Cycle Performance of Turbofan Engines Explained by Pedro Baldó
Cycle Performance of Turbofan and Turbojet Engines Explained.
The most important things to notice from the plots are as follows: 1. There will be a certain maximum Overall Pressure Ratio (OPR) beyond which, no significant change in sfc (specific fuel consumption) will be noticeable. Thus the extra effort in design of leakage-free stages and minimum fabrication tolerances between hub-to-tip blade clearances with stator vanes will not be worth the cost, as there will also be an increase in the possibility of wear, vibrations and expenses due to material finishing and balancing, which will not prove economically worthwhile. 2. The same goes for the maximum temperature at the entrance to the high pressure turbine stage: not only does the NOx production dramatically increase (after 1,200 K (1,697 F) up to 2,500 K (4,040 F)), but also it is obvious that after around a Specific Thrust of 1,100 (N.s)/kg, the temperature isotherms are asymptotic with increasing sfc, (after about 0.40 kg/(hr.N), which means that any increase in temperature with increasing sfc is futile (as the Specific Thrust will not be improved by much). Any attempt to develop an engine after this point on, will be marked by its decreasing life and increasing cost. A perfect example of these, are Lifting Engines (better known as rockets or boosters), where the prime requirement is for maximum thrust per unit weight and volume, with sfc less critical because of the very low running times. These conditions can be met by a low pressure ratio unit, with a very high inlet turbine temperature (permissible because of the very short life requirement). 3. There is a point in the design of a turbofan where the overall efficiency of the cycle is dictated more by changes in the BPR (by-pass ratio) of the engine (how well the lean-or-rich fuel mixture burns in air), than on either OPR or temperature entrance to the high pressure turbine. Thus efficiency seems to be more dependent on high overall pressure ratio (OPR) at low sfc values than on temperature at those same highcompression ratios. In fact, there is a marked break –up in tendency from one to the other. Alternatively, at a certain increasing BPR, dictated by a decreasing minimum fan pressure ratio (FPR), the marginal value of sfc will be found, that produces the peak Specific Thrust at the same temperature of turbine inlet, as the maximum possible net thrust is achieved for any particular power plant at its performance condition. This
condition can greatly vary with changes in the surrounding air density and temperature, which are functions of the altitude at which the engine is operated. The volume flow rate (kg/s) that enters through the engine nacelle will depend on these conditions as well and the fan pressure ratio, also the speed of the engine relative to the surrounding air. The humidity of this air (determined from psychrometric conditions), will influence the mass of air being passed through the engine at any given steady-state condition, and have a direct impact on the cooling of the high temperature developed by the blades of the higher compressor stages and inlet turbine blades. It will also affect how well the stoichiometry of the mixture is burnt-up, and have a direct impact on the thermal efficiency and overall cycle performance of the turbofan. 4. It can be seen that Specific Thrust is strongly dependent on the value of T03, and utilization of the highest possible temperature is desirable in order to keep the engine as small as possible for a given thrust. At a constant pressure ratio, however, and increase in T03 will cause only a marginal increase in sfc. (the higher the OPR, the less the apparent sfc increase with increasing temperature). The gain in Specific Thrust is invariably more important than the penalty in increased sfc, particularly at high flight speeds where small engine size is essential to reduce both weight and drag. The effect of increasing pressure ratio, rc, is clearly to reduce the sfc. At a fixed value of T03, increasing the pressure ratio initially results in an increase in Specific Thrust, but eventually leads to a decrease; and the optimum pressure ratio for a maximum Specific Thrust increases as the value of T03 is increased up to a certain maximum point, for each particular isotherm. 5. The most notable effect of an increase in the design cruising speed is that the optimum compressor pressure ratio for maximum Specific Thrust is reduced. This is because of the larger ram compression in the intake. The higher temperature at the compressor inlet and the need for a higher jet velocity make the requirement for a higher turbine inlet temperature T03 desirable, if not essential for economic operation of justbelow-supersonic/ and subsonic aircraft. 