Injector design — impinging, coaxial, swirl injectors

3.3.34 · Physics › Rocket Propulsion

WHAT karta hai ek injector? (teen physical tasks)

Teen tasks:

Metering — $\overset{m}{˙}$ ko orifices ke through set karna (ek flow-resistance problem).
Atomization — liquid sheets/jets ko tiny droplets mein todna (zyada surface area → tezi se evaporation).
Mixing — fuel aur oxidizer molecules ko sahi ratio mein saath laana.

Neeche di gayi teen classic geometries teeno tasks 2 & 3 ko alag-alag tarike se handle karti hain.

Task 1 — Metering: orifice flow law ko scratch se derive karo

Derivation (Bernoulli, incompressible): Manifold ke andar se (pressure $p_{1}$ , velocity $\approx 0$ ) orifice exit tak (pressure $p_{2} = p_{c}$ , velocity $v$ ) ek streamline lo: $p_{1} + \frac{1}{2} ρ (0)^{2} = p_{2} + \frac{1}{2} ρ v^{2}$ Toh $Δ p = p_{1} - p_{2}$ ke saath: $v = \frac{2 Δ p}{ρ}$

Real orifices perfect nahi hote — jet contract karti hai (vena contracta) aur friction hoti hai. Hum ise ek discharge coefficient $C_{d}$ mein fold kar dete hain (typically $0.6$ – $0.9$ ). Area $A$ ke through mass flow:

Task 2 & 3 — teen injector types

Figure — Injector design — impinging, coaxial, swirl injectors

Har ek ke liye physics knob

Impinging — momentum balance resultant spray direction set karta hai. Agar do jets momentum flux $\overset{m}{˙}_{1} v_{1}$ aur $\overset{m}{˙}_{2} v_{2}$ ke saath half-angle $θ$ par milti hain, toh resultant sheet direction $α$ (axis se) transverse direction mein momentum conservation satisfy karta hai: $tan α = \frac{m ˙ _{1} v _{1} s i n θ _{1} - m ˙ _{2} v _{2} s i n θ _{2}}{m ˙ _{1} v _{1} c o s θ _{1} + m ˙ _{2} v _{2} c o s θ _{2}}$ WHY: collision par jets merge ho jaati hain; total momentum conserve hona chahiye, toh sheet do momenta ke vector sum ke along nikalti hai. Designers transverse component ko null karte hain taaki spray seedha neeche jaye aur wall ko scrub na kare.

Coaxial — atomization velocity ratio / momentum ratio se governed hoti hai. Momentum flux ratio define karo: $J = \frac{ρ _{o} v _{o}^{2}}{ρ _{i} v _{i}^{2}} (outer over inner)$ Zyada $J$ → outer stream inner jet ko zyada aggressively strip karti hai → chote droplets. Yeh shear-atomization principle hai: energy relative velocity $Δ v = v_{o} - v_{i}$ se aati hai.

Swirl — swirl (spray-cone) angle centrifugal vs axial motion se. Injector se nikalte waqt ek fluid element ki tangential velocity $v_{t}$ (spin) aur axial velocity $v_{x}$ hoti hai. Half-cone angle: $tan ϕ = \frac{v _{t}}{v _{x}}$ Zyada strong tangential injection → zyada wide, thin cone → barik atomization. WHY thin sheet achhi atomize hoti hai: ek thin sheet ripples ke liye unstable hoti hai aur jaldi ligaments mein phir droplets mein toot jaati hai.

Worked examples

Common mistakes (steel-manned)

Recall Feynman: 12-saal ke bachche ko samjhao

Socho tum garden hose se spray kar rahe ho. Agar ek mota stream nikalta hai, toh ek jagah bheeg jaati hai aur paani waste hota hai. Agar uspar thumb rakh do, toh woh ek barik mist mein fan ho jaata hai jo sab jagah cover karta hai — jaldi jalta/bheegta hai. Ek rocket injector woh "thumb" hai: woh fuel aur oxygen ki moti streams ko barik mists mein badalta hai aur unhe mix karta hai taaki woh turant aur evenly jalein. Impinging = do streams ko crash karke sheet banao. Coaxial = ek slow stream ke around ek fast stream wrap karo taaki fast wali use shred kare. Swirl = liquid ko spin karo taaki woh thin cone ke roop mein ude. Teeno ek hi cheez chahte hain: tiny droplets, achhi tarah mixed, smoothly burning.

Active recall

Injector ke teen kaam kya hain?

Metering (

\overset{m}{˙}

set karna), atomization (droplets banana), mixing (sahi local O/F).

Bernoulli se orifice velocity derive karo.

p_{1} = p_{2} + \frac{1}{2} ρ v^{2} \Rightarrow v = 2Δ p / ρ

Poora injector mass-flow formula?

\overset{m}{˙} = C_{d} A 2 ρ Δ p

C_{d}

kya hai aur typical range kya hai?

Discharge coefficient (contraction+friction losses), ~0.6–0.9.

Impinging injector kaise atomize karta hai?

Do jets collide karke fan sheet banate hain jo droplets mein toot jaati hai; momentum vectors spray direction set karte hain.

Injector

Δ p ≳ 15%

p_{c}

kyun rakhte hain?

Feed system ko chamber pressure oscillations se decouple karne ke liye → combustion instability rokta hai.

Coaxial injector atomization mechanism?

High-velocity outer annular stream ki shear slow central jet ko strip karti hai; momentum flux ratio

J = ρ_{o} v_{o}^{2} / ρ_{i} v_{i}^{2}

se governed.

Swirl injector spray shape aur uska half-angle?

Hollow cone;

tan ϕ = v_{t} / v_{x}

(tangential over axial velocity).

Chote droplets kyun matter karte hain?

Evaporation/burn time

\propto d^{2}

(

d^{2}

-law); chote droplets finite chamber length ke andar jal jaate hain.

Kaun sa injector single propellant ke saath low

Δ p

par kaam karta hai?

Swirl (centrifugal sheet thinning, shear nahi).

Connections

Combustion Instability — injector $Δ p$ aur feed-coupling mechanism.
Characteristic Velocity c-star — mixing quality $c^{*}$ efficiency set karti hai.
Atomization and the d-squared Law — droplet burn time.
Bernoulli Equation — metering law ki jaad.
Regenerative Cooling — straight-down (non-wall-impinging) spray walls ko kyun protect karta hai.
O/F Ratio and Mixture Ratio — "correct mixing" kya target karta hai.