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Research Papers

# Fundamental Gas Turbine Heat TransferOPEN ACCESS

[+] Author and Article Information
Je-Chin Han

Turbine Heat Transfer Laboratory,
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843-3123
e-mail: jc-han@tamu.edu

Manuscript received October 15, 2012; final manuscript received February 9, 2013; published online May 17, 2013. Assoc. Editor: Srinath V. Ekkad.

J. Thermal Sci. Eng. Appl 5(2), 021007 (May 17, 2013) (15 pages) Paper No: TSEA-12-1176; doi: 10.1115/1.4023826 History: Received October 15, 2012; Revised February 09, 2013

## Abstract

Gas turbines are used for aircraft propulsion and land-based power generation or industrial applications. Thermal efficiency and power output of gas turbines increase with increasing turbine rotor inlet temperatures (RIT). Current advanced gas turbine engines operate at turbine RIT (1700 °C) far higher than the melting point of the blade material (1000 °C); therefore, turbine blades are cooled by compressor discharge air (700 °C). To design an efficient cooling system, it is a great need to increase the understanding of gas turbine heat transfer behaviors within complex 3D high-turbulence unsteady engine-flow environments. Moreover, recent research focuses on aircraft gas turbines operating at even higher RIT with limited cooling air and land-based gas turbines burn coal-gasified fuels with a higher heat load. It is important to understand and solve gas turbine heat transfer problems under new harsh working environments. The advanced cooling technology and durable thermal barrier coatings play critical roles for the development of advanced gas turbines with near zero emissions for safe and long-life operation. This paper reviews fundamental gas turbine heat transfer research topics and documents important relevant papers for future research.

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## Introduction

###### High Temperature Gas Turbines.

Developments in turbine cooling technology play a critical role in increasing the thermal efficiency and power output of advanced gas turbines. To double the engine power in aircraft gas turbines, the rotor inlet temperature should increase from today's 1700 °C to 2000 °C (3100 °F to 3600 °F) using the similar amount of cooling air (3–5% of compressor discharge air). For land-based power generation gas turbines, including power generation (300–400 MW combined cycles), marine propulsion, and industrial applications such as pumping and cogeneration (less than 30 MW), the rotor inlet temperature will increase, but at a rate determined by NOx constraints; with the emphasis on NOx reduction, efficient use of cooling air becomes more important in order to achieve cycle efficiency gains. Therefore, high-temperature material development such as thermal barrier coating (TBC) and highly sophisticated advanced cooling are two important issues that need to be addressed to ensure high-performance, high-power gas turbines for both aircraft and land-based applications.

###### Gas Turbine Heat Transfer.

Figure 1 shows a typical heat flux distribution on the surfaces of a turbine vane and blade and the associated internal and external cooling schemes [1]. As the turbine inlet temperature increases, the heat transferred to the turbine blade also increases. The level and variation in the temperature within the blade material, which cause thermal stresses and blade failures, must be limited to achieve reasonable durability goals. Note that the blade life may be reduced by half if the blade metal temperature prediction is off by only 30 °C (50 °F). Therefore, it is critical to accurately predict the local heat transfer coefficient as well as the local blade temperature in order to prevent local hot spots and increase turbine blade life. Meanwhile, there is a critical need to cool the blades for safe and long-life operation.

###### Gas Turbines Cooling System.

The turbine blades are cooled with extracted air from the compressor of the gas turbine engine. Since this extraction incurs a penalty on the thermal efficiency and power output of the gas turbine engine, it is important to fully understand and optimize the cooling technology for a given turbine blade geometry under engine operating conditions. Gas turbine blades are cooled both internally and externally as shown in Fig. 2 [2]. Internal cooling is achieved by passing the coolant through several rib-turbulated serpentine passages inside of the blade. Both jet impingement and pin-fin cooling are also used as a method of internal cooling. External cooling is also called film cooling. Internal coolant air is ejected out through discrete holes to provide a coolant film to protect the outside surface of the blade from hot combustion gases. The engine cooling system must be designed to ensure that the maximum blade surface temperatures and temperature gradients during operation are compatible with the allowable blade thermal stress for the life of the design. Too little coolant flow results in hotter blade temperatures and reduced component life. Similarly, too much coolant flow results in reduced engine performance. The turbine cooling system must be designed to minimize the use of compressor discharge air for cooling purposes to achieve maximum benefits of the high turbine inlet gas temperature.

In addition to conventional natural gas, syngas or hydrogen (produced from coal gasification) are viable alternative fuels. These coal gasified fuels produce a high percentage of water vapor (steam) and increase heavy heat load to the turbine components. These coal-based fuels may introduce impurities into the mainstream gas which can cause corrosion and erosion on the surface of the airfoils, or the impurities may be deposited on the components. All of these scenarios increase the surface roughness of the components, increase heat transfer, increase aerodynamic losses, increase clogging of film cooling holes, decrease film-cooling effectiveness, and decrease the performance of the turbine. Recent research suggests that the advanced cooling technology and durable thermal barrier coatings still play critical roles for the development of future coal-based gas turbines with near zero emissions (for example, integrated gasification combined cycles (IGCC), thermal efficiency greater 60%).

###### Important Literature Survey.

Research activities in turbine heat transfer and cooling began in the early 1970s; since then, many research papers, state-of-the-art review articles, and book chapters have been published. Several publications are available that address state-of-the-art reviews of turbine blade cooling and heat transfer. These include publications by “Film Cooling” by Goldstein [3], “Turbine Cooling” by Suo [4], “Cooling Techniques for Gas Turbine Airfoils” by Metzger [5], “Some Considerations in the Thermal Design of Turbine Airfoil Cooling Systems” by Elovic and Koffel [6], and “Turbine Cooling and Heat Transfer” by Lakshminarayana [7]. Several review articles related to gas turbine heat-transfer problems by Graham [8] and Simoneau and Simon [9] are also available.

Several Books Have Been Published Since 2000: Gas Turbine Heat Transfer and Cooling Technology by Han et al. [10], Heat Transfer in Gas Turbines edited by Sunden and Faghri [11], Heat Transfer in Gas Turbine Systems edited by Goldstein [12], Special Section: Turbine Science and Technology (included 10 review papers) edited by Shih [13], Heat Transfer in Gas Turbine Systems (included 10 keynote papers) edited by Simon and Goldstein [14]. Meanwhile, many review papers related to gas turbine heat transfer and cooling problems are available: “Convection Heat Transfer and Aerodynamics in Axial Flow Turbines” by Dunn [15], “Gas Turbine Heat Transfer: 10 Remaining Hot Gas Path Challenges” by Bunker [16], “Gas Turbine Film Cooling” by Bogard and Thole [17], “Turbine Blade Cooling Studies” at Texas A&M 1980–2004 by Han [18], “Turbine Cooling System Design-Past, Present and Future” by Downs and Landis [19], and “Aerothermal Challenges in Syngas Hydrogen-Fired and Oxyfuel Turbines” by Chyu et al. [20].

The ASME Turbo Expo (IGTI International Gas Turbine Institute) has made conference CDs available to every year's attendees since 2000. These conference CDs contain all gas turbine heat transfer papers presented in each year's IGTI conference. The numbers of heat transfer related conference papers have increased from about 100 in the year 2000 to about 200 in the year 2010. Approximately 25–30% of each year's conference heat transfer papers have been subsequently published in the ASME Journal of Turbomachinery. These tremendous amounts of conference and journal papers are the main research sources of gas turbine heat transfer and cooling technology for interested readers.

