Heat ( Mass ) Transfer in a Rotating Two-Pass Square Channel Part II : Local Transfer Coefficient , Smooth Channel

Naphthalene sublimation technique and the heat/mass transfer analogy are used to determine the detailed local heat/mass transfer distributions on the leading and trailing walls of a twopass square channel with smooth walls that rotates about a perpendicular axis. Since the variation of density is small in the flow through the channel, buoyancy effect is negligible. Results show that, in both the stationary and rotating channel cases, very large spanwise variations of the mass transfer exist in he turn and in the region immediately downstream of the turn in the second straight pass. In the first straight pass, the rotation-induced Coriolis forces reduce the mass transfer on the leading wall and increase the mass transfer on the trailing wall. In the turn, rotation significantly increases the mass transfer on the leading wall, especially in the upstream half of the turn. Rotation also increases the mass transfer on the trailing wall, more in the downstream half of the turn than in the upstream half of the turn. Immediately downstream of the turn, rotation causes the mass transfer to be much higher on the trailing wall near the downstream corner of the tip of the inner wall than on the opposite leading wall. The mass transfer in the second pass is higher on the leading wall than on the trailing wall. A slower flow causes higher mass transfer enhancement in the turn on both the leading and trailing walls.


INTRODUCTION
The blades in advanced gas turbine engines must withstand intense heat because they are exposed to hot gases at very high temperatures.To keep the blade temperatures below critical levels, air is circulated from the compressors through internal multipass or serpentine shaped cooling channels.Since rotation induces Coriolis and buoyancy forces, and a sharp turn causes secondary flows, the flow patterns in these channels are very different from those in stationary straight channels.Coriolis forces push the flows toward the trailing walls for radially outward flows, and toward the leading Corresponding author.Tel." (409)  845-0171.Fax: (409) 862-2418.E-mail: slau@mengr.tamu.edu.walls for radially inward flows.The temperature differences between the flows and the channel walls cause cross-streamwise variations of buoyancy forces, which induce secondary flows along the radial direction.At the sharp turns, the coolant flows separate at the tips of the inner walls and impinge on the outer walls at the turns.The inter- actions between the forces in the flows due to rotation and those due to the sharp turns result in highly complex flow patterns and large variations of the local heat transfer on all the walls throughout these turbine blade cooling channels.
A survey of the open literature reveals that extensive heat transfer results are available for straight smooth channels, rotating about perpen- dicular axes.Mori and Nakayama (1968)  and Mori  et al. (1971) examined laminar and turbulent heat transfer in rotating pipes.Morris and Ayhan (1979) observed the effect of buoyancy force on heat transfer in a rotating pipe.Clifford et al. (1984)   conducted experiments with a triangular channel and found that overall heat transfer was enhanced by rotation-induced Coriolis forces.Harasgama and Morris (1988) presented heat transfer results for rotating circular, rectangular, and 'triangular channels, and showed that rotation increased overall heat transfer.Han and Zhang (1992) and Han et al. (1994) found that uneven wall tempera- ture and heating condition affected the heat transfer in a rotating smooth square channel with radially outward flow.Soong et al. (1991)  and  Kuo  and Hwang (1996) compared heat transfer rates in rotating smooth rectangular ducts of different aspect ratios for both radially inward and outward flows, and demonstrated that Coriolis force had a larger effect on the heat transfer in a square duct than on that in a rectangular duct.Extensive heat transfer experimental results for rotating serpentine channels with smooth walls were also reported by many researchers.Hajek et al.   (1991) and Wagner et al. (1991a,b) showed that rotation increased the regional heat transfer on the smooth pressure surface or trailing wall of a square channel up to 3.5 times that for a corresponding fully developed flow through a stationary, smooth tube.On the other hand, the leading wall experi- enced regional heat transfer decrease of up to 60% of the stationary tube value.
Yang et al. (1992) and Mochizuki et al. (1994)   also examined the effect of Coriolis and buoyancy forces on the heat transfer in smooth, rotating serpentine channels.Han et al. (1993) studied the effect of uneven wall heating condition on the heat transfer on the walls of a two-pass, smooth, square channel.Dutta et al. (1994) reported the effect of channel orientation on the heat transfer in a rotating two-pass triangular channel with smooth walls.Hwang and Kuo (1994) conducted experi- ments with a rotating smooth three-pass channel, and reported that the heat transfer enhancement on the trailing wall of the first pass with outward flow was more noticeable than that on the walls of the other two passes.Tse (1995) measured the local veloc- ity distributions in a rotating serpentine channel with smooth walls, and compared their experi- mental results with distributions that were predicted numerically by solving the relevant governing conservation equations with a Navier-Stokes code by Rhie (1986).Other recent numerical studies on turbulent flow and heat transfer in rotating smooth channels include Prakash and Zerkle (1992) and Dutta et al. (1994).
In this investigation, the naphthalene sublima- tion technique and the heat/mass transfer analogy are used to determine the detailed local heat/mass transfer distributions on the walls of a two-pass square channel with smooth walls that rotates about a perpendicular axis.Presently, most experimental heat transfer results in the open literature are regionally averaged heat transfer results.Attention is focused on the mass transfer distributions on the two principal walls, that is, the leading and trailing walls, of the test channel.The main objective of this study is to make available detailed local experi- mental heat/mass transfer data to enable better understanding of the effects of rotation and a sharp turn on the local heat/mass transfer distribution in a rotating two-pass square smooth channel, and to LOCAL TRANSFER COEFFICIENT, SMOOTH CHANNEL help improve the design of serpentine cooling channels in the blades of high-performance gas turbine engines.
During the naphthalene sublimation experi- ments, the walls of the test channel and the air that flows through the test channel were both at room temperature.There was no density variation in the test channel due to temperature variation in the flow field.Furthermore, since the naphthalene partial pressure at the test channel walls in all the experiments in this study was very small, the naphthalene vapor concentration at the test chan- nel walls was very small.The maximum density variation in the naphthalene vapor-air mixture that flows through the test channel (the difference between the mixture density at the channel walls and the inlet air density divided by the inlet air density) was found to be 5 x 10-4.Thus, buoyancy effect in actual turbine blade cooling channels, which the test channel modeled, was not simulated, and the results to be presented will illustrate only the effects of Coriolis forces and turn-induced secondary flows on the local heat/mass transfer distribution.

