Abstract
In this work, we theoretically analyzed the main factors affecting performance of multistage energy recovery hydraulic turbine (MERHT), and found that the arc radius (r) of the edge at the outlet section of the runner guide vane is the determining factor of the hydraulic efficiency of hydraulic turbines. To further improve the performance of the MERHT, a numerical model is then proposed to optimize the arc radius. The MERHT-type DCSGT250-175 × 9 was taken in the simulation. The hydraulic efficiency η h and the corresponding distributions of pressure and velocity were numerically studied with four different values of r ranging from 133.5 to 138 mm. It is found that the flow state and the flow field distribution were the best when r equals to 134 mm. With the optimum r, the external diameter of the runner guide vane (D) was further adjusted, which can lead to 3.9% increase of average efficiency according to the simulation results.
1 Introduction
Liquid residual pressure energy is a clean energy source. In many industrial systems such as petrochemical, steel metallurgy, reverse osmosis desalination, water pipeline, etc. [1,2,3], the remaining high-pressure liquid is usually discharged directly or depressurized before being utilized in subsequent processes, which leads to the waste of the residual pressure energy. To recover the energy of the high-pressure liquid, energy recovery hydraulic turbines (ERHTs) that mainly functioned by pump reversal are widely used [4]. Numbers of researches have been done to improve the efficiency of the turbine. Yang et al. [5] proposed a dimensional analysis model to predict the performance of hydraulic turbines, which provides a reference for the selection of hydraulic turbines. Qi et al. [6] developed a multistage hydraulic turbine model by referring to the design method of the turbine runner in the airfoil design. Shahram [7] conducted experimental studies on four centrifugal pumps with different specific speeds. The study found that the head coefficient (the head ratio of the hydraulic turbine to the centrifugal pump at the highest efficiency point) and the flow coefficient (the flow rate ratio the hydraulic turbine to the centrifugal pump at the highest efficiency point) decrease with the increase of the specific speed. Moreover, it is found that the power coefficient (the power ratio the hydraulic turbine to the centrifugal pump at the highest efficiency point) is little dependent on the specific speed. In addition, the author proposed a method to predict the performance of hydraulic turbines based on the performance of centrifugal pumps. Chapallaz et al. [8] proposed the conversion factor of pressure head and flow rate between pumps and turbines, and plotted the conversion factor charts based on the pump-specific speed. Punit [9] developed an optimized process for the prediction and rational selection of hydraulic turbines by experiments. Joshi et al. [10] proposed a performance prediction model for a high-specific speed pump used as a hydraulic turbine. Fernandez [11] studied the performance of hydraulic turbines at different speeds through experiments and then carried out research on the prediction of hydraulic turbine performance. Jiang et al. [12] found that the negative curvature guide vane with head modification is the most efficient for the dual-channel hydraulic turbine. These researches show that many factors can affect the performance of hydraulic turbines. Among them, the guide vane design is one of the most important factors. As a crucial component of the multistage energy recovery hydraulic turbine (MERHT), the front guide vane, in addition to draining and stabilizing fluid and introducing the fluid into the next-stage runner, converts the pressure energy of the liquid flow to the kinetic energy at the outlet. Bad hydraulic performance of the front guide vane can lead to obvious vortexes, secondary flows, or flow separation inside the next-stage runner, which eventually increases the energy loss. Therefore, the hydraulic performance of the front guide vane is the necessary condition to ensure high hydraulic efficiency and the smooth operation of the rotor system. It also has an important impact on the performance of multistage energy recovery turbines [13,14,15,16]. Compared to the front guide vane, the return guide vane only acts as a diversion, and its effect on the performance of MERHT is not so significant relative to the front guide vane. For these reasons, in this article, the influence of the front vane patterns on the performance of hydraulic turbines is studied, and the influence of the main parameter changes of vanes on the performance of hydraulic turbines is analyzed.
2 Analysis of main factors affecting the performance of guide vanes
Figure 1 shows the working principle illustration of the front guide vane. The outlet axial surface speed of the front guide vane can be written as:
where
Working principle illustration of the front guide vane.
The outlet peripheral speed of the front guide vane is:
Since there is no other external torque acting on the fluid from the outlet of the front guide vane to the inlet of the runner, the following relationship can be obtained:
The velocity torque at the outlet of the runner is given by:
where A 2 is axial surface flow area at the outlet of the runner.
