Thermodynamic aspects of solid propellant gas generator for aircraft application

1.1. Defining the research problem

Gas generators are broadly used for military, space and civil applications to perform different roles such as thrusters, signaling, flares, seat ejections, cable cutting, bomb release, stage operation, flare and chaff. They are comprised of a propellant and a pyrotechnic component. The propellant works as the main source of energy for performing the various tasks after applying appropriate stimulus. Due to the propellants being ignited inside a cartridge case, an enormous amount of combusted products is generated. The propellant’s behavior and thermodynamic aspects under given circumstances are very important for that particular application. The gas generator under study here is subjected to various testing and evaluation methods in the development phase. The gas generator described in this paper is used to save a life of the pilot in an emergency situation. This type of testing is performed using the gas generator to save the life of a pilot for various aircraft platforms. The thermodynamics of a gas generator involves science related to the transfer of energy and its results on the substances’ physical properties. This is based on translating the observations of common experiences into thermodynamic laws and these laws preside over the principles of energy conversion.

2.1. Thermodynamic cycle

As far as the gas generator is concerned, fuel in the form of a propellant is already stored in the system. No oxygen is available for the gas generator as in the case of an internal combustion (IC) engine. The pictorial representation of the gas generators pressure vs. volume and temperature vs. entropy curves are illustrated in Figures 1 and 2 respectively (Shekar 2018). However, were one to consider the gas generator as an internal combustion (IC) engine, the process involves no intake stage. This is shown by the dotted line 1-2 in the figures. As the propellant is ignited, heat starts being added and equilibrium in pressure is attained. The heat addition is assumed to occur at a constant pressure and is shown by the line 2-3 in the figures. In many cases, the heat addition can occur at varying pressures. The combustion increases pressure initially and this transient phase can be treated as a compression stroke. The process is not isentropic and can not be represented properly by a single

Figure 2. Temperature vs. entropy. thermodynamic plane. This is shown as expansion stroke by the line 3-4 in the figures. However, the rise in pressure and temperature in the gas generator occurs in milliseconds (ms). Simultaneously, the combustion gases are expelled as a combination of both the expansion and heat ejection stages. Thus, the gas generator has only two valid processes on the thermodynamic plane. Another significant variation is that no cycle occurs once the propellant is initiated. After the propellant is completely burned the system returns to original state. This indicates that the gas generator operates as a single stroke regarding thermodynamic cycle as the operation has no periodicity. A continuous generation of work occurs until the propellant (fuel) is fully consumed. The gas generator device consists of a pyrotechnic component, the propellant and a means of initiation (Cumming, 2009). Using proper means of initiation, huge volume of gases can be generated due to the rapid chemical reactions that occur from burning the propellant. The gas generator consists of different ingredients such as oxidizing and reducing agents. Subjecting the propellant to testing involves evaluating different performance parameters such as heat of combustion, combustion temperature, specific volume, propellant force and burn rate in the test vessel. This article will outline the closed vessel (CV) firing of a gas generator and determine the various thermodynamic properties (Han, 2017). Martiosyan et al. (2009) have explained the design aspects and performance of nanoenergetic gas generator.

3.1. Ratio of Specific heat (γ)

The specific heat of the gaseous product of combustion is basically a measure of temperature rise for a given heat input per unit mass of a given material. The given mass of material with a high specific heat results in a low temperature rise for a constant heat input. The reverse is true for materials with a low specific heat. Alternatively, a constant mass of a material with a high specific heat requires more heat input for a given rise in temperature. The difference in specific heats between specific heat at constant pressure and specific heat at constant volume is equal to the gas constant of the gas whose ratio is expressed by the Greek letter Gamma (γ) for ideal gases. This is also called the heat capacity ratio and adiabatic index and is basically an isentropic expansion factor. Thermodynamically, it also equals enthalpy (h) and the internal energy of the ideal gas (u). The value of γ is related to the degree of freedom available in the molecule (f) and is defined as [1+(2/f)]. However, the value of γ is reduced by the combustion gases containing traces of fuel. The reduction is dependent on the molecular weight of the combustion gases and their relative compressibility. The value of γ is taken as 1.2 for double-base propellant. The value of γ gets lower as temperature and pressure rise.

3.2. Mass generation rate (mg)

This represents the rate at which the propellant is converted into gaseous form by combustion. It is given by the density of the propellant multiplied by the rate of volume consumption of the propellant. The rate of volume consumption is given by the product of the burning area (A) of the propellant and its burn rate (r) which is the consumption rate of the propellant grain or of the whole propellant mass at a constant pressure (P) per unit time. The volume of a grain consumed per unit time is the product of rate of regression (r) and the burning surface area (A). The rate of mass discharge is a function of pressure with higher pressures having higher discharge rates. This is the explosive mass consumed over a given unit of time. The expression for the mass generation rate due to propellant consumption is given below: mg=dm/dt = ρ×A×r(1) Using Vieille’s equation for the mass burning rate dm = pa×k×p dt

where k is a constant that consider the values of ρ, A and α. The burning rate (r) plays an important role in the formulation of the propellant as it indicates the propellant’s functional performance. The burn rate of the propellant is calculated from small slabs. In general, the burn rate is expressed either in mm/s or cm/s based on surface area (A) and pressure (P). This is expressed by the relation r=β Pα where α=pressure index and β=burning rate coefficient.

