Heat transfer engineering an international journal, tập 31, số 10, 2010

Heat Transfer Engineering, 31(10):799–808, 2010 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457630903547461 Film Condensation of R-134a and R-236fa, Part 1: Experimental Results and Predictive Correlation for Single-Row Condensation on Enhanced Tubes MARCEL CHRISTIANS, MATHIEU HABERT, and JOHN R THOME Laboratory of Heat and Mass Transfer (LTCM), Faculty of Engineering Science Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland New predictive methods for falling film condensation on vertical arrays of horizontal tubes using different refrigerants are proposed, based on visual observations revealing that condensate is slung off the array of tubes sideways and significantly affects condensate inundation and thus the heat transfer process For two types of three-dimensional enhanced tubes, advanced versions of the Wolverine Turbo-C and Wieland Gewa-C tubes, the local heat flux is correlated as a function of condensation temperature difference, the film Reynolds number, the tube spacing, and liquid slinging effect The proposed methods work best when using R-134a, as these tubes were designed with this refrigerant in mind INTRODUCTION PREVIOUS HEAT TRANSFER COEFFICIENT STUDIES Tubes in shell-and-tube condensers, widely used in refrigeration, heat pumps, and chemical process industries, are subjected to condensate inundation from the neighboring upper tubes In order to increase the efficiency of these systems, plain tubes were replaced by all types of enhanced tubes, from finned tubes to tubes with advanced two-dimensional (2D) and threedimensional (3D) enhancement geometries However, it is necessary to characterize the performance of new tubes, so that design engineers have a solid foundation on which to base their designs Furthermore, it is of interest to test the performance of these tubes with several refrigerants, such that the differing behavior may be quantified and taken into account during the design stage itself Jung et al [1–3] performed falling film condensation tests using plain, low-fin and enhanced tubes and pure refrigerants R-11, R-12, R-123, R-22, and R-134a, and zeotropic and azeotropic refrigerant mixtures R-407C, R-410A, R-32/R134a, and R-134a/R-123 on a test section comprised of a single tube at a saturation temperature of 39◦ C The finned tubes had 1,024 fins per meter, while the enhanced tube tested was the Turbo-C Chang et al [4] performed tests on single tubes connected by a U-bend, at a saturation temperature of 39◦ C on low-fin and 3D enhanced tubes, using refrigerant R-134a The finned tubes had 1,024 and 1,574 fins per meter, while the two 3D enhanced tubes had T- and Yshape fins Kumar et al [5, 6] tested plain and finned tubes with refrigerant R-134a on single tubes, at a saturation temperature of 39.3◦ C The finned tubes had fin densities of 472 (rectangular), 934, 1,250, 1,560, and 1,875 fins per meter Sreepathi et al [7] tested several proprietary finned tubes, commercial finned tubes (748 and 1,574 fins per meter), and the enhanced tubes Thermoexcel-C and Thermoexcel-CC1 in a single tube configuration, using R-11 and R-123, at saturation temperatures of 23.5 and 27.4◦ C Wen et al [8] studied the performance of four tubes (667 and 1000 fpm, with and without The authors thank the laboratory’s industrial sponsors Johnson Controls, Trane, Wieland Werke, and Wolverine Tube, Inc., for funding this study Special thanks to the tube manufacturers, Wieland Werke and Wolverine Tube, Inc., for supplying the tubes utilized Address correspondence to Prof John R Thome, Laboratory of Heat and Mass Transfer (LTCM), Faculty of Engineering Science, Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Station 9, Lausanne CH-1015, Switzerland E-mail: john.thome@epfl.ch 799 800 M CHRISTIANS ET AL filled fin-roots) in a single tube test section using R-113 at a saturation temperature of 47.6◦ C Kang et al [9] tested low-fin and 3D enhanced tubes in a test section consisting of five horizontal tubes placed on a single horizontal plane (i.e., side by side), at a saturation temperature of 60◦ C, using refrigerant R-134a The tested tubes included one low-fin tube and three Turbo-C variants Gstăohl and Thome [10, 11] performed tests on a single column of several tubes (varying the pitch between tubes), as well as plain, low-fin, and 3D enhanced tubes at a saturation temperature of 31◦ C In these tests, it was possible to vary the overfeed onto the first tube of the column to simulate flow deeper in a bundle The tubes tested were a Turbo-Chil low-fin tube, and both Wolverine and Wieland enhanced condensation tubes (Turbo-CSL and GewaC) using only R-134a As a continuation of this work, Habert et al [12] presented additional flow regime transition criteria for Wieland and Wolverine enhanced tubes using an additional refrigerant (R-236fa) However, in this study, no heat transfer measurements were presented As such, the aim of this article is to present and discuss the results obtained in the LTCM’s falling film facility for advanced versions of the Turbo C and Gewa C 3D enhanced tubes, using both R-134a and R-236fa R-236fa was chosen as a second test fluid because of its compatibility with the experimental test stand In addition to the preceding, prediction methods based on Gstăohl and Thomes [11] original R-134a data-only predictive model are developed and presented EXPERIMENTAL FACILITY The experimental setup is comprised of three circuits, namely, the refrigerant, water–glycol, and water circuits The refrigerant circuit is shown schematically in Figure It comprises an electrically heated evaporator (Figure 1, (1) flooded evaporator) to maintain the desired saturation condition, a condenser (Figure 1, (5) auxiliary overhead condenser) to condense Figure Schematic of the refrigerant circuit in the Falling Film Facility heat transfer engineering any vapor not condensed in the test section, and the test section itself (Figure 1, (4) test section) In the refrigerant circuit, starting from the flooded evaporator (Figure 1, (1) flooded evaporator), the refrigerant flows through the filter (not shown) and the subcooler (Figure 1, (6) liquid subcooler) to the gear pump (self-lubricating without oil: Figure 1, (7) overfeed pump) Parallel to the pump, bypass piping is installed so that, together with a frequency controller on the pump, the desired liquid flow rate can be accurately set A Coriolis mass flow meter (Figure 1, (8) Coriolis mass flow meter) follows, after which an electric heater (Figure 1, (9) liquid heater) is installed to bring the liquid close to saturation conditions at the test section inlet At this point, the liquid enters the test section and is distributed uniformly on the top row of the heated tubes Special care has been taken in the distributor design in order to achieve uniform liquid distribution on the top tube Once the liquid leaves the distributor, it falls onto the top of the cooled tube array, on which the vapor in the test section is partially condensed; the residual liquid leaves the test section by gravity From the exit of the test section, the liquid flows back to the flooded evaporator by the effect of gravity The vapor that runs through the test section is generated in the flooded evaporator, where by natural convection it rises to the top of the test facility It flows in to the top of the test section, where the vapor flow is uniformly distributed over its length, and any remaining vapor is sucked out at the bottom of the test section After exiting the test section from the bottom, it flows back into the condenser, and the liquid drops by gravity back to the flooded evaporator The amount of vapor flow can be controlled by increasing the heat input in the flooded evaporator, which in turn generates more vapor Consequently, to maintain a constant system pressure, the cooling load on the auxiliary condenser is greater In these tests, it was attempted to maintain the vapor velocity as low as possible, such that vapor shear effects were minimized The water circuit (not shown) is responsible for the cooling effect in the test section The water is driven through the test tubes by a centrifugal pump An electronic speed-controller, together with a bypass line, ensures good precision in any water mass flow adjustment The water flows through two liquid– liquid heat exchangers; the first is cooled with industrial water sourced from Lake Geneva at a constant temperature of 7◦ C, while the second is heated with hot water from a closed-loop circuit heated by a heat pump This water has its flow rate set by a computer-controlled valve The water temperature at the test section inlet is thus automatically maintained constant The total water mass flow rate is measured with a Coriolis flow meter (not shown) Before entering the test section, the test-line water flow is split into three subcircuits, each supplying to two tubes in the test section Each subcircuit has two tube passes; i.e., water goes in a copper tube in one direction (left to right) and comes back through the copper tube just above in the opposite direction A water–glycol mixture from a network installation is used as a cold source for the auxiliary condenser vol 31 no 10 2010 M CHRISTIANS ET AL The test section is a rectangular stainless-steel vessel with six large windows