## Gas Turbine Heat Transfer

###### Fundamentals of Gas Turbine Heat Transfer.

Current turbine designs are characterized by an inability to accurately predict heat-transfer coefficient distributions under turbomachinery flow conditions. This results in a nonoptimized design using inordinate amounts of cooling air, which ultimately causes significant penalties to the cycle in terms of thrust and specific fuel consumption. Hot-gas path components include turbine stator vanes and turbine rotor blades. Turbine first-stage vanes (so called nozzle guide vane, NGV) are exposed to high-temperature, high turbulence hot gases from the exit of the combustor as sketched in Fig. 1 [1]. It is important to determine the heat load distributions on the first-stage vanes under engine flow conditions for a typical gas turbine engine. An accurate estimate of the heat-transfer distributions can help in designing an efficient cooling system and prevent local hot-spot overheating. Gas to airfoil heat transfer can be affected by airfoil shape (surface curvature and pressure gradient), boundary layer transitional behavior, free-stream turbulence, airfoil surface roughness, film coolant injection location, flow separation and reattachment, and shock/boundary layer interaction, exit Mach number and Reynolds number.

After accelerating from the first-stage vanes, hot gases move into the first stage rotor blades to produce turbine power as sketched in Fig. 1 [1]. At the inlet of the first-stage rotor blade, both the temperature and turbulence levels are lower compared to the inlet of the first-stage vane. However, the inlet velocity could be two to three times higher. Besides, the blade receives unsteady wake flows from the upstream vane trailing edge (turbulent intensity up to 20%). More importantly, blade rotation causes hot gases to leak from the pressure side through a tip gap to the suction side. This often causes damage on the blade tip near the pressure side trailing-edge region. It is important to understand the complex 3D flow physics and associated heat-transfer distributions on the rotor blade, particularly near the tip region, under typical engine flow conditions. It is important to note that rotation causes the peak gas temperature to shift from the blade pitch line toward the tip region. It is also important to correctly predict the RIT profile as well as the associated unsteady velocity profile and turbulence levels. Many papers were reviewed and cited in Chapter 2 of Han et al. [10].

###### Heat Transfer Through Turbine Stator Vanes.

For typical NGV designs, heat-transfer coefficients on the pressure surface decrease rapidly from the leading edge to about 20% surface distance and then gradually increase toward the trailing edge. The heat-transfer distribution on the pressure surface is not affected by changing the exit Mach number (Mach = 0.75–1.05). On the suction surface, heat-transfer coefficient distributions show laminar boundary layer separation, transition, and turbulent reattachment at about 25% surface distance. The location of the laminar boundary layer transition seems to move upstream with decreasing exit Mach number, and downstream of that location, heat-transfer coefficients are higher with decreasing exit Mach numbers. In regions where the boundary layer remained attached (before transition), there is no apparent effect of the exit Mach number. Moreover, the transition location on the suction surface moves closer to the leading edge with an increase in exit Reynolds number (Re = 1–1.5 × 106). Overall, heat-transfer coefficients over the entire airfoil surface showed significant increases with an increase in exit Reynolds number reported by Nealy et al. [21].

###### Turbulence and Roughness Effects

Combustor generated turbulence (high turbulence intensity up to 20% and large scale) contributes to significant heat transfer enhancement. Turbulence can strongly affect laminar heat transfer to the stagnation region, pressure surface, transition, and turbulent boundary layer heat transfer by Ames [22]. Another severe heat-transfer enhancement factor for NGV heat transfer is the surface roughness effect. Combustion deposits may make the vane surface rough after several hours of operation, and this roughness could be detrimental to the life of the vane due to increased heat-transfer levels that are much higher than design conditions, as well as decreased aerodynamic performance cited by Abuaf et al. [23]. The already enhanced heat-transfer coefficients on the pressure surface due to high free-stream turbulence (Tu = 10%) are unaffected by the surface roughness. However, the effect on suction surface is significant. A combination of surface roughness with high free-stream turbulence causes the boundary layer to undergo transition more rapidly than for the high free-stream turbulence case only by Hoffs et al. [24].

###### Heat Transfer Through Turbine Rotor Blades.

Figure 3(a) depicts a complex flow phenomenon in a turbine rotor hot gas passage including secondary flows, horseshoe vortex, end wall passage vortex, film cooling, tip flows, wakes, and rotation flows [25]. The heat-transfer distributions for not film-cooled blades are higher than those for film-cooled blades at the same engine flow conditions. These heat-transfer distributions could differ for varied engine flow conditions; therefore, it is critical for a designer to be able to accurately predict these distributions for film-cooled or no film-cooled blades in order to design an efficient cooling scheme. Most of the primary results on real rotor/stator heat transfer have been provided by Calspan Advanced Technology Center by Dunn et al. [26,27]. They used a full-stage rotating turbine of the Garrett TFE 731-2 engine with an aspect ratio of around 1.5, as well as a full-stage rotating turbine of an Air Force/Garrett low-aspect-ratio turbine with an aspect ratio of approximately 1.0. They reported heat flux measurements on the NGV airfoil and end wall, the rotor blade, blade tip, and shroud of the turbine. A shock-tunnel facility was intended to provide well-defined flow conditions and duplicate sufficient number of parameters to validate and improve confidence in design data and predictive techniques under development.

Blair et al. [28,29] conducted experiments on a large-scale ambient temperature, turbine-stage model. The turbine-stage model consisted of a stator, a rotor, and an additional stator behind the rotor (1½ stage). They also studied the effects of inlet turbulence, stator-rotor axial spacing, and relative circumferential spacing of the first and second stators on turbine airfoil heat transfer. This test facility was designed for conducting detailed experimental investigations for flow around turbine blading. Guenette et al. [30] presented local heat-transfer measurements for a fully scaled transonic turbine blade. The measurements were performed in the MIT blow down turbine tunnel. The facility has been designed to simulate the flow Reynolds number, Mach number, Prandtl number, corrected speed and weight flow, and gas-to-metal temperature ratios associated with turbine fluid mechanics and heat transfer. They used thin-film heat flux gauges to measure the upstream NGV trailing edge unsteady wake effect on the downstream rotor blade surface time-dependent heat-transfer coefficients. They found that, on the suction surface, the blade-passing effect is stronger at the leading edge and attenuates toward the trailing edge. The steep variations of the heat transfer enhancement on the suction surface indicate strong wake propagation toward the suction surface near the leading edge and then moving toward the pressure surface near the trailing edge.

###### Heat Transfer Through Turbine End-Wall.

Several studies have shown how a horseshoe vortex develops at the leading edge of the turbine vanes and blades, as shown in Fig. 3(b) [39]. Eliminating the formation of the horseshoe vortex at the leading edge of the turbine blade will positively impact the performance of the engine. Adding a fillet at the junction of the airfoil and platform has been shown to eliminate the vortex formed at the leading edge of the blade by Sauer et al. [40]. Not only does the elimination of the horseshoe vortex decrease aerodynamic losses, but it also has a positive impact on the end wall heat transfer and film cooling. Shih and Lin [41] predicted fillets not only reduce aerodynamic losses, but the surface heat transfer is reduced by more than 10% on the airfoil surface and more than 30% on the vane end wall. A second method to mitigate the secondary flow along the end wall is to implement end wall contouring. Kopper et al. [42] determined the secondary losses are reduced by up to 17% through a passage with a contoured end wall (compared to a flat end wall). Saha and Acharya [43] applied nonaxisymmetric profiling to the end wall of rotor blade cascade. Schobeiri and Lu [44] recently reported the efficiency of a three-stage rotating turbine can be greatly improved by applying a physic-based diffuser-flow concept for optimizing nonaxisymmetric end wall contouring.

