| """ |
| power_model.py |
| Onboard Power Consumption Model for the Rotational Spherical Lifting Structure (VCA) |
| |
| Physics chain: |
| omega = 2 * pi * rpm / 60 [rad/s] |
| rho_gas = rho_He_1atm * P_frac [kg/m3] |
| Re = rho_gas * omega * R**2 / mu [dimensionless] |
| Cf = 0.074 / Re**0.2 [dimensionless] |
| P_gas_drag = (3 * pi**2 / 8) * rho_gas * Cf * omega**3 * R**5 [W] |
| P_bearings = Tb * omega [W] |
| P_total = P_gas_drag + P_bearings [W] |
| |
| Baseline validation (He at 1% Patm, R=9.2 m, 600 rpm): |
| P_gas_drag ~ 0.52 MW |
| """ |
|
|
| import math |
|
|
| |
| |
| |
| GAS_PRESETS = { |
| "Helium": { |
| "rho_1atm": 0.164, |
| "mu": 1.96e-5, |
| }, |
| "Air": { |
| "rho_1atm": 1.225, |
| "mu": 1.81e-5, |
| }, |
| "Hydrogen": { |
| "rho_1atm": 0.0838, |
| "mu": 8.90e-6, |
| }, |
| } |
|
|
| |
| BEARING_PRESETS = { |
| "Optimistic": 10.0, |
| "Baseline": 50.0, |
| "Conservative": 200.0, |
| } |
|
|
|
|
| def compute_power( |
| R: float, |
| rpm: float, |
| P_frac: float, |
| rho_1atm: float, |
| mu: float, |
| Tb: float, |
| ) -> dict: |
| """ |
| Compute onboard power consumption for the rotating sphere. |
| |
| Parameters |
| ---------- |
| R : Sphere outer radius [m] |
| rpm : Rotational speed [rev/min] |
| P_frac : Interior gas pressure as fraction of atmospheric (e.g. 0.01 = 1%) |
| rho_1atm : Gas density at 1 atm [kg/m3] |
| mu : Dynamic viscosity of gas [Pa.s] |
| Tb : Bearing drag torque [N.m] |
| |
| Returns |
| ------- |
| dict with keys: |
| omega [rad/s] |
| V_equator [m/s] equatorial surface speed |
| rho_gas [kg/m3] |
| Re [-] |
| Cf [-] |
| P_gas_drag [W] |
| P_bearings [W] |
| P_total [W] |
| """ |
| omega = 2.0 * math.pi * rpm / 60.0 |
| V_equator = omega * R |
| rho_gas = rho_1atm * P_frac |
| Re = rho_gas * omega * R**2 / mu |
| Cf = 0.074 / Re**0.2 |
| P_gas_drag = (3.0 * math.pi**2 / 8.0) * rho_gas * Cf * omega**3 * R**5 |
| P_bearings = Tb * omega |
| P_total = P_gas_drag + P_bearings |
|
|
| return { |
| "omega": omega, |
| "V_equator": V_equator, |
| "rho_gas": rho_gas, |
| "Re": Re, |
| "Cf": Cf, |
| "P_gas_drag": P_gas_drag, |
| "P_bearings": P_bearings, |
| "P_total": P_total, |
| } |
|
|
|
|
| |
| |
| |
| if __name__ == "__main__": |
| result = compute_power( |
| R=9.2, |
| rpm=600.0, |
| P_frac=0.01, |
| rho_1atm=GAS_PRESETS["Helium"]["rho_1atm"], |
| mu=GAS_PRESETS["Helium"]["mu"], |
| Tb=BEARING_PRESETS["Baseline"], |
| ) |
| print("=== Baseline Validation: R=9.2 m, 600 rpm, He at 1% Patm, Tb=50 N.m ===") |
| print(f" omega = {result['omega']:.4f} rad/s") |
| print(f" V_equator = {result['V_equator']:.2f} m/s") |
| print(f" rho_gas = {result['rho_gas']:.6f} kg/m3") |
| print(f" Re = {result['Re']:.4e}") |
| print(f" Cf = {result['Cf']:.6f}") |
| print(f" P_gas_drag = {result['P_gas_drag']/1e6:.4f} MW (target ~0.52 MW)") |
| print(f" P_bearings = {result['P_bearings']/1e3:.4f} kW") |
| print(f" P_total = {result['P_total']/1e6:.4f} MW") |
|
|
