feat: add Rotating Detonation Engine (RDE) combustor element, cycles, and benchmarks

[arushkumarsingh]

Summary

This pull request introduces the Rotating Detonation Engine (RDE) combustor element (RDECombustor), along with associated cycle models, regression benchmarks, and diagnostic viewers for pressure-gain combustion (PGC) in pyCycle.

Key Additions:

1. RDECombustor Element (pycycle/elements/rde_combustor.py):

   • Implements pressure-gain combustion based on the Humphrey constant-volume thermodynamic cycle coupled with Chapman–Jouguet (CJ) detonation wave kinematics.
   • Models injector feed plenum pressure drop ($P_{t,inj} = P_{t,in} \cdot (1 - dPqP_{inj})$) to ensure physical backflow margin.
   • Computes wave kinematics ($M_{CJ}$, detonation velocity $D_{CJ}$, rotational frequency $f_{RDE}$) from flow properties and fuel lower heating value ($Q_{fuel}$).
   • Employs an unsteady realization efficiency factor ($\eta_{rde}$) to model non-ideal wave interactions and expansion losses ($P_{t,out} = P_{t,inj} \cdot [1 + \eta_{rde} (\Pi_{ideal} - 1)]$).
   • Full analytical Jacobian across all 10 state/design variables, verified against complex-step derivatives at machine precision ($< 10^{-15}$).
   • Supports both CEA and TABULAR thermodynamics, as well as on-design Mach number and off-design throat area matching modes.
   • Exported in pycycle.api as pyc.RDECombustor and pyc.print_rde.

2. Cycle Examples:

   • Air-Breathing RDE Ramjet (example_cycles/rde_ramjet.py):
     • Mach 2.5 at 40,000 ft cruise ($W_{air} = 100\text{ lbm/s}$, $FAR = 0.028$).
     • Demonstrates $P_{t4}/P_{t2} = 2.963$ (+211.9% pressure gain vs 0.95 conventional drop), yielding +27.7% Net Thrust & $I_{sp}$ and -21.7% TSFC reduction.
   • Low-CPR RDE Turbojet (example_cycles/rde_turbojet.py):
     • Sea-level static design ($F_n = 11,800\text{ lbf}$, $T_{t4} = 2370^\circ\text{R}$) with multi-point off-design point (OD0).
     • At CPR 13.5, RDE yields -16.08% fuel burn reduction (TSFC = 0.670 vs 0.798).
     • Demonstrates "Low-CPR RDE" architecture (CPR = 8.0), reducing compressor power requirement by -41.3% (allowing elimination of multiple turbomachinery stages) while still achieving -9.64% better TSFC than the conventional 13.5:1 engine.

3. Verification & Regression Benchmark Test Suites:

   • Unit Tests (pycycle/elements/test/test_rde_combustor.py):
     • Validates CEA thermo integration, TABULAR thermo integration, off-design area solver, and complex-step analytic partials (check_partials(method='cs')).
   • Regression Benchmarks:
     • example_cycles/tests/benchmark_rde_turbojet.py: Multi-point regression against locked tolerances for DESIGN and OD0.
     • example_cycles/tests/benchmark_rde_ramjet.py: High-speed ramjet regression benchmarks.

Related Issues

• Closes feature request for Pressure-Gain Combustion (PGC) and Rotating Detonation Engine (RDE) modeling in pyCycle.

Backwards Incompatibilities

None. All existing Brayton cycle elements (Combustor, Compressor, Turbine, etc.) and all existing cycle examples/tests are preserved without modification.

New Dependencies

None.