Hypersonic flow: introduction

Transcription

1 Hyersonic flow: introduction Van Dyke: Hyersonic flow is flow ast a body at high ach number, where nonlinearity is an essential feature of the flow. Also understood, for thin bodies, that if is the thickness-to-chord ratio of the body, is of order. Secial Features Thin shock layer: shock is very close to the body. The thin region between the shock and the body is called the Shock Layer. Entroy Layer: Shock curvature imlies that shock strength is different for different streamlines stagnation ressure and velocity gradients - rotational flow

2 The Hyersonic Tunnel For Airbreathing Proulsion htt://

3 Velocity-Altitude a For Re-Entry Altitude Tyical re-entry case: Very little deceleration until Vehicle reaches denser air (Deliberately so - to avoid large fluctuations in aerodynamic loads and landing oint ) Velocity

4 Atmoshere Trooshere: 0 < z < 0km Stratoshere: 0 < z < 50km esoshere: 50 < z < 80km Thermoshere: z > 80km Ionoshere 65 < 365 km Contains ions and free electrons 60 <z < 85 km NO + 85 <z < 40 km NO +, O + 40 <z < 00 km NO+, O +, O + Z> 00 km N +, O +

5 A Simle odel for Variation of density with altitude d gdz RT ˆ ˆ Neglect dissociation and ionization olecular weight is constant Assume isothermal (T = constant) oor assumtion d g ˆ dz RT ˆ g ˆ 0 loge RT ˆ z

6 High Angle of Attack Hyersonic Aerodynamics

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8 Crocco s Theorem: Ts h 0 u Imlies vorticity in the shock layer. Viscous Layer: Thick boundary layer, merges with shock wave to roduce a merged shock-viscous layer. Couled analysis needed. High Temerature Effects: Very large range of roerties (temerature, density, ressure) in the flowfield, so that secific heats and mean molecular weight may not be constant. Low Density Flow: ost hyersonic flight (excet of hyervelocity rojectiles) occurs at very high altitudes Knudsen No. = L = ratio of ean Free Path to characteristic length Above 0 km, continuum assumtion is oor. Below 60 km, mean free ath is less than mm.

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10 Summary of Theoretical Aroaches Newtonian Aerodynamics: Flow hits surface layer, and abrutly turns arallel to surface. omentum normal to the surface is transferred to normal force on the body. Normal force on body = drag of normal flow comonent. Normal force is decomosed into lift and drag. odified Newtonian Aerodynamics: Account for stagnation ressure dro across shock. Local Surface Inclination ethod : C at a oint is calculated from static ressure behind an oblique shock caused by local l surface sloe at freestream ach number. Tangent Cone aroach: similar to local surface sloe arguments. ach number indeendence: Shock/exansion relations and C become indeendent of ach number at very high ach number. Blast wave theory: Energy of Disturbance caused by hyersonic vehicle is like a detonation wave. Hyersonic similarity: Allows develoing equivalent shock tube exeriments for hyersonic aerodynamics.

11 Hyersonic Aerodynamics Roadma Suersonic Aero Hyersonic Small Disturbance: ach Number Indeendence Non-Equilibrium Gas Dynamics Stagnation Point: CFD Full shock-exansion method With real gas effects Blast Wave Theory Conical Flow / Waveriders Newtonian Aerodynamics Local Surface Inclination ethods Newton Buseman

12 Newtonian Aerodynamics: Flow hits surface layer, and abrutly turns arallel to surface. omentum normal to the surface is transferred to normal force on the body. Normal force on body = drag of normal flow comonent. Normal force is decomosed into lift and drag. D No info on shock. or viscous drag No influence of body shae L N

13 Local Surface Inclination ethods Aroximate methods over arbitrary configurations, in articular, where C is a function of local surface sloe. Newtonian Aerodynamics Newton (687) concet was that articles travel along straight lines without Interaction with other articles, let ellets from a shotgun. On striking a surface, they would lose all momentum erendicular to the surface, but retain all tangential momentum i.e., slide off the surface. Net rate of change of momentum C Sin In 3D flows we relace U n C U Shadow region: C 0 U Sin A U Sin with U n Shadow region is where U n 0

14 Remarks on Newtonian Theory: Poor in low seed flow. Predicts. C l () Works well as ach number gets large and secific heat ratio tends towards.0 Why? Because shock is close to surface, and velocity across the shock is very large most of the normal momentum is lost. () Tends to overredict c and c d (C D ) see (3) Works better in 3-D than in -D (4) In 3-D, works best for blunt bodies; not good for wedges, cones, wings etc.

15 odified Newtonian Was roosed by Lester Lees in 955, as a way of imroving Newtonian theory, and bringing in ach Number deendence. He roosed relacing with C max C C max sin C Here C max is the behind a Normal shock wave, at the stagnation oint. That is, 0 C max U

16 From Rankine-Hugoniot relations, 0 Then 4 0 c

17 In the limit as, We get c 4 4 c max. 839 As.4, As, c max Proosed by Newton

18 Hyersonic Shock & Exansion Relations Why?. Simler than exact exressions - for analysis. Key arameter is seen to be K where is the flow turning angle, for >> and << Oblique Shock Relations tan cot sin cos tan cot sin >>, small >>, small Pressure jum: >> sin sin

19 sin K K 4 4 K K K Defining ressure coefficient g C 4 4 K K C 4 Sin C

20 Next sin u u In the hyersonic limit, Also u u sin u sin Cot u u sin u

21 Density Jum Across Shock sin sin In the hyersonic limit, for large >>, finite Then the temerature jum is: sin T T C 4 Sin C

22 For large but finite, small and tan cot sin cos becomes 4 6 Works for finite values of = K

23 Hyersonic Exansion Wave Relations From Prandtl-eyer theory, tan tan For Also tan x From Taylor series tan x tan x x 3x 3 5x 5..

24 Then K C ) (K f C Note that K K K C ), ( K f

25 ach Number Indeendence As freestream ach number becomes large, Why nondimensionalize by U sin U U Because ~O U sin And it allows cancellation of ach number Examine other relations for roerties downstream of the shock freestream ach number does not aear anywhere.

26 Non-lifting body moving at velocity U, which is inclined at angle to the x-axis: d x m dt d z m dt D DCos DSin mg U d z m U CDS sin mg dt m CDS is the Ballistic Parameter. Assuming that the drag force is >> weight and that is constant because gravitational force is too weak to change the flight ath much Log e U U e 0 CDS ex m sin gz RT