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## Paper FEDSM2005-77084 COMPARISON OF COMPUTATIONAL RESULTS OBTAINED FROM A VOF CAVITATION MODEL WITH EXPERIMENTAL INVESTIGATIONS OF THREE INDUCERS. PART I : Experimental Investigations FEDSM2005-77084

### BibTeX

@MISC{Mejri_paperfedsm2005-77084,

author = {Imene Mejri and Farid Bakir and Robert Rey and Thabet Belamri},

title = {Paper FEDSM2005-77084 COMPARISON OF COMPUTATIONAL RESULTS OBTAINED FROM A VOF CAVITATION MODEL WITH EXPERIMENTAL INVESTIGATIONS OF THREE INDUCERS. PART I : Experimental Investigations FEDSM2005-77084},

year = {}

}

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### Abstract

Abstract The paper presents full 3D numerical simulations and experimental investigations of the cavitating flow through three axial inducers. These inducers are identified by the blades leading edge angle at the periphery β 1T =8°, 10°, 13° and are thus noted as Inducer 8°, Inducer 10° and Inducer 13°. They have the same tip and hub diameters. The numerical and experimental investigations were carried out at the LEMFI-Paris laboratory. This enabled us to explain the cavitating operation for off-design conditions. In Part I of this paper we describe the design methodology adopted for the inducers and which is deduced from literature and in house experience. Then the main experimental results are presented for the studied inducers at a range of flow rates and cavitation numbers concerning : • The overall performances: pressure head coefficient and efficiency versus several flow rates. • Critical cavitation number (5% and 15% of drop) versus the flow rate. In Part II of this paper, a review of the cavitating regime modeling and the cavitation VOF model used for this paper's calculations is firstly presented. The numerical approach is based on a combination of the VOF technique with a truncated version of the Rayleigh-Plesset model predicting the complicated growth and collapse processes of bubbles. The cavitation model also features a control volume finite element discretization and a solution methodology which implicitly couples the continuity and momentum equations together. The numerical results of Part II concern : • The overall performances. • The numerically investigated water vapor volume fraction distributions and other CFD results, which enable us to explain the cavitating behavior for these inducers. • The location and sizes of the blade cavity and backflow vortex. Finally, the comparisons between experimental and simulated results on the overall performances, cavities sizes and cavities location are discussed. A good agreement between experimental and predicted results was found for a range of flow rates. The head breakdown in the simulations started at a different cavitation coefficient than that in the experiment. Nomenclature Introduction Inducers are axial flow impellers having few blades. Their blades are set at a very shallow angle to peripheral direction so that, in short axial length, the blade passages are long. In general, the blades wrap in a helix around a central hub. Inducers are generally located upstream of centrifugal or mixed flow impellers, and serve as a small booster pump for the main impeller. They are designed to resist cavitation and to reduce the NPSH required by pumps. A pump equipped with an inducer may operate at 1/2 to 1/3 the NPSH required levels of a non-inducer version of the same pump. An inducer must have a low weight, which leads to high driving speed and small size [1]. The results are more compact pumps and generally more economical operation. Cavitation is an important phenomenon which can have a profound effect on the performance of a number of devices mainly at the off-design conditions. Examples include pumps, inducers, propellers, and injectors. For the inducers, the cavitation causes operational instability and vibration and excessive wear of mechanical seal, bearing and shaft, which compromise their performances. Although the use of inducers is frequent today, several aspects of their operation and their behavior still remain difficult to model. In order to elucidate some phenomena, affecting the reliability of these devices, their maximum performance and their operational limits, we still rely on experimentation. The appearance of the cavitating structures, their geometry and more generally their static and dynamic properties depend on several parameters which include above all: the blade profile, camber, incidence, stacking, and leading edge shape, as well as the walls roughness, the upstream turbulence, the existence of gas micro-bubbles in the flow, the fluid viscosity, etc. The cavitating pockets can be of several natures; some remain attached to the blades with more or less oscillating lengths and frequencies of release which can vary from a blade to another. They can also be rotating with different rotation frequencies; only steady sheet cavitation is considered in the present paper. Nevertheless, even with continuous cavitation, the flow is always unsteady because of the shedding of bubbles from the trailing edge of continuous cavitation. The prediction of steady cavitation and more specifically the steady cavity length is important for the cavitation CFD has been extensively used to predict the flow through these devices under non-cavitating conditions. However, because of the physical and numerical challenges associated with cavitation, CFD has only recently started to be used to predict cavitating flows. Some of the CFD models developed for cavitation are more adapted to the isolated 2-D profiles for steady [3] and unsteady flows More details concerning the cavitation modeling and the numerical model used for this study will be given in Part II of the paper [5]. Inducers presentation Inducers design methodology When designing an inducer, the first goal is often to look for high suction performances combined with high