situated at the front and rear in order to have full visual access into the experimental setup, to observe the flow on the tubes The copper test tubes had a nominal outer diameter of 18.38 mm and are arranged horizontally in a vertical array The length of the tubes was 554 mm In total, six tubes (i.e., three subcircuits) were installed, at a industry-standard pitch of 38.5 mm Furthermore, a stainless-steel tube with an external diameter of mm was inserted inside each copper test tube Pairs of thermocouples were located at three positions axially along the tube, protruding out through holes to measure the temperature of the water in the annulus between the stainless steel tube and the copper tubes At every location, one thermocouple is facing upward and one is facing downward A copper wire with a rectangular cross section wound helically around the stainlesssteel tube promoted mixing, and further increased the water-side heat transfer coefficient Pressure transducers connected to the test section above and below the array of tubes were used to measure the vapor pressure in the test section The vapor temperature in the test section was measured above and below the tube array using sheathed thermocouples The temperatures of the liquid entering and leaving the test section, as well as the vapor leaving the test section, were measured EXPERIMENTAL ERRORS AND PROCEDURES The internally mounted thermocouples measuring the water temperature within the tube annulus along the axial length of the tubes provide the water temperature profile as a function of the distance x along the tubes Assuming only heat flow in the radial direction, the local heat flux on the outside of the tube, qo , may thus be expressed as qo = ˙ water cp,water m π Do dTwater dx (1) where Do is the outside diameter The value (dTwater /dx) is obtained by differentiating a second-order polynomial fit of the water temperature profile Nearly identical temperatures for the pairs of thermocouples located at each location indicate good mixing of the water (the temperatures were within thermocouple uncertainty), which helps increase the accuracy of the data reduction method To determine the external local heat transfer coefficient, ho , between the outside surface of the copper tubes and the refrigerant, a modified Wilson plot procedure using nucleate pool boiling (as in Robinson and Thome [13]) on the outside of the tubes was implemented The modified Wilson plot method takes into account slight variations in the heat flux by assuming a relation for the external heat transfer coefficient given by ho = Co qo0.7 The internal heat transfer coefficient is the one given by the Gnielinski [14] correlation, hgni , multiplied by a constant Ci that takes into account the increase in heat transfer heat transfer engineering 801 Table Calculated values for the internal heat transfer multiplier Ci Tube Wolverine Turbo (condensing) Wieland Gewa (condensing) Ci [—] δCi [—] δCi /Ci [%] 7.38 4.78 ±0.41 ±0.40 ±5.42 ±8.37 due to any internal enhancement, the reduced flow area, and increased turbulence due to the inserted helical tape The Wilson plot expression for the tubes is thus 1 − Rw qo0.7 = Uo Ci qo0.7 hgni Do Di + Co (2) With changes of the water velocity and temperature rise to maintain a fixed heat flux qo , the values in the square brackets are altered The resulting inverse slope of a line plotted through a plot of the values in the brackets on the left versus the values in the brackets on the right gives the value of Ci , while the inverse of the abscissa intercept yields Co Thus, the heat transfer on the outside of the tube at any location along its axis can be calculated with the value of Ci , along with the measured water temperature profile, the water mass flow rate, and the saturation temperature of the refrigerant However, in this study the local coefficient is only evaluated at the midpoint of every tube This calculated value is a perimeter-averaged heat transfer coefficient based on the external tube diameter The modified Wilson tests were conducted over a water-side Reynolds number range varying from 6,000 to 16,000 Table shows the values of Ci obtained by this study It can be seen that the Ci value obtained for the Wolverine Turbo-C enhanced condensing tube of 7.38 is higher than for the other tube, due to its 3D internal enhancement structure To eliminate all traces of non-condensable gases that might have been introduced into the facility (i.e., during tube or refrigerant changes), a vacuum pump (not shown in Figure 1) is connected to the system and is run until the two low-pressure reference pressure transducers show no more than 100 Pa (absolute) Once the vacuum pump is stopped, the system pressure is monitored to make sure that no leaks are present Only once these two steps have been accomplished is the system refilled with refrigerant to proceed with testing Any remaining traces of non-condensable gases in the system will migrate to the overhead condenser, where they remain The measured saturation temperature using thermocouples and that obtained from the pressure sensors and REFPROP v8 [15] differed by 0.1 K, a value within the uncertainty of both measurements For experiments involving overfeed, the film flow rate of the liquid arriving on the first tube was evaluated from the measured mass flow rate and the tube length, assuming that the refrigerant is at saturation conditions The mass flow of refrigerant condensing on the first tube is calculated by an energy balance on differential elements and added to the film flow rate arriving on the first tube to obtain the film flow rate at the top of the second tube and so on This means an ideal one-dimensional downward flow is assumed on the tube rows and assumes that all the condensate flows from one tube to the next without leaving the vol 31 no 10 2010 802 M CHRISTIANS ET AL Table Uncertainties of measured heat transfer coefficients at the three heat flux conditions tested Array, Turbo C tube, tube spacing 38.5mm, heat flux: 20kW/m2 25000 δho / ho R−134a qo = 40 kW/m2 qo = 60 kW/m2 10.40% 7.01% 6.11% 11.62% 7.25% 6.43% qo = 20 kW/m2 Heat transfer coefficient [W/m K] Tube EXPERIMENTAL RESULTS WITH THE SINGLE-ROW TEST SECTION Tests were performed using the Wolverine Turbo and Wieland Gewa condensing tubes (both of them have an 18.38mm nominal outer diameter) provided by the manufacturing companies Before installation into the test section, the tubes were thoroughly cleaned In the column of six tubes (single vertical row), the center-to-center tube pitch was 38.5 mm, and tests were performed using refrigerants R-134a and R-236fa, at a saturation temperature of 31◦ C Furthermore, tests were performed at constant tube array nominal heat fluxes of 20, 40, and 60 kW/m2 In Figures 2–7, it can be seen that the refrigerant in use has a very large effect on the performance of each tube For these tubes, and at all heat fluxes, the R-236fa results show lower performance over the entire Reynolds number range Furthermore, when using R-134a, the heat transfer performance of the first (top) tube is considerably higher than the rest of the array, something especially true at lower Reynolds numbers This is probably related in some manner to the overfeed from the liquid distributor—the value at the lowest Reynolds number in each diagram for tube (that is, without overfeed) usually aligns well with the trend of the rest of the data For tests at a constant nominal array heat flux, it can be seen that there is a very slight or almost no dependence on the tube row number, a trend that was also evident in the testing presented by Gstăohl and Thome [10] heat transfer engineering 20000 15000 10000 Tube Tube Tube Tube Tube Tube 5000 R−236fa 0 500 1000 1500 2000 Film Reynolds number, Re 2500 [−] 3000 3500 bottom Figure Heat transfer performance of the six Wolverine Turbo C condensing test tubes at a nominal array heat flux of 20 kW/m2 using both R-134a and R-236fa With the Turbo condensing tube/R-134a combination (Figures 2–4), the behavior of the tube is similar to the threedimensional enhanced tubes tested originally by Gstăohl and Thome [10] This similarity is not in terms of the heat transfer coefficient values themselves, since the Turbo-CSL results presented [11] had peaks of roughly 25 kW/m2 -K while this tube’s peak is at 28 kW/m2 -K, but rather in the general form of the evolution of the heat transfer with increasing Reynolds number Also using R-134a, the Wieland Gewa data (Figures 5–7) show that the top two tubes have a large heat transfer peak at lower Reynolds numbers With both tubes, the data at the highest Reynolds numbers fluctuate and still seem to form a plateau like that seen in the Turbo-CSL results [11] In Array, Turbo C tube, tube spacing 38.5mm, heat flux: 40kW/m2 Tube Tube Tube Tube Tube Tube 25000 R−134a tube row In case of no overfeed, a similar procedure was applied, with the initial flow rate onto the top tube set to The two-pass water design gives a nearly uniform axial condensate distribution along the tube array after each pair of tubes The saturation temperatures, as well as the transport and thermodynamic properties, are calculated according to REFPROP v8 [15] from the mean of the pressures measured by pressure transducers above and below the tube array Tests were conducted by gradually decreasing the liquid