VALIDATION OF EQUATIONS LECKNER FOR CALCULATE THE EMIS- SIVITYOFGASCOMBUSTIONMIXTUREOBTAINEDFROMTHECOM- PARATION WITH THE METHOD OF HOTTEL AND THE APPLICA- TION ON AN INDUSTRIAL THREE BED REGENERATIVE CHAMBER COMBUSTION UNIT

This paper investigates the validity of the LECKNER relationsproposed to calculate the emissivity ofmixture of gas combustion in comparation byH.Hottel and R. J. Tucker method for enclosures with surfaces exposed to signi icant thermal radiation. The analysis is focused on a speci ic combustion chamber in a threebed regenerative oxidizer and calculates the coef icient of absorption and the corresponding thermal irradiation lux exchanges among the hot wall surfaces of the chamber. The temperature distribution and the initial composition of the gaseous mixture at the inlet plane were assumed known.


INTRODUCTION
By comparing the online measurements of the chamber wall temperatures in the speci ic plant under consideration, the method proposed by Professor H. Hottel Hottel (1967) was validated for chamber sizes comparable to the one employed in this plant.
The analysis of the waste gas composition involved the calculation of the component'spartial pressures through Dalton's law.
It was assumed that the waste gas components (vapor and carbon dioxide) were grey and followed Lambert's law.
The model of this mixture representing the waste gas assumed a composition of vapor, CO 2 and a non-reacting gas.
The energy exchange among two surfaces of the chamber were evaluated with the help of the beam attenuation constants provided by H. Hottel Hottel (1967), These How to cite this article (APA): Pittas, N., Moutsios, V., Georgiou, D. P., & Muravieva, I. (2021). Validation of equations leckner for calculate the emissivity of gas combustion mixture obtained from the comparation with the method of hottel and the application on an industrial three bed regenerative chamber combustion unit. International Journal of Engineering Technologies and Management data were supplied in the form of diagrams as functions of the parameter pL, where p represents the partial pressure of either the water vapor or the carbon dioxide, and the gaseous mixture temperature. The length L represents the mean beam length between the two surfaces under consideration. The correct value of the attenuation parameter was evaluated through a regression analysis from the experimental data provided by these graphs at a temperature 750 o C. The weak in luence of the overlapping interaction of the emission wavelengths of water vapor and carbon dioxide were added to the above analysis. A inal correction was introduced for the fact that the chamber pressure was sub-atmospheric. These experimental data were next inserted into the conservation equations for the energy exchanged among any two surfaces. These equations were essentially those provided by R.J. Tucker Tucker (19851986). The details of the theoretical model employed for the energy exchange analysis will be discussed below.
This paper compares the values of the thermal coef icients of heat absorption obtained using the classical HOTTEL method and the values from the proposed LECK-NER equation necessary to calculate the thermal luxes in the combustion chamber applied to an operating plant. for neutralizing gaseous pollutants with simultaneous energy recovery.
The calculation of the absorption coef icients of heat radiation is necessary to calculate the thermal radiation between the surfaces, between the surfaces and volumes of the gas mixture and between the volumes of gases into which the inner surface is divided and the volume of the combustion chamber by diagrams of HOTTEL or the polynomials of J. TUCKER. Validation of equations leckner for calculate the emissivity of gas combustion mixture obtained from the comparation with the method of hottel and the application on an industrial three bed regenerative chamber combustion unit The schematic depicted of the combustion chamber is shown below, Figure 1 , and this element is an integral part of the gas pollutant heat processor with simultaneous energy recovery and it's the upper part of it.

