Calculating the Quasi-static Pressures of Confined Explosions Considering Chemical Reactions under the Constant Entropy Assumption

Transcription

1 Appled Mechancs and Materals Onlne: ISS: , ol. 64, pp do:0.4028/ 202 Trans Tech Publcatons, Swtzerland Calculatng the Quas-statc Pressures of Confned Explosons Consderng Chemcal Reactons under the Constant Entropy Assumpton We Zhong,a, Zhou Tan,b orthwest Insttute of uclear Technology, X an, Chna a lengshu222@63.com, b tanzh2003@63.com Keywords: confned explosons; chemcal reactons; constant entropy assumpton; quas-statc pressures; explosve charge volume rato Abstract. On the bass of the energy conservaton and the state equaton of the deal gas, a formula of quas-statc pressures of the confned explosons calculatng was derved under the constant entropy assumpton of the detonaton products expanson and the constant volume assumpton of the chemcal reactons. Takng the TT explosve as an example, the quas-statc pressures of the confned exploson ether consderng the nfluence of the chemcal reactons or not were calculated and the quas-statc pressures of the confned space were obtaned. Introducton The so called "confned exploson" s exploson that happens under constraned condtons, such as explosons happen n the sealed blast chambers or the underground closed blast chambers. The envronment of hgh-temperature and hgh-pressure produced by confned explosons, would result n chemcal reactons between the detonaton products and oxygen of the confned space and change the energy dstrbuton. Ornellas, a scentst at Lawrence Lvermore atonal Laboratory n the USA, was the frst person to research ths problem. Ornellas [] measured the amount of energy respectvely for 25g TT explosves explodng ether n a 5.3L sphercal chamber flled wth oxygen or n a 5.3L vacuum sphercal chamber. The measurement showed that the amount of energy n the chamber flled wth oxygen was bgger than the amount of energy n the vacuum chamber. Ths result ndcated that the chemcal reactons of the detonaton products were very mportant to the total energy of the whole system. A.L. Kuhl et al [2~4] carred on ths work, and they had made systemc research about the confned explosons wth chemcal reactons of the detonaton products. A.L. Kuhl et al consdered that the detonaton products of the confned explosons contaned hgh amounts of carbon (C) and carbon monoxde (CO). As vast amounts of oxygen was contaned n the hgh-temperature and hgh-pressure confned space after explosons, there were chemcal reactons of the carbon and carbon monoxde wth oxygen whch resulted n a marked ncrease n quas-statc pressures of the confned systems. In ths paper, based on the constant entropy assumpton of the detonaton products expanson and the constant volume assumpton of the chemcal reactons, a theoretcal analyss of the confned explosons quas-statc pressures takng consderaton of the chemcal reactons was presented and a formula of the quas-statc pressures was derved. At last we valdate the correctness of the formula by carryng out the expermental research of TT. Formula Dervaton of Calculatng the Quas-statc Pressures The Influence of Explosons on the Quas-statc Pressures On the basc assumpton of the detonaton products expanson wth constant entropy, for the nstantaneous exploson, the state equaton was gven as follows [5]: γ p= Av + f ( v) T All rghts reserved. o part of contents of ths paper may be reproduced or transmtted n any form or by any means wthout the wrtten permsson of Trans Tech Publcatons, (ID: , Pennsylvana State Unversty, Unversty Park, USA-/05/6,04:52:30)

2 Appled Mechancs and Materals ol As the charge denstyρ 0 usually greater than g/cm 3 for common explosves, the nfluence of the pressure caused by the molecular moton of the detonaton products was neglgble. Therefore, we got a smplfed state equaton: γ γ p= Av = Aρ () Where A andγ were constants determned by the physcal characterstcs of explosves. Assumng the detonaton products expanson to be an sentropc process, thenγ could be seen as local sentropc ndex, whch changed durng the detonaton products expanson. Descrbng the state of the expanson at the start by equaton (): p = A v = A ρ (2) γ γ Takng ar as part of the detonaton products, the sentropc expanson formula of the deal gas was: γ γ fnal state fnal state ρfnal state p = A v = A (3) Where A and γ were constants relatng to the assumed expanson. From equaton (2) and equaton (3), we had: γ Aρfnal state pfnal state = p γ A ρ Consderng As and A were both constants, and γ, γ both took on the character of sentropc adabatc ndex, we could reduce above equaton to equaton (4): ρfnal state pfnal state = ( ) γ p (4) ρ Where γ was a constant whch should be determned by experence or experments. pressure calculated from JWL sentropc equaton, andρ The Influence of Chemcal Reactons on the Quas-statc Pressures p was the correspondng densty. Assumng the gas n the confned space was deal gas, the state equaton of the deal gas was [6]: pchemcal = nrt (5) Where p chemcal was the quas-statc pressure caused by the chemcal reactons of the detonaton products, was the volume of the confned space, n was the detonaton product amount of substance, T was the thermodynamcal temperature, and R was the gas constant whose value was 8.34 J mol - K -. Accordng to thermodynamcs [7]: C p C = nr (6) C p, m / C, m = k Where C was the specfc heat capacty at constant pressure, C was the specfc heat capacty p at constant volume, C p,m, C,m were the values of C p and C for mol deal gas, and k was the specfc heat rato. Assumng the chemcal reactons of the detonaton products happened n a constant volume, takng the chemcal reacton of ( =, 2,, ) as an example, from equaton (5) and equaton (6), we obtaned: n RT C T ( pchemcal ) = = ( k ) (7) was

