Turbopump design — centrifugal pump, axial turbine stages, NPSH

3.3.27 · Physics › Rocket Propulsion

Intuition Bada picture

Ek rocket engine propellant ko bahut zyada chamber pressure (maan lo 100–250 bar) par jalata hai. Us chamber mein propellant ko push karne ke liye pump outlet pressure usse bhi zyada honi chahiye. Sirf tank pressure se yeh karna bahut bhaari aur mote tanks maangega — jo dangerous hoga. Isliye hum turbopump use karte hain: ek choti turbine (hot gas se spin hoti hai) usi shaft par ek pump chalati hai jo propellant pressure ko 100× ya usse bhi zyada badha deti hai. YEH KYUN EXIST KARTA HAI: thoda sa propellant gas generator mein jalao, aur iske badle mein halke, low-pressure tanks se kaam chala sakte ho jabki high-pressure chamber ko feed karte raho. Teen design pillars hain: (1) centrifugal pump jo liquid ko energy deta hai, (2) axial turbine stages jo hot gas se power extract karke ise spin karte hain, aur (3) NPSH constraint jo pump inlet ko boil hone (cavitate hone) se rokti hai.

1. Centrifugal Pump — head derive karna

Euler head ko scratch se derive karna (WHY formula aisa dikhta hai)

WHAT chahiye hamein: fluid mein add ki gayi specific energy (energy per unit mass).

HOW — angular momentum bookkeeping. Socho fluid mass flow $\overset{m}{˙}$ impeller se guzar raha hai. Impeller ek torque $T$ lagata hai fluid ki angular momentum change karne ke liye:

$T = \overset{m}{˙} (r_{2} c_{u 2} - r_{1} c_{u 1})$

jahan $c_{u}$ absolute fluid velocity ka tangential (whirl) component hai. Tangential kyun only? Sirf tangential velocity hi axis ke baare mein angular momentum carry karti hai.

Ek shaft jo angular speed $ω$ par spin ho raha ho, usse deliver ki gayi power $P = T ω$ hai. Substitute karo:

$P = \overset{m}{˙} ω (r_{2} c_{u 2} - r_{1} c_{u 1}) = \overset{m}{˙} (u_{2} c_{u 2} - u_{1} c_{u 1})$

blade speed $u = ω r$ use karte hue. Yeh step kyun? $ω r_{2} = u_{2}$ bas rim speed hai — cleaner variable hai.

Energy added per unit mass hai $P / \overset{m}{˙}$ ; $g$ se divide karne par milta hai head $H$ (equivalent liquid column ki height):

$c_{u 1} = 0$ kyun? Liquid ko seedha andar feed karna (radial/axial) matlab no pre-rotation, isliye saari whirl energy is impeller se add hoti hai — simple bhi hai aur given $u_{2}$ ke liye head bhi maximize hoti hai.

Head se pressure rise tak

$Δ p = ρ g H ⟹ Δ p \approx ρ u_{2} c_{u 2}$

Kyun? Head energy/weight hai; $ρ g$ se multiply karo to milti hai energy/volume = pressure.

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

2. Axial Turbine Stages — shaft power kahan se aati hai

Turbine ke liye axial kyun (centrifugal kyun nahi)? Turbine low-density, high-velocity gas handle karta hai; axial rows series mein stack hoti hain aur ek compact, high-power-density machine mein bahut saari energy easily extract kar sakti hain.

Turbine work derive karna (Euler phir — same physics!)

Same angular-momentum argument, lekin ab fluid rotor ko whirl deta hai:

$w_{turb} = u (c_{u, in} - c_{u, out}) = u Δ c_{u}$

Pump se sign flip kyun? Pump whirl add karta hai (work in); turbine whirl remove karta hai (work out). Yahi $u Δ c_{u}$ Euler relation hai.

Shaft shared hai: $P_{turb} = P_{pump} / η_{mech}$ . Yeh dono ko couple karta hai: turbine ko exactly utni power produce karni hogi jitni pump demand kare.

