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Effect of the injection orientation and position on the leakage flow in a honeycomb-tip turbine cascade
International Journal of Heat and Mass Transfer 144 (2019) 118633
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Effect of the injection orientation and position on the leakage flow in a honeycomb-tip turbine cascade Yabo Wang, Yanping Song, Jianyang Yu ⇑, Fu Chen Institute of Propulsion Theory and Technology, Harbin Institute of Technology, Harbin 150001, China
a r t i c l e
i n f o
Article history: Received 24 January 2019 Received in revised form 16 April 2019 Accepted 22 August 2019 Available online 6 September 2019 Keywords: Honeycomb tip Injection orientation Injection position Tip leakage flow Tip cooling
a b s t r a c t The effect of the cooling injection orientation and position on the tip leakage flow has been studied numerically in a honeycomb-tip turbine cascade. The injected fluid enters each honeycomb cavity through the bottom pipe at a fixed incident angle. The effect of the relative casing motion with six casing speeds is considered. The Reynolds-averaged Navier-Stokes (RANS) method and k-x turbulence model were used in the three dimensional computations. Then the leakage mass flow rate and the averaged total pressure loss are evaluated. The static pressure and limiting streamlines on the casing are discussed and the flow direction around the gap are extracted to precisely analyze the leakage feature. Besides, the thermal conditions on the blade tip and suction surface are described by the Nusselt number and adiabatic film cooling effectiveness. Finally, the dimensionless temperature contours and velocity vectors inside the gap are plotted to explore the effect of the injection position. The results indicates that the injection feature mainly depends on the injection orientation and finally determines the aerodynamic and thermodynamic performance. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The tip leakage flow (TLF) induces high energy consumption and serious thermal load on the turbine rotor tip. Relative to other tip designs aimed at relieving the TLF, the shroud tip eliminates the traditional TLF and maintains the lowest aerodynamic loss [1]. In order to reduce the additional blade stress due to this extra tip weight, the scalloped shroud [2] and local cut shroud [3] were proposed. Recently, the winglet-shroud was presented to reduce the total pressure loss by about 2/3 of the reduction by the full shroud [4]. The unshrouded tip designs, such as the squealer tip, the winglet tip and other combined designs, have been widely studied. Zou et al. [5] pointed out that the scraping vortex in the squealer tip acted as an aero-labyrinth to reduce the equivalent leakage outflow area. Coull et al. [6] concluded that the winglet overhangs reduced the aerodynamic loss by altering the leakage flow direction and outflow location. The tip leakage vortex (TLV) moved away from the suction surface, resulting in lower heat transfer there. Yan et al. [7] found that the squealer-winglet tip could further reduce the loss and weaken the tip heat transfer on the basis of the conventional squealer tip. Moreover, the aerodynamic effect
⇑ Corresponding author. E-mail address: [email protected] (J. Yu). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118633 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
of the cooling injections should be considered in the parameter studies and optimization designs for the above tip designs. Chen et al. [8] indicated that the secondary injection into the gap had the ability to suppress the TLF. Niu et al. [9] confirmed this effect and pointed out that the tip heat transfer varied with injection position. The experiment by Volino [10] further showed that inclined injection near the maximum loading could reduce the total pressure loss most effectively. This means that the cooling injection contains the ability to block the TLF while providing the tip cooling protection. Interestingly, Newton et al. [11] observed that the cooling injection located at the separation bubble would be better in the tip protection with the mass flow rate (MRF) close to the leakage outflow. However, the current tip cooling mainly focuses on reducing local high heat transfer or leakage inflow temperature. For example, the squealer tip cooling is usually realized by the cooling injection from the tip holes [12–14] along or parallel to the camber line and the holes on the pressure surface near the casing [12,13]. Similar cooling arrangement applied in winglet tip [15] and squealerwinglet tip [16] did reduce the loss and thermal load. But the mixing cooperation between the injected fluid and the TLF are no longer taken into account. Since the injected fluid destroys the TLF field within the gap, the tip designs would no longer be the optimal choice [17]. Meanwhile, Lim et al. [18] summarized some guidelines on the hole angles to balance the aerodynamic loss and
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Nomenclature Cax Cp H k _ m _ TLF m Ma n Nu Nu p p* q r T V v x y y+ z
blade axial chord [m] static pressure coefficient [–] blade span [m] turbulent kinetic energy [–] mass flow rate [kg s1] tip leakage mass flow rate [kg s1] Mach number [–] rotor speed [rpm] Nusselt number [–] span-wise averaged Nusselt number [–] static pressure [Pa] total pressure [Pa] heat flux [W m2] radius of the rotor tip [m] temperature [K] velocity [m s1] fluctuation velocity [m s1] span-wise direction pitch-wise direction dimensionless wall distance [–] axial direction
Greek
ainc aori apit apit ayaw ayaw q
incident angle [°] orientation angle [°] pitch angle [°] span-wise averaged pitch angle [°] yaw angle [°] span-wise averaged yaw angle [°] density [kg/m3]
h
j g g s
-
non-dimensional temperature [–] thermal conductivity (0.0261 W/(mK)) adiabatic film cooling effectiveness [–] span-wise averaged adiabatic film cooling effectiveness [–] tip gap height [m] total pressure loss coefficient [–] mass flow averaged total pressure coefficient [–]
Subscripts 0 cascade inlet 1 cascade outlet aw adiabatic wall c injection inlet rms root-mean-square Abbreviations FT flat tip HT honeycomb tip LE leading edge MFR mass flow rate PS pressure side PVC passage vortex near the casing SS suction side TE trailing edge TLF tip leakage flow TLMFR tip leakage flow rate TLV tip leakage vortex
heat transfer from the experiments. A variety of hole shapes on simple models also provide new elements in the film cooling design. The study on the diffusion holes by An et al. [19] indicated that the slot-shaped holes contained better cooling coverage than fan-shaped holes. Besides, the trench attached to the traditional holes raised the film cooling effectiveness downstream [20], while
double-jet produced anti-kidney vortexes and a more uniform cooling coverage [21]. The investigation by Fu et al. [22] on the honeycomb tip indicated that the cavity flow helped to suppress the TLF. Wang et al. [23] implemented tangential injections to strengthen the cavity flow to block the TLF. Later on, another study on the cavity depth was carried out and described the enhancement mechanism of cavity vortices preliminarily [24]. However, the injection
Fig. 1. Schematic diagram of the honeycomb tip and cooling injection.
Fig. 2. Schematic diagram of the orientation angle and inclined angle.
Y. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118633 Table 1 Case information for the grid independency validation (HT). Span-wise nodes Grid1 Grid2 Grid3 Grid4 Grid5
111(11) 121(21) 131(31) 141(41) 151(51)
Cell number 6
3.81 10 4.51 106 5.21 106 5.91 106 6.60 106
TLMFR 2.689%ṁ0 2.691%ṁ0 2.649%ṁ0 2.653%ṁ0 2.654%ṁ0
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vector AA0 is parallel to the YZ plane and passes through the symmetry line of honeycomb row. Then in the enlarged views, the pipe of 0.8 mm diameter is placed at each bottom center (O) by default. Fig. 2 describes the orientation angle and inclined angle in detail. The vector OC expresses the injection direction and its projection on the bottom plane (YZ) is OB. The inclined angle (ainc ) rising from OB to OC remains 30° in the present study. The orientation angle (aori ) rotating from OA to OB increases every 30°. Thus, a total of 12 angles from 0° to 330° are included. The orientation angle of 360° also indicates 0°. Besides, the gap height (s) and the cavity depth are both given 1% of the blade span (H). The internal chamber is not concerned in the present calculations for simplification. Particularly, the baseline cases, namely the flat tip and honeycomb tip, are abbreviated as FT and HT, respectively. The cooled cases are named according to the injection position and orientation, separated by a hyphen (-). For example, the CH-0° case indicates that the injection pipe is located at the center of each cavity bottom and its orientation angle is 0°. 2.2. Computational method and turbulence model
Fig. 3. Grid independency validation: the axial distributions of the leakage outflow rate along the SS profile (HT).
orientation and position were not considered completely in the former studies. So the present study focuses on the effect of the injection orientation on the TLF control and tip cooling. The flow feature of the injected fluid are explored. Then the flow field inside the gap and the suction surface cooling are also considered. Finally, the effect of the injection position along the orientation direction is discussed by the inner temperature field. 2. Numerical model and method 2.1. Description of the numerical model The cascade profile is a magnified version of the blade tip in a high-pressure turbine rotor [22]. Fig. 1 provides the schematic diagram of the honeycomb tip, whose geometry and honeycomb arrangement remain the same with the experiment [22]. The
The cascade boundary settings are consistent with the experiment [22]. The no-slip adiabatic or isothermal wall condition is adopted on the surface of the tip and cavities, in order to calculate the cooling effectiveness or Nusselt number. The injection total temperature is 30.0 K higher than the cascade inlet, while the injection total pressure is 99% of the cascade inlet. Finally, the total MFR from the injection pipes is about 0.36% of the main flow. The grid information of the computational domain has been shown in Fig. 1. The dimensionless mesh height y+ is ensured less than 1 on the blade surface to predict the near-wall flow field accurately. Besides, the passage grid remains consistent for all cases, which weakens the numerical disturbance by grid difference. The unstructured grid is employed to gently connect the cavities and pipes. In the present study, the total pressure loss coefficient (-) is defined as,
_ c pc ðm _ c Þp _ 0 p0 þ m _ 0þm m -¼ _ c pc p1 _ 0 p0 p1 þ m m
where p is the local total pressure, p0 the total pressures of the cas_ 0 is cade inflow, and p1 the static pressure of the cascade outflow. m _ c the injection MFR. the cascade inflow mass flow rate (MFR), and m The static pressure coefficient (Cp) is defined as,
Cp ¼
p p1 p0 p1
Fig. 4. Numerical method validation: (a) the axial distributions of the static pressure coefficient (Cp) at 97%H (b) the span-wise distributions of the pitch-wise averaged total pressure loss coefficient (-) at 130%Cax.
