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Russian Aeronautics (Iz VUZ) Volume 55 Issue 4 2012 [Doi 10.3103%2Fs106879981204101] E. M. Kraeva, M. v. Kraev -- Analysis of Three-dimensional Flow in High-speed Pump Centrifugal Impellerspringer

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   ISSN 1068-7998, Russian Aeronautics (Iz.VUZ), 2012, Vol. 55, No. 4, pp. 383–387. © Allerton Press, Inc., 2012. Original Russian Text © E.M. Kraeva, M.V. Kraev, 2012, published in Izvestiya VUZ. Aviatsionnaya Tekhnika, 2012, No. 4, pp. 42–45. 383 AIRCRAFT AND ROCKET ENGINE DESIGN AND DEVELOPMENT Analysis of Three-Dimensional Flow in High-Speed Pump Centrifugal Impeller E. M. Kraeva and M. V. Kraev Siberian State Aerospace University, Krasnoyarsk, Russia Received March 12, 2012 Abstract —Relations for calculating a shear flow in the centrifugal impeller channels are presented. The results of three-dimensional flow visualization in the centrifugal forces field show a satisfactory agreement with calculation data within a wide range of centrifugal pump design and operational parameters. DOI : 10.3103/S106879981204101 Keywords : centrifugal impeller, visualization, blade, channel, flow. High-speed centrifugal pumps are widely used in aircraft, space-rocket and power engineering devices as a liquid working fluid supply unit in plants for generating a pulse producing power in automatic equipment components, cooling and temperature control systems. It is known [1] that the experimental power performance of a centrifugal pump and flow parameters inside the pump differ significantly from parameters calculated for an ideal flow. Such a difference is determined by the impact of different factors describing the real hydrodynamic flow in the centrifugal forces field. The impact of viscous forces, which determine friction and vortex formation losses is particularly important and in high-speed small-sized pumps the active cross-section of the flow affecting the blade channel velocity value and gradients is reduced. Several factors, namely, complex processes inside the flow passage of the closed-type impeller, lack of clear understanding of flow hydrodynamics inside the narrow channels in which the effect of viscous forces is dominant and separation zones are present, the diffusive flow pattern required that special experimental studies were carried out using a full-scale pump of the class being considered. This enabled us to define the main factors affecting the velocity value and distribution in the blade channels taking into account the singularities of channel hydrodynamics proceeding from commensurability of the boundary layer and mainstream core parameters. When studying high-speed pumps, their design features present certain difficulties being complicated by small absolute dimensions of the impeller flow passage; as a result, the tried-and-true research methods being used for large-sized pumps calculation are unsuitable. In this case, very often it is impossible to apply the standard equipment being used in ordinary studies; considerable transverse gradients of the flow parameters complicate the experiments and necessitate creating special devices [2] and new methods of direct or indirect determination of parameters [3]. The studies that do not disrupt the flow structure are particularly valuable; therefore, since the photography survey has to be carried out at considerable angular velocities, that are specific to the high-speed pump, several photography methods were used. These methods combined with the flow visualization technique made it possible to register processes taking place in the blade channels of the high-speed pump at 5001000 ω=  −  rad/s and different operation modes including fully-developed cavitation in the impeller channels. Visual observations were also carried out at stroboscopic illumination. Processes in the impeller blade channels were photographed using the Zenit TTL camera with the Gelios-44M lens, under illumination of  KRAEVA, KRAEV   RUSSIAN AERONAUTICS Vol. 55 No. 4 2012 384 the scene by an electric discharge with the glow time ( ) 6 3410 − τ= × −  s that is produced by a special spark facility. The scene and camera were pre-protected from extraneous illumination. Discharge between electrodes was produced by the capacitor being supplied by the UPU-1M type generator with controllable output voltage varying from 7 to 14 kV. Capacitor charging and discharging was performed remotely using the high-voltage initiating relay. In the course of experimental studies of the impeller channels flow particular attention was paid to developing the visualization techniques, which was performed in the following ways: –by placing fiber vanes in impeller blade channel flow; –applying special coatings on the surface of the impeller channel being