3.1.27 · D1Hypersonic flow — Mach 5+, high temperature effects
Ek hypersonic vehicle air ki motion energy ko itni violently heat mein convert karta hai ki
gas ek simple spring-loaded gas ki tarah behave karna band kar deti hai aur vibrate, toot-phoot,
aur glow karne lagti hai.
Parent page par jo bhi hai woh sirf careful bookkeeping hai ki woh energy kaahan jaati hai — isliye
pehle us page ko padhne se pehle humein har woh symbol apna banana hoga jo speed, temperature, pressure,
aur energy track karne ke liye use hota hai.
Is page mein assume kiya gaya hai ki aapne koi bhi notation pehle nahi dekha. Hum har symbol ek ek karke banate hain, har ek sirf apne se pehle waale par depend karta hai. Upar se neeche padho.
V V kitni tezi se air move karti hai vehicle ke paas se, metres per second mein. Socho tum
re-entry capsule ki naak par khade ho: air tumhari taraf V
Hum stream ko parallel arrows ke bundle ki tarah draw karte hain, sab same length ke (length = speed).
Intuition Speed akela kyun kaafi nahi hai30 m/s par chalti car aur 30 m/s par jaati bullet air ko sirf isliye alag feel karaati hain kyunki air
ki apni "signalling speed" alag hoti hai. Air pressure ripples — sound — bhejonkar aage push back
karti hai. Jo matter karta hai woh hai tumhari speed us speed se compare karke jitni tezi se woh ripples
travel karti hain . Wahi comparison Mach number hai, aage aata hai.
a a kitni tezi se ek chhoti si pressure disturbance gas mein travel karti hai woh hai. Socho air ko
tap karo: woh "tap" a kam jahan air thandi hoti hai.
Topic ko a shock mein pile up ho
jaati hai.
M M = a V sound se kitni baar zyada tezi se ja rahe ho. M = 1 M = 5
M M < 1 M > 1 M
M a same
speed V M ⇒ a ⇒ M M kaahan ?"
M Supersonic Flow & Area-Mach Relations par define kiya gaya hai aur yeh poore parent topic ka
master dial hai.
T T gas molecules ki average jiggling energy measure karta hai jo straight lines mein move karti hain
(translation). Socho ek box mein bouncing balls ka swarm: hotter = faster average bouncing. Hum kelvin
(K) use karte hain, jo absolute zero (koi jiggle nahi) se shuru hota hai, isliye T
Topic ko T kahin jaana
hota hai, aur pehla place jahan woh jaati hai woh yeh jiggling hai — yaani temperature shoot up ho jaata
hai.
Intuition Baad ke liye ek crucial subtletyT translational (aur rotational) jiggling count karta hai. Molecules stretch aur bend bhi
kar sakte hain (vibration) ya toot sakte hain — aur woh hidden energy T show nahi hoti .
Yahi poora reason hai ki γ
p p push per unit area hai jo gas exert karti hai, countless molecules ek surface ko hammer karne
se. Socho ek umbrella par baarish: zyada drops, ya tezi drops, matlab zyada push. p ∞ ∞ undisturbed air ka pressure far upstream, vehicle ke disturb karne se pehle.
ρ ρ gas ke har cubic metre mein kitna mass baith ta hai woh hai. Socho same box mein aur zyada
balls pack karo. ρ ∞ ρ 1 ρ 2 pehle aur
baad ki density (aage dekho).
Topic ko dono ki zaroorat kyun hai: pressure force deta hai (lift, drag, heating loads), aur density
batata hai ki gas얇 thin shock layer mein kitni tightly pack hoti hai.
Parent page symbols par chhote subscripts lagate hai. Har ek flow mein ek jagah hai.
Definition Subscripts padhna
∞ far upstream , calm air jo vehicle mein fly karta hai (V ∞ , p ∞ , ρ ∞ 0 stagnation , jahan flow fully rest mein laya gaya ho (T 0 , h 0 1 shock ke theek pehle ; 2 shock ke theek baad .