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_ TLF =m _ 0 ) and (b) the mass flow averaged total pressure loss (-) at 130%Cax. Fig. 5. Comparisons of (a) the normalized TLMFR (m
Fig. 6. Comparisons of the mass flow averaged loss coefficient (-): (a) the leakage inflow and (b) the leakage outflow.
where p is the local static pressure. The effect of the node number on the tip leakage mass flow rate (TLMFR) has been explored in the HT case. Table 1 lists the case information for the grid independency validation. The span-wise node number above the blade tip varies from 11 to 51. As the node number reaches 31, the TLMFR presents an asymptotic trend. Especially, compared with the thickest case (Grid5), the relative difference is ignorable (less than 0.4%) in the Grid4 case. Fig. 3 further compares the axial distributions of the leakage outflow rate. These lines almost overlaps with each other in the cases Grid3–Grid5. It is indicated that the critical node number is about 31, especially for the hump near 50% of the axial chord length (Cax). Finally, the Grid4 case is adopted in the following calculations. The cell number is about 5.4 106 in the FT case, and it comes up to 6.1 106 in cooled cases. The calculations are completed in the commercial software ANSYS CFX. The two-equation k-x turbulence model is used in solving the Reynolds-averaged Navier-Stokes (RANS) equations. The advantage of the present k-x model is the near-wall treatment at low Reynolds number. The numerical result in the baseline cases is compared with the experimental data [22] in validating the predicting accuracy. The static pressure on the blade surface near the tip and the span-wise loss distribution at 130%Cax (shown in Fig. 1) are plotted together with the measured data in Fig. 4. In detail, the SS pressure peak is associated with the development of the TLV. The over-estimation near 60%Cax indicates that the predicted TLV deviate from the experiment slightly. In Fig. 4(b), the loss in the two rectangles are affected by the TLV and the passage vortex near
the casing (PVC). For the FT case, the loss peak is well predicted in the upper rectangle, while the span-wise position of the loss peak is lower than the experiment in the other rectangle. Yet, both the two peaks is positioned well but over-estimated in the HT case. Firstly, the measuring points downstream the cascade may not be properly arranged to capture the flow features for both cases. The impropriate grid number there also affects the calculating result and post processing. Secondly, the default parameters of the k-x model may be not suitable for the current models and need to be further identified. But overall, the aerodynamic parameters have been well predicted by the k-x model. The validation of the SST model was also conducted in the previous work. The SST model is better is predicting the flow separation caused by the adverse pressure gradient. Thus, the k-x model is employed in all the present computations. Finally, it should be mentioned that there was no published or measured data about the tip heat transfer for the current cascade. Still, the thermodynamic validation was realized using another subsonic cascade in the previous study [23].
3. Result and discussion 3.1. Effect of the injection orientation on the TLF 3.1.1. The TLMFR and total pressure loss _ TLF =m _ 0 ) and the averaged total presThe normalized TLMFR (m
sure loss coefficient (-) are plotted against the injection orientation angle in Fig. 5. The mass flow rates of the leakage inflow
Y. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118633
Fig. 7. Isothermal surfaces (h = 0.2), colored by the normalized turbulence kinetic energy (k=V 2z;0 ).
Fig. 8. Three dimensional streamlines of the injected fluid, colored by the normalized velocity (V/Vz,0).
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and outflow no longer remain equal in the cooled cases. Although no significant reduction of the leakage outflow is realized by the cooling injection on the basis of the honeycomb tip, the leakage inflow rate drops by up to 27.8% in the CH-30° case, compared with the FT case. The leakage outflow might even increase slightly due to injected fluid supplement in the cases, whose orientation angle is between 60° and 300°. The averaged loss at 130%Cax in the cooled cases is lower than the baseline cases, except for the CH240° case. Compared with the FT case, the averaged loss is reduced by up to 4.7% at 130%Cax in the CH-30° case. The averaged loss (-) of the leakage inflow and outflow are compared in Fig. 6. The leakage inflow loss mainly comes from the upstream boundary layer and is reduced in a way similar to the inflow rate. The leakage outflow loss increases obviously in the HT case and then differs with the orientation angle after adding the cooling injections. It is noted that the leakage flow rate is below 3.2% of the main flow. That is, the passage flow provides more contribution in the downstream loss, which is not worsened by the cooling injections.
the small vortex on one or both sides of the injection. At this point, the streamlines keep close to the cavity bottom. Although some streamlines are broken near the cavity sidewalls, it can be inferred that the stagnant fluid will also turns to the cavity bottom after impacting the sidewall. 3.1.3. The flow field inside the gap Based on the injection features, four cooled cases are chosen in analyzing the flow field, that is, the cases CH-0°, CH-30°, CH-180° and CH-210°. The contours of the static pressure coefficient (Cp) and the limiting streamlines on the casing are shown in Fig. 9. The inner static pressure field inside the gap is disturbed apparently by the honeycomb tip and cooling injections. The lowpressure region at the PS middle diminishes in the HT case and trends to disappear as adding the cooling injections. The newly formed Cp gradient along the stream-wise direction fails to press enough passage fluid into the gap. Besides, the expansion of the high-pressure region near the LE also contributes to suppress the
3.1.2. The flow feature of the cooling injection The dimensionless temperature h is defined as,
h¼
T Tc T0 Tc
where T is the local temperature. The turbulence kinetic energy (k) is defined as,
k¼
1 2 v þ v 2y;rms þ v 2z;rms 2 x;rms
where vx,rms, vy,rms and vz,rms are the root-mean-square values of the fluctuation velocities. The temperature field is used to characterize the mixing of the injected fluid and leakage fluid. The isothermal surfaces (h = 0.2) colored by the normalized turbulence kinetic energy (k=V 2z;0 ) are shown in Fig. 7. The injection flow can be roughly divided into the compact type and expanded type, according to the isothermal surface morphology. These two types can be observed in different cavities in all the cases. Firstly, the compact type corresponds to a centralized isothermal surface. It can be inferred that this type keeps and even promotes the original feature of the cavity flow at some special orientations. Secondly, the expanded type appears as the honeycomb bottom is covered by the injected fluid, especially for the orientation angle of 90–240°. Thus, the expanded type would be better in protecting the honeycomb cavity from the thermal load. The injection feature also differs with the cavity position on the blade tip. In the front region near the leading edge (LE), the isothermal surfaces is small and compact due to the weak injection, illustrated in Fig. 8(a). When it comes to the tip middle, the isothermal surface becomes longer or spreads on the cavity bottom. Then in the back region near the trailing edge (TE), the injection feature is similar to that at the tip middle. Meanwhile, the turbulence kinetic energy maintains at a relatively low level for the expanded type, indicating a gentle mixing between the injected fluid and leakage fluid. Three honeycomb rows, namely HR1, HR2 and HR3, have been marked in Fig. 7(a). The three dimensional streamlines of the injected fluid insides the three honeycomb rows are plotted in Fig. 8, colored by the normalized velocity (V/Vz,0). It is noted that the PS injection speed is lower than the SS. Firstly, the injected fluid follows the injection orientation until rushing out of the cavity, which corresponds to the compact injection flow. In particular, the low-speed injected fluid in the near-LE region is involved into the cavity vortices easily. Secondly, for the expanded type, the injected fluid impacts the honeycomb sidewall and then rolls into
Fig. 9. Contours of the static pressure coefficient (Cp) and the limiting streamlines on the casing.
Fig. 10. Disgram of the reattachment lines and separation lines on the casing.
Y. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118633
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Fig. 11. Distributions of the static pressure coefficient (Cp) and its gradient: (a) Line1 and (b) Line2.