investigated; –injecting coloring (tracer) agent into the impeller blade channels, using the unique model fluid machine [2]; –introducing the impurities depositing on the surface of the impeller blade channel. All these techniques make it possible to conduct the studies in a wide range of variation in the design and operational parameters ( ) 22 0.0250.14 m CU   =  −  of the high-speed pump with the impeller flow passage dimensions corresponding to full-scale pumps. The blade outlet angle 2 bl β  value varied from 20 to 110°. The qualitative flow pattern was obtained by pasting silk fiber vanes in different zones of the channel and photographing the rotating impeller illuminated with an electric discharge. It should be noted that despite their relatively small sizes (from 3 to 5 mm long, 0.1 mm in diameter) the vanes provided the high quality of photos at the channel width 3 b ≥  mm; when 3 b <  mm the vanes affected the flow and in a number of experiments they distorted the flow pattern, whereas the smaller vanes were not registered on the film at a short duration discharge ( ) 6 310s, − τ= ×  which is due to the fact that photographing was performed at the high impeller rotational speed. The points of flow trajectory were obtained by visualization in a specially designed fluid machine [2] by injecting the coloring agent through a number of drain holes in the impeller disk. The model fluid machine (Fig. 1) being used for the visual study of the working fluid flow in the impeller blade channels has body 1  with transparent cover 2 , container 9  with water-soluble granules of the coloring agent located inside body 1  on the impeller shaft with blades 4 . Covering disk 5  is transparent, and driving disk 3  has a system of draining channels that connect the container chambers with the blade channels of the impeller being investigated. Container 9  has permeable membranes 8 , which provide the supply of the working fluid to the chamber with the coloring agent granules. When impeller shaft rotates, the container chamber serves as a fluid supercharger that continuously feeds the dissolved coloring agent into the rotating impeller blade channels. By means of photographing the cavities, injecting the coloring agent to the flow and using fiber vanes, we managed to register the trajectories and define the pattern of the flow core motion in the impeller blade channels. To the basic flow features should be added the areas of steady flow fluid motion along the pressure side of the blade and the areas of cocurrent flow on the suction side. The pressure gradient along the impeller blade channel step is established when the fluid flows under the action of the Coriolis and centrifugal forces, resulting in the ε  angle flow shear in the radial plane along the disks confining the channel [4]. The importance of the shear flow calculations Fig. 1.  Scheme of the model fluid machine working section layout: ( 1 ) body; ( 2 ) transparent cover; ( 3 ) impeller driving disk; ( 4 ) impeller blade; ( 5 ) transparent covering disk; ( 6  ) inlet pipe; ( 7  ) coloring agent granules; ( 8 ) permeable membrane; ( 9 ) container with coloring agent granules.    ANALYSIS OF THREE-DIMENSIONAL FLOW IN HIGH-SPEED PUMP RUSSIAN AERONAUTICS Vol. 55 No. 4 2012 385 when analyzing the flow parameters analysis in the impeller channel is related to the fact that the high-speed pump confining disk surfaces are larger than the blade surfaces. Let us restrict ourselves to the simplified analysis of the flow core in the relative motion and consider the balance of volume element of the fluid with dm  mass. We also assume that all streamlines in the impeller channels go at an angle bl β  to the circle. In the coordinate system rotating with the impeller, the fluid in the radial channel is subjected to the action of the centrifugal inertial force 2 dmR ω  that appears due to impeller rotation, as well as of the Coriolis inertial force 2. cR dmw ω  For an inviscid flow core the resultant of these forces is counterbalanced by the pressure force dPdpdF  = ⋅  of the adjacent fluid layers. The pressure gradient is established along the blade channel step, and the fluid equipressure surface will be perpendicular to the resultant force. Hence: 2 22cot. chRchR dmwwdRdtRdmR ωε = = =ωω  (1) For the radial blade machine at the constant angle bl β  of streamline slope relative to the circle, the expression for velocity distribution along the blade channel step will be written in the following way: 0 2. ch wwt  = + ω  (2) Since the cascade pitch is , tDz = π  expression (2) can be represented as: 0 2. ch wwDz = + ωπ  (3) Taking into account that the radial velocity is sin  Ravavbl ww = β  and the value of relative velocity along the channel midline is 0 1, t av wwdt t  = ∫   the expression for calculating the flow velocity along the impeller radius will take the following form: 0 2sinsin. chRavchblbl wwU  z π= β + β  (4) Equation (1) with account for expression (4) will be: 0 24cotsinsin. chaviblbl w Rz πε = β + βω  (5) At the impeller inlet for the relative velocity 1 w  at 11 sin mbl Cw = β  we will obtain: 222 2cot2sin, mavibli CDUDz  πε = + β    (6) where i  D  is the current value of the impeller diameter varying from 1  D  to 2 .  