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Specific values of thrust and fuel consumption are promised to a prospective aircraft customer, and these are derived using procedures detailed in section "Design point performance equations" and "Simple off-design calculation". An explanation for "off-design" is given in "General". An aircraft receives pneumatic, electric and hydraulic power in return for some of the fuel it supplies. This is mentioned in "Installation Effects". These effects define the difference between the performance of an uninstalled engine (as measured on a test bed) and one installed on an aircraft. When air is taken from the compressor and used to cool the turbine it has an adverse effect on the amount of fuel required to give the required thrust. This is covered in "Cooling Bleeds". The effect of fundamental design changes to the engine, such as increased pressure ratio and turbine inlet temperature, is covered in "Cycle improvements'. Ways to increase the pressure ratio are also covered. The effects of over-fueling and under-fueling which occur with changes in thrust demand are covered in the "Transient model". There is an explanation of the Husk plot which is a concise way of summarizing the performance of the engine. The thrust available is restricted by the turbine temperature limit at high ambient temperatures as explained in the "Rated performance" sections.Design point
TS diagram
Temperature vs.Design point performance equations
In theory, any combination of flight condition/throttle setting can be nominated as the engine performance Design Point. Usually, however, the Design Point corresponds to the highest corrected flow at the inlet to the compression system (e.g. Top-of-Climb, Mach 0.85, 35,000 ft, ISA). The design point net thrust of any jet engine can be estimated by working through the engine cycle, step by step. Below are the equations for a single spool turbojet.Freestream
The stagnation (or total) temperature in the freestream approaching the engine can be estimated using the following equation, derived from the Steady Flow Energy Equation: The corresponding freestream stagnation (or total) pressure is:Intake
Since there is no work or heat loss in the intake under steady-state conditions: However, friction and shock losses in the intake system must be accounted for: Where RR is the ram recovery factor, corresponding to the loss of total pressure in the inlet.Compressor
The actual discharge temperature of the compressor, assuming a polytropic efficiency is given by: Normally a compressor pressure ratio is assumed, so:Combustor
A turbine rotor inlet temperature is usually assumed: The pressure loss in the combustor reduces the pressure at turbine entry:Turbine
Equating the turbine and compressor powers and ignoring any power offtake (e.g. to drive an alternator, pump, etc.), we have: A simplifying assumption sometimes made is for the addition of fuel flow to be exactly offset by an overboard compressor bleed, so mass flow remains constant throughout the cycle. The pressure ratio across the turbine can be calculated, assuming a turbine polytropic efficiency: Obviously:Jetpipe
Since, under Steady-State conditions, there is no work or heat loss in the jetpipe: However, the jetpipe pressure loss must be accounted for:Nozzle
Is the nozzle choked? The nozzle is choked when the throat Mach number = 1.0. This occurs when the nozzle pressure ratio reaches or exceeds a critical level: If then the nozzle is CHOKED. If then the nozzle is UNCHOKED.Choked Nozzle
The following calculation method is only suitable for choked nozzles. Assuming the nozzle is choked, the nozzle static temperature is calculated as follows: Similarly for the nozzle static pressure: The nozzle throat velocity (squared) is calculated using the Steady Flow Energy Equation: The density of the gases at the nozzle throat is given by: Nozzle throat effective area is estimated as follows:Gross thrust
There are two terms in the nozzle gross thrust equation; ideal momentum thrust and ideal pressure thrust. The latter term is only non-zero if the nozzle is choked:Unchoked nozzle
The following special calculation is required if the nozzle happens to be unchoked. Once unchoked, the nozzle static pressure is equal to ambient pressure: The nozzle static temperature is calculated from the nozzle total/static pressure ratio: The nozzle throat velocity (squared) is calculated, as before, using the steady flow energy equation:Gross thrust
The nozzle pressure thrust term is zero if the nozzle is unchoked, so only the Momentum Thrust needs to be calculated:Ram drag