###### Thermal Barrier Coating and Spallation Effects.

For safer operation, the turbine blades in current engines use nickel-based super alloys at metal temperatures well below 1000 °C (∼2000 °F). For higher RIT, the advanced casting techniques, such as directionally solidified and single crystal blades with TBC coating, are used for advanced gas turbines. TBC coating serves as insulation for the turbine airfoils and allows a 100–150 °C (∼200 °F–300 °F) higher RIT, thereby enhancing turbine efficiency. There are two types of coating techniques: (1) air plasma spray with plate structure/porosity/low thermal conductivity and (2) electron beam physical vapor deposition with column structure/dense/high thermal conductivity by Nelson et al. [45]. The performance of TBC coatings, the zirconia-based ceramics, depends on the aforementioned coating techniques and the coating thickness (5–50 mil). The United States government laboratories, gas turbine manufacturers, and university researchers have conducted research to identify better coating materials, better coating techniques, controllable coating thicknesses, good bonding coats, and hot corrosion tests for TBC life prediction. It is important to determine the effects of TBC roughness and the potential TBC spallation on turbine aerodynamic and heat-transfer performance. Ekkad and Han [46,47] studied the effect of simulated TBC spallation shape, size, and depth on heat transfer enhancement over a flat surface as well as on a cylindrical leading-edge model. They found that the spallation can enhance the local heat transfer coefficients up to two times as compared to that with the smooth surface.

###### Deposition and Roughness Effects.

Recent experimental work in measuring the formation of deposits has been done under the UTSR program by Bons et al. [48]. In a series of experiments in an accelerated test facility, Wammack et al. [49] investigated the physical characteristics and evolution of surface deposition on bare polished metal, polished TBC with bond coat (initial average roughness was less than 0.6 micrometers) and unpolished oxidation resistant bond coat (initial average roughness around 16 micrometers). Based on these results, they inferred that the initial surface preparation has a significant effect on deposit growth, that thermal cycling combined with particle deposition caused extensive TBC spallation while thermal cycling alone caused none, and finally that the deposit penetration into the TBC is a significant contributor to spallation. Subsequently, Bons et al. [48] made convective heat transfer measurements using scaled models of the deposited roughness and found that the Stanton number was augmented by between 15 and 30% over a smooth surface. They concluded that deposition increased by a factor of two as the mass mean diameter of the particle was increased from 3–16 micrometers. Second, particle deposition decreased with decreasing gas temperature and with increased backside cooling. They found a threshold gas temperature for deposition to occur at 960 °C.

## Gas Turbine Film Cooling

###### Fundamentals of Film Cooling.

In turbine blade film cooling, as sketched in Fig. 2, relatively cool air is injected from the inside of the blade to the outside surface, which forms a protective layer between the blade surface and hot mainstream. Film cooling depends primarily on the coolant-to-hot-mainstream pressure ratio (pc/pt), temperature ratio (Tc/Tg), and the film-cooling-hole location, configuration, and distribution on a film-cooled airfoil. The coolant-to mainstream pressure ratio can be related to the coolant-to-mainstream mass flux ratio (blowing ratio), while the coolant-to-mainstream temperature ratio can be related to the coolant-to-mainstream density ratio. In a typical gas turbine airfoil, the pc/pt ratios vary from 1.02 to 1.10, while the corresponding blowing ratios vary approximately from 0.5 to 2.0. Whereas the Tc/Tg values vary from 0.5 to 0.85, the corresponding density ratios vary approximately from 2.0 to 1.5. In general, the higher the pressure ratio, the better the film-cooling protection (i.e., reduced heat transfer to the airfoil) at a given temperature ratio, while the lower the temperature ratio, the better the film-cooling protection at a given pressure ratio. However, a too high pressure ratio (i.e., blowing too much) may reduce the film-cooling protection because of jet penetration into the mainstream (jet liftoff from the surface). Data from numerous studies available in open literature suggest a blowing ratio near unity is optimum, with severe penalties at either side. As mentioned earlier, turbine-cooling system designers need to know where the heat is transferred from the hot mainstream to the airfoil (Fig. 1) in order to design better film-cooling patterns for airfoils. These film-hole patterns (i.e., film-hole location, distribution, angle, and shape) affect film-cooling performance. The best film cooling design is to reduce the heat load to the airfoils using a minimum amount of cooling air from compressors. Many papers were reviewed and cited in Chapter 3 of Han et al. [10].

###### Flat Plate Film Cooling.

It is common in literature to use a flat plate to perform fundamental studies on various parametric effects on film cooling such as the study done by Goldstein [3]. Moreover, results on flat plates have been used to calibrate and standardize various experimental techniques to measure film cooling effectiveness and heat transfer coefficients. While the best film cooling coverage can be obtained by injecting the fluid parallel to the mainstream, manufacturing constraints dictate that holes be angled. Using film cooling holes perpendicular (90 deg) to the mainstream, results in very low film cooling effectiveness. The use of holes inclined at 35 deg typically gives a balance between film cooling performance and manufacturing ease.

###### Effect of Coolant-Mainstream Blowing Ratio and Density Ratio

Blowing ratio (M) is defined as the ratio of the coolant mass flux to that of the mainstream. In general, regardless of hole-shape and angle, film cooling effectiveness is found to increase with blowing ratio at low blowing ratios (less than 0.5). However, beyond a critical blowing ratio, film cooling effectiveness is found to decline. This decline can be attributed to the phenomenon of film-cooling lift-off from boundary layers, wherein the high momentum film-cooling jet fails to attach with the plate surface and penetrates into the mainstream reported by Goldstein et al. [50] and Pedersen et al. [51]. The coolant to mainstream density ratio (DR) in modern gas-turbine engines is typically around 2.0 due to the coolant temperature being significantly lower than hot mainstream. Scaled down laboratory tests (to simulate engine DR conditions) usually involve chilling the coolant to very low temperatures by Sinha et al. [52] or using a foreign gas with a higher density by Goldstein et al. [50], Pedersen et al. [51], and Ekkad et al. [53]. In general, increasing DR at a given M results in a higher effectiveness, especially at higher blowing ratios, since the momentum of a high density coolant is lower at a given M, there is a lower tendency to lift-off.

###### Effect of Hole Exit Shape and Geometry

Injecting the film coolant at an angle to the mainstream (a compound angle), results in higher film cooling effectiveness due to greater lateral diffusion of the coolant. Compound angled configurations are also found to resist to lift-off more than simple angled configurations by Ekkad et al. [53]. Using shaped film cooling holes (with a fan shaped diffuser on the blade surface) results in a lower tendency to lift off due to the reduction in momentum due to the increase cross-sectional area for the coolant by Goldstein et al. [50], Schmidt et al. [54], and Gritsch et al. [55]. The converging slot-hole (or console) provides the same level of cooling effectiveness as that of the slot or the fan shaped-hole by Sargison et al. [56]. Embedding film cooling holes in slots by Bunker [57], trenches by Waye and Bogard [58], and craters by Lu et al. [59] (to simulate thermal barrier coating sprays) has been found to increase film cooling effectiveness in the proximity of the hole.