Fig. 12. Schematic vectors of the horizontal velocity (Vyz) around the gap.
leakage inflow. Besides, the PS reattachment line and SS separation line separate the leakage inflow and outflow from the passage flow, respectively. This means the leakage fluid is limited from the reattachment line to the separation line in the near-casing region. Then the coordinates of these two featured lines are determined and plotted together in Fig. 10. In the enlarged views, both two lines are the farthest from the blade profile in the FT case and move toward the adjacent blade surface in the HT case. The cooling injection narrows the leakage inflow range but fails to reduce the outflow range, based on the HT case. In particular, the static pressure and its gradient on the two lines, namely Line1 and Line2 (marked in Fig. 10), are extracted in Fig. 11. Line1 passes through the LE along the leakage direction roughly, and Line2 crosses the low-pressure region at the tip middle. The separation bubble induces the Cp drop just downstream
Fig. 13. Axial distributions of the span wise averaged parameters: (a) pitch angle (apit ), (b) yaw angle (ayaw ) and (c) leakage rate around the gap.
the gap entrance. A gentle distribution of the static pressure is newly formed, indicating a weaker leakage inflow, especially on Line2. Furthermore, the separation bubble can be positioned precisely according to the zero Cp gradient. The Cp drop always means an increasing flow velocity for the present subsonic TLF. In the FT case, the Cp gradient reaches its minimum before the separation bubble, when the leakage fluid accelerates into the gap. Interestingly, the Cp gradient after the separation bubble remains a
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Fig. 14. Histograms of (a) the normalized area and (b) heat flux on the tip, honeycomb sidewalls and bottoms.
Fig. 15. Contours of the normalized turbulence kinetic energy (k=V 2z;0 ) inside the gap at: (a) 25%s and (b) 25%s.
Fig. 17. Contours of the adiabatic film cooling effectiveness (g) on the blade tip (Top view).
Fig. 16. Contours of the Nusselt number (Nu) on the blade tip (Top view).
negative constant along Line1 and keeps positive along Line2. In the other cases, the minimum of the Cp gradient increases with the decrease of the leakage inflow rate. The Cp gradient becomes ups and downs under the disturbance of the honeycomb cavities and injections.
In Fig. 12, the horizontal velocity (Vyz) is defined as the projected component of the local velocity (V) on the YZ plane. Then Fig. 12 presents the schematic vectors of this projected velocity around the gap. The PS vectors end at the profile, while the SS vectors start from the profile. For the leakage inflow, the vector lengths decrease obviously, compared with the FT case. The PS vectors rotate negatively around the x-axis, while the SS vectors positively. However, the change of the leakage outflow vectors are complex along the SS profile. In Fig. 13, the pitch angle (apit) is defined on the YZ plane and is the angle from the positive z-axis to the vector Vyz. The yaw angle
Y. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118633
(ayaw) is defined on the XV plane as the angle rising from the vector Vyz to V. Then the two angles and local leakage flow rate are spanwise averaged and plotted around the gap. As marked in the dashed ellipse, the leakage fluid flows around the LE under the obstruction of the near-LE high pressure in the FT case. Then, an opposite change of the pitch angle occurs on both sides of the LE, since the TLF suppression is enhanced by the honeycomb tip and cooling injections. In Fig. 13(b) and (c), the distributions of the
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yaw angle and leakage flow rate can be divided according to the leakage inflow and outflow. The starting position of the leakage outflow is advanced by the cooling injection, confirmed by the increased pitch angle there. The positive yaw angle means that the leakage inflow rushes toward the casing, while the negative value indicates a smooth outflow after the mixing inside the gap. Thus, the leakage inflow leans toward the tip, except for the near-LE region.
Fig. 18. Axial distributions of the pitch-wise averaged (a) Nusselt number (Nu) and (b) adiabatic film cooling effectiveness (g) on the blade tip.
Fig. 19. Secondary flow filed in the upper passage and the thermal condition on the suction surface.
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Fig. 20. Contours of the adiabatic film cooling effectiveness (g) on the suction surface.
_ c =m _ 0 ) against the normalized casing speed Fig. 22. The normalized injection MFR (m (V y;casing =V z;0 ).
Nu ¼
qC ax
jðT w T 0 Þ
where q is the local wall heat flux, T w the isothermal wall temperature and T 0 the inflow temperature. j is the thermal conductivity. The adiabatic film cooling effectiveness (g) is defined as,
g¼
Fig. 21. Normalized heat flux in the rectangle (S1) on the suction surface.
3.1.4. The thermal condition on the blade tip The total area and heat flux on the tip surface, honeycomb sidewalls and bottoms are collected in Fig. 14(a) and (b), respectively. The total heat flux is higher in the HT case than the FT case and decreases as adding the cooling injections. The maximum reduction by about 19.1% is achieved in the CH-210° case, compared with the FT case. In detail, the remaining tip surface remains about 45.4% area of the flat tip but the total heat flux on it reaches 67.6% in the HT case. Then the heat flux on the remaining tip surface is reduced by the cooling injections. Yet, the heat flux per unit area is still higher than the FT case. It is observed that the cavity sidewalls and bottoms always maintain at a low level of heat flux. The contours of the non-dimensional turbulence kinetic energy (k=V 2z;0 ) are presented in Fig. 15. The two span-wise planes are at 25%s and 75%s inside the gap. The inner flow field is disturbed more strongly at 25%s than at 75%s. At 25%s, the honeycomb tip breaks the flat region affected by the PS separation bubble in the FT case. The cooling injections could further diminish this featured region. A more uniform distribution of the turbulence kinetic energy appears over the section, especially in the front region. Besides, the honeycomb tip and cooling injections also disturbs the TLF at 75%s. The Nusselt number (Nu) is defined as,
Table 2 The relative casing speed (Vy,casing/Vz,0). nLISA;R [rpm] Vy,casing [m/s] Vy,casing/Vz,0
0 0 0
900 6.28 0.27
1800 12.57 0.54
2700 18.85 0.81
3600 25.13 1.08
4800 33.51 1.45
T aw T 0 Tc T0
where T aw is the adiabatic wall temperature and T c the injected fluid temperature. The contours of the Nusselt number (Nu) on the blade tip are presented in Fig. 16. In the FT case, the leakage inflow impacts the flat tip after crossing the PS separation bubble, resulting in the region of high heat transfer. The honeycomb tip discrete the Nu distribution on the remaining tip and obtains a low level of heat transfer on the honeycomb bottoms. The cooling injections could weaken the heat transfer on the honeycomb bottoms, especially in the dash ellipses. The accumulation of the injected fluid also helps to weaken the SS heat transfer there. Similar features can be observed in the contours of the adiabatic film cooling effectiveness (g) in Fig. 17. The lower heat transfer often corresponds to a higher cooling effectiveness. The cooling feature on honeycomb bottoms differs with the injection orientation. In Fig. 17(a) and (b), the injected fluid rushes toward the facing sidewalls, leading to relatively small high-cooling regions at the bottom corners. However, in Fig. 17(c) and (d), the injections effectively cools the whole bottoms in the dash ellipses, with the optimal orientation angle of 210°. It is confirmed that the injected fluid does not flow downstream directly but spreads over the whole cavity bottoms. In Fig. 18, the Nusselt number and adiabatic film cooling effectiveness are pitch-wise averaged, and their axial distributions become fluctuating due to the honeycomb tip in HT case. It is confirmed that the Nu on the honeycomb sidewalls and bottoms is much lower than the tip. Furthermore, the cooling injections could reduce the heat load on these walls significantly. The g remains higher on the honeycomb sidewalls and bottoms than the tip, especially for the orientation angles of 180° and 210°. The cooling effect near the LE and TE trends to diminish due to the lack of cooling protection. 3.1.5. The heat transfer on the suction surface The secondary flow field in the upper passage and the thermal condition on the suction surface are shown in Fig. 19. The averaged velocity of the passage flow at 50%H is considered as the main flow
Y. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118633
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_ TLF =m _ 0 ) and (b) the mass flow averaged total pressure loss (-) at 130%Cax. Fig. 23. Comparisons of (a) the normalized TLMFR (m
ability is stronger in the CH-210° case in Fig. 20, its heat flux maintains at a similar level with the HT case. Therefore, it can be inferred that the thermal load on the suction surface is mainly affected by the secondary vortices more than the cooling effect. 3.1.6. The relative casing motion effect For the cases FT, HT, CH-0° and CH-180°, the casing moves towards the positive y-axis direction in this section. The casing speeds are obtained by scaling down the realistic rotational speed of the turbine rotor, as defined in the speed formula below.