6. Summarizing, we can state that: a). Increasing by-pass ratio (BPR) improves sfc at the expense of a significant reduction in Specific Thrust. b). The optimum fan pressure ratio increases with turbine inlet temperature up to a maximum Specific Thrust when no additional decrement in sfc will make a difference, but to start decreasing the Specific Thrust again. c). The optimum fan pass ratio (FPR) decreases with increasing by-pass ratio (BPR), for a minimum sfc and a maximum Specific Thrust. When d (sfc) / d (ST) = 0, the optimum (minimum FPR) is achieved at a given (marginal) T03. d). Any given engine, (whether it be at performance conditions or at sea level), will have two (2) thrusts, (defined as hot mass thrust and cold mass thrust), which cut the by-pass ratio line at the same sfc line. Thus for a low Specific Thrust (maximum force thrust), the bulk of this force will come from the Hot Mass Thrust (that being burnt within the main engine itself when there is no air-flow past the
engine, or relatively low, as in take-off conditions). Conversely, when the Specific Thrust is high (lowest force thrust), the bulk force pushing the engine forward comes from the Cold Mass Thrust (passing through the entrance of the nacelle all the way past through the outer diameter of the engine, out with the hot combustion gases), making this Fan Cold Thrust the driving force of the engine during maximum performance (lowest sfc) conditions. The choice of cycle parameters is dependent upon the aircraft application, and both high and low by-pass ratios are important. In the case of long range subsonic transport, sfc is of major importance and the requirement can best be met by the use of a by-pass ratio between 4.00 and 6.00, and a high overall pressure ratio (OPR), combined with a very high turbine temperature. The thrust of engines of high BPR is very sensitive to forward speed due to the large intake mass flow, and hence large momentum drag. The use of a high BPR will also cause an increase in drag because of the significant increase in frontal area, as the drag caused by the large nacelle itself will be significant. For a by-pass ratio of 5.0:1, the thrust may decrease by about 17%, as an aircraft accelerates from rest to take-off speed. By the same token, the thrust of a turbofan decreases with altitude much more rapidly than in the case of a turbojet, because of the large mass flows involved, and for this reason, if a turbojet and a turbofan are designed for the same cruise thrust, the turbofan will give a significantly higher value of take-off thrust (hot mass thrust), than the turbojet (see for example the PW 1521/1515 as compared to the PW 815/814, which share the same core). 7. Increasing speed at the same altitude with rc and T03 constant for each type of engine has the effect of increasing sfc and reducing Specific Thrust. This will lower the overall efficiency, but at numbers approaching Mach 1.0, efficiency will improve. This is because though Specific Thrust (N.s./kg) is strongly dependent on the value of T03, (utilization of the highest possible temperature at the entrance to the turbine is desirable in order to keep the engine as small as possible for any given Thrust (N)), at a constant pressure ratio, however, an increase in T03 will cause some increase in sfc. As stated earlier in point 4., the gain in Specific Thrust with increasing T03 is invariably more important than the penalty incurred by an increase in sfc. 8. To avoid falling into conjectures regarding T03 and P04/P01 the overall pressure ratio (OPR) for maximum Specific Thrust, (with reheat, P06/P01), we take a fixed fuel-to-air ratio so that both the mentioned variables remain constant. Then, for a fixed BPR, all that is left to calculate is the (FPR) fan pressure ratio, which decreases as the optimum sfc is attained over a range of Specific Thrusts. 9. The higher the altitude, the higher the increase in Specific Thrust (at the expense of a net reduction in real Thrust) and reduced sfc, due to the fall in temperature at the inlet to the hp turbine inlet T03, resulting in a lower compressor work. Thus, as the design cruising speed is increased, the optimum compressor pressure ratio for maximum Specific Thrust is reduced. This is because of the higher ram compression at the intake, improving the isentropic efficiency, (temperature dependent), and the ram efficiency, or propulsive efficiency (Froude Efficiency) (ultimately defined in terms of kinetic energy changes). As an example of this, we can see from the graph of typical turbofan and turbojet cycle performance, that the design point for a Challenger 850, for instance, lies at an overall pressure ratio of 21 and T03 of 1,800 F, but that the real value (as it