###### Effect of Multiple Rows

Multiple rows of film cooling holes are conventionally used in turbine blade designs. Ligrani et al. [60] studied typical distributions with both simple and compound angles. At lower blowing ratios (less than 0.5), the effects of the numbers of rows is fairly insignificant. However, on increasing the blowing ratio, the double jet row showed a higher effectiveness. More recently, Kusterer et al. [61] studied two rows of film cooling holes with opposite orientation and internal supply geometries. These holes resulted in higher film cooling effectiveness by canceling out the counter-rotating ‘kidney’ vortices (which are induced by the interaction of the inclined jet with the mainstream). Dhungel et al. [62] presented measurements of film cooling effectiveness using film cooling holes supplemented with special anti-vortex holes to increase the effectiveness.

###### Turbine Vane Film Cooling.

It is well known that nozzle guide vanes, being just downstream of the combustor exit, experience the hottest gas path temperatures. The vanes also experience high free-stream turbulence caused by combustor mixing flows. Depending on the requirements, vanes are cooled internally and some coolant is ejected out as film cooling. A typical film cooled vane is shown in Fig. 1. Nirmalan and Hylton [63] studied the effects of parameters such as Mach number, Reynolds number, coolant-to-gas temperature ratio, and coolant-to-gas pressure ratio on the C3X vane film cooling. The leading edge has a showerhead array of five equally spaced rows with the central row located at the aerodynamic stagnation point. Two rows each on the pressure and suction surfaces are located downstream. With increasing blowing strength, the effect on the pressure surface increases farther downstream and the suction surface shows higher effectiveness due to favorable curvature. Ames [64] studied film cooling on a similar C3X vane. Turbulence (Tu = 1–12%) was found to have a dramatic influence on pressure surface film cooling effectiveness, particularly at the lower blowing ratios. Turbulence was found to substantially reduce film cooling effectiveness levels produced by showerhead film cooling. Drost and Bolcs [65] found that mainstream turbulence (Tu = 5.5–10%) had only a weak influence on suction surface film cooling. Higher film effectiveness was noted on the pressure surface at high turbulence due to increased lateral spreading of the coolant. Ethridge et al. [66] studied the effect of coolant-to-mainstream density ratio on a vane with high curvature. Dittmar et al. [67] studied different film cooling hole configurations on the suction (convex) surface and concluded that shaped holes provide better coverage at higher blowing ratios by resisting jet penetration into the mainstream.

A typical film cooled blade is shown in Fig. 1. Most experimental results for turbine blades are obtained on simulated cascades under simulated engine conditions. Ito et al. [68] studied the effect of surface curvature and found that film cooling effectiveness is relatively subdued on the concave (pressure) side in comparison with the convex (suction) side, with the flat plate effectiveness values lying in between. Lift-off occurs at a lower blowing ratio on the concave side. However, the curvature of the concave surface results in a reattachment of the lifted-off coolant on the pressure side, resulting in higher downstream effectiveness.

###### Effect of Unsteady Wake and Secondary Flow

A rotating spoke-wheel wake generator installed upstream of a typical high pressure film cooled model turbine blade has been to simulate the effect of an upstream wake by Mehandale et al. [69]. A reduction in film cooling effectiveness due to the unsteady wake was observed across the board. The effect of coolant to mainstream density ratio and an unsteady stator wake was studied by Rallabandi et al. [70] using the pressure sensitive paint method. Foreign gases with variable density (Nitrogen for DR = 1.0, CO2 for DR = 1.5 and a mixture of Ar + SF6 for DR = 2.5) were used to simulate realistic engine density ratios. Results show a longer coolant trace on the suction side compared with the pressure side. Due to the concave geometry of the pressure side, at higher blowing ratios, a reattachment of the lifted off jet is observed. An increase in effectiveness at higher density ratios for a given blowing ratio is observed as well as deterioration in film cooling effectiveness due to the average effect of the unsteady wake. Gao et al. [71] used the pressure sensitive paint method to characterize full coverage film cooling on the blade surface equipped with axial laid-back fan-shaped holes (expansion and diffusion angles of 10 deg) and another with compound angled laid-back fan-shaped holes. The compound angled holes, in general, resulted in a higher film cooling effectiveness than the axial holes. The effects of tip leakage vortices and horseshoe vortices on the film coolant flow-path can be seen. These vortices result in an expansion of the film coolant on the pressure side, and a contraction of the coolant trace on the suction side.

A large semicylinder is conventionally used as a good approximation to the stagnation region on a turbine vane. Initial studies into film cooling effectiveness near the leading edge were performed by Luckey et al. [72]. Ekkad et al. [73] presented the effect of coolant density and free-stream turbulence on a cylindrical leading edge model using a transient liquid crystal technique to obtain the detailed film effectiveness distributions. They showed that the film cooling effectiveness values for air as the coolant are highest at a low blowing ratio of 0.4 and decrease with an increase in blowing ratio up to 1.2. In the meantime, for CO2 as the coolant, the highest film cooling effectiveness is obtained at a blowing ratio greater than 0.8. Gao and Han [74] reported showerhead film cooling effectiveness measurements using pressure sensitive paint method for a cylindrical leading edge model. Leading edges with up to seven rows of radial and compound angled shaped and cylindrical holes were studied for blowing ratios studied range from 0.5 to 2.0 with DR = 1.0, Tu = 7%. Results showed that radial angles performed better than compound angles; shaped holes performed better than cylindrical holes for the range studied.

###### End-Wall Film Cooling.

Due to the large difference in pressure between the pressure and suction side of the blade, secondary vortices are formed in the hub end wall region by Langston [39] as shown in Fig. 3(b). These vortices increase heat transfer, necessitating provisions for aggressive film-cooling of the end wall. To achieve this end, film coolant is typically ejected from the combustor-vane gap and the stator-rotor gap to cool the NGV end wall and rotor blade platform, respectively. Besides this, engine designs also incorporate discrete film cooling holes along the end wall and platform. Friedrichs et al. [75] used an innovative ammonia-diazo mass transfer analogy to measure film cooling effectiveness on the end wall due to discrete holes. The effectiveness corresponding to the film coolant discharged through the combustor-stator gap has been studied by Oke et al. [76] and Zhang and Jaiswal [77]. The additional momentum introduced in the near wall region by the slot coolant tends to reduce the strength of the secondary flows. More recently, the improvement in film cooling due to the usage of shaped holes in the end wall has been studied by Colban et al. [78] and Gao et al. [79]. Results show that shaped holes offer significantly better coverage than cylindrical holes. The effect of hub secondary flows (horseshoe vortices, etc.) on film cooling is evident from the film cooling effectiveness contours. The effect of coolant density ratio on film cooling effectiveness was studied by Narzary et al. [80], with the conclusion that higher density coolants are more resilient to lift-off and result in higher film cooling effectiveness.

Film cooling on the blade tip has a dual purpose-to protect the tip by forming an insulating film, and to reduce hot-gas tip leakage from pressure side to the suction side, reducing heat transfer coefficients on the tip. A review of the work done on tip-gap film cooling by Metzger's group is available in Kim et al. [81]. More recently, Kwak and Han [82] used liquid crystal imaging technique to measure detailed film cooling effectiveness contours on the squealer tip with tip hole cooling. In general, the literature agrees that a higher blowing ratio and a smaller tip clearance result in better film cooling performance. Mhetras et al. [33] used a model rotor blade with a cut-back squealer tip to allow the film coolant accumulated on the tip to discharge, in the process cooling the trailing edge region of the tip, as shown in Fig. 4 [33]. Results (using the pressure sensitive paint method) show that for the tip film cooling holes, the effectiveness increases with blowing ratio. The cutback allows the coolant to flow over the trailing edge region, resulting in higher effectiveness. A blowing ratio of 1.0 seems optimal for the holes on the near-tip region of the pressure side, indicating that liftoff occurs at higher blowing ratios.

