Visualization of turbulent combustion of TNT ... - Springer Link

Shock Waves (2000) 10: 127–136

Visualization of turbulent combustion of TNT detonation products in a steel vessel P. Wola´ nski1 , Z. Gut1 , W.A. Trzci´ nski2 , L. Szyma´ nczyk2 , J. Paszula2 1 2

Warsaw University of Technology, Nowowiejska 25, 00–665 Warsaw, Poland Military University of Technology, Kaliskiego 2, 00–908 Warsaw, Poland Received 29 August 1999 / Accepted 21 January 2000 Abstract. Mixing and afterburning of TNT detonation products in a steel vessel are recorded by the use of the Schlieren visualization system and high speed photography. The vessel is filled with air or 50% oxygen enriched air. Overpressure histories at the vessel wall are also recorded by using pressure transducers. In these experiments nitrogen, air or 50% oxygen enriched air are used as vessel fillers. The Oppenheim-Kuhl theory of thermodynamics of closed systems is applied to estimate the released energy on the basis of pressure histories. Key words: Detonation, Shock waves, Combustion

1 Introduction Effects of turbulent combustion of TNT detonation products in confined explosions have been studied recently in works of Cudzilo and Tr¸ebi´ nski et al. (1998), Cudzilo and Paszula et al. (1998), Paszula et al. (1998), and Kuhl et al. (1998). In the papers of Cudzilo and Tr¸ebi´ nski et al. (1998), Cudzilo and Paszula et al. (1998), the heat effects were measured in a calorimetric bomb of 3.6–liter volume. The bomb was filled with argon, air or oxygen at a pressure of 1 MPa. Experiments indicated the heat effects of 939 cal/g and 3611 cal/g in argon and air (or oxygen) atmosphere, respectively. Other experiments were conducted in an explosion chamber of 150–liter volume (Cudzilo and Paszula et al. 1998, Paszula et al. 1998). The chamber was filled with argon, air or oxygen enriched air at one atmosphere pressure. Measured pressure histories showed enhancements due to after-burning effects. In the work of Kuhl et al. (1998), effects of turbulent combustion induced by explosion of a 0.8 kg charge of TNT in a 17 m3 chamber filled with air were investigated. In this work, flow visualization experiments are conducted in the specially designed vessel. Charges of TNT are detonated in the vessel filled with different gases. Moreover, overpressure histories at the vessel wall are recorded. The averaged histories are the basis for estimation of the energy released during the combustion of the TNT detonation products in air or oxygen-enriched air. Correspondence to: P. Wola´ nski (e-mail: [email protected]) An abridged version of this paper was presented at the 17th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Heidelberg, Germany, from July 25 to 30, 1999.

The Oppenheim-Kuhl theory “Thermodynamics of Closed Combustion Systems” presented in the paper of Oppenheim et al. (1997) is applied.

2 Experimental Visualization of the mixing and afterburning processes was tested in the vessel shown in Fig. 1. The vessel was equipped with 30–cm optical special windows and placed in the observation section of the Schlieren system. Registration of the process was made with the use of the high speed SFR (Superfast Frequency Recording) camera. The vessel was filled with air or 50% oxygen enriched air (oxygen/nitrogen 50/50 in volume) under a pressure 0.1 MPa. Charges of 0.5 and 1 g TNT were used in experiments. Density of the charges varied in the range 1.55–1.58 g/cm3 . Special igniters were used to initiate the detonation of TNT charges. They were made of 0.25 g mass of PETN and 0.02 g of lead azide. Initially, the charge with igniter was placed in the vessel’s center. Such explosions, however, damaged significantly the inner surface of the optical windows. Moreover, the quality of the Schlieren pictures obtained was unsatisfactory. The succeeding experiments were conducted with charges located inside the special cell attached to the top part of the vessel. The Schlieren pictures of the igniter explosion in air are shown in Fig. 2. The igniter of a cylindrical shape was hung vertically in the centre of the vessel. Only on the first frame self illumination of igniter is observed, then Schlieren pictures of the explosion products are visible. Two clouds of explosion products can be distinguished in the pictures. One of them, probably from the explosion

