- Email: [email protected]
Effect of nozzle box arrangement on the aerodynamic performance of a single stage partial admission turbine
Applied Thermal Engineering 159 (2019) 113911
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Effect of nozzle box arrangement on the aerodynamic performance of a single stage partial admission turbine
T
⁎
Yang Pan, Qi Yuan , Guangshuo Niu, Jiawei Gu, Guangyu Zhu School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, PR China Shaanxi Engineering Laboratory of Turbomachinery and Power Equipment, Xi’an Jiaotong University, Xi’an, Shaanxi, PR China
H I GH L IG H T S
effects of nozzle box arrangement on partial admission turbine are revealed. • The admission losses as well as mixing losses introduced by partial admission are analyzed. • Partial blade load changes at the transition region between inlet section and blockage are presented. • The • Small circumferential gap can avoid negative blade tangential force downstream the gap region.
A B S T R A C T
For partial admission turbine, nozzle box arrangement has a profound impact on its aerodynamic performance. Hence, a single stage partial admission turbine with two nozzle boxes under eight arrangements was numerically investigated using CFD of three-dimensional Reynolds-averaged Navier-Stokes and SST turbulence model. Additionally, the turbine at full admission was also studied for comparison. The results show that the extra losses including sector end loss, pumping loss and mixing loss caused by partial admission decelerate to increase with circumferential gaps between nozzle boxes. The detailed loss distributions with a different circumferential gap are illustrated. Moreover, the non-uniformity in static pressure, Mach number distributions and streamlines downstream the gap region are influenced obviously by circumferential gap. Multiple low Mach number lines formed by mixing effect between active fluid and stagnant fluid are also captured. Further, the analysis of excitation force shows that the circumferential gap also changes the blade tangential force and rotor radial force distributions significantly while the change of blade axial force and rotor axial force is relatively lower.
1. Introduction Partial admission is widely used in small turbines when the design mass-flow rate is too small that a normal full-admission design would give small blade heights, which can avoid large secondary flow losses. Also, it can be applied in large steam turbines to regulate the power output, which can significantly reduce the throttling loss. Despite of these advantages, partial admission causes other problems such as additional partial admission losses, exciting forces on blades and flow non-uniformities. Because of the complex characteristics of partial admission, many experimental and numerical investigations have been performed to enhance the understanding of the losses and unsteady flow in partial admission turbines. He [1] conducted a quasi-3D simulation of the unsteady flow in a partial admission turbine and found that the pumping and sucking phenomenon in the first stage results in large unsteady loading and mixing loss and also two inlet sectors are shown to be more detrimental
⁎
than one inlet sector under the same admission degree. Lampart et al. [2] presented the investigations of the unsteady loads by using a 2D turbine model and found that the largest changes in forces are when the rotor blade enters and especially leaves the arc of admission. The dominant frequencies are low multiples of rotational frequency connected with the number of open/partly open nozzle boxes. Sakai [3] compared the results of quasi-3D analysis. According to the experiment, there was an optimum circumferential position of admitted arc from the point of view of turbine efficiency. With the development of computational technology and experimental techniques, three-dimensional effect is taken into consideration to reveal the detail of inside flow of partial admission turbines. Fridh et al. [4] experimentally measured the aerodynamic and efficiency on a cold flow two-stage air test turbine with low reaction steam turbine blades at different degrees of partial admission. The results showed that total-static turbine efficiency drops and the efficiency peak appears at lower isentropic velocity ratios with lower degrees of admission. Gao
Corresponding author. E-mail address: [email protected] (Q. Yuan).
https://doi.org/10.1016/j.applthermaleng.2019.113911 Received 13 November 2018; Received in revised form 24 May 2019; Accepted 3 June 2019 Available online 08 June 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
ηbl γ Δ ε ζ
Nomenclature Latin g p h T P u Ca Xwind Xsegm Nsegm s Cax
circumferential gap stator blade pitch specific enthalpy [kJ/kg] temperature [K] pressure [kPa] blade velocity at midspan [m/s] isentropic velocity at rotor inlet [m/s] windage loss sector end loss nozzle box number specific entropy [kJ/(kg·K)] axial chord of rotor blade
Subscripts t s 0 1 2 3 4 is
total static S0 cross section S1 cross section S2 cross section S3 cross section S4 cross section isentropic
in in in in in
the the the the the
meridional meridional meridional meridional meridional
plane plane plane plane plane
Abbreviation
Greek ηtur ηsta
blade efficiency specific heat ratio difference partial admission degree loss coefficient
NB1 NB2
turbine efficiency stage efficiency
et al. [5] numerically studied the effects of rotor solidity and leakage flow on the unsteady flow in axial turbines. He pointed out that the change of rotor inlet parameters and axial exciting force is relatively lower for leakage model. Song et al. [6] investigated the aerodynamic performance of partial admission dual row control stage at the rated and off-designed operating conditions. The circumferential non-uniformity of aerodynamic parameters and partial admission losses increases with the decrease of the admission degree. Cho et al. [7] experimentally investigated the effects of blade solidity on a linear cascade apparatus. The maximum rotational force increased but the maximum axial force decreased when the solidity decreased. Hushmandi and Fransson [8] detailedly investigated the effects of multinozzle-box and axial gap on the performance of partial admission turbines with a full-3D two-stage turbine model. Results show that the efficiency of the first stage with two inlet sectors was higher than that of the single sector, but the extra mixing losses caused the efficiency to decrease in the downstream stage. Smaller axial gap resulted in better efficiency of the first stage due to lower main flow and leakage flow interactions. Varma and Soundranayagam [9] studied a small partial admission turbine with low aspect ratio blade and found that the correlations of Suter and Traupel for partial admission losses give a reasonably accurate estimate of the partial admission efficiency for small turbine though limited only in the region of design velocity ratio. The stability of high pressure turbine under partial admission is experimentally analyzed by Kanki and Tanitsuji [10]. In addition, a single stage partial admission axial turbine in organic Rankine cycle is analyzed by Martins [11]. Although extensive investigations on partial admission have been done and many of them studied the effect of nozzle box arrangement, the chosen arrangements are mostly simple and uniform such as single nozzle box and two diagonal nozzle boxes. For this reason, this paper presents a deep study of the effects of various nozzle box arrangement on turbine efficiency, pressure distribution and fluid force. The turbine model adopted in this paper is a single stage partial admission turbine with two nozzle boxes. Different arrangements were achieved by changing the circumferential gap between two nozzle boxes. Turbines under 8 cases of nozzle box arrangements were investigated to reveal the effects of circumferential gap on turbine performances. The turbine at full admission was also investigated for comparison.
Nozzle Box 1 Nozzle Box 2
Rotor Stage Stator Stage
Circumferential Gap
Nozzle Box 1
Nozzle Box 2
(a) Computational model with specific circumferential gap Stator blade
Inlet (S0) S1
Outlet (S4)
Rotor blade S2
S3
(b) Cross sections in the meridional plane Fig. 1. Geometrical model of the single stage partial admission turbine.
