1 / 28

IMPACT OF MULTILAYERED EXPLOSIVE CHARGE ON A RIGID WALL

EPNM -2010. IMPACT OF MULTILAYERED EXPLOSIVE CHARGE ON A RIGID WALL. A.A. Shtertser Design & Technology Branch of Lavrentyev Institute of Hydrodynamics SB RAS Tereshkovoi Str., 29, Novosibirsk, 630090 , Russia asterzer@mail.ru. Problem Statement. EPNM -2010.

lenore
Download Presentation

IMPACT OF MULTILAYERED EXPLOSIVE CHARGE ON A RIGID WALL

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. EPNM -2010 IMPACT OF MULTILAYERED EXPLOSIVE CHARGE ON A RIGID WALL A.A. Shtertser Design & Technology Branch of Lavrentyev Institute of Hydrodynamics SB RAS Tereshkovoi Str., 29, Novosibirsk, 630090, Russia asterzer@mail.ru

  2. Problem Statement EPNM -2010 HE are used in experimental investigation of high pressure effect on substance properties, in explosive working of materials (explosive welding, hardening, forming and so on) and in explosive cutting and demolition. As a rule HE charge is positioned in contact with any material or structure. At explosion high impulsive pressure is generated in treated material as high as tens and hundreds of kbar. It is often needed to estimate (even approximately) a pressure profile and total pressure impulse effecting the structure. This problem becomes more complicated if multilayered charge is used consisting of several layers of different HE. Generally speaking, this problem can be solved by numerical calculations with the use of computer. Nevertheless, use of physical models with simple and convenient formulas can give us fundamental understanding of processes running at explosive loading, In this presentation we offer the approach and formulas for estimation of pressure and impulse. This approach is based on known solutions taken from physics of explosion, on results of numerical calculations, and on certain physical considerations.

  3. Problem Statement EPNM -2010 The engineering formulas should be derived to estimate pressure and pulse (impact momentum) effecting the rigid wall at detonation of one- and multi-layered HE charge in one-dimension and two-dimension (plane) geometry. Rigid wall simulates any structural design which is subjected to HE impact. Compressibility of wall material can be considered additionally,and corrections to results of calculations can be made if it’s needed. Explosive is characterized by density е, detonation velocity DH, and adiabatic exponent  of detonation products. Pressure at the Chapman-Jouguet plane is considered to be as detonation pressure PH = eDH2/(+1), where  = 2.8, 2.5, and 2.2 for RDX, amatol, and amatol/ammonium nitrate-1/1 mixture correspondingly.

  4. 4 2 3 3 2 4 1 1 EPNM -2010 One-Dimensional Expansion of Detonation ProductsSingle-Layer Explosive Charge There are two possible variants depending on ignition place b- ignition at the wall a- ignition at the open side of HE charge Explosive charge on the wall: a- DW falls normally on the wall; b- DW moves off the wall. 1- wall, 2- explosive, 3- front of DW, 4- detonation products. Arrays show the direction of DW propagation. Lateral dimension of HE charge and wall are considered to be sufficiently large therefore side flow of detonation products is not taken into account

  5. 3 3 3 64 τ τ τ (1) P = PH ≈ 2,37 PH = P0 27 t t t 8 J = me DH ≈ 0,296 me DH (2) 27 DW falls normally on the wall EPNM -2010 Pressure profile for = 3 is described by expression:  = е / DH P(t) Pressure impulse derived by integration (γ = 3): P0 8 times pressure drop τ 2τ t Pressure profile. Reference time is the moment of ignition. Physics of Explosion / edited by K.P. Stanyukovich, 2 edition, Moscow: Nauka, 1975

  6. DW falls normally on the wall EPNM -2010 For arbitrary γinitial (peak) pressure on the wall P0 can be calculated using the expression*: P0 5γ + 1 + (17γ2 + 2γ + 1)1/2 (3) = PH 4γ P0/PH ratio depends weakly on adiabatic exponent . It changes from 2.6 to 2.3 as  changes from 1 to . For example P0 / PH= 2.40, 2.41 and 2.43 for 2.8 (RDX), 2.5 (amatol) and 2.2 (amatol/ammonium nitrate-1/1 mixture) correspondingly. Rounding to one decimal place, we get that peak pressure can estimated for any by formula: (4) P0 = 2.4 PH *Landau L.D., Lifshitz E.M. Hydrodynamics. 4 edition, Moscow: Nauka, 1988