In general, there is a ram drag penalty for taking air onboard via the intake:Net thrust
The ram drag must be deducted from the nozzle gross thrust: The calculation of the combustor fuel flow is beyond the scope of this text but is proportional to the combustor entry airflow and a function of the combustor temperature rise. Note that mass flow is the sizing parameter: doubling the airflow, doubles the thrust and the fuel flow. However, the specific fuel consumption (fuel flow/net thrust) is unaffected, assuming scale effects are neglected. Similar design point calculations can be done for other types of jet engine e.g. turbofan, turboprop, ramjet, etc. The method of the calculation shown above is fairly crude but is useful for gaining a basic understanding of aeroengine performance. Most engine manufacturers use a more exact method, known as True Specific Heat. High pressures and temperatures at elevated levels of supersonic speeds would invoke the use of even more exotic calculations: i.e. Frozen Chemistry and Equilibrium Chemistry.Worked example
Calculate the net thrust of the following single spool turbojet cycle at Sea Level Static, ISA, usingCooling Bleeds
The above calculations assume that the fuel flow added in the combustor completely offsets the bleed air extracted at compressor delivery to cool the turbine system. This is pessimistic, since the bleed air is assumed to be dumped directly overboard (thereby bypassing the propulsion nozzle) and unable to contribute to the thrust of the engine. In a more sophisticated performance model, the cooling air for the first row of (static) turbine nozzle guide vanes (immediately downstream of the combustor) can be safely disregarded, since for a given (HP) rotor inlet temperature it does not affect either the combustor fuel flow or the net thrust of the engine. However, the turbine rotor cooling air must be included in such a model. The rotor cooling bleed air is extracted from compressor delivery and passes along narrow passageways before being injected into the base of the rotating blades. The bleed air negotiates a complex set of passageways within the aerofoil extracting heat before being dumped into the gas stream adjacent to the blade surface. In a sophisticated model, the turbine rotor cooling air is assumed to quench the main gas stream emerging from turbine, reducing its temperature, but also increasing its mass flow: i.e. The bleed air cooling the turbine discs is treated in a similar manner. The usual assumption is that the low-energy disc cooling air cannot contribute to the engine cycle until it has passed through one row of blades or vanes. Naturally, any bleed air returned to the cycle (or dumped overboard) must also be deducted from the main airflow at the point it is bled from the compressor. If some of the cooling air is bled from part way along the compressor (i.e. interstage), the power absorbed by the unit must be adjusted accordingly.Cycle improvements
Increasing the design overall pressure ratio of the compression system raises the combustor entry temperature. Therefore, at a fixed fuel flow and airflow, there is an increase in turbine inlet temperature. Although the higher temperature rise across the compression system implies a larger temperature drop over the turbine system, the nozzle temperature is unaffected, because the same amount of heat is being added to the total system. There is, however, a rise in nozzle pressure, because the turbine expansion ratio increases more slowly than the overall pressure ratio (which is inferred by the divergence of the constant pressure lines on the TS diagram). Consequently, net thrust increases, implying a specific fuel consumption (fuel flow/net thrust) decrease. Therefore, turbojets can be made more fuel-efficient by raising the overall pressure ratio and turbine inlet temperature in unison. However, better turbine materials and/or improved vane/blade cooling are required to cope with increases in both turbine inlet temperature and compressor delivery temperature. Increasing the latter may also require better compressor materials. Also, higher combustion temperatures can potentially lead to greater emissions ofOther gas turbine engine types
