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Pyrolysis gas jets out from the surface of a solid fuel particle when heated. This study experimentally observes the occurrence of gas jets from heated solid fuel particles. Results reveal a local gas jet occurs from the particle’s surface when its temperature reaches the point at which a pyrolysis reaction occurs. To investigate the influence of the gas jet on particle motion, a numerical simulation of the uniform flow around a spherical particle with a nonuniform outflow or high surface temperature is conducted, and the drag force acting on the spherical particle is estimated. In the numerical study, the magnitude of the outflow velocity, direction of outflow, and Rayleigh number, i.e., particle surface temperature, are altered, and outflow velocities and the Rayleigh number are set based on the experiment. The drag coefficient is found to decrease when an outflow occurs in the direction against the mainstream; this drag coefficient at a higher Rayleigh number is slightly higher than that at a Rayleigh number of zero.

Pulverized coal is mixed with air and burned in pulverized coal combustion devices in power plants and ironworks. When a solid fuel particle such as coal is heated, the flammable gas generated by the pyrolysis reaction jets out from a part of the surface, and combustible components that are not gasified burn at the surface. Although the reaction rate and yields of each component in such a combustion process have been frequently investigated [

In a numerical simulation of a gas-particle flow, an equation has been solved for the motion of a particle in which drag, gravitational, and other forces are included [

The aims of the present work are to clarify the flow around a burning solid fuel particle and to estimate the drag coefficient of the particle. In this paper, a gas jet from a heated coal particle is observed and the gas velocity of the jet and surface temperature of the particle are measured. In addition, the effect of the gas jet and surface temperature on the drag coefficient of a particle are numerically investigated; the numerical simulation supposes a particle Reynolds number for micron-sized particles in pulverized coal combustion and is therefore conducted at low Reynolds numbers (Re = 10 and 200).

^{2}). The distance between the coal particle and the halogen lamp heater was 30 mm.

Type | Senakin coal (bituminous coal) |
---|---|

Water | 3.9% |

Ash | 12.2% |

Volatile Component | 43.3% |

Fixed Carbon | 40.5% |

velocity obtained was compared to that measured with a Pitot tube; the difference between both values was 7% or less and thus velocity measurements were deemed to be valid. At the point at which gas jetted out from the coal, the temperature of the coal particle was measured using infrared thermography (Nippon Avionics Co., Ltd., InfRec Thermo GEAR G120EX) with a spatial resolution of 340 × 240 pixels for an area approximately 100 × 70 mm, and a large measuring accuracy of ±2˚C and 2% was used for the measured temperature.

Size [mm] | Jet Velocity [m/s] | Surface Temperature [K] | |
---|---|---|---|

Sample 1 | 36 × 40 × 15 | 1.50 | 632.0 |

Sample 2 | 27 × 22 × 20 | 1.87 | 717.3 |

Sample 3 | 23 × 15 × 5 | 1.70 | 671.8 |

sample, the jet velocity is the arithmetical mean value of maximum and minimum velocity vectors of the jet, and surface temperature is that of a cell located at the center of the jet taken by an infrared thermography image when the gas had begun to release. Three samples of different sizes were found to have similar jet velocities and surface temperatures of approximately 674 K; this temperature is within the temperature range at which coal pyrolysis reactions take place.

The gas jet was experimentally confirmed to have occurred locally due to a pyrolysis reaction when the coal particle was heated and the surface temperature of the particle increased, as mentioned above. However, using this experiment it was difficult to determine the influence of the jet occurring from the particle surface on the drag forces acting on the particle. The effects of nonuniform outflows and surface temperatures on drag forces acting on the particle were therefore investigated using a numerical simulation as follows.

In this study, OpenFOAM-2.3.1 was used for computational fluid dynamics. The continuity equation, the Navier-Stokes equation, and the energy conservation equation are expressed as follows,

∂ ρ ∂ t + ∇ ⋅ ( ρ u ) = 0 , (1)

∂ ( ρ u ) ∂ t + ∇ ⋅ ( ρ u u ) = − ∇ p + ∇ ⋅ [ μ { ∇ u + ( ∇ u ) T } ] − ∇ ( 2 3 μ ∇ ⋅ u ) + ρ β ( T − T 0 ) g (2)

∂ ( ρ h ) ∂ t + ∇ ⋅ ( ρ h u ) + ∂ ( ρ K ) ∂ t + ∇ ⋅ ( ρ K u ) = ∂ p ∂ t + ∇ ⋅ ( k ∇ T ) , (3)

where ρ is density at a standard temperature, T_{0}; u is the velocity vector; p is pressure; µ is viscosity; β is the thermal expansion coefficient; T is temperature; g is the gravitational acceleration vector; h is enthalpy; K is kinetic energy; and k is thermal conductivity. An incompressible flow was assumed, and ρ in the above equations was constant.

The pressure drag coefficient C_{D}_{p} is expressed as follows,

C D p = 2 D p ρ | U | 2 S = 2 ∫ A − p n x d A ρ | U | 2 S , (4)

where D_{p} is the pressure drag; |U| is the magnitude of mainstream; S is the projected area of sphere; n_{x} is the x-direction component of unit normal vector at each point on the sphere; and A is the surface area of sphere. In this calculation, D_{p} was calculated from the following equation,

D p = ∑ i − p i r i x r A i , (5)

where p_{i} is pressure of the i-th grid on the sphere surface; r_{ix} is the x-direction component of the position vector of the i-th grid from the center of the sphere; r is the radius of the sphere; and A_{i} is the area of the i-th grid. The friction drag coefficient, C_{D}_{f}, is expressed as follows,