2. Numerical setup 2.1. Computational model Fig. 1(a) shows the three-dimensional computational model of the partial admission single stage with a specific circumferential gap which is based on a small-scale experimental rig of Klassen et al. [12]. The outlet Reynolds number based on outlet velocity and rotor blade chord is 3.8 × 104. Note that the model in this paper is based on a small-scale turbine and the Reynolds number is relatively small, hence the results should be calibrated for medium and large-scale turbines according to Capata et al. [13]. The stator stage consists of two nozzle boxes and each box has eight stator cascade passages. In order to avoid the influence of boundary, 150% stator chord length is extended ahead of the stator inlet and 750% rotor chord length is extended behind the rotor 2
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
validated to be reliable.
outlet. Different circumferential gaps are achieved by moving Nozzle Box 2 circumferentially. Eight cases of circumferential gaps in all at the 31% partial admission have been investigated to understand the effect of circumferential distance between nozzle boxes. The partial admission degree is defined by
ε=
zt πdm
3. Results and analysis 3.1. Efficiency and losses Fig. 4 presents the variation of turbine efficiency and stage efficiency with velocity ratio at full admission and partial admission conditions. It is obvious that turbine efficiency increases with velocity ratio and the increase rate becomes lower at high velocity ratio. The turbine efficiency at full admission (ε = 1) is better than that at partial admission (ε = 0.31) due to extra partial admission loss. Further, it can be seen that turbine with single nozzle box (g/p = 0) performs better than that with two diagonal nozzle boxes (g/p = 16) under the same partial admission degree. That is because two nozzle boxes produce more sector end loss and mixing loss at than single nozzle box. Meanwhile, Δηtur at 0.31 velocity ratio shows that these two kinds of losses above cause 2.30% drop in turbine efficiency. And Δηsta at 0.31 velocity ratio shows that the sector end loss causes 1.35% drop in stage efficiency, which means that the mixing loss at downstream of rotor stage accounts for 0.95% drop in turbine efficiency. According to Moroz [15], the partial admission losses are considered as a sum of windage loss and sector end loss. The windage loss expressed by Eq. (4) refers to the effect of pumping in the inactive blade channels rotating in a steam-filled casing. The sector end loss expressed by Eq. (5) originated from the filling and emptying of the passages as the blades pass through the active sector. In addition, partial admission also produces the mixing loss between stagnant fluid and active fluid at the downstream of the rotor stage according to Hushmandi [8]. In order to investigate the extra losses caused by partial admission, Fig. 5 presents the variation of stage efficiency with g/p at different velocity ratio under 0.31 partial admission. Note that mixing loss is not considered here. It can be seen that the stage efficiency decreases with g/p as g/p increasing from 0 to 12 and then becomes smooth when g/p is between 12 and 16. However, the partial admission losses are supposed to be the same for turbines with two nozzle boxes (g/p > 0) at the same velocity ratio and same partial admission degree according to Eqs. (4) and (5). It means that partial admission cannot produce maximum losses when two adjacent nozzle boxes are circumferentially close. Additionally, the effects of velocity ratio can be also described by
(1)
where z means numbers of stator cascade passages, t means stator blade pitch at mean diameter and dm is mean diameter of stator blade. Fig. 1(b) illustrates the definition of several cross planes we studied in this paper. Where S0, S1, S2, S3 and S4 stand for the inlet, the stator inlet, the cross section between stator and rotor stage, the rotor outlet and the outlet respectively. Table gives the blade geometrical parameters of the stage. 2.2. Boundary conditions For the inlet boundary conditions, the absolute total pressure and static temperature are given. At the outlet a static pressure boundary condition was used. The adiabatic and no slip wall condition was applied to all walls. Rotating domains with rotational speed according to Table 2 were set for the rotational blade regions. Detailed boundary conditions are listed in Table 2. 2.3. Computational method and validation Fig. 2 shows the computational grid of the partial admission single stage. A multi-block structural grid is generated for the computational domain using the software ICEM. The HOH type grid is used to generate the mesh for the cascade passages. The grids near the wall are refined to meet the requirements of the turbulence model. The numerical simulations were performed with the CFX commercial software to solve the RANS equations. The convective terms and turbulence were solved with high-order discretization accuracy for all simulations presented here. The “Frozen rotor” model which was adopted by Gao [5] was also applied here to model the frame change at the interface of stator stage and rotor stage. The SST turbulence model was applied with automatic wall function, which has been proven to be accurate in many computations [8,14]. A root mean square error RMS < 10−5 was used for each variable, and static pressure downstream the rotor stage was monitored to ensure that a converged state had been obtained. The mesh sensitivity study was carried out, with three kinds of mesh density using the SST turbulence model, to confirm that the results were not significantly dependent on the mesh size. The details of element number at different mesh density are listed in Table 3. Fig. 3 shows the comparison of total-static efficiency between the numerical results and Klassen’s [12] experimental data. To distinguish between partial admission loss and mixing loss, we defined the turbine efficiency and stage efficiency respectively as Eqs. (2) and (3) in this paper.
ηtur
Tt ,4 ⎞ ⎡ ⎛ Ps,4 ⎟⎞ = ⎜⎛1, − , ⎟ ⎢1 − ⎜ T t ,0 ⎢ ⎝ Pt ,0 ⎠ ⎝ ⎠ ⎣
Tt ,3 ⎞ ⎡ ⎛ Ps,3 ⎟⎞ ηsta = ⎜⎛1, − , ⎟ ⎢1 − ⎜ T t ,1 ⎠ ⎢ ⎝ Pt ,1 ⎠ ⎝ ⎣
3
Xwind ∝
⎜
⎟
(4)
⎟
(5)
The variation of turbine efficiency with g/p at different velocity ratio under 0.31 partial admission is shown in Fig. 6. It is obvious that turbine efficiency changes with g/p in the same pattern with stage efficiency. However, with mixing loss considered, turbine efficiency is a little lower than stage efficiency. And the change rate of turbine efficiency is larger than that of stage efficiency. That is, the mixing loss at the downstream of the gap is also affected by the circumferential distance between two nozzle boxes. To better understand the losses caused by partial admission, the loss
(2)
γ − 1 −1 γ ⎤
⎥ ⎥ ⎦
⎜
u Xsegm ∝ ηbl ⎛ ⎞ Nsegm ⎝ ca ⎠
γ − 1 −1 γ ⎤
⎥ ⎥ ⎦
1 − ε⎛u⎞ ε ⎝ ca ⎠
Table 1 Blade geometrical parameters of the stage.
(3)
It can be seen that the results at middle mesh density almost coincide with that at fine mesh density both under full admission and partial admission. Therefore, the rest of computational analysis was conducted with the middle grid density mesh. Also, it can be found the results at middle mesh density agreed well with the experimental data under different partial admission degrees. Therefore, the numerical method is
Full annulus blade numbers Root diameter/mm Blade height/mm Blade chord/mm Solidity Aspect ratio
3
Stator
Rotor
51 92.445 5.51 11.5 1.96 0.48
95 92.445 5.74 7.92 2.52 0.72
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
Table 2 Boundary conditions of the single stage. Working fluid
Air ideal gas
Inlet total pressure/kPa Inlet static temperature/K Outlet static pressure/kPa Rotational speed/rpm
172 300 68.8 17,500–27,500
Fig. 2. Computational grid of the through flow. Table 3 Element number at different mesh density. Mesh density
Coarse
Middle
Fine
Elements under ε = 1/million Elements under ε = 0.31/million
1.73 1.50
3.48 3.14
7.18 6.30
Fig. 3. Comparison of the turbine efficiency between the numerical results and experimental data.