V y;casing ¼
Fig. 24. Schematic diagram of the injection position (aori = 0° and aori = 180°).
for each axial section. The secondary velocity is the component perpendicular to the main flow direction. It should be mentioned that the h on the blade surface is lower than the main flow. The passage fluid would be cooled, when it flows over the blade surface. Thus in the FT case, the leakage fluid close to the tip surface is of relatively low h and mainly flows into the TLV. Firstly, the TLV sweeps on the suction surface from the reattachment line to separation line. Secondly, the shearing layer between the TLV and PVC carries passage fluid of high h toward the suction surface. Both the two process results in the region of high heat transfer near the reattachment line, especially at 50%Cax. The heat transfer is at a relatively low level in the region near the separation line. In the HT case, the heat flux increases on the blade tip but the leakage flow rate decreased, indicating that the leakage outflow is of lower h than the FT case. After adding the cooling injections, although the heat flux on the blade tip is reduced, the injected fluid of low h helps to reduce the h of the leakage fluid. Then it is observed that the range of low h expands in the TLV affected region at 50%Cax. Meanwhile, the PVC has evolved into the PVC1 and PVC2 at 70% Cax in advance, and the PVC2 core gets further away from the suction surface at 90%Cax. Thus, the sweeping effect of the shearing layer on the suction surface is weakened. That is why the heat transfer is reduced, compared with FT case. As shown in Fig. 20, the cooling intensity on the suction surface is much weaker than that on the blade tip. The cooling intensity differs with the injection orientation in a triangular region, with the highest g concentrated in the front part. Then the normalized heat flux in the rectangular region S1 are compared in Fig. 21. The heat flux is reduced by about 7.5% in the HT case and by about 11.0% in the CH-30° and CH-330° cases. Although the cooling
nLISA;R 2p rLISA;R Ma MaLISA;R 60
where nLISA;R is the rotating speed, r LISA;R the radius of the rotor tip, and MaLISA;R the inlet Mach number of the rotor. A total of six turbine rotor speeds, including the stationary condition and design speed (2700 rpm), are selected. Then the normalized casing speeds (Vy,casing/Vz,0) are listed in Table 2. _ c =m _ 0 ) against the casing speed The injection MFR (m (V y;casing =V z;0 ) is shown in Fig. 22. The injection MFR is always maintained at a relative level, about 0.36 or 0.37 percent of the main flow for the stationary cases. The injection MFR decreases with the casing speed linearly, indicating that the injection strength is weakened. _ TLF =m _ 0 ) and the averaged total presThe normalized TLMFR (m
sure loss coefficient (-) are plotted against the relative casing speed in Fig. 23. The TLMFR decreases as increasing the casing speed, confirming the suppression of the casing motion on the TLF. Yet, the averaged loss at 130%Cax distributes non-linearly against the casing speed. It should be mentioned that the casing motion fails to eliminate the performance improvement. Furthermore, the thermal condition on the blade tip is almost unaffected by the relative casing motion in the injection cases. 3.2. Effect of the injection position on the TLF The injection position is considered only for the orientation angle of 0° and 180°. As shown in Fig. 24, five injection positions are selected by equally dividing the bottom centerline, which is parallel to the vector AA0 . The positions are labeled as P1–P5, and the P3 is located at the bottom center, corresponding to the above cooled cases. 3.2.1. The temperature field inside the gap Figs. 25 and 26 show the contours of the dimensionless temperature (h) and the velocity vectors inside the gap. The vertical sections are the symmetry planes of the honeycomb rows, namely
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Fig. 25. Contours of the dimensionless temperature (h) and velocity vectors inside the gap (aori = 0°).
HR1, HR2 and HR3 in Fig. 7(a). The vectors are plotted by the projected velocities, whose lengths have nothing to do with the velocity magnitude. It is also noted that the h contour greater than 1 has been removed. For the two positions, the injected fluid rushes toward the facing sidewall and mixes with the leakage fluid just above. As the injection position gets close to the facing sidewall, the mixing process is shortened as the injected fluid trends to attach to the facing sidewall. The injection intensity is stronger for the SS pipes, while even no fluid has been injected from some PS pipes at Sta5. In detail, for the orientation angle of 0° in Fig. 25, the leakage fluid impacts on the SS sidewalls and then turns to the cavity bottoms. When the leakage fluid flows back to the PS sidewalls, the injection always keeps tangential to this backflow and mixes with it. The injection also provides the opposite momentum, and this helps to obstruct the TLF. In Fig. 26, the leakage fluid also turns back in the near-LE cavities, pushing the injected fluid toward the PS sidewalls. Yet, the above cavity backflow has disappeared in most cavities, since the injection follows the TLF but is opposite to the backflow. Thus, the injected fluid or mixture is restricted on the cavity bottoms by the upper leakage flow. The low temperature in the SS cavities also comes from the accumulation of the injected fluid. The cavity flow morphology differs with the injection orientation, which finally determines the inner flow and thermal condition.
3.2.2. The TLMFR and tip thermal load _ TLF =m _ 0 ) and heat Figs. 27 and 28 plot the normalized TLMFR (m flux (q/q0) on the blade tip against the injection positions, respectively. These two parameters are always lower in the cooled cases and changes slightly with the injection position. The leakage inflow rate is reduced by up to 28.3% in the P1-0° case, while the minimum of the total heat flux is about 82.6% of the flat tip in the P3-180° case. 4. Conclusion The effect of the injection orientation and position on the tip leakage flow has been studied in the honeycomb tip numerically. The results show that the tip leakage flow and cooling differ with the orientation and position. The main conclusions are listed as follow. 1. When the cooling injection is located at the bottom center, the optimal orientation is the same for suppressing the tip leakage flow, but opposite to that for cooling the honeycomb tip. The relative casing motion reserves the above improvement and helps to reduce the tip leakage flow, while the thermal condition on the blade tip remains unchanged when increasing the casing speed. In detail, for the stationary cases, the TLMFR is
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Fig. 26. Contours of the dimensionless temperature (h) and velocity vectors inside the gap (aori = 180°).
Fig. 27. Distributions of the normalized TLMFR against the injection position. Fig. 28. Histogram of the normalized heat flux (q/q0) on the blade tip.
reduced by about 27.8% and the total pressure loss by about 4.7% for the orientation angle of 30°, compared with the flat tip. The heat flux on the honeycomb tip drops up to about 19.1% for the orientation angle of 210°.
2. The injection flow feature can be divided into the compact type and expanded type. The compact injection follows the injection orientation until out of the cavity. The expanded injection
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trends to be restricted into the bottom corners by the upper leakage flow, covering and cooling the honeycomb tip. The pressure field inside the gap becomes gentle and the pressure gradient drops at the gap entrance. Besides, the flow angle has been improved around the gap. 3. Compared with the flat tip, the total thermal load increases on the honeycomb tip but decreases on the suction surface. After adding the cooling injections, the cooling effectiveness is much higher on the honeycomb tip than the suction surface. The dimensionless temperature of the tip leakage vortex decreases, and the sweeping effect on the suction surface is weakened as the passage vortex moves away from the suction surface. 4. For the orientation angle of 0° and 180°, when the injection position moves along the orientation direction, the injected fluid trends to attach to the facing sidewall. Besides, the TLMFR decreases slightly for both orientations.
Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements The authors acknowledge the support of the China Postdoctoral Science Foundation (No. 2018M631928). Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.118633. References [1] R.S. Bunker, Axial turbine blade tips: function, design, and durability, J. Propul. Power 22 (2006) 271–285, https://doi.org/10.2514/1.11818. [2] N.V. Nirmalan, C.B. Jeremy, Experimental investigation of aerodynamic losses of different shapes of a shrouded blade tip section, ASME Paper No. GT200568903, 2005. https://doi.org/10.1115/GT2005-68903. [3] B. I. Mamaev, M.M. Petukhovsky, A.V. Pozdnyakov, Shrouding the first blade of high temperature turbines, ASME Paper No. TBT2013-2001, 2013. https://doi. org/10.1115/TBTS2013-2001. [4] M. Zhang, Y. Liu, T. Zhang, M. Zhang, Y. He, Aerodynamic optimization of a winglet-shroud tip geometry for a linear turbine cascade, J. Turbomach. 139 (2017) 101011, https://doi.org/10.1115/1.4036647. [5] Z. Zou, F. Shao, Y. Li, W. Zhang, A. Berglund, Dominant flow structure in the squealer tip gap and its impact on turbine aerodynamic performance, Energy 138 (2017) 167–184, https://doi.org/10.1016/j.energy.2017.07.047. [6] J.D. Coull, N.R. Atkins, H.P. Hodson, Winglets for improved aerothermal performance of high pressure turbines, J. Turbomach. 136 (2014) 091007, https://doi.org/10.1115/1.4026909.
