rocketry/docs/ENGINE_DESIGN.md

Engine Design Guide

Overview

The Engine Design tool calculates rocket engine performance, material erosion, and structural requirements. It integrates combustion thermodynamics, ablative material degradation, and hoop stress analysis into a unified interface.

Main Sections

Combustion Design

Configure chamber, nozzle, and propellant properties to predict thrust, Isp, and exit conditions.

Ablative Erosion

Model chamber liner erosion based on pressure-dependent rates and propellant choice.

Structural Sizing

Calculate wall thicknesses and component masses using hoop stress formula.

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Combustion Design

Inputs

Chamber:

• chamberPressure (MPa) — combustion chamber pressure
• nozzleDiameter (mm) — nozzle throat diameter
• expansionRatio — nozzle exit / throat area ratio
• divergenceAngle (°) — nozzle divergence cone angle

Propellant Selection:

• fuelType — dropdown (RP1, Methane, Hydrogen, etc.)
• oxidiserType — dropdown (LOX, N2O4, etc.)
• Note: Propellant properties come from knowledgebase (T0, gamma, Mw, etc.)

Design Options:

• injectorType — impingement, shower-head, multi-element
• coolingMethod — none, regenerative (future)
• nozzleShape — conical (15-20°), bell curve (optional)

Outputs (Computed)

Performance:

• thrustVacuum (kN) — vacuum thrust (accounting for exit pressure)
• thrustSeaLevel (kN) — sea level thrust (accounting for ambient pressure)
• specificImpulseVacuum (s) — Isp in vacuum
• specificImpulseSeaLevel (s) — Isp at sea level
• characteristicVelocity (m/s) — c* = P0·At / ṁ

Combustion Conditions:

• chamberTemperature (K) — adiabatic flame temperature
• exitTemperature (K) — nozzle exit temperature
• machNumber — exit Mach number (computed via bisection)
• exitPressure (MPa) — nozzle exit pressure
• exitDensity (kg/m³) — exhaust density at exit

Nozzle Geometry:

• throatDiameter (mm) — computed from chamber P, thrust, mass flow
• exitDiameter (mm) — exit diameter = throat × √(expansionRatio)
• nozzleLength (mm) — divergence section length
• thrustCoefficient — CF (thrust coefficient for flow)

Flow Properties:

• massFlowRate (kg/s) — propellant mass flow rate
• exitVelocity (m/s) — effective exhaust velocity
• burnRate (mm/s) — for propellant grain design

Key Equations

Thrust (from area and pressure):

F = P0·At·CF + (Pe - P_ambient)·Ae

Where CF is thrust coefficient from isentropic relations.

Specific Impulse:

Isp = Ve / g0
Isp_sl = (Ve - (Pe - P_atm) / ṁ · Ae) / g0

Exit Temperature (isentropic flow):

Te = T0 · (Pe / P0)^((γ-1)/γ)

Mass Flow Rate (from energy balance):

ṁ = P0 · At / c*
c* = √(2·(γ+1)/(γ-1) · R·T0)  for ideal nozzle

Characteristic Velocity:

c* = √(2·(γ+1)/(γ-1) · R·T0 · (2/(γ+1))^((γ+1)/(γ-1)))

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Ablative Erosion (v2)

Material Properties

Each ablative material in the knowledgebase has:

• Density (kg/m³) — ablator material density
• Base Erosion Rate (inch/s) — reference erosion at standard pressure (typically 300 psi)
• Pressure Exponent (n) — power-law sensitivity to pressure

Pressure-Corrected Erosion

The key innovation of v2 is pressure-dependent erosion rates:

erosion_rate(P) = base_rate · (P / P_ref)^n

Where:

• base_rate — from material database (inch/s @ 300 psi)
• P — chamber pressure (Pa)
• P_ref — reference pressure (300 psi = 2.068 MPa)
• n — pressure exponent (material-specific)

Pressure Exponents by Material Class

Composites:

