Staged combustion cycle — full flow, fuel-rich, oxidizer-rich preburners

3.3.22 · Physics › Rocket Propulsion

YE CYCLE EXIST kyun karta hai?

Iska price: poora propellant flow (ya uska zyada hissa) ek hot, high-pressure turbine se guzarna chahiye, isliye plumbing brutal pressures aur temperatures par chalti hai. Engineering ka jahannum, lekin performance ka swarg.

PARTS kya hain?

Teen flavours

NUMBERS kaise kaam karte hain — turbine power balance derive karo

Step 1 — Pump power. Ek pump mass flow $\dot{m}$ ko pressure rise $\Delta p$ se uthata hai. Per unit volume kaam $\Delta p$ hai; per unit mass volume $1/\rho$ hai.

Yeh step kyun? Pressure ke units energy per volume hain ($\text{Pa}={\text{J/m}}^3$), isliye volume flow $\dot{m}/\rho$ se multiply karne par power milti hai.

$P_{\text{pump}}=\frac{\dot{m}\Delta p}{\rho {\eta }_p}$

${\eta }_p$ (< 1) isliye aata hai kyunki real pumps kuch input heat ke roop mein waste karte hain.

Step 2 — Turbine power. Turbine hot preburner gas se enthalpy extract karta hai jab woh pressure ratio ${\pi }_t=p_{in}/p_{out}$ ke across expand hoti hai. Adiabatically expand hote ideal gas ke liye:

$P_{\text{turb}}={\dot{m}}_{pb}{c}_p{T}_{in}{\eta }_t\left[1-{\pi }_t^{-(\gamma -1)/\gamma }\right]$

Yeh step kyun? $c_{p}T$ per unit mass enthalpy hai; bracket woh fraction hai jo ideal expansion se convert hota hai; ${\eta }_t$ turbine efficiency hai.

Step 3 — Power balance (cycle constraint).

$\boxed{P_{\text{turb}}=P_{\text{pump}}⟹{\dot{m}}_{pb}{c}_p{T}_{in}{\eta }_t\left[1-{\pi }_t^{-(\gamma -1)/\gamma }\right]=\sum \frac{\dot{m}\Delta p}{\rho {\eta }_p}}$

Worked examples

Common mistakes (steel-manned)

Flashcards

Connections

• Gas-generator cycle — woh wasteful cousin jo turbine exhaust bahar phenkta hai.
• Expander cycle — regenerative heat use karta hai, koi preburner combustion nahi.
• Turbopump design — pumps jinki power demand cycle set karti hai.
• Specific impulse and chamber pressure — kyun high $p_c$ se $I_{sp}$ badhta hai.
• Combustion stoichiometry and flame temperature — kyun rich mixtures thande chalte hain.
• Regenerative cooling — aksar staged combustion ke saath paired hota hai.
• Rocket thrust equation — jahan recovered propellant finally kaam karta hai.

Concept Map