coefficient defined as Eq. (6) is used in this paper following Denton [16]:
ζ = Ts Δs /(ht ,0 − hsis,4 )
(6)
where Δs is the entropy rise at each point in relation to the entropy at the inlet and Ts is the static temperature at each point. Fig. 7 shows the loss coefficient distributions at the cross section between stator and rotor with different g/p. It can be seen that the losses introduced by partial admission are lower at downstream of nozzle boxes and larger at other regions. Meanwhile, a comparatively low loss area can be found near the pressure side of NB1 (A region), which is mainly caused by the jet flow from the stator passages. In addition, a relatively high loss area can be seen near the suction side of NB2 (B region) in Fig. 7(a) to (e), which is probably related to the stagnant fluid developing in the circumferential direction. As for the circumferential gap area between two nozzle boxes (C region), larger losses are introduced here but not so obvious in Fig. 7(b) to (d) as that in Fig. 7(e) to (h). According to the situation at A region, the jet flow from nozzle box 2 contributes to decreasing the loss within a certain range of angles to some extent. When g/p is relatively small, C region may be still in this range and strongly affected by the jet flow, which suppresses large increase in losses. When g/p is relatively large, the jet flow cannot affect all gap area and then a high loss area can be formed near the suction side of nozzle box 1. Loss coefficient distributions at 50% blade height in the circumferential direction with different g/p are presented in Fig. 8. The jet flow can be seen at A region and the losses are found to be increasing along the direction of rotational speed according to Fig. 8(a). The circumferential gap indeed increases losses at downstream rotor passages. However, only when g/p is big enough (g/p > 4), considerable losses can be seen at C region near the suction side of NB1 according to Fig. 8(d). Additionally, the maximum loss coefficient locates at the
Fig. 4. Variation of turbine efficiency and stage efficiency with velocity ratio at different partial admission degree.
corner of pressure side of nozzle boxes which is mostly related to the vortices here. Meanwhile, the loss coefficient at outlet is found to be almost uniform along the circumferential direction due to mixing effects. 3.2. Pressure distribution and unsteady flow Fig. 9 illustrates the static pressure distributions at S2 and S3 along the circumferential direction with different g/p. Large pressure nonuniformity can be seen at S2 due to partial admission and then reduces after crossing rotor passages. At S2, pressure distributions downstream the nozzle boxes show great oscillations while that at other 4
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
flows this region, sudden increase of flow area causes the increase of Mach number and flow defection and hence forms the “jet flow”. Accordingly, the static pressure decreases dramatically. Even when g/p is quite small such as that in Fig. 9(b), there still exists a pressure drop at nozzle box 2. According to Fig. 9(b) to (d), pressure drop at nozzle box 1 is larger than that at nozzle box 2, which is mainly related to the relative transient position between stator blades and rotor blades. The static pressure near the downstream of nozzle boxes (A region and B region) is slightly smaller than that away nozzle boxes at S2. While the pressure at A region is smaller than that at B region at S3. The normalized static pressure distributions at 50% blade height with different g/p are presented in Fig. 10. It can be seen the pressure drop mentioned above appears at the corner of the pressure side of every separate nozzle box. Moreover, a huge low-pressure area and a relatively small low-pressure area can be found near the inlet section according to Fig. 10(a). When g/p is small, these two areas interact to each other and the huge low pressure area cannot be formed downstream the circumferential gap according to Fig. 10(b) and (c). When g/ p increases, the area of low pressure expands a little (Fig. 10(d)). Additionally, the pressure distributions along the circumferential direction are almost even near the outlet. Fig. 11 presents the Mach number distributions and streamlines at 50% blade height with different g/p. Supersonic area can be seen at the cross section of stator and rotor stage. The jet flow at the pressure side of nozzle boxes forms a small high Mach number and vortices area. Two low Mach number lines can be easily seen at the downstream of rotor stage which are the interfaces between active fluid and stagnant fluid according to Fig. 11(a). When g/p is relatively small (g/p = 0.5), only a little stagnant fluid is produced downstream the blockage between NB1 and NB2. It can be easily affected by the active fluid nearby and hence only produces a small low Mach number area (see Fig. 11(b)). As g/p increases, more stagnant fluid is produced but the active fluid nearby cannot affect them all. Thus a larger low Mach number area is produced and streamlines begin to become a little disorder (see Fig. 11(c)). When g/p becomes 16, this low Mach number area expands to the maximum and accordingly significant disorder streamlines are formed (see Fig. 11(d)).
Fig. 5. Variation of stage efficiency with g/p at different velocity ratio (ε = 0.31).
Fig. 6. Variation of turbine efficiency with g/p at different velocity ratio (ε = 0.31).
circumferential angle seem to be nearly uniform. Additionally, huge pressure drops can be seen at the pressure side of nozzle boxes because of the “Prandtl Meyer Fan-like” structure. When high pressure fluid
Fig. 7. Loss coefficient distributions at S2 with different g/p. 5
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
Fig. 8. Loss coefficient distributions at 50% blade height with different g/p.
suction surface of C1 is very large, which indicates a great power capability. Note that the minimum pressure points on pressure surface and suction surface is caused by fluid acceleration at the throat of rotor passages. Two shock waves can be found near the trailing edge of stator blade and leading edge of rotor blade. The shock wave near the trailing edge causes a pressure rise at the suction surface of C1. The pressure difference between pressure and suction surface of D1 is the very small because rotor passage is full of stagnant fluid, hence D1 almost has no power output.
3.3. Blade load and excitation force Fig. 12 presents the positions of selective rotor blades. Where, A1 to A4 are at the transition region from inlet section to blockage, B1 to B4 are at the transition region from blockage to inlet section, C1 is at the inlet section and D1 is at the blockage. The rotor blade load comparison of C1 and D1 and the Mach number distributions around C1 and D1 are presented in Figs. 13 and 14. It can be seen that the pressure difference between pressure and
Fig. 9. Normalized static pressure distributions at S2 and S3 along circumferential direction with different g/p. 6
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
Fig. 10. Normalized static pressure distributions at 50% blade height with different g/p.
The rotor blade load and Mach number distribution at the transition region from inlet section to blockage are presented in Figs. 15 and 16. It is obvious that the pressure distribution of A1 and A4 is respectively similar to that of C1 and D1. The pressure of the suction surface changes dramatically while the pressure change on pressure surface is very small from A1 to A3. A great pressure drop on the suction surface can be seen at the leading section of A2 which is mainly relevant to the jet flow as shown in Fig. 8. Moreover, the pressure on the suction surface increases at the middle section of A2 because that insufficient high-speed flow into the passage reduces acceleration at the throat area which can be also seen in Fig. 16. When it comes to A3, the pressure on the suction surface is almost uniform along the streamwise location due to the flow deflection while the pressure on the pressure surface remains large for that pressure surface can still be affected by the active fluid. Further, the pressure rises at the suction surface of A3 and A4 disappear for that subsonic flow at this region cannot produces shock waves according to Fig. 16. The rotor blade load and Mach number distribution at the transition region from blockage to inlet section are presented in Figs. 17 and 18. The pressure distribution of B1 and B4 is respectively similar to that of C1 and D1. When blade moves from B1 to B2, the pressure on suction surface changes firstly and then the pressure on pressure surface for that the suction surface of B2 is not completely entering the inlet section and the pressure surface of B1 is at the blockage. The interface
Fig. 12. Positions of selective rotor blades.
Fig. 13. Rotor blade load comparison of C1 and D1 (g/p = 0).
Fig. 11. Mach number distributions and streamlines at 50% blade height with different g/p. 7
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
Fig. 17. Rotor blade load at the transition region from blockage to inlet section (g/p = 0).
Fig. 14. The Mach number distributions around C1 and D1.
Fig. 18. The Mach number distributions around B1-B4.