• PAXS (polyester/glass): n = 0.38
• KFSI (silica/phenolic): n = 0.35
• Carbon phenolic: n = 0.32

Elastomers:

• ZIRCONIA (zirconia/silicone): n = 0.48
• Butyl rubber: n = 0.50

Theory: Lower n = less pressure-sensitive (better for high-P engines)

Example Calculation

Material: PAXS, base_rate = 0.025 in/s, n = 0.38

At different pressures:

• 300 psi: rate = 0.025 × (300/300)^0.38 = 0.025 in/s
• 500 psi: rate = 0.025 × (500/300)^0.38 = 0.032 in/s
• 1000 psi: rate = 0.025 × (1000/300)^0.38 = 0.042 in/s
• 1500 psi: rate = 0.025 × (1500/300)^0.38 = 0.050 in/s

Erosion Calculation

Inputs:

• Chamber pressure (Pa)
• Burn time (s)
• Ablative material (from dropdown)
• Initial liner thickness (mm)

Process:

1. Look up material properties (base_rate, n)
2. Calculate pressure factor: (P / P_ref)^n
3. Apply correction: effective_rate = base_rate × factor
4. Erosion depth: erosion = effective_rate × burn_time
5. Remaining thickness: remaining = initial - erosion

Display:

• Pressure factor (if not 1.0)
• Corrected erosion rate (inch/s)
• Erosion depth (inch)
• Remaining thickness (inch)
• Warning if remaining < 0.5 inch

Thermal Analysis (Future)

Currently, erosion is purely mechanical. Future versions could include:

• Heat flux calculation
• Material melting/sublimation
• Thermal diffusion into structure
• Combined mechanical + thermal erosion

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Structural Sizing

Material Selection

Choose from STRUCTURAL_MATERIALS array:

• Aluminum 6061-T6: Low density, corrosion-resistant
• Stainless Steel 304: High temp, corrosion-resistant
• Inconel 718: High strength at elevated T
• Titanium 6-4: Light, strong, expensive
• CFRP (Carbon Fiber): Highest strength-to-weight

Each has: density (kg/m³), yield strength (MPa), Young's modulus, CTE, limits

Hoop Stress Formula

For thin-walled cylinders:

σ_hoop = (P × r) / t

Solving for wall thickness with safety factor:

t = (P × r) / (σ_yield / SF)

Where:

• P — internal pressure (Pa)
• r — radius (m)
• σ_yield — material yield strength (Pa)
• SF — safety factor (typical: 2.0–4.0)

Component Sizing

Chamber:

• Pressure: P0 (combustion pressure)
• Radius: determined by geometry
• Thickness: t_chamber = (P0 × r) / (σ_y / SF)

Convergent Section (nozzle entrance):

• Pressure: P0 (full chamber pressure)
• Radius: smaller than chamber (converging)
• Thickness: similar to chamber

Throat (narrowest point):

• Pressure: ~P0 (highest local stress)
• Radius: throat_radius (smallest)
• Result: highest stress → thickest wall
• Thickness: t_throat = (P0 × r_throat) / (σ_y / SF)

Divergent Section (nozzle expansion):

• Pressure: decreases from P0 to Pe
• Radius: increasing
• Thickness: typically uses Pe ≈ 0.1·P0 for design
• Lower thickness than chamber

Exit (atmospheric nozzle):

• Pressure: near ambient
• Thickness: minimal (can be thin-walled)

Mass Calculation

Cylindrical section:

m = 2π·r·t·L·ρ

Hemispherical dome (for tanks):

m = 4π·r²·t·ρ

Frustum (truncated cone):

m ≈ π·(r1·L + r2·L)·t·ρ  (simplified)

Total engine dry mass:

m_dry = m_chamber + m_convergent + m_nozzle + m_injector_plate + m_misc

UI Layout

Left Panel (Inputs):

• Material dropdown
• Safety factor slider
• Pressure specifications (chamber, ambient)

Right Panel (Results):

