12.3.1 Recovery Factor, RF

A bare engine on a ground test bed inhales free stream air directly and performs at its best. In contrast, an installed engine in an aircraft can only inhale the airflow diffused through the nacelle/intake duct incurring losses in the pressure head, expressed as recovery loss, defined next.

Intake Pressure Recovery Factor (RF),

12.6

where subscript ‘∞’ represents free stream condition and subscript ‘1’ represent fan face.

For pod mounted high subsonic jet aircraft at cruise Mach, RF is about 0.98.

For fuselage mounted side intake with engine at aft end, at subsonic Mach, RF is about 0.94–0.96.

For nose mounted pitot type long intake with engine at aft end, at subsonic Mach, RF is about 0.92–0.94.

At supersonic speed, shock loss has to be added (see Section 12.8.2).

12.4.1 Simple Straight‐Through Turbojets

The most elementary form of gas turbine is a simple straight‐through turbojet, as shown schematically in Figure 12.5. In this case, the intake airflow goes straight through the whole length of the engine and comes out at a higher velocity and temperature after going through the processes of compression, combustion and expansion. It burns like a stove under pressurised environment. The readers may note the waisting of the airflow passage as a result of compressor reducing the volume while the turbine expands. Typically, at long range cruise (LRC) condition, the free stream tube far upstream is narrower in diameter than at the compressor face. As a result, airflow ahead of the intake plane slows down as a pre‐compression phase.

Components associated with the thermodynamic processes within the engine are assigned with station numbers as given in Table 12.3.

Overall engine efficiency could be improved if the higher energy of the exhaust gas of a straight through turbojet is extracted through additional turbine that can drive an encased fan in front of a the compressor (when it is called turbofan engine) or a propeller (when it is called turboprop engine).

12.4.2 Turbofan – Bypass Engine (Two Flow – Primary and Secondary)

The energy extraction through the additional turbine lowers the rejected energy at the exhaust resulting in lower exhaust velocity, pressure and temperature. The additional turbine drives a fan in front of q compressor. A large amount of air mass flow through the fan provides thrust. The intake air mass flow is split into two streams (Figure 12.6), the core airflow passes through the combustion chamber of the engine as primary flow and is made to burn while the secondary flow through the fan is bypassed (hence also called bypass engine) around the engine and remains as cold flow. It is for this reason that primary flow is also known as hot flow and the secondary bypassed flow as cold flow. Figure 12.6b gives a schematic diagram of a turbofan engine (top Figure 12.6a is that of bare PW 2037 turbofan). Lower exhaust velocity reduces engine noise. At the design point (LRC), lower exhaust pressure permits the nozzle exit area to be sized to make exit pressure equal to ambient pressure (perfectly expanded nozzle), unlike simple turbojets that can have higher exit pressure.

The readers may note that the component station numbering system follows the same pattern as for the simple straight‐through turbojet. The combustion chamber in the middle maintains the same numbers of 2–3. The only difference is the fan exit is with subscript of ‘f’. Intermediate stages of compressor and turbine are primed (′).

Typically, the BPR – (Eq. 12.2) for commercial jet aircraft turbofans (high subsonic flight speed of less than 0.98 Mach) is around 4–6 with large fan face diameter and are invariably pod mounted. Of late, turbofans for the new B787 have exceeded a BPR of 8. Airbus 350 and Bombardier C‐series turbofans have a BPR = 12. For military application (supersonic flight speed up to Mach 2.5), the BPR is around 1–3. Lower BPR keeps the fan diameter smaller and hence lowers frontal drag so it can be integrated within fuselage.

Multi‐spool (shaft) drive shafts offer better efficiency and response characteristics, mostly with two concentric shafts. The shaft driving the low‐pressure (LP) section runs inside the hollow shaft high‐pressure (HP) section – see the diagram in Figure 12.6. Three shaft turbofans have been designed, but most of the current designs have a twin spool. The recent advent of a geared turbofan offers better fuel efficiency.

Lower fan diameter compared to the propeller permits higher rotational speed and offers scope for having a thinner aerofoil section to extract better aerodynamic benefits. The higher the BPR, the better the fuel economy. Higher BPR demands a larger fan diameter when reduction gears may be required to keep the rpm at a desired level. Ultra‐high bypass ratio (UHBPR) turbofans approach the class of ducted fan or ducted propeller or propfan engines. Such engines have been built but their cost versus performance is yet to break into the market arena.

12.4.3 Three Flow Bypass Engine

While the two streams (primary hot core flow and the secondary cold high bypass flow) offer good fuel economy for the high subsonic transport category aircraft operation, they are not is suitable for supersonic military application due to having a large fan face diameter generating high drag. High BPR specific thrust is considerably lower than low bypass ratio of military jet engines. Of current interest for supersonic combat class aircraft engine is pursuing the concept of the adaptive three‐stream bypass jet engine. This improves the fuel economy while keeping the front fan face diameter relatively small.

The adaptive three‐stream jet engine has the third outer flow as a second layer of bypass over the conventional two stream bypass turbofan. The adaptive three‐stream jet engine is a variable cycle engine, because the third airflow stream has a movable internal inlet door that can adjust the second bypass flow during the flight to suit the mission demand. The outer cold third air stream also serves for thermal management of the hot combustion product primary core flow and abates the noise level as well. This arrangement shows improved fuel economy while retaining high specific thrust suiting supersonic military combat aircraft operation. This type of engine is currently in the developmental stage with a technology demonstrator running under test.

