**6. References**

20 Will-be-set-by-IN-TECH

Fig. 12. Ensemble of 100 realizations of yaw angular velocity evolution. Side loads cease at

where *ω*<sup>+</sup> = *ω<sup>y</sup>* and *ω*<sup>−</sup> = *ω<sup>z</sup>* correspond, respectively, to yaw and pitch rate, *A*(*t*) and *D*(*t*) are, respectively, the time-(altitude-)dependent effective damping and diffusion coefficients,

Fundamentally, and as detailed in (Keanini et al., 2011), equation (32) provides the key to analyzing both the rotational and translational rocket response to side loading. Physically, *A*(*t*) is roughly proportional to both the squared moment arm from the rocket center of mass

(altitude-dependent) pressure difference between the interior and exterior of the nozzle, and

Practically, the detailed formulas for *A*(*t*) and *D*(*t*) in (Keanini et al., 2011) are related to both rocket-specific design parameters, as well as universal, non-specific parameters characterizing in-nozzle, shock-boundary layer separation. Thus, as discussed in (Keanini et al., 2011), the formulas allow straightforward identification of design criteria for, e.g., enhancing pitch/yaw damping and/or suppressing diffusive, i.e., stochastic growth of random pitch and yaw.

*ce*, as well as the mass flux magnitude, and is inversely proportional

*D*(*t*)*dW*<sup>±</sup> (32)

*ce*, as well as the squared

*dω*<sup>±</sup> = −*A*(*t*)*ω*<sup>±</sup> ±

to the lateral moment of inertia. Likewise, *D*(*t*) is proportional *L*<sup>2</sup>

the squared altitude-dependent position of the separation-inducing shock.

*t* = 10.85 s. Adapted from (Srivastava et al., 2010).

form of an Ornstein-Uhlenbeck process:

and *W*±(*t*) are Weiner processes.

to the nozzle exit, *L*<sup>2</sup>


**8** 

*1Mexico 2France* 

**Numerical and Experimental Study of Mass** 

*1 Electrical Research Institute, Department of Turbomachinery, Cuernavaca,* 

Rafael Campos-Amezcua1, Sofiane Khelladi2, Zdzislaw Mazur-Czerwiec1, Farid Bakir2, Alfonso Campos-Amezcua1 and Robert Rey2

*2 Arts et Métiers ParisTech, DynFluid Laboratory, Paris,* 

**Transfer Through Cavitation in Turbomachinery** 

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

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

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

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.,

• Geometrical conditions: profile, camber, thickness, incidence, and leading edge shape of

• Local flow conditions: pressure, velocities, turbulence, the existence of gas micro-

• Fluid properties: saturation pressure, density, dynamic viscosity and surface tension. 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).

fluid flow, by the formation of bubbles, regions of vapour or vapour eddies.

rotating blade cavitation (Campos-Amezcua et al., 2009).

the blades, as well as the walls roughness.

The obtained results can be summarized of the following way:

bubbles dissolved in the flow.

**1. Introduction** 

2003), such as:

to the cavitation phenomenon.