###### Trailing-Edge Film Cooling.

A comprehensive survey of film cooling investigations prior to 1971 was done by Goldstein [3] and included data for slots as well as discrete holes. Emphasis was on two-dimensional slots. Taslim et al. [83] found that the lip-to-slot height ratio has a strong impact on film cooling effectiveness. Martini et al. [84] measured the film cooling effectiveness and heat transfer on the trailing edge cutback of gas turbine airfoils with different internal cooling structures using the IR thermography method, showing the strong impact of internal design on the film cooling performance downstream of the ejection slot. The fast decay in film cooling effectiveness was attributed to vortex shedding from the pressure side lip. Recently, Cakan and Taslim [85] measured the mass/heat transfer coefficients on the trailing edge slot floor, slot sidewalls and lands using naphthalene sublimation method. They found that averaged mass-transfer on the land sidewalls are higher than that on the slot floor surface. Choi et al. [86] measured film cooling effectiveness values for different internal cooling configurations on a cut-back trailing edge using the transient liquid crystal method.

###### Effect of Thermal Barrier Coating Spallation.

Thermal barrier coatings (TBC) are often used to protect turbine component metal surfaces from high temperature gases. The spallation can occur at random; that there is no defined shape or size of the spall makes it difficult to analyze the actual spallation phenomena occurring on a real turbine blade. Thus, it needs to be modeled with predefined shape, size, and location to understand its effect on local heat transfer coefficients and film cooling effectiveness. Ekkad and Han [87] studied the detailed heat transfer coefficient and film cooling effectiveness distributions on a cylindrical leading-edge model with simulated TBC spallation using a transient liquid crystal technique. The two rows of film cooling holes located at + 15 deg and −15 deg from stagnation. The simulated spallation cavities were rectangular in shape and had rounded edges and are similar to the spallation that typically occur on the turbine blade. In general, presence of spallation enhances heat transfer coefficients and causes variation in film cooling effectiveness distributions.

###### Effect of Deposition and Blockage on Hole Exits.

Bunker [57] presented an experimental study to determine the effects of typical turbine airfoil protective coatings on film cooling effectiveness due to the partial blockage of film-hole exits by the TBC coatings. The measurements indicated significant degradation to film performance can result from coatings which are deposited in the hole-exit regions, or inside the holes themselves, during the spray application process. Results also show that shaped film holes are generally very tolerant of coatings and do not show the degradation shown for cylindrical holes. Sundaram and Thole [88] used a large-scale turbine vane cascade to study endwall film cooling. They showed that partially blocked holes had the greatest detrimental effect on degrading film-cooling effectiveness downstream of a film-cooling row. Somawardhana and Bogard [89] indicated that as much as 50% degradation occurred with upstream obstructions, but downstream obstructions actually enhanced film cooling effectiveness. The transverse trench configuration performed significantly better than the traditional cylindrical holes, both with and without obstructions and almost eliminated the effects of both surface roughness and obstructions. Ai et al. [90] performed particulate deposition experiments in a turbine accelerated deposition facility to examine the effects of fly ash particle size and trench configuration on deposits near film cooling holes. Deposits that accumulated on the downstream side of the trench between cooling holes eventually changed the geometry of the trench and clogging cooling holes.

###### Film Cooling Under Rotating Conditions.

Due to the difficulty of acquiring data on a rotating blade, literature studying the effect of rotation is very scarce. Dring et al. [91] reported film cooling effectiveness in a rotating configuration in a low speed tunnel. Takeishi et al. [92] also studied film cooling effectiveness on a stator-rotor stage, simulating a heavy duty gas turbine. Measured effectiveness values on the suction side for the rotating turbine blade seemed to match the data from the stationary cascade whereas the rotating effectiveness on the pressure side seemed to be significantly lower than the nonrotating case. Effects of rotation are attributed to the deflection of the film cooling jet due to centrifugal forces. Abhari and Epstein [93] reported film cooling heat transfer coefficients by the superposition method on the short-duration MIT blowdown turbine facility using heat flux gauges. Time resolved heat transfer coefficient data was obtained-and the benefit of using film cooling on the blade surface is evident.

More recently, using the PSP method, film cooling effectiveness values under rotating conditions were measured on the leading edge by Ahn et al. [94], and on the rotor platform by Suryanarayanan et al. [95], using a three stage multipurpose research turbine at the Turbomachinery Performance and Flow Research Laboratory at Texas A&M University. Ahn et al. [94] used two rows of showerhead holes, one on the suction side and the other on the pressure side. Results (using pressure sensitive paint method) showed that the film cooling effectiveness was sensitive to the location of the stagnation line. When running at design condition, the stagnation line was such that coolant would be uniformly dispersed onto the suction and pressure sides. The effect of rotation on the film cooling effectiveness on the end wall was studied by Suryanarayanan et al. [95] due to coolant discharged rotor-stator purge slot and discrete holes under rotating conditions. Results indicated that a blowing ratio of around 1.0 was optimal. Film cooling coverage was also found to be optimal when running at design condition. Also evident are the effects of the passage vortex, as can be seen by the angle of the film coolant traces.

## Gas Turbine Internal Cooling

###### Fundamentals of Internal Cooling.

The gas turbine blades are convectively cooled with compressor bled air passing through the complex shaped internal cooling channels. These channels are specifically designed to fit the blade profile and have irregular cross sections (Figs. 1 and 2). Since the design of these channels varies from blade to blade, and increased complexities of the flow field are introduced by irregular cross sectional shapes, researchers have mostly used square and rectangular channels as models in the study of heat transfer. The square and rectangular channels are categorized by aspect ratio, as seen in Fig. 5 [96]. In this review paper, the channel aspect ratio (AR) is defined as the ratio of the channel width (W) to the channel height (H) or AR = W/H. Furthermore, the channel height is the distance from the suction surface to pressure surface as seen in Fig. 5. The channel width is the dimension of the surface on which the rib turbulators are cast. Another point of clarification is in regard to the distinction between “leading edge,” “leading surface,” “trailing edge,” and “trailing surface.” Commonly, the phrase leading surface has been used interchangeably with suction side/surface. Likewise, trailing surface is interchangeable with the pressure side/surface.

The internal cooling channels near the blade leading edge have been modeled as narrow rectangular channels with AR = 1:4 and 1:2. The cross section of the cooling channels changes along the cord length of the blade due to the blade profile. In the middle of the blade, the channels are square in shape. Towards the trailing edge, the channels have wider aspect ratios of AR = 2:1 and 4:1. An experimental study on the effects of the buoyancy parameter in various aspect ratio channels was performed by Fu et al. [96]. The study considered five different aspect ratio channels (AR = 1:4, 1:2, 1:1, 2:1, and 4:1) with a fully developed flow inlet condition. The results showed that the overall levels of heat transfer enhancement (Nu/Nuo) for all the ribbed channels were comparable. However, significant differences arose in the pressure losses incurred in each of the channels. The 1:4 channel incurred the lowest pressure penalty; therefore, the thermal performance (TP) of the 1:4 channel was superior to the 1:2, 1:1, and 2:1 channels. It is worth noting that the thermal performance takes into account the pressure penalty (f/fo) and the heat transfer enhancement, and for a constant pumping power, TP = (Nu/Nuo)/(f/fo)1/3. Many papers reviewed and cited in chapters 4 and 5 of Han et al. [10].

