Injector design — impinging, coaxial, swirl injectors: Question bank

3.3.34 · D5 · Physics › Rocket Propulsion › Injector design — impinging, coaxial, swirl injectors

Questions se pehle, symbols ka ek one-liner refresher taaki kuch bhi unearned na lage:

Recall Symbol refresher (koi notation unfamiliar lage toh kholein)

$\overset{m}{˙}$ ::: mass flow rate (orifice se ek second mein kilograms propellant). $Δ p$ ::: injector pressure drop = manifold pressure minus chamber pressure, $p_{1} - p_{c}$ . $C_{d}$ ::: discharge coefficient, 0 aur 1 ke beech ek fudge factor jo friction aur jet contraction (vena contracta) dono ko fold karta hai. $J$ ::: do coaxial streams ka momentum flux ratio, $ρ_{o} v_{o}^{2} / ρ_{i} v_{i}^{2}$ (outer over inner). $ϕ$ ::: swirl half-cone angle, jahan $tan ϕ = v_{t} / v_{x}$ (tangential spin speed over axial speed). $c^{*}$ ::: characteristic velocity, ek scoreboard ki combustion kitni completely hui — dekho Characteristic Velocity c-star.

True or false — justify

Naive orifice law

\overset{m}{˙} = C_{d} A 2 ρ Δ p

kehta hai ki

Δ p

double karne se mass flow bhi double ho jaati hai.

False —

\overset{m}{˙} \propto Δ p

hai, toh

Δ p

double karne se flow sirf

2 \approx 1.41

guna hoti hai. Flow double karne ke liye

Δ p

chaar guna karna padega.

Ek bahut smooth, well-rounded orifice ke liye

C_{d}

greater than 1 possible hai.

False —

C_{d}

losses (friction, vena contracta) account karta hai, isliye yeh ideal flow ko sirf kam kar sakta hai; physical ceiling

C_{d} = 1

hai, approach hoti hai lekin kabhi exceed nahi hoti.

Ek swirl injector kisi bhi second stream ke bina, sirf ek akele propellant ko atomize kar sakta hai.

True — swirl centrifugal thinning of a self-supported hollow-cone sheet pe rely karta hai, toh ek propellant jo itna hard spin ho woh khud hi atomize ho jaata hai. Dekho Atomization and the d-squared Law.

Ek coaxial injector mein, agar dono streams same velocity par move karein (

v_{o} = v_{i}

) toh outer stream phir bhi inner jet ko achhe se atomize karti hai.

False — coaxial atomization relative velocity

Δ v = v_{o} - v_{i}

se drive hoti hai;

v_{o} = v_{i}

hone par koi shear nahi hoti aur central jet practically break up hi nahi karti.

Ek balanced (symmetric) unlike-doublet impinging pair, jo axis se equal angles par aim ki gayi ho, spray seedha chamber axis ke neeche karta hai.

True — transverse momentum components cancel ho jaate hain, toh momentum conservation se resultant sheet axis ke along hi nikalti hai (

α = 0

), jo exactly wall-scrubbing se bachata hai.

Injector

Δ p

badhana hamesha combustion stability improve karta hai.

Mostly true ek point tak — zyada

Δ p

feed system ko chamber oscillations se better decouple karta hai, lekin bahut zyada badhane se pump power waste hoti hai aur extra stability bahut kam milti hai, isliye designers

Δ p ≳ 0.15 p_{c}

ke paas rok dete hain. Dekho Combustion Instability.

Δ p

scaling Bernoulli Equation se aati hai, jahan pressure work kinetic energy

\frac{1}{2} ρ v^{2}

mein convert hoti hai.

True — kyunki kinetic energy

v^{2}

ke saath jaati hai,

Δ p = \frac{1}{2} ρ v^{2}

solve karke

v

nikaalein toh square root milti hai, aur

\overset{m}{˙} \propto v

usse inherit karta hai.

Finer atomization (chote droplets) required combustion chamber length ko kam karti hai.