C D f = 2 D f ρ | U | 2 S = 2 ∫ A τ x d A ρ | U | 2 S , (6)

where D_{f} is the friction drag and τ_{x} is the x-direction component of shear stress acting on the sphere surface. This calculation assumes a surface of a virtual sphere with a radius of 1.01r. The tangential component of velocity at each grid on the virtual sphere surface, u_{ti}, was examined. Since flow velocity was zero on the (actual) sphere surface, and the distance between the virtual and the (actual) sphere surfaces was 0.01r, the friction drag was calculated from the following equation,

D f = ∑ i μ u t i 0.01 r A i . (7)

The three-dimensional flow around a rigid sphere of diameter, d, fixed in a uniform mainstream, U, was calculated. The calculation domain is shown in

The governing equations were discretized through a finite volume method, and the merged PISO-SIMPLE (called PIMPLE in OpenFOAM) algorithm was used for pressure-velocity coupling. The calculation domain was divided into approximately 320,000, nonuniformly-spaced computational cells, as shown in

Ra = g β Δ T L 3 ν α , (8)

where g is gravitational acceleration; ΔT is the temperature difference between particle surface and fluid; L is the representative length; ν is the kinematic viscosity; and α is thermal diffusivity. When the physical properties of air at normal temperature were used for β, ν, and α, and the measurement values were used for ΔT and L, an experimental Ra number with an order of 10^{5} was obtained. The Rayleigh number in the calculation was set to 10^{5}, which had the same order as that of the experimental Ra number. The end time of calculations, t_{end}, was

decided so that t_{end} satisfied |U| t_{end}/40d > 2. The flow surrounding a particle with no outflow at Re = 0.4 was calculated in advance. As the drag coefficient was in agreement with one of Stokes’ laws, the calculation method was confirmed to be valid.

The results are shown only at t_{end}, as the flow came up at a steady state. _{D}_{p} and C_{D}_{f}, with an increase in the normalized maximum outflow velocity, V. _{D}_{p} decreased in a negative x-direction outflow. As the outflow velocity increased, upstream pressure decreased, as shown in _{D}_{p} decreased until V = 1 and then increased. C_{D}_{p} gradually increased with outflow toward the y and z directions. C_{D}_{f}

also largely decreased with a negative x-direction outflow, increased with a positive x-direction outflow, but decreased in the event of y- and z-direction outflow. Figures 9(a)-(c) show the velocity magnitude and streamline when the particle

had a positive x-direction outflow, negative x-direction outflow, and positive y-direction outflow, respectively. A separated flow was restrained by the positive x-direction outflow, as shown in _{D}, and V. C_{D} decreased in the event of a negative x-direction outflow and slightly increased in the event of a positive x-direction outflow. For the y- and z-direction outflow events, C_{D} hardly changed because changes in C_{D}_{p} and C_{D}_{f} cancelled each other out.

_{D}_{p}, C_{D}_{f}, and C_{D} at Ra = 0 and 10^{5}. Both C_{D}_{p} and C_{D}_{f} increased with increases in Ra. ^{5}. The fluid flowed closely along the particle surface in the lower position at Ra = 10^{5}, which caused an increase in the friction drag forces. The lower pressure region moved upwards and expanded at Ra = 10^{5} in comparison with Ra = 0; hence, C_{D}_{p} increases when the Ra value is high.

Ra | C_{D}_{p} | C_{D}_{f} | C_{D} |
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0 | 0.47 | 0.38 | 0.85 |

10^{5} | 1.12 | 0.59 | 1.71 |

This study experimentally observed gas jets from a coal particle surface when the particle was heated and numerically investigated the effects of nonuniform outflows and particle temperatures on drag coefficients acting on a spherical particle. The experimental results show that a jet-like outflow occurred from the particle’s surface when the particle was heated to approximately 674 K, and the velocity magnitude of the outflow was approximately 1.7 m/s. From numerical results, the pressure and friction drag coefficients were found to clearly decrease when an outflow occurred in a direction against the mainstream. It was also found that when the Rayleigh number was high, i.e., the particle surface temperature was high, the drag coefficient was slightly higher than one at Ra = 0.

This work was supported by KAKENHI (25630055). We would like to thank Mr. Daiki Ajima for his help with data processing, and Mr. Yuma Onuki and Mr. Shota Iwai for their help while conducting experiments.

Watanabe, M. and Yahagi, J. (2017) Effects of Nonuniform Outflow and Buoyancy on Drag Coefficient Acting on a Spherical Particle. Journal of Flow Control, Measurement & Visualization, 5, 99-110. https://doi.org/10.4236/jfcmv.2017.54008

A: surface area of sphere

A_{i}: area of the i-th grid

C_{D}: drag coefficient

C_{D}_{f}: friction drag coefficient

C_{D}_{p}: pressure drag coefficient

d: diameter

D_{f}: friction drag force

D_{p}: pressure drag force

g: gravitational acceleration vector

g: gravitational acceleration

h: enthalpy

k: thermal conductivity

K: kinetic energy

L: representative length

n_{x}: x-direction component of unit normal vector

p: pressure

p_{i}: pressure of the i-th grid

Ra: Rayleigh number

Re: Reynolds number

r: radius

r_{ix}: x-direction component of position vector of the i-th grid

S: projected area

T: temperature

T_{0}: standard temperature

t_{end}: end time of calculation

u: flow velocity vector

U: velocity vector of uniform mainstream

|U|: magnitude of velocity vector of uniform mainstream

u_{ti}: tangential component of velocity of the i-th grid

V: normalized maximum outflow velocity

α: thermal diffusivity

β: thermal expansion coefficient

ΔT: temperature difference between particle surface and fluid

µ: viscosity

ν: kinematic viscosity

ρ: density at standard temperature

τ_{x}: x-direction component of shear stress