According to the momentum theorem, we have:
The torque power can then be written as:
Neglecting the power loss, the above power equals to the power delivered from the fluid to the blade:
and
Substituting equations (3) and (4) into equation (7), we have
The hydraulic efficiency of hydraulic turbines can then be written as:
where
Since the inlet and the outlet of the hydraulic turbine are on the same level, we have
Substituting equation (8) into equation (9), we have
The outlet excretion coefficient of the front guide vane can be written as:
With equations (11) and (12), the hydraulic efficiency of hydraulic turbines is finally given by:
It can be seen from equation (13) that changing the outlet angle of the front guide vane ∂3 can cause a change in hydraulic efficiency
3 The example parameters and guide vane design
The design parameters of the DCSGT330-175 × 9 turbine are shown in Table 1.
The basic design parameters of the DCSGT330-175 × 9 turbine
| Design head H d/(m) | Design flow Q d/(m3/h) | Rotating speed n/(rpm) | Series N |
|---|---|---|---|
| 1,500 | 330 | 3,680 | 9 |
The specific parameters are shown in Table 2, where D 3 is the base circle diameter of the front guide vane, b 3 is the front guide vane outlet width, α 3 is the outlet angle of the front guide vane, a 3 is the throat plane width, δ 3 is the outlet thickness of the front guide vane, D 4 is the outer diameter of the front guide impeller edge, φ is the spread angle of the diffusion section, and Z 1 is the number of front guide vanes. The original guide vane airfoil and the corresponding three-dimensional solid model of the radial guide vane are shown in Figures 2 and 3, respectively.
Guide vane parameters (mm)
| Series | D 3 | D 4 | b 3 | α 3 | a 3 | δ 3 | φ | Z 1 |
|---|---|---|---|---|---|---|---|---|
| 9 | 280 | 362 | 31.1 | 17.5° | 24 | 2 | 8° | 9 |
Airfoil type of the front guide vane of the original radial vane.
The three-dimensional solid model of the radial guide vane.
4 Optimization of parameters and solutions
According to the practical design experience, the front guide vane design method of the runner vane is basically the same as that of the radial vane. The main structural parameters of the runner vanes were given by: D 3 = 272 mm, D 4 = 360 mm, Z 1 = 9 and Z 2 = 9, where Z 2 is the number of return guide vanes.
The objective function of this optimization design is
5 Numerical simulations for two different types of guide vane
5.1 Numerical simulation for radial guide vane
The numerical simulations of the three-dimensional turbulent flow were carried out by Fluent. The simulation results under typical working conditions are shown in Table 3. To clearly show the influence of these conditions, we also presented the symmetry plane pressure and velocity distribution of the front guide vane region under three conditions: the large flow rate (Q = 380 m3/h), the design flow rate, and the small flow rate (Q = 250 m3/h) in Figure 4, and the flow state and flow field distribution in the guide vanes under the three working conditions was analyzed.
Simulation results of the radial vane turbine under typical conditions
| Estimated flow Q/(m3/h) | Torque M n /(N m) | Inlet pressure P in/(Pa) | Outlet pressure P out/(Pa) | Calculative mass flow Q m/(kg/s) | Efficiency η h/(%) | The conversion head H/(m) |
|---|---|---|---|---|---|---|
| 150 | −54.1475 | 6561178.5 | 204328.09 | 41.3275 | — | 668.91 |
| 200 | 436.6861 | 76,98,493 | 206084.56 | 55.1438 | 40.31 | 784.85 |
| 250 | 1013.9880 | 94,68,984 | 206599.94 | 68.9600 | 60.54 | 965.36 |
| 270 | 1275.9025 | 1,03,26,345 | 207082.75 | 74.4381 | 64.60 | 1052.76 |
| 300 | 1683.0528 | 1,16,58,906 | 207738.55 | 82.4986 | 68.06 | 1188.62 |
| 330 | 2443.4302 | 1,47,13,215 | 209841.91 | 91.3418 | 70.2 | 1500.0 |
| 360 | 2671.6965 | 1,51,17,876 | 209739.59 | 99.8922 | 69.0 | 1541.25 |
| 380 | 3026.4410 | 1,65,53,224 | 210712.61 | 104.9144 | 67.4 | 1687.59 |
Symmetry plane pressure and velocity distribution of second stage front guide vane of optimized radial vane turbine (pressure unit: Pa; speed unit: m/s): (a) pressure distribution under large flow conditions, (b) velocity distribution under large flow conditions, (c) pressure distribution under design conditions, (d) velocity distribution under design conditions, (e) pressure distribution under small flow conditions, and (f) velocity distribution under small flow conditions.