Design point calculations for other gas turbine engine types are similar in format to that given above for a single spool turbojet. The design point calculation for a two spool turbojet has two compression calculations: one for the Low Pressure (LP) Compressor and one for the High Pressure (HP) Compressor. There are also two turbine calculations: one for the HP Turbine and one for the LP Turbine. In a two-spool unmixed turbofan, the LP Compressor calculation is usually replaced by Fan Inner (i.e. hub) and Fan Outer (i.e. tip) compression calculations. The power absorbed by these two "components" is taken as the load on the LP turbine. After the Fan Outer compression calculation, there is a Bypass Duct pressure loss/Bypass Nozzle expansion calculation. Net thrust is obtained by deducting the intake ram drag from the sum of the Core Nozzle and Bypass Nozzle gross thrusts. A two-spool mixed turbofan design point calculation is very similar to that for an unmixed engine, except the Bypass Nozzle calculation is replaced by a Mixer calculation, where the static pressures of the core and bypass streams at the mixing plane are usually assumed to be equal.Off-design
General
An engine is said to be running off-design if any of the following apply: :a) change of throttle setting :b) change of altitude :c) change of flight speed :d) change of climate :e) change of installation (e.g. customer bleed or power off-take or intake pressure recovery) :f) change in geometry Although each off-design point is effectively a design point calculation, the resulting cycle (normally) has the same turbine and nozzle geometry as that at the engine design point. The final nozzle cannot be over or underfilled with the flow. This rule also applies to the turbine nozzle guide vanes, which act like small nozzles.Simple Off-design Calculation
Design point calculations are normally done by a computer program. By the addition of an iterative loop, such a program can also be used to create a simple off-design model. In an iteration, a calculation is undertaken using guessed values for the variables. At the end of the calculation, the constraint values are analyzed, and an attempt is made to improve the guessed values of the variables. The calculation is then repeated using the new guesses. This procedure is repeated until the constraints are within the desired tolerance (e.g. 0.1%). Iteration variables The three variables required for a single spool turbojet iteration are the key design variables: 1) some function of combustor fuel flow e.g. turbine rotor inlet temperature 2) corrected engine mass flow i.e. 3) compressor pressure ratio i.e. Iteration constraints (or matching quantities) The three constraints imposed would typically be: 1) engine match e.g. or or , etc. 2) nozzle area e.g. vs 3) turbine flow capacity e.g. vs The latter two are the physical constraints that must be met, whilst the former is some measure of throttle setting. Note: Corrected flow is the flow that would pass through a device, if the entry pressure and temperature corresponded to ambient conditions at sea level on a Standard Day. Results Plotted above are the results of several off-design calculations, showing the effect of throttling a jet engine from its design point condition. This line is known as the compressor steady state (as opposed to transient) working line. Over most of the throttle range, the turbine system on a turbojet operates between choked planes. All the turbine throats are choked, as well as the final nozzle. Consequently, the turbine pressure ratio stays essentially constant. This implies a fixed. Since turbine rotor entry temperature, usually falls with throttling, the temperature drop across the turbine system, , must also decrease. However, the temperature rise across the compression system, is proportional to .Consequently, the ratio must also fall, implying a decrease in the compression system pressure ratio. The non-dimensional (or corrected flow) at the compressor exit tends to stay constant, because it 'sees', beyond the combustor, the constant corrected flow of the choked turbine. Consequently, there must be a decrease in compressor entry corrected flow, as the compressor pressure ratio falls. Therefore, the compressor steady state working line has a positive slope, as shown above, on the RHS. The ratio is the quantity that determines the throttle setting of the engine. So, for instance, raising intakeComplex Off-design Calculation
A more refined off-design model can be created usingPerformance model
Whatever it's sophistication, the off-design program is not only used to predict the off-design performance of the engine, but also assist in the design process (e.g. estimating maximum shaft speeds, pressures, temperatures, etc. to support component stressing). Other models will be constructed to simulate the behavior (in some detail) of the various individual components (e.g. rotor 2 of the compressor).Installation effects