DETERMINATION OF THE MEAN BEAM LENGTH OF THE COMBUSTION CHAMBER
The evaluation of the elemental partial pressures was based upon Dalton's law and the measured gaseous concentrations. These pressures were combined with the mean beam lengths of the radiation exchanges among the chamber wall surfaces in order to evaluate the free parameter known as "the wave length" p x L (atm x ft). The prediction of the average spatial distribution of the gas temperatures inside the chamber space and the temperature and heat-lux distribution on the walls of the combustion chamber whose geometry and size as well as the enclosed gas properties are speci ied is presented in the following analysis: It was assumed that the gaseous mixture inside the chamber was equivalent to a mixture of two grey gases (Carbon Dioxide (CO 2 ) and water steam (H 2 O)) as well as a neutral gas (Nitrogen (N 2 )). The total emissivity of this gaseous mixture may be evaluated by the following relationship: Were e gi =emissivity a gi =absorption coef icient K i =attenuation coef icient L =mean beam length The emissivity for each of the active exhaust gases i (water vapor (i=1) and carbon dioxide (i=2)) was taken from the data provided in Reference Hottel (1967) as functions of the corresponding values of the wavelength parameters p w L m and p co2 L m .
The actual in situ measurements of the gaseous and the wall temperatures were conducted by a specialized company (ENCO LTD), which provided as well the gaseous concentrations and the corresponding partial pressures for the running conditions of the facility. As reported above, these data provided the basis for the evaluation of the free parameters (p i L) needed for the inal evaluation of the gaseous emissivity for an assumed constant gaseous temperature equal to 750 o C inside the entire chamber. The emissivity evaluation was based on the experimental data provided by the relevant charts in .11 (page 232), Fig 6.9 (page 229), Fig. 6.12 (page 233) of Reference Hottel (1967), with the constant temperature of the enclosed gases inside the chamber transformed into the Rankine scale, i.e. T=1841 o R a .Actually, the emissivity parameter was evaluated by the following relationship: where∆ε = The wavelength overlap parameter These charts apply for a chamber pressurized to a pressure equal to that of the surrounding atmosphere (i.e., 1 atm). When the chamber pressure differs from the atmospheric (in the plant under consideration it was regulated so that it was maintained steady at a magnitude of 0.4 atm) it was necessary to readjust the emissivities determined above by introducing correction coef icients C H 2O and C CO2 , which multiplied the corresponding two emissivities.
T he gas absorptivity and emissivity of the entire mixture were evaluated in a similar manner as the weighted sum of the corresponding contributions for each particular grey gas, i.e.

International Journal of Engineering Technologies and Management Research 61
Validation of equations leckner for calculate the emissivity of gas combustion mixture obtained from the comparation with the method of hottel and the application on an industrial three bed regenerative chamber combustion unit Were ε g =emissivity a g =coef icient of gas absorption a s =coef icient of surface absorption The emissivity-pL relationship for the gaseous mixture may be depicted as the weighted sum of the particular contributions of the gray gases participating in it and this relationship can be expressed as In other words,ε g is an increasing function of pL with an upper limit unity for a large value of the pL parameter. In this limit The mean beam length was de ined by H. Hottel Hottel (1967)to represent the radius of an equivalent hemisphere so that the incident radiation low at the center of the hemispherical base equals the average radiation lux incident to the surfaces surrounding the gas volume. According to this Reference this lux may be given by ( Fig. 7.1, page 257) H. Hottel Hottel (1967)) International Journal of Engineering Technologies and Management Research 63 Validation of equations leckner for calculate the emissivity of gas combustion mixture obtained from the comparation with the method of hottel and the application on an industrial three bed regenerative chamber combustion unit Figure 3 Mean beam length for a sphere according to Hottel Hottel (1967).

APPLICATION
T he determination of the mean beam length for every combustion chamber is fundamental for the calculation of the heat radiation exchange between the isothermal zones on which the combustion chamber is divided. This representation allows for the implementation of the theory of thermal zones. The volume of the combustion chamber under consideration is equal to We consider the dimensions of the interior walls of the combustion chamber L = 9.15m = 30 ft. Elongated and the other two sides each 3.05 m = 10ft. So, the geometric volume of the combustion chamber is And the area surrounding it equals The mean beam length is obtained This empirical formula applies to rectangular shaped combustion chambers and so inallyL m = 7.54ft, and because the percentage of LPG combustion gases in the combustion chamber during the passage of 22,000 Nm 3 /h was measured to con-tain19.8% O2, 0.6% CO2, 6% H2O.