TEST APPARATUS AND PROCEDURE
The main component of the test apparatus was the test section that was a two-pass square channel constructed entirely of aluminum.Both of the two straight segments of the test section and the tip clearance at the sharp 180 turn had a flow cross section of 1.59 cm x 1.59 cm.Each straight segment had a length of 11.11 cm, which was equivalent to seven times the channel hydraulic diameter.The test section had seven separate walls: two principal walls, two inner side walls, two outer side walls, and an end wall.A 1.59cm wide shallow groove was machined off one surface of each wall and the groove was then filled with naphthalene during a casting process.Figure shows a photograph of the naphthalene-coated surfaces of the test section walls.Once these walls were assembled, the interior surfaces of the test section were all mass transfer active, and the two inner walls had a total thickness of 0.79 cm, which was one-half of the channel hydraulic diameter.Note that the walls were designed and constructed such that none of the rims of the walls were exposed to the flowing air during an experiment.
The seven walls of the test section were assembled inside a rectangular aluminum housing that had two parallel square channels separated by a 0.79 cm thick wall.Once the seven individual walls were secure inside this housing, the assembly consisted of an entrance channel, the two-pass test Channel, and an exit channel.The entrance and exit channels had the same cross section as the test section and had lengths of 10 and 20 hydraulic diameters, re- spectively.The end ofthis assembly with the outlet of the exit was welded to a short horizontal aluminum tube that was affixed to the vertical steel shaft of a rotating test rig.The mean rotating radius, that is, the distance from the rotating axis to the middle of the test section, was 30 times the hydraulic diameter of the test section.Figure 2 shows the rotating test rig with the rotating shaft supported by two bearings in a heavy steel cage.A five horse- power electric motor drove the vertical shaft using two pulleys and a belt.The aforementioned short horizontal tube supported the entrance/test/exit channel assembly at one end and an aluminum tube with a counterweight at the other end.
Not shown in Fig. 2 is an aluminum containment tube with the same diameter as the tube with the counterweight that enclosed the entire entrance/ test/exit channel assembly.removable heavy steel meshes that fenced the vertical faces of the steel gage.The meshes were reinforced on the inside with steel angles and thick plywood boards.It should be pointed out that the seven separate walls of the test section and the containment tube were designed such that they might be installed very quickly to minimize mass transfer from the test section walls before and after air was allowed to flow through the rotating test section steadily.Air was drawn through bleed holes on the con- tainment tube and then the inlet/test/exit section assembly with a centrifugal blower.The air then flowed through the hollow rotating shaft, a rotating union, a calibrated orifice flow meter for flow rate measurement, and a gate valve for flow rate control, before it was ducted to an exhaust hood.
To obtain the distributions of the local mass transfer coefficient on the two principal walls of the test section, the surface elevations at a pre- determined grid of points on each of the two naphthalene-coated walls were measured and recorded at the beginning and the end of each test run.Figure 3 shows the grid of points on each wall for local elevation measurement.The elevations were measured with a computer-controlled system that included an electronic depth gage with a lever- type sensor, an electronic amplifier, and a resolu- tion of 0.00025 mm, and a coordinate table with stepper motors.
LOCAL TRANSFER COEFFICIENT, SMOOTH CHANNEL An electronic balance with a resolution of 0.01 mg (or 0.1 mg over a larger range) was used to determine the weights of the seven walls.A U- tube manometer measured the pressures at the ori- fice flow meter and thermocouples measured the air temperatures at the test section inlet and at the orifice flow meter.An electronic tachometer was used to measure the rotational speed.
A test run was initiated by weighing all the walls and by obtaining the initial elevations at the grid of points on each of the two principal walls.The test section and the containment tube were then quickly assembled.After the motor was switched on to rotate the test section at the desired angular velocity, air was drawn through the test section with the blower.A test run typically lasted one to two hours.During the run, the air flow rate and the air temperatures were monitored and recorded periodically.At the completion of the run, each wall was weighed and the elevations at the same grid of points were measured again.
Separate experiments were carried out to deter- mine the correction to the local mass transfer that was necessary due to convection losses during motor and blower start up and shut down, and while the local and overall measurements were conducted.
The local mass transfer coefficient is evaluated as Pw Pb where rh" is the rate of mass transfer per unit surface area, Pw is the naphthalene vapor density at the wall, which is uniform throughout the channel, and Pb is the bulk naphthalene vapor density in the air stream.
The mass flux at each measurement point is evaluated from the density of solid naphthalene, Ps, and the change of elevation during a test run, Az, after applying the correction due to mass losses at the beginning and the end of the test run: where At is the duration of the test run.The naphthalene vapor density at the wall, Pw, in Eq. ( 3) is calculated using the ideal gas law along with the vapor pressure-temperature relation for naphthalene according to Ambrose et al. (1975): T(logoPw) --jao + aE,(x), s-1, 2, and 3, (5)

