and Explosives

Thermochemical Aspects of Combustion

Second, Completely Revised and Extended Edition

Naminosuke Kubota

Propellants and Explosives

For 200 years, Wiley has been an integral part of each generation’s journey,enabling the flow of information and understanding necessary to meet theirneeds and fulfill their aspirations Today, bold new technologies are changingthe way we live and learn Wiley will be there, providing you the must-haveknowledge you need to imagine new worlds, new possibilities, and new oppor-tunities.

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Naminosuke Kubota

Propellants and Explosives

Thermochemical Aspects of Combustion

Second, Completely Revised and Extended Edition

The Author

Prof Dr Naminosuke Kubota

Asahi Kasei Chemicals

Propellant Combustion Laboratory

Arca East, Kinshi 3-2-1, Sumidaku

Tokyo 130-6591, Japan

First Edition 2001

All books published by Wiley-VCH are carefully produced Nevertheless, authors, editors, and publisher do not warrant the information contained

in these books, including this book, to be free of errors Readers are advised to keep in mind that statements, data, illustrations, pro cedural details or other items may inadvertently be inaccurate.

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A catalogue record for this book is available from the British Library.

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© 2007 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim

All rights reserved (including those of translation into other languages) No part of this book may be reproduced in any form − by photoprinting, microfilm, or any other means − nor transmitted or translated in to a machine language without written permission from the publishers Registered names, trademarks, etc used in this book, even when not specifically marked as such, are not to be considered unprotected by law.

Typesettingprimustype Robert Hurler GmbH

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BindingLitges & Dopf Buchbinderei GmbH, Heppenheim

Cover DesignGrafik-Design Schulz, Fußgönheim Printed in the Federal Republic of Germany Printed on acid-free paper

2 Thermochemistry of Combustion 23

3 Combustion Wave Propagation 41

4 Energetics of Propellants and Explosives 69

5 Combustion of Crystalline and Polymeric Materials 113

6 Combustion of Double-Base Propellants 143

Phase 148

Table of Contents

7 Combustion of Composite Propellants 181

Table of Contents

8 Combustion of CMDB Propellants 235

9 Combustion of Explosives 257

Table of Contents

10 Formation of Energetic Pyrolants 273

11 Combustion Propagation of Pyrolants 301

12 Emission from Combustion Products 337

12.6.2.2 Effect of Nozzle Expansion 358

13 Transient Combustion of Propellants and Pyrolants 367

13.4.3.1 Nature of Oscillatory Combustion 386

13.4.3.2 Combustion Instability Test 387

13.4.3.3 Model for Suppression of Combustion Instability 395

14 Rocket Thrust Modulation 405

14.2.3.2 Determination of Design Parameters 418

15 Ducted Rocket Propulsion 439

Table of Contents

15.3.1.1 Non-Choked Fuel-Flow System 446

15.3.1.2 Fixed Fuel-Flow System 446

15.3.1.3 Variable Fuel-Flow System 447

15.5.2.1 Burning Rate and Pressure Exponent 451

Appendix A 469

Appendix B 471

Field 475

Appendix C 477

Shock Wave Propagation in a Two-Dimensional Flow Field 477

Table of Contents

Appendix D Supersonic Air-Intake 483

Preface to the First Edition

Propellants and explosives are composed of energetic materials that produce hightemperature and pressure through combustion phenomena The combustion phe-nomena include complex physicochemical changes from solid to liquid and to gas,which accompany the rapid, exothermic reactions A number of books related tocombustion have been published, such as an excellent theoretical book, Combus-tion Theory, 2nd Edition, by F A Williams, Benjamin/Cummings, New York(1985), and an instructive book for the graduate student, Combustion, by I Glass-man, Academic Press, New York (1977) However, no instructive books related tothe combustion of solid energetic materials have been published Therefore, thisbook is intended as an introductory text on the combustion of energetic materialsfor the reader engaged in rocketry or in explosives technology

This book is divided into four parts The first part (Chapters 1–3) provides briefreviews of the fundamental aspects relevant to the conversion from chemicalenergy to aerothermal energy References listed in each chapter should prove useful

to the reader for better understanding of the physical bases of the energy sion process; energy formation, supersonic flow, shock wave, detonation, and deflagration The second part (Chapter 4) deals with the energetics of chemical com-pounds used as propellants and explosives, such as heat of formation, heat of explo-sion, adiabatic flame temperature, and specific impulse

conver-The third part (Chapters 5–8) deals with the results of measurements on theburning rate behavior of various types of chemical compounds, propellants, and ex-plosives The combustion wave structures and the heat feedback processes from thegas phase to the condensed phase are also discussed to aid in the understanding ofthe relevant combustion mechanisms The experimental and analytical data de-scribed in these chapters are mostly derived from results previously presented bythe author Descriptions of the detailed thermal decomposition mechanisms fromsolid phase to liquid phase or to gasphase are not included in this book The fourthpart (Chapter 9) describes the combustion phenomena encountered during rocketmotor operation, covering such to pics as the stability criterion of the rocket motor,temperature sensitivity, ignition transients, erosive burning, and combustion oscil-lations The fundamental principle of variable-flow ducted rockets is also pre-sented The combustion characteristics and energetics of the gas-generating pro-pellants used in ducted rockets are discussed