12.4.4 Afterburner Engines

The AB is another method of thrust augmentation exclusively meant for supersonic combat category aircraft (the Concorde is the only civil aircraft to use an AB). Figure 12.7 gives a cutaway diagram of a modern AB meant for combat aircraft.

The simple straight‐through turbojets or low bypass ratio turbofans have a relatively small frontal area to give low drag and have excess air in the exhaust flow. If additional fuel can be burned in the exhaust nozzle beyond the turbine exit plane, then additional thrust can be generated to propel the aircraft at a considerably higher speed and acceleration, thereby also giving the chance to improve propulsive efficiency. However, the reason for using AB arises from the mission demand, for example, at takeoff with high payload, acceleration to engage/disengage during combat/evasion manoeuvres and so on. Mission demand overrides the fact that there is a very high level of energy rejection in the high exhaust velocity. The fuel economy with AB degrades – it takes 80–120% higher fuel burn to gain 30–50% increase in thrust. Nowadays, most supersonic aircraft engines have some BPR when afterburning can be done within in the cooler mixed flow past the turbine section of the primary flow.

12.4.5 Turboprop Engines

Lower speed aircraft could use propellers for thrust generation. Therefore, instead of driving a smaller encased fan (turbofan), a large propeller (known as a turboprop) can be driven by gas turbine to improve efficiency as the exhaust energy can be further extracted to very low exhaust velocity (nearly zero nozzle thrust) (Figure 12.8). There could be some residual jet thrust left at the nozzle exit plane when it needs to be added to the propeller thrust. The nozzle thrust is converted into HP and together with the shaft horse power (SHP) generated; it becomes Equivalent Shaft Horse Power (ESHP).

However, a large propeller diameter would limit rotational speed on account of both aerodynamic (transonic blade tips) and structural considerations (centrifugal force). The relative velocity with respect to the propeller blade is the resultant velocity (Figure 12.24) of aircraft speed and the propeller rpm can reach a transonic level when propeller efficiency suffers on account of compressibility effects and possibly trailing edge separation as a result of local shock and boundary layer interaction. Heavy reduction gears are required to bring down propeller rpm to a desirable level. Propeller efficiency drops when aircraft operate at flight speeds above Mach 0.7. For shorter range flights, the turboprop's slower speed does not become time critical to the user and yet it offers better fuel economy. Military transport aircraft are not as time critical as commercial transport and may use a turboprop (e.g. A400). Figure 12.8 gives a schematic diagram of typical turboprop engines. Modern turboprops have up to eight blades (see Section 12.10) allowing reduction of diameter size and operation at a relatively higher rpm. Advanced propeller designs permit aircraft to fly above Mach 0.7.

12.4.6 Piston Engines

Most of the aircraft piston engines are reciprocating types (positive displacement – intermittent combustion), the smaller ones are air‐cooled two‐stroke cycle – the bigger ones (typically over 200 HP) are liquid‐cooled four‐stroke cycle. There are a few rotary type positive displacement engines (Wankel) – in principle, they very attractive but they have some sealing problems. Cost wise, the rotary type positive displacement engines are not popular yet on account of these sealing problems. Cost goes down with an increase in the number of production. Figure 12.9 shows aircraft piston engine with its installation components.

To improve high altitude performance (having low air density) supercharging is used. Figure 12.9 shows vane supercharging type for pre‐compression. Also aviation fuel (AVGAS – petrol) differs slightly from automobile petrol (MOGAS). Of late, some engines for the home‐built category are to use MOGAS. Recently, small diesel engines have been introduced on the market.

Piston engines are the oldest type to power aircraft. Over the life‐cycle of an aircraft, gas turbines prove more cost effective for engine sizes over 500 HP. Currently, general aviation aircraft are the main users of piston engines. Recreational small aircraft are invariably powered by piston engines.

12.6.1 Simple Straight‐Through Turbojet Engine – Formulation

Consider a control volume (CV – dashed line – note the waist like shape the bare simple turbojet) representing a straight through axi‐symmetric turbojet engine as shown in Figure 12.12. The CV and the component station numbers are as per the sketch and convention shown in Figure 12.6. Gas turbine intake starts with a subscript 0 or ∞ and ends at the nozzle exit plane with subscript 5 or e. Free stream air mass flow rate (MFR), , is inhaled into the CV at the front face perpendicular to the flow and fuel MFR (taken from the onboard fuel tank) is added at the combustion chamber and the product flow rate is exhausted out of the nozzle plane perpendicular to flow. It is assumed that inlet face static pressure is p_∞, which is fairly accurate. Pre‐compression exists but for ideal consideration it has no loss.

No flow crosses the other two lateral boundaries of the CV as it is aligned with the walls of the engine. Force experienced by this CV is the thrust produced by the engine. Consider a cruise condition with aircraft velocity of V_∞. At cruise, the demand for air inhalation is considerably lower than at takeoff. Intake area is sized in between the two demands. At cruise the intake stream tube cross‐sectional area is smaller than the intake face area – it is closer to that of exit plane area, A_e (gas exiting at very high velocity). Since this is under ideal conditions, there is no pre‐compression loss, station 0 may be considered as having free stream properties with subscript ∞.

From Newton's second Law,

Applied force, F = rate of change of momentum + net pressure force.

Note that the momentum rate is given by the MFR.

Therefore,

12.7

Net pressure force between the intake and exit planes = (p_eA_e − p_∞A_∞). The axi‐symmetric side pressure at the CV walls cancels out. Typically, at cruise, sufficiently upstream A_e ≈ A_∞.