head rise. The cavitation behavior is more or less taken as a result and checked during experimental studies. The design methodology we used to make up the inducers is a classical procedure equivalent to those found in the bibliography [6][7][8][9][10]. The chosen design for the three inducers corresponds to a compromise between hydraulic performances, manufacture and constraints associated to the existing test rig. The machines are not equipped with stators. A wide variety of parameters must be considered in the design of an advanced industrial inducer. The main parameters used during the design can be classified into main and secondary parameters. The main parameters concern the operational parameters (H, Q, η), the fluid properties, the blade number the external and internal diameters, the solidity, the radially varying work, the stagger angle, the blade angle (particularly at the inducer tip) and the aerodynamic camber. The secondary parameters concern the blade thickness, the tip clearance, the leading edge slant, the sharpening of the leading and trailing edges, the hub shape, etc. First, we chose the operational parameters and the fluid characteristics. Than we verify that the suction specific speed S is compatible with the sought objectives. The blades are flat plate and their number is fixed to 3 to limit the passage area decrease of the fluid. The hub to tip ratio T is chosen between 0.3 and 0.6 and the leading edge blade angle is close to 8° in periphery. The external radius is given by the NASA empirical relation [8]: The stacking of the trailing edge is made radially. For the solidity (=blade length/blade spacing = l/t), we retain a value of 1.8 to 2.5 in periphery. The resulting azimutal angle θ is around 300°. To facilitate the blade construction, we adopted an incidence law corresponding to a blade ruled surface: Inducers characteristics Each inducer was built from one piece of aluminium manufactured by a numerically controlled machine tool provided with 5 axes. In order to provide the inducers blade with better resistance to the erosion by cavitation, a sanding and an anodization of the hubs and blades were done. The inducers are all of type C (also called helical type because of the radial distribution of the inducer blade angle). They differentiate by their blade angle at the tip β 1T =8°, 10°, 13°. The three inducers are thus noted as Inducer 8°, Inducer 10° and Inducer 13°. As it can be seen at General overview of the test rig The LEMFI-Paris axial and centrifugal pumps test rig, is composed of two independent but interconnected loops. The axial pump loop used in this study provided a straight inducer inlet section and is composed with the following main elements ▪ Two storage tanks with a capacity of 4 m 3 each, connected by a 350 mm diameter pipe. They can be loaded and emptied using two electrical control valves. ▪ A liquid ring vacuum pump is used to control the pressure at the free surface inside the storage tanks. ▪ A 22 kW alternative motor ("Brook Hansen") powered by a variable frequency controller was used to drive the tested inducer. The manufacturer gives the electric efficiency of the motor. The rotational speed is measured using a magnetic tachometer (accuracy 0.1%). ▪ A motorized control valve serves to adjust the flow rate accurately. ▪ The inducer equipped with a transparent acrylic cover to enable direct observations of the flow. ▪ A centrifugal pump installed in series with the impeller in order to overcome the circuit losses. ▪ Various measurement instruments and devices: -An ultrasonic flow meter (″A500 -Sparling Meter Flow ″, accuracy 1%), placed at the inlet of the inducer. -Two piezo-resistive manometers (Kistler, type 601A, accuracy 1%). They are positioned at the inlet and outlet sections and measure the average tip pressure (at about 20 mm upstream of the leading edge and 150 mm downstream of the trailing edge of the blade). The signal resulting from these sensors is amplified then treated by a Lecroy spectrum analyzer (type 930 4A). Its connection with a computer enables us to store and to use these signals. -A temperature probe (accuracy 1%): the average temperature during the tests presented below is 18°C. -An accelerometer "Bruel and Kjaer" with a sensibility of 3.5 mV/(m/s²) placed over the transparent cover. Comparison of the inducers performances Experimental observations This section compares the performances of the three machines, namely: overall performances (head, flow rate, efficiency) and the behavior with the critical cavitation characterized by the cavitation coefficient σ C . For the experimental cavitation procedure, the rotational speed is fixed to 1450 rpm, the flow rate is measured by the flow-meter and set to the operating value using the motorized control valve. The inlet pressure drop is realized by the liquid vacuum pump. According to our experience, the pressure drop starts when the cavitating pocket reaches the throat formed by two successive blades where it is quickly dragged to the trailing edge. While retaining this particular criterion for the calculated pocket, we obtain a good approach of the critical NPSH in a range of incidence close to the design point. For certain operating values of flow rates and inlet pressure, some specified types of cavitation were observed. For all tested flow rates, a sudden head drop happens with very low inlet pressure values. The backflow has a circumferential velocity which is about 20 % of the inducer tip speed. Thus, in the shear layer between the swirling backflow and axial main flow, we have an axial vorticity that rolls up and forms a vortex structure surrounding the backflow region. Due to the centrifugal forces, the pressure at the center of these vortices is lowered and cavitation occurs there if inlet pressure is decreased. After the backflow cavitation, we observe a forward rotating cavitation propagating in the same