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1

Effects of the Burning Rate Index on the Pressure Time Profile of Progressive Burning Tubular Rocket Propellant Configurations

Shekhar H.

Central European Journal of Energetic Materials

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2015

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Vol. 12, no. 2

347--357

EN

A theoretical ballistic analysis of tubular rocket propellants burning in the progressive mode was carried out with the objective of ascertaining the effects of the burning rate index on the average pressure and the total burning time of the pressure time profiles. A constant ‘H’ is introduced to obtain close-form expressions for the initial pressure, the maximum pressure, the area under the pressure time profile, the total burning time and the average pressure. The derivation of the total burning time for a progressive burning tubular rocket propellant is a new approach described in this paper. It is observed that the average pressure during propellant combustion varies with the burning rate index. A higher burning rate index of the propellant leads to a lower average pressure for lower burning rate propellants (8 mm/s at 7 MPa) and a higher average pressure for higher burning rate propellants (10 mm/s at 7 MPa). A unique situation occurs for an intermediate burning rate propellant (9 mm/s at 7 MPa), where the maximum pressure was obtained theoretically for a specific value of the burning rate index (0.69).

2

The Applicability of Kamlet’s Method for the Prediction of the Velocity of Detonation (VOD) of Polyurethane (PU) Based Binary Explosive Compositions

Shekhar H.

Central European Journal of Energetic Materials

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2013

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Vol. 10, no. 2

217--223

EN

The velocity of detonation (VOD) of polyurethane (PU) based binary explosive compositions is assessed by Kamlet’s method and compared with experimental results for a few compositions. These compositions are used as booster compositions for the initiation of main charges and the velocity of detonation is determined empirically for compositions with explosives like RDX, HMX, TATB, FOX-7, CL-20. For some of the compositions, the VOD was determined experimentally and found to match the predicted values. For RDX/PU (95/5) explosive composition, the experimental and estimated VODs at 1.66g/cm3 bulk charge density, are 8211 and 8224 m/s respectively. For CL-20/PU (95/5) composition, at a charge density of 1.82 g/cm3 , the calculated VOD was 8775 m/s against the experimental value of 8943 m/s. The applicability of Kamlet’s method for the prediction of the VOD for 95/5 Explosive/PU compositions was also established. These fndings contradict an earlier hypothesis concerning the weight average estimation of Kamlet’s parameter ϕ and establish closer estimates of the VOD using the weight average assessment of the parameters ‘N’, ‘M’ and ‘Q’.

3

Viscoelastic Characterization of Different Solid Rocket Propellants Using the Maxwell Spring-Dashpot Model

Shekhar H., Kankane D. K.

Central European Journal of Energetic Materials

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2012

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Vol. 9, nr 3

189-199

EN

A single spring and a single dashpot in series was utilized to simulate the stress-strain curve for different classes of solid rocket propellants, namely extruded double base propellants (EDBP) and composite propellants (CP), in the uniaxial tensile mode in a constant rate of travel machine. The propellant behaves as a viscoelastic material and invariably exhibits stress relaxation, which cannot be simulated by elastic mechanical property parameters. In order to generate a complete stress-strain curve of a solid rocket propellant under tensile testing, different classes of solid rocket propellants were evaluated and the stress-strain curve generated was modelled using the single spring-single dashpot Maxwell fluid model. Using two constants, called the spring constant (K) and the damping factor (D), it was possible to generate a complete stress-strain curve. Mathematical formulation gives the stress (σ) - strain (ε) relation as….[wzór]. Additionally the physical nature of the spring constant resembles that of the elastic constant and the damping coefficient gives the contribution of the viscous part of the load bearing capacity of solid rocket propellants. The development of a general mathematical formulation, the calculation of constants for different classes of propellants and insight into the viscoelastic nature of propellants are the main themes of this article. For all classes of propellants, two ratios are defined. The first is a dimensionless parameter 'H', which is the ratio of the spring constant to the initial elastic modulus. The second is the ratio of the damping coefficient to the spring constant depicted by parameter 'S'. The spring constant is higher than the initial elastic modulus and the value of 'H' is always higher than 1. For brittle propellants (extruded double base propellants, EDBPs, with a high elastic modulus), the spring constant is numerically very close to the spring constant (H is around 1.75). As the ductility (percentage elongation) of the solid rocket propellants increases (from cartridge loaded composite propellants, CLCPs, to case-bonded composite propellants, CBCPs), the value of parameter 'H' also increases (H ~ 10 for CP). For EDBPs the parameter 'S' is smaller (~ 1.24), but for CLCPs and CBCPs, it is high (S ~ 5 to 8). Both of these ratios are basic properties of the polymeric matrix. The first ratio depicts the departure of the actual stress-strain curve from linearity, while the second ratio is another way of expressing the relaxation time. A higher 'H' indicates a softer and more ductile propellant, while a higher 'S' indicates a shorter relaxation time for the propellant. A lower 'S' indicates that the propellant recovers faster on removal of strain.

4

Theoretical Modelling of Shaped Charges in the Last Two Decades (1990-2010): A Review

Shekhar H.