appears on the plot), is more like 14 and at 1,600 F, giving a lower Specific Thrust for a minimally increased sfc, and a higher Thrust at its operating cruise altitude (41,000 ft), flying at 0.71 Mach (economical long-haul range speed). 10. To keep calculations as simple as possible, the effect of the humidity of the air on the mass flow through the turbine has been omitted. It can have a big effect in wet, take-off conditions, but it would be beneficial, so psychrometric analysis of the air mixture does not seem crucial to take into consideration for minimal critical performance requirements. As a matter of fact, moisture in the air helps cool down the hp temperature of the turbine blades, so this serves as a thrust augmentation phenomenon, rather than a handicap in itself. Besides, denser cool air always improves the stoichiometric characteristics of the burning of the lean/rich fuel mixture, with any excess air being released at the end as additional propelling cold-mass flow. 11. At different flight conditions, both Specific Thrust and sfc will vary due to the change in air mass flow (fuel-to-air ratio), with density, pressure, temperature and humidity changes, and the variation of momentum drag with increasing forward speed. 12. For turbojets in particular (those aircraft operating with low by-pass ratios, BPR), variations of Specific Thrust and sfc with changes in altitude and Mach Number, will be more marked than for turbofans, as the lower hub-to-tip ratio of the compressor blades make turbojets extremely vulnerable to surge effects at high rotational velocities of the blades, making the last stages of a lp compressor stalling a significant (flow reversal) problem. 13. Thrust reaches a minimum with increasing altitude and increasing Mach Number, due to the decrease of ambient pressure and density, before it picks up again because of the ram pressure-ratio effect described before (at subsonic/breaching supersonic Mach Numbers this increase in thrust is substantial). Conversely, Specific Thrust increases significantly with altitude, due to the favorable effect of the lower intake temperature (as mentioned earlier), sfc increases at a decreasing rate (asymptotic) as Mach Number increases, but it is definitely lower at a higher altitude, for the same Mach Number. That being said, sfc is solely dependent upon ambient temperature, but not pressure, and hence its change with altitude is not so marked as that of thrust. It is obvious from the variation of thrust and sfc that the fuel consumption will be greatly reduced at high altitudes. 14. Drop in thrust (N) during take-off is definitely more marked for engines of higher by-pass ratio. For this reason, it is preferable to quote turbofan thrusts at a typical take –off speed, rather than at static conditions. The higher the by-pass ratio (BPR), the lower the hot thrust impulse at takeoff, so the aircraft is highly compromised by its power/weight ratio on minimum take-off distance runway needed for it to become airborne, because of the large momentum drag it needs to overcome in order to generate the necessary lift. It is also a gas - throttler during climbing, funneling as much as 1,257 kg/hr (413.57 gph )(per engine) with two (2) PW 1500 GA (that´s 827 gph required only during take-off) in the case
of a A220-300 and a whooping 5,536 kg/hr (1,821 gph) (per engine) for a A 380 with four (4) RR Trent 970-84/ 970B 84 engines mounted, (that´s 7,285 gph ! only during take-off). 15. On the efficiency of gas turbines – jet propulsion and turbofan engines. In the past, jet propulsion was perceived as a relatively inefficient power source when compared to other power plants- including piston engines at the time. Its efficiencies were as low as 15% (some of them still are !!) in the early 1950´s, today their efficiencies are in the 25% to 55% range (depending on the FPR). The limiting factor for most aircraft engines has always been the inlet turbine temperature. With new schemes of air-cooling, from thrust augmentation using liquid cooling in the combustor and reheat on the lp exit of compressor stages to mixing of cold and hot streams at the exit of hp turbine, and breakthroughs in blade metallurgy, higher turbine temperatures have been achieved. The new jet and turbofan engines have fired inlet temperatures as high as 2,600 F (1,427 C) and pressure ratios of 45 -50:1, with efficiencies of 45 % and above. The design of any modern aircraft power plant must meet the following criteria:
High efficiency High Reliability and 100% Availability. (Zero margin unexpected shutdown). Ease of service, maintainability. Ease of installation, overhaul, refurbishing and commission. Conformance to environmental standards (CAEP/6 & more stringent CAEP /10) Passing of all Black-Belt Six Sigma Reliability Centered Maintenance (RCM) Protocols. Incorporation of Auxiliary and Control Systems which have a high degree of Reliability. Flexibility to meet various service and fuel needs.