Fig. 15. Rotor blade load at the transition region from inlet section to blockage (g/p = 0).
ratio of 0.31. Note that the negative values mean that the direction of axial force is opposite to the main stream direction or the direction of tangential force is opposite to the rotational direction. According to Fig. 19(a), the axial forces of active rotor blades show strong fluctuations while that of inactive rotor blades are nearly equal to zero. The direction of axial forces on the blades at the downstream of the pressure side of nozzle boxes is opposite to the main stream direction which is mostly related to the jet flow. Meanwhile, the largest negative axial force can be also seen in these regions. Moreover, the g/p hardly changes the pattern of distributions except for the circumferential position of the fluctuations of NB2. The largest negative axial force caused by NB 2 still appears even when g/p is very small. In Fig. 19(b), the tangential forces of blades at inlet section show small fluctuations and that of blades at the blockage are stable at small positive values. The negative tangential forces appear at the suction sides of two nozzle boxes, which result in negative work. Except for the circumferential position of fluctuations of NB2, the g/p mainly affects tangential forces at the downstream of the circumferential gap. The forces at this region decrease as g/p increases. The negative tangential forces come out only when the g/p is big enough (g/p = 16). Fig. 20 presents the total force acting on the rotor with different g/p at different velocity ratio. Note that the negative values mean that the direction of axial force is opposite to the main stream. In Fig. 20(a), it can be seen that the rotor axial force increases with velocity ratio. The largest rotor axial force only occurs when g/p is equal to zero, because only one negative axial blade force region can be formed in this situation according to the analysis above. When g/p is greater than zero, the rotor axial force stables at a lower level and the value is mainly
Fig. 16. The Mach number distributions around A1-A4.
between stagnant fluid and active fluid can be seen in Fig. 18. Further, the pressure on the suction surface stabilizes first while the pressure on pressure surface still changes when blades move from B3 to B4 for that suction surface of B4 is just completely at the inlet section. It can be also seen that the minimum pressure point on the pressure surface of B3 is closer to the leading edge than that of B4 due that only a part of high speed fluid from the nozzle box enters the passage. Moreover, the pressure rises can be seen at the suction surface of B3 and B4 due to the shock waves in Fig. 18. Fig. 19 gives the rotor blade force with different g/p at the velocity 8
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
Fig. 19. Rotor blades force with different g/p at 0.31 velocity ratio.
p > 4). The losses at the pressure side of the nozzle box are found to be smaller than that at the suction side due to the jet flow effect. (2) The non-uniformity in static pressure upstream the rotor stage was captured. Deep drops at the pressure side of nozzle boxes appear even when the circumferential gap is quite small. The Mach number distributions and streamlines are influenced obviously by the circumferential gap. Low Mach number regions are formed between active fluid and stagnant fluid. (3) Blade load changes significantly as the blade enters and leaves the inlet section. The jet flow causes a great pressure drop on the suction surface at the leading section as the blade leaves the inlet section. Moreover, the minimum pressure point on pressure surface first appears near the blade leading edge and then moves toward the trailing edge as the blade enters the inlet section. (4) Negative blade axial force appears at the pressure side of nozzle boxes regardless of the circumferential gap while negative tangential force at the suction side of nozzle box 2 exists only when the circumferential gap is big enough. The rotor axial force with zero circumferential gap is the largest because only one negative blade axial force region is created. The rotor radial force decreases with circumferential gap due to balance effect.
related to the relative transient position between stator blades and rotor blades. Fig. 20(b) shows that rotor radial force decreases with velocity ratio. Moreover, the rotor radial force decreases with g/p since the two radial forces caused by two nozzle boxes cancel each other out to a certain extent. When g/p is equal to zero, the balance effect between two forces is the smallest which results in the largest rotor radial force occurs. When g/p is 16, the maximum balance between two forces make rotor radial force almost equal to zero. Moreover, the direction of force changes with g/p which can be used to adjust the load of rotor and improve the stability. 4. Conclusions A small partial admission single stage turbine with two nozzle boxes was numerically investigated to reveal the effect of various nozzle box arrangement on turbine aerodynamic performance. Eight cases of arrangements are detailedly studied in this paper. the conclusions are presented as follows: (1) Due to the increasing extra losses caused by partial admission with an increasing circumferential gap, the turbine efficiency decelerates to decrease. Considerable losses at the downstream of the circumferential gap can be found only when g/p is big enough (g/
Fig. 20. Rotor force with different g/p at different velocity ratio. 9
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
unsteady flow in axial turbine, Appl. Therm. Eng. 128 (2018) 926–939. [6] L. Song, J. Li, K. Wen, Aerodynamic performance analysis of partial admission dual row control stage at different working conditions, J. Mech. Sci. Technol. 30 (1) (2016) 157–169. [7] S.Y. Cho, C.H. Cho, K.Y. Ahn, et al., Forces and surface pressure on a blade moving in front of the admission region, J. Fluids Eng.-Trans. Asme 132 (2010) 121101. [8] N.B. Hushmandi, T.H. Fransson, Effects of multiblocking and axial gap distance on performance of partial admission turbines: A numerical analysis, J. Turbomach. 133 (2011) 031028. [9] A. Varma, S. Soundranayagam, Experimental study of a small partial admission axial turbine with low aspect ratio blade, Proc. Inst. Mech. Eng., Part G: J. Aerospace Eng. 228 (1) (2012) 20–34. [10] H. Kanki, A. Tanitsuji, Stability of high pressure turbine under partial admission condition, Proceedings of IDETC/CIE, 2005, (2005) DETC2005-84774. [11] G.L. Martins, S.L. Braga, S.B. Ferreira, Design optimization of partial admission axial turbine for ORC service, Appl. Therm. Eng. 96 (2016) 18–25. [12] H.A. Klassen, Cold-air investigation of effects of partial admission on performance of 3.75-inch mean-diameter single stage axial-flow turbine, NASA, 1968. [13] R. Capata, E. Sciubba, Experimental fitting of the re-scaled Balje maps for lowreynolds radial turbomachinery, Energies 8 (8) (2015) 7986–8000. [14] P. Lampart, Q. Hirt, Complex multi-disciplinary optimization of turbine blading systems, Arch. Mech. 64 (2012) 153–175. [15] L. Moroz, B. Frolov, O. Guriev, Analysis and optimization of partial admission stages, Proceedings of Asian Congress on Gas Turbines 2014, (2014) ACGT-20140007. [16] J. Denton, The 1993 IGTI scholar lecture: loss mechanisms in turbomachines, J. Turbomach. 115 (1993) 621–656.
Acknowledgement This work is supported by National Natural Science Foundation of China (No. 11872289), the Key Project of Natural Science Foundation of Xi'an Jiao Tong University (No. ZRZD2017025). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.113911. References [1] L. He, Computation of unsteady flow through steam turbine blade rows at partial admission, Proc. Inst. Mech. Eng., Part A: J. Power Energy 211 (1997) 197–205. [2] P. Lampart, M. Szymaniak, R. Rzadkowski, Unsteady load of partial admission control stage rotor of a large power steam turbine, Proceedings of ASME Turbo Expo 2004, (2004) GT2004-53886. [3] N. Sakai, T. Harada, Y. Imai, Application of CFD to partial admission stages of steam turbine, Proceedings of PWR2005, ASME Power, (2005) PWER2005-50346. [4] J.E. Fridh, B. Bunkute, R. Fakhrai, et al., An experimental study on partial admission in a two-stage axial air test turbine with numerical comparisons, Proceedings of ASME Turbo Expo 2004, (2004) GT2004-53774. [5] K.K. Gao, Y.H. Xie, D. Zhang, Effects of rotor solidity and leakage flow on the
10
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Effect of nozzle box arrangement on the aerodynamic performance of a single stage partial admission turbine
T
⁎
Yang Pan, Qi Yuan , Guangshuo Niu, Jiawei Gu, Guangyu Zhu School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, PR China Shaanxi Engineering Laboratory of Turbomachinery and Power Equipment, Xi’an Jiaotong University, Xi’an, Shaanxi, PR China
H I GH L IG H T S
effects of nozzle box arrangement on partial admission turbine are revealed. • The admission losses as well as mixing losses introduced by partial admission are analyzed. • Partial blade load changes at the transition region between inlet section and blockage are presented. • The • Small circumferential gap can avoid negative blade tangential force downstream the gap region.
