MAE 5360: Hypersonic Airbreathing Engines

1. MAE 5360: Hypersonic Airbreathing Engines Component and System Losses Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

2. Altitude vs. Velocity Regime

3. Reynolds Number and Transition • Along flight path with increasing altitude, velocity increases, but density falls rapidly, so for a length the Reynolds number drops • Laminar to turbulent boundary layer transition at high Mach number not well understood, but can get some idea from recent data from NASA Langley Research Center (next slide) • Data is shown for fixed lengths of 3, 10 and 30 meters • Conclusions for typical hypersonic trajectory: • Flow can be regarded as fully turbulent for M0 < 9 • Flow can be regarded as fully laminar for M0 > 15 • Data scatter by factors of 2 around best fit, implies shifts of ±2 in transition Mach number

4. Transition on Sharp Cones

5. Oxygen Kinetics: Sample Calculations and Experiment • Flight Mach number = 20, altitude = 100,000 ft, and pressure into combustor = 0.21 atm • Laminar boundary layer under consideration • Consider two cases: Fluid particle enters boundary layer at 1 m and 10 m • Key results from experimental analysis • Dissociation onset delayed with respect to equilibrium • Dissociation rise slower than equilibrium rate • Maximum T occurs while enthalpy still rising, and the reason is due to lag of atomic oxygen • Even at high-speed, low pressure, not much atomic oxygen produced, with the maximum of around 33% in either case • Kinetic effects must be accounted for in assessing inlet conditions

6. Oxygen Kinetics in Laminar Boundary Layer • Flight Mach Number = 20 • Velocity = 6,400 m/s • P = 0.21 atm • Entry from leading edge

7. Oxygen Kinetics in Laminar Boundary Layer • Flight Mach Number = 20 • Velocity = 6,400 m/s • P = 0.21 atm • Entry from leading edge

8. Relaxation Behind Normal Shocks • Plots show flow variables behind a normal shock wave • Immediately behind the shock, there is no dissociation, and velocity and temperature are those for frozen flow • As dissociation proceeds, velocity and T are reduced (in an oblique shock, flow would turn toward shock front) • First plot shows degree of dissociation • Second plot shows velocity • Third plot shows temperature

9. Hypersonic Similarity for Oblique Shocks • Pressure coefficient for hypersonic and exact shock relations

10. Solutions for External Flow

11. Example of Newtonian Theory Validation • Pressure distribution on a circular cylinder and Newtonian Theory

12. Boundary Layer Effects • Skin friction of laminar compressible boundary layer • Shown for a flat plat with zero pressure gradient

13. Stagnation Point Heat Transfer

14. Shock Boundary Layer Interaction in Cylindrical Ducts • Downstream obstruction of supersonic flow in a duct (such as due to combustion) produces different effects depending on the boundary layer thickness • Critical for isolator modeling (with and without boundary layer suction) • For very thin boundary layers – normal shock wave • For moderately thick boundary layers – single, then multiple lambda-shocks with simultaneous layer separation • For thick boundary layer, multiple X-shocks, with no normal central part. Layer separates, highly dissipative turbulent regions grow along walls, and eventually merge. See Crocco “Pseudoshock”

15. Multiple Shocks in Ducts • Strong wall-region dissipation (but weak dissipation through central oblique shocks) gradually raise wall pressure over 6 – 12 diameters • Plot shows static pressure distribution in ‘pseudo-shocks’ obtained in a pipe with fixed supersonic initial conditions and varying back pressure

16. Boundary Layer Effects • Plot shows experimental pressure ratios of pseudo-shocks and theoretical solution of normal shocks at various Mach numbers • Pressure rise at a point of wall layers merging is about same as a normal shock ratio at starting Mach number

17. Boundary Layer Effects • Example of 23 reaction subset, extracted from a more comprehensive hydrogen – air combustion reaction mechanism • 12 species • Notice that this reaction set includes HO2

18. Limits on P and T imposed by kinetics • Plot shows total reaction time, which is limited by combustion kinetics • The upturn in the total reaction time at high pressure is due to excessive HO2 formation, which scavenges the H radicals • This effect increases the ignition time, and would be completely missed by a simple correlation • Combustor residence times can vary between 0.2 to 0.8 milliseconds for flight Mach number range of 5 – 20 • If we require combustion time scales of less than, say 0.2 milliseconds, need combustor inlet temperatures of more than 1,000 K for any pressure

19. Effect of Additives: H2O2 • Early production of free radicals can shorten the ignition time, allowing ignition at lower temperatures • Hydrogen peroxide (H2O2) is effective down to about 900 K

20. Effect of Additives: Silane • Silane (SiH4) appears to accelerate ignition via a thermal mechanism • Silane is very reactive in air, and the temperature rise due to its own reaction can ignite the hydrogen • Data shown is for 2% Silane

21. Reacting Flow in Nozzles: Hypersonic Regimes • Even if equilibrium is closely approached in the combustor, low pressure still has the effective of producing substantial dissociation • Equilibrium concentrations of several percent (by mole) of OH, H, NO, and O (a very energetic species) are common at stoichiometric conditions near 1 atm • This effect is accentuated by the presence of very energetic ingested boundary layers, where dissociation of O and H species is nearly complete • As the gas expands in the nozzle, the reactions time increases rapidly, and chemical freezing occurs fairly early in the expansion, preventing recovery of most of the dissociation energy

22. WSR Reaction Model: Full Kinetics

23. Diffusion Flames

24. Laminar Flame Speed

25. Turbulent Diffusion Flames

26. Penetration of Transverse Jets into Supersonic Stream • Flame length can be reduced with transverse injection, due to additional fuel penetration (as compared with co-axial injection) • Key flow features are shown in the sketch to the right • The jet obstructs the flow almost as a solid cylinder of height that is about equal to the Mach disc standoff distance

27. Mixing Enhancement in Propulsion Systems • Flow mixing traditionally relied on turbulence to produce required transverse velocity components, which are themselves a result of growth of natural instabilities • Lack of friction loss against surfaces • Simplicity of implementation (ordinary sheer layers) • Small scale, which favors molecular-level mixing • In many hypersonic applications, turbulent mixing is insufficient, and there is strong incentive to shorten mixing length – can use secondary flows • A good example is the generation of axial vorticity by convoluted splitter plates (also called a lobed mixer)

28. Mixing Enhancement in Propulsion Systems

29. Mixing Enhancement in Propulsion Systems • Mixers have been shown to dramatically improve the performance of ejectors, and can be applied to fuel injection systems