Supplemental Readings A A.1 Introduction the flow from supersonic to subsonic speeds in a transonic SBLI. Although it is preferable to design inlets with weaker We will now discuss the basic details about air-breathing terminating shock waves, constraints on overall system size engine intakes which are frequently used in Ramjets and generally limit the compression that can be achieved through Scramjets. In addition, a small discussion about supersonic oblique shock waves. combustion is also provided which help the reader in under- Such strong interactions pose considerable problems for standing the combustion at supersonic Mach numbers. We inlet efficiency. The strong normal or near-normal shock have already referred them many times earlier in the text for waves incur considerable entropy increase and stagnation purposes of explaining the various phenomena. Moreover, we pressure loss, which is a direct performance loss for the sys- do not discuss all possible topics in this appendix but will tem. Further, since the boundary layer already has experienced choose those that are essential for explaining the theories as a number of adverse pressure gradient regions in the previ- presented in the text. ous SBLIs, in turn, the boundary layer becomes more vul- nerable to flow separation, when encountered the final shock wave. Flow separation has an obvious detrimental impact on A.2 Air-Breathing Engine Intakes inlet performance. In addition to the introduction of addi- For jet aircraft operating at supersonic speeds, it is neces- tional stagnation pressure losses, it introduces considerable sary to decelerate and compress the incoming air to subsonic nonuniformity in the flow entering the subsonic diffuser or speeds before entering into the combustor. It is achieved via the combustor. the intake. The simplest form of compression is via a normal Moreover, any flow separations are also likely to introduce shock ahead of a pitot inlet, but this incurs significant stag- considerable unsteadiness into the flow, which can lead to nation pressure losses, rendering this form of intake imprac- unacceptable dynamic loads on the engine. If the terminal tical for M > 2. A better approach is to generate a series (near-normal) shock oscillation is so extreme that it reaches of oblique shock waves that can increase the pressure and the converging part of the inlet geometry, it becomes unstable. reduce the Mach number before eventually changing the flow At this point, it moves rapidly upstream, making more of the state to subsonic through a terminating near-normal shock. flow inside the inlet subsonic, until it is eventually expelled For a given incoming flow Mach number, a series of multiple from the intake causing unstart (or buzz, if this phenomenon is shock waves incurs a smaller entropy production and, thus, periodic). This is comparable to shock stall or shock-induced lower losses than a single normal shock wave. Depending on buffet on transonic wings; such a violent event is extremely whether the oblique shock waves are generated outside the damaging to the engine. Toavoid the problems associated with intake or within the inlet duct, such designs are referred to as strong transonic SBLIs in inlets, the researchers make use of external or internal compression inlets. flow control to enable the boundary layer to stay attached even In either case, the shock wave interacts with the boundary when the shock waves have considerable strength. The most layer growing along the inlet surface. Most of the interactions popular control method is boundary layer suction, or bleed. feature oblique shock waves with supersonic flow on both In any air-breathing engines, an inlet, a combustion cham- sides of the interaction. However, in each inlet design, there ber, and a nozzle are the three main components. Furthermore, is a final terminating, near-normal shock wave that switches it is established that 1% loss in inlet stagnation pressure even- © Springer Nature Singapore Pte Ltd. 2019 393 M. Kaushik, Theoretical and Experimental Aerodynamics, https://doi.org/10.1007/978-981-13-1678-4 394 Appendix A: Supplemental Readings π tually leads to about 1–1.5% loss of engine gross thrust (Intake where D is the ratio of stagnation pressure, and p0,exit and Aerodynamics by J. Seddon and E. Goldsmith 1999). There- p0,entry, respectively, are the stagnation pressure at the inlet fore, an efficient performance of the engine components is of exit and the stagnation pressure at the inlet lip. Also, to a very prime importance for good performance of the whole engine. high degree of approximation the flow in the inlet is assumed Also, designing the engine components with high accuracy is to be adiabatic, that is, no exchange of heat transfer between more critical in the regions of increasing static pressure than the inlet and its surroundings. We have, the areas where