[7] X. Yan, Y. Huang, K. He, J. Li, Z. Feng, Numerical investigations into the effect of squealer–winglet blade tip modifications on aerodynamic and heat transfer performance, Int. J. Heat Mass Transf. 103 (2016) 242–253, https://doi.org/ 10.1016/j.ijheatmasstransfer.2016.07.058. [8] G. Chen, W.N. Dawes, H.P. Hodson, Numerical and experimental investigation of turbine tip gap flow, AIAA Paper No. 93-2253, 1993. https://doi.org/10.2514/ 6.1993-2253. [9] M. Niu, S. Zang, Experimental and numerical investigations of tip injection on tip clearance flow in an axial turbine cascade, Exp. Therm Fluid Sci. 35 (2011) 1214–1222, https://doi.org/10.1016/j.expthermflusci.2011.04.009. [10] R.J. Volino, Control of Tip Leakage in a High Pressure Turbine Cascade Using Tip Blowing, ASME Paper No. GT2016-56511, 2016. https://doi.org/10.1115/ GT2016-56511. [11] P.J. Newton, G.D. Lock, S.K. Krishnababu, H.P. Hodson, W.N. Dawes, Aerothermal investigations of tip leakage flow in axial flow turbines—part III: tip cooling, J. Turbomach. 131 (2009) 11008, https://doi.org/10.1115/ 1.2950060. [12] K. He, Investigations of film cooling and heat transfer on a turbine blade squealer tip, Appl. Therm. Eng. 110 (2017) 630–647, https://doi.org/10.1016/j. applthermaleng.2016.08.173. [13] M. Rezasoltani, K. Lu, M.T. Schobeiri, J.C. Han, A combined experimental and numerical study of the turbine blade tip film cooling effectiveness under rotation condition, J. Turbomach. 137 (2015) 11008, https://doi.org/10.1115/ 1.4028745. [14] K. Lu, M.T. Schobeiri, J.C. Han, Numerical simulation of film cooling on rotating blade tips within a high-pressure turbine, ASME Paper No. GT2013-94806, 2013. https://doi.org/10.1115/GT2013-94806. [15] C. Zhou, H. Hodson, I. Tibbott, M. Stokes, The aerothermal performance of a cooled winglet tip in a high pressure turbine cascade, J. Turbomach. 135 (2013) 031005, https://doi.org/10.1115/1.4006611. [16] X. Yan, Y. Huang, K. He, Investigations into heat transfer and film cooling effect on a squealer-winglet blade tip, Int. J. Heat Mass Transf. 115 (2017) 955–978, https://doi.org/10.1016/j.ijheatmasstransfer.2017.08.090. [17] Q. Zhang, L. He, Turbine blade tip aero-thermal management: some recent advances and research outlook, J. Global Power Propulsion Soc. 1 (2017) 271– 287, https://doi.org/10.22261/JGPPS.K7ADQC. [18] C.H. Lim, G. Pullan, P. Ireland, Influence of film cooling hole angles and geometries on aerodynamic loss and net heat flux reduction, J. Turbomach. 135 (2013) 051019, https://doi.org/10.1115/1.4023088. [19] B. An, J. Liu, S. Zhou, X. Zhang, C. Zhang, Film cooling investigation of a slotbased diffusion hole, ASME Paper No. GT2016-56175, 2016. https://doi.org/10. 1115/GT2016-56175. [20] M.A. Pakhomov, V.I. Terekhov, A.A. Khalatov, I.I. Borisov, Film cooling effectiveness with injection through circular holes embedded in a transverse trench, Thermophys. Aeromech. 22 (2015) 329–338, https://doi.org/10.1134/ S0869864315030075. [21] C. Han, J. Ren, H. Jiang, Multi-parameter influence on combined-hole film cooling system, Int. J. Heat Mass Transf. 55 (2012) 4232–4240, https://doi.org/ 10.1016/j.ijheatmasstransfer.2012.03.064. [22] Y. Fu, F. Chen, H. Liu, Y. Song, Experimental and numerical study of honeycomb tip on suppressing tip leakage flow in turbine cascade, J. Turbomach. 140 (2018) 061006, https://doi.org/10.1115/1.4039049. [23] Y. Wang, Y. Song, J. Yu, F. Chen, Effect of cooling injection on the leakage flow of a turbine cascade with honeycomb tip, Appl. Therm. Eng. 133 (2018) 690– 703, https://doi.org/10.1016/j.applthermaleng.2018.01.090. [24] Y. Wang, Y. Song, J. Yu, F. Chen, Numerical study of the effect of the cavity depth on the leakage control in a cooled honeycomb-tip turbine cascade, Appl. Therm. Eng. 138 (2018) 292–299, https://doi.org/10.1016/j. applthermaleng.2018.04.088.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Effect of the injection orientation and position on the leakage flow in a honeycomb-tip turbine cascade Yabo Wang, Yanping Song, Jianyang Yu ⇑, Fu Chen Institute of Propulsion Theory and Technology, Harbin Institute of Technology, Harbin 150001, China
a r t i c l e
i n f o
Article history: Received 24 January 2019 Received in revised form 16 April 2019 Accepted 22 August 2019 Available online 6 September 2019 Keywords: Honeycomb tip Injection orientation Injection position Tip leakage flow Tip cooling
a b s t r a c t The effect of the cooling injection orientation and position on the tip leakage flow has been studied numerically in a honeycomb-tip turbine cascade. The injected fluid enters each honeycomb cavity through the bottom pipe at a fixed incident angle. The effect of the relative casing motion with six casing speeds is considered. The Reynolds-averaged Navier-Stokes (RANS) method and k-x turbulence model were used in the three dimensional computations. Then the leakage mass flow rate and the averaged total pressure loss are evaluated. The static pressure and limiting streamlines on the casing are discussed and the flow direction around the gap are extracted to precisely analyze the leakage feature. Besides, the thermal conditions on the blade tip and suction surface are described by the Nusselt number and adiabatic film cooling effectiveness. Finally, the dimensionless temperature contours and velocity vectors inside the gap are plotted to explore the effect of the injection position. The results indicates that the injection feature mainly depends on the injection orientation and finally determines the aerodynamic and thermodynamic performance. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The tip leakage flow (TLF) induces high energy consumption and serious thermal load on the turbine rotor tip. Relative to other tip designs aimed at relieving the TLF, the shroud tip eliminates the traditional TLF and maintains the lowest aerodynamic loss [1]. In order to reduce the additional blade stress due to this extra tip weight, the scalloped shroud [2] and local cut shroud [3] were proposed. Recently, the winglet-shroud was presented to reduce the total pressure loss by about 2/3 of the reduction by the full shroud [4]. The unshrouded tip designs, such as the squealer tip, the winglet tip and other combined designs, have been widely studied. Zou et al. [5] pointed out that the scraping vortex in the squealer tip acted as an aero-labyrinth to reduce the equivalent leakage outflow area. Coull et al. [6] concluded that the winglet overhangs reduced the aerodynamic loss by altering the leakage flow direction and outflow location. The tip leakage vortex (TLV) moved away from the suction surface, resulting in lower heat transfer there. Yan et al. [7] found that the squealer-winglet tip could further reduce the loss and weaken the tip heat transfer on the basis of the conventional squealer tip. Moreover, the aerodynamic effect
⇑ Corresponding author. E-mail address: [email protected] (J. Yu). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118633 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
of the cooling injections should be considered in the parameter studies and optimization designs for the above tip designs. Chen et al. [8] indicated that the secondary injection into the gap had the ability to suppress the TLF. Niu et al. [9] confirmed this effect and pointed out that the tip heat transfer varied with injection position. The experiment by Volino [10] further showed that inclined injection near the maximum loading could reduce the total pressure loss most effectively. This means that the cooling injection contains the ability to block the TLF while providing the tip cooling protection. Interestingly, Newton et al. [11] observed that the cooling injection located at the separation bubble would be better in the tip protection with the mass flow rate (MRF) close to the leakage outflow. However, the current tip cooling mainly focuses on reducing local high heat transfer or leakage inflow temperature. For example, the squealer tip cooling is usually realized by the cooling injection from the tip holes [12–14] along or parallel to the camber line and the holes on the pressure surface near the casing [12,13]. Similar cooling arrangement applied in winglet tip [15] and squealerwinglet tip [16] did reduce the loss and thermal load. But the mixing cooperation between the injected fluid and the TLF are no longer taken into account. Since the injected fluid destroys the TLF field within the gap, the tip designs would no longer be the optimal choice [17]. Meanwhile, Lim et al. [18] summarized some guidelines on the hole angles to balance the aerodynamic loss and
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Nomenclature Cax Cp H k _ m _ TLF m Ma n Nu Nu p p* q r T V v x y y+ z
blade axial chord [m] static pressure coefficient [–] blade span [m] turbulent kinetic energy [–] mass flow rate [kg s1] tip leakage mass flow rate [kg s1] Mach number [–] rotor speed [rpm] Nusselt number [–] span-wise averaged Nusselt number [–] static pressure [Pa] total pressure [Pa] heat flux [W m2] radius of the rotor tip [m] temperature [K] velocity [m s1] fluctuation velocity [m s1] span-wise direction pitch-wise direction dimensionless wall distance [–] axial direction
Greek
ainc aori apit apit ayaw ayaw q
incident angle [°] orientation angle [°] pitch angle [°] span-wise averaged pitch angle [°] yaw angle [°] span-wise averaged yaw angle [°] density [kg/m3]
h
j g g s
-
non-dimensional temperature [–] thermal conductivity (0.0261 W/(mK)) adiabatic film cooling effectiveness [–] span-wise averaged adiabatic film cooling effectiveness [–] tip gap height [m] total pressure loss coefficient [–] mass flow averaged total pressure coefficient [–]
Subscripts 0 cascade inlet 1 cascade outlet aw adiabatic wall c injection inlet rms root-mean-square Abbreviations FT flat tip HT honeycomb tip LE leading edge MFR mass flow rate PS pressure side PVC passage vortex near the casing SS suction side TE trailing edge TLF tip leakage flow TLMFR tip leakage flow rate TLV tip leakage vortex
heat transfer from the experiments. A variety of hole shapes on simple models also provide new elements in the film cooling design. The study on the diffusion holes by An et al. [19] indicated that the slot-shaped holes contained better cooling coverage than fan-shaped holes. Besides, the trench attached to the traditional holes raised the film cooling effectiveness downstream [20], while
double-jet produced anti-kidney vortexes and a more uniform cooling coverage [21]. The investigation by Fu et al. [22] on the honeycomb tip indicated that the cavity flow helped to suppress the TLF. Wang et al. [23] implemented tangential injections to strengthen the cavity flow to block the TLF. Later on, another study on the cavity depth was carried out and described the enhancement mechanism of cavity vortices preliminarily [24]. However, the injection
Fig. 1. Schematic diagram of the honeycomb tip and cooling injection.
