Study on the energy conversion characteristics in the impeller of ultra-low specific speed pump as turbine

With the increasing attention to micro-hydropower generation, pump as turbine (PAT) has broad prospects in the field of micro-hydropower generation due to low price and easy maintenance. The ultra-low specific speed has the advantage of large output power under a small flow rate and is widely used in remote areas to realize micro-hydropower generation. In this paper, With the goal of maximizing the output power at a small flow rate, an ultra-low specific speed pump as turbine (USSPAT) of 16.52 is designed. The energy characteristics inside the impeller are studied by means of experimental and simulation. It is found that the main output area in the impeller located in the inlet area of impeller and near Span0.6 area. In addition, it is found that the high-speed jet caused by RSI inside the impeller and the secondary circulation at the outlet area are the main flow structures that hinder the work of the impeller.


Introduction
The PAT was originally used to recover high-pressure residual energy in industrial processes.It is widely applied in the high-pressure recovery in petrochemical, iron and steel metallurgy and other industries [1].With the increasing demand for small-flow water flow development, the PAT is expected to become one of the most widely used equipment in the micro-hydropower in the future due to simple structure, low price and low maintenance cost [2].Because PAT has become more important in the future energy industry, it is particularly important to explor the internal energy conversion of PAT, and improve its hydraulic efficiency.
At present, some problems remain in PAT design, like selection of PAT, inaccurate prediction for efficiency, and large vibration during operation.For this reason, many researchers have explored the design theory and design method of PAT.Derakshan et al. [4] found that the fillet of impeller blade inlet has a noticeable effect on the improvement of efficiency.Stefanizzi et al. [5] tested the pump condition and turbine condition of centrifugal pump by experiment, and the conversion expressions between the performance of the two working conditions is obtained.In order to further improve the design methodology and enhance the prospects of PAT applications, the internal flow characteristics of USSPAT and its design optimization methodology need to be carefully studied [6].Since PAT energy conversion is closely related to its internal flow characteristics, to clearly grasp the internal energy characteristics of PAT.Many scholars have tried to understand its energy conversion characteristics through the study of the internal flow mechanism to improve the efficiency [7].Therefore, an in-depth research of the regularities in the PAT, especially in the impeller, is an important method to improve the operating efficiency.Adu et al. [8] found that the edge of the impeller is the region where the vortex is centrally generated, and at the same time, this location is also the region where the losses are the highest.Binama et al. [9] that the pressure pulsations within the PAT were mainly influenced by the RSI r.Wang et al. [10] found that axial vortices within the PAT are also another important cause of pressure pulsation.Qi et al. [11] found that the vortex formed by the flow diversion is the main sesource for the energy loss of impeller.
At present, the PAT also exists in the high efficiency zone is narrow, the recovery efficiency is low, it is difficult to efficiently utilize the small flow of water.The above problems have become the key technical difficulties in the application of hydraulic turbines in the micro-hydropower industry.Therefore, in this paper, PAT of specific speed just 16.5 has been designed and study the energy characteristics as well as the effect of the unsteady flow structure on the energy conversion of the USSPAT.

Governing equations
To accurately simulate the flow details inside the USSPAT, the turbulence model in this paper selects SST k-, and the model equation is as follows: ( ) Where Pk represents the turbulence generation term.

Geometric model
The fluid field model of USSPAT is shown in figure 1.Most important geometric parameters as follow： the inlet diameter in the impeller is 265 mm.The outlet diameter in the impeller is 55 mm; the number of blades is 8; the diameter of the volute base circle is 275 mm.The specific speed is calculated by equation (3).
where Qd is discharge under design flow rate, and Hd is the head under design flow rate.

Mesh generation
In this paper, ANSYS ICEM is used for mesh generation.The final mesh is shown in figure 2. The number of mesh has an important impact on the simulation of USSPAT.After grid independence verification, 7.24 million was finally selected.

Experimental result
To verify the reliability of the simulation, this paper tests the performance of USSPAT through experiments.The experimental platform is shown in figure 3. The head, efficiency, and shaft power of USSPAT are calculated according to the following formula.
2 60 where M is the torque, Pin and Pout are the total pressure at the inlet and outlet, respectively.

Energy conversion analysis of USSPAT
For rotating machinery, the absolute velocity can be decomposed according to equation ( 7) and the axial velocity, radial velocity and circumferential velocity can be obtained respectively.
where Z V is the axial velocity, r V is the radial velocity u V is the circumferential velocity.From figure 5, the torque of Z V and r V to the spindle is 0, and only cc can drive the impeller to rotate.Therefore, based on the decomposition of the velocity triangle, dimensionless number as shown in equation ( 8) is defined in this paper to characterize the energy conversion ability of USSPAT.
where r represents the distance from the fluid particle to the rotation center.
For USSPAT, the fluid boosts the impeller to rotate clockwise.Therefore, in this coordinate system,  > 0 represents that the fluid particle drives the impeller to rotate counterclockwise.At this time, the fluid has an negative impact on the impeller rotation, and  < 0 represents that the fluid promotes the impeller rotation.
This paper selects the Span 0.2,0.6,0.8 three planes as shown in figure 6 to study the influence of different region on the energy conversion of the USSPAT.Figure7 shows the distribution of  at different planes.The area with the strongest energy conversion ability is located inlet area, that is, the larger diameter in the impeller, the stronger of the output power.Almost all the areas near the outlet are negative power areas, which reduces the power of the USSPAT.Additionally, the negative power area is mainly concentrated near the volute tongue channel affected by RSI and the outlet area of the impeller.Therefore, it can be inferred that the negative power in this area is caused by RSI.The distribution characteristics of ξ also show different characteristics in different planes.The positive power area of the impeller is mainly located at Span0.6, indicating that the impeller output power attenuates from the centre to the impeller wall on both sides.