More often than not, the design point calculation is for an uninstalled engine. Installation effects are normally introduced at off-design conditions and will depend on the engine application. A partially installed engine includes the effect of: a) the real intake having a pressure recovery of less than 100% b) air being bled from the compression system for cabin/cockpit conditioning and to cool the avionics c) oil and fuel pump loads on the HP shaft In addition, in a fully installed engine, various drags erode the effective net thrust of the engine: 1) an air intake spilling air creates drag 2) exhaust gases, exiting the hot nozzle, can scrub the external part of the nozzle plug (where applicable) and create drag 3) if the jet engine is a civil turbofan, bypass air, exiting the cold nozzle, can scrub the gas generator cowl and the submerged portion of the pylon (where applicable) and create drag Deducting these throttle-dependent drags (where applicable) from the net thrust calculated above gives the streamtube net thrust. There is, however, another installation effect: freestream air scrubbing an exposed fan cowl and its associated pylon (where applicable) will create drag. Deducting this term from the streamtube net thrust yields the force applied by the engine to the airframe proper. In a typical military installation, where the engine is buried within the airframe, only some of the above installation effects apply.Transient model
So far, we have examined steady state performance modelling. A crude transient performance model can be developed by relatively minor adjustments to the off-design calculation. A transient acceleration (or deceleration) is assumed to cover a large number of small-time steps of, say, 0.01 s duration. During each time step, the shaft speed is assumed to be momentarily constant. In the modified off-design iteration, is frozen and a new variable, the excess turbine power , allowed to float instead. After the iteration has converged, the excess power is used to estimate the change in shaft speed: Now: Acceleration torque = spool inertia * shaft angular acceleration = / Rearranging: = ( /( )) But: = / So: = ( / ( )) Or approximating: = ( / ( )) This change in shaft speed is used to calculate a new (frozen) shaft speed for the next time interval: = + The whole process, described above, is then repeated for the new time: = + The starting point for the transient is some steady state point (e.g. Ground Idle, Sea Level Static, ISA). A ramp of fuel flow versus time is, for instance, fed into the model to simulate, say, a slam acceleration (or deceleration). The transient calculation is first undertaken for time zero, with the steady state fuel flow as the engine match, which should result in zero excess turbine power. By definition, the first transient calculation should reproduce the datum steady state point. The fuel flow for is calculated from the fuel flow ramp and is used as the revised engine match in the next transient iterative calculation. This process is repeated until the transient simulation is completed. The transient model described above is pretty crude, since it only takes into account inertia effects, other effects being ignored. For instance, under transient conditions the entry mass flow to a volume (e.g. jetpipe) needn't be the same as the exit mass flow; i.e. the volume could be acting as an accumulator, storing or discharging gas. Similarly, part of the engine structure (e.g. nozzle wall) could be extracting or adding heat to the gas flow, which would affect that component's discharge temperature. During a Slam Acceleration on a single spool turbojet, the working line of the compressor tends to deviate from the steady state working line and adopt a curved path, initially going towards surge, but slowly returning to the steady state line, as the fuel flow reaches a new higher steady state value. During the initial overfuelling, the inertia of the spool tends to prevent the shaft speed from accelerating rapidly. Naturally, the extra fuel flow increases the turbine rotor entry temperature, . Since the turbine operates between two choked planes (i.e. the turbine and nozzle throats), the turbine pressure ratio and the corresponding temperature drop/entry temperature, , remain approximately constant. Since increases, so must the temperature drop across the turbine and the turbine power output. This extra turbine power increases the temperature rise across the compressor and, therefore, the compressor pressure ratio. Since the corrected speed of the compressor has hardly changed, the working point tends to move upwards, along a line of roughly constant corrected speed. As time progresses the shaft begins to accelerate and the effect just described diminishes. During a Slam Deceleration, the opposite trend is observed; the transient compressor working line goes below the steady state line. The transient behavior of the high pressure (HP) compressor of a turbofan is similar to that described above for a single spool turbojet.Performance software