CALCULATION EMISSIONS, OF WATER VAPOR AND CO 2 AND ITS MIXTURE IN THE COMBUSTION CHAMBER AND CALCULATION OF ABSORPTION COEFFICIENTS
Dalton's law gives the partial pressures and multiplying the mean beam length corresponding to the orbit to obtain the necessary pL parameters for each component of the waste gas mixture to calculate the corresponding CO 2 and water vapor emissions.
We look at Hottel's tables for CO2 and water vapor emission with PL parameter. The tables are applicable to radiant gases at atmospheric pressure. If they do vary the atmospheric pressure then the corrective factor must be taken into account.
We consider the mixture of constituent gases as a gray gas following Lambert's law so as to reduce the emission calculations in the existing diagrams.
We're counting now The water vapor emission is calculated from Chart 6-1 and equals From chart 6.3 become ∆ε where we have International Journal of Engineering Technologies and Management Research Validation of equations leckner for calculate the emissivity of gas combustion mixture obtained from the comparation with the method of hottel and the application on an industrial three bed regenerative chamber combustion unit become the value of ordinates is equal to 0.9.
The parameter value in the curves with a corresponding trajectory is calculated by de ining the following product: Replacing the values of∆εand theε g H 2 O,2L m = 0.202 ofε g CO 2 ,2L m =0.075 becomes Because the combustion chamber is at a 0.4 atm pressure, we must multiply each of the terms H 2 O and CO 2 by the corresponding correction coef icients resulting from diagrams 8 and 9 (Source Engineering Heat Transfer / Rathore, KapunoFig.13.56, Fig.13.57, Fig.13, respectively, in which the path length is expressed by atm.m rather than atm.ft (as depicted in Fig. 6-10 Hottel) by one atmosphere at a pressure of 0.4 atm.
Further we have  Validation of equations leckner for calculate the emissivity of gas combustion mixture obtained from the comparation with the method of hottel and the application on an industrial three bed regenerative chamber combustion unit we obtain It should be noted that the overall emissivity of the gas mixture is less than the sum of the individual emissions (as if each of the two gases were emitted separately) by a correction factor ∆ε, because each gas behaves as a duplicate in areas between 2.7 m and 15m. Thus, the total radiation is reduced and this correction factor is drastically reduced at temperatures above 1200 o K. And so, because From the diagrams depicted on the Figures4και5we obtain By similar way how calculated K 1 we will calculate K 2 andα g,2 .
And because From diagrams depicted on the igure8 and 9 because the pressure is 0.4 atm becomes and so, we obtain

CALCULATION OF ABSORPTION COEFFICIENTS BY LECKNER
Another way to calculate the absorption coef icients with a large approximation is given algebraically by Leckner's relations.

International Journal of Engineering Technologies and Management Research 69
Validation of equations leckner for calculate the emissivity of gas combustion mixture obtained from the comparation with the method of hottel and the application on an industrial three bed regenerative chamber combustion unit In order to calculate the vapor emissions as well as the CO 2 and therefore the absorption coef icients we will use another algebraic way of calculating the Leckner equation.
Coef icients of the LECKNER equation for water vapor and CO 2 We consider that N 2 has no signi icant emissivity, so we will calculate according to the model the water vapor and carbon dioxide emissivities. c ij ( T 1000 ) i whereT measuredbyK 0 , p w partial pressure of vapor measured by bar and the wave length L e by cm. Int his case L e =7.54ft/3.05ft/m=2.15m=215cmand 1atm=1,01325bar Calculate now ε w the temperature of combustion chamber is 750 0 C= 1023 0 K For j=0 For j=1 For j=2 consequently becomes Calculate now the emissivity ε co2 International Journal of Engineering Technologies and Management Research 71 Validation of equations leckner for calculate the emissivity of gas combustion mixture obtained from the comparation with the method of hottel and the application on an industrial three bed regenerative chamber combustion unit