Fig. 2. Schematic diagram of the orientation angle and inclined angle.
Y. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118633 Table 1 Case information for the grid independency validation (HT). Span-wise nodes Grid1 Grid2 Grid3 Grid4 Grid5
111(11) 121(21) 131(31) 141(41) 151(51)
Cell number 6
3.81 10 4.51 106 5.21 106 5.91 106 6.60 106
TLMFR 2.689%ṁ0 2.691%ṁ0 2.649%ṁ0 2.653%ṁ0 2.654%ṁ0
3
vector AA0 is parallel to the YZ plane and passes through the symmetry line of honeycomb row. Then in the enlarged views, the pipe of 0.8 mm diameter is placed at each bottom center (O) by default. Fig. 2 describes the orientation angle and inclined angle in detail. The vector OC expresses the injection direction and its projection on the bottom plane (YZ) is OB. The inclined angle (ainc ) rising from OB to OC remains 30° in the present study. The orientation angle (aori ) rotating from OA to OB increases every 30°. Thus, a total of 12 angles from 0° to 330° are included. The orientation angle of 360° also indicates 0°. Besides, the gap height (s) and the cavity depth are both given 1% of the blade span (H). The internal chamber is not concerned in the present calculations for simplification. Particularly, the baseline cases, namely the flat tip and honeycomb tip, are abbreviated as FT and HT, respectively. The cooled cases are named according to the injection position and orientation, separated by a hyphen (-). For example, the CH-0° case indicates that the injection pipe is located at the center of each cavity bottom and its orientation angle is 0°. 2.2. Computational method and turbulence model
Fig. 3. Grid independency validation: the axial distributions of the leakage outflow rate along the SS profile (HT).
orientation and position were not considered completely in the former studies. So the present study focuses on the effect of the injection orientation on the TLF control and tip cooling. The flow feature of the injected fluid are explored. Then the flow field inside the gap and the suction surface cooling are also considered. Finally, the effect of the injection position along the orientation direction is discussed by the inner temperature field. 2. Numerical model and method 2.1. Description of the numerical model The cascade profile is a magnified version of the blade tip in a high-pressure turbine rotor [22]. Fig. 1 provides the schematic diagram of the honeycomb tip, whose geometry and honeycomb arrangement remain the same with the experiment [22]. The
The cascade boundary settings are consistent with the experiment [22]. The no-slip adiabatic or isothermal wall condition is adopted on the surface of the tip and cavities, in order to calculate the cooling effectiveness or Nusselt number. The injection total temperature is 30.0 K higher than the cascade inlet, while the injection total pressure is 99% of the cascade inlet. Finally, the total MFR from the injection pipes is about 0.36% of the main flow. The grid information of the computational domain has been shown in Fig. 1. The dimensionless mesh height y+ is ensured less than 1 on the blade surface to predict the near-wall flow field accurately. Besides, the passage grid remains consistent for all cases, which weakens the numerical disturbance by grid difference. The unstructured grid is employed to gently connect the cavities and pipes. In the present study, the total pressure loss coefficient (-) is defined as,
_ c pc ðm _ c Þp _ 0 p0 þ m _ 0þm m -¼ _ c pc p1 _ 0 p0 p1 þ m m
where p is the local total pressure, p0 the total pressures of the cas_ 0 is cade inflow, and p1 the static pressure of the cascade outflow. m _ c the injection MFR. the cascade inflow mass flow rate (MFR), and m The static pressure coefficient (Cp) is defined as,
Cp ¼
p p1 p0 p1
Fig. 4. Numerical method validation: (a) the axial distributions of the static pressure coefficient (Cp) at 97%H (b) the span-wise distributions of the pitch-wise averaged total pressure loss coefficient (-) at 130%Cax.
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_ TLF =m _ 0 ) and (b) the mass flow averaged total pressure loss (-) at 130%Cax. Fig. 5. Comparisons of (a) the normalized TLMFR (m
Fig. 6. Comparisons of the mass flow averaged loss coefficient (-): (a) the leakage inflow and (b) the leakage outflow.
where p is the local static pressure. The effect of the node number on the tip leakage mass flow rate (TLMFR) has been explored in the HT case. Table 1 lists the case information for the grid independency validation. The span-wise node number above the blade tip varies from 11 to 51. As the node number reaches 31, the TLMFR presents an asymptotic trend. Especially, compared with the thickest case (Grid5), the relative difference is ignorable (less than 0.4%) in the Grid4 case. Fig. 3 further compares the axial distributions of the leakage outflow rate. These lines almost overlaps with each other in the cases Grid3–Grid5. It is indicated that the critical node number is about 31, especially for the hump near 50% of the axial chord length (Cax). Finally, the Grid4 case is adopted in the following calculations. The cell number is about 5.4 106 in the FT case, and it comes up to 6.1 106 in cooled cases. The calculations are completed in the commercial software ANSYS CFX. The two-equation k-x turbulence model is used in solving the Reynolds-averaged Navier-Stokes (RANS) equations. The advantage of the present k-x model is the near-wall treatment at low Reynolds number. The numerical result in the baseline cases is compared with the experimental data [22] in validating the predicting accuracy. The static pressure on the blade surface near the tip and the span-wise loss distribution at 130%Cax (shown in Fig. 1) are plotted together with the measured data in Fig. 4. In detail, the SS pressure peak is associated with the development of the TLV. The over-estimation near 60%Cax indicates that the predicted TLV deviate from the experiment slightly. In Fig. 4(b), the loss in the two rectangles are affected by the TLV and the passage vortex near
the casing (PVC). For the FT case, the loss peak is well predicted in the upper rectangle, while the span-wise position of the loss peak is lower than the experiment in the other rectangle. Yet, both the two peaks is positioned well but over-estimated in the HT case. Firstly, the measuring points downstream the cascade may not be properly arranged to capture the flow features for both cases. The impropriate grid number there also affects the calculating result and post processing. Secondly, the default parameters of the k-x model may be not suitable for the current models and need to be further identified. But overall, the aerodynamic parameters have been well predicted by the k-x model. The validation of the SST model was also conducted in the previous work. The SST model is better is predicting the flow separation caused by the adverse pressure gradient. Thus, the k-x model is employed in all the present computations. Finally, it should be mentioned that there was no published or measured data about the tip heat transfer for the current cascade. Still, the thermodynamic validation was realized using another subsonic cascade in the previous study [23].
3. Result and discussion 3.1. Effect of the injection orientation on the TLF 3.1.1. The TLMFR and total pressure loss _ TLF =m _ 0 ) and the averaged total presThe normalized TLMFR (m
sure loss coefficient (-) are plotted against the injection orientation angle in Fig. 5. The mass flow rates of the leakage inflow
Y. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118633
Fig. 7. Isothermal surfaces (h = 0.2), colored by the normalized turbulence kinetic energy (k=V 2z;0 ).
Fig. 8. Three dimensional streamlines of the injected fluid, colored by the normalized velocity (V/Vz,0).
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and outflow no longer remain equal in the cooled cases. Although no significant reduction of the leakage outflow is realized by the cooling injection on the basis of the honeycomb tip, the leakage inflow rate drops by up to 27.8% in the CH-30° case, compared with the FT case. The leakage outflow might even increase slightly due to injected fluid supplement in the cases, whose orientation angle is between 60° and 300°. The averaged loss at 130%Cax in the cooled cases is lower than the baseline cases, except for the CH240° case. Compared with the FT case, the averaged loss is reduced by up to 4.7% at 130%Cax in the CH-30° case. The averaged loss (-) of the leakage inflow and outflow are compared in Fig. 6. The leakage inflow loss mainly comes from the upstream boundary layer and is reduced in a way similar to the inflow rate. The leakage outflow loss increases obviously in the HT case and then differs with the orientation angle after adding the cooling injections. It is noted that the leakage flow rate is below 3.2% of the main flow. That is, the passage flow provides more contribution in the downstream loss, which is not worsened by the cooling injections.