direction and faster than the inducer (Points 2-4). Since the blade-to-blade throat is located more downstream at the shroud, the cavity starts to develop much sooner at shroud than at hub before reaching the blade-to-blade throat. When it reaches this throat, the head-drop begins (Point 5). As the inlet pressure decreases, the cavity lengthens and its thickness decreases (Points 5-6): it is aspired forward in the blade to blade channel. The blockage phenomenon, corresponding to a vapor pocket blocking all the inter-blade passage, depends on the flow rate and on the inducer. The cavitation figures are then very different : the blockage condition could occur upstream, in the flow passage or at the inducer's outlet. On the other hand, we observed that backflow may carry out a rotating cavitation even if head rise is not affected. The observed rotating pocket propagates only on a certain portion of the periphery, with a frequency that is slightly larger than the rotational one. The observed rotating pockets occurrence seems independent of the flow rate; they start to occur when the cavity length reaches certain proportions of the blade spacing. Point Overall performances The flow rate is characterized by the flow coefficient φ. The overall performance in noncavitating regime The cavitating surge does not occur in any of our inducers. It is a large amplitude oscillation of flow rate that results from the interference between cavitation and the whole system including the impeller, placed downstream. It occurs over the entire hydraulic system. The rotating cavitation results from the local interaction between cavitation and the impeller [11]. For the values corresponding to the maximum efficiency, the flow coefficient and the angles of incidence are given in Behavior with cavitation The experimental head-drop curves are presented on The examination of these values shows a general superiority for Inducer 8° concerning the behavior with cavitation. The behavior in cavitating regime is characterized by the cavitation parameters σ C corresponding to head drops of 5% and 15%. Those values of σ C,5% and σ C,15% are determined by the character of the head-drop curves (sudden, smooth,…). The test results concerning the comparison of the performances in cavitating regime are synthesized in One also observes the σ C rises in partial flow, this phenomenon is more significant when β 1T increases. The best σ C value for a head drop of 5 % is obtained, as envisaged, for Inducer 8°. At high flow rates, the critical cavitation number increases for Inducers 8° and 10° but not for Inducer 13°. For a head drop of 15 %, the resistance to the cavitation changes in a variable way: very little for Inducer 10° until very strongly for Inducer 13°. On these figures are also represented the various levels of the K=σ C /2i parameter which controls the onset of cavitation instabilities in various types of machines. This parameter connects the cavity volume to the incidence angle. There are many correlations of σ C /2i with cavitation instabilities (their types, dimensions …) [12,13]. The cavitation types studied through these correlations are cavitation backflow vortices, two modes of rotating cavitation, attached uneven cavitation, surge mode oscillation and cavitation surge, and it was found that the boundaries between these cavitation types are nearly parallel to the iso-σ C /2i curves. A particular value of σ C /2i is the limit between stable and unstable behavior of the cavitation. For the three inducers, the σ C,5% and σ C,15% curves remains between iso-σ C /2i = 0.2 and iso-σ C /2i = 0.8. These values of σ C /2i correspond experimentally to cavitating pockets that are: -identical on the three blades of each inducer; -of rotating cavitation nature or backflow vortices mode. This shows that the rotating cavitation starts to occur at σ C /2i =0.8 (or less, except for Inducer 13° where it starts at σ C /2i =0.4). 15 Copyright © 2005 by ASME In general, the best values of the suction specific speed are observed for flow rates higher than those corresponding to the maximum efficiency. Comments This work enabled us to test three axial inducers for the cavitating regime. The three machines are designed with the same methodology. The experimental results are mainly differentiated by the value of the blade angle around the leading edge at the periphery β 1T = 8°, 10° and 13°. The resistance to the cavitation depends strongly on the blade angle around the leading edge at the periphery. Consequently, it depends on the blade length since the inducers have the same axial length. The blade length fixes the admissible length of the vapor pocket before degradation of the outlet pressure. The experimental results show the overall performances increase with β 1T . On the contrary, they confirm the relative superiority of Inducer 8° through the critical cavitation coefficient of 5%. For a 15% drop, the three inducers have quite the same performance. Contrary to Inducers 8° and 10°, we do not observe, for Inducer 13°, any increase of the critical cavitation number at high flow rates. It is clearly felt that there are many limitations of experimental measurements to describe the development of the flow fields. Then, an important role exists for fully three dimensional viscous flow analyses to fill in the details left by the experimentations. Nevertheless, these 3D analyses in the inducers previously tested may be made difficult by their low spiral angle and their long passages. The real flow pattern within the rotating inducers is complex and three-dimensional. The long but tightly-spiraled passages added to the vapor pockets seem to give rise to secondary flow fields strongly influenced by the blade walls and tip clearance, and that will be studied in Part II. Qualitative and quantitative comparisons between numerical and experimental results will be detailed in Part II of this paper.