Since numerous kinds of energetic materials are used as propellants and sives, it is not possible to present an entire overview of the combustion processes ofthese materials In this book, the combustion processes of typical energetic crystal-line and polymeri c materials and of varioustypes of propellants are presented so as

explo-to provide an informative, generalized approach explo-to understanding their tion mechanisms

combus-Naminosuke Kubota

Kamakura, Japan

March 2001

Preface

Preface to the Second Edition

The combustion phenomena of propellants and explosives are described on the basis

of pyrodynamics, which concerns thermochemical changes generating heat and tion products The high-temperature combustion products generated by propellantsand explosives are converted into propulsive forces, destructive forces, and varioustypes of mechanical forces Similar to propellants and explosives, pyrolants are alsoenergetic materials composed of oxidizer and fuel components Pyrolants react togenerate high-temperature condensed and/or gaseous products when they burn Pro-pellants are used for rockets and guns to generate propulsive forces through deflagra-tion phenomena and explosives are used for warheads, bombs, and mines to generatedestructive forces through detonation phenomena On the other hand, pyrolants areused for pyrotechnic systems such as ducted rockets, gas-hybrid rockets, and ignitersand flares This Second Edition includes the thermochemical processes of pyrolants

reac-in order to extend their application potential to propellants and explosives

The burning characteristics of propellants, explosives, and pyrolants are largely pendent on various physicochemical parameters, such as the energetics, the mixtureratio of fuel and oxidizer components, the particle size of crystalline oxidizers, and thedecomposition process of fuel components Though metal particles are high-energyfuel components and important ingredients of pyrolants, their oxidation and combus-tion processes with oxidizers are complex and difficult to understand

de-Similar to the First Edition, the first half of the Second Edition is an introductory text

on pyrodynamics describing fundamental aspects of the combustion of energeticmaterials The second half highlights applications of energetic materials as propel-lants, explosives, and pyrolants In particular, transient combustion, oscillatory burn-ing, ignition transients, and erosive burning phenomena occurring in rocket motorsare presented and discussed Ducted rockets represent a new propulsion system inwhich combustion performance is significantly increased by the use of pyrolants.Heat and mass transfer through the boundary layer flow over the burning surface ofpropellants dominates the burning process for effective rocket motor operation.Shock wave formation at the inlet flow of ducted rockets is an important process forachieving high propulsion performance Thus, a brief overview of the fundamentals

of aerodynamics and heat transfer is provided in Appendices B−D as a prerequisite forthe study of pyrodynamics

September 2006

XX Preface to the Second Edition

to generate high-pressure combustion products accompanied by a shock wave thatyield destructive forces This chapter presents the fundamentals of thermodynam-ics and fluid dynamics needed to understand the pyrodynamics of propellants andexplosives.

1.1

Heat and Pressure

1.1.1

First Law of Thermodynamics

The first law of thermodynamics relates the energy conversion produced by cal reaction of an energetic material to the work acting on a propulsive or explosive

chemi-system The heat produced by chemical reaction (q) is converted into the internal energy of the reaction product (e) and the work done to the system (w) according to

pressure Both specific heats represent conversion parameters between energy andtemperature Using Eqs (1.3) and (1.5), one obtains the relationship

is given by the sum of the internal energies, which comprise translational energy,

1 Foundations of Pyrodynamics

εt, rotational energy, εr, vibrational energy, εv, electronic energy, εe, and their action energy, εi:

inter-εm = ε t + ε r + ε v + ε e + ε i

A molecule containing n atoms has 3n degrees of freedom of motion in space:

A statistical theorem on the equipartition of energy shows that an energy

amount-ing to kT/2 is given to each degree of freedom of translational and rotational modes, and that an energy of kT is given to each degree of freedom of vibrational modes.

de-fined in Eq (1.6) is given by R = kζ, where ζ is Avogadro’s number, ζ = 6.02214 ×

