Pump Cavitation
Pump Cavitation: Theoretical Foundations
Overview
Pump cavitation is the phenomenon where bubbles form and pop, causing damage, right?
That's roughly correct. When the static pressure of the liquid falls below the saturated vapor pressure, vapor bubbles form and then collapse in the downstream high-pressure region. This collapse generates a localized shock pressure of several GPa, eroding the impeller surface.
Several GPa!? That would definitely cause damage...
It's also serious for performance. It causes head drop, increased vibration, and increased noise. That's why avoiding cavitation is one of the top priorities in pump design.
Definition of NPSH
I often hear about NPSH, but what is its precise definition?
NPSH (Net Positive Suction Head) represents how much margin the liquid has above the vapor pressure on the suction side.
$p_{atm}$: Atmospheric pressure, $p_v$: Saturated vapor pressure, $z_s$: Height from liquid surface to pump center, $h_f$: Friction head loss in the suction pipe. This is the system-side NPSH (Available).
There's also an NPSH on the pump side, right?
NPSH_r (Required) is the minimum NPSH required by the pump itself, defined as the point where the head drops by 3%. For safety, this condition must be met:
It can also be expressed by the cavitation coefficient (Thoma number).
Rayleigh-Plesset Equation
Is there an equation that describes bubble growth and collapse?
The Rayleigh-Plesset equation is fundamental.
$R$: Bubble radius, $p_B$: Pressure inside the bubble, $p_\infty$: Surrounding pressure, $S$: Surface Tension. CFD cavitation models simplify this into a mass transport equation.
The History of Cavitation Troubles for Submarines
The bubble dynamics of pump cavitation (Rayleigh-Plesset equation) began to be treated as a serious practical problem starting with submarine propellers during World War I. Bubbles violently formed and collapsed near the propeller blade tips, causing the dual problems of reduced propulsion efficiency and metal erosion. Post-war research systematized the concept of NPSH (Net Positive Suction Head), which has been carried over into modern pump design.
Computational Methods for Pump Cavitation
Homogeneous Mixture Model
How do you calculate cavitation in CFD?
The most widely used is the Homogeneous Mixture model. It treats the liquid and vapor phases as a single fluid and solves a transport equation for the vapor volume fraction $\alpha_v$.
$\dot{m}^+$ is the evaporation (bubble formation) source term, and $\dot{m}^-$ is the condensation (bubble collapse) source term.
What kind of models are there for the source terms?
Let's compare three representative ones.
| Model | Features | Used in Solvers |
|---|---|---|
| Zwart-Gerber-Belamri | Based on nucleation site density, easy parameter adjustment | CFX (default), STAR-CCM+ |
| Schnerr-Sauer | Based on Rayleigh-Plesset, requires bubble number density specification | OpenFOAM (interPhaseChangeFoam), Fluent |
| Singhal (Full Cavitation) | Considers non-condensable gases, practical | Fluent |
So the Zwart model is standard in CFX, huh.
Yes. Default values are evaporation coefficient $F_{vap}=50$, condensation coefficient $F_{cond}=0.01$. Typical values are nucleation site volume fraction $\alpha_{nuc}=5 \times 10^{-4}$, initial bubble radius $R_B=10^{-6}$ m.
Key Points for Numerical Settings
Are there any tips for getting cavitation calculations to converge?
It's a difficult calculation, so there are several key points.
- Time Step: Unsteady is mandatory. Aim for 1/20 to 1/50 of the time for one blade passage.
- Convergence Criteria: Target RMS residuals of $10^{-5}$ or better (sometimes they only drop to $10^{-4}$ due to cavitation oscillations).
- Initial Conditions: First, get a steady-state solution without cavitation, then turn the cavitation model ON from there.
- Compressibility: Due to the large vapor-liquid density ratio, settings that numerically consider compressibility are necessary.
Zwart, Merkle, SinghalโThe Battle of Three Models
A common question heard on the CFD cavitation analysis front lines: "Which model should I use?" The Zwart model explicitly handles nucleation site density, the Merkle model is an empirical form that reacts directly to pressure difference, and the Singhal (Full Cavitation) model is the most complex configuration that even considers dissolved gases. Benchmark studies sometimes show the ranking changing depending on the case, so it's hard to definitively say "this one is the best." Since results are heavily influenced by initial values, mesh, and empirical constant settings, validation with in-house experiments is essential.
Pump Cavitation in Practice
Procedure for Obtaining NPSH Characteristic Curve
How do I plot an NPSH curve using CFD?
The general method is to gradually lower the inlet total pressure.
1. Baseline Calculation: Obtain a steady-state solution at a sufficiently high NPSHa (no cavitation)
2. Lower Inlet Pressure: Decrease inlet total pressure in steps of 0.1~0.2 atm
3. Unsteady Calculation at Each Point: Perform unsteady calculation for several rotations with the cavitation model ON
4. Record Time-Averaged Head: The point where the head drops by 3% from the baseline is NPSH_r
Isn't a 0.1 atm step size rather coarse?
Since the head drops sharply near NPSH_r, it's efficient to first get a rough overall picture with coarse steps, then refine near the 3% drop point with 0.02~0.05 atm steps.
Visualization and Evaluation
How should I look at cavitation results?
The isosurface of vapor volume fraction $\alpha_v = 0.5$ represents the cavity shape. Related Topics
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