DATA REDUCTION
The Reynolds number and the rotation number are defined, respectively, as Re-#D (1) where a0= 301.6247, al 791.4937, a2 -8.2536, and a3=0.4043;x-(2T-574)/l14; El(x)=x, E2(x)--2x2, and E3(x)=4x -3x.In Eq. ( 5), Pw is in pascals and T is in degrees Kelvin.The bulk density ofnaphthalene in the air stream, Pb, at any streamwise location is calculated as and fD Ro --- (2)   where f is the rotational speed and U is the average velocity of the air flow through the test channel.The rotation number may be considered as the strength of the Coriolis force relative to that of the inertia force.where the cumulative mass, Cm, is the rate of mass at which naphthalene enters the air stream from the portion of the test section walls upstream of the streamwise location, and ( is the volumetric air flow rate.The weights of the test section walls at the beginning and at the end of a test run are used to determine the bulk densities at the turn and at the test section exit.Since the bulk density at the inlet of the test section is zero, the bulk density at any streamwise location is determined by linearly interpolating the bulk density values at the inlet, the sharp turn, and the outlet of the test section.The bulk naphthalene vapor density at the test channel exit is found to be between 18% and 25% of the naphthalene vapor density at the wall. The Sherwood number is hmD Sh --- (7)   The diffusion coefficient for naphthalene vapor in air, A, is calculated by .1.013 105A 0.0681