A B S T R A C T
For partial admission turbine, nozzle box arrangement has a profound impact on its aerodynamic performance. Hence, a single stage partial admission turbine with two nozzle boxes under eight arrangements was numerically investigated using CFD of three-dimensional Reynolds-averaged Navier-Stokes and SST turbulence model. Additionally, the turbine at full admission was also studied for comparison. The results show that the extra losses including sector end loss, pumping loss and mixing loss caused by partial admission decelerate to increase with circumferential gaps between nozzle boxes. The detailed loss distributions with a different circumferential gap are illustrated. Moreover, the non-uniformity in static pressure, Mach number distributions and streamlines downstream the gap region are influenced obviously by circumferential gap. Multiple low Mach number lines formed by mixing effect between active fluid and stagnant fluid are also captured. Further, the analysis of excitation force shows that the circumferential gap also changes the blade tangential force and rotor radial force distributions significantly while the change of blade axial force and rotor axial force is relatively lower.
1. Introduction Partial admission is widely used in small turbines when the design mass-flow rate is too small that a normal full-admission design would give small blade heights, which can avoid large secondary flow losses. Also, it can be applied in large steam turbines to regulate the power output, which can significantly reduce the throttling loss. Despite of these advantages, partial admission causes other problems such as additional partial admission losses, exciting forces on blades and flow non-uniformities. Because of the complex characteristics of partial admission, many experimental and numerical investigations have been performed to enhance the understanding of the losses and unsteady flow in partial admission turbines. He [1] conducted a quasi-3D simulation of the unsteady flow in a partial admission turbine and found that the pumping and sucking phenomenon in the first stage results in large unsteady loading and mixing loss and also two inlet sectors are shown to be more detrimental
⁎
than one inlet sector under the same admission degree. Lampart et al. [2] presented the investigations of the unsteady loads by using a 2D turbine model and found that the largest changes in forces are when the rotor blade enters and especially leaves the arc of admission. The dominant frequencies are low multiples of rotational frequency connected with the number of open/partly open nozzle boxes. Sakai [3] compared the results of quasi-3D analysis. According to the experiment, there was an optimum circumferential position of admitted arc from the point of view of turbine efficiency. With the development of computational technology and experimental techniques, three-dimensional effect is taken into consideration to reveal the detail of inside flow of partial admission turbines. Fridh et al. [4] experimentally measured the aerodynamic and efficiency on a cold flow two-stage air test turbine with low reaction steam turbine blades at different degrees of partial admission. The results showed that total-static turbine efficiency drops and the efficiency peak appears at lower isentropic velocity ratios with lower degrees of admission. Gao
Corresponding author. E-mail address: [email protected] (Q. Yuan).
https://doi.org/10.1016/j.applthermaleng.2019.113911 Received 13 November 2018; Received in revised form 24 May 2019; Accepted 3 June 2019 Available online 08 June 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
ηbl γ Δ ε ζ
Nomenclature Latin g p h T P u Ca Xwind Xsegm Nsegm s Cax
circumferential gap stator blade pitch specific enthalpy [kJ/kg] temperature [K] pressure [kPa] blade velocity at midspan [m/s] isentropic velocity at rotor inlet [m/s] windage loss sector end loss nozzle box number specific entropy [kJ/(kg·K)] axial chord of rotor blade
Subscripts t s 0 1 2 3 4 is
total static S0 cross section S1 cross section S2 cross section S3 cross section S4 cross section isentropic
in in in in in
the the the the the
meridional meridional meridional meridional meridional
plane plane plane plane plane
Abbreviation
Greek ηtur ηsta
blade efficiency specific heat ratio difference partial admission degree loss coefficient
NB1 NB2
turbine efficiency stage efficiency
et al. [5] numerically studied the effects of rotor solidity and leakage flow on the unsteady flow in axial turbines. He pointed out that the change of rotor inlet parameters and axial exciting force is relatively lower for leakage model. Song et al. [6] investigated the aerodynamic performance of partial admission dual row control stage at the rated and off-designed operating conditions. The circumferential non-uniformity of aerodynamic parameters and partial admission losses increases with the decrease of the admission degree. Cho et al. [7] experimentally investigated the effects of blade solidity on a linear cascade apparatus. The maximum rotational force increased but the maximum axial force decreased when the solidity decreased. Hushmandi and Fransson [8] detailedly investigated the effects of multinozzle-box and axial gap on the performance of partial admission turbines with a full-3D two-stage turbine model. Results show that the efficiency of the first stage with two inlet sectors was higher than that of the single sector, but the extra mixing losses caused the efficiency to decrease in the downstream stage. Smaller axial gap resulted in better efficiency of the first stage due to lower main flow and leakage flow interactions. Varma and Soundranayagam [9] studied a small partial admission turbine with low aspect ratio blade and found that the correlations of Suter and Traupel for partial admission losses give a reasonably accurate estimate of the partial admission efficiency for small turbine though limited only in the region of design velocity ratio. The stability of high pressure turbine under partial admission is experimentally analyzed by Kanki and Tanitsuji [10]. In addition, a single stage partial admission axial turbine in organic Rankine cycle is analyzed by Martins [11]. Although extensive investigations on partial admission have been done and many of them studied the effect of nozzle box arrangement, the chosen arrangements are mostly simple and uniform such as single nozzle box and two diagonal nozzle boxes. For this reason, this paper presents a deep study of the effects of various nozzle box arrangement on turbine efficiency, pressure distribution and fluid force. The turbine model adopted in this paper is a single stage partial admission turbine with two nozzle boxes. Different arrangements were achieved by changing the circumferential gap between two nozzle boxes. Turbines under 8 cases of nozzle box arrangements were investigated to reveal the effects of circumferential gap on turbine performances. The turbine at full admission was also investigated for comparison.
Nozzle Box 1 Nozzle Box 2
Rotor Stage Stator Stage
Circumferential Gap
Nozzle Box 1
Nozzle Box 2
(a) Computational model with specific circumferential gap Stator blade
Inlet (S0) S1
Outlet (S4)
Rotor blade S2
S3
(b) Cross sections in the meridional plane Fig. 1. Geometrical model of the single stage partial admission turbine.