  7. 2γ/(γ-1) γ +1 (5) P0 = PH 2γ (6) P0 = 0,3PH DW moves off the wall EPNM -2010 Gaseous detonation products at the wall have zero velocity. For strong DW sound velocity at the wall is c = DH / 2for any. From this it follows that Calculations with the use of this formula give P0 /PH = 0.296, 0.299, 0.305, 0.311 for =3; 2.8 (RDX); 2.5 (amatol); 2,2 (А/AN-1/1) correspondingly. Rounding to one decimal place, we get that initial pressure can be estimated for any HEusing the formula: Landau L.D., Lifshitz E.M. Hydrodynamics. 4 edition, Moscow: Nauka, 1988

  8. P(t) P0 τ = 3δe/DH t DW moves off the wall EPNM -2010 The time point t = 3δe/DH is the sum of DW run time from the wall to the HE charge open end and ofrarefaction wave run time from the charge open end to the wall. During this time pressure is constant and equal to P0 . At t = 3δe/DH pressure drop begins. Pressure profile. Reference time is the moment of ignition.

  9. Gurney Energy EPNM -2010 To derive formula for pressure impulse effecting the wall we make use of R. W. Gurney approach which was developed in 1943-47 for estimation of grenade and shell debris velocities. This approach was later successfully used for calculation of velocities of plates accelerated by explosive layers1, 2. Consider that all chemical energy (heat of explosion) is transformed into kinetic energy of detonation products which move off the wall. This energy per mass unit is calculated using the expression1,2: DH2 (7) E = Q = 2(γ2 – 1) E is referred to as Gurney energy. Here it is equal to heat of explosion Q 1) Deribas A.A. Physics of explosive hardening and welding.Novosibirsk:Nauka, 1980. 2) De Carli P.S., Meyers M.A. Design of Uniaxial Strain Shock Recovery Experiments // Proceed. Int. Conf. "Shock Waves and High-Strain-Rate Phenomena in Metals", Albuquerque, NM, 1980. New York: Plenum Press, 1980. P.341-373, 1033-1039 (Appendix A).

  10. δe dx ρe δe us2 ∫ ρe u2 2 (8) W = = 6 Pressure Impulse EPNM -2010 Consider that mass velocity of gaseous detonation products (DP) changes linearly along the charge thickness еand DP density is everywhere equal to initial HE density e.Then DP kinetic energy is 0 Here us is DP velocity at HE charge free surface. From (7) and (8) we have 1/2 3 us = (6E)1/2 = DH (9) γ2 - 1

  11. Pressure Impulse EPNM -2010 As long as DP velocity distribution is linear, then average u value equals to us/2. Therefore total impulse effecting the wall is me us k(γ) me DH (10) J = = 2 where coefficient k(γ) is defined as 1/2 3 k(γ) = (11) 4(γ2 – 1) For γ = 3 difference of J values calculated by formulas (2) and (10) is 3.4%. This confirms that Gurney approach is quite relevant.

  12. Comparison with numerical calculations EPNM -2010 To verify additionally usefulness of formulas (10, 11) for any γYu. P. Mesheryakov (DTB of LIH) has performed numerical calculations of pressure and total impulsefor two situations: a) DW falls normally on the wall, b) DW moves off the wall. As example the results for amatol (ρe = 1 g/cm3, δe = 10 mm, DH = 4 km/s, γ = 3) are given in the table below.

  13. Comparison with numerical calculations EPNM -2010 It is evident that numerically calculated impulses are actually the same for falling down and moving off DW (the difference is  5%). Results of numerical calculations and estimations using the derived formulas (4, 6, 10) differ in less than 10%. Thus these formulas can be used in practice. Impulse affecting the wall does not depend on a point of ignition, irrespective of where it was done – at the wall or at the open end of HE charge. On the contrary, pressure profile and maximal pressure on the wall depends on a point of ignition substantially.

  14. = = = P(t) 2γ/(γ-1) 1/2 J1 γ + 1 3(γ – 1) (13) P0 λ = = 2 J 2γ γ + 1 J1 J2 τ = 3δe/DH t Pressure Impulse EPNM -2010 Remark should be made concerning pressure profile for DW moving off the wall. Total impulse is the sum of two parts: rectangular part of pressure profile and tail part, where pressure drops, J = J1 + J2. Rectangular part gives contribution to the total impulse 2γ/(γ-1) γ + 1 3P0δe 3 me DH (12) = J1 = DH 2γ γ + 1 The J1/J ratio depends on adiabatic exponent γ only: For estimations one can take λ≈ 0.7 actually for all explosives