16 Patm
where A is in cm2/s, Patm is in pascals, and T is in degrees Kelvin.Equation ( 8) gives the Schmidt number of naphthalene vapor in air of about 2.28.The Sherwood number is normalized by the Sherwood number for a corresponding fully devel- oped flow in a stationary smooth tube, which is determined with the Dittus-Boelter equation: Sho 0.023 Re 8 Sc0"4. (9) The heat/mass transfer analogy relates the Nusselt number to the Sherwood number as follows: .4 Uu \-S-cJ "Sh (10) or Nu /Nuo Sh /Sho (11 It is found that a 0.5C deviation in the surface temperature changes the naphthalene vapor density at the surface by as much as 5 %.The mass flow rate of air, the local naphthalene mass flux, the naphtha- lene vapor density at the wall (relative to pw-Pb), and the bulk naphthalene vapor density in the air stream (relative to pw-Pb), have uncertainties of 4.3%, 3.1%, 7.5%, and 6.7%, respectively.Using the method described in Coleman and Steele   (1989), the maximum uncertainties for the Reynolds number and the Sherwood number are estimated to be 4.8% and 10.8%.

RESULTS
Naphthalene sublimation experiments were con- ducted with Reynolds numbers between 5,500 and 14,500, and rotation number up to 0.24.The Reynolds number and rotation number ranges correspond to mean flow velocities between 5.3 and 14.0 m/s, and rotational speeds up to 770 rpm.
The local mass transfer distributions on the leading and trailing walls of the two-pass test channel with smooth walls are presented as contours of the normalized Sherwood number in this section.
Table I summarizes the conditions of the various test cases.

Stationary Channel
Figures 4(a)-(c) present the local mass transfer distributions on the leading and trailing walls of the test channel in the three cases of no rotation: Cases A, B, and C, respectively.The corresponding Reynolds numbers are 5,500, 10,000, and 14,500.Without rotation, the flow through the two-pass channel should be symmetrical with respect to the midplane between the leading and trailing walls.The figures show that the mass transfer distributions  on the two walls are very similar.Along the first straight pass, the Sherwood number ratio decreases monotonically on both walls with distance from the channel entrance, as the flow develops.The value of Sh/Sho reaches about 1.0 upstream of the turn.Thus, both the flow field and the naphtha- lene concentration field may be considered fully developed entering the turn.
In the turn, a portion of the flow impinges on the end wall and is deflected toward the leading and trailing walls, resulting in high mass transfer along the outer edges of the walls at the turn.The value of Sh/Sho near the end wall is between 2.8 and 3.5 in the three distributions.The presence of a region with relatively slow recirculating flow is evident on each wall near the upstream outer corner of the turn.As much of the flow turns away from this outer corner, Sh/Sho has values between about 1.5 and 2.5, as shown in Figs.4(a)-(c).
The secondary flows that are induced by centri- fugal forces at the turn cause vigorous turbulent mixing, resulting in high Sh/Sho values throughout the turn region.The value of Sh/Sho in the turn is generally higher near the end wall and lower at the tip of the inner wall, except near the upstream outer corner.Also, the values of Sh/Sho in the turn and downstream of the turn are much higher in Case A (Re--5,500) than in Cases B and C (Re--10,000 and 14,500, respectively), indicating higher mass transfer enhancement in the turn and downstream of the turn when the flow rate is lower.As the flow exits the sharp turn and enters the second pass, the flow impinges on the outer side wall and is deflected toward the two principal walls, causing very high mass transfer along the outer edges of the two walls.The mass transfer is also quite high near the inner wall at the entrance of the second straight pass, as some of the flow that separates at the tip of the inner side wall reattaches on the downstream side of the inner wall and spreads toward the leading and trailing walls.
Along the second straight pass, Sh/Sho decreases monotonically, as the flow redevelops.The in- creased turbulence due to the turn results in significantly higher mass transfer on the principal walls in the second pass than in the first pass.The Sh/Sho value decreases to about 1.4 at its exit, in each of Figs.4(a)-(c).
The Sh/Sho distribution in Fig. 4(b) is very similar to the Nu/Nuo distribution for turbulent flow through a stationary square channel with a sharp turn (Re 10,000) given in Fig. 6 "in Ekkad and Han (1995).The heat or mass transfer is high near the end wall and the downstream outer wall.The high heat or mass transfer region near the downstream side of the inner wall that is evident in Fig. 4(b), however, was not observed by Ekkad and  Han (1995).The slight difference in the two dis- tributions may be the result of the different shapes of the tips of the inner walls in the two studies.