the small vortex on one or both sides of the injection. At this point, the streamlines keep close to the cavity bottom. Although some streamlines are broken near the cavity sidewalls, it can be inferred that the stagnant fluid will also turns to the cavity bottom after impacting the sidewall. 3.1.3. The flow field inside the gap Based on the injection features, four cooled cases are chosen in analyzing the flow field, that is, the cases CH-0°, CH-30°, CH-180° and CH-210°. The contours of the static pressure coefficient (Cp) and the limiting streamlines on the casing are shown in Fig. 9. The inner static pressure field inside the gap is disturbed apparently by the honeycomb tip and cooling injections. The lowpressure region at the PS middle diminishes in the HT case and trends to disappear as adding the cooling injections. The newly formed Cp gradient along the stream-wise direction fails to press enough passage fluid into the gap. Besides, the expansion of the high-pressure region near the LE also contributes to suppress the
3.1.2. The flow feature of the cooling injection The dimensionless temperature h is defined as,
h¼
T Tc T0 Tc
where T is the local temperature. The turbulence kinetic energy (k) is defined as,
k¼
1 2 v þ v 2y;rms þ v 2z;rms 2 x;rms
where vx,rms, vy,rms and vz,rms are the root-mean-square values of the fluctuation velocities. The temperature field is used to characterize the mixing of the injected fluid and leakage fluid. The isothermal surfaces (h = 0.2) colored by the normalized turbulence kinetic energy (k=V 2z;0 ) are shown in Fig. 7. The injection flow can be roughly divided into the compact type and expanded type, according to the isothermal surface morphology. These two types can be observed in different cavities in all the cases. Firstly, the compact type corresponds to a centralized isothermal surface. It can be inferred that this type keeps and even promotes the original feature of the cavity flow at some special orientations. Secondly, the expanded type appears as the honeycomb bottom is covered by the injected fluid, especially for the orientation angle of 90–240°. Thus, the expanded type would be better in protecting the honeycomb cavity from the thermal load. The injection feature also differs with the cavity position on the blade tip. In the front region near the leading edge (LE), the isothermal surfaces is small and compact due to the weak injection, illustrated in Fig. 8(a). When it comes to the tip middle, the isothermal surface becomes longer or spreads on the cavity bottom. Then in the back region near the trailing edge (TE), the injection feature is similar to that at the tip middle. Meanwhile, the turbulence kinetic energy maintains at a relatively low level for the expanded type, indicating a gentle mixing between the injected fluid and leakage fluid. Three honeycomb rows, namely HR1, HR2 and HR3, have been marked in Fig. 7(a). The three dimensional streamlines of the injected fluid insides the three honeycomb rows are plotted in Fig. 8, colored by the normalized velocity (V/Vz,0). It is noted that the PS injection speed is lower than the SS. Firstly, the injected fluid follows the injection orientation until rushing out of the cavity, which corresponds to the compact injection flow. In particular, the low-speed injected fluid in the near-LE region is involved into the cavity vortices easily. Secondly, for the expanded type, the injected fluid impacts the honeycomb sidewall and then rolls into
Fig. 9. Contours of the static pressure coefficient (Cp) and the limiting streamlines on the casing.
Fig. 10. Disgram of the reattachment lines and separation lines on the casing.
Y. Wang et al. / International Journal of Heat and Mass Transfer 144 (2019) 118633
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Fig. 11. Distributions of the static pressure coefficient (Cp) and its gradient: (a) Line1 and (b) Line2.
Fig. 12. Schematic vectors of the horizontal velocity (Vyz) around the gap.
leakage inflow. Besides, the PS reattachment line and SS separation line separate the leakage inflow and outflow from the passage flow, respectively. This means the leakage fluid is limited from the reattachment line to the separation line in the near-casing region. Then the coordinates of these two featured lines are determined and plotted together in Fig. 10. In the enlarged views, both two lines are the farthest from the blade profile in the FT case and move toward the adjacent blade surface in the HT case. The cooling injection narrows the leakage inflow range but fails to reduce the outflow range, based on the HT case. In particular, the static pressure and its gradient on the two lines, namely Line1 and Line2 (marked in Fig. 10), are extracted in Fig. 11. Line1 passes through the LE along the leakage direction roughly, and Line2 crosses the low-pressure region at the tip middle. The separation bubble induces the Cp drop just downstream
Fig. 13. Axial distributions of the span wise averaged parameters: (a) pitch angle (apit ), (b) yaw angle (ayaw ) and (c) leakage rate around the gap.
the gap entrance. A gentle distribution of the static pressure is newly formed, indicating a weaker leakage inflow, especially on Line2. Furthermore, the separation bubble can be positioned precisely according to the zero Cp gradient. The Cp drop always means an increasing flow velocity for the present subsonic TLF. In the FT case, the Cp gradient reaches its minimum before the separation bubble, when the leakage fluid accelerates into the gap. Interestingly, the Cp gradient after the separation bubble remains a
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Fig. 14. Histograms of (a) the normalized area and (b) heat flux on the tip, honeycomb sidewalls and bottoms.
Fig. 15. Contours of the normalized turbulence kinetic energy (k=V 2z;0 ) inside the gap at: (a) 25%s and (b) 25%s.
Fig. 17. Contours of the adiabatic film cooling effectiveness (g) on the blade tip (Top view).
Fig. 16. Contours of the Nusselt number (Nu) on the blade tip (Top view).
negative constant along Line1 and keeps positive along Line2. In the other cases, the minimum of the Cp gradient increases with the decrease of the leakage inflow rate. The Cp gradient becomes ups and downs under the disturbance of the honeycomb cavities and injections.
In Fig. 12, the horizontal velocity (Vyz) is defined as the projected component of the local velocity (V) on the YZ plane. Then Fig. 12 presents the schematic vectors of this projected velocity around the gap. The PS vectors end at the profile, while the SS vectors start from the profile. For the leakage inflow, the vector lengths decrease obviously, compared with the FT case. The PS vectors rotate negatively around the x-axis, while the SS vectors positively. However, the change of the leakage outflow vectors are complex along the SS profile. In Fig. 13, the pitch angle (apit) is defined on the YZ plane and is the angle from the positive z-axis to the vector Vyz. The yaw angle
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(ayaw) is defined on the XV plane as the angle rising from the vector Vyz to V. Then the two angles and local leakage flow rate are spanwise averaged and plotted around the gap. As marked in the dashed ellipse, the leakage fluid flows around the LE under the obstruction of the near-LE high pressure in the FT case. Then, an opposite change of the pitch angle occurs on both sides of the LE, since the TLF suppression is enhanced by the honeycomb tip and cooling injections. In Fig. 13(b) and (c), the distributions of the
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yaw angle and leakage flow rate can be divided according to the leakage inflow and outflow. The starting position of the leakage outflow is advanced by the cooling injection, confirmed by the increased pitch angle there. The positive yaw angle means that the leakage inflow rushes toward the casing, while the negative value indicates a smooth outflow after the mixing inside the gap. Thus, the leakage inflow leans toward the tip, except for the near-LE region.
Fig. 18. Axial distributions of the pitch-wise averaged (a) Nusselt number (Nu) and (b) adiabatic film cooling effectiveness (g) on the blade tip.
Fig. 19. Secondary flow filed in the upper passage and the thermal condition on the suction surface.
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Fig. 20. Contours of the adiabatic film cooling effectiveness (g) on the suction surface.
_ c =m _ 0 ) against the normalized casing speed Fig. 22. The normalized injection MFR (m (V y;casing =V z;0 ).
Nu ¼
qC ax
jðT w T 0 Þ
where q is the local wall heat flux, T w the isothermal wall temperature and T 0 the inflow temperature. j is the thermal conductivity. The adiabatic film cooling effectiveness (g) is defined as,
g¼
Fig. 21. Normalized heat flux in the rectangle (S1) on the suction surface.
3.1.4. The thermal condition on the blade tip The total area and heat flux on the tip surface, honeycomb sidewalls and bottoms are collected in Fig. 14(a) and (b), respectively. The total heat flux is higher in the HT case than the FT case and decreases as adding the cooling injections. The maximum reduction by about 19.1% is achieved in the CH-210° case, compared with the FT case. In detail, the remaining tip surface remains about 45.4% area of the flat tip but the total heat flux on it reaches 67.6% in the HT case. Then the heat flux on the remaining tip surface is reduced by the cooling injections. Yet, the heat flux per unit area is still higher than the FT case. It is observed that the cavity sidewalls and bottoms always maintain at a low level of heat flux. The contours of the non-dimensional turbulence kinetic energy (k=V 2z;0 ) are presented in Fig. 15. The two span-wise planes are at 25%s and 75%s inside the gap. The inner flow field is disturbed more strongly at 25%s than at 75%s. At 25%s, the honeycomb tip breaks the flat region affected by the PS separation bubble in the FT case. The cooling injections could further diminish this featured region. A more uniform distribution of the turbulence kinetic energy appears over the section, especially in the front region. Besides, the honeycomb tip and cooling injections also disturbs the TLF at 75%s. The Nusselt number (Nu) is defined as,
Table 2 The relative casing speed (Vy,casing/Vz,0). nLISA;R [rpm] Vy,casing [m/s] Vy,casing/Vz,0
0 0 0
900 6.28 0.27
1800 12.57 0.54
2700 18.85 0.81
3600 25.13 1.08
4800 33.51 1.45
T aw T 0 Tc T0
where T aw is the adiabatic wall temperature and T c the injected fluid temperature. The contours of the Nusselt number (Nu) on the blade tip are presented in Fig. 16. In the FT case, the leakage inflow impacts the flat tip after crossing the PS separation bubble, resulting in the region of high heat transfer. The honeycomb tip discrete the Nu distribution on the remaining tip and obtains a low level of heat transfer on the honeycomb bottoms. The cooling injections could weaken the heat transfer on the honeycomb bottoms, especially in the dash ellipses. The accumulation of the injected fluid also helps to weaken the SS heat transfer there. Similar features can be observed in the contours of the adiabatic film cooling effectiveness (g) in Fig. 17. The lower heat transfer often corresponds to a higher cooling effectiveness. The cooling feature on honeycomb bottoms differs with the injection orientation. In Fig. 17(a) and (b), the injected fluid rushes toward the facing sidewalls, leading to relatively small high-cooling regions at the bottom corners. However, in Fig. 17(c) and (d), the injections effectively cools the whole bottoms in the dash ellipses, with the optimal orientation angle of 210°. It is confirmed that the injected fluid does not flow downstream directly but spreads over the whole cavity bottoms. In Fig. 18, the Nusselt number and adiabatic film cooling effectiveness are pitch-wise averaged, and their axial distributions become fluctuating due to the honeycomb tip in HT case. It is confirmed that the Nu on the honeycomb sidewalls and bottoms is much lower than the tip. Furthermore, the cooling injections could reduce the heat load on these walls significantly. The g remains higher on the honeycomb sidewalls and bottoms than the tip, especially for the orientation angles of 180° and 210°. The cooling effect near the LE and TE trends to diminish due to the lack of cooling protection. 3.1.5. The heat transfer on the suction surface The secondary flow field in the upper passage and the thermal condition on the suction surface are shown in Fig. 19. The averaged velocity of the passage flow at 50%H is considered as the main flow
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_ TLF =m _ 0 ) and (b) the mass flow averaged total pressure loss (-) at 130%Cax. Fig. 23. Comparisons of (a) the normalized TLMFR (m
ability is stronger in the CH-210° case in Fig. 20, its heat flux maintains at a similar level with the HT case. Therefore, it can be inferred that the thermal load on the suction surface is mainly affected by the secondary vortices more than the cooling effect. 3.1.6. The relative casing motion effect For the cases FT, HT, CH-0° and CH-180°, the casing moves towards the positive y-axis direction in this section. The casing speeds are obtained by scaling down the realistic rotational speed of the turbine rotor, as defined in the speed formula below.
