Propeller CFD Analysis
Propeller CFD: Theoretical Foundations
Fundamentals of Propeller Performance
Professor, when predicting ship propeller performance with CFD, what parameters do we look at?
Propeller performance is evaluated by the thrust coefficient $K_T$, torque coefficient $K_Q$, and efficiency $\eta_0$.
Here, $T$ is thrust, $Q$ is torque, $n$ is rotational speed, $D$ is propeller diameter, and $J = V_A/(nD)$ is the advance coefficient. The open water characteristics ($K_T$-$J$ curve and $K_Q$-$J$ curve) represent the fundamental performance of the propeller.
What results are compared against in CFD?
They are compared against towing tank test data for standard propellers (e.g., DTMB 4119, KCS) from ITTC (International Towing Tank Conference) or SMPF (Ship Performance and Propulsion Committee). A difference of within 2% between CFD and experiment for $K_T$ and $K_Q$ is considered good, and within 5% is considered practical.
Approaches to Numerical Modeling
What modeling techniques are there for propeller CFD?
There are mainly three. (1) MRF (Moving Reference Frame): Steady-state calculation using a rotating coordinate system around the propeller. Lowest cost. (2) Sliding Mesh (Rigid Body Motion): Unsteady calculation where the propeller is actually rotated. Accurate for hull-propeller interaction. (3) Overset Mesh (Chimera Method): Handles motion by overlapping background and component meshes. Widely used in STAR-CCM+.
Which one should be used?
MRF is sufficient for calculating open water characteristics. Sliding Mesh or Overset is necessary for a propeller in the ship's wake (self-propulsion condition). For cavitation analysis, unsteady Sliding Mesh is standard.
History of Ship Propeller Theory — Rankine-Froude Momentum Theory (1865)
The first theoretical description of propeller thrust was the "Actuator Disk Theory" by William Rankine (1865) and W.J.M. Froude (1878). It idealized the propeller as a virtual, infinitely thin disk imparting momentum to the flow, deriving the simple formula T = ρA(V+va)×2va (where va is induced velocity). This theory captures the essence of thrust generation physics while being simple to calculate, and is still used for initial power and efficiency estimates in design. The theoretical upper limit of propeller efficiency (Betz limit η=1/(1+va/V)) is also derived from this theory and shares the same mathematical structure as the Betz coefficient for wind turbines (η_max≈59.3%). While 130 years later, CFD enables detailed airfoil analysis by fully modeling the blade, Rankine's insightful simplicity is still recounted in educational settings.
Computational Methods for Propeller CFD
Mesh Design
What should I be careful about when generating mesh for a propeller?
The boundary layer mesh near the blade surface is most critical. Place prism layers with $y^+ \approx 1$ to directly resolve the wall with the SST k-ω model. Local refinement is needed at the leading and trailing edges; at least 10 cells should be placed relative to the leading edge radius. The mesh near the tip also needs to be fine to capture tip vortices.
What's a guideline for cell count?
500,000 to 2 million cells per blade is standard. Using periodic boundary conditions to calculate only one blade can reduce cost to 1/$Z$ (where $Z$ is the number of blades). However, for self-propulsion calculations in a ship's wake, the inflow is non-uniform, so a full-blade model is essential. STAR-CCM+'s Trimmed Mesh or Fluent's Polyhedral Mesh offer a good balance of quality and automation.
Cavitation Analysis
What are the CFD models for cavitation?
The Schnerr-Sauer model and Zwart-Gerber-Belamri model are mainstream. They solve gas-liquid two-phase flow using the VOF method, modeling bubble generation (evaporation) in regions where local pressure falls below vapor pressure and bubble collapse (condensation) in regions where pressure recovers.
In Fluent, enable via Multiphase > VOF > Schnerr and Sauer. In STAR-CCM+, set the Cavitation Model in Physics. In OpenFOAM, use interPhaseChangeFoam (which has the Schnerr-Sauer model built-in).
What points require attention in cavitation analysis?
(1) Very small time steps are required ($\Delta t \sim 10^{-5}$ to $10^{-4}$ s). (2) The mesh must be fine enough to resolve the cavity thickness (a few mm). (3) Adding the Reboud correction (density correction) to the SST k-ω turbulence model improves the behavior of sheet and cloud cavitation.
Why is the "Schnerr-Sauer" Cavitation Model Popular?
When analyzing cavitation in propeller CFD, the Schnerr-Sauer model is the most commonly used among OpenFOAM users. While there are several choices like the Zwart-Gerber-Belamri model, Schnerr-Sauer is favored for its ease of use—it requires no tuning of evaporation/condensation coefficients and works once the bubble nucleus density is set. However, for detailed reproduction of actual cavitation collapse (implosion), LES or high-density meshes are needed, and calculations exceeding 1 billion cells are not uncommon. In practice, maintaining mesh quality where "6 uniform prism layers across the entire blade surface" don't collapse is the first major hurdle.
Propeller CFD in Practice
Self-Propulsion Analysis (Self-Propulsion)
What kind of simulation is self-propulsion analysis?
It simulates the state where the propeller propels the ship by placing both the hull and propeller in the same computational domain. By finding the self-propulsion point where thrust and resistance are balanced, the required horsepower of the actual ship is predicted.
What is the calculation procedure?
(1) First, perform resistance calculation for the hull alone (bare hull resistance). (2) Next, separately calculate the propeller's open water characteristics. (3) Perform a Sliding Mesh calculation for hull+propeller, adjusting rotational speed to find the point where thrust = resistance. STAR-CCM+'s Propeller Performance feature automatically searches for the self-propulsion point.
How is the effect of the ship's wake evaluated?
Calculate the wake distribution (wake fraction) at the propeller plane: $w = 1 - V_A / V_S$. Evaluate both nominal wake (without propeller) and effective wake (with propeller). The non-uniformity of the wake causes propeller fluctuating loads, vibration, and cavitation, so detailed analysis of the circumferential distribution is important.
Benchmarks for Verification
Is there data available for verifying propeller CFD?
Let me list some representative benchmark data.
| Propeller | Blades | Features | Data Source |
|---|---|---|---|
| DTMB 4119 | 3 blades | For non-cavitation verification | ITTC |
| PPTC VP1304 | 5 blades | Cavitation/pressure fluctuation | SVA Potsdam |
| KCS | 5 blades | Self-propulsion and full-scale verification | KRISO |
| Japan Bulk Carrier (JBC) | 4 blades | Full-scale wake and self-propulsion | ITTC/ClassNK |
These are standard benchmarks used to validate CFD codes. When your calculation shows results within ±2% of experimental $K_T$ and $K_Q$, you can confidently apply the method to design.