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Experimental investigation on the leading edge film cooling of cylindrical and laid-back holes with different hole pitches
International Journal of Heat and Mass Transfer 55 (2012) 6832–6845
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Experimental investigation on the leading edge film cooling of cylindrical and laid-back holes with different hole pitches Cun-liang Liu ⇑, Hui-ren Zhu, Zong-wei Zhang, Du-chun Xu School of Power and Energy, Northwestern Polytechnical University, 160#mail-box, 127 You Yi Xi Lu, Xi’an, 710072, China
a r t i c l e
i n f o
Article history: Received 20 February 2012 Received in revised form 7 June 2012 Accepted 29 June 2012 Available online 1 August 2012 Keywords: Turbine blade Leading edge Film cooling Laid-back hole Hole pitch Thermochromic liquid crystal Transient measurement
a b s t r a c t Experimental investigation has been performed to study the film cooling performances of cylindrical holes and laid-back holes on the turbine blade leading edge. Four test models are measured for four blowing ratios to investigate the influences of film hole shape and hole pitch on the film cooling performances. Film cooling effectiveness and heat transfer coefficient have been obtained using a transient heat transfer measurement technique with double thermochromic liquid crystals. As the blowing ratio increases, the trajectory of jets deviates to the spanwise direction and lifts off gradually. However, more area can benefit from the film protection under large blowing ratio, while the is also higher. The basic distribution features of heat transfer coefficients are similar for all the four models. Heat transfer coefficient in the region where the jet core flows through is relatively lower, while in the jet edge region is relatively higher. For the models with small hole pitch, the laid-back holes only give better film coverage performance than the cylindrical holes under large blowing ratio. For the models with large hole pitch, the advantage of laid-back holes in film cooling effectiveness is more obvious in the upstream region relative to the cylindrical holes. For the cylindrical hole model and the laid-back hole model with the same hole pitch, heat transfer coefficients are nearly the same with each other under the same blowing ratios. Compared with the models with large hole pitch, the laterally averaged film cooling effectiveness and heat transfer coefficient are larger for the models with small hole pitch because of larger proportion of film covering area and strong heat transfer region. Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved.
1. Introduction The desire for higher overall efficiency and higher specific power output in gas turbines renders the need for increase in turbine entry temperatures resulting in a need for effective cooling technologies. Film cooling is one of the major cooling technologies for protection of turbine airfoils from the hot gas stream. In a gas turbine, the leading edge of a turbine vane or blade often withstands higher heat loads than any part of the airfoil surface due to the higher temperatures and the increased heat transfer coefficients that occur around the stagnation line. Film cooling is typically applied on the leading edge through an array of hole rows. Increases in film effectiveness in the leading edge will lead to significant benefits in life and efficiency of the turbine blade. Cylindrical hole is the basic configuration for the leading edge film cooling. Cylinder or semi-cylinder model has been often employed by researchers [1] to model the blade leading edge. In this way, the leading edge film cooling can be investigated easily under different flow conditions. In Luckey et al. [2], experiments ⇑ Corresponding author. E-mail address: [email protected] (C.-l. Liu).
were conducted with a single row of spanwise-angled film holes for a range of blowing ratio. Karni and Goldstein [3] studied the effect of blowing ratio and injection location on the mass transfer coefficient of the leading edge region. Mehendale and Han [4,5] investigated the influences of high mainstream turbulence and mainstream Reynolds number on the leading edge film effectiveness and heat transfer coefficient using a blunt body with a semi-cylinder leading edge. Ekkad et al. [6] further presented the effects of coolant density and mainstream turbulence using a transient liquid crystal measurement technique. Ou and Rivir [7] studied the film effectiveness and the heat transfer coefficients on a large scale symmetric circular leading edge with three rows of film holes. The film hole configuration has a smaller injection angle of 20° and a larger hole pitch (p/d = 7.86). They also employed the transient liquid crystal measurement technique. Results showed that turbulence intensity had an attenuation on the film effectiveness as well as on the Frössling number for all blowing ratios. Kim et al. [8] used a cylindrical body model with three different arrangements of injection holes to study the film cooling characteristics under high and low Reynolds numbers. They tried to improve the film cooling performance by different arrangement of injection holes for the turbine blade leading edge region. To
0017-9310/$ - see front matter Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.06.090
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Nomenclature c d D Froe h M p ReD t T U X Y
specific heat of test plate (J/kg K) diameter of the film hole (m) diameter of semi-cylinder model (m) 0:5 Frössling number (¼ NuD =Re0:5 ) D ¼ ðhD=kÞ=ðqg U g D=lg Þ convective heat transfer coefficient [(W=m2 K)] blowing ratio (¼ qc U c =qg U g ) hole pitch (m) Reynolds number based on diameter of semi-cylinder model (¼ qg U g D=lg ) time (s) temperature (°C) velocity (m/s) streamwise coordinate originating at the stagnation line (m) coordinate normal to the model surface (m)
consider and investigate the effect of the oscillation of the stagnation line position, which was caused by the blade passing through wakes from upstream vanes, on the leading edge film cooling, Johnson et al. [9] developed an experimental facility and carried out the experimental study. Dyson et al. [10] measured the overall effectiveness of a simulated turbine blade leading edge model with matched Biot number to the engine conditions. Overall effectiveness was measured for pitch variation from 7.6d to 9.6d for a range of blowing ratio and attack angle. More information on the leading edge film cooling of cylindrical holes can be found in Han et al. [1]. Many studies show that using shaped holes is an effective way to improve the film cooling performance [11]. The study of Goldstein et al. [12] reported a significant increase in film cooling effectiveness as well as greater lateral coolant coverage for fan-shaped holes compared with standard cylindrical holes. Schmidt et al. [13], Gritsch et al. [14] and Yu et al. [15] further investigated the improvement in film cooling performance brought by laid-back hole, fan-shaped hole and laid-back fan-shaped hole. However, the above studies were performed on flat plate model. Until more recent time, shaped holes gradually came into consideration for the leading edge film cooling. Reiss and Bölcs [16] compared the
Z
spanwise coordinate (m)
Greek symbols a radially inclined angle of the film hole (°) g film cooling effectiveness q density (kg/m3) k thermal conductivity of test plate, (W/m K) l viscosity ( Kg/(ms)) Subscripts aw adiabatic wall c jet g mainstream i initial t = 0 s surface
film cooling performances of cylindrical holes, laid-back holes, and fan-shaped holes on a cylinder leading edge model with five hole rows. The effects of shaped holes with compound angle orientation were studied using the transient liquid crystal measurement technique. They found that laidback holes gave the best overall film cooling performance. The fan-shaped holes performed better than cylindrical holes, but not as well as laid-back holes. Cylinder model with three rows of radially inclined holes, including cylindrical holes, laid-back holes and tear-drop shaped holes, were investigated in Kim et al. [17] with an infrared thermography method. They showed that the holes with a laid-back type exit produced higher film cooling effectiveness than the tear-drop shaped holes. Both laid-back holes and tear-drop shaped holes were found to perform better than the cylindrical holes. Mouzon et al. [18] compared the film performances of laid-back holes and cylindrical holes on a three-row leading edge model using the infrared thermography method. They found that the laid-back holes resulted in much higher net heat flux reduction than the cylindrical holes. Falcoz et al. [19,20] investigated cylindrical holes, conical holes, and laid-back holes on a blunt model with numerical and experimental methods respectively. Experiment studies were
Fig. 1. Sketch of the experiment system.
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Fig. 2. Configurations of the test model.
Fig. 3. Configurations of the film holes.
performed with the transient liquid crystal measurement technique. Their results indicated that the laid-back holes had a better lateral film coverage. However, the best spanwise averaged film cooling effectiveness was achieved by conical holes. Lu et al. [21] also studied the effects of hole orientation and hole shape on the leading edge film cooling. They examined compound angle cylindrical holes and compound angle laid-back fan-shaped holes on a blunt model with a semi-cylinder leading edge. They found that the shaped holes produced much higher effectiveness than the cylindrical holes. For the compound angle holes, cooling effectiveness was improved at lower blowing ratios. Gao et al. [22] studied the effects of film hole geometry and angle on the turbine blade leading edge film cooling experimentally using the pressure sensitive paint technique (PSP). The leading edge was modeled by a semi-cylinder and an after-body. Four different film cooling hole configurations were compared: radial and compound angle cylin-
drical holes, radial and compound angle laid-back fan-shaped holes. The results showed that the shaped holes provided higher film cooling effectiveness than the cylindrical holes, particularly at higher average blowing ratios. The objective of the present study is to further explore the potential improvement of film cooling with shaped holes for the leading edge region. Film cooling performances of laid-back holes and cylindrical holes on the leading edge model have been investigated. Special attention is focused on the influence of hole pitch of the film holes. We know that large hole pitch can reduce the number of film holes thus resulting in a reduction of the coolant flux on a certain geometry and flow condition. But large hole pitch can also reduce the proportion of film covering area according to our experience. How much difference is there between large and small hole pitch for the leading edge film cooling performances of cylindrical holes and laid-back holes? That is what this paper intends to show. Transient liquid crystal measurement technique has been used in the present work to obtain detailed distributions of film cooling effectiveness and heat transfer coefficient. 2. Experimental apparatus and approach 2.1. Experimental apparatus Fig. 1 shows a schematic of the overall experimental setup. The mainstream travels through valves, settling chamber with three flow-conditioning screens in it, contraction section with a contraction ratio of 5.4-to-1 before entering the mesh heater. Moreover, another contraction with a contraction ratio of 2-to-1 is placed after the mesh heater to ensure a uniform mainstream entering the test tunnel which is a Perspex rectangular duct with 220 mm in width and 110 mm in height. The light source and the CCD camera for the liquid crystal measurement are placed outside of the test tunnel, as indicated in Fig. 1. The secondary flow travels through the flow meter, valve, air heater and a bypass system
C.-l. Liu et al. / International Journal of Heat and Mass Transfer 55 (2012) 6832–6845
Fig. 4. Liquid crystal image and calibration curves of the double-TLC.
