ashfordeOU Free Turbine (propulsion/turboprop/free-turbine)
Use when the task is free-turbine turboprop or turboshaft power section sizing: gas generator to power turbine matching, shaft power, and reduction gearbox selection.
Domain quick reference
A free-turbine layout has two mechanically independent shafts: the gas generator (compressor plus its turbine) and the power turbine, connected only aerodynamically through the exhaust stream. The power turbine converts the gas generator exhaust enthalpy drop into shaft power and drives the propeller or rotor through a reduction gearbox.
Power-turbine exit temperature follows the expansion:
t06 = t05 * (1 - eta_pt * (1 - pr**((1-gamma)/gamma)))
with t05 the power-turbine inlet (gas generator exhaust) temperature in K, pr = p5/p6 the expansion ratio (> 1), eta_pt the polytropic efficiency in (0, 1], and gamma air-standard 1.4.
Shaft power: P = m_dot * cp * (t05 - t06) with m_dot in kg/s and cp in J/(kg K); torque Q = P / omega with omega = 2 * pi * rpm / 60.
Blade speed at the mean diameter: u = pi * diameter * rpm / 60 in m/s. Gear ratio G = n_pt / n_prop, normally well above 1 because the free turbine runs fast for blade aerodynamics.
Specific fuel consumption: sfc = mf * 3600 * 1000 / P in kg/(kW h).
Flow function FF = m_dot * sqrt(t05) / p5 in kg sqrt(K) / Pa is the corrected-flow compatibility parameter: the power-turbine nozzle must swallow the gas generator exhaust at every operating point.
Workflow
- Establish the gas generator exhaust state: m_dot, t05, p5, and the chosen expansion ratio and polytropic efficiency.
- Compute t06 and the shaft power with power_turbine_power.
- Convert to torque at the power-turbine speed with shaft_torque and the blade speed with blade_speed from the mean diameter.
- Select the reduction gearbox with gear_ratio to the propeller or rotor speed.
- Close the loop with specific_fuel_consumption and flow_function; use free_turbine_assessment for the full dict.
Pitfalls
- Using a pressure ratio below 1: the expansion ratio must exceed 1 (pressure falls across the turbine).
- Confusing the two shafts: the power turbine speed and the propeller speed differ by the gear ratio; torque and SFC must be evaluated at the shaft that carries them.
- Ignoring the flow function: the gas generator and power turbine only stay matched if the nozzle swallows the exhaust at every point.
- Applying compressor polytropic efficiency signs to the turbine: the turbine exit temperature falls as efficiency rises.
Behavior contract (gate 3)
The free-turbine logic is exercised by the gate 3 contract test: scripts/test_free_turbine.py against scripts/free_turbine_logic.py (stdlib unittest, offline). Run: python3 scripts/test_free_turbine.py
Compliance
- The free-turbine matching relations are common turbomachinery methodology, paraphrased here. FAR-33 is cited as reference only for the engine certification context; no proprietary or copyrighted text is reproduced.
- compliance: STANDARDS-REF, gated: false.