Therefore,

12.8

Then

And V_∞ = Ram drag (with a −ve sign, it has to be drag). It is the loss of momentum seen as drag on account of slowing down of the income air as ram effect.

This gives,

A_e (p_e − p_∞) = pressure thrust. In general, subsonic commercial transport turbofans have convergent nozzle, its exit area is sized in a way that in cruise, p_e ≈ p_∞ (known as a perfectly expanded nozzle). It is different for military engines especially with afterburning, when p_e > p_∞, thus requiring a convergent‐divergent nozzle.

For a perfectly expanded nozzle (p_e − p_∞),

12.9

Further simplification is possible by ignoring the effect of fuel flow, , since  » .

Then the thrust for perfectly expanded nozzle is,

12.10

At sea level static takeoff thrust (T_SLS) ratings V_∞ = 0,

which makes,

12.10a

The expression indicates that the thrust increase can be achieved by increasing intake air MFR and/or increasing exit velocity.

Equation 12.4 gives propulsive efficiency,

12.11

Clearly, a jet propelled aircraft with low flight speed will have poor propulsive efficiency, η_p. Jet propulsion is favoured for aircraft flight speed above Mach 0.6.

The next question is where does the thrust act? Figure 12.13 [1] shows a typical gas turbine where the thrust is acting. It is all over the engine and the aircraft realises the net thrust transmitted through the engine‐mount bolts.

12.6.2 Bypass Turbofan Engines – Formulation

Typically, in this book a long duct nacelle is preferred to obtain better thrust and fuel economy offsetting the weight gain as compared to short duct nacelles (see Figure 12.17). Note that pressure rise across fan (secondary cold flow) is substantially lower than pressure rise of the primary airflow. Also note that the secondary airflow does not have heat addition as in the primary flow. The cooler and lower exit pressure of the fan exit, when mixed with the primary hot flow within the long duct, brings the final pressure lower than the critical pressure (V_e just reaches sonic speed) favouring a perfectly expanded exit nozzle (p_e = p_∞). Through mixing, there is reduction in jet velocity, which offers a vital benefit of noise reduction to meet the airworthiness requirements. A long duct nacelle exit plane can be sized to expand perfectly.

Primary flow has a subscript designation of p and secondary flow has a subscript designation of s. Therefore, F_p and V_ep stand for primary flow thrust and exit velocity, respectively, and F_s and V_es stand for bypass‐flow thrust and its exit velocity, respectively. Thrust (F) equations of perfectly expanded turbofans are separately computed for primary and secondary flows, and then added to obtain the net thrust, F, of the engine (perfectly expanded nozzle, i.e. p_e = p_∞).

Specific thrust in terms of primary flow becomes (f = fuel to air ratio)

12.12

If fuel flow is ignored, then

12.13

or

12.14

At a given design point, that is, BPR, flight speed V_∞, fuel consumption, and are held constant. Then the best specific thrust and KE can be found by varying the fan exit velocity for a given V_ep. This is when setting their differentiation with respect to V_es equal to zero. (This may be taken as trend analysis for ideal turbofan engines. The real engine analysis is more complex.)

Then by differentiating Eq. 12.13,

12.15

And Eq. 12.14 becomes

12.16

Combine Eqs. 12.15 and 12.16,

And since BPR ≠ 0, then the optimum has to be when

12.17

that is, the best specific thrust is when the primary (hot core flow) exit flow velocity equals the secondary (cold fan flow) exit flow velocity.

Equation 12.4 gave turbojet propulsive efficiency, η_p = for a simple turbojet engine, but in the case of a turbofan there are two exit plane velocities: one each for hot core primary flow (V_ep) and cold fan secondary flow (V_es). Therefore, an equivalent mixed turbofan exit velocity (V_eq) could substitute for V_e in Eq. 12.4. Fuel flow rates are small and can be ignored. The equivalent turbofan exit velocity (V_eq) is obtained by equating the total thrust (perfectly expanded nozzle) as if it is a turbojet engine with total mass flow ( + ):

Thus

12.18

Then turbofan propulsive efficiency,

12.19

Large engines could benefit from weight savings by installing short duct turbofans.

12.6.3 Afterburner Engines – Formulation

Figure 12.14 gives a schematic diagram with the station numbers for the afterburning jet engine. To keep numbers consistent with the turbojet numbering system, there is no difference between stations 4 and 5 representing turbine exit condition. Station 5 is the start and station 6 is the end of afterburning. Station 7 is the final exit plane. Figure 12.14 also shows the real cycle of afterburning in a T‐s diagram.

Afterburning is deployed only in military vehicles (except in the supersonic Concorde aircraft) as a temporary thrust augmentation device to meet mission demand at takeoff and/or for fast acceleration/manoeuvre to engage/disengage in combat. Afterburning is applied at full throttle by flicking a fuel switch. The pilot can feel its deployment with sudden increase in ‘g’ level in the flight direction. The ground observer would notice a sudden increase in noise level, which can exceed the physical threshold. Afterburning glow is visible at the exit nozzle, in darkness it is depicted as a spectacular plume with supersonic expansion diamonds. In the absence of any downstream rotating machines, the afterburning temperature limit can be raised to around 2000–2200 K at the expense of a large increase in fuel flow (a richer fuel/air ratio than in the core combustion).

