Showing papers by "Stuart W. Churchill published in 1981"

Fully developed laminar convection from a helical coil

Abstract: A general correlating equation has been developed for all Prandtl and Dean numbers. This expression was constructed by joining the theoretical Nusselt number for a straight tube, a theoretical asymptote for the regime of creeping secondary flow, a semi-theoretical expression for the boundary layer regime and an asymptotic value of Nu for the intervening regime of flow.The arbitrary coefficients and exponents in the model were evaluated using experimental and numerically computed values. Slightly differing sets of coefficients are required for uniform wall temperature and longitudinally uniform heating with uniform peripheral wall temperature. All prior theoretical results were for toroidal flow (zero pitch). A numerical solution was developed for helical flow (finite pitch). These results confirm the validity of neglecting pitch for tightly wound coils but suggest a generalization of the correlating equation for large pitch.

The effect of a non-uniform surface temperature on laminar natural convection in a rectangular enclosure

Abstract: Three dimensional solutions were developed for natural convection in a 2 × 1 × 1 rectangular enclosure by finite-difference calculations. Sawtooth temperature distributions with different amplitudes and orientations were imposed on the lower (2×1) surface to simulate the effect of cooling coils or jackets on the collector plate of a flat-plate solar heater. The shorter dimension of the enclosure was progressively inclined. The circulation patterns were not changed significantly by the surface temperature distributions. The variation of the Nusselt number with inclination was not changed significantly but the magnitude increased with the amplitude of the surface temperature variations for inclinations of less than 90 degrees. It is concluded that the collecting plate of a solar collector should be maintained as nearly isothermal as possible to minimize heat losses by natural convection through the air gap.

THE FORMATION OF THERMAL AND FUEL NOx FOR RADIANTLY STABILIZED COMBUSTION

Abstract: Previous studies of combustion in a refractory tube with premixed propane and air or vaporized hexane droplets in air have demonstrated the existence of multiple stationary states; thin, stable and non-oscillatory flames; and a low production of thermal NOx (5–40 ppm). These studies were all limited to an equivalence ratio of approximately 0.80. In the current work a complete range of equivalence ratios was investigated for hexane droplets, vaporized completely prior to combustion. The concentration of thermal NOx was found to peak at about 100 ppm for the stoichiometric ratio, to fall off rapidly as the equivalence ratio increased above unity and to fall off even more rapidly to less than 5 ppm as the equivalence ratio decreased to 0.6. The decrease for 1 is presumably due to the absence of free oxygen as well. Experiments were also carried out for hexane doped with 0.795% wt. nitrogen in the form of diethylamine, isobutylamine, pyridine and piperidine. The formation of NOx from these materials was found to be independent of the residence time in the post-flame zone. This result implies complete conversion within the flame front in accordance with prior conjectures. The conversion of fuel-nitrogen to NOx was essentially 100% for 0.6 1 and precipitously for 1, again in agreement with the observations of prior investigators for flat laminar flames.

A theoretical model for combustion reactions inside a refractory tube

Abstract: A kinetic and thermal model has been developed for the evaporation and combustion of a single chain of uniformly sized droplets of hexane in a turbulent stream of air inside a refractory tube. A single global rate expression is utilized for the oxidation of hexane to CO and H20, but 44 reversible, free-radical mechanisms thereafter. Adiabatic flow is postulated for the post-flame zone and plug flow throughout. An integro-differential energy balance for the wall is avoided by the use of an experimental wall temperature profile for each set of conditions. The model is restricted to external conditions such that evaporation is completed prior to ignition. Calculated concentrations of NO are in good agreement with measured values for fuel-lean mixtures over a wide range of post-flame residence times. Calculated concentrations of CO are up to twice as high as experimental values but demonstrate the same dependence on residence time and equivalence ratio, suggesting that some of the individual rate con...

The use of speculation and analysis in the development of correlations

Abstract: Speculative analysis is shown to be effective Tor the development of asymptotes which are in turn useful for the development of correlating equations. Speculation is here defined as the selective elimination of variables among a complete set, or of terms in a model. The results of such speculation must be evaluated by comparison with experimental data and theoretical solutions. This procedure is illustrated for several processes of fluid flow and heat transfer. Guidelines are developed for its efficient application. Imprecision of the available data and their failure to extend to asymptotically large and small values is found to be a limiting factor in evaluating speculations and discriminating between competitive ones.

THE PREDICTION OF NOx FORMATION FOR THE COMBUSTION OF NITROGEN-DOPED DROPLETS OF HEXANE INSIDE A REFRACTORY TUBE

Abstract: The detailed kinetic model developed by Tang and Churchill for the prediction of the combustion of premixed-gaseous or evaporated-liquid hydrocarbon fuels in a refractory plug flow burner has been extended to account for nitrogen compounds in the fuel. In the modified model the nitrogen compounds are postulated to decompose thermally to HCN in the flame front prior to oxidation. The concentrations of NO2 computed from this model for 0.795% wt. nitrogen in hexane are found to be in excellent agreement with measured values for fuel-lean mixtures doped with diethylamine, isobutylamine, pyridine and piperidine, and in fair agreement for fuel-rich mixtures up to an equivalence ratio of 1.3. The formation of NO2 from fuel-nitrogen is found to be essentially complete after 1 ms in the postflame zone. All nitrogen-containing species except N2 and NO are computed to be in negligible concentration for fuel-lean mixtures. Significant concentrations of HCN, NH3 and HN2 are predicted for the combustion of ver...

Comment on “a rational approximation of the effectiveness factor”

Abstract: (1981). COMMENT ON “A RATIONAL APPROXIMATION OF THE EFFECTIVENESS FACTOR”. Chemical Engineering Communications: Vol. 13, No. 1-3, pp. 185-187.