Numerical investigation of internal explosions in steel pipes P. Bonalumi, M. Colombo, M. di Prisco
2 FORMULATION OF THE PROBLEM General Framework • Project: ACCIDENT - Advanced Cementitious Composites In DEsign and coNstruction of safe Tunnel • Cooperation between Italy and Switzerland funded by INTERREG programme and supported by the European Community and the Switzerland Confederation • Aim: Design of a precast tunnel lining, to be built by means of TBM technology, considering exceptional loads. Material : Mechanical characterization at Meso-structure: Study of soil-structure Structure : Fire and blast tests within high temperature and high strain rate interaction under shocks waves (shock tube) concrete pipes embedded in soil P. Bonalumi, M. Colombo, M. di Prisco
3 FORMULATION OF THE PROBLEM Definition of the problem Open-ended steel pipe subjected to a single centred internal detonation 5 Reflected pressure transducers • 10 mm thick • 1 m long • 0.61 m outer diameter 1 Incident pressure transducer P. Bonalumi, M. Colombo, M. di Prisco
4 FORMULATION OF THE PROBLEM Definition of the problem • Nature of explosive High Energy Solid Explosive • Quantity of the explosive 3, 6, 12, 24 grams charges • Shape of the charge Cylindrical charge • Explosion kind Single point explosion • Explosion position Centre of the pipe middle section P. Bonalumi, M. Colombo, M. di Prisco
5 NUMERICAL MODELLING Framework of the problem OBJECTIVE: Assessment of the prediction capabilities of the numerical model MODELS: Axisymmetric 2D and 3D simulations of 3-grams explosive tests NUMERICAL CODE: EUROPLEXUS - CFD explicit finite element code for transient dynamic problems - Developed by the European Joint Research Centre (JRC) of Ispra and Commissariat à l’Energie Atomique (CEA) of Saclay P. Bonalumi, M. Colombo, M. di Prisco
6 NUMERICAL MODELLING Models 2D 3D_A 3D_B 3D_C Elements Mesh Bubble Structure Fluid Size Size Type N. Smallest size Type N. Smallest size 2D 0.6 x 1 m 2-nodes shell 48 10 mm 4-nodes quadrilateral 5760 10 x 10 mm 40 x 40 mm 3D_A 0.6 x 0.6 x 1m 4-nodes shell 576 20 x 20 mm 8-nodes hexahedron 107328 2 x 2 x 3 mm 40x40x40mm 3D_B 1.2 x 1.2 x 1m 4-nodes shell 1280 30 x 25 mm 8-nodes hexahedron 61440 20x20x25mm 40x40x80mm 3D_C 1.2 x 1.2 x 1m 4-nodes shell 1280 30 x 25 mm 8-nodes hexahedron 61440 20x20x25mm 40x40x80mm P. Bonalumi, M. Colombo, M. di Prisco
7 NUMERICAL MODELLING Description STRUCTURE: Lagrangian description FLUID: Eulerian description FLUID-STRUCTURE INTERACTION: Arbitrary Lagrangian Eulerian - Permanent - Conforming P. Bonalumi, M. Colombo, M. di Prisco
8 NUMERICAL MODELLING Materials { EXPLOSIVE : Baloon model STEEL STRUCTURE : Linear-elastic AIR Density 7800 kg/m 3 ρ Young’s modulus E 210000 N/mm 2 [Brode1955, Larcher2010] OVERPRESSURE BUBBLE Poisson’s ratio 0.3 • Bubble of high compressed air ν • Larger than the real solid explosive { • Bubble overpressure: p bub = f ( V bub , W ) Inviscid and Compressible FLUID : Note V bub , W tnt : Perfect gas p = � ( � � 1) e int • Detonation energy: e TNT = W � 4520 kJ / kg p TNT = e TNT • W TNT Overpressure : ( � � 1) V bub Pressure p 101325 Pa � bub = � 0.2205log( p TNT ) + 2.265 Specific heat ratio 1.4 γ p bub = p TNT + p 0 • Bubble Overpressure: Density 1.2 kg/m 3 ρ � bub p bub p 0 Internal energy e int 2.0833 x10 5 Nm/kg f bub = e int, bub = e int � f bub P. Bonalumi, M. Colombo, M. di Prisco
9 NUMERICAL MODELLING Results - Pressure 2D POINT A POINT B 3D_A A B B A 3D_A POINT A POINT B 3D_B - 3D_C A B A B P. Bonalumi, M. Colombo, M. di Prisco
10 NUMERICAL MODELLING Results - Radial Displacements POINT A ZOOM _ POINT A 2D 3D_A A B POINT B ZOOM _ POINT B B A CPU = 6 min CPU = 160 min P. Bonalumi, M. Colombo, M. di Prisco
11 NUMERICAL MODELLING Results - Radial Displacements POINT A ZOOM _ POINT A 3D_A 3D_B - 3D_C A B A B POINT B ZOOM _ POINT B CPU = 160 min CPU_B = 81 min CPU_C = 441 min P. Bonalumi, M. Colombo, M. di Prisco
12 NUMERICAL MODELLING NUMERICAL RESULTS EXPERIM. 3D_C PRESSURE HISTORY Comparison numerical - 1 D p INC E experimental results F B (explosion section and end section) p1,p2,p3,p4,p5 - p INC Pressure transducers for 3g charge [mm] LONGITUDINAL SECTION TRANSVERSAL SECTION First Peak of First Peak of Reflected Pressure History eflected Pressure History Pressure history along Pressure history along the tube he tube axis axis at the tube at the tube internal surface nternal surface Average Average curve on 12 urve on 12 nominal identical tests ominal identical tests Representative curve on 12 Representative curve on 12 nominal identical tests ominal identical tests p INC p INC p1 p1 p1 p1 P. Bonalumi, M. Colombo, M. di Prisco
13 NUMERICAL MODELLING NUMERICAL RESULTS PRESSURE HISTORY D Comparison numerical-experimental results p INC E along the tube longitudinal axis F B p1,p2,p3,p4,p5 - p INC for 3g charge Pressure transducers [mm] LONGITUDINAL SECTION TRANSVERSAL SECTION First Peak of First Peak of Reflected Pressure History eflected Pressure History at the tube at the tube internal surface nternal surface Representative Representative curve on 12 curve on 12 nominal identical tests ominal identical tests 5 4 1 P. Bonalumi, M. Colombo, M. di Prisco
14 NUMERICAL MODELLING Conclusions Regarding pressure-time history: - In this case, 2D model shows a quite good agreement with 3D model 2D model is satisfactory in predicting blast loads on structure - Boundary conditions have negligible influence on pressure-time history - Small differences of bubble size and shape have negligible influence on the pressure- time function (just small Regarding radial displacement-time history: - 2D model shows a good agreement with 3D model (especially for the first milliseconds) - Boundary conditions influence the response of the pipe central section Regarding experimental pressure-time history: - 3D model satisfactorily predicts the peak pressures and the pressure-time function, but overestimates the wave propagation along the pipe. P. Bonalumi, M. Colombo, M. di Prisco
15 Numerical investigation of internal explosions in steel pipes …Thank you for your attention!!! P. Bonalumi, M. Colombo, M. di Prisco
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