Cavitation
Cavitation is the formation, growth, and subsequent collapse or persistence of vapor-filled cavities within a liquid. It occurs when the local static pressure falls sufficiently far below the liquid’s saturation vapor pressure that evaporation proceeds at available nucleation sites. The resulting cavities are commonly called bubbles, although many cavitating structures are elongated sheets, coherent vortices, or irregular clouds rather than isolated spherical bubbles.
Cavitation differs from boiling because it is initiated primarily by a reduction in pressure rather than by an increase in temperature. Both processes nevertheless represent liquid-to-vapor phase transitions, and the local thermodynamic state governs the rate at which vapor enters or leaves a cavity. When a cavity is transported into a region of higher pressure, vapor condenses and the surrounding liquid accelerates inward. Rapid collapse produces intense local pressure fluctuations, high-speed microjets, and transient heating.
Physical basis
For a liquid at temperature (T), the equilibrium vapor pressure (p_v(T)) defines the pressure at which a planar liquid–vapor interface can exist in thermodynamic equilibrium. In a flowing liquid, cavitation becomes thermodynamically possible when the local pressure approaches or falls below (p_v). Actual inception also depends on the liquid’s dissolved-gas content, its microscopic contaminants, and the pressure history of pre-existing cavities.
A perfectly homogeneous liquid can sustain substantial negative absolute pressure because creating a new interface requires work against surface tension. This condition is described as the tensile strength of the liquid. Ordinary engineering liquids contain heterogeneous nucleation sites that greatly reduce the tension required for cavity formation. Such sites include gas pockets trapped in surface crevices and microscopic bubbles stabilized by contamination at their interfaces. Cavitation therefore usually begins at pressures considerably above the homogeneous nucleation limit.
Surface curvature modifies the pressure balance across a cavity according to the Young–Laplace equation. For a spherical interface of radius (R), the surface-tension contribution to the internal pressure is
[ \Delta p_\sigma = \frac{2\sigma}{R}, ]
where (\sigma) is the liquid–vapor surface tension. Small nuclei require a larger internal pressure than large nuclei, so a population of cavities does not become unstable at a single universal pressure. The distribution of nucleus sizes instead gives cavitation inception a measurable dependence on water quality and prior exposure to pressure.
The dimensionless cavitation number expresses the available pressure margin relative to the dynamic pressure:
[ \sigma_c = \frac{p_\infty-p_v}{\tfrac{1}{2}\rho U^2}, ]
where (p_\infty) is a reference pressure, (\rho) is liquid density, and (U) is a representative velocity. Lower values generally correspond to more extensive cavitation for a fixed geometry and flow regime. The inception value remains dependent on surface condition, dissolved gas, turbulence, and the chosen reference quantities.
Bubble dynamics
The radial motion of an approximately spherical cavity in an incompressible Newtonian liquid is represented by the Rayleigh–Plesset equation:
[ \rho\left(R\ddot R+\frac{3}{2}\dot R^2\right)
p_B(t)-p_\infty(t) -\frac{4\mu\dot R}{R} -\frac{2\sigma}{R}, ]
where (R(t)) is the bubble radius, (p_B(t)) is the pressure immediately inside the bubble, (p_\infty(t)) is the pressure in the distant liquid, and (\mu) is dynamic viscosity. The equation combines liquid inertia with viscous resistance and capillary pressure. Thermal transport, acoustic radiation, liquid compressibility, and nonequilibrium evaporation require extensions when collapse velocities become a significant fraction of the speed of sound.
Lord Rayleigh analyzed the inertial collapse of an empty spherical cavity in 1917 while investigating damage to marine propellers. In the idealized case of constant external pressure and negligible viscosity, surface tension, and internal gas, the collapse time is proportional to the initial radius:
[ t_c \approx 0.915 R_0 \sqrt{\frac{\rho}{p_\infty-p_v}}. ]
The ideal solution develops an unbounded wall velocity at zero radius. Physical bubbles depart from that singular limit because residual gas is compressed, liquid compressibility radiates pressure waves, and the interface loses spherical symmetry.
Collapse near a solid boundary is strongly asymmetric. The boundary restricts liquid motion on one side of the cavity, causing the opposite interface to accelerate inward and form a liquid microjet directed toward the surface. The jet and the accompanying pressure pulse load a small area for a short interval. Repeated loading produces plastic deformation and fatigue in susceptible materials, after which fragments detach and leave the pitted morphology associated with cavitation erosion.
Flow structures
Hydrodynamic cavitation develops wherever acceleration or rotation creates a sufficiently low-pressure region. On a hydrofoil, the pressure reduction near the suction surface can support an attached vapor sheet. The sheet terminates where pressure recovery causes condensation, and an upstream-moving re-entrant flow can detach part of it. The detached volume then breaks into a cloud of cavities whose collective collapse generates stronger pressure fluctuations than the collapse of many uncorrelated bubbles.
Vortex cavitation occurs within the low-pressure core of a rotating flow. Tip vortices shed by a marine propeller provide a common example because circulation concentrates pressure reduction along a slender, persistent path. The vapor-filled core can extend far downstream before pressure recovery and viscous diffusion eliminate the structure.