The afterburning exit nozzle would invariably run choked (at sonic speed) and would require a convergent‐divergent nozzle to make supersonic expansion to increase gain in momentum for thrust augmentation. Typically, to gain a 50% thrust increase, fuel consumption increases by about 80–120%. That is why it is used for short periods, not necessarily in one burst. Interestingly enough, afterburning in bypass engines is an attractive proposition because afterburning inlet temperature is lower. In fact, all modern combat category engines use a low BPR of 1–3 resulting in a smaller frontal area suited to in‐fuselage installation.

Losses in afterburning exit nozzles are high – the flame holders and act as obstructions. It is desirable to diffuse flow speed at the afterburner to around 0.2–0.3 Mach – this results in a small bulge in the jet pipe diameter around that area. The combat aircraft fuselage has to house this.

12.6.4 Turboprop Engines – Formulation

Section 12.4.4 described turboprops. It has considerable similarity with turbojets/turbofans except that the high energy of exhaust jet is utilised to drive a propeller by incorporating additional low‐pressure turbine stages as shown in Figure 12.8. Thrust developed by the propellers is the propulsive force for the aircraft. There could be a small amount of residual thrust left at the nozzle exit plane that should be added to the propeller thrust. The relation between thrust power (T_P) and gas turbine shaft power (SHP) is related to the propeller efficiency, η_prop as:

12.20

ESHP is a convenient way to define the combination of shaft and jet power as follows:

12.21

Evidently, aircraft at the static condition will have ESHP = SHP, as the small thrust at the exit nozzle is not utilised. As speed increases, ESHP > SHP as long as there is some thrust at the nozzle. Power specific fuel consumption (psfc) and specific power (weight‐to‐power ratio) are expressed in terms of ESHP.

12.7.1 Subsonic Civil Aircraft Nacelle and Engine Installation

The nacelle is a multi‐functional system comprising of (i) inlet, (ii) exhaust nozzle, (iii) TR, if required and (iv) noise suppression system. The design aim of the nacelle is to minimise associated drag, noise and provide airflow smoothly to the engine at all flight conditions.

As of today, except for Concorde, all civil aircraft are subsonic with a maximum speed less than Mach 0.98. All subsonic aircraft use some form of pod mounted nacelle, in a way this has become generic in design. Figure 12.16 shows a turbofan installed in a civil aircraft nacelle pod. The under‐wing nacelle is the current best practice but for smaller aircraft, ground clearance issues force a nacelle to be fuselage mounted. An over‐wing nacelle like that of VFW614 is a possibility yet to be explored properly (Honda jet aircraft have reintroduced it).

There are two types of podded nacelles. Figure 12.17a shows a long duct nacelle where both the primary and secondary flows mix within it. The mixing increases the thrust and reduces the noise level compared to the short duct nacelles, possibly compensating the weight gain through fuel and cost saving. Figure 12.17b shows short duct nacelle in which the bypassed cold flow does not mix with the hot core flow. The advantage is that there is considerable weight saving by cutting down the length of the outside casing of the nacelle by not extending up to the end. Short duct nacelle length can vary.

The aircraft performance engineers are to substantiate to the certification authorities that the thrust available from the engine after deducting the losses is sufficient to cater for the full flight envelope as specified. In hot and high altitude conditions, it can become critical at aircraft takeoff if (i) the runway is not sufficiently long and/or at high altitude, (ii) if there is an obstruction to clear or (iii) ambient temperature is high. In that case, the aircraft may takeoff with lighter weight. Airworthiness requirements require that the aircraft has to maintain a minimum gradient (Chapter 15) at takeoff with the critical one engine inoperative. Customer requirements could demand more than the minimum requirements.

12.7.2 Turboprop Integration to Aircraft

The turboprop nacelle is also a multi‐functional system comprising of (i) inlet, (ii) exhaust nozzle and (iii) noise suppression system. Thrust reversing can be achieved by changing the propeller pitch angle sufficiently. There are primarily two types of turboprop nacelles as shown in Figure 12.18. The scoop intake could be above or below (as a chin) the propeller spinner. Interestingly, quite a few turboprop nacelles have an integrated undercarriage mount with storage space in the same nacelle housing as can be seen in Figure 12.18a. The other kind is with annular intake as shown in Figure 12.18b. Installation losses are of the same order as discussed in the turbofan installation.

Turboprop nacelle position is dictated by the propeller diameter. The key geometric parameters for turboprop installation are shown in Figure 12.19.

Figure 12.19a shows wing mounted turboprop installation. Overhang should be as far forward the design can take, like that of turbofan overhang to reduce interference drag. For high wing aircraft, the turboprop nacelle is generally under the wing, like the Bombardier Q400 aircraft. For low wing aircraft, nacelles are generally over the wing to get propeller ground clearance. Both types can house the undercarriage. The propeller slipstream assists lift and has a strong effect on static stability, flap deployment aggravates the stability changes. Depending on the extent of wing incidence with respect to the fuselage, there is some angle between wing chord line and the thrust line – typically from 2 to 5°.

A fuselage mounted propeller‐driven system arrangement is shown in Figure 12.19b. Note the angle between the thrust line and the wing chord line as it is with wing mounted propeller nacelle. Sometimes, propeller axis is given about a degree down inclination with respect to fuselage axis. This assists longitudinal stability. To counter the propeller slipstream effect, an inclination of a degree or two in the yaw direction can be given. Otherwise, the V‐tail can be given such inclination to counter the effect.

Piston engine nacelles on the wing follow the same logic. The older designs had more closely coupled installations.