Central European Journal of Energetic Materials

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2012

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Vol. 9, nr 2

155-185

EN

Shaped charges are used for the penetration of targets in all three dimensions of warfare - land, air and naval. With fillings of high explosives compositions inside, they generate a thin high velocity metal jet, which can perforate the targets. Shaped charges can penetrate tanks with thick armour protection, they can destroy bunkers, they can destroy aircraft and are also useful for attacking ships or submarines. Although shaped charges have a very long history since the Second World War, theoretical modelling efforts started with the steady state theory of Birkhoff in 1948. This theory was modified by the non-steady state theory known as the PER theory of shaped charges. Later, several contributions from experimental evidence were incorporated in the theoretical formulations, and the mathematical models were refined by including the virtual origin, and physical qualities of the jet breakup time, defragmentation into particulates time, the diameter of the metal jet, wave amplitude etc. To review the development of theoretical modelling of shaped charges, three stages are defined. The first is the development until 1990, when the theory of shaped charges was fully developed and penetration predictions with fairly good accuracy were possible. The second stage reviews work carried out in the last decade of the 20th century. During this period good experiments were planned, parametric study was carried out and the results incorporated in the mathematical model of shaped charges. The third stage is all work done in the 21st century (2000-2010), when the tools for advanced diagnostics, new fabrication and inspection, as well as new liner materials were incorporated. The anomalies obtained were resolved by further refinements in the developed theoretical models. The unexplored areas of the theoretical modelling of shaped charges are also enumerated in this paper.

5

Studies on Empirical Approaches for Estimation of Detonation Velocity of High Explosives

Shekhar H.

Central European Journal of Energetic Materials

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2012

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Vol. 9, nr 1

39-48

EN

Despite many computer based codes like CHEETAH, TIGER, RUBY, BKW, etc. the velocity of detonation (VOD) for explosive molecules and explosive mixtures (formulations) is estimated by several empirical formulations. This article discusses various approaches for the estimation of the velocity of detonation by empirical mathematical equations. The formulation proposed by Kamlet in 1968 is the oldest one and it is confirmed to be more reliable by many subsequent researchers. The method proposed by Rothstein (1978), Xiong (1985), Stein (1990), Keshavarz (2006) are discussed and compared for conventional explosive molecules like RDX, HMX, TNT, PETN, and HNS. The values of the velocity of detonation for these molecules are found to be very close to each other. Further comparison of empirical mathematical formulations was carried out for four other explosive molecules of relatively recent origin (CL-20, FOX-7, TATB and NTO). These molecules were selected as they were unknown at the time of the proposed formulations except that by Keshavarz (2006). For CL-20, the velocity of detonation by different methods is 9345.1 m/s (Kamlet), 9378.8 m/s (Rothstein), 9116.0 m/s (Xiong), 9383.7 m/s (Stein) and 9887.9 m/s (Keshavarz) respectively. The method proposed by Keshavarz gives a higher value of the velocity of detonation than the others. For FOX-7, the values are 8636.6 m/s (Kamlet), 8733.3 m/s (Rothstein), 8766.1 m/s (Xiong), 8645.0 m/s (Stein) and 8245.3 m/s (Keshavarz) respectively. In this case the Keshavarz approach gives a lower value of the velocity of detonation. For these molecules, the results by the Xiong method is very close to that obtained by the Kamlet method. Deviation, as well as dispersion of the calculated values by other methods, is on the high side.

6

Mathematical Formulation and Validation of Muraour's Linear Burning Rate Law for Solid Rocket Propellants

Shekhar H.

Central European Journal of Energetic Materials

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2012

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Vol. 9, nr 4

353-364

EN

Linear variation of burning rate with pressure (burning rate, r = H + Sp), referred in the literature as Muraour's law, is adopted as the burning rate law for solid rocket propellants. The two constants 'H' and 'S' are the vacuum burning rate and the slope of burning rate variation, respectively. The conventional power law of the burning rate, r = apn, is also analyzed and its practical, anomalous behaviour such as zero burning rate at zero pressure, the reduction in pressure sensitivity of the burning rate at higher pressures, the lower burning rate for the high pressure index in typical situations etc, are explained with illustrations. Like the conventional power law of burning rate, the linear burning rate law considered here is also empirical but mathematically simpler than the power law. Using burning rate and pressure data from various literature sources similar regression coefficients are observed for the conventional power law as well as for the alternative linear burning rate law. The mathematical concept for the evolution of the pressure time profile with the considered linear burning rate law is developed and validated practically with the actual firing of rocket propellants as uninhibited, tubular configurations in a ballistic evaluation motor (BEM). Close matching of the firing curve, predicted by the conventional power law and by the proposed linear burning rate law validates the mathematical formulation. The considered linear burning rate law is simple, easy to apply and gives a better representation of the burning rate behaviour of solid rocket propellants.

7

Explosive Characteristics and Shaped Charge Applications of Nitromethane (NM): A Review

Shekhar H.

Central European Journal of Energetic Materials

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2012

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Vol. 9, nr 1

87-97

EN

Nitromethane (NM or CH3NO2 ) has a wide range of applications as a detonating homogeneous liquid explosive. Although, its use as a liquid propellant is more pronounced, the determination and characterization of NM and its mixtures for their various detonation properties has gained in importance. Various researchers have performed initiation studies of NM by shock and jet, and the presence of a superdetonation zone has also been debated. The opacity or otherwise of the reaction and detonation zones has been investigated experimentally. Sensitization or dilution of NM by various additives and the effect on the detonation behavior has also been investigated. In recent times, the use of NM as a field-filled homogeneous filling in shaped charges for the disposal of unexploded ordnance has gained in importance. The experimental observations and related theoretical aspects for the use of NM as a filling for shaped charges are illustrated in this article. Overall, NM can be thought suitable as a viable future alternative for both commercial and military applications.