Foundations — Turbopump design — centrifugal pump, axial turbine stages, NPSH

3.3.27 · D1 · Physics › Rocket Propulsion › Turbopump design — centrifugal pump, axial turbine stages, N

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1. "Kitna stuff move hota hai" ke absolute basics

Mass flow rate — $\dot{m}$

Picture. Ek pipe socho. Usmein ek invisible slice draw karo. Un kilograms ko count karo jo ek second mein us slice ko cross karte hain — woh number hi $\dot{m}$ hai. Upar chhota dot ka matlab hamesha "per second" hota hai (ek rate).

Topic ko kyun chahiye. Ek rocket engine ek flow machine hai — propellant continuously stream karta rehta hai. Jo bhi power aur force hum compute karte hain woh "per second" hai, isliye hume pata hona chahiye ki har second kitna mass stream hota hai.

Density — $\rho$

Picture. Ek $1\text{m}\times 1\text{m}\times 1\text{m}$ box. Isme liquid bharo aur weigh karo. Water deta hai $1000\text{kg}$, toh ${\rho }_{\text{water}}=1000$. Liquid hydrogen (LH₂) fluffy hai: usi box mein sirf $71\text{kg}$.

Topic ko kyun chahiye. LH₂ ka itna halka hona hi exactly reason hai ki uske pressure numbers baad mein bade "column heights" mein kyun badal jaate hain — yeh fact apni pocket mein rakhna.

2. Circles aur spinning — rotation ko speed mein convert karna

Angular speed — $\omega$

Radian kya hai? Ek circle ke around walk karo. Ek poora loop $2\pi \approx 6.28$ radians hai. Toh radian bas degrees ki jagah $\pi$ number use karke "kitna turn" measure karne ka tarika hai.

RPM se $\omega$

Engineers spin ko RPM (revolutions per minute — poore turns har minute) mein quote karte hain. Convert karne ke liye:

$\omega =\frac{2\pi N}{60}$

Blade speed — $u=\omega r$

Picture. Neeche figure dekho: same $\omega$ axis ke paas chhoti speed deta hai ($u_1=\omega r_1$) aur rim par badi speed ($u_2=\omega r_2$). Subscript bas kaunsa radius batata hai: $1$ = inlet (axis ke paas, "eye"), $2$ = outlet (rim).

Topic ko kyun chahiye. Poora pump liquid ko fast rim speed $u_2$ tak drag karne se kaam karta hai. Kyunki head $u_2^2$ ki tarah badhta hai, bada rim ya tez spin design mein sabse bada lever hai.

3. Ek velocity ko useful pieces mein todna

Jab liquid impeller rim se nikalta hai toh woh kisi direction mein move karta hai — partly baahir, partly sideways (circle ke around). Hume in dono ko alag karna hoga.

Picture. Rim par khade ho aur fluid ka velocity arrow draw karo. Ise do directions par drop karo: ek straight baahir pointing (radial), ek sideways circle ke along (tangential). Sideways wala $c_u$ hai.

• $c_{u1}$ = inlet par whirl. Design choice: aksar $c_{u1}=0$ (liquid seedha andar aata hai, koi pre-spin nahi).
• $c_{u2}$ = outlet (rim) par whirl — yeh woh whirl hai jo impeller add karta hai.

4. Energy per kilogram, aur "head"

Torque — $T$

Power — $P=T\omega$

Gravity — $g$

$g\approx 9.81{\text{m/s}}^2$ woh acceleration hai jo gravity girne wali cheezoon ko deta hai. Yeh isliye appear hota hai kyunki hum energy ko liquid ki equivalent height ke roop mein measure karna choose karte hain (aage).

Head — $H$

Pressure — $p$, aur rise $\Delta p$

$\Delta p$ (triangle $\Delta$ ka matlab "change in" hai) woh pressure hai jo pump add karta hai: outlet minus inlet.

5. Gas-side extra symbols (turbine ke liye)

Turbine hot gas se spin hota hai, aur gas ko kuch aur letters chahiye.

• $c_p$ — specific heat at constant pressure: ek kilogram gas ko fixed pressure par ek degree warm karne ke liye kitne joules chahiye. Units $\text{J/(kg⋅K)}$. Bada $c_p$ = gas dene ke liye bahut thermal energy store karta hai.
• $T_0$ — stagnation (total) temperature: woh temperature jo gas ko milti agar use smoothly rest par laaya jaaye. Socho "kul thermal energy ready hai." Units: kelvin, $\text{K}$.
• $\gamma$ — heat capacity ratio ("gamma"): ek pure number (~1.2–1.4) jo describe karta hai ki gas squeeze hone par kaise heat up hota hai. Yeh control karta hai ki expansion kitni energy release kar sakta hai.
• ${\pi }_t$ — turbine pressure ratio: turbine ke across inlet pressure ko outlet pressure se divide kiya. Bada ratio = gas ke expand hone aur energy dene ke liye zyada room.
• $\eta$ — efficiency ("eta"): actually captured ideal energy ka fraction, $0$ aur $1$ ke beech. Subscripts batate hain kaunsa device: ${\eta }_t$ turbine, ${\eta }_{\text{pump}}$ pump, ${\eta }_{\text{mech}}$ shaft bearings/seals.

6. Boiling-safety symbols

• $p_v$ — vapor pressure: woh pressure jiske neeche liquid apni current temperature par boil karta hai. LOX aur LH₂ pehle se iske paas hain — dangerous.
• $z$ — static height: tank pump ke upar kitna ooncha hai. Ooncha tank = gravity extra push deti hai (helps).
• $h_{\text{loss}}$ — friction head loss: "push" ke metres jo neeche aate time pipe walls se rubbing mein kha jaate hain (hurts).
• NPSH — Net Positive Suction Head: safety margin, metres mein, pump inlet par liquid ko actually jo pressure hai aur jis pressure par woh boil karega, in dono ke beech.

Prerequisite map

Har root symbol teen pillars mein se ek ko feed karta hai — pump head, turbine power, NPSH — jo milke hain turbopump. Related cycle ideas Gas Generator Cycle aur Staged Combustion Cycle mein hain; pump/turbine same physics share karte hain jaise Euler Turbomachinery Equation, aur inlet-boiling logic Bernoulli's Principle par tiki hai.

Equipment checklist

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