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P. Wola´ nski et al.: Visualization of turbulent combustion of TNT detonation products

Fig. 1. Picture a and schematic diagram b of the explosion vessel

of lead azide, is expanding in the radial direction of the igniter, the second one is propagating mainly in the axial direction. Shock wave is visible in front of the latest one. This means that the cylindrical charge of PETN detonates in the axial direction. Turbulent flow of the explosion products is observed in the last pictures. The succeeding experiments were made for the charges of TNT located in the central part of the cell. Schlieren pictures of expansion of TNT detonation products in the vessel are shown in Figs. 3–4 for air and in Figs. 5–6 for oxygen enriched air. After detonation of the charge, an intensive shock wave is generated in the gas filling the cell in all directions. In the first stage of expansion, the shock wave and the boundary of the detonation products propagating to the bottom of the vessel are visible. Initial strong shock wave is soon followed by another shock wave. This wave is generated by the reflection of the initial wave from the upper wall of the cell. The second wave is accelerated due to the afterburn of the detonation products and additional heat release. It eventually merges with the front shock. Since not all carbon produced during explosion is burned during the initial stage of expansion, big part of created cloud is not transparent to the flash light illumination. Due to this fact, the observation of the cloud’s structure is impossible during further stages of the expansion. Instabilities formed at the contact boundary between the detonation products and air are visible on the pictures. These instabilities result in mixing of hot detonation products with air and the combustion process of the mixture is possible. From comparison of the pictures presented in Figs. 3–6 it follows that the image of the initial stage of expansion of the detonation products is similar for 0.5 and 1 g of TNT detonated in air or oxygen enriched air. However, more instabilities and more detailed structure of the turbulent flow are clearly visible in the vessel filled with oxygen enriched air. This means that greater amount of carbon particles are burned during the first stage of detonation products expansion. Final effect of afterburning of TNT detonation products in air or oxygen enriched air can be estimated on the basis of pressure histories at the vessel wall.

To measure overpressure histories of the afterburning process, the windows in the vessel were replaced by metal plates. A pressure transducer (Kistler 601A) was mounted in the middle of the plate. The vessel was filled with nitrogen, air or 50% oxygen enriched air under a pressure 0.1 MPa. The charge of 1 g TNT with an igniter was placed in the centre of the cell. The igniter was made from 0.15 g PETN, 0.15 g RDX and 0.02 g of lead azide. The signal of overpressure from the gauge was recorded by a digital storage scope DS–8621 (Iwatsu Electric Co., Ltd.). The records were made at 0.1 V/div. and 500 µs/div. Selected overpressure records from the vessel are presented in Fig. 7 (dotted lines). The time-axis on the figures starts from different values, because the storage scope recorded signals during some period of time before the first reverberation of the shock wave at the vessel wall. The overpressure records have the oscillating nature due to the gasdynamical processes (acceleration, reflection and reverberation of shock waves) occurring in the vessel. The amplitudes of oscillations decrease with increasing the time of recording. Using the experimental records the mean overpressure histories were obtained by the method described by Neuwald et al. (1997). The averaged overpressure was obtained by the following equation Z τ 1 t+ 2 ∆paver (t) = ∆p(t)dt . (2.1) τ t− τ2 Chosen value of τ (τ = 2 ms) was about two times longer than the time-duration of a main single peak of overpressure recorded in the vessel. The results are presented in Fig. 7 and summarized in Fig. 8. From analysis of the averaged pressure histories from Figs. 7 and 8 it follows that, initially, gasdynamical processes proceeding in the gaseous medium influence strongly the average pressure at the vessel wall. After the first reverberations of shock waves at the vessel wall, the decrease of mean value of overpressure is caused mainly by the heat losses to the wall. Thus, the mean overpressure was determined for the time when the influence of the gasdynamical processes could be negligible. It was assumed that the first dynamical stage of shock wave reverberations at the wall lasted about 5 ms. After that period of time, the time-dependence of the mean overpressure can be approximated by the following function ∆pmean (t) = ∆p0 e−a(t−t0 )