Over the years a number of software packages have been developed to estimate the design, off-design and transient performance of various types of gas turbine engine. Most are used in-house by the various aero-engine manufacturers, but several software packages are available to the general public (e.g. NPSS http://www.npssconsortium.org, GasTurb http://www.gasturb.de, EngineSim http://www.grc.nasa.gov/WWW/K-12//airplane/ngnsim.html, GSP https://www.gspteam.com/, PROOSIS http://www.proosis.com).Husk plot
A Husk Plot is a concise way of summarizing the performance of a jet engine. The following sections describe how the plot is generated and can be used.Thrust/SFC loops
Specific Fuel Consumption (i.e. SFC), defined as fuel flow/net thrust, is an important parameter reflecting the overall thermal (or fuel) efficiency of an engine. As an engine is throttled back there will be a variation of SFC with net thrust, because of changes in the engine cycle (e.g. lower overall pressure ratio) and variations in component performance (e.g. compressor efficiency). When plotted, the resultant curve is known as a thrust/SFC loop. A family of these curves can be generated at Sea Level, Standard Day, conditions over a range of flight speeds. A Husk Plot (RHS) can be developed using this family of curves. The net thrust scale is simply relabeled , where is relative ambient pressure, whilst the SFC scale is relabeled , where is relative ambient temperature. The resulting plot can be used to estimate engine net thrust and SFC at any altitude, flight speed and climate for a range of throttle setting. Selecting a point on the plot, net thrust is calculated as follows: Clearly, net thrust falls with altitude, because of the decrease in ambient pressure. The corresponding SFC is calculated as follows: At a given point on the Husk Plot, SFC falls with decreasing ambient temperature (e.g. increasing altitude or colder climate). The basic reason why SFC increases with flight speed is the implied increase in ram drag. Although a Husk Plot is a concise way of summarizing the performance of a jet engine, the predictions obtained at altitude will be slightly optimistic. For instance, because ambient temperature remains constant above 11,000 m (36,089 ft) altitude, at a fixed non-dimensional point the Husk plot would yield no change in SFC with increasing altitude. In reality, there would be a small, steady, increase in SFC, owing to the falling Reynolds number.Thrust lapse
The nominal net thrust quoted for a jet engine usually refers to the Sea Level Static (SLS) condition, either for the International Standard Atmosphere (ISA) or a hot day condition (e.g. ISA+10 °C). As an example, the GE90-76B has a take-off static thrust of 76,000Other trends
The Husk Plot can also be used to indicate trends in the following parameters: 1) turbine entry temperature So as ambient temperature falls (through increasing altitude or a cooler climate), turbine entry temperature must also fall to stay at the same non-dimensional point on the Husk Plot. All the other non-dimensional groups (e.g. corrected flow, axial and peripheral Mach numbers, pressure ratios, efficiencies, etc. will also stay constant). 2) mechanical shaft speed As ambient temperature falls (through increasing altitude or a cooler climate), mechanical shaft speed must also decrease to remain at the same non-dimensional point. By definition, compressor corrected speed, , must remain constant at a given non-dimensional point.Rated Performance
Civil
Nowadays, civil engines are usually flat-rated on net thrust up to a 'kink-point' climate. So at a given flight condition, net thrust is held approximately constant over a very wide range of ambient temperature, by increasing (HP) turbine rotor inlet temperature (RIT or SOT). However, beyond the kink-point, SOT is held constant and net thrust starts to fall for further increases in ambient temperature. Consequently, aircraft fuel load and/or payload must be decreased. Usually, for a given rating, the kink-point SOT is held constant, regardless of altitude or flight speed. Some engines have a special rating, known as the 'Denver Bump'. This invokes a higher RIT than normal, to enable fully laden aircraft to Take-off safely from Denver, CO in the summer months. Denver Airport is extremely hot in the summer and the runways are over a mile above sea level. Both of these factors affect engine thrustMilitary
