To study the unsteady flow and related energy conversion process in the volute of a pump-as-turbine (PAT) device, six different working conditions have been considered. Through numerical calculation, the spatio-temporal variation of static pressure, dynamic pressure, total pressure and turbulent energy dissipation have been determined in each section of the volute. It is concluded that the reduction of the total power of two adjacent sections of the PAT volute is equal to the sum of the power lost by the fluid while moving from one section to the other and the power output from the two adjacent sections. For a fixed flow rate, the percentage of static pressure energy at the outlet of the PAT is roughly similar to that of the corresponding volute section, and both show a gradually increasing trend. The turbulent dissipation rate on each section of the PAT volute displays a similar a spatio-temporal behavior for different flow rates.
In recent years, as most countries, especially developing countries, have begun to face serious energy and environmental problems, attention has shifted towards clean and renewable energy [
Based on the advantages and wide application of PAT, many scholars have also conducted research on various aspects of PAT. By illustration, there have been investigations into the PAT internal flow field [
As is well known, the internal flow of hydraulic machinery is unsteady, and PATs are no exception. The present study is an in-depth study based on previous research [
In the present study, the MH48-12.5 centrifugal pump was taken as the research object. The performance parameters of the centrifugal pump under pump conditions are shown in
Flow |
Head |
Rotation speed |
Specific speed |
---|---|---|---|
12.50 | 30.70 | 2900 | 48 |
Part | Parameters | Numerical value |
---|---|---|
Impeller | Impeller inlet diameter |
48 |
Inlet angle |
32.5 | |
Outlet angle |
14 | |
Outlet width of impeller |
6 | |
Number of blades |
4 | |
Impeller outlet diameter |
165 | |
Blade shape | Cylinder-shaped | |
Volute | Volute base circle diameter |
170 |
Volute inlet width |
16 | |
Volute outlet diameter |
32 | |
Volute section shape | Horseshoe |
Flow |
Head |
Rotation speed |
---|---|---|
27.50 | 72.21 | 2900 |
Based on the different mesh sizes, 6 sets of mesh schemes were generated for the model, and then numerical calculations were performed, respectively. The results of the relationship between the number of meshes and the hydraulic efficiency of the PAT are presented in
Based on the applicability of the turbulence model used in the numerical calculation of PAT in the relevant literature [
where
The relatively steady initial flow field is conducive to unsteady numerical calculation, so this paper uses the steady calculation result as the initial flow field for unsteady numerical calculation. The three-dimensional unsteady numerical simulation of PAT using ANSYS FLUENT 14.5 software [
Boundary name | Boundary type |
---|---|
Inlet | Velocity inlet |
Outlet | Pressure outlet |
Wall | Standard wall function |
For in-depth analysis of the unsteady process of energy conversion in the volute of PAT, the volute inlet extension and the volute were divided into 15 sections. The specific positions are shown in
As detailed in
From Section 7 to the Section 14 (volute region) of the volute, the static pressure power, dynamic pressure power, and total pressure power in these 8 sections also exhibited a period in which the quantity of pulsations was equal to the number of blades within one cycle of the impeller rotation. Furthermore, the average value of static power, dynamic power, and total power decreased along each section, with the reduction of the total power of the two adjacent sections equaling the sum of the power lost by the fluid flowing from one section to the next and the output power from the two adjacent sections. Moreover, as observed in the figure, the pulsation of static pressure power, dynamic pressure power, and total pressure power on the two adjacent sections are not synchronized as the power pulsations on these 8 sections are related to the time required for the blades to pass through each section. In the present paper, the quantity of blades in the PAT geometric model is 4, meaning the included angle between the two adjacent blades is 90°. Additionally, from the Section 7 to the Section 14 of the volute, the angle between the two adjacent sections was 45°, and the angle between the interphase sections was 90°. As detailed in the figure, the interphase section with the simulation law was synchronous as they reach the peak or trough at the same time.
As observed in
Regarding the extension section of the volute inlet, since the flow area was equal, the proportion of static pressure energy to the total pressure energy was almost equal too. Meanwhile, in the contraction section, the flow area gradually decreased, meaning the proportion of static pressure energy to the total pressure energy also gradually decreased. After entering the volute section from the volute contraction section, because the volute was connected to the impeller, a part of the fluid entered the impeller from the volute exit, indicating that the change in the proportion of static pressure energy on each section can be narrowed down to the effect of these two parts. There are two common results: one is the ratio of energy at the outlet of the volute, that is, the proportion of the static pressure energy at the outlet of the volute to the total pressure energy; another is that there is a certain energy conversion in the volute section.
In order to clarify whether energy conversion was the primary cause of the change in the proportion of static pressure energy to the total pressure energy in the volute section,
According to
From
(1) In the extension and contraction sections of the PAT volute, the static pressure power and the total pressure power exhibited a periodic pulsation law within one cycle of the impeller rotation, and the dynamic pressure increased as the flow cross-sectional area gradually decreased; in the volute section of PAT, the static pressure power, dynamic pressure power and total pressure power also obeyed a periodic pulsation law, with the number of pulsations equaling the number of blades within one cycle of the impeller, and the static pressure power, dynamic pressure power and total pressure power average value being reduced along each section successively.
(2) When the impeller rotated for one cycle, the ratio of static pressure energy to the total pressure energy in each section of the PAT volute under different flow rates yielded a similar pulsation law, displaying periodic changes. In addition, the amplitude of the pulsation increased with the increase in flow rate, and there were different energy conversion processes under small flow and large flow conditions.
(3) The turbulent dissipation rate on each section of the volute possessed a similar time-domain change rule under different flow rates, and the number of fluctuations equaled the quantity of blades on all sections preceding the tongue; as the constant flow rate increased, the average value and fluctuation amplitude of the turbulent energy dissipation rate on each section of the volute gradually increased.