#### An Introduction to Cavitation in Hydro Turbomachinery

A major concern for pump system engineers over the last fifty years has been caviation. Cavitation is defined as the formation of vapor bubbles in low pressure regions within a flow. Generally, this phenomenon occurs when the pressure value within the flow-path of the pump becomes lower than the vapor pressure; which is defined as the pressure exerted by a vapor in thermodynamic equilibrium conditions with its liquid at a specified temperature. Normally, this happens when the pressure at the suction of the pump is insufficient, in formulas NPSHa ≤ NPSHr, where the net positive suction head is the difference between the fluid pressure and the vapor pressure at the pump suction and the “a” and “r” stand respectively for the values available in the system and required by the system to avoid cavitation in the pump.

The manifestation of cavitation causes the generation of gas bubbles in zones where the pressure gets below the vapor pressure corresponding to that fluid temperature. When the liquid moves towards the outlet of the pump, the pressure rises and the bubbles implode creating major shock waves and causing vibration and mechanical damage by eroding the metal surfaces. This also causes performance degradation, noise and vibration, which can lead to complete failure. Often a first sign of a problem is vibration, which also has an impact on pump components such as the shaft, bearings and seals.

The vapor pressure for any liquid, is directly proportional to temperature and changes non-linearly according to the law of Clausius-Clapeyron. By regulating the pressure to which a fluid is subjected, you can change its vapor pressure and eventually make it boil at room temperature. In Figure 1 you can see the vapor pressure variation as a function of the ambient temperature for different fluids with different boiling points at  aforementioned ambient temperature.

For instance, if we take water vapor pressure at 100° C , Pa  is about 101000. However, if we reduce temperature to 5° C, the water’s vapor pressure decreases sensibly to about 872 Pa. In summary, a temperature or pressure variation will affect the boiling point of the fluid, hence its vapor pressure.
This means that the installation location has an impact on vapor pressure depending on the altitude and therefore the ambient pressure. This element should be considered on a system level to account for the possibility of cavitation occurrence.

So how can we avoid cavitation? As mentioned previously, cavitation doesn’t occur when: NPSHa > NPSHr. While NPSHa is a system parameter, the NPSHr depends on the pump design and is specified by the pump manufacturer for appropriate setup and installation of the pump within the system. The engineer should also account for a “safety” margin to avoid that unexpected fluctuations might cause the onset of cavitation.

purely  from a fluid mechanics perspective, we can define the degree of cavitation with a non-dimensional parameter called cavitation number, which is defined as seen in Figure 2:

where pref  Is the pressure taken in the reference point, pv is vapor pressure, ρ is fluid density and V is the characteristic velocity of the flow. Both parameters have to be specified for each practical situation. For instance, in the case of a cavitating flow past a single foil, the reference pressure and velocity are usually chosen in a point far from the foil in the undisturbed flow. Large values of the cavitation number corresponds to non cavitating flow,  and as these  correspond to large values for the difference between reference pressure and vapour pressure.

However, these parameter results are more important when cavitation occurs, as it gives a measure of the cavitation extent. In fact, we can identify a critical value of the cavitation number σwhich corresponds to the appearance of cavitation in the flow. Considering the fully wetted flow, cavitation occurrence can be witnessed by either decreasing the reference pressure value or increasing velocity, with consequent decrease in cavitation number. Any additional reduction will lead to an additional development of cavitation within the flow. It should be noted that if reference pressure is again increased starting from cavitating flow, the cavitation disappears for σ values often higher than the critical cavitation number as a hysteresis effect can be observed.

If we look at cavitating flows within pumps and hydro-turbomachinery, we can witness very complex shapes and a wide variety of cavitation types, which can be summarized as follows:

1. Attached cavities: In this case, cavitation appears as cavities attached to the suction side of the foil. It is called partial when the cavities covers only part of the foil or supercavity when it fully covers the suction side and closes downstream the trailing edge.
2. Travelling bubble cavitation: this case presents isolated or small groups of bubbles depending on their nucleus density
3. Cavitation clouds: These shows aggregates of various forms
4. Cavitating vortices: These vortices can be more or less structured and are observed at the tip of 3D foils (or in the turbulent wake of bluff bodies)

Interactions between bubbles or with solid components, instabilities, turbulence and other phenomena can sensibly complicate the mentioned shapes and therefore the analysis of cavitation phenomena in different flow regimes within turbomachinery.

The analysis and study of cavitation can be a very difficult topic and the fluid mechanics and thermodynamics formulation to describe the connected phenomena very complex.

A thorough description can be found on the book “Fluid Dynamics of Cavitation and Cavitating Turbopumps” by L. D’Agostino, M.V.Salvetti