• Wall thickness breakdown (chamber, throat, exit)
• Mass breakdown (chamber, convergent, divergent, injector, total)
• Material properties (yield, density, limit temp)
• Stress utilization (if known)

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Workflow Example: Design LOX/RP1 Engine

Step 1: Set Combustion Conditions

1. Select fuelType = RP1
2. Select oxidiserType = LOX
3. Set chamberPressure = 200 bar
4. Set nozzleDiameter = 50 mm
5. Set expansionRatio = 8 → Result: Thrust ≈ 150 kN, Isp ≈ 310 s

Step 2: Design Ablation

1. Select ablativeMaterial = PAXS
2. Set initialLinertThickness = 10 mm
3. Set burnTime = 60 s → Result: Erosion ≈ 1.5 mm, Remaining ≈ 8.5 mm (OK)

Step 3: Size Structure

1. Select structuralMaterial = Inconel718
2. Set safetyFactor = 3.0 → Result:

• Chamber wall: 2.1 mm
• Throat wall: 2.8 mm
• Divergent: 1.5 mm
• Total dry mass: 2.3 kg

Step 4: Export

• Export as JSON: Download engine specs
• Import into rocket design tool
• Calculate vehicle TWR, delta-v, etc.

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Advanced Topics

Regenerative Cooling

Not yet implemented, but conceptually:

• Propellant flows through cooling jackets before injection
• Removes heat from chamber walls
• Allows higher chamber pressure or thinner walls
• Adds complexity (adds ~0.5 kg per engine)

Implementation would add:

• Cooling jacket dimensions
• Heat transfer correlation (Dittus-Boelert, etc.)
• Pressure drop calculation
• Temperature rise of propellant

Ablator Recession Modeling

Current model assumes uniform erosion. Advanced model would include:

• Surface recession rate (different from bulk erosion)
• Spallation (chunks breaking off at high pressure)
• Chemical reaction (oxidation, decomposition)
• Thermal gradient (erosion depends on depth)

This requires:

• Heat conduction equation (PDE)
• Boundary conditions (heat flux from combustion)
• Material properties (k, cp, melt point)
• Solver (e.g., finite difference)

Combustion Instability

Not modeled currently, but factors affecting it:

• Injector design (pattern, element size, momentum ratio)
• Chamber L (characteristic length)* = V / At
  • Higher L* = more residence time = higher c*
  • Typical range: 30–60 inches
• Baffle plates (reduce acoustic resonance)

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Knowledgebase Integration

Accessing Propellant Data

• Knowledgebase → Fuels / Oxidisers
• View all available propellants
• Copy properties into engine design

Accessing Material Data

• Knowledgebase → Structural Materials
• Compare yield strengths, densities, costs
• Select best for your application

Ablative Materials

• Knowledgebase → Ablative Materials
• View pressure exponents
• Notes on applications (chamber, nozzle, etc.)

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Troubleshooting

Chamber pressure seems too high / low?

• Check propellant selection (wrong fuel/oxidizer?)
• Verify chamber geometry (radius, length)
• Check for typos in input values

Erosion warning?

• Select ablator with lower pressure exponent (more stable)
• Reduce chamber pressure if possible
• Increase initial liner thickness
• Shorten burn time

Structural mass too heavy?

• Switch to lighter material (Ti-6-4 vs SS)
• Reduce safety factor (if acceptable for design)
• Increase chamber pressure radius (less stress)
• Use thinner walls for non-critical sections

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References

• Huzel, D. K., & Huang, D. H. (1992). Modern engineering for design of liquid-propellant rocket engines. AIAA.
• NASA SP-273: Liquid Rocket Engine Combustion Instability. (PDF)
• Crespo, A., & Liñán, A. (1975). Asymptotic analysis of unsteady flame oscillations in liquid propellant rocket motors. SIAM Journal on Applied Mathematics, 29(3), 521–533.

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Last Updated: 2025-02 | Status: Current (v2 — Pressure-Corrected Ablation)