Modelling of cornflour
dust explosion using an
open source code
Outline
• Background and Objectives
• Method
• Verification of Model Implementation
• Model Validation
• Conclusions
Outline
• Background and Objectives
• Method
• Verification of Model Implementation
• Model Validation
• Conclusions
Background
4
• Dust explosion threats the industries which deal with combustible powders, e.g. pellets, food, metal and so on;
• National and global statistics, e.g. Swedish working environment authority, and Combustible Dust Incident Report by DustSafetyScience;
• “Dark figure” - unreported incidents;
• Once per week instead of once per month (Nessvi and Persson 2019); • One seventh incidents were reported in Germany from 1965 – 1985
(Eckhoff 2003, Yuan 2015);
Objectives
5
• to improve the understanding of dust explosions;
• to provide an OpenFOAM-based numerical tool for accurately estimating the consequence of dust explosions.
Outline
• Background and Objectives
• Method
• Verification of Model Implementation
• Model Validation
• Conclusions
Method
• Flame Speed Closure model focusing on flame propagation in a turbulent premixed flame
• FSC model was quantitatively tested for laboratory gaseous turbulent premixed flames from different groups with different conditions.
• Dust explosion resembles that of a gas explosion for fine dust particles and high volatile content (Bradley et al 1988, 1989).
Method
Combustion progress variable c
Image by Fox & Weinberg, Proc. R. Soc. London A268:222-239, 1962.
δ
L
<<δ
Unburned
t
c=0
Burned
c=1
Flame brush
0<c<1
Method
Flame Speed Closure (FSC) Model
9 𝜕 ҧ𝜌 ǁ𝑐
𝜕𝑡 + ∇. 𝜌ҧ𝐮 ǁ𝑐 = ∇. [ ҧ𝜌ሺ𝜅 + 𝐷𝑡)∇ ǁ𝑐] + 𝜌𝑢𝑈𝑡 ∇ ǁ𝑐 + 𝑄 + ҧ𝜌𝑊𝑖𝑔𝑛 transient
convection
flame structure (thickness)
burning velocity ignition
X
Truncated model 𝐷𝑡 = 𝐷𝑡,∞ 1 − exp −𝑡𝑓𝑑 𝜏𝐿 𝑈𝑡 = 𝑈𝑡,∞ 1 − 𝜏𝐿 𝑡𝑓𝑑 + 𝜏𝐿 𝑡𝑓𝑑exp − 𝑡𝑓𝑑 𝜏𝐿 Τ 1 2 𝑈𝑡,∞ = 𝐴𝑢′𝐷𝑎1 4Τ = 𝐴𝑢′3 4Τ 𝐿1 4Τ 𝑆𝐿1 4Τ 𝛿𝐿− Τ1 4 𝐷𝑡,∞ = 𝐶𝜇 𝑃𝑟𝑡 ෨𝑘2 ǁ𝜀 = 𝐶𝜇 𝑃𝑟𝑡 ෨𝑘1 2Τ 𝐿 𝐶𝑑Outline
• Background and Objectives
• Method
• Verification of Model Implementation
• Truncated FSC model: 1-D planar flame in “frozen” turbulence • Truncated FSC model: 3-D spherical flame in “frozen” turbulence • Complete FSC model: 1-D laminar planar flame
• Complete FSC model: 3-D spherical flame in “frozen” turbulence
• Model Validation
• Conclusions
11
Verification of Model Implementation
Layout of 1-D planar flame. 1-D planar flame in “frozen” turbulence
Truncated FSC model: 1-D planar flame in “frozen” turbulence
Truncated FSC model: 1-D planar flame in “frozen” turbulence
Truncated FSC model: 3-D spherical flame in “frozen” turbulence
CompleteFSC model: 1-D laminar planar flame 𝜕 ҧ𝜌 ǁ𝑐
𝜕𝑡 + ∇. 𝜌ҧ𝐮 ǁ𝑐 = ∇. [ ҧ𝜌ሺ𝜅 + 𝐷𝑡)∇ ǁ𝑐] + 𝜌𝑢𝑈𝑡∇ ǁ𝑐 + 𝑄+ ҧ𝜌𝑊𝑖𝑔𝑛
Complete FSC model: 3-D spherical flame in “frozen” turbulence
Outline
• Background and Objectives
• Method
• Verification of Model Implementation
• Model Validation
• Experimental and numerical setup
• Extra source terms in standard 𝑘 − 𝜀 turbulence model • Summary of model constants
• First test of model
• Conclusions
Cornflour explosion in Leeds combustion vessel
∞
∞
∞
∞
Illustration of Cornflour dust-air explosion in fan-stirred combustion vessel from Leeds
Extra source terms in standard 𝒌 − 𝜺 turbulence model
Turbulence is stable with extra source term!
Outline
• Background and Objectives
• Method
• Verification of Model Implementation
• Model Validation
• Experimental and numerical setup
• Extra source terms in standard 𝑘 − 𝜀 turbulence model
• Summary of model constants
• First test of model
• Conclusions
Summary of model constants
22 Parameter Value Turbulence model 𝐶𝜇[-] 0.09 𝐶1[-] 1.44 𝐶2[-] 1.92 𝜎𝑘[-] 1.0 𝜎𝜀[-] 1.3Combustion model 𝑡𝑟[s] 3.4e-11
𝛩 [K] 2e4
Table 7 Model constants and input parameters that were not varied in the present study.
Parameter Value range Note
Ignition model 𝑊0[-] - case dependent
𝑡0[s] around 1 ms
𝜎𝑡[s] 𝜎𝑡 = 𝑡0/5 depends on 𝑡0
𝜎𝑟[m] around 1 mm related to ignition kernel
Turbulence model 𝑃𝑟𝑡[-] 0.3-1.0
activation timing of
turbulence model 1 ms 𝐶𝑑[-] 0.37-2.0
Combustion model 𝐴 [-] 0.35-0.5 0.4 for gas burning
Conclusions
• FSC model has been implemented in OpenFOAM;
• The implementation has been verified against analytical solutions for 1-D planar and 3-D spherical turbulent flames;
• The developed code is being validated against small-scale dust-explosion experiments performed using the well-known Leeds combustion vessel.
• The first test shows that the trend, i.e. an increase in turbulent velocity fluctuation, an increase in flame speed, is predicted by the code.
• In the next step, more physics will be added. Validation with large-scale experiments with complicated geometry will be performed.