As we have already seen, the two factors that most affect high turbine efficiencies are overall pressure ratio, rc (OPR) and turbine inlet temperature, T03. The axial flow compressor, which produces the high pressure gas in the turbine, has seen dramatic changes since the pressure ratios have increased from 7:1 to 45:1 during the last 70 years. Some aircraft engines still use a combination of centrifugal and axial compressors to deliver high pressure air to the combustor before being directed to the high pressure turbine for expansion, but the right turbine-compressor “ matching ” must be achieved, mainly because the rotational velocities between the rotational components are so different. Reduction gears are many times necessary, and the right engine architecture must be sought – whether a multi-spool, two- spool, three-spool-geared-fan for turbofans or a twin spool arrangement be used. Single spool configurations were often enough for simple jet engines, but with the slight
introduction of modest BPR, the configuration for these small engines is always a challenge to adequately meet. The increase in pressure ratio increases the turbine thermal efficiency, when accompanied with the increase in turbine firing temperature. This increase is almost linear. At around an sfc of 0.25 kg/kN.hr, and 500 (N.s./kg), a sharp break in this trend occurs, and the pressure ratio increase dominates exponentially over Specific Thrust with little changes (small differential decreases, in sfc, as temperature lines soar vertically upward crossing over higher efficiency contour lines), as temperature almost remains constant for a steady-state performance of an engine (Mach Number, altitude and heat rate remaining constant). Thus increasing the pressure ratio increases the overall efficiency over an isotherm (constant temperature line), but beyond a certain value at any given firing temperature, the overall thermal cycle efficiency will dramatically decrease. If the pressure ratios are increased indefinitely, this will play unfavorably on the operating range of the turbine hp compressor, causing it to be much more intolerant to dirt build-up due to the inlet air, clogging critical passages and tolerances between stator and rotor parts, creating large drops in cycle efficiency and performance. In some cases, as mentioned before, it can lead to compressor surge, which in turn can lead to flameout and thermal choke, and even serious damage and failure of the compressor blades and the radial and thrust bearings of the different pressure stages both on the compressor and turbine of the jet or turbofan. 16. The effect of temperature is very predominant - for every 100 F (55.5 C) increase in temperature, the work output increases approximately 10%, and gives about 1.5% increase in efficiency. Higher pressure ratios and turbine inlet temperatures improve efficiencies on the simple gas turbine (Brayton-based air cycle). The net output work of any given power plant, will be limited to a 190 Btu/lb-air, 441.93 KJ/kg on a 2,600 F (1,427 C), or in the case of the RR Trent 972-84/ 972B 84 (larger than the one mentioned before), with a mass flow rate of 930 - 1, 245 kg/s, this would give a 32.95 - 96.28 MW/ engine work output at an efficiency of 36%. This engine has a 43.9 OPR and a 8.8:1 BPR, so the temperature is likely to be much lower (of the order of 1,255 F, 922K) effectively giving a 100 Btu/lb-air, 232.60 KJ/kg, or a work output between 10.57 - 31,7 MW/ engine, at a net efficiency of 30%, which is much more likely. Consider just for comparison´s sake, that a common aero-derivative steam turbine, operating on coal, would produce around 580 MW, and if it is on a COGEN (COSAG) cycle, it would probably increase its output to 820 MW, per single turbine). This plant´s net heat-rate would be around 7,500- 8,200 Btu/kW.hr of generation, which would make the plant´s net efficiency (PNE, thermal) equal to 40 -45%, as compared to the turbofan above, with a net heat-rate of 43,100 KJ/kg (18,539 Btu/lb), burning at its performance condition an sfc of 0.0576 kg/kN.hr, or 0.247 kg/KW.hr (10,646 Btu/kW.hr),(assuming a cruise velocity of 270 m/s), giving a cycle efficiency of 32 %. The difference, of course, lies in the regeneration of the ground plant (heat exchangers, cooling units requiring 0.4 – 0.5 x 106 gpm of water to increase cycle efficiency), which we don´t have the neither the luxury, much less the means-by, to have at 50,000 ft in the air. If it is true that gas turbines don´t need water to cool them down, they certainly do still need plenty of air (which doesn´t do the job as well, since the heat capacities of the working fluids are so very different). 