Workshop Paris, November 2006

Transcription

1 SAFe and Efficient hydrocarbon oxidation processes by KINetics and Explosion expertise and development of computational process engineering tools Project No. EVG1-CT Workshop Paris, November 2006 Work Package 3: Modelling/ Prediction of Explosion Indices Sub Package 3.7: Modelling of explosion propagation Explosion propagation, Pmax, Model demonstration W. Glinka, G. Rarata 1

2 Introduction Goal: Evaluation of Explosion Hazard in Industrial Conditions by Simulation of an explosion in vessels of different shapes with obstacles and venting 2

3 Basic parameters of explosion The minimizing of the losses and minimizing of costs of the protection requires some knowledge about the explosion course. At the first step of estimating the potential danger we need to know only few basic parameters: flammability limits FL, maximum pressure of explosion P max maximum ratio of pressure rise (dp/dt) max. P max is the key factor which defines the possible losses and required structure strength. (dp/dt) max is the factor which describes the dynamics of the explosion. max, 3

4 Physics of explosion In adiabatic vessel theoretically the maximum pressure should depend only on properties of mixture. In real objects the P max depends on many complex factors. The most important are: kind and composition of mixture (heat of reaction, specific heat, l.b.v.), initial pressure, initial temperature, place of ignition, internal flow, gas velocity, initial turbulence, heat transfer, shape and size of the vessel, external conditions. CP Φ QR P T Pa Ta 4

5 Sources of explosion data Experimental Data reliable data but for limited number of flammable mixtures, initial conditions, shapes of vessels. The problem is how to use these data to real industrial conditions (big scale, wider range of reactants, elevated initial conditions). Numerical Modelling possibility of modelling wide range of situations but less accurately. Limited efficiency of computers and acceptable time of calculation force serious simplification in mathematical models. 5

6 Possible tools for P max and (dp/dt) dt) max estimation CFD-DNS DNS with full chemical kinetics - theoretically accurate but practically not available yet and ineffective simplified CFD (e.g. RANS, LES) ) and simplified chemical kinetics (e.g. one step reaction, flamelets,, CMC) - flexible and accurate but only for advanced users, time consuming phenomenological models based on experiments `` - limited range of applications but very effective and accurate for some cases simple zero-dimensional models based on thermodynamics - very simple, good for parametric analysis, for all users. `` 6

7 Program Explosion Pressure 7

8 Equilibrium explosion Pressure the simplest calculation Program Explosion Pressure calculates the maximum possible explosion pressure. It allows estimation of explosion pressure in seconds. It is a very convenient tool for simple parametric study. Assumptions: The explosion occurs in closed vessel. Combustion products are in thermo-chemical equilibrium. The products consist of limited list of most important species. There is no heat and mass exchange. Products of the explosion are semi-ideal ideal gas. These simplifications allow creating simple and universal mathematical atical model but they also lead to some inaccuracy of calculation. 8

9 Program Explosion Pressure 9

10 Comparison with experiment P [bar] Calculation Experiment: 1.2m3 vessel 1 4% 6% 8% 10% 12% 14% 16% mole fraction of CH4 10

11 Program FireBall 11

12 Main objectives of the FireBall program 1. Pressure history P = f(t) 2. Maximum pressure P max 3. Maximum pressure rise rate (dp/dt) max 12

13 Model ofo explosion propagation and (dp/dt) max - main assumptions 1. The model describes explosion of combustible mixture in closed and vented vessels. 2. The model takes into account influence of heat transfer, obstacles and varring position of ignition. 3. The model is zero-dimensional. Fresh and burnt mixtures are treated as homogeneous mixtures. 4. Flame is spherical. 5. The products of combustion are in thermochemical equilibrium. 6. Dynamics of the explosion is simulated by use of turbulent burning velocity. 7. The model is able to simulate explosion in vessels of certain shapes (spherical, cylindrical, cubic). 8. The combustion mode is deflagration. Flame front Obstacles Vent Ignition 13

14 Structure of the model initial conditions: fuel,ox., φ, p o, To,Eign initial (laminar) flame speed f( fuel,ox., φ, p o, T o,eign) laminar flame speed f( fuel,ox., φ, p, T,r fl) turbulent flame speed f(u, l u ) products composition model: stoichiometric or equlibrium heat transfer flame propagation, SCOPE model M b=f(u t, s, A), r t=f(u t) gas state, p, T, u T, b E, x... turbulence model u =f(v,l,r fl,u t,re) vents models velocity of gas, v=f(e,vents, obstacles?) obstacles model 14