Analysis of unstable flow structures in impeller
The above areas need to be studied in detail to deeply study the energy conversion characteristics in USSPAT.Figure 8 shows the each position of USSPAT.The dimensionless number W* of velocity is defined by equation ( 9) to facilitate the flow structure study in the impeller.
where, u2 is the circumferential velocity, and W is the relative velocity.Figure 9 shows the distribution of W* at the middle plane in the impeller inlet area at the design condition.Under the design flow rate, the W* in S1 is much larger than that in other areas, indicating that this position is most affected by RSI.The S2 region is also close to the tongue, but its W * is the same as other positions away from the tongue and much smaller than the W* at S1, indicating that the short blade B2 has an inhibitory effect on the partition and RSI cause the high-speed jet in the S1 region.10.The W* in the outlet region of the long blade corresponding to the tongue shows an increasing trend.This is because the influence of RSI on the fluid in the impeller along the runner channel gradually decline.The reduction of the flow area in the outlet region of the short blade leads to an increase in W*.A climbing of W* caused by the variety in that area exceeds the effect of RSI on W*.In addition, a region of high velocity is created at about 325°, which is formed by the secondary circulation at the impeller outlet.This region coincides almost exactly with the impeller outlet negative work region of section 4.1.Therefore, the negative work at the outlet area of runner is mainly because the secondary circulation.

Flow analysis in impeller under design flow rate
The velocity streamlines as well as W* distributions of the USSPAT impeller at span0.5 were comparatively analysed.The velocity streamlines as well as W* distributions are given in figure 11 for each flow rate, respectively.Referring to negative power area in the section 4.1, the negative work region of the impeller flow field near the tongue is closely related to its internal high-velocity jet, so it can be assumed that the negative work region inside the impeller is formed by its internal high-velocity jet.RSI is the basic reason for generation of the high-velocity jet.Therefore, RSI is the root cause of negative work generation in this region.In addition, under the design condition, according to the distribution of W* and the causes of vortex, the internal vortex structure can be divided into three categories: A, B and Among them, the A-type vortex is formed by the shocking loss caused by the difference between the fluid flow angle and the blade placement angle, and the A-type vortex is mainly generated at the inlet area of runner.The B-type vortex is mainly formed by the jet-wake phenomenon formed by the intersection of the high-speed jet from tongue channel and the low-speed flow in another area at the outlet of the short blade.This type of vortex is mainly formed RSI.Flow separation in the impeller form the C-type vortex.Due to the narrow outlet area at the long blade, it is difficult to diffuse to the downstream outlet area, thus forming many C-type vortices, which mainly occur near the trailing edge (TE) area.

Conclusion
The energy characteristics of USSPAT are studied by flow phenomenon analysis and dimensionless number.The following conclusions can be obtained： (1) The numerical simulation method used in this paper is feasible and the simulation results are reliable.
(2) The internal work area of USSPAT is located in larger diameter area of impeller and the area near SPAN0.6.The negative power area in the runner is located in the flow channel near the partition and the outlet area of runner.
(3) The causes of negative power in different regions are different.The main reason that hinders the impeller from doing work in the flow field near the tongue is the high-speed jet caused by RSI.The cause for negative power in the outlet in impeller is the secondary circulation generated by the impeller outlet.

Figure 2 .
Figure 2. Meshing of the global computational domain.2.4.Mesh generationCFX software is used to simulate the internal flow of USSPAT.The inlet pressure and outlet mass flow rate are selected as boundary conditions.The specific values are selected according to the experiment.The medium is 25 °C water.The rotation speed is set to 1500r / min.The Frozen Rotor mode is selected as the interface between the impeller and other surfaces.The transient simulation time step is 3.4483 × 10 -4 .

Figure 3 .
Figure 3. Experimental setup with instrumentations.Figure4shows results between the USSPAT numerical simulation and the experimental.Under each working condition, the numerical simulation results are basically the same as the experimental results, and the change trend is consistent.In general, the numerical simulation results are reliable.

Figure 4 Figure 4 .
Figure 3. Experimental setup with instrumentations.Figure4shows results between the USSPAT numerical simulation and the experimental.Under each working condition, the numerical simulation results are basically the same as the experimental results, and the change trend is consistent.In general, the numerical simulation results are reliable.

Figure 7 .
Figure 7.The contour of  at different Span under design flow rate.

Figure 8 .
Figure 8. Selection of the blade channel of USSPAT.Figure9shows the distribution of W* at the middle plane in the impeller inlet area at the design condition.Under the design flow rate, the W* in S1 is much larger than that in other areas, indicating that this position is most affected by RSI.The S2 region is also close to the tongue, but its W * is the same as other positions away from the tongue and much smaller than the W* at S1, indicating that the short blade B2 has an inhibitory effect on the partition and RSI cause the high-speed jet in the S1 region.

Figure 9 .
Figure 9. W* distribution at impeller inlet.The distribution of W* at the middle position at the long blade outlet area is shown in figure10.The W* in the outlet region of the long blade corresponding to the tongue shows an increasing trend.This is because the influence of RSI on the fluid in the impeller along the runner channel gradually decline.The reduction of the flow area in the outlet region of the short blade leads to an increase in W*.A climbing of W* caused by the variety in that area exceeds the effect of RSI on W*.In addition, a region of high velocity is created at about 325°, which is formed by the secondary circulation at the impeller outlet.This region coincides almost exactly with the impeller outlet negative work region of section 4.1.Therefore, the negative work at the outlet area of runner is mainly because the secondary circulation.

Figure 11 .
Figure 11.Velocity distribution in the impeller.