Solid propellants — fuel + oxidizer in polymer matrix: Question bank

3.3.35 · D5 · Physics › Rocket Propulsion › Solid propellants — fuel + oxidizer in polymer matrix

Spot the error

"Thrust

= \overset{m}{˙} v_{e}

, aur

\overset{m}{˙} = ρ_{p} A_{b} r

, toh ek bada chamber zyaada thrust deta hai."

Chamber volume akele kuch nahi karta; sirf burning surface

A_{b}

\overset{m}{˙}

mein aata hai. Ek bada khaali chamber ek chhoti burning area ke saath chhota thrust deta hai.

"Kyunki

r = a p_{c}^{n}

hai, chamber pressure 40% badhane se burn rate bhi 40% badh jaata hai."

Sirf tab jab

n = 1

ho.

n < 1

ke saath rate

(1.4)^{n}

ki tarah badhta hai, jaise

(1.4)^{0.35} \approx 1.13

— lagbhag 13%, 40% nahi. Woh sub-linear response hi motor ko self-limiting banata hai.

"Star-shaped port isliye use hota hai taaki rising thrust curve ke liye burning area grow kare."

Ulta hai: star geometry isliye choose ki jaati hai taaki

A_{b}

roughly constant rahe (neutral), flat thrust de. Ek plain cylindrical port woh hai jiska area grow karta hai (progressive).

"Kyunki oxygen andar carry ki jaati hai, zyaada oxidizer hamesha zyaada thrust deta hai."

Thrust burn area aur exhaust speed par depend karta hai, na ki kitna oxidizer unburned baitha hai. Fuel-matching ratio se zyaada oxidizer sirf mass waste karta hai aur flame ko thanda kar sakta hai,

v_{e}

ghataata hai.

"Burn rate

r

woh speed hai jis par gas nozzle se nikalta hai."

Nahi —

r

solid mein andar jaane wali flame front ki linear recession speed hai (millimetres per second mein). Exhaust speed

v_{e}

hazaaron metres per second hai; yeh dono unrelated quantities hain.

\overset{m}{˙} = ρ_{p} A_{b} r

mein extra

r

hai, isliye faster burn hamesha bigger area se behtar hai."

Dono symmetrically multiply karte hain; koi rule se dominant nahi hota. Ek large slow-burning surface aur ek small fast-burning surface identical

\overset{m}{˙}

de sakti hain — design inhe trade off karta hai.

Why questions

Ek rocket ko apna oxidizer kyun carry karna padta hai jabki jet engine nahi karta?

Jet atmospheric oxygen breathe karta hai aur hawa ke upar mar jaata hai; rocket ko vacuum mein operate karna hota hai, isliye woh propellant mein chemically oxygen pack karta hai taaki self-sufficient rahe — is reaction ke baare mein Newton's Third Law dekhein jo usse drive karta hai.

Grain (port) shape ek "pre-recorded thrust program" ki tarah kyun kaam karta hai?

Kyunki

\overset{m}{˙} \propto A_{b}

aur motor ko throttle nahi kiya ja sakta, sirf lever yeh hai ki flame front aage badhne par

A_{b}

kaise evolve karta hai — port shape carve karna

A_{b} (t)

curve fix kar deta hai, isliye thrust-vs-time curve bhi.

Stability condition specifically

n < 1

kyun hai,

n \leq 1

n < 0.5

kyun nahi?

Exactly

n = 1

par ek pressure perturbation na badhti hai na ghatat proportionally — marginal, unsafe;

n < 1

ke liye pressure rise burn rate ko proportionality se kam badhata hai, isliye extra gas spike sustain nahi kar paata aur pressure settle ho jaata hai.

Binder ko koi bhi hydrocarbon fuel ki jagah polymer kyun hona chahiye?

HTPB jaisa polymer rubbery aur castable hota hai: ise oxidizer crystals ke aas paas pour kiya ja sakta hai aur ek crack-free grain mein cure kiya ja sakta hai jo apna wajan aur launch acceleration survive kar sake, jabki ek loose hydrocarbon structure hold nahi kar sakta.

Pressure term

(p_{e} - p_{a}) A_{e}

thrust equation mein aata hi kyun hai?