film flow rate on the top tube at a fixed heat flux The data were logged only if steady-state conditions were attained An error analysis was performed, and the mean relative errors in the local heat transfer coefficient at a saturation temperature of 31◦ C are tabulated in Table A more detailed description of the test facility, data reduction methods, and measurements accuracies can be found in Gstăohl and Thome [10, 11] Heat transfer coefficient [W/m K] Wolverine Turbo (condensing) Wieland Gewa (condensing) 20000 15000 10000 5000 R−236fa 0 500 1000 1500 2000 2500 Film Reynolds number, Re bottom 3000 [−] 3500 4000 Figure Heat transfer performance of the six Wolverine Turbo C condensing test tubes at a nominal array heat flux of 40 kW/m2 using both R-134a and R-236fa vol 31 no 10 2010 M CHRISTIANS ET AL Array, Turbo C tube, tube spacing 38.5mm, heat flux: 60kW/m2 20000 15000 10000 R−134a R−134a 25000 Heat transfer coefficient [W/m K] Heat transfer coefficient [W/m K] Array, Gewa C tube, tube spacing 38.5mm, heat flux: 40kW/m2 Tube Tube Tube Tube Tube Tube 25000 803 5000 20000 15000 10000 5000 R−236fa Tube Tube Tube Tube Tube Tube 500 1000 1500 2000 Film Reynolds number, Re 2500 [−] R−236fa 3000 3500 500 bottom 1000 1500 2000 2500 Film Reynolds number, Re bottom 3000 [−] 3500 4000 Figure Heat transfer performance of the six Wolverine Turbo C condensing test tubes at a nominal array heat flux of 60 kW/m2 using both R-134a and R236fa Figure Heat transfer performance of the six Wieland Gewa C condensing test tubes at a nominal array heat flux of 40 kW/m2 using both R-134a and R-236fa contrast to the results of Gstăohl and Thome [10, 11], the heat transfer degradation with increasing Reynolds number is not as severe; while it does occur at essentially the same Reynolds number, and with the same slope, the heat transfer coefficient stabilizes at ∼50 to 60% of the peak measured heat transfer coefficient, while for the tubes tested by Gstăohl and Thome, the plateau was found at around 20% of the peak heat transfer coefficient value Evidently, this will have a beneficial effect on condenser performance For the Wieland tube, tubes through are closely grouped The general trend for the tubes in the array is an increase to a stable plateau Furthermore, tubes and are the only ones to show significant heat transfer degradation as the film velocity increases This could be due to a type of en- trance effect (impingement) only apparent due to the surface’s geometry Using R-236fa, Figures 2–4 show that for the Wolverine condensing tube, the behavior of the heat transfer coefficient is vastly different In this case, the heat transfer coefficient slowly increases to a band within which the heat transfer fluctuates yet remains bound As neither the type of tube, nor the geometric distribution, nor the measurement technique was changed, it can be safely concluded that the difference in heat transfer evolution and the degradation of performance with respect to the R-134a tests is solely a function of the thermophysical properties of the refrigerant under consideration Looking at the Wieland tube Array, Gewa C tube, tube spacing 38.5mm, heat flux: 60kW/m Array, Gewa C tube, tube spacing 38.5mm, heat flux: 20kW/m2 25000 R−134a R−134a Heat transfer coefficient [W/m K] 20000 15000 10000 Tube Tube Tube Tube Tube Tube R−236fa 5000 20000 2 Heat transfer coefficient [W/m K] 25000 500 1000 1500 2000 Film Reynolds number, Re 2500 [−] 3000 15000 10000 Tube Tube Tube Tube Tube Tube 5000 R−236fa 3500 0 500 1000 bottom Figure Heat transfer performance of the six Wieland Gewa C condensing test tubes at a nominal array heat flux of 20 kW/m2 using both R-134a and R-236fa heat transfer engineering 1500 2000 2500 Film Reynolds number, Re 3000 [−] 3500 4000 4500 bottom Figure Heat transfer performance of the six Wieland Gewa C condensing test tubes at a nominal array heat flux of 60 kW/m2 using both R-134a and R-236fa vol 31 no 10 2010 804 M CHRISTIANS ET AL Table Comparison of the physical properties of the two refrigerants at 31◦ C Property M [kg/kmol] pcrit [kPa] hlv [J/kg] σ[Nm] ρl [kg/m3 ] cpl [J/kg-K] kl [W/m-K] µl [Pa s] underneath it as θcrit = arcsin R-134a R-236fa 102.03 4060 172,000 0.0073 1,184 1,451 0.0780 1.835 × 10−4 152.04 3200 142,000 0.0094 1,340 1,280 0.0711 2.649 × 10−4 data (Figures 5–7), these results differ from the R-134a data in that they are contained within a small band, and lower in magnitude Furthermore, the maximum tube peak using R134a was around 23 kW/m2 -K, while with R-236fa this peak was found at 12.5 kW/m2 -K The large difference in absolute performance (and with respect to increasing Reynolds number) can be attributed to the geometric design of the tubes themselves; both of these were optimized for R-134a condensate drainage, and using a different refrigerant is going to have an impact on performance Table shows a comparison of the physical properties of the two refrigerants at 31◦ C In both falling film evaporation and condensation, two thermodynamic properties that have large influence are the liquid viscosity and the surface tension It can be seen that there is a 36% difference in viscosity and 25% difference in surface tension between the two refrigerants at a saturation temperature of 31◦ C This will primarily affect the thickness of the liquid film and its interaction with the tube UPDATED PREDICTION METHOD θ = dRe + e (3) where the coefficients a, b, and c for the tubes that were tested are given in Table in [11] However, it was found that for 3D enhanced tubes, as the Reynolds number increased, a fraction of the liquid refrigerant left the tube array sideways [16] This was due to the fact that the liquid film did not fall as a stable sheet, but rather fell with an oscillatory motion Thus, they calculated the critical angle (a function of the tube geometry and tube pitch) for which the liquid film would begin to not reattach the tube heat transfer engineering (5) The portion of liquid that leaves the tube is assumed to be proportional to the ratio of (θ – θcrit )/θ This means that the film Reynolds number on the top of the nth tube in the array can be expressed as θcrit Rebottom,n−1 (6) θ Once the actual amount of liquid that falls on the top of the tube is known, Eq (3) can be used to determine the heat flux on the tube Thus, the heat flux of the nth tube becomes Retop,n = qo = a + c θcrit Retop,n θ Tb (7) To apply, the calculation is started on the top tube of the array As long as there is no slinging (i.e., θ ≤ θcrit ), Eq (3) is used to determine the heat transferred by the tube, and the amount of liquid leaving the bottom of the tube can be calculated In this case, all the liquid flowing off the bottom of the tube is assumed to fall on top of the tube below (Retop,n = Rebottom,n−1 ) As soon as the liquid starts to sling out (i.e., when θ > θcrit ), Eq (6) can be used to determine the amount of liquid that arrives on the tube below Equation (7) is used to determine the heat flux transferred by the tube To determine the heat transfer coefficient from the preceding equation, it suffices to divide the heat flux by the temperature difference, that is, Background qo = (a + cRetop ) T b (4) where ro is the tube radius and p is the tube pitch Then, the slinging angle is defined as a linear function of the Reynolds number hc,o = a + c Gstăohl and Thome [11] presented two heat transfer models for 3D enhanced condensing tubes: the first for when there is no slinging (of condensate off the side of the tube), while the second one takes into account the reduction of the Reynolds number due to the slinging They first correlated the heat flux to the Reynolds number on top of the tube by ro p − ro θcrit Retop θ T b−1 (8) The empirical constants for the slinging-heat transfer correlation for the tubes tested by Gstăohl and Thome are given in Table of [11], but are also reproduced in Table of this article for completeness Updated Model The preceding method is fluid/enhanced tube specific, and hence, to update its validity for the new tubes, it is evident that the coefficients utilized should be modified to better fit the new data This is also required, since no general model accounting for the enhancement geometry and its dimensions is available for these fluid/enhanced tubes combinations in the literature A nonlinear least-squares optimization method was utilized to minimize the difference between the prediction method and the measured heat transfer data The optimization process was started from multiple initial positions (spread from the upper to vol 31 no 10 2010 M CHRISTIANS ET AL 805 Table Coefficients in Eqs (7) and (8) and relative errors of the prediction methods for the single row data Tube Refrigerant Turbo Turbo Gewa Gewa TurboCSL Gewa C R-134a R-236fa R-134a R-236fa R-134a R-134a a [W/m2 -K] c [W/m2 -K] b[—] 25,700 11,100 19,250 10,850 25,500 25,200 0.8599 0.7738 0.9042 0.7314 0.91 0.87 d[—] 10−4 3.08 × 0 0.00027 0.00018 –6.0805 −0.5938 −0.607 1.2548 −9.7 −6.5 the lower bounds of the parameter constraints), and all arrived either at the presented solution or very close, showing that the minimum found is a global minimum rather a local minimum The coefficients for use in Eqs (7) and (8) are shown in Table There are four sets of coefficients, one for each tube/refrigerant combination tested Figure shows a comparison of the prediction