It can be seen from Table 3 that the turbine shaft performs negative work at a flow rate less than 150 m3/h, showing that, instead of recovering energy, the turbine becomes an energy-consuming device under the condition. The turbine recovery efficiency reaches the maximum value at the design flow rate, showing that the design point is the best operating point [20,21]. It is also shown in the table that the closer the working condition point is to the design working condition point, the higher the recovery efficiency. Specifically, when the flow rate is 330 m3/h, the recovery efficiency is above 70%. Under other conditions, the recovery efficiency is below 70%, and the average efficiency is 53.43%.
It can be seen from Figure 4 that the pressure distribution is uniform under the large flow and design conditions while uneven under small flow conditions since local high-pressure zones appears near the inlet and outlet of the front guide vane. For all these three working conditions, the local low-pressure zones appear at the outlet of the front guide vane, which is consistent with recent researches [22,23]. The outlet velocity distribution of the front guide vane is relatively uniform under the large flow and the design flow conditions, since no obvious vortexes and secondary flows appear. However, under the small flow condition, the velocity distribution is uneven, and the inlet and outlet speeds of the front guide vane are disordered, resulting in significant secondary flows and vortexes. The liquid velocity is very small at the inlet of the front guide vane, causing a large pressure. The pressure at the outlet of the working face of the front guide vane increases, generating a force pointing to the inlet of the front guide vane, resulting in a distinct secondary flow and vortex. A local low-pressure zone occurs due to the transition between the pressure energy and the kinetic energy at the outlet of the front guide vane.
5.2 Numerical simulation of the runner guide vanes before optimization
The simulations are further carried out for the performance of the original runner guide vanes with parameters given in Section 3. The pressure and the velocity distributions of the second-stage front guide vane under the design condition were obtained, as shown in Figure 5.
The pressure and velocity distribution of the second stage front guide vane symmetry plane of the preliminary designed runner guide vane turbine (pressure unit: Pa; speed unit: m/s): (a) pressure distribution and (b) velocity distribution.
It can be seen from Figure 5 that the pressure and the velocity distributions of the front guide vane region are not uniform. There is a local high-pressure zone at the outlet of the front guide vane, and the velocity distributions are uneven. These uneven distributions of pressure and velocity result in significant secondary flows and vortices within the vanes. Therefore, the MERHT vanes must be optimized to ensure good hydraulic performance inside the vanes.
5.3 The optimal guide vane according to the optimization scheme
To improve the performance of the turbine, we further numerically studied the performance with the presented values of r in Section 3. The work conditions are chosen the same as in the above simulations: large flow rate (Q = 380 m3/h), design flow rate, and small flow rate (Q = 250 m3/h). Using Fluent software, we obtained the symmetry plane pressure and velocity distributions of the second-order front guide vane region of the scheme I, as shown in Figure 6.
The symmetry plane pressure and velocity distribution of the second-order front guide vane of the scheme I (pressure unit: Pa; speed unit: m/s): (a) pressure distribution under large flow conditions, (b) velocity distribution under large flow conditions, (c) pressure distribution under design conditions, (d) velocity distribution under design conditions, (e) pressure distribution under small flow conditions, and (f) velocity distribution under small flow conditions.
As we can see from Figure 6, the pressure distribution is more uneven from the inlet to the outlet of the front guide vane under large flow and design conditions compared to the small flow condition. While the velocity distributions are all uneven for these three conditions, the disorder flow, vortexes, and secondary flows are distinct at the outlet of the front guide. Moreover, the outlet velocity is almost zero under the large flow and the small flow conditions. The reason is probably that r in scheme I is larger than the designed one, so the outlet angle is larger than that of the designed front guide vane. According to the triangle of the outlet velocity distribution of the front guide vane, (a) the increase in the outlet angle results in an increase of speed at the outlet shaft surface, (b) a larger impact can be generated on the outlet of the working surface, and (c) these effects cause an increase in pressure and a decrease in speed. The increase of the pressure at the outlet will generate a force pointing to the inlet of the front guide vane on the fluid, resulting in a distinct secondary flow and vortex. According to the requirements for the flow regime and flow field distribution of hydraulic turbine, scheme I is not suitable for this MERHT.