12.7.3 Combat Aircraft Engine Installation

A combat aircraft has engines integral with the fuselage, mostly buried inside but in some cases, with two engines, they can bulge out to the sides. Therefore, pods do not feature unless they are required for having more than two engines on a large aircraft. Figure 12.20 shows a turbofan installed on to a supersonic combat aircraft.

The external contour of the engine housing is integral to fuselage mouldlines. Early designs had the intake at the front of the aircraft; a pitot type for a subsonic fighter (Sabrejet F86 etc.) and with a movable centre body for a supersonic fighter (MIG 21). The long intake duct snaking inside the fuselage below the pilot seat incurs high losses. Side intakes overtook nose intake designs. A possible choice for side intakes is given in Section 5.12 – primarily, they are side or chin mounted. A plate is kept above the fuselage boundary layer on which the intake is placed. A centre body is required for aircraft speed capability above Mach 1.8, otherwise it can be a pitot intake.

Aircraft performance engineers must be given the following data to generate the installed engine performance.

1. Intake losses plus losses arising from supersonic shock waves and the duct length.
2. Exit nozzle losses. Military aircraft nozzle design is complex.
3. Additional losses at the intake and nozzle on account of suppression of exhaust temperature for stealth.
4. Compressor air‐bleed for the ECSs, for example, cabin air‐conditioning and pressurisation, de‐/anti‐icing and any other purpose.
5. Power off‐takes from the engine shaft to drive the electric generator, accessories, for example, pumps and so on.

Military aircraft have excess thrust (with or without afterburner) to cater for hot and high‐altitude conditions and operating from short airfields, and they are capable of climbing at steeper angles than civil aircraft. When thrust/weight ratio is more than 1, then the aircraft is able to climb up vertically.

12.8.1 Civil Aircraft Subsonic Intake Design

Engine mass flow demand varies a lot as shown in Figure 12.21. To size intake area, the reference cross‐section of incoming air mass stream tube is taken at the maximum cruise condition as shown in Figure 12.21a, when it has cross‐sectional area almost equal to that of highlight area (i.e. A_∞ = A₁). The ratio of MFR in relation with the reference condition (air mass flow at maximum cruise) is a measure of spread the intake would encounter. At the maximum cruise condition, MFR = 1 as a result of A_∞ = A₁ (critical operation). At normal cruise conditions the intake air mass demand is lower (MFR < 1 (sub‐critical operation), shown in Figure 12.21b). At the maximum at takeoff rating (MFR > 1), intake air mass flow demand is high and the streamline patterns is shown in Figure 12.21c. Variation in intake mass flow demand is quite high.

If the takeoff airflow demand is high enough then a blow‐in door can be provided, which closes automatically when the demand drops off. Figure 12.21d shows a typical flow pattern at incidence at high demand, when an automatic blow‐in door may be necessary. At idle, the engine is kept running with very little trust generation (MFR « 1). At inoperative conditions, the rotor is kept windmilling to minimise drag. If the rotor seizes due to mechanical failure then there will be considerable drag rise.

Currently, the engine (fan) face Mach number should not exceed Mach 0.5 to avoid degradation due to compressibility effects. At a fan face Mach number above 0.5, the relative velocity at the fan tip region approaches near sonic speed on account of high blade rotational speed.

The purpose of the intake is to serve engine airflow demand as smoothly as it is possible – there should be no flow distortion at the compressor face on account of any separation and/or flow asymmetry. Nacelle intake lip cross‐section is designed with the similar logic behind designing the aerofoil leading edge cross‐section – to ensure flow does not separate within the flight envelope. More detail on subsonic pod mounted intake design is given in [8–10].

12.8.2 Military Aircraft Supersonic Intake Design

Chart described various types of supersonic inlet configurations shown in Section 5.16.1. The two main types are featured at the (i) fuselage nose with a centre body and (ii) fuselage, side mounted. In this section, their aerodynamic considerations are given. Military aircraft have supersonic capabilities and therefore have to manage shock losses (RF, Eq. 12.6 and Figure 12.22) associated with its intake. This can be done by designing supersonic intake oblique shock to develop in stages with a series of deflection angles (typically 5–10°, depending on the number of stages). Normally, three oblique shocks suffice (Figure 12.22) [6, 10]. An increase in number of deflection angles offers diminishing returns to improve RF. The best design is an Oswatitsch curved contour design, which generates infinite weak Mach waves with minimum loss, ideally in an isentropic process; that is, no loss. Oswatitsch intakes are used in hypersonic air‐breathing engines.

12.8.2.1 Intake at Fuselage Nose with a Centre Body

Ideally, at design point M_des, (at supersonic cruise), the bow shock wave just attaches to the intake lip, which is sharp compared to a subsonic intake lip. Figure 12.23 gives four kinds of flow regime associated with supersonic intake with a fixed centre body. Four types of operating situation arise as follows:

1. At the design flight speed, seen as critical operation, when it is desirable that the oblique shock wave just touches the lip followed by other shocks culminating with a normal shock at the throat beyond which airflow becomes subsonic (Figure 12.23a). The captured free stream tube is same as the highlight area. Intake area is sized to inhale air mass at critical operation.
2. If the back pressure is lower than the critical operation (on account of throttle action) then more air mass is inhaled and the throat area remains supersonic, pushing back a stronger normal shock. This is known as supercritical operation (Figure 12.23b). The captured free stream tube is still the same as the highlight area and oblique shock position depends on the aircraft speed.
3. When the back pressure is high, especially when the aircraft is below critical speed, then less air is inhaled, the aircraft is still at supersonic speed, the oblique shock is wider and is followed by a normal shock that pops outside ahead of the nacelle lip and is known as the sub‐critical operation (Figure 12.23c). The captured free stream tube is smaller than the highlight area. It is not as efficient as the critical operation but loss is less than supercritical operation.
4. The last one could happen with a particular combination of aircraft speed (below critical) and air mass inhalation when the normal shock outside keeps oscillating, which starves the engine and it runs erratically, possibly leading to flameout. This is known ‘buzz’ (Figure 12.23d).