Fig. 5. Distributions of local film cooling effectiveness under M = 0.7.
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Fig. 6. Distributions of local film cooling effectiveness under M = 1.
which consists of two solenoid valves and enters the test model from the bottom. In the present experiment, four test models with different filmhole configurations have been investigated. The material of these four models is Plexiglas with a conductivity of 0.17 W/m K. The test model is placed in the middle of the test channel with a distance of 90 mm to either side wall. Except for the film-hole configuration and the hole pitch, the other geometry parameters of the four models are the same with each other. Each test model is made up of a semi-cylinder which is used to model the leading edge and an after-body. Configurations of the test model from two perspective views are shown in Fig. 2. The semi-cylinder had a diameter D of 40 mm and wall thickness of 10 mm. The hollow cavity in the test model served as the secondary flow passage. The secondary flow in the passage is in a crossflow pattern which is also indicated in Figs. 2 and 3. Three rows of film holes are located at 0° (stagnation line) and 30° on either side of the leading edge model and arranged in stagger pattern. Two kinds of film hole row arrangement have been investigated: one with a hole pitch of 5d, and the other with a hole pitch of 8d where d denotes the diameter of the metering part of film hole. All the film holes are oriented in the radial (spanwise) direction and orthogonal to the local mainstream direction. Laid-back film hole and cylindrical hole with the same radially inclined angle a ¼ 30 have been are investigated and compared. The configurations of the film holes are
shown in Fig. 3. The laid-back film hole has an additional forward expansion of 10° from the film hole axis which produces a 3 mm longer hole-exit for both configurations relative to the cylindrical holes. The metering part of the laid-back hole has the same diameter of d = 3 mm as the cylindrical hole, and the length to diameter ratio of all the holes is 6.67. 2.2. Operating conditions The velocity and temperature of the mainstream were measured by the Pitot tube and thermocouples upstream of the leading edge model. The secondary flow temperature was measured by the thermocouples in the coolant supply passage. Because the temperature difference between the mainstream and the secondary flow was not very large, the density ratio qc =qg was nearly equal to 1. The Reynolds number based on the mainstream velocity and the semi-cylinder model diameter, ReD , was kept as 38,000. The turbulence intensity of mainstream was of the order of 2%. In the present study, four blowing ratios with the value of 0.7, 1, 1.4 and 2 were tested for all the four test models. The calculation of the blowing ratio M was based on the mainstream approach velocity, not the local mainstream velocity, and the average coolant flow velocity at the hole inlet which was obtained by averaging the total flow rate with the film hole numbers and the hole inlet cross-sectional area. So the blowing ratio M is a kind of average blowing ratio which is
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Fig. 7. Distributions of local film cooling effectiveness under M = 1.4.
an average value for the test model, not an exact value for a certain hole. Local surface pressure variations will undoubtedly cause blowing ratio variation from row to row, but this variation is small in the present three-hole-row model according to the study in Gao et al. [22].
where the T aw ðtÞ stands for the adiabatic wall temperature. This value can be replaced by the film cooling effectiveness, which is defined by:
g¼
T aw ðtÞ T g ðtÞ T c ðtÞ T g ðtÞ
ð2Þ
2.3. Measurement approach Transient heat transfer measurement technique based on thermochromic liquid crystal imaging has been employed in the present experiment. This technique for three-temperature, film cooling problem was first introduced by Vedula and Metzger [23]. Drost et al. [24], Chambers et al. [25] and Liu et al. [26] employed and further developed this technique. The data analysis is based on the theory of one-dimensional unsteady heat conduction with a boundary condition of the third kind (convective heat exchange with the free stream) at the outer surface. The mathematic model of the present transient heat transfer measurement is:
8 2 @Tðy;tÞ Tðy;tÞ > ¼ qkc @ @y ; y P 0; t P 0; > 2 > @t > > < y ¼ 0; t ! 1 : h½T s ðtÞ T aw ðtÞ ¼ k @Tðy¼0;tÞ ; @y > > ðtÞ; Tð0; tÞ ¼ T > s > > : t ¼ 0; y ! 1 : T i ðyÞ ¼ T i :
ð1Þ
The variations of mainstream temperatures and jet temperatures with time are approximated by power series of the following forms,
T g ðtÞ ¼
M X m¼0
Bm
tm ; Cðm þ 1Þ
T c ðtÞ ¼
N X An n¼0
tn Cðn þ 1Þ
ð3Þ
usually chosen of 4th to 5th order. Eqs. (1)–(3) can be solved analytically using the Laplace transform technique. The solution is a equation of wall surface temperature T s with respect to time t. It is also the equation to calculate h and g. Since the leading edge configuration is modeled by a semicylinder in the present experiment, wall curvature effects on the transient heat transfer measurement need to be considered. A simplified model for the curvature effect, described by Buttsworth and Jones [27], was shown to be applicable if used within certain limits regarding the measurement times according to Wagner et al. [28]. With this simplified model introduced by Buttsworth and Jones [27], the final equation of h and g is given for a convex surface:
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Fig. 8. Distributions of local film cooling effectiveness under M = 2.
PN
2n n¼0 An gb
T s ðtÞ ¼
pffi ðb t Þk k¼0 Cðkþ1Þ E0 2
P2n
1 k=hD PM
2m m¼0 Bm ð1 gÞb
þ
P2m
pffi ðb tÞk k¼0 Cðkþ1Þ E0 2
1 k=hD
þ
T i ðE0 1Þ þ Ti 1 k=hD
ð4Þ
pffiffiffiffiffiffiffiffi pffiffi 2 where b ¼ ðh k=DÞ= qck; E0 ¼ eb t erfcðb t Þ, D is the diameter of the semi-cylinder model. According to Wagner et al. [28], Eq. (4) takes curvature effects accurately into account as long as sR ¼ 4kt=qcD2 < 0:02 which is true in the present experimental measurement. In the present work, wall surface temperature T s ðtÞ was measured with the mixture of two narrow-band thermochromic liquid crystals. Description about the double-TLC method can be referred to Ireland and Jones [29]. Four tests were carried out at identical momentum flux ratios, whereas the mainstream temperature and the jet temperature were varied. This multiple-test method is according to Drost et al. [24]. Before starting a test, the heated secondary flow discharged into environment through solenoid valve (see Fig. 1). A transient test was initiated by switching the solenoid valve and the butterfly valve simultaneously to introduce the mainstream and the heated secondary flow injection into the test section. Initiation of the test also triggered the mesh heater to heat mainstream and an automated data acquisition system for record-
ing the thermocouple (TC) readings in the mainstream and the secondary flow. Simultaneously, a CCD camera started to record the video image of the liquid crystal coated on the test surface. Different tests at identical momentum flux ratio were distinguished by varying the power of heating mainstream and the secondary flow to produce different T g ðtÞ and T c ðtÞ. Fig. 4 (a) shows a liquid crystal image of the test model with cylindrical holes for the M = 1 case. It also indicates that the stagnation line coincided with the geometric leading edge and that there was flow symmetry around the model. For TLC measurement, TLC calibration is very important. In this work, calibrations were run in the test tunnel under the same light conditions with the measurement. And the influence of view angle of the camera was also checked. Fig. 4 (b) shows that the change of view angle can only influence the green intensity value at a certain pixel location, but has no influence on the corresponding temperatures of the green intensity peaks. So the intensity based processing of the TLC image shown in Ref. [29], in which the surface temperature is determined by finding the peak of the green intensity, can be applied in the present experiment. Error analysis has been performed with the method proposed by Kline and McClintock [30]. In the present transient liquid crystal measurement, the measurement uncertainties included temperature uncertainties: DT g , DT c , DT i , DT s ; and time uncertainty pffiffiffiffiffiffiffiffiDt in T g ðtÞ, T c ðtÞ, T s ðtÞ; and material property uncertainty D qck. The estimated uncertainty intervals with a confidence interval of 95%
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Fig. 9. Comparisons of laterally averaged film cooling effectiveness between different holes.
