OCR Text |
Show if the operating condition is near the baseline case. In Eq.(l), xi is the independent parameter and the superscript '0' denotes the reference condition. This expression shows the usefulness of the derivative of "1 to be obtained from the parametric study . EFFECT OF FURNACE SIZE - The furnace size affects the overall thermal efficiency and the relative importance of convection vs. radiation . The furance size was varied as shown in Table 2 where the thermal performances are com pared. Note that the aspect ratio is maintained constant, and the heat input to the furance is at a rate of 0.5 MW/m of sink length. Table 2 illlustrates the change in the thermal performance of the furnace as its length is varied. The radiative heat transfer rate to the sink decreases as the furnace size decreases. This is because the gas emissivity decreases as the furnace becomes smaller. However, the decrease in the radiative heat flux is not directly proportional to the furnace size; scaling down the furnace to one tenth of the length for the reference case decreases the radiative heat flux to on ly about one half. The convective heat flux, on the other hand, increases as the furnace size decreases. The fraction of convection to the total heat transfer (in percent) is higher for smaller furnaces: from 0.8% for the 5 m by 1 m furnace to 14.6% for the 0.5 m by 0.1 m furnace . The convective contribution is relatively small compared to radiative contribution and the total heat flux at the siI}f is smaller for the smaller furnace. Enomoto et al. performed an experimental study on a small-size furnace (3ftx3ftx Ift) and reached the conclusion that the convection heat transfer rate is only 1 per~ent of the total heat fbansfer rate. However, ~ai et al. and Lebedev et al. found that the convecttve contribution can be as high as about 30 percent or more for many cases. The discrepancy between these two findings may be attributed to high local velocity of the gas and low gas temperature for the latter two studies. Thus, it can be concluded that the radiation predominates over convection even for a small furnace . EFFECT OF FIRING ANGLE - The effects of obliquie firing are examined by changing the firing angle . The thermal performance is summarized in Table 3. For oblique firing at a downward angle of 30 degrees, the flow field reveals a large recirculation above the inlet. The flame is reduced in length in the flow direction and expanded in the transverse direction due to vigorous mixing. This results in a short flame length along the flow direction . In the given range of variation of the firing angle perturbation, heat transfer rate increases as the firing angle increases, whether upward or d.ownward . . This is due to the following factors: 1) rapId combustton of fuel close to the inlet increases the residence time for the hot gas to lose energy, and 2) the direct impingement of the hot gas on the sink . The first effect has the greater influence, while the second effect enhances both the local radiative transfer as well as the local convective transfer. 137 The optimum firing angle for maxlmlzmg the thermal efficiency was not sought for in thi s study, since it depends strongly on the thermal boundary conditions at the burner ,ort and the type of flame . However, Dzyuzer et al. obtained experimentally the optimum firing angle for a glass melting tank as 20 -23 degrees downward . For the adiabatic burner ports and a premixed flame studied here , the shorter the flame and the greater is the angle of firing , whether upward or downward, the greater is the thermal efficiency . Upward directed firing is not as effective as downward directed firing for improving the total thermal efficiency. More uniform heat flux distribution is obtained for upward directed firing. EFFECTS OF THERMAL INSULATION OF R E FR ACTO R IE S - Poor in su latin g properties of refractory walls are detrimental to the thermal performance of a furnace . Poor insulation reduces the heat transfer rate to the sink by lowering the inside surface temperature of the walls and thereby decreasing the emiSSIOn of radiation from the refractory. The optimization of the thermal conductance of the refractory walls requires the knowledge of the change of the thermal efficiency with the change in the insulation characteristics. The results of sensitivity studies are summarized in Table 4. The four perturbations of the overall heat loss coefficient from the inside of the refractory to the ambient cover the range of practical values. The calculations show little difference in the flow and combustion fields. The heat transfer rates to the sink and the temperature of the crown are higher for lower thermal conductances of the furnace walls both locally and overall (Table 4) . The heat losses to the ambient increase almost proportionally to the overall heat transfer coefficient since the refractory temperature depends little on the insulation for the range expected in practical situations. It is interesting to note that the increase in the heat transfer rate to the sink for the better insulated furnace is only slightly smaller than the decrease in the heat loss to the ambient. EFFECT OF SINK EMISSIVITY - The sink emissivity of a material depends strongly on the oxidation level , deposits etc. The emissivity is an important model parameter which controls radiation heat transfer rate to the sink. The effect of emissivity on the total (convective plus radiative) heat flux along the sink is shown in Figure 5 and the heat transfer results are summarized in Table 5. Radiation heat transfer to the sink increases with an increase in the sink emissivity. Convection heat transfer increases as the sink em issivity is decreased. This is because the temperature of the waste gas is higher when the sink emissivity is smaller. The net transfer rate to the sink is highly sensitive to the emissivity of the sink , especially when the emissivity is smaller than 0.5 . |