2. Numerical setup 2.1. Computational model Fig. 1(a) shows the three-dimensional computational model of the partial admission single stage with a specific circumferential gap which is based on a small-scale experimental rig of Klassen et al. [12]. The outlet Reynolds number based on outlet velocity and rotor blade chord is 3.8 × 104. Note that the model in this paper is based on a small-scale turbine and the Reynolds number is relatively small, hence the results should be calibrated for medium and large-scale turbines according to Capata et al. [13]. The stator stage consists of two nozzle boxes and each box has eight stator cascade passages. In order to avoid the influence of boundary, 150% stator chord length is extended ahead of the stator inlet and 750% rotor chord length is extended behind the rotor 2
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
validated to be reliable.
outlet. Different circumferential gaps are achieved by moving Nozzle Box 2 circumferentially. Eight cases of circumferential gaps in all at the 31% partial admission have been investigated to understand the effect of circumferential distance between nozzle boxes. The partial admission degree is defined by
ε=
zt πdm
3. Results and analysis 3.1. Efficiency and losses Fig. 4 presents the variation of turbine efficiency and stage efficiency with velocity ratio at full admission and partial admission conditions. It is obvious that turbine efficiency increases with velocity ratio and the increase rate becomes lower at high velocity ratio. The turbine efficiency at full admission (ε = 1) is better than that at partial admission (ε = 0.31) due to extra partial admission loss. Further, it can be seen that turbine with single nozzle box (g/p = 0) performs better than that with two diagonal nozzle boxes (g/p = 16) under the same partial admission degree. That is because two nozzle boxes produce more sector end loss and mixing loss at than single nozzle box. Meanwhile, Δηtur at 0.31 velocity ratio shows that these two kinds of losses above cause 2.30% drop in turbine efficiency. And Δηsta at 0.31 velocity ratio shows that the sector end loss causes 1.35% drop in stage efficiency, which means that the mixing loss at downstream of rotor stage accounts for 0.95% drop in turbine efficiency. According to Moroz [15], the partial admission losses are considered as a sum of windage loss and sector end loss. The windage loss expressed by Eq. (4) refers to the effect of pumping in the inactive blade channels rotating in a steam-filled casing. The sector end loss expressed by Eq. (5) originated from the filling and emptying of the passages as the blades pass through the active sector. In addition, partial admission also produces the mixing loss between stagnant fluid and active fluid at the downstream of the rotor stage according to Hushmandi [8]. In order to investigate the extra losses caused by partial admission, Fig. 5 presents the variation of stage efficiency with g/p at different velocity ratio under 0.31 partial admission. Note that mixing loss is not considered here. It can be seen that the stage efficiency decreases with g/p as g/p increasing from 0 to 12 and then becomes smooth when g/p is between 12 and 16. However, the partial admission losses are supposed to be the same for turbines with two nozzle boxes (g/p > 0) at the same velocity ratio and same partial admission degree according to Eqs. (4) and (5). It means that partial admission cannot produce maximum losses when two adjacent nozzle boxes are circumferentially close. Additionally, the effects of velocity ratio can be also described by
(1)
where z means numbers of stator cascade passages, t means stator blade pitch at mean diameter and dm is mean diameter of stator blade. Fig. 1(b) illustrates the definition of several cross planes we studied in this paper. Where S0, S1, S2, S3 and S4 stand for the inlet, the stator inlet, the cross section between stator and rotor stage, the rotor outlet and the outlet respectively. Table gives the blade geometrical parameters of the stage. 2.2. Boundary conditions For the inlet boundary conditions, the absolute total pressure and static temperature are given. At the outlet a static pressure boundary condition was used. The adiabatic and no slip wall condition was applied to all walls. Rotating domains with rotational speed according to Table 2 were set for the rotational blade regions. Detailed boundary conditions are listed in Table 2. 2.3. Computational method and validation Fig. 2 shows the computational grid of the partial admission single stage. A multi-block structural grid is generated for the computational domain using the software ICEM. The HOH type grid is used to generate the mesh for the cascade passages. The grids near the wall are refined to meet the requirements of the turbulence model. The numerical simulations were performed with the CFX commercial software to solve the RANS equations. The convective terms and turbulence were solved with high-order discretization accuracy for all simulations presented here. The “Frozen rotor” model which was adopted by Gao [5] was also applied here to model the frame change at the interface of stator stage and rotor stage. The SST turbulence model was applied with automatic wall function, which has been proven to be accurate in many computations [8,14]. A root mean square error RMS < 10−5 was used for each variable, and static pressure downstream the rotor stage was monitored to ensure that a converged state had been obtained. The mesh sensitivity study was carried out, with three kinds of mesh density using the SST turbulence model, to confirm that the results were not significantly dependent on the mesh size. The details of element number at different mesh density are listed in Table 3. Fig. 3 shows the comparison of total-static efficiency between the numerical results and Klassen’s [12] experimental data. To distinguish between partial admission loss and mixing loss, we defined the turbine efficiency and stage efficiency respectively as Eqs. (2) and (3) in this paper.
ηtur
Tt ,4 ⎞ ⎡ ⎛ Ps,4 ⎟⎞ = ⎜⎛1, − , ⎟ ⎢1 − ⎜ T t ,0 ⎢ ⎝ Pt ,0 ⎠ ⎝ ⎠ ⎣
Tt ,3 ⎞ ⎡ ⎛ Ps,3 ⎟⎞ ηsta = ⎜⎛1, − , ⎟ ⎢1 − ⎜ T t ,1 ⎠ ⎢ ⎝ Pt ,1 ⎠ ⎝ ⎣
3
Xwind ∝
⎜
⎟
(4)
⎟
(5)
The variation of turbine efficiency with g/p at different velocity ratio under 0.31 partial admission is shown in Fig. 6. It is obvious that turbine efficiency changes with g/p in the same pattern with stage efficiency. However, with mixing loss considered, turbine efficiency is a little lower than stage efficiency. And the change rate of turbine efficiency is larger than that of stage efficiency. That is, the mixing loss at the downstream of the gap is also affected by the circumferential distance between two nozzle boxes. To better understand the losses caused by partial admission, the loss
(2)
γ − 1 −1 γ ⎤
⎥ ⎥ ⎦
⎜
u Xsegm ∝ ηbl ⎛ ⎞ Nsegm ⎝ ca ⎠
γ − 1 −1 γ ⎤
⎥ ⎥ ⎦
1 − ε⎛u⎞ ε ⎝ ca ⎠
Table 1 Blade geometrical parameters of the stage.
(3)
It can be seen that the results at middle mesh density almost coincide with that at fine mesh density both under full admission and partial admission. Therefore, the rest of computational analysis was conducted with the middle grid density mesh. Also, it can be found the results at middle mesh density agreed well with the experimental data under different partial admission degrees. Therefore, the numerical method is
Full annulus blade numbers Root diameter/mm Blade height/mm Blade chord/mm Solidity Aspect ratio
3
Stator
Rotor
51 92.445 5.51 11.5 1.96 0.48
95 92.445 5.74 7.92 2.52 0.72
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
Table 2 Boundary conditions of the single stage. Working fluid
Air ideal gas
Inlet total pressure/kPa Inlet static temperature/K Outlet static pressure/kPa Rotational speed/rpm
172 300 68.8 17,500–27,500
Fig. 2. Computational grid of the through flow. Table 3 Element number at different mesh density. Mesh density
Coarse
Middle
Fine
Elements under ε = 1/million Elements under ε = 0.31/million
1.73 1.50
3.48 3.14
7.18 6.30
Fig. 3. Comparison of the turbine efficiency between the numerical results and experimental data.