1023mol−1

When the temperature of a molecule is increased, rotational and vibrationalmodes are excited and the internal energy is increased The excitation of eachdegree of freedom as a function of temperature can be calculated by way of statis-tical mechanics Though the translational and rotational modes of a molecule arefully excited at low temperatures, the vibrational modes only become excitedabove room temperature The excitation of electrons and interaction modes usu-ally only occurs at well above combustion temperatures Nevertheless, dissocia-tion and ionization of molecules can occur when the combustion temperature isvery high

When the translational, rotational, and vibrational modes of monatomic, tomic, and polyatomic molecules are fully excited, the energies of the molecules aregiven by

dia-εm = ε t + ε r + ε v

εm = 3 × kT/2 = 3 kT/2 for monatomic molecules

εm = 3 × kT/2 + 2 × kT/2 + 1 × kT = 7 kT/2 for diatomic molecules

εm = 3 × kT/2 + 2 × kT/2 + (3 n − 5) × kT = (6 n − 5) kT/2 for linear molecules

εm = 3 × kT/2 + 3 × kT/2 + (3 n − 6) × kT = 3(n − 1) kT for nonlinear molecules

Since the specific heat at constant volume is given by the temperature derivative of

the internal energy as defined in Eq (1.7), the specific heat of a molecule, c v,m, is resented by

rep-c = d /dT = dε /dT + dε /dT + dε /dT + dε /dT + dε /dT J molecule−1K−1

1.1 Heat and Pressure

Thus, one obtains the specific heats of gases composed of monatomic, diatomic,and polyatomic molecules as follows:

The specific heat ratio defined by Eq (1.9) is 5/3 for monatomic molecules; 9/7 fordiatomic molecules Since the excitations of rotational and vibrational modes onlyoccur at certain temperatures, the specific heats determined by kinetic theory aredifferent from those determined experimentally Nevertheless, the theoretical re-sults are valuable for understanding the behavior of molecules and the process ofenergy conversion in the thermochemistry of combustion Fig 1.1 shows thespecific heats of real gases encountered in combustion as a function of tempera-

temperature, as determined by kinetic theory However, the specific heats of tomic and polyatomic gases are increased with increasing temperature as the ro-tational and vibrational modes are excited

dia-1.1.3

Entropy Change

Entropy s is defined according to

Fig 1.1 Specific heats of gases at

con-stant volume as a function of temperature.

1 Foundations of Pyrodynamics

col-adiabatic conditions, ds becomes a positive value, and then Eqs (1.13) and (1.14) are

no longer valid However, when these physical effects are very small and heat lossfrom the system or heat gain by the system are also small, the system is considered

to undergo an isentropic change

1.2

Thermodynamics in a Flow Field

1.2.1

One-Dimensional Steady-State Flow

1.2.1.1 Sonic Velocity and Mach Number

The sonic velocity propagating in a perfect gas, a, is given by

Using the equation of state, Eq (1.8), and the expression for adiabatic change,

Eq (1.14), one gets

Mach number M is defined according to

where u is the local flow velocity in a flow field Mach number is an important

para-meter in characterizing a flow field

1.2 Thermodynamics in a Flow Field

1.2.1.2 Conservation Equations in a Flow Field

Let us consider a simplified flow, that is, a one-dimensional steady-state without viscous stress or a gravitational force The conservation equations of con-tinuity, momentum, and energy are represented by:

flow-rate of mass in − flow-rate of mass out = 0

If one can assume that the process in the flow field is adiabatic and that dissipative

effects are negligibly small, the flow in the system is isentropic (ds = 0), and then

Eq (1.21) becomes

Integration of Eq (1.22) gives

Eq (1.7) into Eq (1.23), one gets

The changes in temperature, pressure, and density in a flow field are expressed

as a function of Mach number as follows:

(1.25)

(1.26)

(1.27)

1 Foundations of Pyrodynamics

1.2.2

Formation of Shock Waves

One assumes that a discontinuous flow occurs between regions 1 and 2, as shown

in Fig 1.2 The flow is also assumed to be one-dimensional and in a steady state,and not subject to a viscous force, an external force, or a chemical reaction

The mass continuity equation is given by

where m is the mass flux in a duct of constant area, and the subscripts 1 and 2

indi-cate the upstream and the downstream of the discontinuity, respectively ing Eq (1.29) into Eq (1.30), one gets

Fig 1.2 Shock wave propagation.