V y;casing ¼
Fig. 24. Schematic diagram of the injection position (aori = 0° and aori = 180°).
for each axial section. The secondary velocity is the component perpendicular to the main flow direction. It should be mentioned that the h on the blade surface is lower than the main flow. The passage fluid would be cooled, when it flows over the blade surface. Thus in the FT case, the leakage fluid close to the tip surface is of relatively low h and mainly flows into the TLV. Firstly, the TLV sweeps on the suction surface from the reattachment line to separation line. Secondly, the shearing layer between the TLV and PVC carries passage fluid of high h toward the suction surface. Both the two process results in the region of high heat transfer near the reattachment line, especially at 50%Cax. The heat transfer is at a relatively low level in the region near the separation line. In the HT case, the heat flux increases on the blade tip but the leakage flow rate decreased, indicating that the leakage outflow is of lower h than the FT case. After adding the cooling injections, although the heat flux on the blade tip is reduced, the injected fluid of low h helps to reduce the h of the leakage fluid. Then it is observed that the range of low h expands in the TLV affected region at 50%Cax. Meanwhile, the PVC has evolved into the PVC1 and PVC2 at 70% Cax in advance, and the PVC2 core gets further away from the suction surface at 90%Cax. Thus, the sweeping effect of the shearing layer on the suction surface is weakened. That is why the heat transfer is reduced, compared with FT case. As shown in Fig. 20, the cooling intensity on the suction surface is much weaker than that on the blade tip. The cooling intensity differs with the injection orientation in a triangular region, with the highest g concentrated in the front part. Then the normalized heat flux in the rectangular region S1 are compared in Fig. 21. The heat flux is reduced by about 7.5% in the HT case and by about 11.0% in the CH-30° and CH-330° cases. Although the cooling
nLISA;R 2p rLISA;R Ma MaLISA;R 60
where nLISA;R is the rotating speed, r LISA;R the radius of the rotor tip, and MaLISA;R the inlet Mach number of the rotor. A total of six turbine rotor speeds, including the stationary condition and design speed (2700 rpm), are selected. Then the normalized casing speeds (Vy,casing/Vz,0) are listed in Table 2. _ c =m _ 0 ) against the casing speed The injection MFR (m (V y;casing =V z;0 ) is shown in Fig. 22. The injection MFR is always maintained at a relative level, about 0.36 or 0.37 percent of the main flow for the stationary cases. The injection MFR decreases with the casing speed linearly, indicating that the injection strength is weakened. _ TLF =m _ 0 ) and the averaged total presThe normalized TLMFR (m
sure loss coefficient (-) are plotted against the relative casing speed in Fig. 23. The TLMFR decreases as increasing the casing speed, confirming the suppression of the casing motion on the TLF. Yet, the averaged loss at 130%Cax distributes non-linearly against the casing speed. It should be mentioned that the casing motion fails to eliminate the performance improvement. Furthermore, the thermal condition on the blade tip is almost unaffected by the relative casing motion in the injection cases. 3.2. Effect of the injection position on the TLF The injection position is considered only for the orientation angle of 0° and 180°. As shown in Fig. 24, five injection positions are selected by equally dividing the bottom centerline, which is parallel to the vector AA0 . The positions are labeled as P1–P5, and the P3 is located at the bottom center, corresponding to the above cooled cases. 3.2.1. The temperature field inside the gap Figs. 25 and 26 show the contours of the dimensionless temperature (h) and the velocity vectors inside the gap. The vertical sections are the symmetry planes of the honeycomb rows, namely
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Fig. 25. Contours of the dimensionless temperature (h) and velocity vectors inside the gap (aori = 0°).
HR1, HR2 and HR3 in Fig. 7(a). The vectors are plotted by the projected velocities, whose lengths have nothing to do with the velocity magnitude. It is also noted that the h contour greater than 1 has been removed. For the two positions, the injected fluid rushes toward the facing sidewall and mixes with the leakage fluid just above. As the injection position gets close to the facing sidewall, the mixing process is shortened as the injected fluid trends to attach to the facing sidewall. The injection intensity is stronger for the SS pipes, while even no fluid has been injected from some PS pipes at Sta5. In detail, for the orientation angle of 0° in Fig. 25, the leakage fluid impacts on the SS sidewalls and then turns to the cavity bottoms. When the leakage fluid flows back to the PS sidewalls, the injection always keeps tangential to this backflow and mixes with it. The injection also provides the opposite momentum, and this helps to obstruct the TLF. In Fig. 26, the leakage fluid also turns back in the near-LE cavities, pushing the injected fluid toward the PS sidewalls. Yet, the above cavity backflow has disappeared in most cavities, since the injection follows the TLF but is opposite to the backflow. Thus, the injected fluid or mixture is restricted on the cavity bottoms by the upper leakage flow. The low temperature in the SS cavities also comes from the accumulation of the injected fluid. The cavity flow morphology differs with the injection orientation, which finally determines the inner flow and thermal condition.
3.2.2. The TLMFR and tip thermal load _ TLF =m _ 0 ) and heat Figs. 27 and 28 plot the normalized TLMFR (m flux (q/q0) on the blade tip against the injection positions, respectively. These two parameters are always lower in the cooled cases and changes slightly with the injection position. The leakage inflow rate is reduced by up to 28.3% in the P1-0° case, while the minimum of the total heat flux is about 82.6% of the flat tip in the P3-180° case. 4. Conclusion The effect of the injection orientation and position on the tip leakage flow has been studied in the honeycomb tip numerically. The results show that the tip leakage flow and cooling differ with the orientation and position. The main conclusions are listed as follow. 1. When the cooling injection is located at the bottom center, the optimal orientation is the same for suppressing the tip leakage flow, but opposite to that for cooling the honeycomb tip. The relative casing motion reserves the above improvement and helps to reduce the tip leakage flow, while the thermal condition on the blade tip remains unchanged when increasing the casing speed. In detail, for the stationary cases, the TLMFR is
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Fig. 26. Contours of the dimensionless temperature (h) and velocity vectors inside the gap (aori = 180°).
Fig. 27. Distributions of the normalized TLMFR against the injection position. Fig. 28. Histogram of the normalized heat flux (q/q0) on the blade tip.
reduced by about 27.8% and the total pressure loss by about 4.7% for the orientation angle of 30°, compared with the flat tip. The heat flux on the honeycomb tip drops up to about 19.1% for the orientation angle of 210°.
2. The injection flow feature can be divided into the compact type and expanded type. The compact injection follows the injection orientation until out of the cavity. The expanded injection
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trends to be restricted into the bottom corners by the upper leakage flow, covering and cooling the honeycomb tip. The pressure field inside the gap becomes gentle and the pressure gradient drops at the gap entrance. Besides, the flow angle has been improved around the gap. 3. Compared with the flat tip, the total thermal load increases on the honeycomb tip but decreases on the suction surface. After adding the cooling injections, the cooling effectiveness is much higher on the honeycomb tip than the suction surface. The dimensionless temperature of the tip leakage vortex decreases, and the sweeping effect on the suction surface is weakened as the passage vortex moves away from the suction surface. 4. For the orientation angle of 0° and 180°, when the injection position moves along the orientation direction, the injected fluid trends to attach to the facing sidewall. Besides, the TLMFR decreases slightly for both orientations.
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