Optical visualization as an effective tool for studying the flow structure in a small-sized centrifugal electric pump

. The article is devoted to the substantiation of the need for optical visualization of the structure of a 2-dimensional flow in small-sized centrifugal electric pumps of the spacecraft thermal control system. Reducing the size of the interblade channels of the pump impeller makes it impossible to use traditional methods of flow sensing due to disturbances introduced by the probes. Due to the lack of experimental data, in the study of flows in small pumps, a flow model developed for full-size centrifugal pumps is used. The most common of these are the Euler jet model or the two-zone jet-trail model. Studies by numerical methods based on these models cannot be verified for adequacy to real flows due to the lack of experimental data necessary to validate the results obtained. Under such conditions, the study of the flow structure by experimental methods, in particular, using optical visualization by the method of indicator washable coatings in the near-wall layer of the interblade channels of the impeller of pumps, becomes important. This article describes: 1) the technology of imaging; 2) structural elements of the flow, which are identified in the flow patterns in the near-wall layer; 3) results of visualization of the flow in the impellers of centrifugal pumps with a diameter of 41  10 -3 m. New data are obtained on the structure of the flow under flow regimes in the non-self-similar zone of the Reynolds number in relative motion.


Introduction
The autonomy of spacecraft necessitates the use of circulation systems in them that reproduce the processes that are natural for the existence of the biosphere on Earth. Centrifugal pumps are built into the circulation circuit of the thermal control system, which ensure the flow of the heat carrier [1,2].
The total coefficient of performance (COP) and head coefficient of small-sized centrifugal pumps are 2...4 times less than those of full-sized designs. The reason is in the special hydrodynamics of currents [3]. With the miniaturization of the structure, the Reynolds number in relation to the relative motion is reduced to the values Rew2=10 3 ... 10 4 . The forces of viscous friction begin to dominate in the flow with a simultaneous increase in the instability of the laminar boundary layer due to the longitudinal diffuseness of the channels. Due to this, a significant non-uniformity of the field of velocities and pressures occurs in the flow. In the radial direction of the interblade channels, an unreasonably large positive pressure gradient is formed, which stimulates flow separation and reduces the hydraulic COP. In the circumferential direction, there is an insufficient or even absent static pressure gradient, which increases the "slip" of the flow (reduction of the swirl angle of the flow at the periphery of the impeller) and reduces the head coefficient. The combination of these factors leads to a decrease in the efficiency of energy conversion, and, accordingly, to a decrease in COP and an increase in radial dimensions.

Current state of the problem
At the moment, in the theory of bladed machines, the hydrodynamics of flows in circular lattices of small sizes, called the impeller of the pump, in which the Reynolds numbers in relative motion have low values that lie outside the self-similar regime zone, have not been sufficiently studied. The foundation of numerous studies in the field of the theory of vane machines is the Euler jet model of the flow, based on the hypothesis of the absence of zones of different energy in circular lattices. In the works of Howard I., Osborne G., Seleznev K.P. and Galerkin Yu.B. a more complex model of the "jet-wake" flow with two energy zones is described: a jet -a high level and a wake -a low energy level [4,5], see Fig. 1. There is almost no work in the literature on the flow structure in small blowers. Known studies in the field of small-sized centrifugal superchargers are mainly devoted to a comparative analysis of pressure and efficiency characteristics of small and large superchargers in order to correct the calculation methods by introducing correction empirical coefficients into them [3]. The lack of experimental data on the flow structure in small blowers is due to the large error in flow sensing due to disturbances introduced into the flow by probes whose dimensions are commensurate with the height of the channels. Visualization of the flow structure in the surface layer of the channel walls using a washable indicator that does not disturb the flow is an important direction in the study of flow hydrodynamics in small blowers, in particular, centrifugal pumps.

Visualization of the flow structure in a small centrifugal pump
The importance of visualization for understanding the physical processes occurring in a liquid or gas flow lies in the fact that one can observe the flow pattern as a whole [6][7][8][9]. The basic provisions of fluid and gas mechanics were largely obtained by experimental visualization. Many of them are reflected in Van Dyke's famous album of fluid and gas flows [10].
Due to the significant lack of experimental data on the subject under consideration, the results obtained using optical visualization of the flow structure are of undoubted scientific significance for validating numerical flow models in small-sized lattices.
Optical visualization makes it possible to identify vortex structures and vortex lines, as well as flow separation and reattachment lines, based on known definitions and criteria [10][11][12][13][14]. For small-sized channels, at the moment, this type of study is perhaps the only way to obtain reliable information about the flow structure, since the use of scientific visualization based on numerical calculations does not guarantee the accuracy of the study due to the lack of experimental physical visualization as a means of control and verification of numerical calculations.

Imaging technique in this study
Visualization was carried out as follows. Before testing, a special indicator containing a binder and an optically contrasting fine powder was applied to the streamlined surface. When flowing around the surface, due to the local shear stress at each point of the near-wall layer, the indicator film is washed away and at the moment when the surface tension at the interface "indicator -channel surface" becomes greater than the surface tension at the interface "working fluid (liquid) -channel surface", the tracer residues contract into bundles, which are identified as streamlines of a stationary laminar flow. Through the transparent window of the experimental setup, operational control of the contrast level of the flow pattern is carried out in order to timely terminate the experiment when the required image quality is achieved. The result of the experiment is a picture of a stationary twodimensional flow in all interblade channels of the impeller. The distribution of the indicator in the form of discrete streamlines, zones of complete or partial washout of the indicator over the surface makes it possible to identify vortex structures, lines of separation and reattachment of the flow, zones of laminar and turbulent flow.