method found using the nonlinear least-squares optimization and the measured heat transfer coefficient data obtained using the Turbo enhanced condensing tube and R-134a This method predicts 87% of the results within an error range of ±15%, while 100% of the data are within a ±30% error band Comparing the obtained coefficients to those found by Gstăohl and Thome (Table of [11]), it is found that the resulting coefficients are similar in magnitude (a = ∼25,000, b = ∼0.8, c = ∼−6.5, d = ∼0.0004, e = 0) Continuing the analysis of the results obtained with the Turbo enhanced tube (now using R-236fa), the same optimization algorithm was implemented (using Gstăohl and Thomes model), even though the data not show a pronounced degradation in heat transfer The prediction method (using the coefficients shown in Table 4), plotted on the same figure as the results, is shown in Figure For R-236fa, this method only predicts 70% of the data within ±15%, and 95% of the data to within 30% ε [%] 0.005 0.005 0.005 0.08 0.14 −0.78 2.85 −0.85 2.76 −2.4 −1.9 σ [%] 9.17 17.07 9.49 17.48 12.9 10.1 However, the R-236fa data are, for most of the tube/refrigerant configurations, relatively constant, showing little influence with respect to Reynolds number The optimization algorithm shifted the onset of the plateau region to a smaller Reynolds number by first suppressing the slinging angle (θ) such that it has almost no effect It also flattened the prediction by setting a yintercept 50% lower than has been previously calculated (for R-134a and the different tubes tested), and slightly decreasing the power of the exponent b that affects the temperature difference T Furthermore, for R-236fa, the multiplier c acts to suppress the influence of both the slinging angle and the Reynolds number, rather than to amplify it as seen in the R-134a results Applying the method to the Wieland Gewa C enhanced condensing tube and test refrigerant R-134a results in the prediction shown in Figure 10 The method predicts 90% of the results within an error range of ±15%, while 100% of the data are within a ±30% error band Comparing the empirical coefficients to those found by Gstăohl and Thome for the Gewa-C, it is found that the resulting (a) y-intercept coefficient and (b) temperature difference exponent are similar in magnitude (a = ∼20,000, b = ∼0.9, c = ∼−0.6, d = ∼0, e = ∼0) However, there is a relatively large change for the Reynolds number multiplier c, R−236fa, Turbo, tube spacing 38.50mm R−134a, Turbo, tube spacing 38.50mm Tube Tube Tube Tube Tube Tube Model 25000 Tube Tube Tube Tube Tube Tube Model 25000 20000 Heat transfer coefficient [W/m K] 20000 Heat transfer coefficient [W/m K] e[—] 15000 10000 10000 5000 5000 15000 500 1000 1500 2000 Film Reynolds number, Re bottom,n−1 2500 [−] 3000 3500 Figure Prediction method for the single-row Turbo condensing tube data using R-134a heat transfer engineering 0 500 1000 1500 Film Reynolds number, Re 2000 [−] 2500 3000 bottom,n−1 Figure Prediction method for the single-row Turbo condensing tube data using R-236fa vol 31 no 10 2010 806 M CHRISTIANS ET AL perform this is as explained for the R-134a results The c multiplier acts to slightly amplify the Reynolds number effect, as was the case with the previous results obtained by Gstăohl and Thome Presently, it is not possible to present one set of constants a– e that works for all the fluid/enhanced tubes combinations To achieve this, one needs first to develop a theory-based 3D condensation model, and then a predictive-based slinging model; such a model requires local film flow measurements and is a good topic of research for the future CONCLUSIONS Figure 10 Prediction method for the single-row Gewa condensing tube data using R-134a which in this case acts to suppress the the influence of both the slinging angle and the Reynolds number, rather than amplify it (that is, this tube slings less) The optimization algorithm shifted the onset of the plateau region to a much smaller Reynolds number by suppressing the slinging angle (θ) such that it has almost no effect The prediction method for the Gewa condensing tube/R236fa configuration (using the coefficients shown in Table 4) is plotted on the same figure as the results in Figure 11 For R-236fa, this method predicts 70% of the data within ±15% and 90% of the data to within 30% As with the R-134a data, the optimization algorithm shifted the onset of the plateau region to a smaller Reynolds number The method utilized to The heat transfer performance of the new versions of the Wolverine Turbo C and Wieland Gewa C condensing tubes, using refrigerants R-134a and R-236fa, has been measured Using R-134a, the heat transfer coefficient of the two enhanced tubes varied as a function of the film Reynolds number, and was characterized by two distinct zones At low film Reynolds numbers, the top tubes of the array showed a large peak in the measured heat transfer coefficients (most probably, this is an impingement effect due to the surface geometry), after which the heat transfer coefficient decreased almost linearly Above a certain film Reynolds number, the heat transfer coefficient decreases much more slowly and achieves an almost constant value (that is, reaches a plateau) Using R-236fa, this large degradation in heat transfer with increasing film Reynolds number was not seen; in fact, there was almost no change in the heat transfer performance with increasing film Reynolds number (only fluctuation within a bound region) For both 3D enhanced tubes, as well as both refrigerants, the local heat flux on a tube in the array was correlated as a function of the condensation temperature difference and the condensate inundation in the form of the film Reynolds number falling on the tube The coefficients in the correlation were found to be close for both tubes apart from the coefficient c, which corresponds to the slope in the deterioration in heat transfer performance with increasing film Reynolds number When using R-134a, the heat transfer coefficient of the Gewa-C condensing tube decreases less rapidly with increasing film Reynolds number; however, the peak reached is not as large as that found using the Turbo-C tube Using R-134a, the mean relative error of the fluid/enhanced tube specific method was less than 1%, with a standard deviation of less than 10% Using R-236fa, the measurements were predicted by their respective methods with mean relative errors of less than 3% and standard deviations of less than 18% NOMENCLATURE Figure 11 Prediction method for the single-row Gewa condensing tube data using R-236fa heat transfer engineering a b C prediction method constant, W/m2 -K prediction method constant Wilson plot method constant vol 31 no 10 2010 M CHRISTIANS ET AL c cp d D e h hlv k M ˙ m p pcrit q R r Re T U x prediction method constant, W/m2 -K specific heat at constant pressure, J/(kg-K) prediction method constant diameter, m prediction method constant local heat transfer coefficient, W/(m2 -K) heat of vaporization (J/kg) thermal conductivity, W/(m-K) molar mass (kg/kmol) mass flow rate, kg/s center to center tube pitch, m critical pressure, kPa local heat flux relative to a surface, W/m2 thermal resistance m2 K/W tube radius, m film Reynolds number, /µ temperature, K overall thermal resistance, K/W coordinate in axial direction, m Greek Symbols T ε θ θcrit ρ σ µ condensation temperature difference, Tsat − Tw mean relative error film mass flow rate on one side per unit length of tube, kg/(m-s) slinging angle, rad critical deflection angle, defined by Eq (4), rad density, kg/m3 standard deviation kinematic viscosity, Pa-s Subscripts bottom i gni l n o sat top v w at the bottom of the tube internal side of tube Gnielinski (heat transfer coefficient) saturated liquid number of rows measured from top row external side at fin tip saturated conditions at the top of the tube saturated vapor wall REFERENCES [1] Jung, D., Chae, S., Bae, D., and Yoo, G., Condensation Heat Transfer Coefficients of Binary HFC Mixtures on Low Fin and Turbo-C Tubes, International Journal of Refrigeration, vol 28, no 2, pp 212–217, 2005 heat transfer engineering 807 [2] Jung, D., Kim, C.-B., Cho, S., and Song, K., Condensation Heat Transfer Coefficients of Enhanced Tubes With Alternative Refrigerants for CFC11 and CFC12, International Journal of Refrigeration, vol 22, no 7, pp 548–557, 1999 [3] Jung, D., Kim, C.-B., Hwang, S.-M., and Kim K.-K., Condensation Heat Transfer Coefficients of R22, R407C, and R410a on a Horizontal Plain, Low Fin, and Turbo-C Tubes, International Journal of Refrigeration, vol 26, no 4, pp 485–491, 2003 [4] Chang, Y.-J., Hsu, C T., and Wang, C.