In a centrifugal pump, cavitation commonly begins near the impeller inlet, where acceleration and blade loading reduce pressure. Vapor occupies part of the passage and alters the effective flow area, producing head loss and unsteady forces when the cavities condense farther through the impeller. The associated operating threshold is characterized through net positive suction head, which relates inlet total pressure to vapor pressure in units of liquid head.
In a hydraulic turbine, pressure can reach cavitating conditions near runner-blade surfaces or within the draft-tube vortex. The resulting vapor structures modify efficiency and impose fluctuating loads on the runner and surrounding structure. Their location depends on runner geometry, discharge, rotational speed, and the elevation-dependent pressure at the turbine outlet.
Acoustic cavitation
An alternating acoustic pressure field produces acoustic cavitation when its tensile phase expands suitable nuclei. Cavities that undergo modest oscillations over many cycles exhibit stable cavitation. Their periodic motion interacts with the surrounding sound field and generates harmonic, subharmonic, and broadband emissions.
Inertial acoustic cavitation occurs when a bubble expands substantially during a low-pressure interval and then collapses during compression. The collapse concentrates mechanical energy into a small volume and produces shock waves, microjets, and extreme transient conditions inside the bubble. Gas compression and vapor reactions under these conditions contribute to sonochemistry, while optical emission from collapsing acoustically driven bubbles is termed sonoluminescence.
In ultrasonic cleaning, cavitation creates localized liquid motion and repeated impulsive loading near immersed surfaces. In ultrasonic machining, related oscillatory phenomena contribute to material removal in conjunction with abrasive particles. Medical lithotripsy also involves cavity growth and collapse around shock-wave-exposed tissues and calculi, although the biological effects depend on the spatial and temporal distribution of the acoustic field.
Marine engineering and historical development
Cavitation acquired engineering significance during the nineteenth century as marine propulsion systems reached higher shaft speeds and power densities. Osborne Reynolds connected pressure reduction in rapidly moving water with the formation of vapor and investigated the mechanical consequences of disturbed flow. Stanley Barnaby subsequently associated the loss of propeller thrust on fast vessels with cavity formation around the blades, distinguishing the phenomenon from ordinary ventilation in which atmospheric air is drawn from the free surface.
During the 1890s, Charles Algernon Parsons and You Watanabe examined the relation between propeller loading, rotational speed, and the sudden loss of effective blade area during trials associated with the steam-turbine vessel Turbinia. Their measurements treated the vapor region as a pressure-induced phase change rather than as entrained atmospheric air. The resulting propulsion arrangement distributed power among multiple shafts and propellers, reducing the load carried by each blade while preserving the turbine’s high rotational output.
Early observations were largely macroscopic, relying on thrust changes, vibration, and visible cavities. Later work combined controlled water tunnel experiments with high-speed photography and pressure measurements. These methods established that inception, attached-sheet behavior, cloud shedding, and erosive collapse are distinct stages rather than interchangeable descriptions of a single flow condition.
Mechanical and chemical effects
Cavitation erosion results from accumulated impulsive loading rather than from vapor chemically dissolving a surface. Individual collapse events affect microscopic regions, but repeated events create work hardening, cracking, and eventual material loss. The erosion rate depends on collapse intensity and frequency as well as the mechanical properties and microstructure of the exposed material.
The same flow can also contribute to corrosion. Removal of a protective oxide film exposes fresh material to the liquid, while electrochemical attack changes the surface that receives subsequent impacts. Cavitation erosion and corrosion therefore interact even though their underlying mechanisms remain distinct.
Cavitation also generates broadband noise and structural vibration. Pressure fluctuations arise from cavity-volume changes, periodic detachment of vapor structures, and collapse-induced shock waves. In rotating machinery these fluctuations interact with blade-passing frequencies and structural modes, producing spectral components that identify the spatial and temporal organization of the cavitating flow.
Thermal effects become important in liquids whose vaporization absorbs a substantial fraction of the available local energy. Evaporation cools the cavity interface and lowers the local vapor pressure, thereby limiting further growth. This thermodynamic suppression is especially relevant to cryogenic fluids and hot liquids, for which an isothermal treatment overestimates cavity size.
Representation in engineering analysis
Cavitation-resistant hydraulic configurations reduce the magnitude or duration of low-pressure regions and limit the intensity of subsequent pressure recovery. Propeller designs distribute circulation over blade area, while pump inlet arrangements determine acceleration and incidence before the impeller. Surface finish influences the number of persistent nuclei attached to a boundary, although nuclei carried in the liquid remain important.
Numerical descriptions range from discrete bubble models to continuum mixture formulations. Discrete approaches track individual cavities or representative bubble populations and resolve their interaction with a computed pressure field. Continuum approaches assign vapor and liquid volume fractions within each computational region, with mass-transfer models representing evaporation and condensation. Both approaches require assumptions concerning nuclei, turbulence, and phase-change rates because these processes occur across scales smaller than those directly resolved in most computational fluid dynamics calculations.
Experimental similarity requires more than matching the cavitation number. The Reynolds number controls viscous scaling, while the gas content and nucleus-size distribution determine inception behavior. Differences in surface roughness and compressibility further separate model-scale cavity patterns from those of full-scale machinery. Consequently, geometrically similar flows at the same nominal cavitation number do not necessarily exhibit identical inception or erosion.