Criteria for identification of flow patterns
The sizes and location of the areas: near-wall laminar and turbulent flows, laminarturbulent transition, flow separation, vortex structures were determined on the basis of known criteria for identifying flow structural elements [10][11][12][13].
The quantitative information obtained after processing the experimental visualization contains the following parameters characterizing the flow: • Angles of deviation of the surface streamline from the direction of the potential flow.
• Projections of friction stress on the wall in relative and translational flow.
• Radial boundaries of the location of different energy zones in the flow. • The specific gravity of the two-dimensional projection of each flow zone in the volume of the interscapular space.
The zone was identified according to the following features: • Laminar flow zone -discrete streamlines.
• Turbulent flow zone -the absence of an indicator coating on the washed surface.
• Laminar-turbulent transition zone -the residual layer of the indicator coating that does not contain discrete streamlines.
• Flow separation zone -a layer of not washed off indicator.

Impeller geometry
On Fig. 2 shows two sections of the impeller in the circumferential and meridional planes of the sections, on which the dimensions are indicated: D1 and D2 -respectively, the diameters of the inlet and outlet of the impeller, 1l and 2l -respectively, the angles of the blades at the inlet and outlet of the impeller, b1 and b2 -respectively, the height of the blades at the inlet and outlet of the impeller. The longitudinal degree of diffuseness of the interblade channels W, equal to the ratio of the relative velocities at the inlet and outlet of the impeller w2/w1, was calculated by the formula: The inlet and outlet of the impeller. The longitudinal degree of where 1 and 2 are the narrowing coefficients of the width of the channels in the circumferential direction due to the thickness of the blades at the inlet and outlet of the impeller.

Results
On the Fig. 3 the picture of the flow in the interblade channels of the impeller of a smallsized centrifugal electric pump with the following parameters is presented: number of blades z=6, diffuseness degree of interblade channels W=2, angle of blades at inlet 1l=30, angle of blades at outlet 2l=45, Reynolds number in relative motion Rew2 = 1624, angular speed =628 sec -1 .
The flow pattern in the near-wall layer captured the following flow structure. At the inlet section, from the hub to the beginning of the interscapular channels, a zone of laminar flow is observed. At the interface between the pressure side of the blade and the main disk of the impeller, there is a turbulent flow zone extended along the entire blade with a width of 0.036D2. Parallel to the turbulent flow zone in the form of a strip with a width of 0.1D2, there is a turbulent-laminar transition zone, behind which a laminar flow zone begins towards the rear side of the blades. This zone has the form of a curvilinear triangle bounded by: 1) an imaginary straight line connecting the starting point of the pressure side of the blade with the end point of the back side of the blade, 2) the periphery of the impeller, 3) the boundary with the turbulent-laminar transition. Along the back side of the blade, starting from the leading edge, a vortex zone is formed with flow separation at a distance of 0.05D2 from the blade, extended along the blade at a distance of 0.5D2. The separation zone width is insignificant and amounts to 0.07D2.
Additionally, flow patterns were visualized in the impeller with an increased blade angle 2l=60 while maintaining W=2 and in the impeller with 2l=60+ turbulator, on the periphery of which a flow turbulator in the form of a grid was installed.
Despite the difference in the geometry of the interblade channels of the impeller and the installation of the turbulator, the composition, location and size of zones with different energy levels, while maintaining the degree of diffusivity W=2, have minor differences, see Fig. 4. It can be stated that the dominant factor affecting the flow structure is the degree of diffuseness of the channels, which forms a positive static pressure gradient in the longitudinal direction and stimulates vortex formation and flow separation.
The nature of the kinematic inhomogeneity of the flow is characterized by Fig. 5. On it in vector form, without taking into account the module of vectors, the distribution of the angles of inclination of the relative velocity vector in the middle part along the radius and on the periphery of the interblade channels of the impeller is shown. In the circumferential direction, in the direction from the pressure to the back sides of the blades, the uneven distribution of the angles of inclination of the relative velocity vector is due to the existence of zones with different types of flows in the flow.

Discussion
The results of the study on optical visualization of the flow in the interblade channels of the impeller of a small-sized centrifugal electric pump with a degree of channel diffuseness W=2 allow us to formulate the following important conclusions: • The determining role in the mechanism of flow structuring is played by the degree of diffusivity of the channels W, which characterizes the ratio of the cross-sectional areas of the channels at the outlet and inlet to the interblade channels. The blade angles at the outlet 2l, on the value of which the length and curvature of the channels depend (the larger 2l, the smaller the length and curvature of the channels), with a constant degree of diffuseness, have little noticeable effect on the flow structure.
• The zone of vortex formation with flow separation in the form of a narrow strip stretched along the back side of the blades in the middle of the length from the beginning of the interblade channels.
The flow structure in the flow cavity of the studied class of centrifugal electric pumps has a complex character, due to the increased degree of diffuseness of the impeller interblade channels and small Reynolds numbers in relative motion. The formation of the optimal flow structure in small-sized pumps cannot be carried out, as is customary in fullsize designs, by improving the 3D geometry of the interblade space. It is required to study the principles of optimization of the flow structure, alternative to the geometric one.