  15. Pressure Impulse (data for calculations) EPNM -2010

  16. Multilayered Charge EPNM -2010 Multilayered HE charges give possibility to vary pressure profile shape in a wide diapason, at that mass of a charge is constant. Multilayered HE charges are used in experiments and can be used effectively in explosive metalworking. A.I.Gulidov (ITAM SB RAS) has performed numerical calculations for 2- and 3-layered charges with ignition point at the wall and at the charge open end. The next combinations were considered (count of layers from the wall): 1) Three-layered charge. Layer 1: RDX, δe =132 mm(e =1 g/cm3 , DH = 6.2 km/s, =2.8); layer 2: A/AN-1/1,δe = 135 mm(e =1 g/cm3 , DH =4.0 km/s,  =2.2); layer 3: uglenitE6, δe = 80 mm(e =1 g/cm3 , DH =2.0 km/s,  =2.2); 2) Three-layered charge. Layer 1 : Amatol/RDX-3/2,δe = 45 мм (e = 1 г/см3 , DH = 5.6 км/с,  = 2.8); Layer 2: A/AN- 1/1,δe = 45 mm(e = 1 g/cm3 , DH = 4.0 km/s, = 2.2); Layer 3: ANFO,δe = 90 mm(e = 1 g/cm3 , DH= 2.9 км/с,  =2.2); 3) Two-layered charge.Layer 1: A/AN -1/1,δe = 60 мм (e =1 g/cm3 , DH =4.0 km/s, =2.2); Layer 2: ANFO,δe = 60 mm(e =1 g/cm3 , DH =2.9 km/s, =2.2); 4) Two-layered charge. Layer 1: PlasticEVV-11,δe = 5 mm(e =1.6 g/cm3 DH =7.6 km/s,  = 2.8); Layer 2: ANFO,δe = 120 mm (e =1 g/cm3 , DH =2.9 km/s, =2.2);

  17. J = ∑ Ji = ∑ k(γi) mei DHi (14) EPNM -2010 Pressure Impulse of Multilayered HE Charge Analysis of numerical calculations show that total impulse can be estimated by additivity method using the formula Ji– impulse of i-layer of explosive charge. Summation is made by number of explosive layers. For DW falling down on the wall P(t) is well described by formula (1) derived for one-layer charge: P(t) = P0 (τ/t)3. At that, time parameter  = 2J/P0 , where J is calculated by (14). Initial pressure P0 is find using formula (3) or estimated as P0 = 2.4 PH with accuracy reasonable for practice. For DW moving off the wall pressure profile has a step-wise shape. The number of steps equals to number of explosive layers. Pressure at any step can be estimated using formula (5) or more approximately as P0i = 0.3 PH. Time duration of any can be calculated using the expression τi = λiJi / P0i (15)

  18. EPNM -2010 Pressure Impulse of Multilayered HE Charge(results of numerical and analytical calculations) Average difference between results of analytical and numerical calculations is about 8%.

  19. 3 2 4 1 Sliding Detonation. One-Layer HE charge EPNM -2010 Sliding detonation is mostly used in explosive working of materials DW is perpendicular to the wall. 1- rigid wall; 2- explosive layer; 3- DW front; 4- detonation products flying away. Array shows the direction of DW movement. Peak pressure on the wall is equal to detonation pressure P0 = PH, and pressure profile is well described by exponential function P = P0 exp (- t / τ ) (16) 1/2 e 3(γ + 1) (23) τ = DH 4(γ – 1)

  20. Sliding Detonation. One-Layer HE charge EPNM -2010 As the DP flow is two-dimensional gas velocity has two components – normal and tangential to the load wall surface. Therefore total impulse affecting the wall is less than in one-dimensional case. And Gurney energy is also less than heat of explosion. De Carly P.S. and Meyers M.A. have suggested the formula for calculation of Gurney energy. Here u- mass velocity of DP in Chapman-Jouguet point. The meaning of (17) is that kinetic energy of DP connected with mass velocity parallel to the wall surface is subtracted from heat of explosion. From (17) and (7) we get DH2 E = Q – u2/2= Q - (17) 2(γ + 1)2 And for coefficient k(γ) De Carli P.S., Meyers M.A. Design of Uniaxial Strain Shock Recovery Experiments // Proceed. Int. Conf. "Shock Waves and High-Strain-Rate Phenomena in Metals", Albuquerque, NM, 1980. New York: Plenum Press, 1980. P.341-373, 1033-1039 (Appendix A). 1/2 1 3 DH2 k (γ) = E = (18) (19) (γ + 1) 2(γ - 1) (γ – 1)(γ + 1)2

  21. EPNM -2010 Sliding Detonation. Arbitrary angle of DW collision with the wall 4 4 3 3 2 2 α α 1 1 a- regular mode b 4 3 DW falls down on the wall at the angle α (a), DW moves off the wall at the angle α (b), irregular mode with Mach stem (c). 1- rigid wall, 2- explosive layer, 3- DW front, 4- DP,5- Mach stem, α- angle between DW front and the wall. Array shows the direction of DW movement, D= DH/Sinα. 2 5 α 1 c- irregular mode Stationary sliding detonation with inclined DW front can be realized only with use of additional explosive layer with greater detonation velocity. On picture (a) this imagined layer is on the top of layer 2, whereas on picture (b) this imagined additional layer is on the wall. Thickness of additional layer is supposed to be much less than thickness of a charge 2, therefore its input in total impulse is negligible.