-C., Single-Tube Performance of Condensation of R-134a on Horizontal Enhanced Tubes, ASHRAE Transactions, vol 102, no 1, pp 821–829, 1996 [5] Kumar, R., Varma, H K., Mohanty, B., and Agrawal, K N., Condensation of R-134a Vapor Over Single Horizontal Circular Integral-Fin Tubes With Trapezoidal Fins, Heat Transfer Engineering, vol 21, no 2, p 29, 2000 [6] Kumar, R., Gupta, A., and Vishvakarma, S., Condensation of R134a Vapour Over Single Horizontal Integral-Fin Tubes: Effect of Fin Height, International Journal of Refrigeration, vol 28, no 3, pp 428–435, 2005 [7] Sreepathi, L K., Bapat, S L., and Sukhatme, S P., Heat Transfer During Film Condensation of R-123 Vapour on Horizontal Integral-Fin Tubes, Journal of Enhanced Heat Transfer, vol 3, no 2, pp 147–164, 1996 [8] Wen, X L., Briggs, A., and Rose, J W., Enhancement of Condensation Heat Transfer on Integral-Fin Tubes Using Radiused Fin-Root Fillets, Journal of Enhanced Heat Transfer, vol 1, no 2, pp 211–217, 1994 [9] Kang, Y T., Hong, H., and Lee, Y S., Experimental Correlation of Falling Film Condensation on Enhanced Tubes With HFC134a; Low-Fin and Turbo-C Tubes, International Journal of Refrigeration, vol 30, no 5, pp 805811, 2007 [10] Gstăohl, D., and Thome, J R., Film Condensation of R-134a on Tube Arrays With Plain and Enhanced Surfaces: Part I, Experimental Heat Transfer Coefficients, Journal of Heat Transfer, vol 128, pp 21–32, 2006 [11] Gstăohl, D., and Thome, J R., Film Condensation of R-134a on Tube Arrays With Plain and Enhanced Surfaces: Part II, Prediction Methods, Journal of Heat Transfer, vol 128, pp 33–43, 2006 [12] Habert, M., Ribatski, G., and Thome, J R., Experimental Study on Falling Film Flow Pattern Map and Intercolumn Distance With R-236fa, ECI International Conference on Boiling Heat Transfer, Spoleto, Italy, 2006 [13] Robinson, D M., and Thome, J R., Local Bundle Boiling Heat Transfer Coefficients on a Plain Tube Bundle (RP-1089), HVAC and R Research, vol 10, no 1, pp 33–51, 2004 [14] Gnielinski, V., New Equations for Heat and Mass Transfer in Turbulent Flow Through Pipes and Ducts, Forschung Im Ingenieurwessen, vol 41, no 1, pp 359–368, 1975 [15] NIST, NIST Thermodynamic Properties of Refrigerants and Refrigerant Mixtures Database, ver 8.0, Gaithersburg, MD, 2007 [16] Gstăohl, D., and Thome, J R., Visualization of R-134a Flowing on Tube Arrays With Plain and Enhanced Surfaces Under Adiabatic and Condensing Conditions, Heat Transfer Engineering, vol 27, pp 44–62, 2006 vol 31 no 10 2010 892 S B ISLAMI ET AL Upper view Upper view d 15° b) Sh1 a) Cy l Upper view w h 15° c) Trenched-Sh1 d 15° d) Sh2 Upper view 15° w h e) Trenched-Sh2 the film hole exit is located The side walls of the slot are perpendicular to the bottom surface of slot Case 4: Conically flared shaped hole (Sh2) Configuration of this shaped hole is taken from [20] and [21] It is conically flared, with a 15◦ angle of expansion below the exit (Figure 2d) Case 5: Trenched conically flared shaped hole (Trenched-Sh2) This case is like case 3, except that the shaped hole of case is used instead of forward diffused shaped hole (Figure 2e) Case 6: Laterally diffused shaped hole (Sh3) In this case, cylindrical hole has been expanded in spanwise direction a 15◦ angle of expansion below the exit (Figure 2f) Case 7: Trenched laterally diffused shaped hole (Trenched-Sh3) The shaped hole of case has been placed in a traverse slot just like case It can be seen in Figure 2g f) Sh3 w h g) Trenched-Sh3 Figure Film hole configurations: (a) cylindrical, (b) forward-diffused, (c) trenched forward-diffused, (d) conically flared, (e) trenched conically flared, (f) lateral-diffused, (g) trenched lateral-diffused (shown on a flat surface to more clarification) Case 1: Cylindrical hole (Cyl) This case is used as a baseline case to ensure that the main characteristics of typical film cooling through a cylindrical hole are captured (Figure 2a) Case 2: Forward diffused shaped hole (Sh1) This case is a 15◦ forward-diffused hole The exact shape of the hole can be seen in Figure 2b Configuration of the shaped hole is taken from Schmidt et al [19] Case 3: Trenched forward diffused shaped hole (Trenched-Sh1) In this case, a surface slot is located transverse to the mainstream flow direction The slot is fed by the same row of discrete coolant supply holes of case Based on the slot– hole arrangement development by Bunker [13], a row of inclined film holes is placed within a shallow surface trench The shallow trench depth, h, is less than half of the film hole throat diameter (= 0.43d) as shown in Figure 2c The trench width, w, is equal to the elliptic footprint major axis, where heat transfer engineering BOUNDARY CONDITIONS Boundary conditions are taken from the experimental test case (Ardey and Fottner [3]) and are listed in Table The blowing ratio given in Table is the averaged blowing ratio of all ejection holes of both the suction side row and the pressure side row of holes Flow field prediction has been performed only for the validation of results All results for cooling effectiveness are taken from aerothermal conditions Computational domain and boundary conditions can be seen in Figure At walls, the no-slip condition is used, i.e., the velocity components of the flow are set to zero, in conjunction with the standard wallfunction approach The walls are adiabatic boundaries At the outlet boundary, the static pressure is fixed to the corresponding experimental value At the inlet boundary flow angle, the total pressure Pt1 and the total temperature Tt1 are prescribed, such as to match the corresponding experimental conditions Also freestream turbulence intensity, Tu, and µt /µl ratio are 5% and 100, respectively At the plenum inlet boundary, the experimental values for the flow angle, the total pressure Ptc , and the total temperature Ttc are prescribed, while lower values are used for turbulence intensity and eddy viscosity Tu = 1% and µt /µl = 10, respectively For aerodynamic calculations Ttc / Tt1 is 1.0 and for aerothermal calculations it is 0.5 Table Boundary conditions Blowing ratio Total pressure Total temperature Main flow angle Static pressure Cooling fluid inlet conditions Total pressure (Ttc /Tt1 )aerodynamic (Ttc /Tt1 )aerothermal vol 31 no 10 2010 M = 1.1 Pt1 = 19,650 N/m2 Tt1 = 303.15 K α1 = 43◦ P2 = 14,640 N/m2 Ptc = 21,710 N/m2 1.0 0.5 S B ISLAMI ET AL 893 Figure Computational grid the state variable becomes smaller than a convergence criterion (which is taken as 10−4 in this study); and (b) there is no observable change in all variables prediction for additional iterations (which is taken as 100 iterations in this study) RESULTS AND DISCUSSION Flow Field Figure Computational domain and boundary conditions COMPUTATIONAL GRID Ardey [26] 116150 221035 494302 0.9 0.8 P/Pt1 A computational grid has been generated by ANSYS ICEMCFD The quality of a computational solution is strongly linked to the quality of the grid mesh So a highly orthogonalized, nonuniform, multi-block fine-grid mesh was generated with grid nodes considerably refined in the near-wall region and in the inlet and the exit hole vicinity The normalized y+ values at the near wall node are kept within the wall function limits Figure shows a sample multi-block grid used Refinement of the grid was done according to the variables gradient One example of a grid sensitivity study can be seen in Figure This test has lead to 221,035 nodes for the cylindrical hole case In order to validate the accuracy of the numerical calculations, static pressure distributions in the mid-planes of the ejection holes have been compared with the Ardey and Fottner results [3] for the film cooling flow field (Figure 6) In this figure, X is the coordinate along the chord line The agreement between the results is very good on the pressure side (PS) and the rear part of the suction side (SS) In the front part of the suction THE NUMERICAL METHOD 0.7 The mathematical film-cooling model consists of the RANS (Reynolds-averaged Navier–Stokes equations), the energy equation, and the standard k–ε model with wall function The governing equations are solved using a three-dimensional finitevolume method that allows the use of arbitrary nonorthogonal multi-block grids The pressure–velocity coupling algorithm is based on a linearization that is similar to the well-known SIMPLEC procedure and called SIMPLEST [22] The two convergence criteria used are basically: (a) The residual for each of heat transfer engineering 0.6 0.5 0.2 0.4 0.6 0.8 x/L Figure Grid sensitivity (aerodynamic calculations for cylindrical hole) vol 31 no 10 2010 894 S B ISLAMI ET AL Figure Pressure distribution of the mid span (flow field computation for cylindrical hole) side, the pressure is somewhat underestimated in the calculation This deviation may be related to neglecting the influence of three-dimensional (3-D) flow phenomena in the calculations The long cascade inflow channel in the experiments develops a thick side wall boundary layer Thus, the development of a vane horseshoe vortex and a passage vortex in the cascade influences the pressure distribution on the vane surface [5] Figure displays the isentropic Mach number on the surface of the blade, which has been calculated from the static pressure distribution Agreement with experimental results is good where the Mach number is increased after the hole locations because of coolant injection Figure also shows the velocity vectors in planes perpendicular to the blade surface at s/L = 0.05 on both the suction side and pressure side, in comparison with the results of Ardey and Fottner [4] As can be seen, the general trend of velocity vectors is very similar to the experimental results of Ardey and Fottner [4] Table shows the computed blowing ratios on the suction and pressure sides for the cylindrical hole Experimental values for aerodynamic calculations are taken from Bohn and Kusterer [5], while the numerical values are the result of an averaging of Figure (a) Isentropic Mach number distribution of the mid span in the vicinity of the holes (flow field