Modified Porosity Distributed Resistance Combined to Flamelet Combustion Model for Numerical Explosion Modelling

Transcription

1 Modified Porosity Distributed Resistance Combined to Flamelet Combustion Model for Numerical Explosion Modelling Dr. Sávio Vianna School of Chemical Engineering University of Campinas - UNICAMP

2 University of Campinas School of Chemical Engineering UNICAMP Turbulent reactive flow modelling and process safety On going research Carbon dioxide dispersion modelling Water mist modelling in explosion scenarios within 3D Navier-Stokes solver Development of simpler explosion models using CFD (Computational Fluid Dynamics) findings Detonation modelling within a 2D/3D Euler code Optimisation of gas detectors to prevent explosive atmosphere Contact: Dr. Sávio S.V. Vianna Lecturer School of Chemical Engineering University of Campinas - UNICAMP Tel: Fax: savio@feq.unicamp.br

3 Topics Problem outline and motivation Governing equations Flow modelling Combustion modelling Cold flow results Explosion results Final comments

4 Motivation Blast wall Blast wall Control Utilitie Room s Living Quarter LQ

5 Motivation

6 Governing equations The conservation principle applied to the following quantities; mass momentum mass fraction mixture fraction energy turbulent kinetic energy dissipation rate of turbulent kinetic ( ρ φ ) t + ( ρũ j φ) x j x j ( Γ φ (ρ, u, E, c, f, k, ε) φ x j ) = S φ

7 Porosity Modelling Volume Porosity β v = V f V f +V S = V f ΔxΔyΔz Area porosity in x direction β x = dydz ΔyΔz Unstructured environment Structured mesh solver

8 Porosity Modelling Via PorTool

9 The Model ( β v ρũ) + (β j ρ ũ j ũ) P =β t x v + β j σ +β j x j x v ρ g+r i j 1 R i = f i A Turbulence w Modelling 2 ρ u i u i f i =f (Re) A w = (1 β v )/δx avg ( β v ρ k) + ( β j ρ ũ j k ) = j( t x j x β μ eff j σ k ( β v ρ ε) + ( β j ρ ũ j ε ) = j( t x j x β μ eff j σ ε G=G R1 +G R2 k x j) +G β v ρ ε i ε x j) +f 1 C 1 ε k G f 2 C 2 β v ρ ε 2 k G ( u x j ) 2 G R1 =C s μ eff [(u u s ) 2 + (v v s ) 2 + (w w s ) 2 ]A w 2 G R2 =C B ρ u i 3 ( 1 β i 1 ) 2 A w

10 Combustion modelling ( β v ρ c) t + ( β j ρũ j c) x j x j( β j μ eff σ c c x j) = w Combustion closure model w turb = R Σ=(ρ R u l )Σ Flame surface area per unit volume Σ= g c(1 c) σ y L y Length scale of wrinkling L y =C L L L f( u' u L ) f( =[ u L) ' u 1 1 ( [ 1 1+ C 1 exp w1 1+C w2 (u ' /u L )])] (u ' /u L )

11 Cold flow results

12 Cold flow results

13 Cold flow results

14 Mobil British Gas test case The box is 9m long with cross section 4.5 x 4.5 m Pipe diameter is 18cm The box is filled with CH4 Iginition is centre located at wall opposite to vented wall Vent area 2.25 m 2

15 Mobil British Gas test case Full geometry Porosity model Porous model

16 3D Solvex test case MPDR* Model Vianna S.S.V. and Cant R.S. Journal of Loss Prev. Proc. Ind. (2009) doi: /j.jlp Watterson et al. Full geometry Int. Journal of Numerical Methods in Fluids Vol. 26 pages

17 3D Solvex test case The box is 10m long, 8.75m wide and 6.26m high. Pipe diameter is 50cm and rows are staggered positioned Ignition is centred located at wall opposite to the vented end. Vent area m 2

18 DnV test case Open wall

19 Statistical analysis

20 Final comments and the away ahead The PDR approach combined with flamelet modelling is implemented within an unstructured mesh flow solver. Results are compared against various experimental data and good agreement is observed. Further work is necessary to improve prediction of turbulence generated by obstacles not resolved in the mesh. Further investigation is required to investigate the behaviour of the MPDR model in more complex geometries The concept of porosity, as presented here, might be of some use in oil reservoir modelling The application of porous tagged cells in water mist modelling for explosion mitigation is currently under investigation Simpler explosion models are under investigation taking into account the propagation speed and flame area using CFD as benchmarking. These models are important at early stages of design when the geometry is not available. The models can also be used to predict overpressure in storage facilities and blast waves. High order finite volume method applied to explosion modelling is also worth investigating