coefficient defined as Eq. (6) is used in this paper following Denton [16]:
ζ = Ts Δs /(ht ,0 − hsis,4 )
(6)
where Δs is the entropy rise at each point in relation to the entropy at the inlet and Ts is the static temperature at each point. Fig. 7 shows the loss coefficient distributions at the cross section between stator and rotor with different g/p. It can be seen that the losses introduced by partial admission are lower at downstream of nozzle boxes and larger at other regions. Meanwhile, a comparatively low loss area can be found near the pressure side of NB1 (A region), which is mainly caused by the jet flow from the stator passages. In addition, a relatively high loss area can be seen near the suction side of NB2 (B region) in Fig. 7(a) to (e), which is probably related to the stagnant fluid developing in the circumferential direction. As for the circumferential gap area between two nozzle boxes (C region), larger losses are introduced here but not so obvious in Fig. 7(b) to (d) as that in Fig. 7(e) to (h). According to the situation at A region, the jet flow from nozzle box 2 contributes to decreasing the loss within a certain range of angles to some extent. When g/p is relatively small, C region may be still in this range and strongly affected by the jet flow, which suppresses large increase in losses. When g/p is relatively large, the jet flow cannot affect all gap area and then a high loss area can be formed near the suction side of nozzle box 1. Loss coefficient distributions at 50% blade height in the circumferential direction with different g/p are presented in Fig. 8. The jet flow can be seen at A region and the losses are found to be increasing along the direction of rotational speed according to Fig. 8(a). The circumferential gap indeed increases losses at downstream rotor passages. However, only when g/p is big enough (g/p > 4), considerable losses can be seen at C region near the suction side of NB1 according to Fig. 8(d). Additionally, the maximum loss coefficient locates at the
Fig. 4. Variation of turbine efficiency and stage efficiency with velocity ratio at different partial admission degree.
corner of pressure side of nozzle boxes which is mostly related to the vortices here. Meanwhile, the loss coefficient at outlet is found to be almost uniform along the circumferential direction due to mixing effects. 3.2. Pressure distribution and unsteady flow Fig. 9 illustrates the static pressure distributions at S2 and S3 along the circumferential direction with different g/p. Large pressure nonuniformity can be seen at S2 due to partial admission and then reduces after crossing rotor passages. At S2, pressure distributions downstream the nozzle boxes show great oscillations while that at other 4
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
flows this region, sudden increase of flow area causes the increase of Mach number and flow defection and hence forms the “jet flow”. Accordingly, the static pressure decreases dramatically. Even when g/p is quite small such as that in Fig. 9(b), there still exists a pressure drop at nozzle box 2. According to Fig. 9(b) to (d), pressure drop at nozzle box 1 is larger than that at nozzle box 2, which is mainly related to the relative transient position between stator blades and rotor blades. The static pressure near the downstream of nozzle boxes (A region and B region) is slightly smaller than that away nozzle boxes at S2. While the pressure at A region is smaller than that at B region at S3. The normalized static pressure distributions at 50% blade height with different g/p are presented in Fig. 10. It can be seen the pressure drop mentioned above appears at the corner of the pressure side of every separate nozzle box. Moreover, a huge low-pressure area and a relatively small low-pressure area can be found near the inlet section according to Fig. 10(a). When g/p is small, these two areas interact to each other and the huge low pressure area cannot be formed downstream the circumferential gap according to Fig. 10(b) and (c). When g/ p increases, the area of low pressure expands a little (Fig. 10(d)). Additionally, the pressure distributions along the circumferential direction are almost even near the outlet. Fig. 11 presents the Mach number distributions and streamlines at 50% blade height with different g/p. Supersonic area can be seen at the cross section of stator and rotor stage. The jet flow at the pressure side of nozzle boxes forms a small high Mach number and vortices area. Two low Mach number lines can be easily seen at the downstream of rotor stage which are the interfaces between active fluid and stagnant fluid according to Fig. 11(a). When g/p is relatively small (g/p = 0.5), only a little stagnant fluid is produced downstream the blockage between NB1 and NB2. It can be easily affected by the active fluid nearby and hence only produces a small low Mach number area (see Fig. 11(b)). As g/p increases, more stagnant fluid is produced but the active fluid nearby cannot affect them all. Thus a larger low Mach number area is produced and streamlines begin to become a little disorder (see Fig. 11(c)). When g/p becomes 16, this low Mach number area expands to the maximum and accordingly significant disorder streamlines are formed (see Fig. 11(d)).
Fig. 5. Variation of stage efficiency with g/p at different velocity ratio (ε = 0.31).
Fig. 6. Variation of turbine efficiency with g/p at different velocity ratio (ε = 0.31).
circumferential angle seem to be nearly uniform. Additionally, huge pressure drops can be seen at the pressure side of nozzle boxes because of the “Prandtl Meyer Fan-like” structure. When high pressure fluid
Fig. 7. Loss coefficient distributions at S2 with different g/p. 5
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
Fig. 8. Loss coefficient distributions at 50% blade height with different g/p.
suction surface of C1 is very large, which indicates a great power capability. Note that the minimum pressure points on pressure surface and suction surface is caused by fluid acceleration at the throat of rotor passages. Two shock waves can be found near the trailing edge of stator blade and leading edge of rotor blade. The shock wave near the trailing edge causes a pressure rise at the suction surface of C1. The pressure difference between pressure and suction surface of D1 is the very small because rotor passage is full of stagnant fluid, hence D1 almost has no power output.
3.3. Blade load and excitation force Fig. 12 presents the positions of selective rotor blades. Where, A1 to A4 are at the transition region from inlet section to blockage, B1 to B4 are at the transition region from blockage to inlet section, C1 is at the inlet section and D1 is at the blockage. The rotor blade load comparison of C1 and D1 and the Mach number distributions around C1 and D1 are presented in Figs. 13 and 14. It can be seen that the pressure difference between pressure and
Fig. 9. Normalized static pressure distributions at S2 and S3 along circumferential direction with different g/p. 6
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
Fig. 10. Normalized static pressure distributions at 50% blade height with different g/p.
The rotor blade load and Mach number distribution at the transition region from inlet section to blockage are presented in Figs. 15 and 16. It is obvious that the pressure distribution of A1 and A4 is respectively similar to that of C1 and D1. The pressure of the suction surface changes dramatically while the pressure change on pressure surface is very small from A1 to A3. A great pressure drop on the suction surface can be seen at the leading section of A2 which is mainly relevant to the jet flow as shown in Fig. 8. Moreover, the pressure on the suction surface increases at the middle section of A2 because that insufficient high-speed flow into the passage reduces acceleration at the throat area which can be also seen in Fig. 16. When it comes to A3, the pressure on the suction surface is almost uniform along the streamwise location due to the flow deflection while the pressure on the pressure surface remains large for that pressure surface can still be affected by the active fluid. Further, the pressure rises at the suction surface of A3 and A4 disappear for that subsonic flow at this region cannot produces shock waves according to Fig. 16. The rotor blade load and Mach number distribution at the transition region from blockage to inlet section are presented in Figs. 17 and 18. The pressure distribution of B1 and B4 is respectively similar to that of C1 and D1. When blade moves from B1 to B2, the pressure on suction surface changes firstly and then the pressure on pressure surface for that the suction surface of B2 is not completely entering the inlet section and the pressure surface of B1 is at the blockage. The interface
Fig. 12. Positions of selective rotor blades.
Fig. 13. Rotor blade load comparison of C1 and D1 (g/p = 0).
Fig. 11. Mach number distributions and streamlines at 50% blade height with different g/p. 7
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
Fig. 17. Rotor blade load at the transition region from blockage to inlet section (g/p = 0).
Fig. 14. The Mach number distributions around C1 and D1.
Fig. 18. The Mach number distributions around B1-B4.