for the present experiment were: DT g ¼ DT c ¼ DT i ¼ DT s ¼ pffiffiffiffiffiffiffiffi 0:2 C; Dt ¼ 0:1 s; D qck ¼ 20. The temperature and time uncertainties in T g ðtÞ and T c ðtÞ were assessed to be the uncertainties of the fitting coefficients in Eq. (3). According to the uncertainty intervals given above, the relative uncertainty in heat transfer coefficient was about 8%, and in local film cooling effectiveness was about 20% at g ¼ 0:1 and 4% at g ¼ 0:7. It should be noted that the measurement uncertainties vary with the heat transfer coefficient and adiabatic wall temperature and therefore are different at every position in the test surface. Especially in the region around the hole exit, the 3-D heat conduction could lead to a remarkable error in the values. 3. Results and discussion Due to the flow symmetry, the measurement results on one side of the cylinder are presented in the middle of one hole-pitch region in the form of contour plots showing the surface distribution. The mainstream direction is toward the right. The secondary flow direction in the cavity is from the top down. The hole exit region is colored as red which represents the value of 1 in the film cooling effectiveness contours, and blue which represents the value of 0 in the heat transfer contours. Laterally averaged results of film cooling effectiveness and heat transfer coefficient are shown as function of streamwise coordinate. The effect of the hole exit region on the laterally averaged results was account for by excluding the points in this region. For example, the data on the points which
are in the hole exit region 3 6 X=d 6 4 are not used to calculate the laterally averaged film cooling effectiveness of the line Z=d ¼ 0. Since the data analysis is based on one-dimensional heat conduction equation, the data in the proximity of the hole exits are not valid, and may therefore not be considered for a quantitative discussion. Moreover, to authors’ knowledge, there is no effective way at present to estimate the effects of the convection in the hole inner face on the transient measurement results near the hole exits. However, it is possible to estimate the influenced area by the convection in the hole inner face through comparing the TLC color changing time around the hole exit and the penetration time calculated with t 6 d2 qc=4k in which the d is the penetration depth from the hole inner face to the wall. An area of about d/2 around the hole exit is estimated to be influenced. But the authors hold the opinion that those data still contain some useful information and can be used for a qualitative discussion, because the TLC images contain some information of the basic heat transfer feature in this region even though the quantities of the heat transfer results are not right. For example, the fast color change of the TLC near the hole exit reflects the strong heat transfer in this region. The coordinates in the figures are those introduced in Fig. 2. 3.1. Results of film cooling effectiveness Fig. 5 shows the film cooling effectiveness distributions for the four test models under blowing ratio M = 0.7. For all the four cases, the trajectory of jets from both the first row and the second
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Fig. 10. Distributions of local heat transfer under M = 0.7.
row is nearly aligned with the mainstream direction because of the small blowing ratio of jets. For the cases of cylindrical hole and laid-back hole with p = 5d, the jet from the first row flows across the upper part of the hole exit in the second row and joins into the jet from the second row. Moreover, for the laid-back hole case which has more intersection area of holes between the first row and the second row in the streamwise direction, the jet from the second row is split shown in Fig. 5 to form a low cooling effectiveness region between X/d = 6, . . . , 8 and Z/d = 1, . . . , 2. In authors’ opinion, it is caused by a vortex formed from the interaction between the jet from the first row and the mainstream. And due to the even lower blowing ratio of jet from the laid-back hole, this vortex can have a notable effect on the jets from the second laid-back hole row and split them. For the cases of p = 8d, because of the large hole spacing in the spanwise, jet from the first row flows over the top of the hole in the second row without contact and flows parallel with the jet from the second row. The jets in all the four cases attach on the wall surface very well due to the small blowing ratio. For the cylindrical hole cases, the peak of high cooling effectiveness lies in the vicinity of the lower part of hole exit because the secondary flow direction is from the top down. For the laid-back hole cases, the peak of cooling effectiveness lies more near the hole centerline because of a reduction in the real blowing ratio resulting from a larger hole exit, especially
for the second row where the mainstream velocity is large. Compared with the cylindrical holes, the jets from the laid-back holes can cover more area. And compared with the p = 8d cases, the proportion of film covering area is much larger for the p = 5d cases, and the flow feature is also more complex due to the interaction between jets and mainstream. Figs. 6–8 show the film cooling effectiveness distributions of the four test models under blowing ratio M = 1, 1.4 and 2 respectively. From these figures, we can see that as the blowing ratio increases, the trajectory of jets from the second row deviates from the hole centerline more and more. The location of peak cooling effectiveness also moves lower and lower. However, no matter under which blowing ratio, jets from the laid-back holes can cover more area compared with the cylindrical holes, and the proportion of film covering area is much larger for the p = 5d cases compared with the p = 8d cases. Under the condition of M = 1, jet from the first row flows across the entire hole exit in the downstream and merges into the jet from the second row for the p = 5d cases. So the region right upstream of the hole in the second row, where the film cooling effectiveness is very low under M = 0.7, is well covered by the film. For the p = 8d cases, jet from the first row flows across the upper part of the hole exit in the second row resulting in a similar cooling effectiveness distribution feature with that of p = 5d cases under M = 0.7. But due to the larger blowing ratios of
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Fig. 11. Distributions of local heat transfer under M = 1.
the jets, the vortex structure formed between the jet from the first row and the mainstream cannot split the jets from the second laid-back hole row. This is different from the case of M = 0.7. As shown in Fig. 7, jet from the first row hole can be seen to flow mainly in the spanwise direction due to the strong lateral momentum of jet under M = 1.4 and the small mainstream velocity in this region for both cylindrical hole cases. In the first row of the p = 5d model of cylindrical hole, jet from the upper hole impinges on the jet from the lower hole and changes its flow direction to the streamwise because the spanwise spacing is small and the lateral momentum of the jet is strong. Also due to this pressing effect from the upper jet, the jet from the first row hole can cover a large area between the first row and the second row. Only a small region is left not being well covered. However, in the downstream region of the second row, the condition is not improved very much compared with M = 1, there is still a large region not well covered. For the case of laid-back hole with p = 5d, almost the entire region between the first row and the second row is well covered by the jets from the first row. And the film coverage in the region downstream of the second row is also improved relative to M = 1, and is much better than the cylindrical hole case. For the p = 8d case, the flow pattern is similar with that of the p = 5d case under M = 1, jet from the first row flows across the downstream hole exit and merges into the jet from the second row. The film coverage in the region
right upstream of the second row hole is improved, while the condition in the rest region between the first row and the second row gets worse. We can also see the lift-off and reattachment of the jet from the first row hole of cylindrical hole case with p = 8d. The reason is because the spanwise spacing is large and the pressing effect from the upper jet is small. Under the condition of M = 2, Fig. 8 shows that the peak film cooling effectiveness of cylindrical hole cases is much lower than that under smaller blowing ratios for both p = 5d and p = 8d cases. It indicates that the jets detach more from the wall because of strong exit momentum. However, the influence region of the jets is larger because of large jet flux. For the p = 5d case of cylindrical hole, the film coverage around the first row is much better than the p = 8d case because of the stronger pressing effect between the adjacent jets. For the laid-back hole cases, the expanded hole exit reduces the jet momentum and there is no obvious jet lift-off. The film coverage is much better than the cylindrical hole cases, especially in the region between the first row and the second row. Fig. 9 presents the laterally averaged results of film cooling effectiveness. We can see that under M = 0.7, laid-back holes with p = 5d give the highest film cooling effectiveness in the upstream region between the first row and the second row. However, in the downstream region of the second row, cylindrical holes with p = 5d give the highest film cooling effectiveness. As a whole, the
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Fig. 12. Distributions of local heat transfer under M = 1.4.
film coverage performances of laid-back holes and cylindrical holes with p = 5d are almost the same under M = 0.7, and better than the cooling performances of p = 8d cases. Film cooling effectiveness of laid-back holes with p = 8d is higher than that of cylindrical holes with p = 8d in the whole streamwise region under M = 0.7 because of better film attachment and larger film coverage. Similar conclusions can be drawn for the cases under M = 1 with those under M = 0.7. Under large blowing ratios like M = 1.4 and M = 2, laidback holes with p = 5d have obvious advantage in the performance of film cooling effectiveness. And the cooling performance of laidback holes with p = 8d is almost the same with that of cylindrical holes with p = 5d under M = 2. In the upstream region, cylindrical holes with p = 8d give the worst performance in film cooling effectiveness. 3.2. Results of heat transfer coefficient The obtained heat transfer coefficient is presented in dimensionless form by Frössling number which is defined as the Nusselt number divided by the square root of Reynolds number. Fig. 10 shows the heat transfer coefficient distributions for the four test models under blowing ratio M=0.7. There is a low heat transfer region close to the lower part of the hole exit in the first row for all the four cases. As shown in Fig. 5 this region is just where the jet core flows through. We know that the region around
the first row is the mainstream stagnation region where the heat transfer should be very strong. So this low heat transfer region is mainly because the jet coverage reduces the enhancing effect of the flow stagnation. In addition to this region, there is another low heat transfer coefficient region close to the second row hole exit relative to the heat transfer coefficient in its neighboring region over and below it. As shown in Fig. 5, this low heat transfer coefficient region is also where the core of jet from the second row hole flows through. And the high heat transfer coefficient region is the jet edge region in which the strong heat transfer should be caused by the intense turbulence produced from the interaction between the mainstream and the jet. The heat transfer coefficient around the upper part of the hole exit in the first row is also relatively higher for the same reason. The lowest heat transfer coefficients occur in the regions with no or little influence of the jets. So the basic distribution features of the heat transfer coefficient are the same for the four models, especially for the models with the same pitch-to-hole. However, compared with the p = 5d cases, the p = 8d cases have relatively lower heat transfer coefficient value and larger low heat transfer coefficient region because a large area cannot be or can only be little influenced by the jets in the p = 8d models. Figs. 11–13 show the heat transfer coefficient distributions for the four test models under blowing ratio M = 1, 1.4 and 2 respectively. Compared with the heat transfer coefficient distributions
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Fig. 13. Distributions of local heat transfer under M = 2.
