Download - Compressible flow-Aerothermodynamics
Hypersonic Educational Initiative
Introduction toHypersonic Aerothermodynamics
Iain D. BoydDept. Aerospace Eng.University of Michigan
Ann Arbor, MI
Graham V. CandlerDept. Aerospace Eng. & Mech.
University of MinnesotaMinneapolis, MN
Hypersonic Educational Initiative
1. Hypersonic Gas Dynamics
1.1 Introduction and ExamplesOutline (1)
1. Hypersonic Gas Dynamics (1.5 hours)1.1 Introduction and Examples1.2 Post-shock conditions: perfect gas vs. equilibrium gas
Iteration approach for post-shock conditionsExamples
1.3 Reacting gas effects:Finite-rate reactions – nonequilibrium vs. equilibriumIonizationRadiation
1.4 Transport phenomena
Hypersonic Educational Initiative
Outline (2)
2. Hypersonic Aerodynamics: Pressure (1.0 hours)2.1 Exact and approximate equilibrium gas solutions:
Stagnation pointsCones and wedges
2.2 Mach number independence2.3 Newtonian and Modified Newtonian aerodynamics2.4 Examples
Hypersonic Educational Initiative
Outline (3)
3. Hypersonic Aerothermodynamics: Heat Transfer (1.0 hours)3.1 Introduction:
role of aerodynamic heatinghypersonic boundary layers
3.2 Boundary layer equations, Lees-Dorodnitsyn transformation3.3 Flat plate / wedge / cone solutions3.4 Stagnation point solution3.5 Transition to turbulence3.6 Wall catalysis3.7 Examples
Hypersonic Educational Initiative
Outline (4)
4. Viscous Interactions (1.0 hours)4.1 Leading edge interactions4.2 Effect on high-altitude L/D; scaling for vehicles4.3 Shock-BL interactions, shock-shock interactions
5. Thermal Protection Systems (1.0 hours)5.1 Passive:
re-radiative cooling, equilibrium wall boundary conditionrole of wall temperature, material propertiesexamples
5.2 AblativeSurface ablatorsPyrolyzing ablators
Hypersonic Educational Initiative
Outline (5)
6. Aerothermodynamics of Hypersonic Vehicles (1.0 hours)Ballistic entryLifting capsule re-entry: ApolloHigh-lift re-entry: ShuttleAerocapture / AerobrakingAirbreathing scramjets
Hypersonic Educational Initiative
What is Hypersonic Flow?
• Hypersonic aerothermodynamic phenomena:– strong shock waves with high temperature– not calorifically perfect (variable γ)– chemical reactions– significant surface heat flux– several different types of vehicles:
• missiles, space planes, capsules, air-breathers
• Working definition of hypersonic flow:
M = (U / a) >> 1
Hypersonic Educational Initiative
Hypersonic Examples:I. Missiles
• Mission: high-speed delivery of explosives• Aerodynamics: slender body with blunt nose• Propulsion: rockets, ramjets• Examples: AMRV, SCUD, Patriot, Hy-Fly
Hypersonic Educational Initiative
Hypersonic Examples:II. Space Planes
• Mission: orbital re-entry• Aerodynamics: gliders with thermal protection• Propulsion: none (except small control thrusters)• Examples: Space Shuttle, Buran, Hermes
Hypersonic Educational Initiative
Hypersonic Examples:III. Air-breathing Systems
• Missions: launch, cruise, orbital re-entry• Aerodynamics: slender with integrated engines• Propulsion: ram/scram-jets, rockets, turbojets• Examples: X-15, NASP, X-43, X-51
Hypersonic Educational Initiative
Hypersonic Examples:IV. Planetary Entry
• Missions: EDL, aero-braking, aero-capture• Aerodynamics: very blunt, thick heat shield• Propulsion: none (sometimes RCS)• Examples: Apollo, MSL, CEV (Orion)
Hypersonic Educational Initiative
• Flight vehicles:– WAC Corporal missile (1949, M~8)– Vostok I (1961, M~25)– X-15 (1963-1967, M~7)– Space Shuttle (1981-???, M~25)– HyShot (2002, M~8)– X43 (2004, M>7)– Hy-CAUSE (2007)
• Recent programs without flight:– NASP, Hermes, AFE, AOTV (1990)– VentureStar-X33 (2000)
Hypersonic VehicleHistorical Overview
Hypersonic Educational Initiative
Some CurrentHypersonic Programs
Falcon (DARPA)
Orion(NASA)X51
(AFRL)
HyBoLT (NASA/ATK)
Hypersonic Educational Initiative
Hypersonic Tales of Woe
• Hypersonics produces unexpected phenomena
• X15 test flight with dummy scramjet installed:– unexpected shock interactions generated– burned holes in connection pylon
• First re-entry of Space Shuttle (STS-1):– larger than expected nose-up pitch generated– required near-maximum deflection of body flap
• Shock-shock interactions:– heating amplified significantly– leading edges, cowl lips,
engine flow paths
Hypersonic Educational Initiative
• Ballistic missiles:– mission: short flight, fast impact– rocket launch, ballistic entry– no thrust or lift during entry (T=0, L=0)– fixed flight path at large angle (γ=const)
Re-entry Trajectories
• Trajectory equations for Earth centered system:
WD
LT, U
γ
!