static pressure decreases. This is because of boundary layer separation in the presence of adverse pressure τ = T0,exit = D 1(A.2) gradient. Clearly, the inlet design is more challenging than the T0,entry nozzles which are subjected to favorable pressure gradients. τ where D is the ratio of stagnation temperature, and T0,exit and T0,entry, respectively, are the stagnation temperature at the A.3 Engine Inlets exit and the stagnation temperature at the lip. The design of subsonic inlet is greatly influenced by the two major require- An inlet is the device which recovers pressure energy by ments; to prevent the separation of boundary layer at high reducing the kinetic energy of the flow. Depending on the angles of attack and need of high mass flow during landing flight Mach numbers, they are categorized into; subsonic or and takeoff; and to suppress the formation of both internal supersonic inlets. Inlets find tremendous application predom- and external shock waves at transonic flight Mach numbers. inantly in jet engines. But these two requirements are contradictory to each other, because a thick inlet lip is the best suited for high angle of attack engine operation, whereas a thin lip is suitable to high A.3.1 Subsonic Inlets Mach number requirements. With the advent of modern com- puting, it is now feasible to obtain analytical estimation of the It is known that the flow entering into the compressor of a tur- complex flow fields and the associated losses to develop the bojet engine must have the Mach number (M) in the range of best compromised inlet designs. 0.4−0.7, where the upper limit is suitable for transonic com- pressors or fans. Further, if the engine has to operate for the A.3.1.1 Flow through the Inlet (Internal Flow) subsonic level flight at M = 0.85, then the inlet must cause the Based on varied flight Mach numbers and mass flow require- flow deceleration from 0.85 to about 0.6. It should be noted ments of the engine, an inlet has to operate at different that the flow undergoes both external and internal deceleration freestream conditions. To investigate the inlet performance, in an intake. The properly designed intake should minimize or let us consider two typical subsonic freestream conditions eliminate boundary layer separation even during the pitch and and their corresponding thermodynamic processes on T − S yaw motions of the aircraft. Also, there should be minimum diagrams of an aggregate fluid lump as shown in Fig. A.1. stagnation pressure loss in an inlet and it must deliver a uni- In this figure, freestream conditions are depicted by sub- form flow to the compressor. A nonuniform flow at the entry script “a” upstream of the inlet and Aa is the streamtube cross- to the compressor not only affects its efficiency drastically but sectional area. The concept of streamtube introduced here is also, it may lead to flow-induced vibrations thereby causing very useful and resembles an aerodynamic duct. The airflow the failure of blades. In addition, as the diffuser is required to enteringintotheinletmayeitherundergoaccelerationordecel- have a stable operation in both subsonic and supersonic flow eration in the aforesaid aerodynamic duct. During level cruise regimes, its design becomes more challenging. motion, where an aircraft flies at high Mach number with rela- Typically, a subsonic inlet suffers mainly from the follow- tivelylowermassflowattheinlet,airexperiencessomedeceler- ing three types of losses: ationexternaltointake,showninFig.A.1a.Thus,anincreasein cross-sectionalareaofthestreamtubefromfreestreamtointake 1. Losses due to wall friction. entry can be observed. In other flight modes, such as during 2. Losses due to shock waves (at high subsonic or transonic takeoff and landing, the mass flow requirement is high but the flight conditions). aircraftspeedislow.Intheselow-speedhigh-thrustflightoper- 3. Losses due to separation the flow. ations, the streamtube resembles a converging duct as shown in Fig. A.1b, which illustrates the external acceleration of air As the flow passes through the inlet, all the above factors before entering into the inlet. Essentially, in both of the afore- cause loss of stagnation pressure. That is, saidcases,theairundergoesachangeofstateoutsidetheintake following an isentropic process as there is no physical surface π = p0,exit < D 1(A.1)involved to introduce friction. p0,entry Appendix A: Supplemental Readings 395 p 0a p T 0a 02 p 0a 02 2 1 2 02s 2 a 2s A a Enthalpy (h) p 1 1 p a a Ta Inlet Entropy (s) (a) During level cruise motion (high Mach number flight or low air mass flow rate). p 0a p p T0a 0a 02 2 1 2 02s 2 a 2s A a Enthalpy (h) p a a p 1 1 Ta Inlet Entropy (s) (b) During landing or take-off (low Mach number flight or high air mass flow rate). Fig. A.1 Streamline patterns and the corresponding h − s diagrams for subsonic inlets The external acceleration, shown in Fig.