Vintage Loss
Vintage Loss: Theoretical Foundations
Overview
What is windage loss? It's a term I'm not very familiar with.
It's the power loss due to friction between the air (or fluid) and a rotating body and a stationary wall. It becomes significant enough to be non-negligible in high-speed rotating machinery. It's particularly important in turbine generators, flywheels, high-speed motors, etc.
Friction Loss of a Rotating Disk
Specifically, how much loss are we talking about?
The friction loss of a rotating disk in a closed space is expressed as follows.
$C_M$ is the moment coefficient, which is a function of the rotational Reynolds number $Re_\theta = \rho \omega r^2 / \mu$ and the gap ratio $s/r$.
It's proportional to $\omega^3$? The effect of rotational speed is significant.
Yes. Doubling the rotational speed makes the windage loss eight times greater. That's why it can become a dominant loss source in high-speed rotating machinery.
Flow Regime
Are there laminar and turbulent flows in the gap flow as well?
Yes. The classification by Daily & Nece (1960) is widely used.
| Regime | $Re_\theta$ | Gap Ratio | Characteristics |
|---|---|---|---|
| I: Laminar·Merged BL | Low | Small | Boundary layers from both walls merge |
| II: Laminar·Separated BL | Low | Large | BLs are independent, core rotation |
| III: Turbulent·Merged BL | High | Small | Most common industrial condition |
| IV: Turbulent·Separated BL | High | Large | Core rotation present |
Most industrial turbo machinery falls under Regime III or IV.
Empirical Formula for $C_M$
Are there empirical formulas for the moment coefficient?
For Regime III, Daily's formula is representative.
By comparing CFD results with this empirical formula, the validity of the calculation can be conveniently verified.
Fluid Mechanics of Rotating Disks—von Karman's Disk Analysis (1921) and Stokes' Pioneering Work
The flow around a disk rotating in a stationary fluid was analyzed by Theodore von Karman (1921). He not only studied Karman vortices behind rotors but also derived an exact analytical solution for the boundary layer on a rotating disk (von Karman boundary layer), formulating the relationship between disk torque and eddy viscosity. Cochran (1934) computed this solution with higher accuracy, and Daily & Nece (1960) expanded the model through experiments, laying the foundation for today's correlation formulas. Modern turbo machinery disk cavity CFD is an evolved form that starts from von Karman's analysis a century ago, numerically adding complex three-dimensional effects such as multi-stage, multi-body rotation, and hot gas ingestion. It is noteworthy that the work of a scientist who left revolutionary achievements through a mathematical approach is directly applied to jet engine cooling design 100 years later.
Computational Methods for Vintage Loss
CFD Model Configuration
How do you model windage loss calculation in CFD?
Model the gap space between the rotating disk and stationary wall as the fluid domain.
- Rotating Wall: Disk surface (No-Slip, specify rotational speed)
- Stationary Wall: Casing inner surface (No-Slip, zero velocity)
- Inlet/Outlet: Set if there is leakage flow into the gap
If axisymmetric, a 2D axisymmetric model is sufficient. If there are 3D effects (bolt heads, cooling holes, etc.), use a sector model.
Turbulence Model Selection
Which turbulence model is suitable?
SST k-omega is recommended. Since the BL near the rotating wall is important, ensure y+ < 1 with a Low-Re approach. k-epsilon is not recommended as it struggles to accurately capture rotational effects near walls.
| Turbulence Model | Windage Prediction Accuracy | Notes |
|---|---|---|
| SST k-omega (Low-Re) | ±5~10% | Recommended |
| k-epsilon + Wall Function | ±15~25% | Insufficient accuracy near wall |
| RSM (Reynolds Stress) | ±3~8% | Captures swirling effects, high cost |
| LES | ±2~5% | Highest accuracy but high cost |
Is RSM good?
In rotating disk flow, the anisotropy of Reynolds stress is strong between the circumferential and radial directions. RSM (e.g., BSL-RSM) directly models this anisotropy, which can sometimes improve accuracy over SST. However, computational cost increases by 1.5~2 times.
Mesh Requirements
How much mesh is needed inside the gap?
A guideline is 40~60 cells in the gap direction (axial) and 100~200 cells in the radial direction. Place prism layers on both walls and ensure y+ < 1. For 2D axisymmetric, tens of thousands of cells are sufficient.
Windage Loss Calculation—Daily-Nece Correlation and CFD Accuracy Comparison
The windage loss torque M of a rotating disk can be calculated from the experimental correlation formula by Daily & Nece (1960). Different coefficient formulas apply to each of the four flow regimes (combinations of G and Reomega). In the turbulent regimes (III, IV), M is proportional to the square of rotor speed and the fifth power of radius, and inversely proportional to Re to the 1/5 power. This correlation is still widely used for initial estimates in engine/turbine design, but errors can exceed 30% when conditions deviate from the applicable range (G=0.02~0.2, Reomega=10^4~10^7). Comparison studies with CFD report that for disk gaps G<0.02 (narrow gaps) or actual shapes with recesses/holes in the disk, the Daily-Nece formula tends to predict 10~20% lower loss than CFD, according to multiple papers. For complex engine disk shapes, the standard procedure is to perform an initial estimate with the correlation formula, then always verify precisely with CFD.
Vintage Loss in Practice
Rotor System Temperature Rise
Does temperature increase due to windage loss?
All loss becomes heat. In a sealed space, if cooling is insufficient, temperature continues to rise. This becomes a problem in steam turbine chambers or motor air gaps.
If the cooling flow rate $\dot{m}_{cooling}$ is low, the temperature rise becomes large.
Can CFD also predict temperature distribution?
By enabling the energy equation and solving with CHT (Conjugate Heat Transfer), the rotor thermal state can be predicted. This is important for materials that are sensitive to temperature.
Practical CAE quality notes for Vintage Loss
Vintage Loss should be treated as an engineering model, not as an isolated formula. In fluid simulation, reliable results come from a clear chain of assumptions: governing physics, material data, boundary conditions, numerical discretization, solver settings, and post-processing criteria. Before using this note in a design review, identify which quantities are prescribed, which are solved, and which are only diagnostic indicators.
Model setup checklist
- Define the scope: decide whether Vintage Loss is being used for screening, detailed design, failure investigation, or verification of another simulation.
- Check dimensions and units: keep SI units internally and document every conversion applied to loads, geometry, material constants, and time or frequency scales.
- State assumptions explicitly: record linearity, steady-state or transient behavior, small-deformation limits, continuum assumptions, and any symmetry or ideal boundary conditions.
- Compare with a baseline: use a hand calculation, limiting case, mesh refinement trend, or independent solver result before accepting the final value.
Validation signals
| Review item | What to verify | Typical warning sign |
|---|---|---|
| Inputs | Geometry, material data, loads, and constraints match the intended fluid simulation problem. | Correct-looking plots with unrealistic magnitudes or units. |
| Numerics | Mesh, time step, convergence tolerance, and solver options are adequate for Windage Loss. | Large changes after small mesh or tolerance adjustments. |
| Physics | The selected theory remains valid in the expected stress, temperature, velocity, or frequency range. | Results are used outside the assumptions stated in the model. |
For production use, keep the model file, input table, result plots, and review comments together. This makes Vintage Loss traceable and prevents the page from being used as a black-box answer without engineering judgment.