U ˙ "
g=L
W# 1#
U2
gR
$
% &
'
( ) cos(" )
!
T
W"
˙ U
g=
D
W+ sin(# )
Hypersonic Educational Initiative
• Air-breathing vehicle:– missions: cruise, orbital return– completely reusable– powered take-off and entry– constant for engine efficiency
• Space Shuttle:– mission: orbital return– rocket launch– equilibrium glide entry– no thrust, L/D~1, γ~0 (shallow entry)
Re-entry Trajectories
!
1
2"U
2
Hypersonic Educational Initiative
Flight Velocity
Hypersonic Educational Initiative
Stagnation Point Heating
Hypersonic Educational Initiative
Stagnation PointTemperature
Hypersonic Educational Initiative
Deceleration Levels
Hypersonic Educational Initiative
1.2 Post-Shock Conditions
• Perfect-gas shock relations:
• Density ratio asymptotes to:
• Pressure and temperature are quadratic in M
– Makes sense: energy is conserved
Hypersonic Educational Initiative
Post-Shock Conditions
• Post-Shock Temperature:
Temperatures rapidlybecome huge!
Hypersonic Educational Initiative
Post-Shock Conditions
• Variation of air internal energy with T:
10% departure fromcalorically perfect gasequation of state =onset of hypersonic flow
Hypersonic Educational Initiative
Post-Shock Conditions
• More fundamentally – 1D gas dynamics:
• Plus equations of state:
• No exact solutions
Thermally perfect,calorically imperfect
General equilibriumgas mixture
Hypersonic Educational Initiative
Post-Shock Conditions
• Hypersonic limit:
• Note that post-shock enthalpy and pressure onlydepend on upstream conditions in hypersonic limit.
Can solve for thethermodynamic state
Hypersonic Educational Initiative
Post-Shock Conditions
• Iterative solution to shock relations:
• Guess a value of ε = εi and iterate:
Use tables, NASA CEA, etc.
Hypersonic Educational Initiative
Equilibrium Air
Temperature (K) Z = Compressibility
Hypersonic Educational Initiative
Post-Shock Conditions
• Example: M = 12 at 30 km altitude:
Imperfect Perfect
Hypersonic Educational Initiative
Post-Shock Conditions
• Perfect-gas vs. equilibrium post-shock conditions:
Difference is due toenergy storage ininternal energymodes + chemistry
Hypersonic Educational Initiative
Post-Shock Conditions
• Post-shock pressure has weak dependence on non-ideal gas effects (just through (1- ε))
• Post-shock temperature and density have strong Machnumber (free-stream speed) dependence– Density ratio > (γ + 1)/(γ - 1) = 6– Temperature decreases significantly
• Concept of γ no longer has much meaning; if:
• Matlab code: ftp://ftp.aem.umn.edu/users/candler/HEI/mollier.m
Hypersonic Educational Initiative
1.3 Reacting Gas Effects
• Analysis of Earth hypersonic vehicles at U<8km/s:– 5-species air model sufficient: N2, O2, NO, N, O
• Reactions:– Dissociation-recombination:
– Zeldovich exchange:!
N2
+ M" N + N + M
!
N2
+O" NO+ N
!
NO+O"O2
+ N!
O2
+ M"O+O+ M
!
NO+ M" N +O+ M
Hypersonic Educational Initiative
Finite Rate of Reactions
• For illustration, consider:– 2-species: N2, N
• Each reaction proceeds at a finite rate:
• Forward rate coefficients measured experimentally, kf (T)
• Backward rate coefficients from equilibrium constant:
partition functions Q from quantum+statistical mechanics
!
N2
+ M" N + N + M
!
N2
+ N2"kb1
k f 1
N + N + N2
!
N2
+ N"kb 2
k f 2
N + N + N
!