For aircraft operating above Mach 2, a movable centre body keeps the oblique wave at the lip as the shock angle changes with speed change. The simplest centre body is a cone (or half cone for side mounted nacelles). The cone could be stepped to make multiple oblique shocks at reduced intensity; that is, lowering shock loss. A movable centre body (Figure 5.34, MIG21 showing extended and retracted centre body positions) can keep oblique shock at the intake lip and can manage ‘buzz’ better. Aircraft must avoid buzz occurring and modern designs have a FBW/FADEC to keep clear of it.

12.8.2.2 Intake at the Fuselage Side

Current intake position is at fuselage side or at underbelly, reducing the long intake duct of nose intake by about 25–35%, reducing duct loss and duct weight. For fuselage mounted single engine, a small bend of intake duct is required to have the bifurcated duct to meet before it reaches engine face. For twin engine aircraft, relatively straighter separate ducts offer better design with less duct loss, thus offering better RF. A chin mounted intake escapes duct bifurcation.

Figure 12.24 shows a typical side mounted supersonic intake similar to what an F14 Tomcat fighter aircraft has. It has a rectangular intake seen as a 2D intake, but not exactly. The Concorde underwing supersonic intake has similar design considerations.

The supersonic nacelle, as shown in Figure 12.24, is a complex modern design. It dispenses with the older practices of having a centre body by movable doors operated by separately managed actuators. For mass flow demand at low speed operation, especially, at full throttle takeoff rating, the throat opening is kept at maximum. Flap doors are adjusted to reduce throat area with speed increase. At maximum speeds over Mach 2.0, the two stage doors have stepped deflection to develop a total of three weaker oblique shocks, followed by a normal shock, making airflow diffuse to around Mach 0.5 at the engine face. At the top, there is a bleed door to serve both as boundary layer bleed as well as a dumping excess intake air mass flow. Normally, these are integrated with FBW/FADEC and activate automatically.

Modern combat aircraft with advance missiles have beyond visual range (BVR) capabilities. In an air‐superiority role, rapid manoeuvre at high speed is the combat specification for which a typical maximum speed is of the order of Mach 1.8 (≈F16 variant) when the requirement for a movable centre body/flap doors is not stringent. For side intakes, boundary layer bleed plates serve as the centre body to position oblique shock at the lip (critical design point operation). A Diverterless Supersonic Inlet (DSI – Figure 5.33) eliminates the need for a splitter plate, while compressing the air to slow it down from supersonic to subsonic speeds.

12.9.1 Civil Aircraft Exhaust Nozzles

Civil aircraft nozzles on which the TR is integrated are conical. Small turbofan aircraft may not need a TR but aircraft of RJ (regional jet) size and above use one. Inclusion of a TR may slightly elongate nozzle length – this will be ignored in this book.

In general, nozzle exit area is sized as a perfectly expanded nozzle (p_e = p_∞) at the LRC condition. At higher engine ratings it has p_e > p_∞. The exit nozzle of a long duct turbofan does not run choked at cruise ratings. At takeoff ratings, the back pressure is high at lower altitude, therefore a long duct turbofan could escape from running choked (low‐pressure secondary flow mixes within the exhaust duct). The exhaust nozzle runs in a favourable pressure gradient, hence its shaping means it is relatively simpler to establish its geometrical dimensions. However, this is not simple engineering it for elevated temperature and to suppress noise level.

The nozzle exit plane is at the end of engine. Its length from the turbine exit plane is about 0.8–1.5 fan face diameter. Nozzle exit area diameter may be taken to be coarsely as half to three‐quarters of the intake throat diameter in this study.

12.9.2 Military Aircraft TR Application and Exhaust Nozzles

An afterburning military engine TR is integral with the nozzle design and is positioned at the fuselage end. Afterburning engine nozzles always runs choked at the maximum rating and have a variable convergent‐divergent (de Laval) nozzle to match with the throttle demands. Of late, all the latest combat aircraft have thrust vectoring capabilities by deflecting the exhaust jet at the desired angles, affecting aircraft manoeuvrability capabilities.

The full extent of TR deployment is shown in Figure 12.25 (the last figure). This has an integral mechanism capable of adjustment for all demands. The diagram shows that the integral mechanism can even provide a mild form of in‐flight thrust reversing to spoil thrust (air‐braking action) to wash out high speed at its approach to land or in combat to a considerably lower speed.