$P_{pump} = \frac{m ˙ _{prop} g H}{η _{pump}} = \frac{m ˙ _{prop} Δ p}{ρ η _{pump}}$

3. NPSH — pump ko khud boil hone se rokna

Tank se NPSH $_{A}$ derive karna (WHY har term)

Tank surface se pump inlet tak energy conservation (Bernoulli + losses) apply karo:

$tank press head \frac{p _{tank}}{ρ g} + static height z - friction h_{loss} = \frac{p _{inlet}}{ρ g} + \frac{v ^{2}}{2 g}$

Inlet par vapor pressure ke upar available total (stagnation) head ke liye rearrange karo:

Common Mistakes (Steel-manned)

Recall Feynman: 12-saal ke bacche ko explain karo

Socho tum ek bottle mein paani daalna chahte ho jisme pehle se bahut zyada pressure hai. Normal squirt bottle nahi jeet sakti. Toh tum ek ghoomta hua fan (impeller) use karte ho jo paani ko ek circle mein super fast fling karta hai — zyada fast ghoome to paani "zyada powerful tarike se maarta hai," isliye exit par bade pressure ke saath jaata hai. Uss fan ko ghomaane ke liye tumhe motor chahiye, isliye tum usi stick par ek choti si chakki (turbine) par hot gas foonkte ho — gas chakki ko push karti hai, chakki fan ghomaati hai. Ek dikkat: agar paani ko bahut zyada kheecho, to woh bubbles mein boilne lagta hai (jaise hila hua soda), jo fan ko kharab kar deta hai. NPSH bas "boilne se pehle kitna room hai" wali safety number hai — ise positive rakho!

Connections

Euler Turbomachinery Equation — pump aur turbine dono ke liye ek master relation.
Bernoulli's Principle — inlet pressure drop aur NPSH ko underpin karta hai.
Cavitation — woh failure mode jisse NPSH bacha ke rakhta hai.
Gas Generator Cycle & Staged Combustion Cycle — turbine drive gas kahan se aati hai.
Chamber Pressure and Thrust — pump discharge target set karta hai.
Specific Impulse — cycle choice pump work vs. $I_{s p}$ ko trade karta hai.

Flashcards

Rocket ko pressure-fed tanks ki jagah turbopump kyun chahiye?

Bahut zyada chamber pressure ko feed karne ke liye jabki tanks halke aur low-pressure rahe; turbine thoda sa jala hua gas lekar huge pump head deta hai.

No inlet swirl ke saath Euler pump head batao.

H = u_{2} c_{u 2} / g

, jahan

u_{2} = ω r_{2}

rim speed hai aur

c_{u 2}

exit whirl velocity hai.

Head density par kyun depend nahi karta lekin pressure rise karta hai?

Head energy per unit weight hai (

H = u_{2} c_{u 2} / g

); pressure energy per unit volume hai (

Δ p = ρ g H

), isliye

ρ

se multiply karne par density wapas aati hai.

Head rim speed ke saath roughly kaise scale karta hai?

H \sim u_{2}^{2} / g

, isliye shaft speed double karne se head chaar guna ho jaata hai.

Turbine stage work per unit mass likho.

w = u Δ c_{u}

(blade speed × whirl mein change), wohi Euler relation jaise pump mein hai lekin energy extract karta hai.

Pump aur turbine coupled kyun hain?

Same shaft: common

ω

aur

P_{turb} = P_{pump} / η_{m ec h}

, isliye ek ko size karna doosre ko constrain karta hai.

NPSH_A define karo.

NPSH_{A} = \frac{p _{t ank} - p _{v}}{ρ g} + z - h_{l oss}

: vapor pressure ke upar inlet head margin.

Safe-operation NPSH condition kya hai?

NPSH_{A} > NPSH_{R}

; warna inlet pressure

p_{v}

se neeche girti hai aur pump cavitate karta hai.

Inducer kya karta hai?

Impeller ke aage ek slender axial screw jo flow ko pre-pressurize karta hai, NPSH_R lower karta hai taaki tank halka reh sake.

Maximum shaft speed ultimately kya limit karta hai?

Suction/cavitation (NPSH_R speed ke saath badhta hai), head production nahi.

LH₂ metres mein huge NPSH values kyun deta hai?

Iski density tiny hai (~71 kg/m³), isliye koi bhi pressure margin ek bahut lamba equivalent liquid column convert ho jaata hai.