Ke =k f
kb="Qproducts
"Qreactants
Hypersonic Educational Initiative
Finite Rate of Reactions
• Net rate of change in concentration of a species:– contributions from forward and backward directions
• Chemical equilibrium:– final state reached instantaneously– production of each species balanced by its destruction– analytical solution for our system:
– α=mass fraction, m=atom mass, ρ=density, V=volume,θd=dissociation temperature
!
d[N2]
dt= "k f 1[N2
][N2]" k f 2[N2
][N]+ kb1[N][N][N2]+ kb2[N][N][N]
!
" 2
1#"=m
$V
QN
2
QN2
exp(#%d /T)
Hypersonic Educational Initiative
Finite Rate of Reactions
• Chemical equilibrium:– O2 dissociates before N2 (has lower θd)– fewer atoms at high pressure (more recombination)
Hypersonic Educational Initiative
Finite Rate of Reactions• Chemical nonequilibrium:
– equilibrium end state reached only after finite time– in a flow field, this translates as finite distance
Hypersonic Educational Initiative
Nonequilibrium
• Impact of chemical nonequilibrium:– chemical composition mainly affects energy of flow
• exothermic reactions consume energy• catalysis: fraction of atoms reaching the vehicle
surface may recombine releasing heat– scaling:
• nonequilibrium flow occurs at lower densityand/or smaller body length scales
!
large Kn "#$L%
1
&$L
!
small Re "#$U$L
µ$
Hypersonic Educational Initiative
Ionization• Very high temperature reacting air (U>8km/s):
– N2, O2, NO, N, O, N2+, O2+, NO+, N+, O+, e-
• Reactions:– dissociation-recombination:
– exchange:
– associative Ionization:
– direct Ionization:
!
N2
+ M" N + N + M
!
N2
+O" NO+ N
!
N + N" N2
++ e
#
!
N + e"# N
++ e
"+ e
"
Hypersonic Educational Initiative
Ionization
• Equilibrium solution (Saha) for [N, N+, e-] system:
– φ=ion mole fraction,– C=constant,– p=pressure,– θi=ionization temperature
!
" 2
1#" 2= C
T5 / 2
pexp(#$i /T)
Hypersonic Educational Initiative
Ionization• Significance:
– plasma causes communications blackout– highly catalytic ions are source of heating
Hypersonic Educational Initiative
Radiation• Another important process at high temperature:
– activation-deactivation:
– spontaneous emission:– analysis is complex, no closed form expressions– research area, e.g. NEQAIR (NASA-ARC)
• Radiative heating important at U>12km/s:– e.g. stagnation point heating correlation (Martin)
– also proportional to shock layer thickness– Stardust: radiation provides 10% of total heating
!
N*" N + h#
!
N + e"# N
*+ e
"
!
˙ q rad "RNU8.5#1.6
Hypersonic Educational Initiative
1.4 Transport Phenomena
• Generated by gradients in flow properties:– diffusion (Fick’s Law):DAB=diffusion coefficient
– viscosity (Newtonian fluid):µ = viscosity coefficient
– thermal conduction (Fourier’s Law):κ = thermal conductivity coefficient
!
JA = "#DAB
dCA
dy
!
" = µdu
dy
!
q = "#dT
dy
Hypersonic Educational Initiative
Diffusion
• Affects continuity and energy equations
• Influences transport of species to surface
• Coefficient evaluation:– for simple gas (self diffusion)
– for gas mixture
– are diffusion collision integrals
– averaged binary coefficient D1m often used
!
Dii
=3
8"
#mikT
#$ii
(1,1)
!
Dij"kT
p
(mi + m j )kT
mim j
1
#$ij
(1,1)
!
"ij
(1,1)
Hypersonic Educational Initiative
Viscosity
• Affects momentum and energy equations
• Influences surface shear stress
• Coefficient evaluation:– for simple gas
– various mixing rules
– are viscosity collision integrals!
µi=5
16
"mikT
"#ii
(2,2)
!
µ = µ("ij
(1,1),"ij
(2,2))
!
"ij
(2,2)
Hypersonic Educational Initiative
Thermal Conductivity
• Affects energy equations
• Influences surface convective heat flux
• Coefficient evaluation:– for simple gas (Eucken)
– various mixing rules
– are again viscosity collision integrals– curve fits for collision integrals from the literature
!
"i=5
16
#mikT
#$ii
(2,2)
1
Mi
Cv
+9
4Ru
%
& '
(
) *
!
" ="(#ij
(1,1),#ij
(2,2))
!
"ij
(2,2)