(2.2)

where t0 is the time of the first reflection of the shock wave at the vessel wall, ∆p0 and a are constants. To determine those constants, the averaged overpressures for all shots (3 or 4) for given type of gas filling the vessel were used. The approximating lines (without symbols) are presented in Fig. 8. The calculated values of ∆p0 and a are presented in Table 1. In case of nitrogen filler, the parameter a can be associated with the heat transfer to the vessel wall. For air or oxygen enriched air in the vessel, the parameter a depends on not only heat losses but the heat released due to combustion of the TNT products as well. The parameter


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Fig. 2. The high speed Schlieren pictures of the igniter explosion in air. Time interval between pictures – 32 µs

∆p0 can be treated as a mean value of overpressure at the wall of the vessel isolated adiabatically from surroundings. Its value is used to estimate the energy released during combustion of the detonation products in air or oxygen enriched air. The initial pressure, pi , for post-explosion combustion of TNT charge and igniter is assumed to be equal the mean pressure in the vessel filled with nitrogen (pi = (∆p0 )nitrogen + 0.1 MPa = 0.124 MPa). The final pressure, pf , for the combustion process in air or oxygen enriched air is equal 0.160 and 0.165 MPa, respectively.

3 Calculations The detonation wave in the RDX/PETN igniter and TNT charge transforms the solid explosive into gaseous detonation products, rich in carbon, carbon monoxide and hydrogen. The products of detonation can serve as a fuel, which will react when mixed with oxygen from air. As a result, the exothermic process of combustion leads to

Table 1. Calculated parameters for relation ∆pmean (t) = ∆p0 e−a(t−t0 ) Type of gas in the vessel

∆ p0 [MPa]

a · 103 [1/s]

nitrogen air oxygen enriched air

0.024 0.060 0.065

12.9 0.6 0.4

consumption the fuel and generation of combustion products. Turbulent mixing takes place in closed vessel during the expansion and consecutive compression of detonation products. Blast waves propagating in the gaseous medium strongly influence the pressure at the vessel wall (see Fig. 7). But after some period of time, the average pressure at the wall is almost constant. Its value is connected with the heat releasing during the detonation process and the exothermic process of combustion. To estimate the fuel consumption and total amount of the heat

130


Fig. 3. The high speed Schlieren pictures of the 0.5 g of the TNT explosion in air. Time interval between pictures – 32 µs; delay to the first picture – 160 µs

Fig. 4. The high speed Schlieren pictures of the 1.0 g of the TNT explosion in air. Time interval between pictures – 32 µs; delay to the first picture – 125 µs


131

Fig. 5. The high speed Schlieren pictures of the 0.5 g of the TNT explosion in the 50% oxygen enriched air. Time interval between pictures – 32 µs; delay to the first picture – 100 µs

Fig. 6. The high speed Schlieren pictures of the 1.0 g of the TNT explosion in the 50% oxygen enriched air. Time interval between pictures – 32 µs ; delay to the first picture – 107 µs

132


Fig. 8. Summary of averaged overpressures for 1 g TNT and approximating lines Fig. 7. Variation of the overpressure (dotted lines) at the vessel wall after detonation of 1 g of TNT and averaged overpressure (solid lines)

released in the vessel the Oppenheim-Kuhl (Oppenheim et al. 1997) theory of thermostatics of closed combustion systems is applied. 3.1 Formulation

ered as spatially uniform, so that pk = p .