Furthermore, this is also based on the propellant composition (fuel and oxidizer content of the propellant) and conditions prevailing inside the combustion chamber. The burn rate affects the gas pressure and gas velocity. This affects the rate of heat transfer from the hot gas into the propellant. If the initial propellant temperature is high, the burn rate also increases. The propellant having already gained the heat tends to burn faster due to the temperature gradient that drives the burning rate, the bulk temperature. Smaller the grain sizes for a particular propellant increase the total surface area per unit weight for burning. Because the propellant density is constant, decreases in grain size will increase in total surface area per unit volume. The surface area per unit volume is called the specific surface of propellant and is measured in cm-1 units.

3.3. Combustion heat (Qv)

Combustion heat of substance is also known as the calorific value or the energy value. This can be defined as the amount of heat liberated when a given amount of the substance undergoes combustion. Usually, heat of combustion is considered to be a synonym of calorific value, which can be defined as the total amount of energy liberated when a given mass of a substance undergoes complete combustion in the presence of (an adequate quantity of) oxygen under standard conditions for temperature and pressure. The concept of the heat of combustion of a propellant is extremely important considering rocket, missile and power cartridge applications. The propellants used in these areas are often selected based on their calorific values (a value that denotes the heat of combustion of the fuel). The greater the heat of combustion of propellant, the greater the amount of power that can be produced from it inside combustion chamber. Combustion heat is determined as : Qv= Qp+RT×Δn(3) where Qp=heat of combustion at constant pressure (kJ/mol), Qv=heat produced at constant volume (kJ/mol), R=the gas constant (8.314 J/mol K), Δn=moles difference between reactant and products of one kg gas, and T is temperature (K).

3.4. Specific volume (v)

Specific volume is a property of materials, defined as the number of cubic meters occupied by one kilogram of a particular substance. Specific volume is determined as

This is measured in (litere/kg) and ni(g) is the amount of substance for ith gas products of one kg of combustion gas.

3.5. Peak pressure (Pmax)

Using the first-order approximation, the peak pressure generated inside the cartridge is obtained by assuming instantaneous propellant burning as: m RT Pmax mp R Tf = =∑ pi i fi (V-b) (V-bi) 

where mp is mass of combustion product gases, Pmax is peak pressure, R is the universal gas constant, Ri is the gas constant of ith propellant product gases, Tfi is adiabatic flame temperature of the ith propellant, b is co-volume of the ith propellant product gases, and V is volume The value of R is 8.31343 J/mole/K At any given instance, the mp generated by the propellant burning relates to the grain geometry of the propellant and can be expressed as a polynomial with powers of λ and dimensionless length, which characterizes the geometry of the propellant defined as a web. n mp=mpo kj λi (6) j

where mpo is the initial mass of unburned propellant The above relation is also known as a form function. The coefficients kj are determined according to the propellant grain geometry. At each time frame, the combustion gases inside chamber are assumed to be in thermodynamic equilibrium with the pressure related to the equation of state for non-ideal gases.

3.6. Force constant (F)

This is one of the essential parameters of the propellant related to maximum work carried out by the propellant unit mass and is part of the utilizable energy in performing the work. The work done is expressed as product of distance covered and force. This energy is much lower than the heat from the explosion. Usually an important relationship exists between the propellant mass and maximum pressure. It is called impetus or the force constant and is denoted by F. F=

where F also equals Tf The term n, is the number of moles of a gas per unit mass and is directly proportional to the gas volume (V) at standard temperature and pressure (STP). V can be substituted for n, and Q for Tf because the two are mutually proportional. In the expression F = Power = Tf×α×Q×V(8) QV is known as the characteristic product of the propellant. The closed vessel (CV) technique is generally used to determine various parameters such as co-volume and the force constant by burning the propellant at a 0.2 g/cc loading density. Maximum pressure and burning rate can be also determined. The propellant testing in a CV is more economical compared to the actual dynamic firing, as it only requires about 200 to 300 gram of propellant versus the several kilograms. Using F, the maximum energy (E) available from the propellant is estimated as E=

3.8. Thermodynamic relations

As per the first law of thermodynamics, the state of the gas in the system can be determined as (Nag, 2018) Q= ΔU+W(10) Here Q is the energy supplied to the system and ΔU is the change in internal energy, W is the work done by the system is expressed as:

The right-hand side is the dot product of the two vectors and gives a scalar quantity. Eq. 7 can also be rewritten as:

W= Fdx(12) Using material mechanics F=P×A(13) where, F is the resultant force that is expressed as the product of average pressure P acting on the cross-sectional area A of the body. Substituting this in Eq 12, gives

W= P×A×dx(14) where dx is the length displacement which means volume can be expressed as dv = A×dx. Putting this in Eq 14, gives

W= P×dv(15) Here the gas compression is assumed to be adiabatic frictionless compression with no leakage. The combustion chamber possesses very little room for oxygen as it is filled with the propellant. The chamber is where the propellant combusts and has volume Vc which is given by Vc πd2 = (16) 4  According to the ideal gas law, the pressure P can be expressed as: mg×R×T P= (17) V  where, mg is the mass of the gas, V is the specific volume of the gas, P is the gas pressure, R is the gas constant and T is the absolute gas temperature. Putting Eq 14 into Eq 12 gives dV (18) V  which shows that the work done by the gas on the projectile is a function of temperature and gas volume.

