| OCR Text |
Show Appropriate substitution in Eq. 5, as indicated, leads to the Firing Equation, Eq. 1, with the parameter, 0.0, no longer a constant but taking the output-dependent form: where: ~ = C1.o0 • Ht / If. m. This expression has not previously been reported. For our purposes in this paper we now address the problem of establishing the relationship between He determined at different stoichiometries. This relationship is obtained from Eq. 5 using the proposition based substantially on experimental observation, as the source for Eq. 10, that: the wall loss, Hw, is primarily a function of the furnace operating conditions, and is thus dominated or determined by the output conditions, as shown by Eq. 10, not by the input or firing conditions. Consequently, if we then write the firing rate and exhaust enthalpy with additional subscripts, sand E, to represent stoichiometric and excess air firing conditions, respectively, we can write: = Hf.E .(1 - hg,E / he) [12] Using Eq. 9 to substitute for hg in Eq. 12, and rearranging, we get the expression below (Eq. 13) for the ratio of the firing rates at different stoichiometries, for a given output, in terms of the Intrinsic Efficiency factors (0-0°) and maximum outputs, noting that the maximum outputs are themselves functions of equivalence ratio as given elsewhere [5]. Evaluation of the terms in brackets in Eq. 13, however, shows that their ratio approximates to unity so that we can use the approximation given in the RHS term as the ratio of the two Intrinsic Efficiency factors: Hf,E C1.o,.o . [(1 - H. / H. m.a) / (1 - 0-0/. H. / H.m,,)] a.o,. ° = [13] The Intrinsic Efficiency factors (Uo 0) written as functions of equivalence ratio become: 1 - C1.o,. ° hg.s° / he (1 + Gs}.Cp.(Tg ,. ° - To) ---------- = ---------- = ---------------------------- [14] 1 - C1.o.E ° hg,E° / he (1 + G, / ~).Cp . (Tg,E ° - To) 6 |