12.10.1 Propeller‐Related Definitions

Industry uses propeller charts, those incorporate some special terminologies. Definitions of the necessary terminologies/parameters are given here:

D = Propeller diameter = 2 × r

n = Revolution per second (rps)

ω = Angular velocity

N = Number of blades

b = Propeller blade width (varies with radius, r)

P = Propeller power

C_p = Power coefficient (not to confuse with pressure coefficient) = P/(ρn³D⁵)

T = Propeller thrust

C_Li = Integrated design lift coefficient (C_Ld = sectional lift coefficient)

C_T = Propeller thrust coefficient = T/(ρn²D⁴)

β = Blade pitch angle subtended by the blade chord and its rotating plane (also known as geometric pitch)

p = Propeller pitch = no slip distance covered in one rotation = 2πrtanβ (explained previously)

V_R = Relative velocity to the blade element = √(V² + ω²r²) (Blade Mach No: = V_R/a)

ϕ = Angle subtended by the relative velocity = tan⁻¹(V/2πnr) or tanϕ = V/πnD. It is the pitch angle of the propeller in flight and is not the same as blade pitch, which is independent of aircraft speed.

α = Angle of attack = (β − ϕ)

J = Advance ratio = V/(nD) = πtanϕ (a non‐dimensional quantity − analogous to α).

AF = Activity factor = (10⁵/16)

TAF = Total activity factor = N × AF (N is number of blades – it gives an indication of power absorbed).

It is found that at around 0.7r (tapered propeller) to 0.75r (square propeller), the blades give the aerodynamically average value that can be applied uniformly over the entire radius to obtain the propeller performance.

Figure 12.26 shows a two‐bladed propeller along with a blade elemental section, dr, at radius r. The propeller has diameter, D. If ω is the angular velocity then the blade element linear velocity at radius r is ωr = 2πnr = πnD, where n is the number of revolution per unit time. An aircraft with true airspeed of V and with propeller angular velocity of ω, will have blade element moving in a helical path. At any radius, the relative velocity, V_R has angle ϕ = tan⁻¹(V/2πnr). At the tip ϕ_tip = tan⁻¹(V/πnD).

However, irrespective of aircraft speed, the inclination of blade angle from the rotating plane can be seen as solid‐body screw thread inclination and is known as pitch angle, β. The solid‐body screw like linear advancement through one rotation is called propeller pitch, p. The pitch definition has a problem as unlike mechanical screws, the choice of inclination plane is not standardised. It can be the zero‐lift line, which is aerodynamically convenient or the chord line, which is easy to locate or the bottom surface – each plane will give a different pitch. All these planes are interrelated by fixed angles. This book takes the chord line as the reference line for the pitch as shown by blade pitch angle, β, in Figure 12.24. This gives propeller pitch, p = 2πr tanβ.

Since the blade linear velocity ωr varies with radius, its pitch angle needs to be varied as well to make the best use of the blade element aerofoil characteristics. When β is varied in such a way that the pitch is not changed along the radius then the blade has constant pitch. This means that β decreases with increase in r (variation in β is about 40° from root to tip).

Blade angle of attack,

12.22

This brings out an analogous non‐dimensional parameter, J = advance ratio = V/(nD) = πtanϕ.

Blade pitch should match with aircraft speed, V, to keep blade angle of attack α to produce best lift. To cope with aircraft speed change, it benefits if the blade is rotated (varying the pitch) about its axis through the hub to maintain favourable α at all speeds. It is then called a variable pitch propeller. Typically, for pitch variation, the propeller is kept at constant rpm with the help of a governor, when it is called a constant speed propeller. Almost all aircraft flying at higher speed will have constant speed variable pitch propeller (when done manually it is β‐controlled). The smaller low speed aircraft are with fixed pitch that would run best at one combination of aircraft speed and propeller rpm. If the fixed pitch is meant for cruise then at takeoff (low aircraft speed and high propeller revolution) the propeller would be less efficient. Typically, aircraft designers would like to have fixed pitch propeller matched for the climb, a condition in between cruise and takeoff to minimised the difference between the two extremes. Obviously, for high speed performance it should match the high speed cruise condition. Figure 12.28 shows the benefit of constant speed variable pitch propeller over the speed range.

The β‐control can extend to reversing of propeller pitch. A full reverse thrust acts as all the benefits of TR describe in Section 12.9. The pitch control can be made to ‘fine‐pitch’ to produce zero thrust when the aircraft is static. This could assist aircraft to wash out speed especially at approach to land.

When the engine fails, that is the system senses insufficient power, the pilot or the automatic sensing device elects to feather the propeller (Figure 12.25). Feathering is changing β to 75–85° (maximum coarse) when propeller slows down to zero rpm – producing net drag/thrust (part of propeller has thrust and the rest drag) to zero.

Windmilling of propeller occurs when the engine has no power and is free to rotate driven by the relative airspeed to the propeller when aircraft is in flight. The β angle is in a fine position.

Installed turboprop thrust is obtained by reducing the thrust by the various loss factors. In addition fuselage factors of fuselage blockage factor f_b and excrescence factor f_h (see Section 11.16) are to be applied further reducing the thrust level.

12.11.1 Momentum Theory – Actuator Disc

The classical incompressible inviscid momentum theory provides the basis of propeller performance [13]. In the theory, the propeller is represented by a thin actuator disc of area, A, placed normal to free stream velocity, V₀. This captures a stream tube within a CV having a front surface sufficiently upstream represented by subscript ‘0’ and at sufficiently downstream by subscript ‘3’ (Figure 12.29). It is assumed that thrust is uniformly distributed over the disc and the tip effects are ignored. Whether the disc is rotating or not is redundant, as flow through it is taken without any rotation. Station numbers just in front and aft of the disc are designated 1 and 2.