True — evaporation time

d^{2}

ke saath scale karti hai (

d^{2}

-law), toh chote droplets jaldi jalte hain aur propellant ek chhote chamber mein hi react kar leta hai.

Wider swirl cone angle

ϕ

generally ek thinner sheet aur finer atomization deta hai.

True — zyada tangential velocity cone ko wider karti hai aur sheet ko thinner stretch karti hai, aur thin sheets ripples ke liye jaldi unstable ho jaati hain aur droplets shed karti hain.

Ek bade orifice ki jagah bahut se chote orifices use karne se total metered mass flow change ho jaati hai agar

Δ p

unchanged ho.

False — total flow total open area par depend karti hai; same area ko bahut saare holes mein split karne par

\overset{m}{˙}

fixed rehta hai jabki mixing improve hoti hai (zyada, finer jets).

Spot the error

"Kyunki

\overset{m}{˙} = C_{d} A 2 ρ Δ p

hai, ek denser propellant same orifice se dheemar flow karta hai, toh ise flow reduce karne ke liye use karo."

Error — density mass-flow formula ke andar appear karti hai, aur zyada

ρ

\overset{m}{˙}

badhti hai (har unit volume mein zyada mass). Velocity

v = 2Δ p / ρ

density ke saath ghatti hai, lekin mass flow — jo actually poocha gaya hai — badhti hai.

"Coaxial aur swirl injectors identically atomize karte hain; bas differently-shaped clouds banate hain."

Error — coaxial ek second high-velocity stream ke shear se atomize karta hai (bada

Δ v

chahiye); swirl apni sheet ki centrifugal thinning use karta hai (kam

Δ p

par bhi kaam karta hai, akele bhi). Alag physics, alag failure modes.

Δ p

kam karna free efficiency hai kyunki pump work ghatti hai aur mixing ek alag concern hai."

Error — bahut kam

Δ p

chamber pressure oscillations ko orifice se peeche push karne deta hai, feed aur chamber ko Combustion Instability mein couple karta hai. Metering, stability, aur

Δ p

alag nahi kiye ja sakte.

"Bade droplets theek hain, chamber garam hai toh eventually jal jaayenge."

Error — burn time

\propto d^{2}

hai, toh diameter double karne par burn time chaar guni ho jaati hai; agar droplet finite chamber se unburned nikal jaaye, toh

c^{*}

efficiency girti hai. Dekho Characteristic Velocity c-star.

"Impinging spray angle

tan α = \frac{m ˙ _{1} v _{1} sin θ _{1} - m ˙ _{2} v _{2} sin θ _{2}}{m ˙ _{1} v _{1} cos θ _{1} + m ˙ _{2} v _{2} cos θ _{2}}

ke liye, numerator dono jets ko sum karta hai toh ek symmetric pair sideways spray karta hai."

Error — dono jets axis ke opposite sides par hote hain, toh unke transverse (

sin

) terms opposite signs lete hain aur subtract hokar zero ho jaate hain; numerator vanish karta hai aur

α = 0

, matlab seedha neeche.

"Kyunki

tan ϕ = v_{t} / v_{x}

hai, zero axial velocity wala swirl injector

0^{\circ}

(pencil) jet produce karta hai."

Error —

v_{x} \to 0

ke saath ratio

v_{t} / v_{x} \to \infty

ho jaata hai, toh

ϕ \to 9 0^{\circ}

: ek flat radial disc, pencil nahi. Bada

v_{x}

hona cone ko narrow karta hai.

Why questions

Mass-flow law mein

Δ p

par linear dependence ki jagah square root kyun hoti hai?

Kyunki pressure work kinetic energy

\frac{1}{2} ρ v^{2}

mein convert hoti hai, aur energy

v^{2}

ke saath scale karti hai; us relationship ko invert karke

v

nikaalein toh square root aati hai, jo

\overset{m}{˙} \propto v

phir carry karta hai.

Designers

Δ p

ko chamber pressure ke roughly 15–25% par deliberately kyun rakhte hain, ise minimize karne ki jagah?

