3.3.22 · D1Staged combustion cycle — full flow, fuel-rich, oxidizer-ric
Ek rocket engine ek aisi machine hai jo propellant ko bahut zyada high-pressure wali aag mein dhakelta hai , aur us pressure ke khilaaf dhakelnay ka sirf ek hi tarika hai — ek pump jo hot-gas turbine se ghoomti hai . Parent page ke har symbol (m ˙ Δ p ρ c p T γ π t η kya turbine itni power bana sakti hai ki pump chal sake?
Is page pe assume kiya gaya hai ki tumhe kuch bhi nahi pata . Hum har letter ko earn karenge — parent note ko use karne ki permission tabhi milegi. Upar se neeche padho — har idea agley ka foundation hai.
Definition Mass flow ratem ˙ mass of propellant hai jo har second ek point se guzarta hai , kilograms per second (kg/s rate hai.
Socho tum ek moti pipe ke paas stopwatch lekar khade ho. Ek second mein liquid oxygen ka ek tukda tumhare paas se guzar jaata hai. Us tukde ko tolo — woh number hi m ˙ m ˙ = 500 kg/s
Topic ko iski zaroorat kyun hai: thrust literally hai "tum kitni tezi se mass ko peeche phenkte ho," isliye har power aur thrust equation m ˙ Rocket thrust equation .
ρ ek cubic metre mein kitna mass packed hai , kg/m 3 ρ LOX ≈ 1140 kg/m 3
Do identical 1-litre bottles: ek paani se bhari, ek liquid hydrogen se bhari. Paani wali bottle kaafi bhaari hai. Density matlab hai tumhari bottle ka wazan — bas itna hi.
1/ ρ ρ 1/ ρ ek kilogram kitna volume leta hai . Ek pump volume move karta hai, isliye jab hum mass flow m ˙ volume flow mein convert karte hain m ˙ / ρ
Pressure p force ek area pe faila hua , pascals mein: 1 Pa = 1 N/m 2 bar bhi use karte hain: 1 bar = 1 0 5 Pa
Intuition Picture — pressure yaani volume per stored energyNeeche wala piston dekho. Pressure p A d p ⋅ A × = p A d A d volume hai jo sweep hua. Toh
work = p × volume ⟹ p = volume energy . Pa = J/m 3 Ek pascal yaani joules per cubic metre. Yeh ek equivalence poore power balance ki neenv hai.
Δ p Δ Δ p = p out − p in pump ne pressure kitna boost kiya . Agar pump propellant ko 5 bar se 305 bar tak le jaaye, toh Δ p = 300 bar = 3 × 1 0 7 Pa
Topic ko iski zaroorat kyun hai: chamber high pressure p c Δ p p c Δ p Specific impulse and chamber pressure se jud ta hai.
Intuition Formula ko pictures se banana
Ek cubic metre ko andar dhakelnay ki energy = Δ p hi hain joules per cubic metre).
Cubic metres flowing per second = m ˙ / ρ
Multiply karo: energy-per-volume × energy per second = power .
P pump = m ˙ ⋅ ρ 1 ⋅ Δ p = ρ m ˙ Δ p
Power P har second deliver ki gayi energy , watts mein (1 W = 1 J/s MW tens of MW maangta hai — ek choti power station ki power, ek microwave ke size ke box mein.
Topic ko iski zaroorat kyun hai: yeh cycle ka "demand" side hai — pumps power maangti hain, aur turbine ko woh supply karni padti hai.
η 0 aur 1 ke beech ka fraction hai jo bataata hai ki ideal work ka kitna hissa tumhe actually milta hai . η p = 0.7 η t = 0.75
Socho ek leaky bucket-chain paani utha rahi hai. Tum 10 buckets effort daalte ho; sirf 7 upar pahunchte hain. Woh "7 out of 10" hi η kho ta hai, tumhe ideal se zyada feed karna padta hai — isliye η p denominator mein baithta hai:
P pump = ρ η p m ˙ Δ p . pakad nahi paati , uska useful output chota hota hai — isliye η t multiplier ke roop mein baithta hai. Yaad rakho: denominator demand ko bada karta hai, multiplier supply ko chota karta hai. Dono tumhein hurt karte hain — iska matlab hi hai "real machine."
T gas kitni hot hai , in formulaon ke liye hamesha kelvin (K ≈ 300 K ≈ 3300 K
c p c p constant pressure par gas ke ek kilogram ko ek kelvin garam karne mein kitne joules lagte hain , J / ( kg ⋅ K ) c p ≈ 14000 J / ( kg K )
c p T c p T = kg ⋅ K J × K = kg J . c p T hot gas ke har kilogram mein stored heat energy — turbine ke liye tank mein fuel. Gas jitni zyada garm ho (T c p
Intuition "Rich burning" flame temperature kyun giraa deti hai — ek line meinChemical energy released Q Δ T = Q / ( m c p ) m aur c p wahi Q Δ T . Yahi poori wajah hai ki ek preburner off-stoichiometric chalti hai — dekho Combustion stoichiometry and flame temperature .
Definition Pressure ratioπ t letter hai, 3.14159 nahi) yaani turbine inlet pressure divided by outlet pressure :
π t = p out p in . π t = 1.5 > 1
Intuition Picture — gas ek paddle-wheel ko dhakelta haiHot gas turbine se guzar ke expand hoti hai. Expanding gas blades par dhakelta hai — woh push shaft ko ghoomata hai. Jitna bada pressure drop (bada π t [ 1 − π t − ( γ − 1 ) / γ ] woh fraction hai jo gas ki heat energy ka ek perfect expansion shaft work mein convert karta hai . Jab π t = 1 π t
γ do specific heats ka ratio , γ = c p / c v γ ≈ 1.2 1.4 > 1
Intuition Yeh exponent mein kyun rehta haiγ adiabatic expansion — koi heat leak nahi hoti) toh pressure aur temperature kaise trade off hote hain. Zyada springy gas (zyada γ ( γ − 1 ) / γ gas se set ek fixed number hai , roughly 0.286 γ = 1.4
power balance turbine equals pump
Khud ko test karo — right side cover karo aur aawaaz mein jawaab do.
m ˙ "per second" — yeh ek rate batata hai, yahan kg per second.
Hum pressure ko J/m³ kyun likh sakte hain? Kyunki work = pressure × volume, isliye pressure = energy per volume (Pa = J/m 3
1/ ρ Woh volume jo ek kilogram occupy karta hai (m³/kg) — yeh mass flow ko volume flow mein convert karta hai.
Δ p Pressure boost p o u t − p in
η p η t Ek real pump ko zyada input chahiye (÷ by <1 ise badhata hai); ek real turbine kam output deti hai (× by <1 ise ghataata hai).
Product c p T Gas ke har kilogram mein stored heat energy (J/kg) — turbine ki fuel supply.
Rich burning flame temperature kyun giraata hai? Δ T = Q / ( m c p ) m c p Q
π t Inlet-over-outlet pressure; gas ko energy release karne ke liye pressure drop karna padta hai, isliye out < in.
Bracket 1 − π t − ( γ − 1 ) / γ π t = 1 Zero — koi pressure drop nahi matlab koi expansion nahi, koi shaft work nahi.
Power balance ek sawaal ka jawaab deta hai? Kya turbine exactly woh power produce karti hai jo pumps maangti hain?
Parent topic: Staged combustion cycle · Neighbours: Gas-generator cycle , Expander cycle , Turbopump design , Regenerative cooling