Effect of Rotation
Figures 5(a) and (b) show the Sh/Sho distributions on the leading and trailing walls in Cases D and F, with Re-10,000 and Ro-0.05 and 0.09, respec- tively.Rotation changes the mass transfer distribu- tions on the leading and trailing walls considerably.
In the first straight pass, the rotation-induced Coriolis forces push the flow toward the trailing wall.Cross stream secondary flows reduce the mass transfer on the leading wall and increase the mass transfer on the trailing wall.Figure 5(a) shows that the value of Sh/Sho on the leading wall decreases to as low as 0.45 along the first pass.Similarly, with   Ro 0.09, the value of Sh/Sho on the leading wall is as low as 0.3 in the first pass.A slightly asymmetric inlet flow may have caused the higher leading wall mass transfer near the outer wall than near the inner wall.On the trailing wall, the value of Sh/Sho ranges between 1.1 and 1.4, and the mass transfer distribu- tions do not have significant spanwise variations.
Attention is now focused on the turn.Rotation significantly increases the mass transfer on the leading wall in the turn, especially in the upstream half of the turn.The mass transfer on the leading wall is considerably higher in the turn than in the first pass, and there is a rather abrupt increase of the mass transfer at the turn entrance.The Sh/Sho values on the leading wall in the upstream half of the turn are larger than those in the downstream half of the turn.The trend is the opposite of that in the corresponding no-rotation case (Case B).The high mass transfer region near the end wall is shifted toward the upstream corner of the turn, and is much wider, spreading across almost the entire edge of the wall.With rotation, the leading wall mass transfer is lower in the downstream half of the turn than in the upstream half of the turn.A low mass transfer region, with Sh/Sho values as low as 1.5, is evident on the leading wall at the turn exit near the tip of the inner side wall.
Figures 5(a) and (b) show that rotation also increases the mass transfer on the trailing wall, more in the downstream half of the turn than in the upstream half of the turn.The Sh/Sho values in the upstream half of the turn are higher than those in the no-rotation case, whereas the Sh/Sho values in the downstream half of the turn are about the same as those in the no-rotation case.
In the second pass, while the high mass transfer region along the outer side wall on the leading wall is not affected by rotation, the high mass transfer region along the outer side wall on the trailing wall is shifted upstream toward the second outer corner of the turn.With increasing rotational speed, the local peak in the leading wall mass transfer distribution along the inner wall is reduced and that in the trailing wall mass transfer distribution along the inner wall are moved to a location very close to the second inner corner of the turn.
The mass transfer is generally higher in the second pass than in the first pass on both of the principal walls.The increased turbulence induced by the turn enhances the mass transfer on both walls in the second pass.Since the flow in the second pass is radially inward, Coriolis forces are supposed to increase the mass transfer on the leading wall and reduce that on the trailing wall.
However, the interaction between secondary flows that are caused by the turn and Coriolis forces (which are relatively small in these cases of low LOCAL TRANSFER COEFFICIENT, SMOOTH CHANNEL rotational speeds) keeps the mass transfer on the leading wall almost the same as that on the trailing wall, except far downstream of the turn, where the mass transfer is slightly lower on the trailing wall.Along the second pass, as the flow redevelops, the mass transfer on the two walls decreases, with values of Sh/Sho drop about 1.2.
Figures 6(a)-(c) present the local mags transfer distributions in Cases E, H, and I, with rotation numbers of 0.09 and 0.16, and 0.24, respectively.The Reynolds numbers in all three cases are 5,500.The distributions are similar qualitatively to those for the two higher Reynolds number cases: Cases D and F. They again show that increasing the rotational speed reduces the mass transfer on the leading wall and increases that on the trailing wall, in the first pass.Figure 6(c) demonstrates that increasing the rotation number to 0.24 intensifies the cross stream vortices.Coriolis forces push much of the flow toward the trailing wall, and results in a large difference between the mass transfer on the leading wall and that on the trailing wall in the first pass: with Sh/Sho values of less than 0.3 versus values of about 1.6.
With Ro-0.24, the effect of Coriolis forces on the mass transfer on the leading and trailing walls for the radially inward flow in the second pass becomes evident.In the second pass, the mass transfer is higher on the leading wall than on the trailing wall.The high mass transfer regions on the leading wall along the end wall and the down- stream outer side wall have very large Sh/Sho values of over 4.0.On the trailing wall, there is a high mass transfer region at the downstream outer corner of the turn.However, the region does not extend as far downstream along the outer side wall as the opposite high mass transfer region on the leading wall.exceeding 4.0 on the trailing wall very close to the downstream inner corner of the turn.Also, there is not a local peak in the leading wall Sh/Sho distribu- tion along the downstream side of the inner wall.Finally, high rotational speed reduces the leading  wall mass transfer at the tip of the inner wall in the turn.
Figure 7 gives the local mass transfer distribu- tions in Case G, with Ro =0.09 and Re 14,500.
Comparing Figs.5(b), 6(a), and 7 (Cases E, F, and G), it is evident that increasing the Reynolds number from 5,500 to 14,500 does not change the trends of the local distributions on the two walls.
Increasing the Reynolds number decreases slightly the difference between the Sh/Sho values on the leading wall and those on the trailing wall in the first straight pass.The Reynolds number effect is, however, much more obvious in the turn.A slower flow causes higher mass transfer enhancement in the turn on both the leading and trailing walls.