under M = 0.7, we can see that the basic distribution features of heat transfer coefficient are the same for the four models under all the blowing ratios. Generally speaking, heat transfer coefficient in the region where the jet core flows through is relatively lower, while in the jet edge region the heat transfer coefficient is relatively higher because of the intense turbulence caused by the flow interaction. And from these four figures, we can also see that the heat transfer coefficient of each model increases as the blowing ratio increases. For the p = 8d models of cylindrical hole and laidback hole, there is a large area in the downstream region after the second row which is not or little influenced by the jets because of large hole-to-hole spacing. In these regions, the heat transfer coefficient is relatively lower. Compared with the p = 8d models, the p = 5d models have much higher heat transfer coefficient values and larger proportion of high heat transfer coefficient region because of small hole-to-hole spacing resulting in a strong interaction between jets and mainstream. Especially for the p = 5d models of cylindrical hole and laid-back hole under blowing ratios larger than M = 1.4, the intense interaction between jet and mainstream highly enhances the heat transfer in two regions. One is the region around the hole exit in the first row except the part below the hole exit where the jet core flows through. And the other is the region around the hole exit in the second row except the parts where the jet core flows through.
Fig. 14 also shows the comparisons of laterally averaged heat transfer coefficients between different holes. The averaged heat transfer coefficients of cylindrical hole model and laid-back hole model with the same hole-to-hole pitch are nearly the same with each other under the same blowing ratios, except the p = 5d models under M = 2 in which the cylindrical holes give higher heat transfer coefficient than the laid-back holes. The averaged heat transfer coefficients of p = 5d models are higher than those of p = 8d models along the whole streamwise region under all the four blowing ratios. And as the blowing ratio increases, the difference between the averaged heat transfer coefficients of p = 5d models and p = 8d models gets larger. 3.3. Comparison with other results Fig. 15 shows the comparisons of the present results to the data reported by Ou and Rivir [7], Kim et al. [17] and Gao et al. [22]. The measured film cooling effectiveness and heat transfer coefficient are consistent with the published data, considering the differences in the experiments. In Gao et al. [22], the distance between the first and the second hole row is 6.33d. So in the region downstream of X/d = 2, the effectiveness from Gao et al. [22] is lower than the present result. In Ou and Rivir [7], the spanwise inclination angle a is 20 . Therefore, the jets attached on the wall much closer, thus,
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Fig. 14. Comparisons of laterally averaged Froe between different holes.
the laterally averaged effectiveness and heat transfer coefficient are larger than the present results under relatively larger blowing ratio of M = 1.4, especially in the region near the hole row. 4. Conclusion Film cooling performances of cylindrical holes and laid-back holes on the turbine blade leading edge have been studied in this paper. Experimental measurements are carried out to investigate the influences of film hole shape and hole pitch on the film cooling performances. Three rows of holes are arranged in a semi-cylinder model which is used to model the blade leading edge. Four blowing ratios are tested for two hole pitches. Transient heat transfer measurement technique with double thermochromic liquid crystals is used in the present experiment. The following conclusions can be drawn: For all the four leading edge models, the trajectory of jets is nearly aligned in the mainstream direction under small blowing ratio of M = 0.7, and the jets attach on the wall surface very well. As the blowing ratio increases, the trajectory of jet from the second row hole deviates to the spanwise direction gradually, and the jet from the first row hole almost flows in the spanwise direction. Under blowing ratios larger than 1, the jets lift off from the model surface because of strong exit momentum, while the influence region of the jets is larger because of large jet flux. More area can benefit from the film coverage. For the models with p = 5d, the film
coverage performances of laid-back holes are almost the same with those of cylindrical holes under small blowing ratio. But as the blowing ratio increases, the laid-back holes give better and better performances of film coverage. The laid-back holes provide an about 55% percent increase in the averaged film cooling effectiveness under M = 2. Flow interaction is more intense for the p = 5d cases than the p = 8d cases because of narrow hole-to-hole spacing. In the first row, due to the pressing effect from the upper jet, the jet from the lower hole can cover large area between the first row and the second row. For the models with p = 8d, the advantage of laid-back holes in film cooling effectiveness is more obvious in the upstream region between the first row and the second row relative to the cylindrical holes. And compared with the p = 8d models, the proportion of film covering area is much larger for the p = 5d models. No matter under small or large blowing ratios, the basic distribution features of heat transfer coefficient are the same for the cylindrical hole models and the laid-back hole models. Heat transfer coefficient in the region where the jet core flows through is relatively lower, while in the jet edge region is relatively higher because of the intense turbulence caused by the flow interaction. For every model, heat transfer coefficient increases as the blowing ratio increases. Compared with the p = 8d models in which large area cannot be or can only be little influenced by the jets, the p = 5d models have much higher heat transfer coefficient values and larger proportion of high heat transfer coefficient region
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Acknowledgement This work is sponsored by the National Basic Research Program of China (China 973 Program) under number of 2007CB707701. References
Fig. 15. Comparison of laterally averaged results to published data.
because of narrow hole-to-hole spacing resulting in a strong interaction between jets and mainstream, especially under large blowing ratios. The laterally averaged heat transfer coefficients of cylindrical hole model and laid-back hole model with the same hole-to-hole spacing are nearly the same with each other under the same blowing ratios. And as the blowing ratio increases, the difference in the laterally averaged heat transfer coefficient between the p = 5d models and the p = 8d models gets larger.
[1] J.C. Han, S. Dutta, S.V. Ekkad, Gas Turbine Heat Transfer and Cooling Technology, Taylor & Francis, New York, 2000. [2] D.W. Luckey, D.K. Winstanley, G.J. Hames, M.R. L’Ecuyer, Stagnation region gas film cooling for turbine blade leading edge applications, AIAA J. Aircraft 14 (1977) 494–501. [3] J. Karni, R.J. Goldstein, Surface injection effect on mass transfer from a cylinder in crossflow: a simulation of film cooling in the leading edge region of a turbine blade, ASME J. Turbomach. 112 (1990) 418–427. [4] A.B. Mehendale, J.C. Han, Influence of high mainstream turbulence on leading edge film cooling heat transfer, ASME J. Turbomach. 114 (1992) 707–715. [5] A.B. Mehendale, J.C. Han, Reynolds number effect on leading edge film effectiveness and heat transfer coefficient, Int. J. Heat Mass Transfer 36 (1993) 3723–3730. [6] S.V. Ekkad, J.C. Han, H. Du, Detailed film cooling measurements on a cylindrical leading edge model: effect of free-stream turbulence and coolant density, ASME J. Turbomach. 119 (1998) 594–600. [7] S. Ou, R.B. Rivir, Leading Edge film cooling heat transfer with high free stream turbulence using a transient liquid crystal image method, Int. J. Heat Fluid Flow 22 (2001) 614–623. [8] K.S. Kim, Y.J., Kim, S.M. Kim, Enhancement of Film Cooling Performance at the Leading Edge of Turbine Blade, ASME Paper No. GT2006-90321, 2006. [9] R. Johnson, D. Bogard, J. Piggush, A. Kohli, M. Blair, Experimental Study of the Effects of an Oscillating Approach Flow on Overall Cooling Performance on a Simulated Turbine Blade Leading Edge, ASME Paper No. GT2009-60290, 2009. [10] T.E. Dyson, D.G. Bogard, J.D. Piggush, A. Kohli, Overall Effectiveness for a Film Cooled Turbine Blade Leading Edge With Varying Hole Pitch, ASME Paper No. GT2010-23707, 2010. [11] R.S. Bunker, A review of shaped hole turbine film cooling technology, ASME J. Heat Transfer 127 (2005) 441–453. [12] R.J. Goldstein, E.R.G. Eckert, F. Burggraf, Effects of hole geometry and density on three-dimensional film cooling, Int. J. Heat Mass Transfer 17 (1974) 595– 607. [13] D.L. Schmidt, B. Sen, D.G. Bogard, Film cooling with compound angle holes: adiabatic effectiveness, ASME J. Turbomach. 118 (1996) 807–813. [14] M. Gritsch, A. Schulz, S. Witting, Adiabatic wall effectiveness measurements of film cooling holes with expanded exits, ASME J. Turbomach. 120 (1998) 549– 556. [15] Y. Yu, C.-H. Yen, T.I.-P. Shih, M.K. Chyu, S. Gogineni, Film cooling effectiveness and heat transfer coefficient distributions around diffusion shaped holes, ASME J. Heat Transfer 124 (2002) 820–827. [16] H. Reiss, A. Bölcs, Experimental study of showerhead cooling on a cylinder comparing several configurations using cylindrical and shaped holes, ASME J. Turbomach. 