  22. Regular and Irregular DW reflection EPNM -2010 Light emission of detonation front fixed using SNEF-4 camera (exposure time 50 ns) 1- DW front with greater velocity; 2- DW front with lesser velocity; 3- the Mach stem Calculations for regular reflection using gas-dynamic equations show that P0/PH ratio depends weakly on γand α. At collision angle α> αcr regular reflection is impossible and shock-wave configuration with Mach stem appears. For widely used HE critical angle lies between 400 and 450. For example, forTNT/RDX -50/50 (=3), powdered RDX (=2.8), amatol (=2.5), andA/AN- 50/50 (=2.2) αcr = 40.7, 41.3, 42.4 and 44.10 correspondingly. In the region of DW irregular reflection (450 550) pressure behind the Mach stem is greater than pressure arising at normal collision of DW with the wall. When changes from 550to 900P/PHdrops monotone to 1. M. Adamec, B.S. Zlobin, A.A. Shtertser. Reflection of Oblique Detonation Waves from Metal Backings // Combustion, Explosion, and Shock Waves. 1991. Vol. 27, No. 3. P. 385-387

  23. EPNM -2010 Regular and Irregular DW reflection (dependence of pressure on collision angle) Calculations for γ= 3

  24. EPNM -2010 Sliding Detonation. DW moves off the wall at the angle α Calculations using gas-dynamic equations show that P0/PH ratio depends weakly on γ. Diagram is graphed for γ= 3

  25. DH3 α3 DH2 α2 DH1 α1 EPNM -2010 Sliding Detonation. Arbitrary angle of DW collision with the wall. Multilayered charge. Using the aforesaid De Carli and Meyers approach we can get for Gurney energy and k(γ) DH2 1 Sin2α E = - (24) Angles of DW fronts are connected with detonation velocities by expressions Sin 2 = DH2 / DH1 , Sin 3 = DH3 / DH1. Whole of DW configuration moves with velocity equal to maximal DH. Total impulse can be find using the formula 2(γ + 1) γ - 1 γ + 1 1/2 3 γ - 1 k (γ, α) = 1 - Sin2α (25) 4(γ2 - 1) γ+ 1 J = Σ Ji= Σ k(γi, αi) meiDHi Sliding detonation in multilayered HE charge. DH1 DH2 DH3.

  26. CONCLUSION EPNM -2010 The developed approach, obtained formulas, and data presented in tables and diagrams permit to make quickly estimation of pressure profile and total impulse affecting the rigid wall for one-layered and combined multilayered HE charge Thank you foryour attention

  27. Pressure Impulse of One-Layer HE Charge EPNM -2010 1- DW falls down on the wall4 2- DW moves off the wall

  28. EPNM -2010 Pressure Impulse of Multilayered HE Charge(DW moves off the wall) 1) Three-layered charge. Layer 1: RDX, δe =132 mm(e =1 g/cm3 , DH = 6.2 km/s, =2.8); layer 2: A/AN-1/1,δe = 135 mm(e =1 g/cm3 , DH =4.0 km/s,  =2.2); layer 3: uglenitE6, δe = 80 mm(e =1 g/cm3 , DH =2.0 km/s,  =2.2); 2) Three-layered charge. Layer 1 : Amatol/RDX-3/2,δe = 45 мм (e = 1 г/см3 , DH = 5.6 км/с,  = 2.8); Layer 2: A/AN- 1/1,δe = 45 mm(e = 1 g/cm3 , DH = 4.0 km/s, = 2.2); Layer 3: ANFO,δe = 90 mm(e = 1 g/cm3 , DH= 2.9 км/с,  =2.2); 3) Two-layered charge.Layer 1: A/AN -1/1,δe = 60 мм (e =1 g/cm3 , DH =4.0 km/s, =2.2); Layer 2: ANFO,δe = 60 mm(e =1 g/cm3 , DH =2.9 km/s, =2.2); 4) Two-layered charge. Layer 1: PlasticEVV-11,δe = 5 mm(e =1.6 g/cm3 DH =7.6 km/s,  = 2.8); Layer 2: ANFO,δe = 120 mm (e =1 g/cm3 , DH =2.9 km/s, =2.2); Calculations we made till 1000 µs

More Related