###### Mid-Chord Rib Turbulated Cooling.

In advanced gas turbine blades, rib turbulators are often cast on two opposite walls of internal coolant passages to augment heat transfer as seen in Fig. 2(b) [2]. Rib turbulators are also widely known as “trip strips” as they simply trip the boundary layer in the internal cooling channel. The heat transfer augmentation in rectangular coolant passages with rib turbulators primarily depends upon the rib turbulators' geometry, such as rib size, shape, distribution, flow-attack-angle, and the flow Reynolds number. There have been many basic studies by Han et al. [97-99] to understand the heat transfer augmentation versus the pressure drop penalty by the flow separation caused by rib-turbulators. The Reynolds numbers based on coolant channel hydraulic diameter vary from 10,000 to 80,000. However, the Reynolds numbers can be up to 500,000 for the coolant passages in large power generation turbine blades. In general, repeated ribs, used for coolant passages, are nearly square in cross section with a typical relative rib height of 5–10% of the coolant channel hydraulic diameter (e/D), a rib spacing-to-height ratio (p/e) varying from 5 to 15, and a rib flow-attack-angle around 30 deg to 60 deg.

In general, smaller rib height is more efficient for higher Reynolds number flows, and the heat transfer enhancement decreases but pressure drop penalty increases with the Reynolds number. For example, the heat transfer can be enhanced about three times with five times the pressure drop penalty in a square channel with typical rib geometry (e/D = 0.06, p/e = 10, and 45 deg rib flow-attack-angle) at a Reynolds number around 30,000. Han and Zhang [100] showed that the V-shaped ribs provide better heat transfer performance than the typical angled rib geometry for a given pressure drop penalty. Smaller gas turbine blades have larger blockage ribs with e/D = 0.1 ∼ 0.2 at closer spacing with p/e = 3 ∼ 5 reported by Taslim and Lengkong [101].

###### Heat Transfer Correlation.

More recently, Rallabandi et al. [102] performed systematic experiments to measure heat transfer and pressure losses in a stationary square channel with 45 deg round/sharp edged ribs at a wide range of Reynolds numbers ranging from 30,000 to very high flows of Re = 400,000. These high Reynolds are typical of land based turbines. The correlations of Han and Park [99] were modified to fit into the new extended parameter range. This work has extended the e+ (a nondimensional roughness Reynolds number) range of previous work from e+= 1,000 (Re = 70,000, e/D = 0.078) to e+ = 18,000 (Re = 400,000, e/D = 0.18). With round edged ribs, the friction was lower, resulting in a smaller pressure drop. The heat transfer coefficients for the round ribs, on the other hand, were similar to sharp edged ribs.

###### Rotational Effect on Internal Passage Flow and Heat Transfer.

Rotation induces Coriolis and centrifugal forces which produce cross-stream secondary flow in the rotating coolant passages; therefore, heat transfer coefficients in rotor coolant passages are very much different from those in nonrotating frames. One important finding from recent studies is that rotation can greatly enhance heat transfer on one side of the cooling channel and reduce heat transfer on the opposite side of the cooling channel due to rotating-induced secondary flow, depending on the radial outflow or inflow of the cooling passages (Fig. 5). Without considering rotational effect, the coolant passage would be overcooled on one side while overheated on the opposite side. Recent studies focus on the combined effects of rotation, channel shape, orientation, and aspect ratio on rotor coolant passage heat transfer with various high performance rib turbulators. Results show that the channel shape, orientation, and aspect ratio significantly change local heat transfer coefficient distributions in rotor coolant passages with rib turbulators.

###### Fluid Flow in Rotating Coolant Passages.

Heat transfer is a side effect of the flow field. Flow in a rotating channel is significantly different from flow in a nonrotating channel. The secondary flow in rotation redistributes velocity and also alters the random velocity fluctuation patterns in turbulent flows. Cheah et al. [103] used the LDA to measure velocity and turbulence quantity in a rotating two-pass channel. Bons and Kerrebrock [104] measured the internal flow in a rotating straight smooth-wall channel with particle image velocimetry (PIV) for both heated and nonheated cases. Liou et al. [105] measured pressure and flow characteristics in a rotating two-pass square duct with 90-deg ribs by using the LAD. Rotation shifts the bulk flow toward the trailing side, and the turbulence profile shows a different distribution in rotation. The above-mentioned flow measurements help to understand the flow physics and serve to explain the heat transfer results obtained in two-pass rotating channels with smooth and ribbed walls.

###### Square Cross-Section Serpentine Channel.

Heat transfer in rotating multipass coolant passages with square cross section and smooth walls was reported by Wagner et al. [106]. Results show that the heat transfer coefficient can enhance 2–3 times on the trailing surface and reduce up to 50% on the leading surface for the first-pass radial outward flow passage; however, the reverse is true for the second-pass radial inward flow passage due to the flow direction change. Results also show that the heat transfer difference between leading and trailing surfaces is greater in the first-pass than that in the second-pass due to the centrifugal buoyancy opposite to the flow direction. Heat transfer in rotating multipass coolant passages with square cross section with 45 deg rib turbulated walls was reported by Johnson et al. [107]. Results show that rotation and buoyancy in general have less effect on the rib turbulated coolant passage than on the smooth-wall coolant passage. This is because the heat transfer enhancement in the ribbed passages is already up to 3.5 times higher than in the smooth passages; therefore, the rotational effect is still important but with a reduced percentage. Results also show that, like a nonrotating channel, the 45 deg ribs perform better than 90 deg ribs and subsequently better than the smooth channel.

###### Wall Heating Condition Effect.

Since the temperature difference between the coolant and the channel walls varies along the coolant passages, so does the rotation buoyancy. Therefore, it is expected that the channel wall heating conditions would affect rotor coolant passage heat transfer. Han et al. [108] studied the uneven wall temperature effect on rotating two-pass square channels with smooth walls. They concluded that in the first pass, the local uneven wall temperature interacts with the Coriolis force-driven secondary flow and enhances the heat transfer coefficients in both leading and trailing surfaces as compared with the uniform wall temperature case. Zhang et al. [109] studied the influence of wall heating condition on the local heat transfer coefficient in rotating two-pass square channels with 90 deg ribs and 60 deg ribs on the leading and trailing walls, respectively. They concluded that the uneven wall temperature significantly enhances heat transfer coefficients on the first-pass leading and second-pass trailing surfaces as compared with the uniform wall temperature condition.

###### Channel Orientation Effect.

Since the turbine blade is curved, the rotor blade cooling passage can have different channel orientations with respect to the rotating plane. Johnson et al. [110] studied the effects of rotation on the heat transfer for smooth and 45 deg ribbed serpentine channels with channel orientations of 0 deg and 45 deg to the axis of rotation. They found that the effects of Coriolis and buoyancy forces on heat transfer in the rotating channel are decreased with the channel at 45 deg compared to the results at 0 deg. This implies that the difference in heat transfer coefficient between leading and trailing surfaces due to rotation will be reduced when the channel has an angle to the axis of rotation. Dutta and Han [111] used high performance broken V-shaped ribs in rotating two-pass square channels to study the effect of channel orientation on heat transfer. The channel orientation with respect to the rotation axis influences the secondary flow vortices induced by rotation, as shown in Fig. 5. They concluded that the broken V-shaped ribs are better than the 60 deg angled ribs; the parallel 45 deg angled ribs are better than the crossed 45 deg angled ribs. In general, the difference between leading and trailing wall heat transfer coefficients is reduced for the channel with a 45 deg angle to the axis of rotation.