17. Environmental Considerations – Environmental considerations are critical in the design of any turbofan, let alone turbojet, turboprop, prop-fan, unducted-fan or turbo-shaft engine. The engine´s impact on the environment must be within legal (international) limits, and thus must be
addressed by the designer carefully. Combustors are the most critical component and thus, great care, conscience and thought must be taken to design them to provide low-smoke (unburnt rich-fuel) mixture, low CO2 and low NOX, outputs. The high temperatures (above 1,200 K, (1,700 F) up to and including 2,500 K, (4,040 F)), result in the increased levels of NOx emissions from the combustor canisters in the primary zone. NOx, together with CH4 and CO2 is one of the principal green-house effect gases affecting the ozone layer at the top of the atmosphere, existing at the inversion layer between the troposphere (20,000 m) and mesosphere. In 1977, it was recognized that there were a number of ways to control oxides of nitrogen: a. b. c. d. e.
Use a rich primary zone in which little NO is formed, followed by rapid dilution in the secondary zone Use a very lean primary zone to minimize peak temperature by dilution Use water or steam admitted with the fuel for cooling the small zone downstream from the fuel nozzle Use of inert exhaust gas recirculated into the reaction zone Catalytic exhaust cleanup
Wet control became the preferred method in the 1980´s and most of the 1990´s since both dry controls and catalytic clean up were at very early stages of development. There has been a gradual tightening of the NOx limits over the years from 75 ppm down to 25 ppm, and now with the CAEP/10 limits, the new goals are to reduce these emissions down to 9 ppm by 2025. Advances in combustion technology now make it possible to control the levels of NOx production at source, eliminating the need for wet controls. Although water injection is still used, (not only for control of emissions, but also for thrust augmentation, as shall be seen ahead), dry-control combustion technology has become the preferred method for some of the major OEMs. Pratt and Whitney uses it in their PW 300, 500, 600 and 800 family of engines, and has implemented it in the commercial turbofan versions of these engine cores; the PurePower ™ Engine family of aircraft (turbofan) power plants: PW 1200G, 1500G, 1100-JM and 1400G respectively. The great dependence of NOx formation on temperature reveals the direct effect of water (or steam injection, mixed with glycols) on NO x reduction. Recent research at Papagayo Laboratories in Roanoke, VA, USA, conducted by Baldo (et al.), published in the Journal of Fluid Dynamics, No. 3,144, paper No 31,078, 06/09/2013, has shown an 85% reduction of NOx by steam or water injection with optimizing combustor aerodynamics. Temperature and pressure gradients have been monitored on selected stations downstream the cowl down through the primary into the dilution zone, for a growing laminar boundary - layer that eventually turns turbulent as the gases from the flame-tube mix with the combustion gases. In a typical combustor, the flow entering the primary zone is limited to about 10 %. The rest of the flow is used for mixing the combusted air and cooling the combustor can. The maximum temperature reached in the primary or stoichiometric zone is about 4,040 F (2,230 C), and, after mixing the combustion process with the cooling air, the temperature drops down to a flat-bottom low of 2,500 F (1,370 C).
