### 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**

**δ**

_{L}

_{L}**<<δ**

**<<δ**

**Unburned**

_{t}

_{t}**c=0**

**c=0**

**Burned**

**c=1**

**c=1**

**Flame brush**

**0<c<1**

**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 𝐷_{𝑡}= 𝐷

_{𝑡,∞}1 − exp −𝑡𝑓𝑑 𝜏

_{𝐿}𝑈𝑡 = 𝑈𝑡,∞ 1 − 𝜏

_{𝐿}𝑡

_{𝑓𝑑}+ 𝜏

_{𝐿}𝑡

_{𝑓𝑑}exp − 𝑡

_{𝑓𝑑}𝜏

_{𝐿}Τ 1 2 𝑈

_{𝑡,∞}= 𝐴𝑢′𝐷𝑎1 4Τ = 𝐴𝑢′3 4Τ 𝐿1 4Τ 𝑆

_{𝐿}1 4Τ 𝛿

_{𝐿}− Τ1 4 𝐷

_{𝑡,∞}= 𝐶𝜇 𝑃𝑟

_{𝑡}෨𝑘2 ǁ𝜀 = 𝐶

_{𝜇}𝑃𝑟

_{𝑡}෨𝑘1 2Τ

_{𝐿}𝐶

_{𝑑}

### 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

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[-] 1.3

**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

### 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.