_{1}

The article is dedicated to the issues of heat transfer, radiant heat transfer in particular, between fluidized bed of coke and water-cooled panels arranged inside it in a staggered order. The model by A.F. Chudnovsky describing radiant heat transfer in a porous body (disperse medium) as applied to coke bed has been updated.

Earlier publications by the author give a description of an energy technological boiler (ETB) for cooling coke and thermal preparation of coal blend in which use is made of heat tubes (

The ETB design is described in detail in [

fer [

Considered in the present publication is heat transfer in the coke cooling process as a factor defining the ETB vertical dimensions. The coal blend heating chamber provides an opportunity to intensify heat exchange, in particular at the expense of counter-flow of cold (280˚C) coke-oven gas present in the flue of a coke-oven battery. This method was patented by the author in co-authorship with V.M. Ljapunov [

Initial findings on coke heat transfer coefficients at its contact with water- cooled panels were made in an experiment conducted with the participation of the author in a pilot plant at the Krivorozhsky Coking Plant [

These results were included in the thermal design, the first variant of the ETB

technical project with a plan to utilize a flowing heat changer for heating water and generating superheated steam in a combined process. The technical project has developed by the Belgorodenergomash Company in 1993. According to this variant, heat transfer to coal blend was ensured by mixing coke and coal blend in a drum-type heat changer.

The parabolic nature of experimental curves in

λ c . eff = 2 ε 2 σ d eff T c 3 , (1)

where λ c . eff is effective coefficient of heat conductivity, radiant heat transfer for the most part, in a disperse medium bed;

ε is bed particles emissivity factor (blackness degree);

σ is Stefan-Boltzmann constant;

T c is average coke bed absolute temperature, ˚К;

d eff is effective particle size;

2 = φ―is total angular radiation coefficient of a prismatic pore computed by Chudnovsky for his interlump void model presented in the form of an oblong parallelepiped.

In passing over to the outer (near-wall) row of particles in coke bed, and assuming as a hypothesis that the entire temperature gradient between coke and panel wall is accounted for by the near-wall row of particles of thickness d_{eff}, then Formula (1) may be rearranged as follows:

α c . eff = λ c . eff / d eff f = 2 ε 2 σ T 3 (2)

where α c . eff is effective coefficient of coke heat transfer.

In Krivorozhsky pilot plant a coke piece (scrab) effective size was d_{eff} = 55 mm.

In further profound analysis of simulation environment of heat transfer in a pilot plant it was established that the ETB heat-exchange element model implemented in the pilot plant at the Krivorozhsky Coking Plant was slightly different from the designed (full-scale) heat changer in shape of the surface exposed to radiant heat flow: that of the panels with heat tubes and flowing heat changer tubes. Panel surface of full-scale heat changer makes by polished steel sheet (see section AA,

In the pilot plant model, the panel surface is formed of channel bars welded in row, with welding joints interrupting the heat exchange receiving surface, and so, instead of a continuous sheet (in full-scale variant) there is present a row of relatively narrow plates (see below,

α c . eff = φ ε 1 ε 2 σ T 1 3 (3)

where φ angular radiation coefficient;

ε 1 , ε 2 ―blackness degree of coke and steel sheet.

The results of α c . eff calculations by formula (2) are shown in

Let us consider the causes of this divergence. The main cause is the following. In Formula (1) the value emissivity factor ε are assumed to be equal for two opposite planes of a pore, since the formula has been derived for a closed pore inside bed. However, for an open pore located at bed edge, ε 2 should be substituted for the product of ε 1 ε 2 , where ε_{1} is coke emissivity factor, and ε_{2} is panel material emissivity factor.

For polished steel sheet in the temperature range of t = 500 - 900 ˚ C , the reference-book gives the value of ε 2 = 0.50 - 0.53 , and for coke, ε 1 = 0.80 - 0.86 . Thus the product of values ε 1 ε 2 = 0.43 , instead of ε 1 2 = 0.69 according to Chudnovsky’s canonical formula, which is 1.6 times less. Plot α_{c}_{.calc} (τ) recalculated with account for this relation is shown on curve 2 (

Let us consider further, in accordance with Chudnovsky’s model [

φ = 4 ( φ 0 + 4 ψ ) = 4 ( 0.2 + 4 ⋅ 0.075 ) = 2 (4)

where φ 0 ―angular coefficient of radiation from bottom of pore to 6-th plane;

ψ ―angular coefficient of radiation from side planes of pore to 6-th plane.

Let us consider φ as angular coefficient of radiation from bottom, with taking into account mutually disposition and sizes of two parallel planes: pore bottom (coke) and steel panel wall (

In consideration of our case, in passing to the outer (near-wall) row of coke particles, let us note also that the interlump pore becomes open from the side of the parallelepiped sixth plane, which is the surface of the water-cooled panel. Here small gap h may appear between coke and the panel due to coke particles scuffing on panel surface, mainly on coating sheet welding joins (see

Radiation from bottom of an open pore prevails among other kinds of heat exchange between coke and panel, first, due to bottom high temperature Т_{1} which is approximately 100˚C - 200˚C higher than temperature Т_{2} of the ridge contacting the water-cooled panel (see

In the reference-book [_{12} = 0.6, while the classical work by R. Ziegel and G. Howell [_{12} = 0.42 for similar surfaces. We take the average value of φ_{12,full-sc} = 0.51.

In the pilot plant model where the flat bottom of a pore radiates upon a system of narrow metal strips interrupted with welding joints, coefficient φ_{12} varies

for different sizes of rectangular strips from 0.2 to 0.5 [_{12} = 0.35. This coefficient corresponds to the physical model geometry in the pilot plant experiment. Then the full-scale/model ratio of angular radiation coefficients for bottom φ 12 нат / φ 12 мод = 0.51 / 0.35 = 1.457 .