15 Explosion modelling in Safekinex project Work Package 2: Experiments on explosion safety Sub Package 2.6: Experimental determination of the Pmax and (dp/dt)max as function of P,T, fuel type and Φ DATA Work Package 3: Modelling/Prediction of Explosion Indices Sub Package 3.1: Modelling of laminar burning velocity Work Package 3: Modelling/Prediction of Explosion Indices Sub Package 3.7: (experimental extension): Experiments on flame-obstacle interactions, venting, influence of ignition position SUBMODEL Sub Package 3.2: Maximum explosion pressure (equilibrium model) Literature review: Experimental determination of the Pmax and (dp/dt)max as function of P,T, fuel type and Φ,experiments on flame-obstacle interactions, venting, influence of ignition position Work Package 3: Modelling/Prediction of Explosion Indices Sub Package 3.7: Modelling of laminar burning velocity 15

16 Submodels Laminar burning velocity is calculated by use of following equation. Coefficients have been obtained by fitting numerical or experimental data (WP 3.1) Turbulent burning velocity is calculated by use of flame surface model where L f is an empirical coefficient which describes relation between radius of flame r fl and integral scale of turbulence L. The program can use two models of heat transfer: Forssling model and turbulent heat transfer model (recommended). The latter one uses one empirical coefficient HTC which connects the Nuselt number of the heat transfer and intensity of the turbulence in the products. The program includes a simple free convection model. This model uses one experimental coefficient C x which describes aerodynamic drag between fresh and burnt mixture. The obstacle model is based on assumption that every obstacle is a source of turbulent kinetic energy (k) generated in flow inducted by the propagating flame, where a obst is an experimental coefficient which indicates the strength of interaction. The model of vents describes only mass outflow from the vessel. The mass flow rate trough the vessel depends on flow coefficient k vent of the specific venting device. 2 τ η ξ( φ σ) T p γα φ 0 0 ( ) SL = (1 + ) W e 1 ff T p L = Lr f fl Nu = HTC u + u + F = g( ρ ρ ) V b a k = C BR u dm dt v u ' ( ' pr buoyancy) 1only conduction b b 2 2 D g = A k ρu v vent v F d x α = C π r ρ β ( u u ) 2 bb ub fl b

17 Assumed geometry of the flame and shape of vessels It is assumed that flame is spherical at any time. When flame touches the walls the flame surface lays on the part of the sphere which is inside the vessel. ut r ut Spherical vessel Cubic vessel Dimensions and coordinate systems for different vessels: a) sphere, b) horizontal cylinder, c) horizontal cylinder with domes, d) vertical cylinder, e) vertical cylinder with domes, f) cube. ut ut ut Elongated cylindrical vessel 17

18 Output information The program calculates following variables: maximum pressure P max, maximum pressure rise rate (dp/dt) max, history of evolution of main parameters: pressure, temperature of the fresh mixture, temperature of the burnt mixture, radius of flame, mass fraction of the burnt mixture, composition of the burnt mixture. The data are saved in a text file in format which can be easily handled by most of postprocessing software (Excel, Tecplot, etc). 18

19 Structure of the software The software contains two parts: Fireball.exe which actually is the numerical code, FireBallFace.exe which is an interface to the main program. The two parts communicate each other by files which store all information about performed tasks. Thanks to that structure, the simulation program Firebal.exe can be used as a separate tool, or even invoked by others applications. However the users are advised to use the graphical interface which is the simplest way of introducing necessary data. The software contains, apart from the executable files, set of data files: thermodynamic data (THERMO.DAT), transport properties (Transport.dat) properties of selected combustible mixtures (Mixtures.mix). The files are provided with the program, however users can use any file of appropriate format. This allows some flexibility and advanced users can create own data which fit better for their specific needs. 19

20 Presentation of the program 20

21 Example 1 This example presents simulation of explosion of methane-air mixture in spherical, closed tank (1.25 m 3 ) without any obstacles p [bar] p [bar] %CH %CH t [s] t [s] p [bar] 5 4 p [bar] experiment model (no convection) model (free convection) 9.5%CH %CH t [s] t [s] 21

22 Example 2 This example shows the case where use of the program is not recommended- for elongated vessels. The vessel, a pipe with mylar diaphragm, was filled with stoichiometric methane-air mixture. 22