Kyunki nozzle exit par exhaust gas exit plane par

p_{e}

pressure se push karta hai jabki ambient

p_{a}

par push karta hai; net static-pressure force momentum thrust mein add (ya subtract) hoti hai — nozzle physics De Laval Nozzle mein develop ki gayi hai.

40% pressure rise se sirf ~13% burn-rate rise milna ek feature kyun hai?

Woh sub-linear (

n < 1

) response disturbances damp karta hai: ek random pressure bump disproportionately thoda extra gas produce karta hai, isliye chamber khud ko correct karta hai detonation ki taraf accelerate hone ki jagah.

Edge cases

Agar chamber pressure momentarily zero ke paas girti hai (near burnout) toh burn rate

r

ka kya hoga?

r = a p_{c}^{n}

aur

n > 0

ke saath, jaise

p_{c} \to 0

burn rate

r \to 0

— motor tail off karta hai aur extinguish ho sakta hai, kyunki combustion sustain karne ke liye koi driving pressure nahi hota.

Agar flight ke dauran grain mein crack ban jaaye, toh

A_{b}

ka kya hoga aur yeh dangerous kyun hai?

Crack new burning surface expose karta hai, isliye

A_{b}

jump karta hai,

\overset{m}{˙}

aur

p_{c}

badhata hai; zyaada pressure

r

aur badhata hai — ek unplanned area spike jo case ko over-pressurize aur burst kar sakta hai.

Do motors same total mass same

v_{e}

ke saath burn karte hain; kya woh same total impulse aur same peak thrust deliver karte hain?

Same total impulse (woh total mass aur

v_{e}

par depend karta hai, Specific Impulse aur Tsiolkovsky Rocket Equation se juda hai), lekin peak thrust bahut alag ho sakta hai kyunki yeh har grain ki largest instantaneous

A_{b}

track karta hai.

Ek pure end-burner ke liye, thrust curve ka bilkul shuru aur bilkul end par limiting behaviour kya hoga?

Almost flat poore samay:

A_{b}

(fixed cross-section face) ignition se burnout tak essentially constant rehta hai, isliye thrust level rehta hai jab tak propellant consume nahi ho jaata aur abruptly end ho jaata hai.

Kya hota hai pressure term ka agar nozzle over-expanded ho (

p_{e} < p_{a}

), jaise sea level par vacuum nozzle ke saath?

Tab

(p_{e} - p_{a}) A_{e} < 0

, isliye static-pressure contribution thrust se subtract karta hai — ambient air exhaust se zyaada push back karta hai, net thrust reduce karta hai.

Degenerate limit

A_{b} \to 0

mein (sari surface burn ho gayi), thrust ka kya hota hai?

\overset{m}{˙} = ρ_{p} A_{b} r \to 0

, isliye momentum thrust

\overset{m}{˙} v_{e} \to 0

; sirf ek vanishing residual pressure term bach sakta hai, aur motor effectively khatam ho jaata hai.

Agar

n = 0

ho (burn rate pressure se independent), kya motor stable hai, aur kya yeh realistic hai?

Pressure perturbations ke liye perfectly stable (ek bump

r

mein kuch nahi badalta), lekin real propellants hamesha kuch pressure dependence dikhate hain, isliye

n = 0

ek achievable value ki jagah ek idealized boundary hai.

Recall

Recall Sharp rehne ke liye ek-line refutations

"Hawa chahiye" ::: oxidizer grain mein bound hai; vacuum mein bhi jalta hai.
"Binder inert hai" ::: HTPB fuel aur structure dono hai.
"Zyaada mass = zyaada thrust" ::: thrust $A_{b}$ track karta hai, total mass nahi.
" $n$ kuch bhi ho sakta hai" ::: $n < 1$ zaroori hai warna runaway.
"Grain shape cosmetic hai" ::: yahi thrust program hai.

Connections

Parent: Solid propellants — yahan har trap ke peeche poori derivations.
Liquid Propellants — throttleable, restartable contrast.
De Laval Nozzle — pressure term ka origin.
Specific Impulse — jahan total impulse aur $v_{e}$ rehte hain.
Tsiolkovsky Rocket Equation — total-impulse consequences.
Newton's Third Law — reaction principle.
Combustion Chemistry — kyun binder fuel count hota hai.

Question bank — Solid propellants — fuel + oxidizer in polymer matrix

True or false — justify