122 (2000) 161–169. [17] Y.J. Kim, S.M. Kim, Influence of shaped injection holes on turbine blade leading edge film cooling, Int. J. Heat Mass Transfer 47 (2004) 245–256. [18] B.D. Mouzon, E.J. Terrell, J. E. Ablert, and D. G. Bogard, Net Heat Flux Reduction and Overall Effectiveness for a Turbine Blade Leading Edge, ASME Paper No. GT2005-69002, 2005. [19] C. Falcoz, B. Weigand, P. Ott, A comparative study on showerhead cooling performance, Int. J. Heat Mass Transfer 49 (2006) 1274–1286. [20] C. Falcoz, B. Weigand, P. Ott, Experimental investigations on showerhead cooling on a blunt body, Int. J. Heat Mass Transfer 49 (2006) 1287–1298. [21] Y.P. Lu, D. Allison, S.V. Ekkad, Turbine blade showerhead film cooling: influence of hole angle and shaping, Int. J. Heat Fluid Flow 28 (2007) 922–931. [22] Z.H. Gao, J.C. Han, Influence of film-hole shape and angle on showerhead film cooling using PSP technique, ASME J. Heat Transfer 131 (2009) 061701. [23] R. J. Vedula, D. E. Metzger, A Method for the Simultaneous Determination of Local Effectiveness and Heat Transfer Distributions in Three Temperature Convection Situations, ASME paper No. 91-GT-345, 1991. [24] U. Drost, A. Bolcs, A. Hoffs, Utilization of the Transient Liquid Crystal Technique for film Cooling Effectiveness and Heat Transfer Investigations on a Flat Plane and a Turbine Airfoil, ASME Paper No. 97-GT-026, 1997. [25] A.C. Chambers, D.R.H. Gillespie, P.T. Ireland, A novel transient liquid crystal technique to determine heat transfer coefficient distributions and adiabatic wall temperature in a three temperature problem, ASME J. Turbomach. 125 (2003) 538–546. [26] C.L. Liu, H.R. Zhu, J.T. Bai, D.C. Xu, Experimental research on the thermal performance of converging slot holes with different divergence angles, Exp. Therm. Fluid Sci. 33 (2009) 808–817. [27] D.R. Buttsworth, T.V. Jones, Radial conduction effects in transient heat transfer experiments, Aeronaut. J. (1997) 209–212. [28] G. Wagner, E. Schneider, J. von Wolfersdorf, Method for analysis of showerhead film cooling experiments on highly curved surfaces, Exp. Therm. Fluid Sci. 31 (2007) 381–389. [29] P.T. Ireland, T.V. Jones, Liquid crystal measurements of heat transfer and surface shear stress, Meas. Sci. Technol. 11 (2000) 969–986. [30] S.J. Kline, F.A. McClintock, Describing uncertainties in single-sample experiments, J. Mech. Eng. 75 (1953) 3–8.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental investigation on the leading edge film cooling of cylindrical and laid-back holes with different hole pitches Cun-liang Liu ⇑, Hui-ren Zhu, Zong-wei Zhang, Du-chun Xu School of Power and Energy, Northwestern Polytechnical University, 160#mail-box, 127 You Yi Xi Lu, Xi’an, 710072, China
a r t i c l e
i n f o
Article history: Received 20 February 2012 Received in revised form 7 June 2012 Accepted 29 June 2012 Available online 1 August 2012 Keywords: Turbine blade Leading edge Film cooling Laid-back hole Hole pitch Thermochromic liquid crystal Transient measurement
a b s t r a c t Experimental investigation has been performed to study the film cooling performances of cylindrical holes and laid-back holes on the turbine blade leading edge. Four test models are measured for four blowing ratios to investigate the influences of film hole shape and hole pitch on the film cooling performances. Film cooling effectiveness and heat transfer coefficient have been obtained using a transient heat transfer measurement technique with double thermochromic liquid crystals. As the blowing ratio increases, the trajectory of jets deviates to the spanwise direction and lifts off gradually. However, more area can benefit from the film protection under large blowing ratio, while the is also higher. The basic distribution features of heat transfer coefficients are similar for all the four models. Heat transfer coefficient in the region where the jet core flows through is relatively lower, while in the jet edge region is relatively higher. For the models with small hole pitch, the laid-back holes only give better film coverage performance than the cylindrical holes under large blowing ratio. For the models with large hole pitch, the advantage of laid-back holes in film cooling effectiveness is more obvious in the upstream region relative to the cylindrical holes. For the cylindrical hole model and the laid-back hole model with the same hole pitch, heat transfer coefficients are nearly the same with each other under the same blowing ratios. Compared with the models with large hole pitch, the laterally averaged film cooling effectiveness and heat transfer coefficient are larger for the models with small hole pitch because of larger proportion of film covering area and strong heat transfer region. Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved.
1. Introduction The desire for higher overall efficiency and higher specific power output in gas turbines renders the need for increase in turbine entry temperatures resulting in a need for effective cooling technologies. Film cooling is one of the major cooling technologies for protection of turbine airfoils from the hot gas stream. In a gas turbine, the leading edge of a turbine vane or blade often withstands higher heat loads than any part of the airfoil surface due to the higher temperatures and the increased heat transfer coefficients that occur around the stagnation line. Film cooling is typically applied on the leading edge through an array of hole rows. Increases in film effectiveness in the leading edge will lead to significant benefits in life and efficiency of the turbine blade. Cylindrical hole is the basic configuration for the leading edge film cooling. Cylinder or semi-cylinder model has been often employed by researchers [1] to model the blade leading edge. In this way, the leading edge film cooling can be investigated easily under different flow conditions. In Luckey et al. [2], experiments ⇑ Corresponding author. E-mail address: [email protected] (C.-l. Liu).
were conducted with a single row of spanwise-angled film holes for a range of blowing ratio. Karni and Goldstein [3] studied the effect of blowing ratio and injection location on the mass transfer coefficient of the leading edge region. Mehendale and Han [4,5] investigated the influences of high mainstream turbulence and mainstream Reynolds number on the leading edge film effectiveness and heat transfer coefficient using a blunt body with a semi-cylinder leading edge. Ekkad et al. [6] further presented the effects of coolant density and mainstream turbulence using a transient liquid crystal measurement technique. Ou and Rivir [7] studied the film effectiveness and the heat transfer coefficients on a large scale symmetric circular leading edge with three rows of film holes. The film hole configuration has a smaller injection angle of 20° and a larger hole pitch (p/d = 7.86). They also employed the transient liquid crystal measurement technique. Results showed that turbulence intensity had an attenuation on the film effectiveness as well as on the Frössling number for all blowing ratios. Kim et al. [8] used a cylindrical body model with three different arrangements of injection holes to study the film cooling characteristics under high and low Reynolds numbers. They tried to improve the film cooling performance by different arrangement of injection holes for the turbine blade leading edge region. To
0017-9310/$ - see front matter Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.06.090
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Nomenclature c d D Froe h M p ReD t T U X Y
specific heat of test plate (J/kg K) diameter of the film hole (m) diameter of semi-cylinder model (m) 0:5 Frössling number (¼ NuD =Re0:5 ) D ¼ ðhD=kÞ=ðqg U g D=lg Þ convective heat transfer coefficient [(W=m2 K)] blowing ratio (¼ qc U c =qg U g ) hole pitch (m) Reynolds number based on diameter of semi-cylinder model (¼ qg U g D=lg ) time (s) temperature (°C) velocity (m/s) streamwise coordinate originating at the stagnation line (m) coordinate normal to the model surface (m)
consider and investigate the effect of the oscillation of the stagnation line position, which was caused by the blade passing through wakes from upstream vanes, on the leading edge film cooling, Johnson et al. [9] developed an experimental facility and carried out the experimental study. Dyson et al. [10] measured the overall effectiveness of a simulated turbine blade leading edge model with matched Biot number to the engine conditions. Overall effectiveness was measured for pitch variation from 7.6d to 9.6d for a range of blowing ratio and attack angle. More information on the leading edge film cooling of cylindrical holes can be found in Han et al. [1]. Many studies show that using shaped holes is an effective way to improve the film cooling performance [11]. The study of Goldstein et al. [12] reported a significant increase in film cooling effectiveness as well as greater lateral coolant coverage for fan-shaped holes compared with standard cylindrical holes. Schmidt et al. [13], Gritsch et al. [14] and Yu et al. [15] further investigated the improvement in film cooling performance brought by laid-back hole, fan-shaped hole and laid-back fan-shaped hole. However, the above studies were performed on flat plate model. Until more recent time, shaped holes gradually came into consideration for the leading edge film cooling. Reiss and Bölcs [16] compared the
Z
spanwise coordinate (m)
Greek symbols a radially inclined angle of the film hole (°) g film cooling effectiveness q density (kg/m3) k thermal conductivity of test plate, (W/m K) l viscosity ( Kg/(ms)) Subscripts aw adiabatic wall c jet g mainstream i initial t = 0 s surface
film cooling performances of cylindrical holes, laid-back holes, and fan-shaped holes on a cylinder leading edge model with five hole rows. The effects of shaped holes with compound angle orientation were studied using the transient liquid crystal measurement technique. They found that laidback holes gave the best overall film cooling performance. The fan-shaped holes performed better than cylindrical holes, but not as well as laid-back holes. Cylinder model with three rows of radially inclined holes, including cylindrical holes, laid-back holes and tear-drop shaped holes, were investigated in Kim et al. [17] with an infrared thermography method. They showed that the holes with a laid-back type exit produced higher film cooling effectiveness than the tear-drop shaped holes. Both laid-back holes and tear-drop shaped holes were found to perform better than the cylindrical holes. Mouzon et al. [18] compared the film performances of laid-back holes and cylindrical holes on a three-row leading edge model using the infrared thermography method. They found that the laid-back holes resulted in much higher net heat flux reduction than the cylindrical holes. Falcoz et al. [19,20] investigated cylindrical holes, conical holes, and laid-back holes on a blunt model with numerical and experimental methods respectively. Experiment studies were
Fig. 1. Sketch of the experiment system.