23 Summary 1. Program Explosion Pressure is a convenient tool for quick and ease estimation of the maximum possible explosion pressure. 2. Program FireBall simulate course of explosion and provides: 1. pressure profile P = f(t) (and other variables T,r fl and composition as well), 2. maximum explosion pressure P max, 3. maximum pressure rise rate (dp/dt) max. 3. The model is based on five empirical coefficients : L f : depends on mixture kind HTC : depends on size and shape of the vessel C x : depends on size and shape of the vessel a obst : depends on obstacle shape k vent : depends on valve design 4. The coefficients has been estimated by fitting simulation data to experimental data for several typical situations (mixture, shape and size of vessel). 5. The program will be distributed with set input files with: thermodynamic data, transport data, mixture properties data (laminar burning velocity and L f ), guidelines/tables for setting up appropriate empirical coefficients. 23

24 Thank you 24

25 Appendix 25

26 Explosion model main equations Mass balance (including venting) Energy balance du dt u dm = dt fl u u dm dt uv h u + dmu dt dl dt dmufl dmuv dmuv = = Aflu fl ρu dt dt dt dqu du dm b fl dmbv dl dqb = uu hb dt dt dt dt dt dt Pressure equation V mb = ρb + dm ρ u fl dm ρ b bv Π p p + dp 1 γ b mu + ρu dm ρ u fl dm ρ u uv p p + dp 1 γ u Procedure of calculation of explosion propagation 26

27 Laminar burning velocity Laminar burning velocity is a function of equivalence ratio, diluent ratio, pressure and temperature. It is a specific property of the combustible mixture. 2 τ η ξ( φ σ) T p γα φ SL = (1 + ) W e 1 ff T p α 0 0 β ( ) Each mixture is defined by set of coefficients which can be obtained by numerical simulation (WP 3.1) or by fitting experimental data. Example: The coefficients for methane-air mixture Parameter Z Gülder [28] 1 Present work / γ / 1.8 U lo [m/s] Experiment Aproxim ation φ τ W (cm/s) η ξ σ /

28 Turbulent burning velocity In this model turbulent burning velocity depends on disturbed area of the flame A t, mean flame area A m and laminar burning velocity u l : u u t l = At A m One can derive following differential equations which describe development of the flame surface and turbulent burning velocity: dut 4h h dh h du = u l dt L L dt L dt dh h = 1 u ' dt L The turbulence may be induced by the flame propagation and intensified by other sources e.g. obstacles. Intensity of turbulence u is calculated by use of Karlovitz approach. L = L r f fl l L f is empirical coefficient which describes relation between radius of flame r fl and integral scale of turbulence L 1 u l u' fl = ut 1 3 ut 2 u ' = ( ) 2 n u' fl + i 1 vh p Lu t = k i 28

29 Heat Transfer Three sources of heat loses were considered: Radiation of the hot products of combustion (a few percent). Convective heat transfer between hot products and wall (when they are in contact) what is driven by two phenomena (main source of the heat loses) a) turbulence and movement of gaseous product caused by expansion of hot gases (internal movement), b) natural convection driven by buoyancy of hot products immersed in cold fresh mixture. Convective heat transfer between compressed fresh mixture (up to 500 K) and walls (meaningless). Two models are applied in the program: Frossling model, Turbulent heat transfer model (recomended). This model uses one empirical coefficient HTC which connects the Nuselt number of the heat transfer and intensity of turbulence in the products. The program includes a simple free convection model. This model uses one experimental coefficient C x between fresh and burnt mixture. which describes aerodynamic drag 29

30 Obstacles The model is able to simulate obstacles of simple geometry. The obstacles are described by: r obst size of obstacle d elem size of elements BR blockage ratio C D drag coefficient experimental coefficient a obst The influence of obstacle can be properly simulated when the obstacle is symmetrical in reference to the flame. The idea of the submodel is that every obstacle is a source of turbulent kinetic energy (k) generated by flow inducted by the propagating flame. where: u g A obs A 0 velocity of gas, a k = C BR u 2 2 D g total area occupied by the obstacle at given radius, BR = total cross-section of the channel or area of the flame. A obst A 0 30

31 Vents The model of vents describes only mass outflow from the vessel what results in smaller pressure increase. No influence on turbulence, flame area and turbulent burning velocity is taken into account. Two kinds of the venting device are distinguished: 1. diaphragm which is burst off when differential pressure crosses the opening pressure. 2. valve which is opened when differential pressure rises above opening pressure but the valve is closed when the differential pressure comes back to closing value which is lower than opening pressure. The vent is described by following information: Vent name Kind of vent Vent position Area of vent Flow coefficient Opening pressure Closing pressure Vent open time name of particular vent, kind of the vessel, place where the vent is installed (coordinates), area of the free flow trough the vent, (k vent ) flow coefficient of the device. opening differential pressure in bars. closing differential pressure in bars (only for type: valve). this parameter describes dynamic properties of the vents. It is time measured from the moment when the opening differential pressure is achieved to the moment of full opening of the vessel. 31