**1. Introduction**

22 Will-be-set-by-IN-TECH

176 Mass Transfer - Advanced Aspects

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The vapour generation in a liquid can be caused by two different mechanisms: following a heat input, thus an increase in temperature at constant pressure, which is well known as the boiling phenomenon, or, at constant temperature, a decrease of pressure, which corresponds to the cavitation phenomenon.

When the liquid pressure decreases below the saturation pressure, some liquid undergoes a phase change, from liquid to vapour. The saturation pressure, *pv*, is a fluid property which depends strongly on the fluid temperature. The cavitation phenomenon is manifested, in the fluid flow, by the formation of bubbles, regions of vapour or vapour eddies.

The cavitation phenomenon frequently occurs in hydraulic machines operating under low pressure conditions. The cavitation phenomenon causes several undesirable effects on this type of machines, for example: the noise generated by the mass transfer between the phases, the efficiency loss of the hydraulic machines, and the erosion of certain elements caused by the vapour bubbles collapses near walls. Additionally, it should be mentioned the flow instabilities caused by the vapour appearance, such as alternate blade cavitation and rotating blade cavitation (Campos-Amezcua et al., 2009).

The formation of cavitating structures in the hydraulic machines, their geometry and more generally, their static and dynamic properties, depend on several parameters (Bakir et al., 2003), such as:


This chapter presents an analysis of the cavitating flows on three axial inducers. These studies include numerical analyses at a range of flow rates and cavitation numbers, which were validated with experimental tests (Campos-Amezcua et al., 2009; Mejri et al., 2006). The obtained results can be summarized of the following way:

Numerical and Experimental Study of Mass Transfer Through Cavitation in Turbomachinery 179

(a) (b) (c)

β*=16°* 

Table 1. Principal characteristics of inducers used for the cavitating analyses

*D* diameter **Greek Subscript**  *fcav* detachment frequency *α* vapour volume fraction *1, 2* inlet, outlet *l* blade chord length *β* blade tip angle *a* axial direction

*lcav* cavitation length *η* efficiency *B* bubble *p* pressure *γ* vapour mass fraction *c* condensation

*R* radius *ω* rotational speed *g* gas *St* Strouhal number *ρ* density *l* liquid *T* cycle period *σ* cavitation number *nom* nominal *t* time *σs* surface tension *t* blade tip *U* tangential velocity *v* vapour

Φ

Ψ

(c) Two-blade aircraft inducer with β=4°

**Nomenclature** 

*Pv* saturation pressure

*v* velocity magnitude

*Q* flow rate

**Parameters Industrial inducer**

Fig. 1. Inducers used for the numerical and experimental study in cavitating regime. (a) Three-blade industrial inducer with β=16° (b) Three-blade industrial inducer with β=8°

**Maximal efficiency** 57% 54.1% 15.5% **Nominal flow rate coeff.** 0.159 0.076 0.014 **Nominal head coeff.** 0.310 0.228 0.188 **Blade number** 3 3 2 **Blade tip angle** 16° 8° 4° **Tip solidity** 2.95 2.45 3 **Rotational velocity** 1,450 RPM 1,450 RPM 8,000 RPM

**Industrial inducer** β*=8°* 

flow coefficient *cav* cavitation

head coefficient *e* vaporization

**Aircraft inducer**  β*=4°* 

	- a. Steady state performances: pressure head coefficient and efficiency versus flow rates.
	- b. Steady state cavitating behaviour of the studied inducers.
	- a. Steady and unsteady states performances: pressure head coefficient and efficiency versus flow rates.
	- b. Steady and unsteady states cavitating behaviour of the studied inducers.
	- c. Vapour distributions and other numerical results, which enable to explain the cavitating behaviour for these inducers.
	- d. The fluid flow instabilities generated by the presence of vapour.

The numerical simulations were performed using the commercial code *Fluent*, which is based on a cell-centred finite-volume method. The cavitation model used for the calculations assumes a thermal equilibrium between the phases. It is based on the classical conservation equations of the vapour phase and a mixture phase, with mass transfer due to the cavitation, which appears as a source term and a sink term in the vapour mass fraction equation. The mass transfer rate is derived from a simplified Rayleigh–Plesset model for bubble dynamics. The experimental tests were carried out at the DynFluid Laboratory of Arts et Métiers ParisTech.

Next, the different cases studied in this work, to understand the cavitating behaviour of the inducers, are described:

a. Cavitating flow through venturi geometry.

This part presents the numerical validation of the cavitating flow through a 2D simple geometry. On the one hand, the numerical results demonstrate the influence of the turbulence model to predict instabilities in non-homogeneous flows. On the other hand, the intrinsic instabilities were detected and compared to experimental data.

b. Analysis of cavitating flow in two-dimensional inducers – blades cascades.

This part presents the steady and unsteady numerical study carried out on two blades cascades: first, on a two-blade aircraft inducer, and then, on a three-blade industrial inducer, see Fig. 1. This analysis confirms the influence of blades number and the solidity on the behaviour of the instabilities of cavitating flow. Various forms and behaviours of vapour have been observed in the blades cascades, such as: stable blade cavitation, alternate blade cavitation and rotating blade cavitation.

c. Experimental study and numerical analysis of the cavitating flow in three-dimensional inducers.

This part presents the steady and unsteady numerical simulations, and experimental investigations in steady state of the cavitating flow through of the three inducers presented in the Fig. 1. The flow behaviour in the inducers is modified by the appearance of the cavitation on the leading edge. These cavitating behaviours change with respect to the operating conditions of the inducer: flow rates and cavitation levels.

Fig. 1 shows the three inducers used for the numerical and experimental study in cavitating regime, and the Table 1 presents the main characteristics of these inducers.