###### Rotation Number and Buoyancy Parameter.

It is worthwhile, then, to develop nondimensional parameters that may be used to correlate rotating effects to heat transfer. The rotation number (Ro) has been widely accepted to establish the strength of rotation by considering the relative strength of the Coriolis force compared to the bulk inertial force. As such, the rotation number is defined as Ro = ΩDh/V. The buoyancy parameter (Bo) is useful to include the effects of density variation (centrifugal effects) and is defined as the ratio of the Grashoff number to the square of the Reynolds number; both of which are based on the channel hydraulic diameter. Thus Bo = (Δρ/ρ)(Ro2)(R/Dh). Typical rotation numbers for aircraft engines are near 0.25 with Reynolds numbers in the range of 30,000. One method to achieve conditions similar to a real gas turbine engine in the laboratory is to use air at high pressures. As the pressure of the air increases, so will the density. For a fixed Reynolds number, dynamic viscosity, and hydraulic diameter, an increase in density will proportionately decrease the bulk velocity. A lower bulk velocity will in turn increase the rotation number since the rotation number is the ratio of the Coriolis force to bulk inertial force. Increasing the range of the rotation number and buoyancy parameter is very important since gas turbine engineers can utilize these parameters in their analysis of heat transfer under rotating conditions.

###### Rectangular Cross-Section Two-Pass Channel.

Zhou and Acharya [112] studied a 4:1 aspect ratio channel with a rotation number of 0.6 at a Reynolds number of 10,000. Huh et al. [113] increased the range of the rotation number by a factor of 4 for the AR = 2:1 channel. Huh et al. [114] studied heat transfer in a 1:4 aspect ratio channel (Fig. 5). Results show that heat transfer on the trailing surface with radially outward flow does indeed increase under rotating conditions due to the flow phenomena previously described. Rotation reduces the heat transfer on the leading surface by a very significant 50%. However, due to buoyancy effects, the leading surface heat transfer trends reverse after a critical rotation number is reached. With radially inward flow, the heat transfer in the smooth channel shows the expected behavior on the leading wall. Surprisingly, however, due to the aspect ratio of the channel, the heat transfer on the trailing wall also increases. In square channels this is not the case.

A gas turbine blade experiences high heat loads on the tip portion due to high velocity fluid leakage between the rotating blade and casing. Until recently, most of the studies that have considered heat transfer in multipass internal serpentine channels provided minimal information on heat transfer on the inside of the blade tip. Even fewer studies are available that consider the effect of rotation on blade tip cap heat transfer. The effects of rotation on tip cap internal heat transfer in rectangular channels with AR = 2:1 was presented in the study by Huh et al. [113] and Huh et al. [114], which provided heat transfer results on the tip cap of the 1:4 aspect ratio channel. Results reveal that rotation helps to increase cooling of the blade tip internal surface. Rotation doubles the heat transfer coefficients on the tip cap surface in both passages.

###### Developing Flow Entrance Effect.

Some gas turbine blade designs provide a developing flow entrance. It is well accepted that due to the thin boundary layer, heat transfer with developing flow is markedly different from fully developed flows. Wright et al. [115] performed experiments in channels with three different entrance geometries. They concluded that the entrance condition will enhance the heat transfer. They also pointed out that the effect of the entrance weakens as the rotation number increases. The influence of the entrance geometry also is stronger in the smooth channel when compared to the ribbed channel. Huh et al. [113] studied a sudden expansion from a circular tube to the rectangular cross section of the channel. Notable is the lack of degradation in heat transfer, until large Bo values, on the leading surface for the developing flow cases. Heat transfer is clearly dominated by the entrance.

Jet impingement cooling is most suitable for the leading edge of the blade where the thermal load is highest and a thicker cross section of this portion of the blade can suitably accommodate impingement cooling (Figs. 1 and 2). There are many studies focused on the effects of jet-hole size and distribution, jet-to-target surface distance, spent-air cross flow, cooling channel cross section, and the target surface shape on the heat transfer coefficient distribution (for example, Chupp et al. [116], Metzger et al. [117], etc.). Recent studies have considered the combined effects of target surface roughening coupled with jet impingement for further heat transfer enhancement. Taslim et al. [118] investigated heat transfer on a curved target surface to more realistically simulate the leading edge of the blade. Three different roughening techniques were studied: conical bumps, tapered radial ribs, and sand paper type roughness. Kanokjaruvijit and Martinez-Botas [119] showed that by impinging on the dimple, higher energetic vortices were generated and thus heat transfer was increased. Since the leading edge of the gas turbine blade incorporates a showerhead film cooling design, Taslim and Khanicheh [120] showed that the heat transfer can be significantly increased by including the film cooling holes on the target plate.

###### Rotational Effect on Impingement Cooling.

All of the studies previously mentioned considered jet impingement heat transfer under stationary conditions. Of course, however, the turbine blade is rotating. Overall, the effectiveness of the jet is reduced under rotating conditions due to deflection from the target surface. Epstein et al. [121] studied the effect of rotation on impingement cooling in the leading edge of a blade. They reported that the rotation decreases the impingement heat transfer, but the effective heat transfer is better than a smooth rotating channel. Mattern and Hennecke [122] reported the effect of rotation on the leading edge impingement cooling by using the naphthalene sublimation technique. They found that the rotation decreases the impingement heat transfer for all staggered angles. Glezer et al. [123] studied the effect of rotation on swirling impingement cooling in the leading edge of a blade. They found that screw-shaped swirl cooling can significantly improve the heat-transfer coefficient over a smooth channel and the improvement is not significantly dependent on the temperature ratio and rotational forces. Parsons et al. [124] studied the effect of rotation on impingement cooling in the mid-chord region of the blade. A central chamber serves as the pressure chamber, and jets are released in either direction to impinge on two heated surfaces. The jet impinging directions have different orientations with respect to the direction of rotation. They reported that the rotation decreases the impingement heat transfer on both leading and trailing surfaces with more effect on the trailing side (up to 20% heat transfer reduction).

###### Trailing-Edge Pin Fins Cooling.

Pin-fins are mostly used in the narrow trailing edge of a turbine blade where impingement and ribbed channels cannot be accommodated due to manufacturing constraint (Figs. 1 and 2). Pin-fins commonly used in turbine blade cooling have pin height-to-diameter ratio between $12$ and 4. Heat transfer in turbine pin-fin cooling arrays combines the cylinder heat transfer and end wall heat transfer. Due to the turbulence enhancement caused by pins (wakes and horseshoe vortex), heat transfer from end-walls is higher than smooth wall cases; however, casting pins will cover a considerable end wall area, and that area needs to be compensated for by the increased pin surface area for cooling. In addition to flow disturbances, pins conduct thermal energy away from the end wall surface. Long pins can increase the effective heat transfer area and perform better than short pins. There have been many investigations that studied the effects of pin array (inline or staggered), pin size (length-to-diameter ratio = 0.5 to 4), pin distribution (streamwise-and spanwise-to-diameter ratio = 2 to 4), pin shape (with and without a fillet at the base of the cylindrical pin; oblong, cube, and diamond shaped pins as well as the stepped diameter cylindrical pins), partial length pins, flow convergence and turning, and with trailing edge coolant extraction on the heat transfer coefficient and friction factor distributions in pin-fin cooling channels (for example, Metzger et al. [125], Chyu et al. [126], etc.)