computation for cylindrical hole) (b) Velocity vectors comparison in planes perpendicular to blade surface at s/L = 0.05 the flow values at the middle of the ejection holes The comparison of the data shows that the numerical values are close to the experimental values The errors are within a 5% range relative to the experimental values In aerothermal calculations, the ratio of the total temperature of cooling flow and main flow is Table Blowing ratios for cylindrical holes Aerodynamic calculations Experiment 1.02 Ejection hole (SS): Ejection hole (PS): Present calculation Experiment Present calculation 0.987 1.15 1.094 Aerothermal calculations Ejection hole (SS): Experiment Present calculation (no experiment) 1.376 heat transfer engineering Ejection hole (PS): Experiment Present calculation (no experiment) 1.512 vol 31 no 10 2010 S B ISLAMI ET AL ωn α Normal Plane View direction to the normal plane y n z Figure Normal plane location at s/d = after trailing edge of hole approximately 0.5, which will lead to increased blowing ratios if the other boundary conditions remain the same Aerothermal Fields Aerothermal fields have been computed for all hole configurations in terms of film cooling effectiveness and vorticity contours The normal plane that has been used to compute the vorticity contours is shown in Figure Figures 9–15a–c show the cooling effectiveness contours on blade surface, velocity vectors on mid span plane, and vorticity contours on a plane normal to the blade surface at s/d = after the trailing edge of the hole, respectively, for various hole configurations The left-hand column of plots is related to the suction side while the right-hand column is related to the pressure side in Figures 9–15 Figure 9a shows that for a cylindrical hole (cyl), coolant traces on the suction side are much longer than on the pressure side The convex surface of the suction side produces a favorable pressure gradient and coolant stays close to the surface up to the blade trailing edge, while the concave surface on the pressure side causes flow separation due to the adverse pressure gradient Then it reattaches to the surface at downstream Figure 9b shows that there is a strong reverse flow on the pressure side after injection This reverse flow is developed from the difference between the far-field cross-flow pressure and the lowered pressure in the wake According to the study of Haven and Kurosaka [23], the penetrating reverse flow at the hole trailing edge acts like a cross-flow at the leading edge, and the ensuing concave warping of the trailing-edge vortex sheet thus induces an anti-kidney pair The vertical position of the anti-kidney pair is near the surface of the plate and underneath the jet, which tends to suppress the jet’s vertical velocity at the centerline and near downstream edge of the hole, so in spite of the suction side, a further lift-off of cooling fluid is prevented near the injection point (Figure 9a, right) Figure 9c, right, shows the anti-kidney pair together with the distinct kidney vortices at the sides of the pressure-side jet There is also another weak kidney-type vortex pair at the top of the anti-kidney vortex, which has been called unsteady kidney vortices by Haven and Kurosaka [23] This pair induces an heat transfer engineering 895 upward velocity, which adds to that of the lower kidney vortices and promotes the jet lift-off According to the view initially proposed by Scorer [24], kidney vortices are the downstream manifestation of vorticity, initially arising from within the sidewall boundary layer of the hole passage These counter-rotating vortex pairs push the coolant upward and pull the hot gases toward the surface Kidney vortices are strong for cylindrical holes on the suction side (Figure 9c, left), so it is clear from Figure 9a that the jet lifts off from the surface on suction side near the injection point; therefore, a low effectiveness region can be seen in this figure It is obvious from Figure 10a that for forward-diffused shaped hole (Sh1), the jet reattaches to the surface sooner than that for cylindrical hole on the suction side Also, it can be seen from this figure that the lateral spreading of coolant is more than that for the cylindrical hole on the pressure side As the coolant enters the diffused section, it is slowed down, so low exit plane y-momentum content resulted and lateral coverage enhanced On the pressure side the strength of the anti-kidney vortex is lower than that for cylindrical holes since the reverse flow is weaker in this case (Figure 10b) It can be seen from Figure 10c, left, that the strength of the kidney vortex and that of the upward flow have weakened and the center of vortices moves laterally Figure 10c, right, shows that the kidney vortices have been almost destroyed and only the anti-kidney vortex pushes the coolant toward the surface Figure 11a shows better coolant coverage for the trenched forward-diffused shaped hole (Trenched-Sh1) than previous configurations for both streamwise and spanwise directions It is obvious from Figure 11b that the reverse flow region has been reduced in comparison with the Sh1 hole on the pressure side, so the anti-kidney vortex is weaker Also, because of a more lateral spreading of coolant, the distance between the pair of anti-kidney vortices has been increased Figure 11c shows that the strength of kidney vortices is higher for the Sh1 hole on the suction side when compared with other configurations, but they penetrate more in the lateral direction than in the vertical direction The downstream wall of slot provides an obstruction to the coolant flow and, as a result, the coolant is forced to spread laterally into the slot and along the hot surface The coolant thus stays in close contact with the hot surface, rather than undesirably mixing with the hot gases This is in line with the findings of Lu and Ekkad [15], who pointed out that the effectiveness improvement in the trenched holes is due to coolant flow being accommodated first in the two-dimensional slot before exiting to the mainstream flow and spreading laterally over the surface in a way similar to twodimensional film cooling flow The conically flared hole (Sh2) has an expansion in both streamwise and spanwise directions, so coolant spreading is higher than that for the Sh1 hole (Figure 12a) As can be seen, jet lifting off on the suction side has been eliminated, so the cool gas core spreads more than previous configurations It is interesting to note that for the hole configurations (cyl), (Sh1), (Trenched-Sh1), and (Sh2), Figures 9b, 10b, and 11b show that vol 31 no 10 2010 896 S B ISLAMI ET AL Figure Heat transfer and flow pattern of cylindrical hole (right: pressure side, left: suction side): (a) film cooling effectiveness contours on blade surface, (b) velocity vectors on mid span plane, (c) vorticity contours on a plane normal to the blade surface at s/d = after trailing edge of hole there is a reverse flow exactly after injection on both sides of the blade According to Haven [25], the reverse flow, in addition to causing the warping of the hole trailing-edge vorticity, draws the cross-flow boundary layer fluid passing along the side of the hole into the underside of the jet By this, the vorticity heat transfer engineering associated with the cross-flow boundary layer diverted away from the jet by the horseshoe vortices is now pumped into the jet, where it combines with the tilted trailing-edge boundary layer, strengthens the downstream kidney vortices, and as a result reduces the cooling effectiveness Diffusion of the Sh2 vol 31 no 10 2010 S B ISLAMI ET AL 897 Figure 10 Heat transfer and flow pattern of forward-diffused hole (right: pressure side, left: suction side): (a) film cooling effectiveness contours on blade surface, (b) velocity vectors on mid span plane, (c) vorticity contours on a plane normal to the blade surface at s/d = after trailing edge of hole hole in directions and (Figure 12b) causes more reduction of jet momentum than that for the Sh1 hole Therefore, the reverse flow happens sooner and inside the hole pipes This prevents cross-flow boundary layer fluid pumping into the jet and increases the cooling effectiveness on both sides, so kidney heat transfer engineering vortices are very weak in Figure 12c Since the reverse flow has been reduced considerably, the anti-kidney vortex system has been eliminated on the pressure side and only weak kidney vortices make the jet moves away from the surface A loweffectiveness region in the streamwise direction is due to this vol 31 no 10 2010 898 S B ISLAMI ET AL Figure 11 Heat transfer and flow pattern of trenched forward-diffused hole (right: pressure side, left: suction side): (a) film cooling effectiveness contours on blade surface, (b) velocity vectors on mid span plane, (c) vorticity contours on a plane normal to the blade surface at s/d = after trailing edge of hole vortex system and has been shown in Figure 12a, right, by an arrow According to the reasoning just given for the trenched Sh1 hole, locating the Sh2 hole inside the slot would result in a more lateral spreading, which is clear in Figure 13a Once again, heat transfer engineering Figure 13b shows that there is a much weaker reverse flow exactly after injection on both sides of the blade Figure 13c shows that kidney vortices have become stronger than