Rocket Turbopump

Rocket Turbopump (propulsion/turbomachinery/rocket-turbopump)

Use when the task is pump-level sizing of the turbopump in a liquid rocket engine: turning a required discharge pressure rise and propellant flow into the pump head, the dimensionless specific speed, the impeller tip speed and diameter from the design head coefficient, the pump power at the pump efficiency, and the suction performance picture from the available net positive suction head and the suction specific speed. This leaf implements the standard pump sizing relations in pure Python, stdlib only, SI units throughout. It pairs with propulsion/rocket/rocket-engine-cycle, which fixes the feed architecture and the cycle-level discharge pressure and flow this pump must deliver, and with propulsion/axial-compressor/turbine-stage, which models the drive turbine on the same shaft. Boundary: this leaf owns pump geometry, efficiency bookkeeping, and cavitation; the cycle leaf owns the power balance. Air compressor stages belong to propulsion/turbomachinery/centrifugal-compressor.

Domain quick reference

• Shaft speed: omega = 2 * pi * rpm / 60 (rad/s) from the rotational speed in rpm (omega_from_rpm).
• Pump head rise: H = dp / (rho * G0), with dp the discharge pressure rise in Pa, rho the propellant density, G0 = 9.80665 m/s^2 (head_rise_m).
• Dimensionless specific speed: N_s = omega * sqrt(Q) / (G0 * H)^0.75, with Q the volume flow in m^3/s (specific_speed). This is the pump type number that tells whether an impeller, mixed-flow, or axial pump suits the duty.
• Impeller tip speed from the head coefficient: u2 = sqrt(G0 * H / psi) with the design head coefficient psi = 0.55 for a centrifugal pump impeller (impeller_tip_speed). The head coefficient compares the Euler head to the blade speed squared.
• Impeller diameter from the tip speed and shaft speed: D = 2 * u2 / omega (impeller_diameter).
• Pump power: P = Q * dp / eta, the hydraulic power at the pump efficiency eta, in W (pump_power).
• Available NPSH: NPSH = (p_inlet - p_vapor) / (rho * G0) in meters, the suction head above vapor pressure at the pump inlet (npsh_available).
• Dimensionless suction specific speed: S = omega * sqrt(Q) / (G0 * NPSH)^0.75, the suction analogue of N_s (suction_specific_speed).
• Cavitation verdict: acceptable when S >= S_CRIT, cavitation-risk otherwise, with S_CRIT = 3.0 the conventional suction specific speed limit for a rocket turbopump stage (cavitation_verdict).
• Units are SI throughout: rad/s, m, m^3/s, Pa, kg/m^3, W.
• ECSS frames the space propulsion context; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the pump duty: rpm, volume flow Q, discharge pressure rise dp, density rho, and efficiency eta (from the rocket-engine-cycle output for the discharge pressure and flow).
2. Convert the shaft speed with omega_from_rpm and the head with head_rise_m.
3. Compute the dimensionless specific speed with specific_speed to confirm the centrifugal pump type for the duty.
4. Get the impeller tip speed with impeller_tip_speed at the design head coefficient, then the diameter with impeller_diameter; compare D with the geometric envelope of the engine.
5. Compute the pump power with pump_power and carry it back to the cycle power balance (rocket-engine-cycle owns the balance itself).
6. Assess suction performance: npsh_available from the inlet and vapor pressures, then suction_specific_speed from omega, Q, and the available NPSH.
7. Judge the cavitation margin with cavitation_verdict against S_CRIT.
8. Run the whole chain in one call with size_pump, which returns the dict with omega, head_m, specific_speed, tip_speed_ms, diameter_m, power_W, npsh_m, suction_specific_speed, and verdict.
9. Confirm the deterministic checks with the contract test scripts/test_rocket_turbopump.py.

Worked example

LOX pump: rpm 18000, Q = 0.04 m^3/s, dp = 10 MPa, rho = 1141 kg/m^3, eta = 0.68, p_inlet = 0.5 MPa, p_vapor = 0.03 MPa.

• Shaft speed: omega = 2 * pi * 18000 / 60 = 1884.96 rad/s.
• Head: H = 10e6 / (1141 * 9.80665) = 893.70 m.
• Specific speed: N_s = 1884.96 * 0.2 / (9.80665 * 893.70)^0.75 = 0.4162, a low specific speed typical of a high-head centrifugal turbopump stage.
• Tip speed: u2 = sqrt(9.80665 * 893.70 / 0.55) = 126.23 m/s, a moderate tip speed for a LOX pump.
• Diameter: D = 2 * 126.23 / 1884.96 = 0.1339 m, about 134 mm.
• Pump power: P = 0.04 * 10e6 / 0.68 = 588235 W, about 588 kW for the oxidizer pump.
• Available NPSH: NPSH = (0.5e6 - 0.03e6) / (1141 * 9.80665) = 42.00 m.
• Suction specific speed: S = 1884.96 * 0.2 / (9.80665 * 42.00)^0.75 = 4.123, above the 3.0 limit, so the verdict is acceptable.
• Flip case: the verdict flips to cavitation-risk when S drops below 3.0. With the inlet pressure raised to 1.0 MPa the available NPSH grows to 86.69 m, S falls to 2.394, and size_pump returns cavitation-risk. Model note: in this sizing model S is computed from the available NPSH, so S falls as the available suction head grows; the deterministic flip case in the contract test raises the inlet pressure accordingly.

