Numerical Prediction of Cavitation: Improving Pump Design

Numerical Prediction of Cavitation:
Improving Pump Design

Increased requirements in power per unit of volume for modern centrifugal pumps have made cavitation the main limiting factor in pump design. Using an inventive method, Sulzer Pumps now can take into account the cavitation behaviour during the design process. It helps to improve suction capabilities and to reduce erosion and vibration, especially for high suction specific speed pumps.

Demand for higher power per volume, driven by manufacturing costs reduction, has changed the limits of modern pump design. The traditional approach tries to avoid cavitation if possible because of the damage it may cause in the impeller. Today, pump designers increasingly consider incipient cavitation and the effects of the flow’s three-dimensional behaviour when they define the blade shape. The classical onedimensional design rules applied for decades are no longer sufficient. For this reason, there is a strong need for more accurate numerical tools to predict the cavitation behaviour of pumps.

IMPROVING SUCTION CAPABILITIES
The use of numerical tools to design and optimise the hydraulics of pumps is nowadays a standard in the industry. Up to now, this optimisation has mainly focused on the efficiency and the stability of the head curve through a better control of the recirculation and a reduction of secondary flows. Increasingly, cavitation is also a major limiting factor in pump design.
Nevertheless, only a few attempts have been made to improve cavitation in pumps using numerical approaches. Mostly, this optimisation is limited to changes of the blade profile and finer adaptation of vane inlet angles. They were based upon results obtained from cavitation-free flow analysis using methods of computational fluid dynamics (CFD). While this approach usually helps to delay cavitation inception, it does not support the designer in improving the suction capabilities of the pump. Suction capabilities strongly depend on the way the cavitation develops along the vane as a function of the pressure level and how its presence affects the performance of the pump.

An optimisation of the suction capabilities is only possible if one is able to control the effect of a modification of the vane shape on the cavitation development and to predict when this cavitation development will impair the head developed by the pump. For that reason, there is a strong need for an accurate and rapid method to predict the three-dimensional cavities development as well as the associated performance drop. This is especially true for the design of high-suction specific speed pumps for which a smooth operation at part load can only be obtained by optimising the vane shape, taking into account the three-dimensional behaviour of the flow.

FAST NUMERICAL METHOD
Some commercial CFD codes offer two-phase flow models, allowing a phase change in the flow calculation to simulate cavitation. These methods are certainly able to realistically model the phenomena involved in the cavitation development, but their application needs an unsteady approach. Due to the long computation time, this technique doesn’t meet the requirements during a design process. To predict the cavitation in pumps, Sulzer Pumps uses a simplified version of a cavity interface tracking method developed at the Laboratory of Hydraulic Machines of the Swiss Federal Institute of Technology in Lausanne (LMHEPFL). In its original form, this method iteratively adapts the cavity shape in order to reach a given condition, which can be a specific velocity or pressure, at its boundary.
Experiments show that the shape of the cavity can be determined with a fast, non-iterative formula, the well-established Rayleigh-Plesset equation, as long as the cavity development does not affect the main flow. This condition is approximately met in most cases if the cavity doesn’t reach the throat of the blade-to-blade channel.
For this method, a commonly used flow calculation program, which solves the Reynolds-averaged Navier-Stokes equations, yields the cavitation-free pressure distribution in the impeller’s flow field. Then a typical nucleus size, which would induce cavitation, is chosen. Along the mesh lines of the calculation grid, the nucleus size is compared to the critical radius according to the minimum pressure. If the critical size that causes the explosive development of the nuclei is too small, the calculation is not performed and the point is considered free of cavitation or corresponding to development of isolated bubbles. The calculation of bubble growth and collapse gives a rapid estimation of the detachment and the closure location of the attached cavity. The cavity length is then defined. The envelope of bubbles over the profile approximates the cavity shape (Fig. 1).
The incipient cavitation coefficient, which is an important characteristic value to describe the pumps operational behaviour, is defined as the first non-zero cavity length along the vane span. Due to surface tension and bubble dynamic effects, this value does not correspond to the minimum pressurecoefficient along the vane. Therefore, the incipient cavitation coefficient can’t be predicted based only on the minimum pressure calculated from the cavitation-free condition.

REDUCING THE RISKS OF VIBRATION AND EROSION
With the aid of this new tool, Sulzer engineers can calculate the evolution of the length of an attached cavity with the NPSH (net positive suction head) value taking into account the viscous, turbulent and three-dimensional nature of the flow in a pump. With this knowledge, they can predict the head impairment due to the cavitation development. The cavitation development can take place on the suction side (Fig. 2) or on the pressure side of the vanes (Fig. 3), depending on the flow rate. It has to be noted that, at part-load, the head impairment is most of the time caused by the cavity reaching the blade-to-blade throat at the hub even if the cavity starts to develop at the shroud much sooner than at hub (Fig. 4). This is due to the fact that the throat area is positioned more downstream at shroud than at hub, allowing a larger cavity to develop before reaching the blade-to-blade throat. It indicates the necessity to calculate accurately the cavity length along the span of the vane as a function of the cavitation coefficient to be able to predict the associated head impairment.
Such a procedure can also significantly improve the reliability of high-suction specific speed pumps, allowing to better forecast the effect of possible inlet recirculation at part-load on cavitation behaviour. Cavitation associated with inlet recirculation is one of the possible causes of vibration at partload. If cavitation can be avoided during the design process, it is possible to extend the operating range of a pump.
For the pump designer, this method will help to improve the suction capabilities of the impellers by an accurate prediction of the effects of geometry modifications.
The accurate prediction of the cavity length is also used to better estimate the erosion rate for different rated operating points and by this means to more precisely predict the requested NPSH for a safe operation with reduced costs for model testing.

PROVEN BY MEASUREMENTS
Previous to the use in the industrial design process the cavitation prediction program was applied to a variety of radial and semi-axial pumps spanning the range of possible application.
For a radial volute pump of medium specific speed, predicted and measured cavity lengths are compared (Fig. 5). The numerical results fit very well the measured ones. The example illustrates one of the advantages of using such a cavitation prediction tool. No cavity length measurement was available for flow coefficient around the local calculated maximum in the visible cavitation inception. For that reason, the required cavitation-free NPSH across the entire flow range based on the measurementdata was probably underestimated for this pump. With the insight gained from the numerical calculation, it is possible to operate this pump in a wider range of operation than previously expected.

Measurements performed for a pump with the specific speed of nq = 33 (specific speed of pump stage [min–1]; VS Ns = 1700) clearly show that the new calculation program can predict the limits of cavitation-free operating condition with great accuracy (Fig 6). Thanks to the improved numerical prediction, the understanding regarding pump operational range has been improved.

DuPont, Philippe, "Numerical Prediction of Cavitation: Improving Pump Design." Sulzer Technical Review, 2/2001: 24-27.

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