Azimuthally Uniform Film Cooling via Large Helical Manifolds: A Parametric Exploration with Full Epistemic Uncertainty Quantification for Reusable High-Pressure Methalox Rocket Nozzles

High-pressure (>20 MPa) liquid oxygen/methane rocket engines suffer peak throat heat fluxes of 120–170 MW/m², far beyond the capability of conventional regenerative cooling alone. This work examines whether passive, azimuthally uniform fuel film cooling delivered through large helical manifolds can reduce heat flux sufficiently to enable >200-cycle reusability without plasma augmentation or ablative liners. Using Latin-Hypercube sampling across six major uncertain parameters (bleed fraction, blowing correlation constants, mixing efficiency, bare heat flux, plasma efficiency, and material properties), a 10 000-run Monte Carlo analysis yields the following 95 % credible intervals for a 100 kN vacuum-optimized engine at 30 MPa chamber pressure: - Vacuum specific impulse: **377.4 – 385.9 s** - Throat recession rate (GRCop-42): **42 – 112 µm/s** - Sweet-spot operation: **≈17 % methane bleed** → **≈383 ± 4 s** with >200-flight life The helical manifold is shown to be the critical enabler of azimuthal uniformity, converting discrete-port film cooling into a continuous curtain. Prior art search reveals no previous integration of large-aspect-ratio helical manifolds with metered 14–22 % fuel bleed for heat-flux reduction in high-pressure methalox engines. The Problem: Rocket engines running on liquid oxygen + methane (like SpaceX's Raptor) get insanely hot at the throat - the narrowest part of the nozzle. We're talking 120-170 megawatts per square meter. For reference, the sun hitting Earth is about 1,400 W/m². This is ~100,000x more intense. Traditional cooling (pumping cold fuel through channels in the walls) can't handle it alone at these pressures (30 MPa = ~4,400 psi - about 300x your car tire). The Proposed Solution: Spray a thin film of cold methane fuel along the inside of the throat walls before it burns. Think of it like sweating - evaporative cooling. The fuel film absorbs heat before it can damage the metal. The Trade-off: More film cooling = cooler walls = longer engine life But that fuel doesn't burn efficiently = less thrust per pound of propellant (lower Isp) What They Found (Monte Carlo = "run 10,000 random simulations"): Sweet spot: ~17% of the methane goes to film cooling You still get ~383 seconds of specific impulse (pretty good - Raptor is ~380s) Engine lasts 200+ flights before the throat erodes away Throat erosion: 42-112 micrometers/second (human hair is ~70µm thick) Why It Matters: Reusable rockets need engines that survive hundreds of firings. This says "yes, you can do it with just fuel film cooling" - no exotic plasma systems or sacrificial ablative coatings needed. TL;DR: Spray 17% of your fuel on the walls as a coolant, lose ~1% efficiency, gain a rocket engine that doesn't melt for 200+ flights.