D  In the case of a curved blade, the current value of the blade slope angle i β  relative to the circle of i  D  diameter equals to: 2222 arccoscos,22 iibliblbli  R DR DRRR  β = β + −    (7) so expression (6) will take the following form 2222222 24cotsinarccoscos.22 miavibliiblbli CDR DRUDzDRRR   πε = + β + −       (8) The flow core shear angle was calculated for the conventional assumed linear velocity distribution with respect to the channel step and the characteristic blade profile. As will be further shown, the effect of blade profile slight curvature on the flow shear can be neglected. Besides, the real pattern of the viscous  KRAEVA, KRAEV   RUSSIAN AERONAUTICS Vol. 55 No. 4 2012 386 flow in the impeller channel is much more complex as compared to that accepted in the flow model analysis. On the high pressure blade side, where velocity is lower, boundary layer separation can occur; however, the Coriolis inertial force presses the jet being separated to the blade, whereas the low-energy area of low pressure is formed on its suction side. Since visualization of surface streamlines by injecting the coloring agent to the flow can give only the qualitative pattern as the jet sizes can be compared to the boundary layer thickness, more clear-cut patterns of surface streamlines were obtained by applying a thin coating layer (10–15 µ m) on the blade channel surface; its compositions includes as a substrate the ED-5 grade compound with 2–3% of finely divided carbon powder (soot) or biro ink with the particle size equal to 2–3 µ m. The coating was applied to the prepared surface of the impeller, which was made from the material providing the reliable adhesiveness with the coating during tests corresponding to operating regimes of the full-sizes pump. It should be mentioned that to find the desired suitable composition, we tested many conventional solutions like oil-base paint, liquid pigments, compositions including kerosene, soot and oleic acid, machinery oil or TSIATIM-221 and soot and etc. which turned out to be unacceptable in studying. In comparing the data obtained with the investigation results of other authors we have received the further support that both the research method and coating composition are acceptable. It is possible to warm water not more than by 40 ° С  to get a more clear-cut flow pattern when operating under conditions of low consumption and reduced test cycle. The further increase of the water and impeller temperature leads to a sharp decrease of adhesiveness between the coating and impeller surface and even to stratification of a binder and filler. The tests showed the feasibility of using the surface streamlines visualization technique not only for qualitative analysis, but also for quantitative calculations of flow parameters along the impeller disks. It is significant that photos of the surface streamlines (Fig. 2) produced more accurate results than measurements with the use of probes. (a) (b) (c) Fig. 2.  Pattern of surface streamlines on the impeller disks: (a) 2 30; bl β = °  (b) 2 45; bl β = °  (c) 2 60 bl β = °   ( 628 ω =   rads;   5 1210 V   − = ×    3 ms; 3; w  =   ) 1 30 bl β = ° . In the course of studies we varied main design and operational parameters of the high-speed pump impeller operation, for example, we tested impellers which had the 2 bl β  angle values equal to 30, 45, 60, 75, 90° at 22 0.00850.125 bD  =  − , as a result, we obtained the flow patterns in the impeller channels with the divergence degree 0.569.0. W   =  −  In this case, the value of the channel width was varied not only at the outlet 2 , b  but also at the inlet 1 . b  The consumption of the working fluid (distilled water) varied from the zero value to 1.5. nom VV  =    Taking into account that a divergent type of blade channels is typical for high-speed pump impellers, particular attention was paid to estimating the limiting value of . ch W   Figure 3 shows the dependence of the value of the surface streamlines deflection angle along the impeller channel midline calculated using Eq. (6). Figure 3 also shows the experimental values of the flow shear angle along the channel midline and experimental results from [4, 5] at the regimes corresponding to the design one. Figure 4 shows the change of the surface streamlines deflection angle at different values of

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