(3.2)

The balances of mass, volume and energy are expressed, respectively, as (3.3) mR + mP = mS vR mR + vP mP = vS mS

(3.4)

uR mR + uP mP = uS mS

(3.5)

where mk is the mass of component or system.

In the method, the internal energy, uk , is assumed as the thermodynamic function, while k = Φ, Ω, R, P, and S, referring, respectively, to fuel (detonation products), oxidizer (air), reactants (detonation products and air being in proportion like in the vessel), products of combustion and system. Fuel mass fraction in reactants is F = 1/(1 + λ), where λ denotes the oxidizer/fuel ratio in the vessel. Instead of the temperature, adopted here as the principal thermodynamic reference co-ordinate is wk ≡ pk vk

(3.1)

where p and v denote the thermodynamic pressure and specific volume. The thermodynamic pressure is consid-

3.2 Initial state Thermodynamic properties of the TNT/RDX/PETN detonation products and air under the initial pressure, pi , are evaluated by the following manner. First, the “mechanical detonation energy” at volume v, Ed (v), is calculated. It represents the amount of energy transferring into mechanical work during adiabatic expansion of the detonation products from Chapman-Jouguet state to volume v. This energy is defined by the relation (Fickett and Davis 1979 ) Z v u2CJ p dv (3.6) + Ed (v) = − 2 vCJ

P. Wola´ nski et al.: Visualization of turbulent combustion of TNT detonation products Table 2. Composition of detonation products frozen at 1800 K Species

Fractions [mole/kg]

H2 O N2 CO CO2 CH4 H2 Cs

7.668 7.339 9.736 5.199 1.137 1.431 11.000

∆hΩ = hΩ (vΩi − hΩ (vΩ,isoch )

Table 3. Initial parameters of air and detonation products

Air

Detonation products

where u denotes mass velocity, symbol CJ means that parameters are evaluated at the Chapman-Jouguet point. The detonation energy transfers into the kinetic and internal energies of air and kinetic energy of detonation products. According to the Oppenheim theory (Oppenheim and Maxson 1991), the kinetic processes in a closed system are neglected. Thus, the detonation energy must be distributed between the internal energies of the detonation products and air. To determine these energies, the following procedure is applied. It is assumed that the detonation products expand along the CJ isentrope and, simultaneously, air is compressed adiabatically. Reactions in the detonation products are frozen at 1800 K (Souers and Kury 1993). For calculation of the explosive system tested, TNT charge and igniter are replaced by the mixture of 1 g TNT, 0.15 g PETN, and 0.15 g RDX. Frozen composition of the detonation products for this mixture is presented in Table 2. We assume that the expansion process ends when pressure in the detonation products and air is just the same. It take place at p = 0.10175 MPa. The calculated detonation energy (Ed ) of 1126 cal/g corresponds to this pressure. The increase of the internal energy of air during the adiabatic compression, ∆ uadiab , is 24 calories per gram of explosive. All thermochemical calculations in this work are performed by the use of the CHEETAH code (Fried 1996). In the next step, an isochoric process is assumed for the detonation products and air. Spatially uniform pressure increases to p = pi . This process can be connected with transformation of the kinetic energy into the internal energy of gases. The increase of the internal energy of air and detonation products during the izochoric process, ∆uisoch , is 1056 calories per gram of explosive. From comparison of a sum of ∆uadiab and ∆uisoch with Ed , it follows that almost whole mechanical detonation energy is consumed. But at the end of the isochoric process, the volume of the detonation products and air is different from the vessel’s volume. Thus, in final step, the states of the gases are assumed to change under the constant pressure, pi . In this process, the increase of enthalpy for the detonation products and air can be written in the following manner (3.7) ∆hΦ = hΦ (vΦi − hΦ (vΦ,isoch ) (3.8)

where isoch denotes the states of the detonation products and air after the end of the isochoric process. The balance