Ek stiff pressure drop orifice se flow ko chamber pressure ke wobbles ke baare mein nearly insensitive banata hai, feed system ko combustion oscillations se decouple karta hai aur instability suppress karta hai.

Coaxial injector ke outer stream ko fast kyun hona chahiye exactly isliye kyunki woh light hai (jaise gaseous H₂)?

Atomization momentum flux

ρ v^{2}

se drive hoti hai; kam density

ρ

ko enough

J

build karne ke liye high

v

se compensate karna padta hai taaki dense central jet ko shear karke tod sake.

Ek thin liquid sheet thick jet se better kyun atomize hoti hai?

Ek thin sheet small surface ripples se easily destabilise ho jaati hai jo grow karti hain, use ligaments mein tear karti hain, aur phir fine droplets mein — ek thick jet iska resist karta hai aur bahut lambe time tak coherent rehta hai.

Unlike-impinging doublet ek hi point par mix aur atomize kyun karta hai, jabki like-on-like dono tasks alag karta hai?

Unlike impingement mein, fuel collision par oxidizer se milta hai, toh smashing sheet already mixed sheet hai; like-on-like same-with-same ko collide karta hai, pehle atomize karta hai aur mixing ke liye baad ki diffusion par rely karta hai.

Impinging designers resultant sheet ka "transverse momentum null" kyun karte hain?

Taaki spray axis ke seedha neeche jaaye instead of wall ki taraf angle karne ke; ek sideways spray hot combustion ko chamber wall ke against scrub karta hai aur burn-through ka risk hota hai. Dekho Regenerative Cooling.

Har injector element par local mixture ratio kyun matter karta hai, sirf overall chamber

O / F

nahi, jo actually performance aur wall heat control karta hai?

Combustion locally milliseconds mein hoti hai, toh ek globally-correct chamber mein phir bhi fuel-rich aur ox-rich streaks ho sakti hain jo efficiency hurt karti hain ya walls overheat karti hain — dekho O/F Ratio and Mixture Ratio.

Edge cases

Δ p = 0

hone par jet velocity

v = 2Δ p / ρ

ka kya hota hai?

v = 0

: koi pressure difference nahi toh koi driving work nahi, toh kuch bhi flow nahi karta — orifice effectively closed hai, chahe area kuch bhi ho.

Agar sirf ek jet fire kare (

\overset{m}{˙}_{2} v_{2} = 0

) toh impinging formula kya deta hai?

tan α = tan θ_{1}

, toh "resultant" bas bachne wala jet apne hi angle par hota hai — balance kho jaata hai aur single jet off-axis spray karta hai, likely ek wall ki taraf.

Swirl injector ke liye, pure axial flow

v_{t} = 0

ki limit mein cone angle kya hai?

tan ϕ = 0/ v_{x} = 0

, toh

ϕ = 0

: ek seedha pencil jet jisme koi swirl nahi — poor atomization, kyunki centrifugal thinning mechanism off ho gayi hai.

Coaxial injector ke liye, agar inner jet momentarily stalled ho (

v_{i} = 0

) toh

J

kya hai?

J = ρ_{o} v_{o}^{2} /0 \to \infty

: formula diverge karta hai, signalling ki ek motionless core par maximal shear hai — practically outer stream completely aur violently inner jet ko shred karti hai.

Discharge coefficient

C_{d} \to 0

ka physical meaning kya hai?

Orifice apne geometric area ke liye almost koi flow pass nahi kar raha — extreme choking ya blockage; available pressure work ka almost sab kuch useful jet velocity banne ki jagah lost ho jaata hai.

d^{2}

-law picture mein droplet diameter

d \to 0

hone par atomization ko kya limit karta hai?

Burn time zero ki taraf collapse ho jaati hai, jo completeness ke liye ideal hai, lekin real sprays

d

ko indefinitely shrink nahi kar sakti — energy cost aur sheet stability ek practical floor set karte hain. Dekho Atomization and the d-squared Law.