Verification

• Confirm omega_from_rpm(18000) returns 1884.96 rad/s within 0.1 and that 3000 rpm returns exactly 100 * pi rad/s.
• Confirm head_rise_m(10e6, 1141) returns 893.70 m within 0.1 and is linear in the pressure difference.
• Confirm specific_speed(1884.96, 0.04, 893.70) returns 0.4162 within 0.001 and scales with omega and sqrt(Q).
• Confirm impeller_tip_speed(893.70, 0.55) returns 126.23 m/s within 0.1 and scales with sqrt(H); impeller_diameter(126.23, 1884.96) returns 0.1339 m within 0.001 and is inversely proportional to omega.
• Confirm pump_power(0.04, 10e6, 0.68) returns 588235 W within 10.
• Confirm npsh_available(0.5e6, 0.03e6, 1141) returns 42.00 m within 0.01 and is linear in the pressure difference; raising the vapor pressure to 0.2 MPa lowers it by exactly 0.17e6 / (rho * G0).
• Confirm suction_specific_speed(1884.96, 0.04, 42.00) returns 4.123 within 0.01 and that the verdict is acceptable at S = 3.0 and flips to cavitation-risk below it.
• Confirm size_pump reproduces every anchor in one dict and flips the verdict to cavitation-risk at an inlet pressure of 1.0 MPa.
• Confirm every non-positive rpm, flow, pressure rise, density, head, NPSH, and omega, every efficiency outside (0, 1], every non-positive head coefficient, and every inlet pressure at or below the vapor pressure raises ValueError.
• Run the contract test offline: python3 scripts/test_rocket_turbopump.py (34 tests, deterministic).

Related leaves

• propulsion/rocket/rocket-engine-cycle: fixes the feed architecture and the discharge pressure and flow this pump must deliver; owns the cycle-level pump and turbine power balance.
• propulsion/turbomachinery/centrifugal-compressor: the sibling turbomachinery design method for air compressor stages.
• propulsion/axial-compressor/turbine-stage: the drive turbine on the same shaft as this pump.

Pitfalls

• Misreading the suction specific speed direction: in this sizing model S is computed from the AVAILABLE NPSH, so S falls as the available suction head grows - the flip case raises the inlet pressure to 1.0 MPa, NPSH grows to 86.69 m and the verdict flips to cavitation-risk, the opposite of the intuition that more inlet head always helps.
• Reading the verdict boundary as a soft margin: cavitation_verdict is acceptable at S >= S_CRIT = 3.0 and flips to cavitation-risk below it, so the boundary is exact and deterministic, not a trend to eyeball.
• Sizing the pump at the cycle discharge pressure without the pump inlet state: npsh_available needs the inlet pressure above the vapor pressure; an inlet at or below the vapor pressure raises ValueError because the suction head is unphysical.
• Applying the cavitation judgment to the drive turbine or the air side: this leaf owns pump geometry, efficiency and cavitation only - the cycle power balance belongs to rocket-engine-cycle and air compressor stages to centrifugal-compressor.
• Quoting the specific speed without the pump type context: N_s = 0.4162 is a low specific speed typical of a high-head centrifugal turbopump stage, so the number must be read against the impeller, mixed-flow or axial pump selection it implies.
• Trusting the 0.55 head coefficient blindly: impeller_tip_speed runs at the design head coefficient psi = 0.55, a conventional centrifugal value - a different impeller design needs its own psi before the tip speed and diameter are quoted.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_rocket_turbopump.py

The test covers the LOX worked-example anchors (omega 1884.96 rad/s, head 893.70 m, N_s 0.4162, tip speed 126.23 m/s, diameter 0.1339 m, power 588235 W, NPSH 42.00 m, S 4.123, verdict acceptable), scaling and round-trip identities, the verdict boundary at S = 3.0 and the flip to cavitation-risk below it (including the size_pump flip case at a 1.0 MPa inlet pressure), agreement between size_pump and the individual functions, and ValueError rejection of non-physical inputs.

Compliance

• Standards referenced, not reproduced: ECSS is a free ESA standard family (ecss.nl/standards); the pump sizing relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.