133

mΩi vΩi hΩi uΩi TΩi γΩ

126 g 834 cm3 /g 15.75 cal/g −9.29 cal/g 363 K 1.40

mΦi vΦi hΦi uΦi TΦi γΦ

1.3 g 1462 cm3 /g −1097 cal/g −1141 cal/g 677 K 1.24

Fig. 9. Diagram of energy balance in vessel at the initial state

of the energy in the vessel for the constant pressure process can be written in the following way mΩi ∆hΩ +mΦi ∆hΦ = mΦi (Ed −∆uadiab −∆uisoch ) (3.9) where mΦi and mΩi are masses of an explosive charge and air, respectively. The volume of gases is restricted by the vessel volume, Vc . Thus, mΦi vΦi + mΩi vΩi = Vc .

(3.10)

Equations (3.9) and (3.10) can be solved graphically (Fig. 9). In this way, the initial conditions for fuel (detonation products) and oxidizer (air) are obtained. They are presented in Table 3. Symbols T and γ denote the temperature and adiabatic exponent, respectively. 3.3 Le Chatelier diagram The thermodynamic properties of the components (Ω, Φ, P, R) are expressed in terms of the Le Chatelier diagram

134


from the initial point on line R at the initial enthalpy and pressure and at the initial energy and volume, respectively. 3.4 Solution The mass, volume and energy balances (3.3 ÷ 3.5) can be rewritten in the non-dimensional form

Fig. 10. Le Chatelier diagram for confined combustion of explosion products in air

(Oppenheim and Maxson 1991) - a plot of the loci of their states on the plane of internal energy, u, as a function of the parameter w. As it is shown in work of Kuhl et al. (1998), loci of states of the components are, within the regimes of their applicability, practically linear, and they can be expressed by straight lines. All the co-ordinates are normalised with respect to the initial state of air. Thus, the normalised pressure and specific volume are P ≡ p/pi and V ≡ v/vΩi , while the thermodynamic reference parameters and internal energies are expressed as wk wΩi

(3.11)

uk − u0 = −Qk + Ck Wk wΩi

(3.12)

Wk ≡ Uk ≡

where u0 denotes the value of uΩ for wΩ = 0. Symbols Ck and Qk are the coefficients of linear functions. Linearized version of the Le-Chatelier diagram for the system investigated is presented in Fig. 10. Lines Φ and Ω are obtained by assuming, that the detonation products and air are compressed adiabatically from their initial states (Table 3). Line R is calculated from relation (3.13) ωR = F ωΦ + (1 − F )ωΩ where ω denotes W or U . It represents states of reactants. Line P is obtained from calculations of equilibrium states of the products of reaction of the explosive and air in the vessel volume. Calculated values of Ck , Qk are given in Fig. 10. A change of state taking place in the course of the combustion process of the detonation products corresponds to a jump from point on line R to one of line P. Points hp and vp on line P represents the states of equilibrium attained

YΦ + YΩ + YP = 1

(3.14)

YΦ WΦ + YΩ WΩ + YP WP = WS

(3.15)

YΦ UΦ + YΩ UΩ + YP UP = US

(3.16)

where Yk = mk /mS represents mass fractions of components. The mass fraction of products YP is adopted as a progress parameter and it is written as Y . Then YΦ = F (1 − Y ) and YΩ = (1 − F )(1 − Y ). For the combustion process in an adiabatic enclosure we have US = USi = F UΦi + (1 − F )UΩi . Taking into account the linear relations (3.12), the balance equations can be solved for the products fraction Y=

