Modelling of cornflour dust explosion using an open source code

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Full text

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Modelling of cornflour

dust explosion using an

open source code

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Outline

• Background and Objectives

• Method

• Verification of Model Implementation

• Model Validation

• Conclusions

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Outline

• Background and Objectives

• Method

• Verification of Model Implementation

• Model Validation

• Conclusions

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Background

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• 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);

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Objectives

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• to improve the understanding of dust explosions;

• to provide an OpenFOAM-based numerical tool for accurately estimating the consequence of dust explosions.

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Outline

• Background and Objectives

• Method

• Verification of Model Implementation

• Model Validation

• Conclusions

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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).

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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

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Method

Flame Speed Closure (FSC) Model

9 𝜕 ҧ𝜌 ǁ𝑐

𝜕𝑡 + ∇. 𝜌෥ҧ𝐮 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 𝐶𝑑

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Outline

• 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

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Verification of Model Implementation

Layout of 1-D planar flame. 1-D planar flame in “frozen” turbulence

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Truncated FSC model: 1-D planar flame in “frozen” turbulence

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Truncated FSC model: 1-D planar flame in “frozen” turbulence

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Truncated FSC model: 3-D spherical flame in “frozen” turbulence

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CompleteFSC model: 1-D laminar planar flame 𝜕 ҧ𝜌 ǁ𝑐

𝜕𝑡 + ∇. 𝜌෥ҧ𝐮 ǁ𝑐 = ∇. [ ҧ𝜌ሺ𝜅 + 𝐷𝑡)∇ ǁ𝑐] + 𝜌𝑢𝑈𝑡∇ ǁ𝑐 + 𝑄+ ҧ𝜌𝑊𝑖𝑔𝑛

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Complete FSC model: 3-D spherical flame in “frozen” turbulence

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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

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Cornflour explosion in Leeds combustion vessel

Illustration of Cornflour dust-air explosion in fan-stirred combustion vessel from Leeds

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Extra source terms in standard 𝒌 − 𝜺 turbulence model

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Turbulence is stable with extra source term!

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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

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Summary of model constants

22 Parameter Value Turbulence model 𝐶𝜇[-] 0.09 𝐶1[-] 1.44 𝐶2[-] 1.92 𝜎𝑘[-] 1.0 𝜎𝜀[-] 1.3

Combustion 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

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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.

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Thank you!

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