Fig. 15. Rotor blade load at the transition region from inlet section to blockage (g/p = 0).
ratio of 0.31. Note that the negative values mean that the direction of axial force is opposite to the main stream direction or the direction of tangential force is opposite to the rotational direction. According to Fig. 19(a), the axial forces of active rotor blades show strong fluctuations while that of inactive rotor blades are nearly equal to zero. The direction of axial forces on the blades at the downstream of the pressure side of nozzle boxes is opposite to the main stream direction which is mostly related to the jet flow. Meanwhile, the largest negative axial force can be also seen in these regions. Moreover, the g/p hardly changes the pattern of distributions except for the circumferential position of the fluctuations of NB2. The largest negative axial force caused by NB 2 still appears even when g/p is very small. In Fig. 19(b), the tangential forces of blades at inlet section show small fluctuations and that of blades at the blockage are stable at small positive values. The negative tangential forces appear at the suction sides of two nozzle boxes, which result in negative work. Except for the circumferential position of fluctuations of NB2, the g/p mainly affects tangential forces at the downstream of the circumferential gap. The forces at this region decrease as g/p increases. The negative tangential forces come out only when the g/p is big enough (g/p = 16). Fig. 20 presents the total force acting on the rotor with different g/p at different velocity ratio. Note that the negative values mean that the direction of axial force is opposite to the main stream. In Fig. 20(a), it can be seen that the rotor axial force increases with velocity ratio. The largest rotor axial force only occurs when g/p is equal to zero, because only one negative axial blade force region can be formed in this situation according to the analysis above. When g/p is greater than zero, the rotor axial force stables at a lower level and the value is mainly
Fig. 16. The Mach number distributions around A1-A4.
between stagnant fluid and active fluid can be seen in Fig. 18. Further, the pressure on the suction surface stabilizes first while the pressure on pressure surface still changes when blades move from B3 to B4 for that suction surface of B4 is just completely at the inlet section. It can be also seen that the minimum pressure point on the pressure surface of B3 is closer to the leading edge than that of B4 due that only a part of high speed fluid from the nozzle box enters the passage. Moreover, the pressure rises can be seen at the suction surface of B3 and B4 due to the shock waves in Fig. 18. Fig. 19 gives the rotor blade force with different g/p at the velocity 8
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
Fig. 19. Rotor blades force with different g/p at 0.31 velocity ratio.
p > 4). The losses at the pressure side of the nozzle box are found to be smaller than that at the suction side due to the jet flow effect. (2) The non-uniformity in static pressure upstream the rotor stage was captured. Deep drops at the pressure side of nozzle boxes appear even when the circumferential gap is quite small. The Mach number distributions and streamlines are influenced obviously by the circumferential gap. Low Mach number regions are formed between active fluid and stagnant fluid. (3) Blade load changes significantly as the blade enters and leaves the inlet section. The jet flow causes a great pressure drop on the suction surface at the leading section as the blade leaves the inlet section. Moreover, the minimum pressure point on pressure surface first appears near the blade leading edge and then moves toward the trailing edge as the blade enters the inlet section. (4) Negative blade axial force appears at the pressure side of nozzle boxes regardless of the circumferential gap while negative tangential force at the suction side of nozzle box 2 exists only when the circumferential gap is big enough. The rotor axial force with zero circumferential gap is the largest because only one negative blade axial force region is created. The rotor radial force decreases with circumferential gap due to balance effect.
related to the relative transient position between stator blades and rotor blades. Fig. 20(b) shows that rotor radial force decreases with velocity ratio. Moreover, the rotor radial force decreases with g/p since the two radial forces caused by two nozzle boxes cancel each other out to a certain extent. When g/p is equal to zero, the balance effect between two forces is the smallest which results in the largest rotor radial force occurs. When g/p is 16, the maximum balance between two forces make rotor radial force almost equal to zero. Moreover, the direction of force changes with g/p which can be used to adjust the load of rotor and improve the stability. 4. Conclusions A small partial admission single stage turbine with two nozzle boxes was numerically investigated to reveal the effect of various nozzle box arrangement on turbine aerodynamic performance. Eight cases of arrangements are detailedly studied in this paper. the conclusions are presented as follows: (1) Due to the increasing extra losses caused by partial admission with an increasing circumferential gap, the turbine efficiency decelerates to decrease. Considerable losses at the downstream of the circumferential gap can be found only when g/p is big enough (g/
Fig. 20. Rotor force with different g/p at different velocity ratio. 9
Applied Thermal Engineering 159 (2019) 113911
Y. Pan, et al.
unsteady flow in axial turbine, Appl. Therm. Eng. 128 (2018) 926–939. [6] L. Song, J. Li, K. Wen, Aerodynamic performance analysis of partial admission dual row control stage at different working conditions, J. Mech. Sci. Technol. 30 (1) (2016) 157–169. [7] S.Y. Cho, C.H. Cho, K.Y. Ahn, et al., Forces and surface pressure on a blade moving in front of the admission region, J. Fluids Eng.-Trans. Asme 132 (2010) 121101. [8] N.B. Hushmandi, T.H. Fransson, Effects of multiblocking and axial gap distance on performance of partial admission turbines: A numerical analysis, J. Turbomach. 133 (2011) 031028. [9] A. Varma, S. Soundranayagam, Experimental study of a small partial admission axial turbine with low aspect ratio blade, Proc. Inst. Mech. Eng., Part G: J. Aerospace Eng. 228 (1) (2012) 20–34. [10] H. Kanki, A. Tanitsuji, Stability of high pressure turbine under partial admission condition, Proceedings of IDETC/CIE, 2005, (2005) DETC2005-84774. [11] G.L. Martins, S.L. Braga, S.B. Ferreira, Design optimization of partial admission axial turbine for ORC service, Appl. Therm. Eng. 96 (2016) 18–25. [12] H.A. Klassen, Cold-air investigation of effects of partial admission on performance of 3.75-inch mean-diameter single stage axial-flow turbine, NASA, 1968. [13] R. Capata, E. Sciubba, Experimental fitting of the re-scaled Balje maps for lowreynolds radial turbomachinery, Energies 8 (8) (2015) 7986–8000. [14] P. Lampart, Q. Hirt, Complex multi-disciplinary optimization of turbine blading systems, Arch. Mech. 64 (2012) 153–175. [15] L. Moroz, B. Frolov, O. Guriev, Analysis and optimization of partial admission stages, Proceedings of Asian Congress on Gas Turbines 2014, (2014) ACGT-20140007. [16] J. Denton, The 1993 IGTI scholar lecture: loss mechanisms in turbomachines, J. Turbomach. 115 (1993) 621–656.
Acknowledgement This work is supported by National Natural Science Foundation of China (No. 11872289), the Key Project of Natural Science Foundation of Xi'an Jiao Tong University (No. ZRZD2017025). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.113911. References [1] L. He, Computation of unsteady flow through steam turbine blade rows at partial admission, Proc. Inst. Mech. Eng., Part A: J. Power Energy 211 (1997) 197–205. [2] P. Lampart, M. Szymaniak, R. Rzadkowski, Unsteady load of partial admission control stage rotor of a large power steam turbine, Proceedings of ASME Turbo Expo 2004, (2004) GT2004-53886. [3] N. Sakai, T. Harada, Y. Imai, Application of CFD to partial admission stages of steam turbine, Proceedings of PWR2005, ASME Power, (2005) PWER2005-50346. [4] J.E. Fridh, B. Bunkute, R. Fakhrai, et al., An experimental study on partial admission in a two-stage axial air test turbine with numerical comparisons, Proceedings of ASME Turbo Expo 2004, (2004) GT2004-53774. [5] K.K. Gao, Y.H. Xie, D. Zhang, Effects of rotor solidity and leakage flow on the
10