−1+kP WS +WΩ (1−kP ) ΩP +WΩ (1−kP )+F [WΦ (kΦ −kP )+WΩ (kP −1)−ΩΦ ] +

F [1 − WΩ + kΦ (WΦ −WΦi )−kP (WΦ −WΩ )] ΩP +WΩ (1−kP )+F [WΦ (kΦ −kP )+WΩ (kP −1)−ΩΦ ] (3.17)

where kΦ = CΦ /CΩ , kP = CP /CΩ , ΩP = QP /CΩ , ΩΦ = QΦ /CΩ . The reference parameters for the reactants are expressed in terms of P by virtue of an adiabatic relation 1− 1 (3.18) Wk = Wki P γk where k = Ω, Φ. Values of γk are given in Table 3. For the system isolated adiabatically, the following relation is true WS = WSi P ; (3.19) where WSi = F WΦi + (1 − F ). Calculations start at points i on the Le Chatelier diagram (Fig. 10). From Eqs. (3.17–3.18), the fraction of combustion products, Y , for following states of the combustion process is obtained as a functions of P . Chosen states calculated for Φ, Ω, R, P, and S are shown on the lines in Fig. 10 as small points. Calculations are continued until Y = 1 and final points (f) are achieved. Calculated thermodynamic parameters of components are also shown in Fig. 11 as functions of P . The maximal value of P (Pmax = 1.33) corresponds to full combustion of the detonation products. At the end, the heat released in the vessel, Q, can be obtained from the relation Q = Ed + Y (Qcomb − Ed ), where Qcomb = 3192 cal/g is the heat of combustion of the TNT/PENT/RDX charge. Diagrams of the heat release, Q, and the additional heat of combustion, ∆Q = Y (Qcomb − Ed ), against pressure P are presented in Fig. 11.


135

Fig. 11. Profiles of thermodynamic parameters with respect to dimensionless pressure

From experiments it follows that the mean pressures after the explosion of the TNT/PETN/RDX charges in the vessel filled with nitrogen and air are 0.124 and 0.160 MPa, respectively. Therefore, the ratio of the final to initial pressure for the combustion of the detonation products in air is 1.29. By comparing this estimation with the values of dimensionless pressure on Fig. 11, we can say that the detonation products are not completely consumed (Yf,air = 0.87) and additional energy, ∆Q, of about 1800 cal/g is released during the combustion process in air atmosphere. However, from experiments it results, that the ratio of pressures in the vessel filled with oxygen enriched air and filled with nitrogen is about 1.33. This value corresponds to the maximal value of P . This means, that the detonation products are fully burned in the vessel filled with oxygen enriched air and additional energy of about 2070 cal/g is liberated.

4 Summary Visualization of mixing and afterburning of the detonation products of condensed explosive in a 107–liter steel vessel filled with gases containing oxygen has been conducted in this work. Charges of 0.5 and 1 g TNT were detonated in the vessel by the use of special igniters. Air or 50% oxygen enriched air are vessel fillers. A Schlieren system and a high speed SFR camera are applied to record the process of mixing of detonation products with a gas filling the vessel. Instabilities formed at the contact boundary between the detonation products and air are visible on the pictures obtained. These instabilities result in mixing of hot detonation products with air and the combustion process of the mixture takes place. The images of the initial stage of expansion of the detonation products are similar for 0.5 and 1 g of TNT detonated in air or oxygen enriched air. More instabilities and more detailed structure of the turbulent flow are clearly visible in the vessel filled with oxygen enriched air. In this case, greater amount of carbon

particles are burned during the first stage of expansion of the detonation products. To determine the final effect of afterburning of TNT detonation products in air or oxygen enriched air, overpressure at the vessel wall is measured by using a pressure transducer. Moreover, similar measurement is conducted for the vessel filled with nitrogen. It is found, that the mean overpressures increase about 2.5 and 2.7 times for air and oxygen enriched air, respectively, as compared with nitrogen atmosphere. The overpressure histories are averaged and used to estimate the fuel consumption and total amount of the heat released in the vessel by applying the Oppenheim-Kuhl theory of thermostatics of closed combustion systems. It is inferred that the detonation products are not fully consumed and additional energy of about 1800 cal/g is liberated during the combustion process in air filler. However, the detonation products are fully burned in the vessel filled with oxygen enriched air releasing additional energy of about 2070 cal/g.

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