that for the Sh2 hole without slot, on the suction side In spite of more lateral coverage of coolant, which is shown in Figure 13c, left, kidney vol 31 no 10 2010 S B ISLAMI ET AL 899 Figure 12 Heat transfer and flow pattern of conically flared hole (right: pressure side, left: suction side): (a) film cooling effectiveness contours on blade surface, (b) velocity vectors on mid span plane, (c) vorticity contours on a plane normal to the blade surface at s/d = after trailing edge of hole vortices cause jet lifting off from the surface Also, comparison of the suction-side effectiveness between Figures 12a and 13a shows that the coolant core spreading in the streamwise direction has been decreased Figure 13c, right, shows that kidney vortices are weaker than that for the Sh2 hole on the pressure side, heat transfer engineering so streamwise coverage is higher (Figure 13a) But spanwise effectiveness is not considerably higher than that for the Sh2 hole It is obvious that because of lateral diffusion of the Sh3 hole, its lateral effectiveness will be higher on both sides of vol 31 no 10 2010 900 S B ISLAMI ET AL Figure 13 Heat transfer and flow pattern of trenched conically flared hole (right: pressure side, left: suction side): (a) film cooling effectiveness contours on blade surface, (b) velocity vectors on mid span plane, (c) vorticity contours on a plane normal to the blade surface at s/d = after trailing edge of hole the blade (Figure 14a) Kidney vortices for this case have been weakened and are completely close to the suction-side surface, so the streamwise effectiveness is high Figure 14b shows that a weak reverse-flow region exists after the pressureside hole, so a weak anti-kidney vortex pair is created (Figheat transfer engineering ure 14c) But since the kidney vortices are stronger, streamwise effectiveness reduces in the injection location (Figure 14a, right) The combined effect of lateral diffusion of the Sh3 hole and its trenching increases the spanwise effectiveness more than that vol 31 no 10 2010 S B ISLAMI ET AL 901 Figure 14 Heat transfer and flow pattern of lateral-diffused hole (right: pressure side, left: suction side): (a) film cooling effectiveness contours on blade surface, (b) velocity vectors on mid span plane, (c) vorticity contours on a plane normal to the blade surface at s/d = after trailing edge of hole for all other cases, which is clear in Figure 15a Figure 15b shows that reverse flow has been decreased on the pressure side in comparison with the Sh3 hole, so anti-kidney vortices have weakened and their distance has been increased, as shown in Figure 15a As can be seen from Figure 15c, on the suction side, the core of kidney vortices is stronger for the Sh3 hole but its penetration heat transfer engineering in the vertical direction is lower and in the lateral direction is higher, compared with other configurations A small vortex pair has been created at the sides, which rotates in the reverse direction of the kidney vortices and decreases a little their effect Re-increasing of cooling effectiveness at the sides is due to these vortices vol 31 no 10 2010 902 S B ISLAMI ET AL Figure 15 Heat transfer and flow pattern of trenched lateral-diffused hole (right: pressure side, left: suction side): (a) film cooling effectiveness contours on blade surface, (b) velocity vectors on mid span plane, (c) vorticity contours on a plane normal to the blade surface at s/d = after trailing edge of hole Figure 16 shows the trenching effect on three types of shaped holes It is clearly shown that except for the suction side of Sh2 and Sh3 holes, trenching increases both centerline and laterally averaged effectiveness of all other configurations Trenching has a reverse effect on the effectiveness of Sh2 and Sh3 on the suction side Also, trenching has the most effect on centerline heat transfer engineering and laterally averaged effectiveness of Sh1 The effect of trenching on laterally averaged effectiveness of Sh2 and Sh3 has been decreased after s/L > 0.6 As can be seen from this figure, the main effect of trenching is the reduction of jet lifting off from blade surface and so the prevention of sudden lowering of cooling effectiveness after injection location Also, trenching vol 31 no 10 2010 S B ISLAMI ET AL 0.6 0.6 Sh1 Trenched-Sh1 0.5 Laterally averaged η 0.6 0.4 SS 0.2 0.4 0.3 0.2 SS 0.1 PS PS 0 0.3 0.6 0.9 1.2 1.5 0.3 0.6 s/L 0.9 1.2 1.5 s/L (a) 0.6 Sh2 Trenched-Sh2 0.6 SS 0.4 Sh2 Trenched-Sh2 0.5 Laterally averaged η Centerline η 0.8 0.2 0.2 0.1 0.3 0.2 SS 0 0.3 0.6 0.9 0.3 0.6 PS 1.2 1.5 0.3 0.6 0.9 1.2 0.9 1.2 1.5 s/L 1.5 s/L (b) (a)Suction Side 0.6 Sh3 Trenched-Sh3 0.6 SS 0.4 0.2 0.3 0.6 0.9 0.4 1.2 1.5 s/L SS 0.2 Cyl Sh1 Sh2 Sh3 Trenched-Sh1 Trenched-Sh2 Trenched-Sh3 0.5 0.3 0.1 PS 0.6 Sh3 Trenched-Sh3 0.5 Laterally averaged η 0.8 Centerline η 0.3 0.1 s/L 0.4 0.4 PS Cyl Sh1 Sh2 Sh3 Trenched-Sh1 Trenched-Sh2 Trenched-Sh3 0.5 PS 0.3 0.6 0.9 1.2 1.5 s/L (c) Figure 16 Effect of trenching on cooling effectiveness distribution on blade surface (right: laterally averaged effectiveness; left: centerline effictiveness) has more effect on the suction side than on the pressure side Figure 17 compares the lateral effectiveness of seven configurations on both the suction side and pressure side It is obvious that the effectiveness of shaped holes and the effectiveness of trenched shaped holes are considerably higher than that for cylindrical holes Figure 17a shows that on the suction side, Sh2 and Sh3 holes have more effectiveness than that for Sh1 holes at the injection point This is also true for their trenched cases, but after about s/L > 0.75, Trenched-Sh1 and Trenched-Sh2 have the same effectiveness Finally, the Trenched-Sh3 holes have the highest laterally averaged effectiveness on the suction side It can be seen from Figure 17b that there is not any difference between using Sh1 or Sh2 hole configurations except at s/L > 0.2 on the pressure side At the injection location, effectiveness of Sh2 and Sh3 holes is almost similar, but further downstream, the Sh3 hole is more effective In spite of the preceding discussion, Trenched-Sh1 and Trenched-Sh2 holes have almost the same effectiveness near the injection point, while downstream, heat transfer engineering Laterally averaged η Centerline η 0.8 Laterally averaged η Sh1 Trenched-Sh1 903 0.4 0.3 0.2 0.1 00 0.2 0.4 0.6 0.8 s/L (b)Pressure Side Figure 17 Laterally averaged cooling effectiveness comparison: (a) suction side, (b) pressure side Trenched-Sh1 is better Also for the pressure side, Trenched-Sh3 holes have the highest laterally averaged effectiveness CONCLUSIONS Computational results are presented for a row of coolant injection holes on each side of a high pressure turbine blade near the leading edge Seven hole configurations have been used, to show the effect of various diffused shaped holes and also the effect of their trenching on film cooling effectiveness: The following conclusions emerged from the present investigation: vol 31 no 10 2010 904 S B ISLAMI ET AL For the cylindrical hole (cyl), coolant traces on the suction side are much longer than that on the pressure side Kidney vortices are strong for cylindrical holes on the suction side, so the jet lift-off from the surface reduces cooling effectiveness on the front part of injection location The reverse flow on the pressure side behind injection hole induces an anti-kidney pair, which tends to suppress the vertical velocity of jet at the centerline and near the downstream edge of the hole, so further jet lift-off of cooling fluid is prevented For the forward-diffused shaped hole (Sh1), the lateral spreading of coolant is more than that for the cylindrical hole on the pressure side On the pressure side, the strength of antikidney vortex is lower than that for cylindrical holes, since the reverse flow is weaker in this case Trenched forward-diffused shaped holes (Trenched-Sh1) show better coverage for both streamwise and spanwise directions The strength of kidney vortices is higher than that for the Sh1 hole on the suction side but they tend to penetrate more in the lateral direction than in the vertical direction Also that reverse flow region has been reduced in comparison with the Sh1 hole on the pressure side, so the anti-kidney vortex is weaker The conically flared hole (Sh2) has an expansion in both the streamwise and spanwise directions, so coolant spreading is higher than that for the Sh1 hole This dual expansion causes more reduction in the jet momentum than that for the Sh1 hole Therefore, the reverse flow just described happens sooner and inside the hole pipes This prevents cross-flow boundary layer fluid pumping into the jet and increases the cooling effectiveness on both sides For the trenched conically flared hole (Trenched-Sh2), coolant core spreading in the streamwise direction has been decreased Kidney vortices are weaker than that for the Sh2 hole on the pressure side, so streamwise coverage is higher However, spanwise effectiveness is not considerably higher than that for the Sh2 hole Because of lateral diffusion of the Sh3 hole, its lateral effectiveness will be high on both sides A weak reverse flow region exists after the pressure-side hole, so a weak antikidney vortex pair is created But since the kidney vortices are stronger, streamwise effectiveness is reduced in the injection location