Figure 7 shows the symmetry plane pressure and velocity distribution of the second-order front guide vane of the scheme II. It can be seen from the figure that from the inlet of the front guide vane to the outlet, the pressure distributions under these operating conditions is evener than that of the scheme I. The local low-pressure zone appears at the outlet of the front vane. The velocity distribution under the three conditions is also relatively uniform. However, under small flow conditions, the individual outlet velocities of the front vane are almost zero, resulting in significant secondary flows and vortexes. The main reason for these phenomena is that in the scheme II, r 2 = 135 mm, which is smaller than the r in the scheme I. As shown in Figure 5, the outlet angle is small. According to the triangle of the outlet velocity distribution of the front guide vane, the decrease in outlet angle results in a decrease in the speed of the outlet shaft surface, which generates a small impact on the outlet working surface, these effects cause a decrease in pressure and an increase in speed. Under the small flow condition, the fluid at some outlets is subjected to forces points to the inlets of the front guide vanes, resulting in distinct secondary flow and vortexes. Due to the transition between pressure energy and kinetic energy at the outlet of the front guide vane, a local low-pressure zone occurs. According to the requirements for the flow regime and flow field distribution of the hydraulic turbine, scheme II is also not suitable for this MERHT.
The symmetry plane pressure and velocity distribution of the second-order front guide vane of the scheme II (pressure unit: Pa; speed unit: m/s): (a) pressure distribution under large flow conditions, (b) velocity distribution under large flow conditions, (c) pressure distribution under design conditions, (d) velocity distribution under design conditions, (e) pressure distribution under small flow conditions, and (f) velocity distribution under small flow conditions.
Figure 8 shows the symmetry plane pressure and velocity distribution of the second-order front guide vane of scheme III. It can be seen from Figure 8 that the pressure distribution under the large flow rate and the design conditions are more uniform compared with schemes I and II. In addition, the local low-pressure zones appear at the individual outlets under the small flow condition. The local low-pressure zones appear at the outlets of the front guide vanes under these three conditions. The velocity distributions under the large flow rate and the design condition are also relatively uniform, and the secondary flows and the vortexes are not obvious. The outlet speed of the guide vane is disordered under the small flow condition. As shown in Figure 5, the outlet angle of this scheme is smaller than the outlet angles in schemes I and II. According to the triangle of the outlet velocity of the front guide vane, the decrease in outlet angle results in a decrease in the outlet shaft surface speed, which generates a small impact on the outlet of the working surface, these effects result in a decrease in pressure and an increase in speed. The pressure at the outlet of the working face of the front guide vane changes evenly and does not produce significant secondary flows and vortexes. Due to the adequate transition between pressure energy and kinetic energy at the outlet of the front guide vane, a local low-pressure zone occurs. According to the requirements for the performance of MERHT, the scheme III is suitable for this MERHT.
The symmetry plane pressure and velocity distribution of the second-order front guide vane of the scheme III (pressure unit Pa; speed unit: m/s): (a) pressure distribution under large flow conditions, (b) velocity distribution under large flow conditions, (c) pressure distribution under design conditions, (d) velocity distribution under design conditions, (e) pressure distribution under small flow conditions, and (f) velocity distribution under small flow conditions.
Figure 9 shows the symmetry plane pressure and velocity distribution of the second-order front guide vane of the scheme IV. It can be seen from Figure 9 that the pressure distribution under the three working conditions is uneven in the front guide vane. A local high pressure occurs at the joint of the arcs of a and b of the working face of the front guide vane, and a local low-pressure region appears at the outlet of the front guide vane. The speeds are also unevenly distributed under these three conditions, and the speed reaches the maximum at the joint of the arcs a and b. The velocity is disordered at the outlet of the front guide vane under small flow condition, generating obvious vortices and secondary flows. In scheme IV, r 4 = 133.5 mm which is smaller than the values in the first three schemes. As shown in Figure 5, the outlet angle is also the smallest one. According to the triangle of the outlet velocity of the front guide vane, the decrease in outlet angle results in a decrease in the outlet shaft surface speed, which generates a small impact on the outlet of the working surface, resulting in a decrease in pressure. At the joint of the arcs a and b, which locates at the outlet of the guide vane (see Figure 1), the fluid is subjected to a force points to the inlet of the front guide vane, resulting in a distinct secondary flow and vortex. Due to the transition between pressure energy and kinetic energy at the outlet of the front guide vane, a local low-pressure zone occurs. These results show that there is also a limit to the change of the arc radius and the angle of the outlet of the guide vane face. According to the performance requirements for MERHTs, scheme IV is not suitable for this MERHT.
The symmetry plane pressure and velocity distribution of the second-order front guide vane of the scheme IV (pressure unit: Pa; speed unit: m/s): (a) pressure distribution under large flow conditions, (b) velocity distribution under large flow conditions, (b) pressure distribution under design conditions, (d) velocity distribution under design conditions, (e) pressure distribution under small flow conditions, and (f) velocity distribution under small flow conditions.