1.2 Thermodynamics in a Flow Field

Combining Eqs (1.33) and (1.34), the Mach number relationship in the upstream

1 and downstream 2 is obtained as

(1.35)One obtains two solutions from Eq (1.35):

Substituting Eq (1.37) into Eq (1.34), one obtains the pressure ratio as

(1.38)Substituting Eq (1.37) into Eq (1.33), one also obtains the temperature ratio as

(1.39)The density ratio is obtained by the use of Eqs (1.38), (1.39), and (1.8) as

(1.40)Using Eq (1.24) for the upstream and the downstream and Eq (1.38), one obtainsthe ratio of stagnation pressure as

(1.41)The ratios of temperature, pressure, and density in the downstream and upstreamare expressed by the following relationships:

(1.42)

(1.43)

1 Foundations of Pyrodynamics

(1.44)where ζ = (γ + 1)/(γ − 1) The set of Eqs (1.42), (1.43), and (1.44) is known as theRankine−Hugoniot equation for a shock wave without any chemical reactions The

relationship of p2/p1and ρ2/ρ1at γ = 1.4 (for example, in the case of air) shows thatthe pressure of the downstream increases infinitely when the density of thedownstream is increased approximately six times This is evident from Eq (1.43),

Though the form of the Rankine−Hugoniot equation, Eqs (1.42)−(1.44), is tained when a stationary shock wave is created in a moving coordinate system, thesame relationship is obtained for a moving shock wave in a stationary coordinatesystem In a stationary coordinate system, the velocity of the moving shock wave

ob-is u1and the particle velocity u p is given by u p = u1− u2 The ratios of temperature,pressure, and density are the same for both moving and stationary coordinates

A shock wave is characterized by the entropy change across it Using the equation

of state for a perfect gas shown in Eq (1.5), the entropy change is represented by

Substituting Eqs (1.38) and (1.39) into Eq (1.45), one gets

(1.46)

Eqs (1.37) and (1.41) The ratios of temperature, pressure, and density across the

Eqs (1.25)−(1.27) The characteristics of a normal shock wave are summarized asfollows:

1.2.3

Supersonic Nozzle Flow

When gas flows from stagnation conditions through a nozzle, thereby undergoing

an isoentropic change, the enthalpy change is represented by Eq (1.23) The flowvelocity is obtained by substitution of Eq (1.14) into Eq (1.24) as

where the subscript e denotes the exit of the nozzle The mass flow rate is given by

the law of mass conservation for a steady-state one-dimensional flow as

where ˙m is the mass flow rate in the nozzle, ρ is the gas density, and A is the

cross-sectional area of the nozzle Substituting Eqs (1.48), (1.5), and (1.14) into Eq (1.49),one obtains

Differentiation of Eq (1.50) yields

(1.51c)

(1.52)

(1.53)

and γ are given In addition, T, p, and ρ are obtained by the use of Eqs (1.25), (1.26),

and (1.27) Differentiation of Eq (1.53) with respect to Mach number yields

Eq (1.54):

(1.54)

flow, the so-called “nozzle throat”, in which the flow velocity becomes the sonicvelocity Furthermore, it is evident that the velocity increases in the subsonic flow of

a convergent part and also increases in the supersonic flow of a divergent part

The velocity u*, temperature T*, pressure p*, and density ρ*in the nozzle throatare obtained by the use of Eqs (1.16), (1.18), (1.19), and (1.20), respectively:

(1.55)(1.56)

(1.57)

(1.58)

For example, T*/T0= 0.833, p*/p0= 0.528, and ρ*/ρ0= 0.664 are obtained when γ =

1.2 Thermodynamics in a Flow Field

than the temperature decrease when the flow expands through a convergentnozzle The maximum flow velocity is obtained at the exit of the divergent part ofthe nozzle When the pressure at the nozzle exit is a vacuum, the maximum velocity

is obtained by the use of Eqs (1.48) and (1.6) as

(1.59)

terms of the nozzle throat area A t (= A*) and the chamber pressure p c (= p0) is givenby

Momentum Change and Thrust

One assumes a propulsion engine operated in the atmosphere, as shown in

Fig 1.3 Air enters in the front end i, passes through the combustion chamber c, and is expelled from the exit e The heat generated by the combustion of an

energetic material is transferred to the combustion chamber The momentum

balance to generate thrust F is represented by the terms:

p i A i = pressure force acting at i

p e A e = pressure force acting at e

F + p a (A e − A i) = force acting on the outer surface of engine

where u is the flow velocity, ˙m is the mass flow rate, A is the area, and the subscripts

i, e, and a denote inlet, exit, and ambient atmosphere, respectively The mass flow

the difference in the mass flow rates at the exit and the inlet, ˙m e − ˙m i In the case of

repre-sented by

the exit when ˙m e , A e , and p aare given

dF/dA e = u e d ˙m g /dA e + ˙m g du e /dA e + A e dp e /dA e + p e − p a (1.64)