CONCLUDING REMARKS
Naphthalene sublimation experiments have been conducted to determine the detailed local mass transfer distributions on the leading and trailing walls of a two-pass square channel with smooth walls that rotates about a perpendicular axis.The following conclusions may be drawn" 1.In both the stationary and rotating channel cases, very large spanwise variations of the mass transfer exist in the turn and in the region immediately downstream of the turn in the second straight pass.
2. In the first straight pass, the rotation-induced Coriolis forces reduce the mass transfer on the leading wall and increase the mass transfer on the trailing wall.There is a larger streamwise mass transfer variation on the leading wall of the first straight pass than on the opposite trailing wall.
3. In the turn, rotation significantly increases the mass transfer on the leading wall, especially in the upstream half of the turn.Rotation also increases the mass transfer on the trailing wall, more in the downstream half of the turn than in the upstream half of the turn.
4. The mass transfer is higher in the second pass than in the first pass on both of the principal walls due to the increased turbulence at the turn.
Immediately downstream of the turn, rotation causes the mass transfer to be much higher on the trailing wall near the downstream corner of the tip of the inner wall than on the opposite leading wall.The mass transfer'in the second pass is higher on the leading wall than on the trailing wall.
5. A slower flow causes higher mass transfer enhancement in the turn on both the leading and trailing walls.

FIGURE
FIGURENaphthalene-coated test section walls.

FIGURE 3
FIGURE 3 Grid of local elevation measurement points.
FIGURE 4(a) Local mass transfer distributions on leading and trailing walls, Case A, Ro 0.0 and Re--5,500.
FIGURE 5(a) Local mass transfer distributions on leading and trailing walls, Case D,Ro=0.05 and Re= 10,000.

Figure 6
Figure 6(c) clearly indicate a peak with values FIGURE 6(a) Local mass transfer distributions on leading and trailing walls, Case E, Ro 0.09 and Re 5,500.

E
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TABLE Conditions
Local mass transfer distributions on leading and trailing walls, Case G, Ro 0.09 and Re= 14,500.