Modeling Dust Explosions

Introduction

Dust explosions are a major safety topic, on every plant, that handles flammable granular or pulverized substances. Commonly dusts are characterized by two scalars, the maximum explosion pressure and the maximum rate of pressure rise. With that method it is not possible to know how the flame front and the pressure act in the geometry. When a description of the behavior of a dust explosion in the geometry is needed, a CFD (Computational Fluid Dynamics) model, which can describe the physics of a dust explosion, has to be used

For the modeling of gas explosion, two types of combustion models are common. On the one hand chemical and mixture limited reaction models like the eddy dissipation concept, on the other hand flame speed approaches. To model the dust explosion with a chemical and mixture limited reaction model, the pyrolysis of the dust has to be characterized. The calculation of the pyrolysis in the dust particles needs a kinetic and enormous computing recourses.

If a flame speed approach is used, the durst can be characterized by the laminar flame speed and the burnable fuel fraction as function of the dust concentration and the heat of combustion. The flame speed approach is also relatively cheap in terms of computing resources.

So a CFD code to model dust explosions, which is based on a flame speed approach was developed. This solver is based on the XiFOAM solver of the software package OpenFOAM.

Description of the model

Basic concept

The key parameter is the turbulent flame speed, which is highly depended to the turbulence and also depends on the laminar flame speed. The laminar flame speed is a function of the dust concentration. These values are based on measurements with a Siwek 20-liter vessel. With the pressure time curve from the experiment, the laminar flame speed can be calculated, shown by Skjold [1]. It is also possible to calculate the burnable fuel fraction by energy balancing. Figure 1 shows the laminar flame speed and burnable fuel fraction of lycopodium as function of the concentration.

The influence of the turbulence on the flame speed follows the description of Dahoe [2].

Figure 1: laminar flame speed and burnable fuel fraction of lycopodium as function of the concentration

Particle and gas motion

To describe the movement of the dust particles an Eulerian approach was chosen because of the high particle count. In bigger geometries a Lagrangen approach is too expensive in terms of computing resources.

The exchange coefficient for momentum K is based on the work of Syamlal [3] and the drag coefficient, to calculate is described by the Schiller Neuman approach [4]. The granular pressure ps and the granular temperature are computed by an analytical published by Syamlal [5].

Equation 1 describes the momentum equation of the gaseous phase and equation 2 the momentum equation of the particle phase.

                                                        (1)

                                    (2)

Equation 3 and 4 show the continuity equation. The source term on the right side, describes the mass transfer between the phases through the combustion process.

                                                                       (3)

                                                                       (4)

A comparison between the used Eulerian and the Fluent DPM model is shown in figure 3. In a simple 2D geometry, shown in figure 2 particles where injected. The curves in figure 3 show the dust concentration on the Y axis after different times.

Figure 2: Geometry for comparison between the used Eulerian and the Fluent DPM model

Figure 3: Comparison between the used Eulerian and the Fluent DPM model

Turbulence modeling

Early simulations had shown that the in OpenFOAM implemented RANS fail. The reason for that is the high relative velocity in front of the flame front. The high relative velocity generates turbulent kinetic energy behind the particles. To model this effect an additional source tem, based on the consistent approach of Crowe [6] was implemented in the k equation of the standard k-e model. Equation 5 shows the modified k equation.

                                             (5)

Combustion model

Like in every flame speed approach the state of combustion is defined by a progress variable, in this case called C. If C has a value of 1 the dust-air mixture is unburned. For a burned mixture C has a value of 0. The source tem of conservation equation for C, which is shown in equation 6, includes the laminar flame speed, the variable Bsh, which describes the ratio between the laminar and the turbulent flame speed and the magnitude of the gradient of C. That source term is also used in other equations, to describe changes based on combustion processes. 

                                           (6)

Energy Equations

To be able to consider the high relative velocities in front of the flame front, for each phase a separate energy equation was implemented. The energy equation for the gaseous phase, shown in equation 7, has two source terms. The first one describes the energy of combustion based on the heat of combustion, dust concentration, the burnable fuel fraction and the combustion source term. The second term describes the energy exchange to the particle phase, based on the heat exchange coefficient of Ranz-Marshall [4].

The energy equation for the particle phase, shown in equation 8 has just a storage function. The source term just describes the energy transfer to the gaseous phase.

(7)

                                                                                               (8)

Species Equation

The density of the gas is a very important parameter for expansion. It is based on pressure, temperature and the molar mass. To describe the molar mass the variable b was introduced. This variable describes the off gas- air mixture. The conservation equation for b is shown in equation 9. The source term is based on a coefficient, dust concentration, the burnable fuel fraction and in the combustion source term.

                                (9)

Results and comparison to the experiment

To evaluate the model, in house experiments from Kern [7] were used. Figure 4 shows the experimental set up. A screw conveyer delivers a defined amount on dust, in that case lycopodium, in to a vertical duct.When the dust gets a constant defined concentration, the mixture is ignited by an electric spark.

Figure 4: Experimental set up

In figure 5 the comparison of the flame front between experiment and the model is shown. For a concentration of 300g/m³ lycopodium. The model fits well to the experiment in the first 200ms. After that the results gets different. The reason is that the momentum out of the duct influences turbulence after 200ms. In the experiment a flame arrester at the top of the duct and the off gas system has to be used. This parts are not implemented in the model.

In the future, experiments with the duct at another location are planned, where no flame suppression barrier and the off gas system is needed.

Figure 5: comparison between experiment and model

<>List of abbreviations

aEff	Effective thermal diffusivity	t	Time
b	Progress variable off gas- air mixture	Tg	Temperature gaseous phase
Baus	Burnable fulefraction	Tp	Temperature particle phase
Bsh	Ratio between laminar and turbulent flamespeed		Velocity vector gaseous phase
C	Progress variable flamefront	Ulam	Laminar flame speed
D	Dust concentration		Velocity vector particle phase
eps	Dissipation of the turbulent kinetic energie	ag,p	Heat exchange coefficient
	Gravity vector		Volume fraction gaseous phase
HVbr	Heat of combustion		Stress tensor gaseous phase
K	Momentum exchange coefficient		Stress tensor particle phase
p	Pressure	ρ	Density gaseous phase
ps	Granular pressure	ρ unburned	Density gaseous phase unburned
QVbr	Chemical coefficient

<>

<>Literature

[1]        T. Skjold, B.J. Arntzen, O.R. Hansen, O.J. Taraldset, I.E. Storvik, R.K. Eckhoff, Simulating Dust Explosions with the First Version of DESC, Process Safety and Environmental Protection, Volume 83, Issue 2, March 2005,151–160

[2]        A.E., Dahoe, 2000. Dust explosions: a study of flame propagation, PhD

thesis, Delft University of Technology, Delft, Holland

[3]        M. Symlal, J. O'Brain, (1989), “Computer Simulation of Bubbles in a Fluidized Bed”, AIChE Symp. Series 85, 22-31

[4]        FLUENT (2010), “FLUENT (2003), “Ansys Fluent Theory Guide”, Fluent Inc

[5]        M. Symlal, J. O'Brain, W. Rogers, (1993), “MFIX Documentation”, National Technical Information Service, Springfield, US.

[6]        C. T. Crowe, On models for turbulence modulation in fluid-particle, International Journal of Multiphase Flow 26 (2000) 719-727

[7]        H. Kern, K. Held, H. Raupenstrauch, Investigations on the influence of the oxygen concentration on the flame propagation in lycopodium/air mixtures, ACHEMA 2012

Frankfurt, June 21st 2012