Coefficient φ_{0} in formula (3) will be equal to φ 0 = 0.2 ⋅ 1.457 = 0.291 . By substituting this value in Formula (4), we obtain the total (integral) angular radiation coefficient φ = 4 ( 0.291 + 4 ⋅ 0.075 ) = 2.364 , instead of 2.0, i.e., φ increases by 18% (assuming that the for porous surface angular radiation coefficients ψ of the pore side planes remain unchanged). Proportionally with φ, heat transfer coefficient α_{c}_{.eff} (average for all stages) also increases by 18%. This is the primary factor of heat transfer coefficient increase in final calculations as compared with that in publication [

The calculated radiation coefficients for model and full-scale plants, also for the resulting similarity constants heat transfer coefficients for all heat changer stages, are given in

With new input data, emissivity factor К 2 = ε 1 ε 2 / ε 2 = 1.07 ; and, according to the known formula, with same areas of parallel surfaces radiating upon one

another, the reduced emissivity factor is: ε п = 1 / ( 1 / ε 1 + 1 / ε 2 − 1 ) = 0.746 for model and 0.784 for full-scale plant. Similarity constant К ″ 2 = ε full − scale / ε model = 1.05 , which closely approximates К_{2}.

The temperature factor for first stage К 3 = ( Т full − scale / Т mod ) 3 = 1.374 (see _{c}_{.eff} included in the heat transfer equation increases 2.11 times in the heat changer first stage and 1.25 times in the second and subsequent stages, as compared with the values adopted in the industrial heat exchanger thermal design [

Quantity | Value for model plant | Value for full-scale plant, industrial ETB | Full-scale/model plant ratio (similarity constant) | ||||||
---|---|---|---|---|---|---|---|---|---|

Bottom-to-panel angular radiation coefficient φ_{0} | 0.2 - 0.5; φ_{0.av.} = 0.35 | after [^{}}^{ } φ_{0av} = 0.51 | |||||||

Coke-to-panel integral angular radiation coefficient φ | 2 | 2.364 | |||||||

Integral emissivity factor ε_{1}ε_{2} | |||||||||

Reduced emissivity factor | 0.746 | 0.784 | |||||||

Temperature factor _{av.full-sc.} 920˚C, mod-800˚C] 2 stage full-sc.?T_{av}^{3}^{ }[t_{av.full-sc.}-700˚C, mod -700˚C] | 1073^{3} 973^{3 } | 1193^{3} 973^{3} | |||||||

Resulting similarity | 1 stage constant │ 2 stage | |||||||||

^{2}К for stage 1 | 51 (after experiment [ | ||||||||

for stage 2 | 47 (after experiment [ | 59.3 | |||||||

For 3, 4, 5, 6 stages Stage No. → | 3 | 4 | 5 | 6 | 3 | 4 | 5 | 6 | 3 - 6 |

α_{mod.} and α_{full-sc.} for 3 - 6 stages, W/m^{2}К | 38 | 37 | 36 | 35 | 47.3 | 46 | 45 | 44 | 1.246 |

Note: By fraction the maximum and minimum values are shown.

The total heat flux, as per the above outlay, is equal to

Q = a c eff F ( T c − T w ) = φ ε 1 ε 2 σ T 3 F ( T c − T w ) (5)

where F is effective area of coke radiating surface;

( T c − T w ) is temperature gradient between the outer (near-wall) row of coal pieces and the water-cooled panel wall.

For other designations see above.

By substituting the average values of coefficients included in Formula (5), we obtain the ETB stage 1 thermal consumption of 17.4 MW which, at steam turbine plant and turbo-generator efficiency of about 30%, converts to the ETB stage 1 electrical output of ~5.2 MW, with the aggregate stage 1 and stage 2 electrical output of about 7.2 MW. Thus the energy saving is also a feature of the given technology, that essentially increase its economic efficiency.

Into conclusion, we compare our results with other author’s experimental data (

As it can see, results of comparison with experiments by other authors are quite satisfactory.

1) Heat engineering calculations (inclusive heat balance) show that building of ETB is possible, and ETB highly effective as a heat changer. All calculations carried out using in our researching received heat transfer coefficients. There is represented comparison with Russian, Ukrainian and German author’s data about heat transfer coefficients of coke.

2) Besides coke making advantages there is profit at energy saving: attached to ETB, steam turbine plant can generate electric power about 5 - 7 MW by coke battery productivity 100 t/h.

3) Ecologic advantages of this technology are combining process of coal blend thermal preparation and coke cooling in one hermetic corpus, issued from a minimum number of overloads [

Authors | Conditions | Temperature, ˚C | α_{c.eff}, W/m^{2}K |
---|---|---|---|

Starovoit et al. | Coke bed at USTK *) | 850 | 100 |

Golubev et al. | Single piece at USTK | - | 120 |

Zabezhinsky | Processing of experimental data of model plot plant | 900 | 90 - 110 |

Zabrodsky | Fluidized bed | 1000 | 100 |

Zabrodsky | Fluidized bed, ∆T ≤ 100˚C, ultimate value | 1000 | 186 |

*Coke dry cooling plant.

4) Economic evaluations show [

Zabezhinskiy, L.D. (2017) Simulation of Radiant Heat Transfer on the Border of Coke Bed and Metal Surface of Heat Transfer Passage. Journal of Applied Mathematics and Physics, 5, 83-91. http://dx.doi.org/10.4236/jamp.2017.51009