Intuition "Stagnation" (subscript 0) kyun show ka star haiBlunt body ke bilkul aage ek single point hota hai jahan air fully ruk jaati hai: stagnation
point . Wahan ki saari motion energy heat ban gayi hai, isliye T 0 sabse zyada hoti hai. Poori "kyun itna garam hota hai" ki story T 0
Stagnation quantities Stagnation Properties & Isentropic Relations ka subject hain.
h h gas ke har kilogram mein stored total internal + flow energy hai. Abhi iska deep definition
nahi chahiye — h h = c p T c p
Topic ko is ki zaroorat kyun hai: yeh woh single equation hai jo kehta hai "gas garam isliye hoti hai
kyunki woh ruk gayi**." T 0
Yeh chaar describe karte hain ki koi particular gas energy kaise store karti hai . Yeh temperature aur
baaki sab ke beech bridge hain.
R R pressure, density, aur temperature ko link karta hai : p = ρR T
γ γ = c v c p single number jo capture karta hai ki gas kitni "springy" hai . Thandi air mein
γ = 1.4 γ drop
karta hai kyunki energy vibration aur broken bonds mein chhup jaati hai.
Intuition Picture: degrees of freedomf x y z degree of freedom f f ⇒ ⇒ c v ⇒ γ = 1 + f 2
In constants ka real-gas behaviour
Real Gas Thermodynamics & Dissociation par hai.
θ θ oncoming stream aur us surface ke beech ka angle hai jo air hit karti hai. Socho flow ek
ramp ko skim kar rahi hai: θ C p = 2 sin 2 θ θ
α α poora body flow ke relative kitna tilt hai woh hai. Flat plate ke liye, windward face ka
θ α
R n R n body ka front kitna rounded hai woh hai. Bada R n R n 1/ R n
Shock angles aur unki equations Normal and Oblique Shock Waves se aate hain.
C p C p = 2 1 ρ ∞ V ∞ 2 p − p ∞ wo extra pressure jo ek surface feel karti hai, flow ki motion energy density ke
units mein measured . Denominator 2 1 ρ ∞ V ∞ 2 dynamic pressure kehte
hain — woh "punch" jo stream carry karta hai. Isse divide karne par C p
Topic ko C p C p = 0.134 Mach-independence principle ka essence.
stagnation temperature T0
specific heat ratio gamma
real gas and dissociation
Ise aise padho: temperature speed of sound set karti hai , jo speed ke saath M M γ stagnation temperature set karte hain; woh high temperature
degrees of freedom kholti hai, jo γ real-gas effects mein feed back
karti hai — woh loop jo hypersonics ko special banata hai.
Right side cover karo aur khud ko test karo. Agar koi bhi answer surprise kare, to woh section dobara
padho.
M Tumhari speed V a
Same speed alag Mach numbers kyun ho sakti hai? Kyunki a a M
Temperature T nahi karta? Yeh translational/rotational jiggling count karta hai; yeh vibration ya bond-breaking energy count nahi karta .
Subscripts ∞ 0 1 2 Far upstream; stagnation (fully stopped); shock ke theek pehle; shock ke theek baad.
Woh energy equation batao jo naak ko garam karti hai. h + 2 1 V 2 = h 0 = const
γ Ratio c p / c v 1.4
Zyada degrees of freedom f γ Zyada f c v γ = 1 + 2/ f
Woh do identities kaunsi hain jo energy equation ko T 0 / T = 1 + 2 γ − 1 M 2 c p = γ R / ( γ − 1 ) a 2 = γ R T
C p Pressure coefficient ( p − p ∞ ) / ( 2 1 ρ ∞ V ∞ 2 )
Nose radius R n Stagnation heat flux
1/ R n ki tarah scale karta hai, isliye blunter (bada
R n ) matlab kam heating.
Ready ho? Hypersonic flow — Mach 5+, high temperature effects par wapas jao aur us page par har symbol
woh hoga jo tum pehle se mil chuke ho.