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Fig. 2. Configurations of the test model.
Fig. 3. Configurations of the film holes.
performed with the transient liquid crystal measurement technique. Their results indicated that the laid-back holes had a better lateral film coverage. However, the best spanwise averaged film cooling effectiveness was achieved by conical holes. Lu et al. [21] also studied the effects of hole orientation and hole shape on the leading edge film cooling. They examined compound angle cylindrical holes and compound angle laid-back fan-shaped holes on a blunt model with a semi-cylinder leading edge. They found that the shaped holes produced much higher effectiveness than the cylindrical holes. For the compound angle holes, cooling effectiveness was improved at lower blowing ratios. Gao et al. [22] studied the effects of film hole geometry and angle on the turbine blade leading edge film cooling experimentally using the pressure sensitive paint technique (PSP). The leading edge was modeled by a semi-cylinder and an after-body. Four different film cooling hole configurations were compared: radial and compound angle cylin-
drical holes, radial and compound angle laid-back fan-shaped holes. The results showed that the shaped holes provided higher film cooling effectiveness than the cylindrical holes, particularly at higher average blowing ratios. The objective of the present study is to further explore the potential improvement of film cooling with shaped holes for the leading edge region. Film cooling performances of laid-back holes and cylindrical holes on the leading edge model have been investigated. Special attention is focused on the influence of hole pitch of the film holes. We know that large hole pitch can reduce the number of film holes thus resulting in a reduction of the coolant flux on a certain geometry and flow condition. But large hole pitch can also reduce the proportion of film covering area according to our experience. How much difference is there between large and small hole pitch for the leading edge film cooling performances of cylindrical holes and laid-back holes? That is what this paper intends to show. Transient liquid crystal measurement technique has been used in the present work to obtain detailed distributions of film cooling effectiveness and heat transfer coefficient. 2. Experimental apparatus and approach 2.1. Experimental apparatus Fig. 1 shows a schematic of the overall experimental setup. The mainstream travels through valves, settling chamber with three flow-conditioning screens in it, contraction section with a contraction ratio of 5.4-to-1 before entering the mesh heater. Moreover, another contraction with a contraction ratio of 2-to-1 is placed after the mesh heater to ensure a uniform mainstream entering the test tunnel which is a Perspex rectangular duct with 220 mm in width and 110 mm in height. The light source and the CCD camera for the liquid crystal measurement are placed outside of the test tunnel, as indicated in Fig. 1. The secondary flow travels through the flow meter, valve, air heater and a bypass system
C.-l. Liu et al. / International Journal of Heat and Mass Transfer 55 (2012) 6832–6845
Fig. 4. Liquid crystal image and calibration curves of the double-TLC.
Fig. 5. Distributions of local film cooling effectiveness under M = 0.7.
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Fig. 6. Distributions of local film cooling effectiveness under M = 1.
which consists of two solenoid valves and enters the test model from the bottom. In the present experiment, four test models with different filmhole configurations have been investigated. The material of these four models is Plexiglas with a conductivity of 0.17 W/m K. The test model is placed in the middle of the test channel with a distance of 90 mm to either side wall. Except for the film-hole configuration and the hole pitch, the other geometry parameters of the four models are the same with each other. Each test model is made up of a semi-cylinder which is used to model the leading edge and an after-body. Configurations of the test model from two perspective views are shown in Fig. 2. The semi-cylinder had a diameter D of 40 mm and wall thickness of 10 mm. The hollow cavity in the test model served as the secondary flow passage. The secondary flow in the passage is in a crossflow pattern which is also indicated in Figs. 2 and 3. Three rows of film holes are located at 0° (stagnation line) and 30° on either side of the leading edge model and arranged in stagger pattern. Two kinds of film hole row arrangement have been investigated: one with a hole pitch of 5d, and the other with a hole pitch of 8d where d denotes the diameter of the metering part of film hole. All the film holes are oriented in the radial (spanwise) direction and orthogonal to the local mainstream direction. Laid-back film hole and cylindrical hole with the same radially inclined angle a ¼ 30 have been are investigated and compared. The configurations of the film holes are
shown in Fig. 3. The laid-back film hole has an additional forward expansion of 10° from the film hole axis which produces a 3 mm longer hole-exit for both configurations relative to the cylindrical holes. The metering part of the laid-back hole has the same diameter of d = 3 mm as the cylindrical hole, and the length to diameter ratio of all the holes is 6.67. 2.2. Operating conditions The velocity and temperature of the mainstream were measured by the Pitot tube and thermocouples upstream of the leading edge model. The secondary flow temperature was measured by the thermocouples in the coolant supply passage. Because the temperature difference between the mainstream and the secondary flow was not very large, the density ratio qc =qg was nearly equal to 1. The Reynolds number based on the mainstream velocity and the semi-cylinder model diameter, ReD , was kept as 38,000. The turbulence intensity of mainstream was of the order of 2%. In the present study, four blowing ratios with the value of 0.7, 1, 1.4 and 2 were tested for all the four test models. The calculation of the blowing ratio M was based on the mainstream approach velocity, not the local mainstream velocity, and the average coolant flow velocity at the hole inlet which was obtained by averaging the total flow rate with the film hole numbers and the hole inlet cross-sectional area. So the blowing ratio M is a kind of average blowing ratio which is
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Fig. 7. Distributions of local film cooling effectiveness under M = 1.4.
an average value for the test model, not an exact value for a certain hole. Local surface pressure variations will undoubtedly cause blowing ratio variation from row to row, but this variation is small in the present three-hole-row model according to the study in Gao et al. [22].
where the T aw ðtÞ stands for the adiabatic wall temperature. This value can be replaced by the film cooling effectiveness, which is defined by:
g¼
T aw ðtÞ T g ðtÞ T c ðtÞ T g ðtÞ
ð2Þ
2.3. Measurement approach Transient heat transfer measurement technique based on thermochromic liquid crystal imaging has been employed in the present experiment. This technique for three-temperature, film cooling problem was first introduced by Vedula and Metzger [23]. Drost et al. [24], Chambers et al. [25] and Liu et al. [26] employed and further developed this technique. The data analysis is based on the theory of one-dimensional unsteady heat conduction with a boundary condition of the third kind (convective heat exchange with the free stream) at the outer surface. The mathematic model of the present transient heat transfer measurement is:
8 2 @Tðy;tÞ Tðy;tÞ > ¼ qkc @ @y ; y P 0; t P 0; > 2 > @t > > < y ¼ 0; t ! 1 : h½T s ðtÞ T aw ðtÞ ¼ k @Tðy¼0;tÞ ; @y > > ðtÞ; Tð0; tÞ ¼ T > s > > : t ¼ 0; y ! 1 : T i ðyÞ ¼ T i :
ð1Þ
The variations of mainstream temperatures and jet temperatures with time are approximated by power series of the following forms,
T g ðtÞ ¼
M X m¼0
Bm
tm ; Cðm þ 1Þ
T c ðtÞ ¼
N X An n¼0
tn Cðn þ 1Þ
ð3Þ
usually chosen of 4th to 5th order. Eqs. (1)–(3) can be solved analytically using the Laplace transform technique. The solution is a equation of wall surface temperature T s with respect to time t. It is also the equation to calculate h and g. Since the leading edge configuration is modeled by a semicylinder in the present experiment, wall curvature effects on the transient heat transfer measurement need to be considered. A simplified model for the curvature effect, described by Buttsworth and Jones [27], was shown to be applicable if used within certain limits regarding the measurement times according to Wagner et al. [28]. With this simplified model introduced by Buttsworth and Jones [27], the final equation of h and g is given for a convex surface:
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Fig. 8. Distributions of local film cooling effectiveness under M = 2.