3 398 Appled Mechancs, Materals, Industry and Manufacturng Engneerng Accordng to thermodynamcs [7], makngu the nternal energy of the system: (d U ) = C dt (8) Then, U U = C T C T 0 0 Accordng to thermodynamcs, when the absolute zero of temperature [7]: U = C T = And here: Q = U = C T (9) WhereQ was the heat released by chemcal reacton of ( =, 2,, ). ReplacngC T of equaton (7) by equaton (9), we got: Q ( pchemcal ) = ( k ) Consderng all chemcal reactons: Q pchemcal = ( p ) = [( k ) ] Formula of Calculatng the Quas-statc Pressures (0) chemcal = = It was easy to get the formula of calculatng the quas-statc pressures of the confned explosons by equaton (4) and equaton (0): n ρ γ P= P ( ) + ( k ) Q ρ = In ths paper, we got contnuous values of sentropc adabatc ndexγ and specfc heat rato k by Langrange nterpolaton usng some expermental data. Example The exploson equaton of TT was: C 7 H 5 O 6 3 =2.5H 2 O+3.5CO+3.5C+.5 2 () The exploson happened n a sealed chamber whch was flled wth ar (O 2 ~2%, 2 ~78%, oble Gases ~0.96%, CO2~0.03%, H 2 O and other~0.03%), and the probable reactons for dfferent explosve charge volume ratos were shown n Table. Table Reactons after the confned exploson explosve charge volume rato Q/ (kg/m 3 ) the probable reactons [0,0.373) C+O 2 CO 2, CO+0.5O 2 CO 2 [0.377,0.4874) C+O 2 CO 2, CO+0.5O 2 CO 2, CO+H 2 O CO 2 +H 2 [0.4874,0.5570) C+O 2 CO 2, CO+0.5O 2 CO 2, CO+H 2 O CO 2 +H 2 [0.5570,.40) C+0.5O 2 CO, CO+0.5O 2 CO 2, CO+H 2 O CO 2 +H 2 [.40,3.899) C+0.5O 2 CO 2, C+H 2 O CO+H 2, CO+H 2 O CO 2 +H 2 [3.899,+ ) C+0.5O 2 CO 2, C+H 2 O CO+H 2, C+2H 2 CH 4

4 Appled Mechancs and Materals ol The expresson of the specfc heat rato k was [5]: 2 n ( C p,m) n ( a+ bt + ct + ) 2 = = T 2 c n ( C,m) n ( a + bt + ct + ) R n 2 = = T = k = = Where was the number of the components, n was the amount of substance of component. As equaton (2) was complex, values ofγ and k were obtaned by Langrange nterpolaton n ths paper, whose results were shown n Fg.. c (2) Fg. Plot of γ or k wth explosve charge volume rato Q/ Accordng to the method provded n ths paper, the quas-statc pressures of confned exploson of TT were obtaned, and the plots of quas-statc pressures p wth explosve charge volume rato Q/ for consderng chemcal reactons and not consderng chemcal reactons compared wth the expermental data were shown n Fg. 2. Fg.2 Plot of quas-statc pressures p wth explosve charge volume rato Q/ Fg. 2 ndcated that the calculatng results consderng the chemcal reactons agreed well wth the expermental data, but the results not consderng the chemcal reactons were very dfferent from the expermental data. Conclusons In ths paper, a formula of calculatng the quas-statc pressures of confned explosons consderng the chemcal reactons of the detonaton products was proposed. Takng the exploson n a sealed chamber of TT as an example, ths formula was proved to be correct. By comparng the calculatng results of quas-statc pressures consderng the chemcal reactons and not consderng the chemcal reactons wth expermental data, we confrmed that the chemcal reactons of the detonaton products had evdent effects for the quas-statc pressures.

5 400 Appled Mechancs, Materals, Industry and Manufacturng Engneerng References [] D.L. Ornellas: Techncal Report UCRL-5282, Lawrence Lvermore atonal Laboratory, CA [2] A.L. Kuhl and H. Rechenbach: Proceedngs of the Combuston Insttute. ol.32 (2009), p [3] A.L. Kuhl, J.W. Forbes and J.B. Chandler: 34 th Int. Annual Conf. of ICT [4] A.L. Kuhl and B. Khasanov: 38th Int. Annual Conf. of ICT [5] B.P. Zhang, Q.M. Zhang and F.L. Huang: Detonaton physcs(weapon Industry Press, Bejng.2000). [6] S.H. Zhang: College Physcs Book Two-Thermal Physcs (Tsnghua Unversty Press, Bejng.2002). [7] Y.J. Yn, Z.K. X and S.Y. Zhang: The concse Course of Physcal Chemstry (4 th Edton) (Hgher Educaton Press, Bejng.2009).

6 Appled Mechancs, Materals, Industry and Manufacturng Engneerng / Calculatng the Quas-Statc Pressures of Confned Explosons Consderng Chemcal Reactons under the Constant Entropy Assumpton / DOI References [2] A.L. Kuhl and H. Rechenbach: Proceedngs of the Combuston Insttute. ol. 32 (2009), pp /j.proc [6] S.H. Zhang: College Physcs Book Two-Thermal Physcs (Tsnghua Unversty Press, Bejng. 2002) /ls