The rating systems used on military engines vary from engine to engine. A typical military rating structure is shown on the left. Such a rating system maximizes the thrust available from the engine cycle chosen, whilst respecting the aerodynamic and mechanical limits imposed on the turbomachinery. If there is adequate thrust to meet the aircraft's mission in a particular range of intake temperature, the engine designer may elect to truncate the schedule shown, to lower the turbine rotor inlet temperature and, thereby, improve engine life. At low intake temperatures, the engine tends to operate at maximum corrected speed or corrected flow. As intake temperature rises, a limit on (HP) turbine rotor inlet temperature (SOT) takes effect, progressively reducing corrected flow. At even higher intake temperatures, a limit on compressor delivery temperature (''T''3) is invoked, which decreases both SOT and corrected flow. The effect of design intake temperature is shown on the right-hand side. An engine with a low design ''T''1 combines high corrected flow with high rotor turbine temperature (SOT), maximizing net thrust at low ''T''1 conditions (e.g. Mach 0.9, 30000 ft, ISA). However, although turbine rotor inlet temperature stays constant as ''T''1 increases, there is a steady decrease in corrected flow, resulting in poor net thrust at high ''T''1 conditions (e.g. Mach 0.9, sea level, ISA). Although an engine with a high design ''T''1 has a high corrected flow at low ''T''1 conditions, the SOT is low, resulting in a poor net thrust. Only at high ''T''1 conditions is there the combination of a high corrected flow and a high SOT, to give good thrust characteristics. A compromise between these two extremes would be to design for a medium intake temperature (say 290 K). As ''T''1 increases along the SOT plateau, the engines will throttle back, causing both a decrease in corrected airflow and overall pressure ratio. As shown, the chart implies a common ''T''3 limit for both the low and high design ''T''1 cycles. Roughly speaking, the ''T''3 limit will correspond to a common overall pressure ratio at the ''T''3 breakpoint. Although both cycles will increase throttle setting as ''T''1 decreases, the low design ''T''1 cycle has a greater 'spool-up' before hitting the corrected speed limit. Consequently, the low design ''T''1 cycle has a higher design overall pressure ratio."Jet Propulsion" Nicholas Cumpsty , "Some constraints on combat aircraft engines"pp206-209, fig15.9Nomenclature
* flow area * calculated nozzle effective throat area * design point nozzle effective throat area * nozzle geometric throat area * shaft angular acceleration * arbitrary lines which dissect the corrected speed lines on a compressor characteristic * specific heat at constant pressure for air * specific heat at constant pressure for combustion products * calculated nozzle discharge coefficient * thrust coefficient * ambient pressure/Sea Level ambient pressure * turbine enthalpy drop/inlet temperature * change in mechanical shaft speed * excess shaft power * excess shaft torque * compressor polytropic efficiency * turbine polytropic efficiency * acceleration of gravity * gross thrust * net thrust * ram drag * ratio of specific heats for air * ratio of specific heats for combustion products * spool inertia * mechanical equivalent of heat * constant * constant * constant * flight Mach number * compressor mechanical shaft speed * compressor corrected shaft speed * turbine corrected shaft speed * static pressure * stagnation (or total) pressure * compressor pressure ratio * intake pressure recovery factor * gas constant * density * specific fuel consumption * stator outlet temperature * (turbine) rotor inlet temperature * static temperature or time * stagnation (or total) temperature * intake stagnation temperature * compressor delivery total temperature * ambient temperature/Sea Level, Standard Day, ambient temperature * total temperature/Sea Level, Standard Day, ambient temperature * velocity * mass flow * calculated turbine entry corrected flow * compressor corrected inlet flow * design point turbine entry corrected flow * corrected entry flow from turbine characteristic (or map) * combustor fuel flowNotes
References
* Kerrebrock, Jack L. (1992), ''Aircraft Engines and Gas Turbines'', The MIT Press, Cambridge, Massachusetts USA. {{ISBN, 0 262 11162 4 Jet engines Aircraft performance