relationship

is equal to the ambient pressure

However, it must be noted that Eq (1.62) is applicable for ramjet propulsion, as

in ducted rockets and solid-fuel ramjets, because in these cases air enters throughthe inlet and a pressure difference between the inlet and the exit is set up The mass

case of ramjet propulsion

1.3.2

Rocket Propulsion

Fig 1.4 shows a schematic drawing of a rocket motor composed of propellant, bustion chamber, and nozzle The nozzle is a convergent−divergent nozzle de-signed to accelerate the combustion gas from subsonic to supersonic flow throughthe nozzle throat The thermodynamic process in a rocket motor is shown in

propellant contained in the chamber burns and generates combustion products,

com-1.3 Formation of Propulsive Forces

If one can assume that (1) the flow is one-dimensional and in a steady-state,(2) the flow is an isentropic process, and (3) the combustion gas is an ideal gas and

the specific heat ratio is constant, the plots of p vs v and of h vs s are uniquely

where Δh is the heat of reaction of propellant per unit mass The expansion process

c 씮 t 씮 e shown in Fig 1.4 follows the thermodynamic process described in

specific heat ratio of the combustion gas:

(1.74)

of the pressure and the physical dimensions of the combustion chamber and

energetics of combustion

1.3 Formation of Propulsive Forces

1.3.2.3 Specific Impulse

propel-lant combustion, which is represented by

is expressed in terms of seconds Thermodynamically, specific impulse is the tive time required to generate thrust that can sustain the propellant mass against

(1.76)

combustion products, γ varies relatively little among propellants It is evident from

specific impulse I sp,max is obtained when p e = p a:

(1.78)

In addition, the specific impulse is given by the thrust coefficient and the teristic velocity according to

in-dication of the overall efficiency of a rocket motor

1.3.3

Gun Propulsion

1.3.3.1 Thermochemical Process of Gun Propulsion

Gun propellants burn under conditions of non-constant volume and non-constantpressure The rate of gas generation changes rapidly with time and the temperaturechanges simultaneously because of the displacement of the projectile in the com-

1 Foundations of Pyrodynamics

linear burning rate is assumed to be expressed by a pressure exponent law, the called Vieille’s law, i e.:

de-pendent on the composition of the propellant, and a is a constant dede-pendent on the

initial chemical composition and temperature of the propellant

The fundamental difference between gun propellants and rocket propellants lies

in the magnitude of the burning pressure Since the burning pressure in guns is tremely high, more than 100 MPa, the parameters of the above equation are empiri-cally determined Though rocket propellant burns at below 20 MPa, in general, theburning rate expression of gun propellants appears to be similar to that of rocketpropellants The mass burning rate of the propellant is also dependent on the burn-ing surface area of the propellant, which increases or decreases as the burningproceeds The change in the burning surface area is determined by the shape anddimensions of the propellant grains used

ex-The effective work done by a gun propellant is the pressure force that acts on thebase of the projectile Thus, the work done by propellant combustion is expressed

in terms of the thermodynamic energy, f, which is represented by

generated by the combustion of unit mass of propellant in the standard state The

thermody-namic energy of rocket propellants

The thermal energy generated by propellant combustion is distributed to various

follows:

The remaining part of the energy, 32 %, is used to accelerate the projectile It is vious that the major energy loss is the heat released from the gun barrel This is anunavoidable heat loss based on the laws of thermodynamics: the pressure in thegun barrel can only be expended by the cooling of the combustion gas to the at-mospheric temperature

ob-1.3 Formation of Propulsive Forces

where M w is the mass of the projectile, u is its velocity, x is the distance travelled, t is

With fixed physical dimensions of a gun barrel, the thermodynamic efficiency of agun propellant is expressed by its ability to produce as high a pressure in the barrel

as possible from a given propellant mass within a limited time

In general, the internal pressure in a gun barrel exceeds 200 MPa, and the

pres-sure exponent, n, of the propellant burning rate given by Eq (1.80) is 1 When n = 1,

the burning rate of a gun propellant is represented by

where r is the burning rate, p is the pressure, and a is constant dependent on the

chemical ingredients and the initial temperature of the propellant grain The

volumetric burning rate of a propellant grain is represented by S(t)r, where S(t) is the surface area of the propellant grain at time t The volumetric burning change of

the propellant grain is defined by

dz/dt = V(t)/V0

(1.83)

pro-pellant grain at time t, and z is a geometric function of the grain The surface area

ratio change, termed the “form function”, ϕ, is defined according to

1 Foundations of Pyrodynamics