5.1. Double-base propellant for gas generator

This study has chosen a propellant with a tubular shape, single-axial perforation without inhabitation, and neutral type burning due to this propellant being able to burn from inside to out and outside to in so that the burning surface area remains constant. The propellant used in harness purpose must be non-hygroscopic and compatible with the casing material in which it is to be loaded. Brass has been selected for the case material as it meets the obturation requirements. Based on the above requirements, a double-base propellant has been chosen consisting of nitro-glycerine (NG) and nitro-cellulose (NC) with other ingredients added to improve the properties. The percentage of the chemical contents and physical properties of the double-base propellant as used for this application are given in Table 1. The photo of the double-base propellant is given in Figure 4. Diethyl phthalate (DEP) has the role of an inert plasticizer (non-energetic). The carbamite works as a stabilizer so as to increase the shelf life of the propellant and reduce the degradation of the NC. The candela wax acts as wear reducing agent. The propellant’s chemical content in percentage dictates the total amount of thermal energy released by burning. The gas generator using the propellant has polymeric macro-molecules with oxidizer and fuel. The double-base propellant is a homogenous mixture of NG, NC and other additives. Upon ignition this propellant produces smokeless combustible products. These combustible

Table 1. Chemical content and the physical properties of double-base propellant (HEMRL, Propellant Specification 2018) Chemical contents (percentages) NC (12 % N content) NG DEP Carbamite Candela wax

NC: Nitro-cellulose; OD: Outer diameter; NG: Nitro-glycerine; DEP: Diethyl phthalate

1.57. g/cc

Figure 4. Photo of the double-base propellant. products are namely nitrogen oxides, water vapor and condensable gases. This propellant may react to provide a detonation velocity between 6-7 km/s when confined under specific circumstances. However, with proper compounding, it will undergo the deflagration phenomenon. Most of the propellant undergoes deflagration which is the main requirement for operating the harness mechanism.

6.1. Pressure-time (P-t) profile of the gas generator

The CV is cylindrical in shape where the cartridge is loaded. This is to allow various performance parameters to be evaluated in the laboratory. The experimental firing procedure consists of the CV body, a gauge adapter, the cartridge, the firing mechanism, a copper washer and the closing plug. The firing mechanism is placed at one end and the closing plug at the opposite end. A copper washer is placed on the closing plug to avoid the combustion products from leaking after the propellant is burned. A Yokogawa scope corder and charge amplifier are used to

Figure 5. Engineering schematic of the CV. CV: Closed vessel.

record pressure. A gauge adapter with pressure sensor is fitted to the vessel body. The selected pressure sensor has a small size, fast response, durability, hermetically sealed construction, sensitivity to 0.39 pC/psi, a measurement range up to 15000 psi and a rise time of ≤ 1 μs. The vessel has been designed and fabricated for realizing the performance parameters (Parate et al 2019). The CV schematic is shown in Figure 5. The striker for the firing mechanism strikes the cap and indents it. This action crushes the sensitive composition between the cap and anvil in the base of the gas generator. The flash passes through the two flash holes to ignite booster and propellant. The pressure-time (P-t) profile produced after firing the cartridge in the CV is shown in Figure 6. The peak (i.e. maximum) pressure generated in the CV is 3.84 MPa and the corresponding time is 258.43 milliseconds. The methodology is similar for evaluating the performance parameters of the cartridge in the CV (Parate et al 2021).

6.2. Energy balance equation

As the propellant burns inside the CV, its chemical energy is converted into gas energy resulting in high pressure and high temperature of the combustion products. During the burning, two assumptions are used (Parate et al 2018). •

The system is adiabatic (no heat transfer- due to the rapid burning process) where the propellant ignition takes place and

The exothermic reaction within the CV is due to the decomposition

According to the first assumption, (propellant+booster)→Gas+Energy

where dQ, dU, and dW are the heat supplied to the system, the internal energy and the work performed. As the vessel experiences no heat transfer and no deformation, dU=0. However, in real practice heat loss will always occur from the vessel to the surroundings. This can be observed from the P-t profile as shown in Figure 6. Ideally the profile should be a straight line after attaining peak pressure. However, a pressure drop occurs after reaching maximum pressure. No system exists in the universe where heat loss doesn’t occur. Heat loss can be minimized for maximum utilization of work.

23.27. g /mole

0.04542 mole/g 531.32 cal/g 1.2448 2944 K 830 cal/g 0.3488 cal/g/°C 962.75 cc 0.989 m3/kmol 1052 J/g 925 cal/g 0.3488 cal/g/°C 260 MPa