PN
2n n¼0 An gb
T s ðtÞ ¼
pffi ðb t Þk k¼0 Cðkþ1Þ E0 2
P2n
1 k=hD PM
2m m¼0 Bm ð1 gÞb
þ
P2m
pffi ðb tÞk k¼0 Cðkþ1Þ E0 2
1 k=hD
þ
T i ðE0 1Þ þ Ti 1 k=hD
ð4Þ
pffiffiffiffiffiffiffiffi pffiffi 2 where b ¼ ðh k=DÞ= qck; E0 ¼ eb t erfcðb t Þ, D is the diameter of the semi-cylinder model. According to Wagner et al. [28], Eq. (4) takes curvature effects accurately into account as long as sR ¼ 4kt=qcD2 < 0:02 which is true in the present experimental measurement. In the present work, wall surface temperature T s ðtÞ was measured with the mixture of two narrow-band thermochromic liquid crystals. Description about the double-TLC method can be referred to Ireland and Jones [29]. Four tests were carried out at identical momentum flux ratios, whereas the mainstream temperature and the jet temperature were varied. This multiple-test method is according to Drost et al. [24]. Before starting a test, the heated secondary flow discharged into environment through solenoid valve (see Fig. 1). A transient test was initiated by switching the solenoid valve and the butterfly valve simultaneously to introduce the mainstream and the heated secondary flow injection into the test section. Initiation of the test also triggered the mesh heater to heat mainstream and an automated data acquisition system for record-
ing the thermocouple (TC) readings in the mainstream and the secondary flow. Simultaneously, a CCD camera started to record the video image of the liquid crystal coated on the test surface. Different tests at identical momentum flux ratio were distinguished by varying the power of heating mainstream and the secondary flow to produce different T g ðtÞ and T c ðtÞ. Fig. 4 (a) shows a liquid crystal image of the test model with cylindrical holes for the M = 1 case. It also indicates that the stagnation line coincided with the geometric leading edge and that there was flow symmetry around the model. For TLC measurement, TLC calibration is very important. In this work, calibrations were run in the test tunnel under the same light conditions with the measurement. And the influence of view angle of the camera was also checked. Fig. 4 (b) shows that the change of view angle can only influence the green intensity value at a certain pixel location, but has no influence on the corresponding temperatures of the green intensity peaks. So the intensity based processing of the TLC image shown in Ref. [29], in which the surface temperature is determined by finding the peak of the green intensity, can be applied in the present experiment. Error analysis has been performed with the method proposed by Kline and McClintock [30]. In the present transient liquid crystal measurement, the measurement uncertainties included temperature uncertainties: DT g , DT c , DT i , DT s ; and time uncertainty pffiffiffiffiffiffiffiffiDt in T g ðtÞ, T c ðtÞ, T s ðtÞ; and material property uncertainty D qck. The estimated uncertainty intervals with a confidence interval of 95%
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Fig. 9. Comparisons of laterally averaged film cooling effectiveness between different holes.
for the present experiment were: DT g ¼ DT c ¼ DT i ¼ DT s ¼ pffiffiffiffiffiffiffiffi 0:2 C; Dt ¼ 0:1 s; D qck ¼ 20. The temperature and time uncertainties in T g ðtÞ and T c ðtÞ were assessed to be the uncertainties of the fitting coefficients in Eq. (3). According to the uncertainty intervals given above, the relative uncertainty in heat transfer coefficient was about 8%, and in local film cooling effectiveness was about 20% at g ¼ 0:1 and 4% at g ¼ 0:7. It should be noted that the measurement uncertainties vary with the heat transfer coefficient and adiabatic wall temperature and therefore are different at every position in the test surface. Especially in the region around the hole exit, the 3-D heat conduction could lead to a remarkable error in the values. 3. Results and discussion Due to the flow symmetry, the measurement results on one side of the cylinder are presented in the middle of one hole-pitch region in the form of contour plots showing the surface distribution. The mainstream direction is toward the right. The secondary flow direction in the cavity is from the top down. The hole exit region is colored as red which represents the value of 1 in the film cooling effectiveness contours, and blue which represents the value of 0 in the heat transfer contours. Laterally averaged results of film cooling effectiveness and heat transfer coefficient are shown as function of streamwise coordinate. The effect of the hole exit region on the laterally averaged results was account for by excluding the points in this region. For example, the data on the points which
are in the hole exit region 3 6 X=d 6 4 are not used to calculate the laterally averaged film cooling effectiveness of the line Z=d ¼ 0. Since the data analysis is based on one-dimensional heat conduction equation, the data in the proximity of the hole exits are not valid, and may therefore not be considered for a quantitative discussion. Moreover, to authors’ knowledge, there is no effective way at present to estimate the effects of the convection in the hole inner face on the transient measurement results near the hole exits. However, it is possible to estimate the influenced area by the convection in the hole inner face through comparing the TLC color changing time around the hole exit and the penetration time calculated with t 6 d2 qc=4k in which the d is the penetration depth from the hole inner face to the wall. An area of about d/2 around the hole exit is estimated to be influenced. But the authors hold the opinion that those data still contain some useful information and can be used for a qualitative discussion, because the TLC images contain some information of the basic heat transfer feature in this region even though the quantities of the heat transfer results are not right. For example, the fast color change of the TLC near the hole exit reflects the strong heat transfer in this region. The coordinates in the figures are those introduced in Fig. 2. 3.1. Results of film cooling effectiveness Fig. 5 shows the film cooling effectiveness distributions for the four test models under blowing ratio M = 0.7. For all the four cases, the trajectory of jets from both the first row and the second
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Fig. 10. Distributions of local heat transfer under M = 0.7.
row is nearly aligned with the mainstream direction because of the small blowing ratio of jets. For the cases of cylindrical hole and laid-back hole with p = 5d, the jet from the first row flows across the upper part of the hole exit in the second row and joins into the jet from the second row. Moreover, for the laid-back hole case which has more intersection area of holes between the first row and the second row in the streamwise direction, the jet from the second row is split shown in Fig. 5 to form a low cooling effectiveness region between X/d = 6, . . . , 8 and Z/d = 1, . . . , 2. In authors’ opinion, it is caused by a vortex formed from the interaction between the jet from the first row and the mainstream. And due to the even lower blowing ratio of jet from the laid-back hole, this vortex can have a notable effect on the jets from the second laid-back hole row and split them. For the cases of p = 8d, because of the large hole spacing in the spanwise, jet from the first row flows over the top of the hole in the second row without contact and flows parallel with the jet from the second row. The jets in all the four cases attach on the wall surface very well due to the small blowing ratio. For the cylindrical hole cases, the peak of high cooling effectiveness lies in the vicinity of the lower part of hole exit because the secondary flow direction is from the top down. For the laid-back hole cases, the peak of cooling effectiveness lies more near the hole centerline because of a reduction in the real blowing ratio resulting from a larger hole exit, especially
for the second row where the mainstream velocity is large. Compared with the cylindrical holes, the jets from the laid-back holes can cover more area. And compared with the p = 8d cases, the proportion of film covering area is much larger for the p = 5d cases, and the flow feature is also more complex due to the interaction between jets and mainstream. Figs. 6–8 show the film cooling effectiveness distributions of the four test models under blowing ratio M = 1, 1.4 and 2 respectively. From these figures, we can see that as the blowing ratio increases, the trajectory of jets from the second row deviates from the hole centerline more and more. The location of peak cooling effectiveness also moves lower and lower. However, no matter under which blowing ratio, jets from the laid-back holes can cover more area compared with the cylindrical holes, and the proportion of film covering area is much larger for the p = 5d cases compared with the p = 8d cases. Under the condition of M = 1, jet from the first row flows across the entire hole exit in the downstream and merges into the jet from the second row for the p = 5d cases. So the region right upstream of the hole in the second row, where the film cooling effectiveness is very low under M = 0.7, is well covered by the film. For the p = 8d cases, jet from the first row flows across the upper part of the hole exit in the second row resulting in a similar cooling effectiveness distribution feature with that of p = 5d cases under M = 0.7. But due to the larger blowing ratios of
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Fig. 11. Distributions of local heat transfer under M = 1.
