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Aviation History
1949
1949 - 2040.PDF
8o6 FLIGHT, 22 December 1949 TAILPIPE REHEAT : : : without reheat are equal, whence we may write: v8 The thrust for a given mass flow under static conditions is directly proportional to thk jet velocity, and therefore: or the thrust and nozzle size increase directly as the square root of the absolute gas temperature. The fuel consumption is given by the expression: W, x Calorific Value = (W_ + W',) x Cp X (T'5 â T6) SYMBOLS USED ( ) indicates reheat conditions. A3 area, propulsion nozzle. C.H.U. Centigradeheat unit. Cp specific heat at constant pressure. CV calorific value. F thrust. 1 combustion intensity. P5 total pressure, propulsion nozzle. Tj, total-tempera-ture, propulsion nozzle. V ;, velocity, propulsion nozzle. YV aiff*mass flow.W fuel mass flow. Naturally, these figures will differ somewhat from those obtained in practice, but for the sake of comparison values are shown on Fig. 3 as they would apply to a Goblin unit. It will be seen that for an increase of 30 per cent in s.l.s. thrust a reheat specific consumption of 4.2 lb/hr/lb would be required. Fig. 3 shows that for this case an ideal so-or tpmperature ratio of 1.68 is required, al- though the actual temperature will be higher when all neces- sary adjustments for losses are made. The various values ot the inlet Mach number and tempera- ture ratio are givfin in Fig. 4 and the con- clusion to be drawn may be summarized as follows: (a) The lower the inlet Mach number the smaller is the loss in total pressure due to combustion. (b) If the inlet Mach number is in excess of 0.35 it will not be possible to ex- ceed a tempera- ture ratio of 2.3 before choking occurs at the end of the combustion zone. (c) At an inlet Mach number of 0.5, and neglecting skin friction and "cold" losses, the maximum permissible temperature ratio would be 1.46 if an increase in turbine unit temperatures is to be avoided. For the desired increase of 30 per cent, the maximum inlet Mach number would be about 0.36 which not only would give choking at the end of the tailpipe, but at a temperature ratio of 2.2 would use all the available oxygen. This condition is not wholly satisfactory and the true maximum line for the Goblin, see Fig. 5, is an inlet Mach number of 0.34. Maximum economy would be obtained by lowering the inlet Mach number, but below 0.2 this would involve very large tailpipe-diameters and the penalties of increased weight and cowlings. Further, the rate of proportionate increase between M = o.3 and M=o.2 for a 30 per cent increase in thrust is small. Small losses are inevitable in any form of air flow ducting, due to friction and eddy formation. A stable flame cannot be formed in a moving gas stream unless the flame velocity exceeds the gas velocity. Flame velocities of 25-30 ft/sec can be expected, a figure well below that of the gases in a tailpipe even after diffusion. Accordingly, some form of stabilizer must be used to form eddies, thus reducing the local velocity to a figure at which continuous burning can proceed. Inevitably such a stabilizer will introduce losses. The introduction of an obstruction in the tailpipe tends to 1-4 1-6 V8 2-0 TEMPERATURE RATIO Fig. 3. Theoretical performance of tail pipe with no losses. LIMIT FOR CONSTANTTURBINE PRESSURE l:2 1-4 1-6 18 20 TEMPERATURE RATIO Fig. 5. Theoretical increase in thrust of Goblin unit under s.l.s. conditions. increase the pressure drop from the turbine to the nozzle for d. given gas flow and, if no change is made in the nozzle size, will lead to a decrease in pressure ratio across the turbine and a drop in turbine speed. If the speed is to be restored the turbine entry temptiature must be raised by increasing the amount ot fuel, which will not only increase the total temperature of the gases at the nozzle but may give a greater thrust. To obtain a true con- ception of '' cold '' losses a common datum was necessary a::d turbine out- let conditions were selected. The correction to be applied to the ob- served thrusts to reduce them to this common level can be obtained from com- parative test bed figures with different nozzles, or it can be calculated. A conservative value of 1.5 per cent is taken as the basis on an analysis of test results, but the fitting of a variable nozzle may increase this value. PERCENTAGE TOTAL PRESSURE LOSS^ The effect of reheat at varying forward speeds is best illus- trated from the appli- cation quoted, namely,- 30 per cent reheat on the Goblin. Changes in altitude affect the pro- portion figure slightly, but in general it is less than 2 per cent and its effects have been aver- aged out Fig. 6 shows the variation in propor- tionate thrust increase lor a given temperature ratio with forward speed, at all altitudes up to 50,000ft. Some idea of the general trend of fuel consumption may be obtained from the curves in Fig. 7 show- ing variation in specific consumption at various speeds and altitudes and changes in the amount of reheat. For the combustion system to function smoothly a stable flame must be formed which is easily ignitable and will burn steadily over a wide range of mixture strengths and mass flows. The method of flame stabilization must avoid high losses when the reheat system is not in operation. Many factors are involved in the combustion process and information, gathered from many report?, indicates con- ilicting conditions. (a) The high tem- peratures a t which combus- tion is initiated aids vaporiza- tion, widens the stability limits and tends to produce a short flame. (b) The high pro- Fig. 6. Effect of forward speed on proportionate thrust at all altitudes from sea level to 50,000ft. M V6 1-8 TEMPERATURE RATIO Fig. 4. Gas flow characteristics for combustion in parallel pipe for various inlet Mach numbers. bJm < | 40-0 (X. 2: tâ UJ < 200 zUJ ec IJU 250 S00 FORWARD SPEED (m.p.h) 650
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