18. On the design of the Axial Flow Turbine – There are two types of axial turbine; (1) the impulse type; (2) the reaction type. The impulse turbine has its entire enthalpy drop at the nozzle; therefore, it has a very high velocity entering the rotor. The reaction turbine divides the enthalpy drop between the nozzle and the rotor. Most axial flow turbines consist of more than one stage, the front stages are usually impulse (zero reaction), while the later stages have about a 50% reaction. The impulse stages produce about twice the output of a comparable 50% reaction stage, while the efficiency of an impulse stage is less than that of a 50% reaction stage. 19. The high temperatures that are now attainable in the turbine section are due to improvements of the metallurgy of the blades in the turbines. Development of directionally solidified blades, circuit-printed for air-bled heat exchanged within its structure, as well as the new single (monolithic) crystal blades, with the new linings (internal high-alloy linings, highly-ductile material foil spliced over a greater surface area), and the new cooling schemes (in counter-flow to the direction the air is moving over its surface) are responsible for the allowed increase in firing temperatures. The high pressure ratio in the compressor also causes the cooling air used in the first stages of the turbine to be very hot. The temperatures exiting the last stage of the high pressure compressor can reach as high as 1,200 F (649 C). This is the case of the 1500GA for the A220-300, with no need for reheating as the temperature of the hot gases decreases to 778 F (414.3 C) after expansion through the hp turbine out to the exhaust with the cold thrust + hot thrust mass of mixed gases. The cooling schemes are limited in the amount of air they can use before there is a negative effect in overall thermal efficiency, due to an increase in the amount of air used in cooling. The rule of thumb in this area is that, if you need more than 8% of the air for cooling, you are losing the advantage from the increase in the firing temperature. This is why this technique for cooling scheme is so much more effective for turbofans of higher by-pass ratios (BPR) than 8.21 and above: over 90% of the total mass air flow is cold mass flow. So in general, we should expect choked nozzle flows for these aircraft engines, and no reheat needed. These leads to a condition of maximum thrust for the lowest sfc at the operating altitude, given a fixed BPR and temperature inlet to turbine fixed. It also exhibits low FPR (Fan Pressure Ratios) ranging from 1.75 HIGH for a BPR of 8.1 to a LOW of 0.95 for a BPR of 12. Fan pressure ratio should decrease with increasing BPR, but this condition can vary, depending on the altitude the plane is flying at, the thrust the engines develop at that altitude, the air density at that particular altitude and the barometric pressure at the said altitude, assuming constant humidity, mass air flow and minimum pressure drops (velocity changes) within the combustor, at a constant Mach Number (at the designed cruise conditions). If the FPR should increase above a certain value were a lower BPR to be used, then serious modifications to the different cross-sections of the nacelle have to be made (fan, compressor section, combustor turbine, exit diffuser), in order to keep velocity pressure changes down to a minimum (minimize friction-losses that make the boundary layer increase and flow separate and become turbulent, effectively reducing the mass flow through the engine). The injection of steam (about 5% by weight of total air-mass flow) amounts to about 12% more thrust. This is why engines in humid conditions, at sea level and low temperatures, are operating at their ideal thermodynamic conditions. Most of the times, however, it is difficult to combine low temperatures with humid conditions, as air tends to become more dry (moisture condenses), as temperature drops. Only in the tropics,
can you get the combination of both, right after a heavy rainfall, when the moist-saturated air is usually quite low in temperature because of the cooling wet-bulb temperature of the moist air is almost at its dew-point temperature (saturation). If steam is injected, it must be at least 40 bar (relative to its altitude pressure) above the compressor discharge pressure. The way steam is injected must be done very carefully, so as to avoid compressor surge. These are not new concepts, and have been used and demonstrated in the past, with turbofans and turbojet aircraft alike. 