the jets, the vortex structure formed between the jet from the first row and the mainstream cannot split the jets from the second laid-back hole row. This is different from the case of M = 0.7. As shown in Fig. 7, jet from the first row hole can be seen to flow mainly in the spanwise direction due to the strong lateral momentum of jet under M = 1.4 and the small mainstream velocity in this region for both cylindrical hole cases. In the first row of the p = 5d model of cylindrical hole, jet from the upper hole impinges on the jet from the lower hole and changes its flow direction to the streamwise because the spanwise spacing is small and the lateral momentum of the jet is strong. Also due to this pressing effect from the upper jet, the jet from the first row hole can cover a large area between the first row and the second row. Only a small region is left not being well covered. However, in the downstream region of the second row, the condition is not improved very much compared with M = 1, there is still a large region not well covered. For the case of laid-back hole with p = 5d, almost the entire region between the first row and the second row is well covered by the jets from the first row. And the film coverage in the region downstream of the second row is also improved relative to M = 1, and is much better than the cylindrical hole case. For the p = 8d case, the flow pattern is similar with that of the p = 5d case under M = 1, jet from the first row flows across the downstream hole exit and merges into the jet from the second row. The film coverage in the region
right upstream of the second row hole is improved, while the condition in the rest region between the first row and the second row gets worse. We can also see the lift-off and reattachment of the jet from the first row hole of cylindrical hole case with p = 8d. The reason is because the spanwise spacing is large and the pressing effect from the upper jet is small. Under the condition of M = 2, Fig. 8 shows that the peak film cooling effectiveness of cylindrical hole cases is much lower than that under smaller blowing ratios for both p = 5d and p = 8d cases. It indicates that the jets detach more from the wall because of strong exit momentum. However, the influence region of the jets is larger because of large jet flux. For the p = 5d case of cylindrical hole, the film coverage around the first row is much better than the p = 8d case because of the stronger pressing effect between the adjacent jets. For the laid-back hole cases, the expanded hole exit reduces the jet momentum and there is no obvious jet lift-off. The film coverage is much better than the cylindrical hole cases, especially in the region between the first row and the second row. Fig. 9 presents the laterally averaged results of film cooling effectiveness. We can see that under M = 0.7, laid-back holes with p = 5d give the highest film cooling effectiveness in the upstream region between the first row and the second row. However, in the downstream region of the second row, cylindrical holes with p = 5d give the highest film cooling effectiveness. As a whole, the
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Fig. 12. Distributions of local heat transfer under M = 1.4.
film coverage performances of laid-back holes and cylindrical holes with p = 5d are almost the same under M = 0.7, and better than the cooling performances of p = 8d cases. Film cooling effectiveness of laid-back holes with p = 8d is higher than that of cylindrical holes with p = 8d in the whole streamwise region under M = 0.7 because of better film attachment and larger film coverage. Similar conclusions can be drawn for the cases under M = 1 with those under M = 0.7. Under large blowing ratios like M = 1.4 and M = 2, laidback holes with p = 5d have obvious advantage in the performance of film cooling effectiveness. And the cooling performance of laidback holes with p = 8d is almost the same with that of cylindrical holes with p = 5d under M = 2. In the upstream region, cylindrical holes with p = 8d give the worst performance in film cooling effectiveness. 3.2. Results of heat transfer coefficient The obtained heat transfer coefficient is presented in dimensionless form by Frössling number which is defined as the Nusselt number divided by the square root of Reynolds number. Fig. 10 shows the heat transfer coefficient distributions for the four test models under blowing ratio M=0.7. There is a low heat transfer region close to the lower part of the hole exit in the first row for all the four cases. As shown in Fig. 5 this region is just where the jet core flows through. We know that the region around
the first row is the mainstream stagnation region where the heat transfer should be very strong. So this low heat transfer region is mainly because the jet coverage reduces the enhancing effect of the flow stagnation. In addition to this region, there is another low heat transfer coefficient region close to the second row hole exit relative to the heat transfer coefficient in its neighboring region over and below it. As shown in Fig. 5, this low heat transfer coefficient region is also where the core of jet from the second row hole flows through. And the high heat transfer coefficient region is the jet edge region in which the strong heat transfer should be caused by the intense turbulence produced from the interaction between the mainstream and the jet. The heat transfer coefficient around the upper part of the hole exit in the first row is also relatively higher for the same reason. The lowest heat transfer coefficients occur in the regions with no or little influence of the jets. So the basic distribution features of the heat transfer coefficient are the same for the four models, especially for the models with the same pitch-to-hole. However, compared with the p = 5d cases, the p = 8d cases have relatively lower heat transfer coefficient value and larger low heat transfer coefficient region because a large area cannot be or can only be little influenced by the jets in the p = 8d models. Figs. 11–13 show the heat transfer coefficient distributions for the four test models under blowing ratio M = 1, 1.4 and 2 respectively. Compared with the heat transfer coefficient distributions
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Fig. 13. Distributions of local heat transfer under M = 2.
under M = 0.7, we can see that the basic distribution features of heat transfer coefficient are the same for the four models under all the blowing ratios. Generally speaking, heat transfer coefficient in the region where the jet core flows through is relatively lower, while in the jet edge region the heat transfer coefficient is relatively higher because of the intense turbulence caused by the flow interaction. And from these four figures, we can also see that the heat transfer coefficient of each model increases as the blowing ratio increases. For the p = 8d models of cylindrical hole and laidback hole, there is a large area in the downstream region after the second row which is not or little influenced by the jets because of large hole-to-hole spacing. In these regions, the heat transfer coefficient is relatively lower. Compared with the p = 8d models, the p = 5d models have much higher heat transfer coefficient values and larger proportion of high heat transfer coefficient region because of small hole-to-hole spacing resulting in a strong interaction between jets and mainstream. Especially for the p = 5d models of cylindrical hole and laid-back hole under blowing ratios larger than M = 1.4, the intense interaction between jet and mainstream highly enhances the heat transfer in two regions. One is the region around the hole exit in the first row except the part below the hole exit where the jet core flows through. And the other is the region around the hole exit in the second row except the parts where the jet core flows through.
Fig. 14 also shows the comparisons of laterally averaged heat transfer coefficients between different holes. The averaged heat transfer coefficients of cylindrical hole model and laid-back hole model with the same hole-to-hole pitch are nearly the same with each other under the same blowing ratios, except the p = 5d models under M = 2 in which the cylindrical holes give higher heat transfer coefficient than the laid-back holes. The averaged heat transfer coefficients of p = 5d models are higher than those of p = 8d models along the whole streamwise region under all the four blowing ratios. And as the blowing ratio increases, the difference between the averaged heat transfer coefficients of p = 5d models and p = 8d models gets larger. 3.3. Comparison with other results Fig. 15 shows the comparisons of the present results to the data reported by Ou and Rivir [7], Kim et al. [17] and Gao et al. [22]. The measured film cooling effectiveness and heat transfer coefficient are consistent with the published data, considering the differences in the experiments. In Gao et al. [22], the distance between the first and the second hole row is 6.33d. So in the region downstream of X/d = 2, the effectiveness from Gao et al. [22] is lower than the present result. In Ou and Rivir [7], the spanwise inclination angle a is 20 . Therefore, the jets attached on the wall much closer, thus,
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Fig. 14. Comparisons of laterally averaged Froe between different holes.
the laterally averaged effectiveness and heat transfer coefficient are larger than the present results under relatively larger blowing ratio of M = 1.4, especially in the region near the hole row. 4. Conclusion Film cooling performances of cylindrical holes and laid-back holes on the turbine blade leading edge have been studied in this paper. Experimental measurements are carried out to investigate the influences of film hole shape and hole pitch on the film cooling performances. Three rows of holes are arranged in a semi-cylinder model which is used to model the blade leading edge. Four blowing ratios are tested for two hole pitches. Transient heat transfer measurement technique with double thermochromic liquid crystals is used in the present experiment. The following conclusions can be drawn: For all the four leading edge models, the trajectory of jets is nearly aligned in the mainstream direction under small blowing ratio of M = 0.7, and the jets attach on the wall surface very well. As the blowing ratio increases, the trajectory of jet from the second row hole deviates to the spanwise direction gradually, and the jet from the first row hole almost flows in the spanwise direction. Under blowing ratios larger than 1, the jets lift off from the model surface because of strong exit momentum, while the influence region of the jets is larger because of large jet flux. More area can benefit from the film coverage. For the models with p = 5d, the film
coverage performances of laid-back holes are almost the same with those of cylindrical holes under small blowing ratio. But as the blowing ratio increases, the laid-back holes give better and better performances of film coverage. The laid-back holes provide an about 55% percent increase in the averaged film cooling effectiveness under M = 2. Flow interaction is more intense for the p = 5d cases than the p = 8d cases because of narrow hole-to-hole spacing. In the first row, due to the pressing effect from the upper jet, the jet from the lower hole can cover large area between the first row and the second row. For the models with p = 8d, the advantage of laid-back holes in film cooling effectiveness is more obvious in the upstream region between the first row and the second row relative to the cylindrical holes. And compared with the p = 8d models, the proportion of film covering area is much larger for the p = 5d models. No matter under small or large blowing ratios, the basic distribution features of heat transfer coefficient are the same for the cylindrical hole models and the laid-back hole models. Heat transfer coefficient in the region where the jet core flows through is relatively lower, while in the jet edge region is relatively higher because of the intense turbulence caused by the flow interaction. For every model, heat transfer coefficient increases as the blowing ratio increases. Compared with the p = 8d models in which large area cannot be or can only be little influenced by the jets, the p = 5d models have much higher heat transfer coefficient values and larger proportion of high heat transfer coefficient region
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Acknowledgement This work is sponsored by the National Basic Research Program of China (China 973 Program) under number of 2007CB707701. References
Fig. 15. Comparison of laterally averaged results to published data.
because of narrow hole-to-hole spacing resulting in a strong interaction between jets and mainstream, especially under large blowing ratios. The laterally averaged heat transfer coefficients of cylindrical hole model and laid-back hole model with the same hole-to-hole spacing are nearly the same with each other under the same blowing ratios. And as the blowing ratio increases, the difference in the laterally averaged heat transfer coefficient between the p = 5d models and the p = 8d models gets larger.
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