The impulse given by the disc (propeller) increases the velocity from the free stream value of V₀, smoothly accelerating, to V₂ behind the disc and continuing to accelerate to V₃ (station 3) until the static pressure equals the ambient pressure p₀. The pressure and velocity distribution along the stream tube is shown in Figure 12.29. There is a jump of static pressure across the disc (from p₁ to p₂) but there is no jump in velocity change.

Newton's law gives that the rate of change of momentum is the applied force; in this case it is the thrust, T. Consider station 2 of the stream tube immediately behind the disc producing the thrust. It has MFR, = ρA_discV₂. The change of velocity is ΔV = (V₃ − V₀). This is the reactionary thrust experienced at disc through the pressure difference multiplied by its area, A.

Thrust produced by the disc

12.23

Equating, Eq. 12.23 can be rewritten as

12.24

The incompressible flow Bernoulli's equation cannot be applied through the disc imparting energy. Instead, two equations are set up, one for conditions ahead of the disc and the other aft of it. Ambient pressure p₀ is the same everywhere.

Ahead of the disc,

12.25

Aft of the disc,

12.26

Subtracting the front relation from the aft relation,

12.27

Since there is no jump in velocity across the disc, the last term drops out.

Next substitute the value of (p₂ − p₁) from Eq. 12.24 into Eq. 12.27.

12.28

Note that (V₃ − V₀) = ΔV when subtracted from Eq. 12.28, it gives 2V₃ = 2V₂ + ΔV.

Or

12.29

It says that half of the added velocity, ΔV/2, is ahead the disc and the rest, ΔV/2, is added aft of the disc.

Using conservation of mass, A₃V₃ = A₁V₁, Eq. 12.23 becomes

12.30

Using Eqs. 12.29 and 12.30, the thrust Eq. 12.23 can rewritten as

12.31

Applying to aircraft, V₀ may be seen as aircraft velocity, V, by dropping the subscript ‘0’. Then useful work rate (power, P) done on the aircraft is

12.32

For the ideal flow without the tip effects, the mechanical work produced in the system is the power, P_ideal, generated to drive the propeller is force (thrust, T) times velocity, V₁, at the disc.

12.33

Therefore, ideal efficiency,

12.34

The real effects will have viscous, propeller tip effects and other installation effects. In other words, to produce the same thrust, the system has to provide more power (in case of piston engine it is seen as Brake Horse Power (BHP) and in case of turboprop as ESHP, where ESHP is the equivalent shaft horse power that converts the residual thrust at the exhaust nozzle to HP, dividing by an empirical factor 2.5. The propulsive efficiency as given in Eq. 12.34 can be written as

12.35

This gives,

12.36

12.11.2 Blade Element Theory

Practical application of propellers is obtained through blade element theory as given next. Propeller blade cross‐sectional profile has the same functions as that of wing aerofoil, that is, to operate at the best L/D.

Figure 12.26 shows that a blade elemental section, dr, at radius r, is valid for any number of blades at any radius, r. As blades are rotating elements, their properties would vary along the radius.

Figure 12.26 gives the velocity diagram showing an aircraft with a flight speed of V with its propeller rotating at n rps, which would make its blade element advance in a helical manner. V_R is the relative velocity to the blade with angle of attack α. Here, β is the propeller pitch angle as defined before. Strictly speaking, each blade rotates in the wake (downwash) of the previous blade, but the current treatment ignores this effect to use propeller charts without appreciable error. Figure 12.26 also gives the force diagram at the blade element in terms of lift, L, and drag, D, that is normal and parallel, respectively, to V_R. Then the thrust, dT, and force, dF (producing torque) on the blade element can be easily obtained, by decomposing lift and drag in the direction of flight and in the plane of propeller rotation, respectively. Integrating over the entire blade length (non‐dimensionalised as r/R – an advantage to be applicable to different sizes) would give the thrust, T, and torque producing force, F, by the blade. The root of the hub (with spinner or not) does not produce thrust and integration is normally carried out from 0.2 to the tip, 1.0, in terms of r/R. When multiplied by the number of blades, N, it gives the propeller performance.

Therefore,

12.37

And

12.38

From the definition, Advance ratio, J = V/(nD).

It can be shown that the thrust to power ratio is best when the blade element works at the highest lift to drag ratio (L/D_max). It is clear that a fixed pitch blade works best at a particular aircraft speed for the given power rating (rpm) – typically the climb condition is matched for the compromise. It is for this reason, constant speed variable pitch propellers have better performance over a wider aircraft speed range. It is convenient to express thrust and torque in non‐dimensional form as given next. From dimensional analysis (note that the denominator does not have the ½):

12.39

In the foot–pound system (FPS),

12.40

where σ = ambient density ratio for altitude performance

12.41

12.42

12.43

In FPS system,

12.44

where N stands for r.p.m and n stands for r.p.s. The wider is the blade the would be the power absorbed to a point when any further increase would offer diminishing returns in increasing thrust.

A non‐dimensional number defined as

expresses the integrated capacity of the blade element to absorb power. It indicates that increase of blade width outwardly is more effective than at the hub direction.

expresses the integrated capacity of the total number of blades of a propeller to absorb power.

A piston engine or a gas turbine would drive the propeller. Propulsive efficiency, η_p, can be computed by using Eqs. 12.35, 12.39 and 12.44.

Propulsive efficiency

12.45

12.12.1 Propeller Performance – Blade Numbers 3 ≤ N ≥ 4

Using these graphs, linear extrapolation could be made for two and five bladed propellers with similar AF and so on. Reference [15] treats the subject in detail with propeller charts for other AF values.