20. Thrust AugmentationIf the thrust of an engine has to be increased above the original design value, several alternatives are available. Increase of turbine inlet temperature, will, as we have seen, increase Specific Thrust, and above certain Mach Number, the thrust for a given engine size. Alternatively, the mass flow through the engine could be increased without altering the cycle parameters. Both of these methods imply some redesign of the engine, and either or both may be used to uprate an existing engine. Frequently, there will be a requirement for a temporary increase in thrust: for take-off, for acceleration from subsonic to supersonic speed, or during difficult maneuvers; the problem then becomes one of thrust augmentation. Numerous schemes have been proposed, but of these, the two methods most widely used are liquid injection and reheat (also known as afterburning). Liquid injection has the double advantage, as we have already touched base, of environmentally-cleaner combustion as well as increasing the take-off thrust. Substantial quantities of liquid are required, but if the liquid is consumed during take-off, and initial climb, the weight penalty is not significantly important. Spraying water into the compressor inlet causes evaporation of the water droplets, resulting in the extraction of heat from the air, the effect of this is equivalent to a drop in compressor inlet temperature. This increases the overall pressure ratio and mass flow, resulting from the effective increase in rotational speed. In practice, a mixture of water and ethanol is used: the methanol lowers the freezing point of water, and in addition it will burn when it reaches the combustion chamber. Liquid is sometimes injected directly into the combustion chamber. The resulting temporary blockage forces the compressor to operate at a higher pressure ratio, causing the thrust to increase. In both cases, the mass of liquid injected adds to the useful mass flow, but this is a secondary effect. In the case of reheat, providing that the blades are not overstressed due to high rotational velocities involved, the temperature allowable after reheat is much higher than the turbine inlet temperature. Stoichiometric combustion is desirable for maximum thrust augmentation and final temperatures of the order of 2,000 K (3,140 F) are possible. The large increase in fuel flow required is evident from the relative temperature rises in the combustion chamber and reheat system, and the penalty in increased sfc is heavy. Assuming that a choked, convergent nozzle is used, the jet velocity will correspond to the sonic velocity at the appropriate temperature in the plane of the nozzle. If reheat is used, the gross momentum thrust, relative to that of the simple jet, will be increased in the ratio √(T06/T04), the temperatures of the outlet and inlet to the compressor, respectively.
Needless to mention, reheat should only be used for short periods, as only a fraction of increased thrust is obtained at the expense of a fourfold increase in fuel flow. Reheat offers greater gains for turbofans because of the relatively low temperature after mixing of the hot and cold streams, and the larger quantity of excess air available for combustion. It is essential for reheated turbojets to incorporate a variable area nozzle, because of the large change in density of the flow approaching the nozzle due to the large change in temperature. This is why there are nozzles fitted with reverse thrusters and hub-to-tip diameter-changing-guide vanes through the diffuser, to adapt to these sudden variations in the exhaust velocity of the gases (B737´s). Reheat will normally be brought into operation when the engine is running at its maximum rotational speed, corresponding to its maximum un-augmented thrust. The reheat system is designed so that the engine continues to operate at the same speed when the reheat is applied, and hence the nozzle must pass the same mass flow at a much reduced density. Hence the volume flow is reduced by the same measure, acquiring almost incompressible fluid characteristics. This can only be achieved if a variable area nozzle is fitted, permitting a significant increase in nozzle area. The pressure thrust will also increase due to the enlarged nozzle area. 21. Even when not in use, a reheat system incurs some penalty in pressure loss due to the presence of the burners and flame stabilizing devices. Another disadvantage of this method of thrust augmentation is that the very high jet velocities resulting from a large degree of reheat, herald the generation of a noisy exhaust. Fortunately, reheat systems as those used for the most advanced large and mid-sized business jets, such as those fitted in the Citation Longitude, Bombardier Global 7500 and 8000, the Boeing BBJ 787- 9 Max, and Gulfstreams G700, G650 ER and G280 are only required to produce about a 10 % thrust increase and the resulting increase in noise level is not as serious as might be expected. This is why the turbofans have an advantage over the turbojets in that, because of their reduced mean jet velocity, turbofans produce less exhaust noise than turbojets. At first sight it would appear that noise considerations would demand the highest possible by-pass ratio, resulting in a low jet velocity, and consequently lower FPR (fan pressure ratio). Unfortunately however, in the real turn of events, as by-pass ratio is increased, the resulting high speed of the fan leads to a large increase in fan noise. Indeed, at final approach conditions, with the engine operating at a low thrust setting, the fan noise predominates; fan noise is produced at discrete frequencies which can be much more irritating than the broad band jet-noise. The problem can be alleviated by acoustic treatment of the intake duct, avoiding the use of inlet guide vanes, and carefully choosing axial spacing between the fan rotor and stator blades. Whether you decide, as a designer, to indulge in such a choice because of the stringent space requirements, depends on the luxury you have to enjoy in making that decision, which will probably increase the cost of the final (as-built) engine.