According to the above analysis, scheme III, with radius r 3 equals to 134 mm, is the best solution for the design of the guide vane of the MERHT. Based on these results, we can change the outer diameter D 4 in scheme III to ensure the best flow rate for the requirements. The relevant parameters of optimized front guide vane are given in Table 4, the corresponding airfoil shape is shown in Figure 10, and the three-dimensional solid model is shown in Figure 11.
Relevant parameters of the front guide vane of the optimized runner guide vane (length unit: mm)
| Series | D 3 | D 4 | b 3 | α 3 | a 3 | δ 3 | φ | Z 1 |
|---|---|---|---|---|---|---|---|---|
| 9 | 272 | 357 | 31.1 | 15.5° | 24 | 2 | 8° | 9 |
Airfoil type of the front guide vane of the optimized runner guide vane.
The three-dimensional solid model of the optimized runner guide vane: (a) solid model and (b) solid model of the flow channel.
The simulation results under typical working conditions were also obtained by the numerical simulations of three-dimensional turbulent flow by Fluent software, as shown in Table 5.
The simulation results of the optimized runner guide vane turbine under typical working conditions
| Estimated flow Q/(m3/h) | Torque M n /(N m) | Inlet pressure P in/(Pa) | Outlet pressure P out/(Pa) | Calculative mass flow Q m/(kg/s) | Efficiency η h/(%) | The conversion head H/(m) |
|---|---|---|---|---|---|---|
| 135 | −0.5218 | 4,72,832 | 202232.58 | 37.3453 | — | 761.85 |
| 150 | 146.7373 | 77,85,057 | 204296.28 | 41.3275 | 17.9 | 793.68 |
| 200 | 693.8386 | 91,24,898 | 204915.73 | 55.1438 | 53.8 | 930.28 |
| 250 | 1336.4696 | 10,990,798 | 206732.88 | 68.9600 | 68.5 | 1120.50 |
| 270 | 1630.8401 | 11,916,251 | 207321.31 | 74.4381 | 71.3 | 1214.85 |
| 300 | 2107.2806 | 13,479,565 | 208268.83 | 82.4986 | 73.5 | 1374.23 |
| 330 | 2579.7200 | 1,47,13,219 | 208286.98 | 91.3418 | 74.1 | 1500.0 |
| 360 | 3348.7838 | 1,79,28,766 | 209788.7 | 99.8922 | 72.6 | 1827.82 |
| 380 | 3844.3198 | 1,98,08,746 | 210606.33 | 104.9144 | 71.4 | 2019.49 |
It can be seen from Table 5 that the turbine works almost zero when the flow rate is reduced to 135 m3/h, showing that the turbine can no longer recover energy when the flow rate is reduced to below 50% of the design flow. Under the design condition, the recovery efficiency reaches the maximum value, the turbine works at the best condition. When the flow rate is greater than the design flow, its efficiency drops slightly. It can be seen that the closer the operating flow is to the design operating point, the higher the recovery efficiency. When the flow rate is greater than 270 m3/h, the recovery efficiency can reach over 70%.
6 Conclusion
The efficiency of MERHT is related to the guide vane type and the radius of the guide vane arc. The performance of the runner vanes is apparently better than that of radial guide vanes. Changing the arc radius and outlet placement angle of the outlet section of the runner-type guide vane is an effective way to obtain a good guide vane, and there is an optimum value of these geometrical parameters. The outer diameter of the runner guide vanes can be optimized after obtaining the optimum arc radius and outlet placement angle, and the average efficiency of the optimized multistage ERHT model can be increased by 3.9%.
The influence of the vane type on the performance of the ERHT is distinct. The solution to optimize the runner guide vane by the orthogonal test method is feasible and has achieved good results. It provides a good way for improving the performance of multistage energy hydraulic turbines. The method applied in this work can be also extend to optimize the structures, such as impeller, volute, etc., of the hydraulic turbine, which can further improve the performance of the hydraulic turbine.
Nomenclature
-
-
meridional velocity
- R
-
radii
- b
-
guide vane width
-
-
exclude coefficient
- M
-
angular momentum
- ω
-
angular velocity
- u
-
circumferential velocity
- β
-
established angle
- ∂
-
settling angle
- Z
-
number of blades
Greek symbols
- Q
-
volume flow, m3 h−1
- M n
-
torque, N m
- H
-
height of water head, m
- P
-
pressure, Pa
- Q m
-
quality flow, kegs’−1
Acknowledgments
Project (13zx7145) supported by Research Foundation for PhD of Southwest University of Science and Technology (13zx7145). A Project Supported by Scientific Research Fund of Sichuan Provincial Education Department (18ZA0496).
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