The combined effect of lateral diffusion of Sh3 hole and its trenching increases the spanwise effectiveness more than that for all other cases It has been found that except at the suction side of the Sh2 and Sh3 holes, trenching increases both centerline and laterally averaged effectiveness of all other configurations Also trenching has the most effect on centerline and laterally averaged effectiveness of Sh1 Trenching has more effect on the suction side than on the pressure side Results showed that effectiveness of shaped holes and trenched shaped holes are considerably higher than that for cylindrical holes The trenched Sh3 hole has the highest laterally averaged effectiveness on both the suction side and pressure side heat transfer engineering NOMENCLATURE d h H k L M Ma n p/d P PS Pt r Re s SS t/L T Tt Tu u∗ U w x X y y+ z diameter of cylindrical part of film hole, m slot height, m vane height, m turbulent kinetic energy, m2 s−2 chord length, m blowing ratio = (ρU )c /(ρU )∞ Mach number normal coordinate along the plane which is normal to blade surface, m pitch-to-diameter ratio of film hole pressure, Pa pressure side total pressure, Pa surface curvature, m Reynolds number axial surface coordinate, m suction side cascade pitch ratio static temperature, K total temperature, K turbulence intensity√ friction velocity = τw /ρ, m s−1 velocity, m s−1 slot width, m coordinate along the blade surface, m coordinate along the chord line, m coordinate normal to the blade surface, m the normalized distance = yuν∗ coordinate in the lateral direction, m Greek Symbols α β βs ε γr γs η µl µt ρ τw ω absolute velocity angle, degree relative velocity angle, degree staggering angle, degree dissipation rate of turbulent kinetic energy, m2 s−3 radial ejection angle, degree streamwise ejection angle, degree adiabatic film cooling effectiveness (T − T∞ )/ (Tc − T∞ ) laminar dynamic viscosity, kg m−1 s−1 turbulent dynamic viscosity, kg m−1 s−1 density of the fluid, kg m−3 wall shear stress, kg m−1 s−2 vorticity vector, s−1 Subscripts c inlet flow outlet flow coolant vol 31 no 10 2010 S B ISLAMI ET AL is w ∞ isentropic conditions wall free stream [16] REFERENCES [17] [1] Garg, V K., Heat Transfer on a Film-Cooled Rotating Blade, NASA Rept NASA/CR-1999-209301, Glenn Research Center, Lewis Field Cleveland, OH, 1999 [2] Goldstein, R J., Film Cooling, in Advances in Heat Transfer, Academic Press, New York, pp 321–377, 1971 [3] Ardey, S., and Fottner, L., Flow Field Measurements on a Large Scale Turbine Cascade With Leading Edge Film Cooling by Two Rows of Holes, ASME 97-GT-524, 1997 [4] Ardey, S., and Fottner, L., A Systematic Experimental Study on the Aerodynamics of Leading Edge Film Cooling on a Large Scale High Pressure Turbine Cascade, ASME 98-GT-434, 1998 [5] Bohn, D E., and Kusterer, K A., Aerothermal Investigations of Mixing Flow Phenomena in Case of Radially Inclined Ejection Holes at the Leading Edge, Trans ASME: Journal of Turbomachinery, vol 122, pp 334–339, 2000 [6] Bohn, D E., and Kusterer, K A., Blowing Ratio Influence on Jet Mixing Flow Phenomena at the Leading Edge, Proc 37th AIAA Aerospace Sciences Meeting and Exhibit, Aachen, Germany, AIAA 99-0670, 1999 [7] Cutbirth, J M., and Bogard, D G., Thermal Field and Flow Visualization within the Stagnation Region of a Film-Cooled Turbine Vane, Trans ASME: Journal of Turbomachinery, vol 124, pp 200–206, 2002 [8] Colban, W F IV, A Detailed Study of Fan-Shaped Film-Cooling for a Nozzle Guide Vane for an Industrial Gas Turbine, Ph.D thesis, Faculty of Virginia Polytechnic Institute and State University, Blacksburg, VA, 2005 [9] Waye, S K., and Bogard, D G., High-Resolution Film Cooling Effectiveness Comparison of Axial and Compound Angle Holes on the Suction Side of a Turbine Vane, Trans ASME: Journal of Turbomachinery, vol 129, pp 202–211, 2007 [10] Barthet, S., and Bario, F., Experimental Investigation of Film Cooling Flow Induced by Shaped Holes on a Turbine Blade, Annals of the New York Academy of Sciences, vol 934, pp 313– 320, 2001 [11] Han, J C., and Teng, S., Effect of Film-Hole Shape on Turbine Blade Film Cooling Performance, NASA Rept., NASA/CR2000-209932, Glenn Research Center, Lewis Field Cleveland, OH, 2000 [12] Bunker, R S., Bailey, J C., Lee, C P., and Abuaf, N., Method for Improving the Cooling Effectiveness of a Gaseous Coolant Stream, and Related Articles of Manufacture, US patent, US 6,234,755 B1, 2001 [13] Bunker, R S., Film Cooling Effectiveness Due to Discrete Holes Within Transverse Surface Slots, GE Research & Development Center Technical Information Series, 2001CRD204, 2002 [14] Altorairi, M S., Film Cooling From Cylindrical Holes in Transverse Slots, M.S thesis, Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College, 2003 [15] Lu, Y., and Ekkad, S V., Predictions of Film Cooling from Cylindrical Holes Embedded in Trenches, Proc 9th AIAA/ASME Joint heat transfer engineering [18] [19] [20] [21] [22] [23] [24] [25] [26] 905 Thermophysics and Heat Transfer Conference, San Francisco, CA, AIAA 2006-3401, 2006 Waye, S K., and Bogard, D G., High-Resolution Film Cooling Effectiveness Measurements of Axial Holes Embedded in a Transverse Trench With Various Trench Configurations, Trans ASME: Journal of Turbomachinery, vol 129, pp 294–302, 2007 Lu, Y., Dhungel, A., Ekkad, S V., and Bunker, R S., Effect of Trench Width and Depth on Film Cooling from Cylindrical Holes Embedded in Trenches, ASME GT2007-27388, 2007 Sundaram, N., and Thole, K A., Bump and Trench Modifications to Film Cooling Holes at the Vane Endwall Junction, Trans ASME: Journal of Turbomachinery, vol 130, 041013, pages, 2008 Schmidt D L., Sen, B., and Bogard, D G., Film Cooling With Compound Angle Holes: Adiabatic Effectiveness, Trans ASME: Journal of Turbomachinery, vol 118, pp 807–813, 1996 Camci, C., and Arts, T., An Experimental Convective Heat Transfer Investigation Around a Film-Cooled Gas Turbine Blade, Trans ASME: Journal of Turbomachinery, vol 112, pp 497–503, 1990 Medic, G., and Durbin, P A., Toward Improved Film Cooling Prediction, Trans ASME: Journal of Turbomachinery, vol 124, pp 193–199, 2002 Spalding, D B., Mathematical Modeling of Fluid Mechanics, Heat Transfer and Mass Transfer Processes, Mech Eng Dept., Imperial College of Science, Technology and Medicine, London, Rep HTS/80/1, 1980 Haven, B A., and Kurosaka, M., Kidney and Anti-Kidney Vortices in Cross-Flow Jets, Journal of Fluid Mechanics, vol 352, pp 27– 64, 1997 Scorer, R S., Natural Aerodynamics, Pergamon Press, New York, pp 194, 210, 1958 Haven, B A., The Effect of Hole Geometry on the Near Field Character of Cross-Flow Jets, Ph.D thesis, Department of Aeronautics and Astronautics, University of Washington, Seattle, 1996 Ardey, S., 3D-Messung des Străomungsfeldes um die filmgekăuhlte Vorderkante einer Referenzschaufel, Ph.D thesis, University of the Armed Forces, Munich, 1998 Sima Baheri Islami is an assistant professor at University of Tabriz, Iran She received her B.Sc degree in 2000 and M.Sc degree in 2003, in mechanical engineering, both from the University of Tabriz She is doing her Ph.D in thermofluid engineering at the University of Tabriz under the supervision of Dr Alavi Tabrizi and co-supervision of Prof Bassam Jubran Her research interests are in film cooling with focus on hole configurations, jet flows, and aerodynamics S P Alavi Tabrizi received the Ph.D degree in thermofluid engineering from the University of Liverpool, UK, in 1996 He was educated at the University of Tabriz, Iran, graduating in 1974 with an M.Sc degree in mechanical engineering He was head of the department for five years and dean of faculty for four years at the University of Tabriz His research interests are jet flows, turbomachinery, and film cooling vol 31 no 10 2010 906 S B ISLAMI ET AL Bassam A Jubran is a professor of thermofluid engineering He was educated at Cardiff University (formally University of Wales), UK, graduating in 1980 with a B.Sc honors degree in mechanical engineering He obtained his Ph.D., also from the University of Wales, in 1984 Professor Jubran joined the Department of Aerospace Engineering at Ryerson University, Toronto, Canada, in 2004 He served as editor-in chief of the Journal of Engineering Research, and he is now on the editorial board of the International Journal of Low Carbon Technologies, published by Manchester University Press, UK He has published more than 120 papers in top international peer journals and international conference proceedings heat transfer engineering Esmaeil Esmaeilzadeh received a Ph.D degree in thermofluid engineering from the University of Paris VI, France, in 1977 He was educated at the University of Paris VI, France, graduating in 1974 with an M.Sc degree He did postdoctoral research in the University of Kyoto, Japan He was head of his department at the University of Tabriz for four years Also he has been head of the fluid mechanics laboratory at the University of Tabriz for 27 years Currently, he is an associate professor at the University of Tabriz His research interests are experimental fluid mechanics, two-phase gas– solid and gas–liquid flows, convective heat transfer of single- and two-phase flows, heat transfer enhancement, and applications of EHD in fluid flow and heat transfer He has published more than 70 papers in international journals and conference proceedings vol 31 no 10 2010