###### Rotational Effect on Pin Fins Cooling.

Wright et al. [127] studied the effect of rotation on heat transfer in narrow rectangular channels (AR = 4:1 and 8:1) with typical pin-fin array used in turbine blade trailing edge design and oriented at 150 deg with respect to the plane of rotation. Results show that turbulent heat transfer in a stationary pin-fin channel can be enhanced up to 3.8 times that of a smooth channel; rotation enhances the heat transferred from the pin-fin channels up to 1.5 times that of the stationary pin-fin channels. Most importantly, for narrow rectangular pin-fin channels oriented at 135 deg with respect to the plane of rotation, heat transfer enhancement on both the leading and trailing surfaces increases with rotation. This provides positive information for the cooling designers.

###### Rotational Effect on Wedge-Shaped Cooling Channel.

The trailing edge cooling passage has been represented with wide aspect rectangular channels. However, the cross sectional shape is best represented with a wedge or trapezoid. To enhance heat transfer in this region of the blade, the leading and trailing surfaces are roughened with ribs or pin-fins. Further protection is provided with coolant ejection from the narrow portion of the channel (Fig. 5), and the additional effects of Coriolis induced secondary flows and centrifugal driven buoyancy alter the heat transfer characteristics. Chang et al. [128] studied heat transfer in rib roughened trapezoidal duct with bleed holes. Liu et al. [129] considered heat transfer in a trailing edge cooling passage with smooth walls with trailing edge slot ejection. The channel was placed at an angle of 135 deg respective of the direction of rotation. Most notably, for all three surfaces, the Nusselt number ratios increase as the rotation number increases. The heat transfer enhancement with slot ejection is much higher than the cases without slot ejection. Rallabandi et al. [130] studied the effect of full length conducting, partial length conducting and nonconducting pins in a wedge-shaped channel with trailing edge bleeding. The rotational effects were altered in different regions by the presence of the pins.

###### Rotational Effect on Dimples Cooling.

Dimples are recently being considered for turbine blade trailing edge cooling designs. Dimples provide reasonable heat transfer enhancement with a relatively low pressure loss penalty as compared with the ribs and pin-fins. The dimple cooling can be a good choice if the pressure loss is the main concern in the cooling design. Due to the disturbance enhancement caused by dimples, heat transfer from dimpled surface is higher than the smooth wall conditions. This is because dimples induce flow separation and reattachment with pairs of vortices. In addition to flow disturbances, dimples increase heat transfer area. In general, higher heat transfer enhancement occurs on the flow reattached regions either at the dimple cavity downstream or on the dimple downstream flat surface. The heat transfer enhancement is typically around 2–2.5 times that of the smooth wall value with 2–4 times pressure loss penalty and is fairly independent of Reynolds number and channel height or aspect ratio. There have been a number of studies that evaluated the effects of dimple size, dimple depth (depth-to-print diameter ratio = 0.1 to 0.3), distribution, shape (cylindrical, hemispheric, and teardrop), and channel height on the heat transfer coefficient and friction factor distributions in dimple cooling channels (for example, Mahmood et al. [131], etc.). However, the majority of investigations involving dimple cooling have been limited to stationary channels that are applicable for stator blade trailing edge cooling designs; only a few studies focus on rotor blade dimple cooling. Zhou and Acharya [132] studied heat/mass transfer in a rotating square channel with typical dimple array. They found that rotation enhances heat transfer on the trailing dimple surface and reduces heat transfer on the leading dimple surface in a similar manner as the rotational effect on the trailing and leading surfaces of the square channel with ribs. Griffith et al. [133] studied heat transfer in rotating rectangular channels (AR = 4:1) with typical dimple array. The results show that rotation enhances heat transfer on both trailing and leading surfaces of the narrow dimpled channel in a similar trend as the rotational effect on the trailing and leading surfaces of the narrow rectangular channel with pins; however, the heat transfer enhancement of the pinned channel exceeds that of the dimpled channel. Additionally, the dimpled channel oriented at 135 deg with respect to the plane of rotation provides greater overall heat transfer enhancement than the orthogonal dimpled channel.

## Numerical Modeling

###### CFD for Turbine Internal Cooling.

In recent years, many researchers have made computational studies on internal cooling channels of the rotating blade. Numerical predictions provide the details that are difficult to obtain by experiments. Moreover, the increase in computation power in desktop computers has made it economical to optimize the design parameters based on numerical analyses. Most common models are based on a two-equation turbulence model; namely, the k–ε model, low Reynolds number k–ε model, the two-layer k–ε model, and the low Reynolds number k–ω model. The Reynolds averaged Navier–Stokes (RANS) and large–eddy simulations (LES) are the most commonly used simulation methods for turbine blade internal flow and heat transfer predictions. Direct numerical simulation (DNS) is to solve every flow in detail. The extremely small grid spacing and time increments makes this type of simulations extremely expensive in terms of time and computational resources. Jang et al. [134] employed Reynolds stress turbulence model to predict the flow and heat transfer in turbine blade cooling passage with rib turbulators. They concluded the second moment solutions display large anisotropy in turbulent stress and heat flux distributions. With rotation, the Coriolis and buoyancy forces result in strong nonisotropic turbulence flows. Viswanathan and Tafti [135] present the large eddy simulations (LES) of flow and heat transfer in rotating square duct with 45 deg rib turbulators. The unsteady temperature field in periodic domain is computed directly. The authors observe that the large scale vortices play a major role in the mixing of the core fluid and the near-wall heated fluid, the vortex shedding behind the ribs are responsible for the large spike in the energy spectrum, and the time variation of the flow rate is attributed to the variation dominated by the vortex shedding frequency.

###### CFD for Conjugate Heat Transfer and Film Cooling.

Turbine internal cooling and film cooling are the major cooling techniques that applied to turbine blades. In both types of cooling, heat is removed by means of both convection and conduction. Moreover, convection and conduction are effected from each other. Conjugate heat transfer is basically termed as the interaction between the convection heat transfer from the surrounding fluid and the conduction heat transfer through the solid body. The conduction heat transfer is affected from the convection heat transfer of the surrounding fluid. Thus, they should be solved simultaneously. This coupling of solid to fluid is usually done by using the same wall temperature for the adjacent fluid block and solid block. The conjugate CFD methods provide good predictions for heat transfer analysis in turbine blades. Eliminating the heat transfer coefficient calculation by utilizing the relationship between solid and fluid interface, conjugate methods can provide direct solutions. There is much commercially available software (i.e., Ansys Fluent, Ansys Cfx, Star CCM, etc.). However, the accuracy of conjugate methods must be compared with experimental data and still remains to be improved. For example, Shih et al. [139] performed an extensive study on the effects of Biot number on temperature and heat-flux distributions in a TBC-coated flat plate cooled by rib-enhanced internal cooling. He and Oldfield [140] conducted a study on modeling effect of hot streak on TBC-coated turbine vane heat transfer by unsteady conjugate heat transfer.

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Taslim, M. E., and Lengkong, A., 1998, “45 deg Staggered Rib Heat Transfer Coefficient Measurements in a Square Channel,” ASME J. Turbomach., 120(3), pp. 571–580.
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## Figures

Fig. 1

Cross-sectional view and heat flux distribution of a cooled vane and blade [1]

Fig. 2

Gas turbine blade cooling schematic: (a) film cooling, (b) internal cooling [2]

Fig. 3

(a) Typical film cooled airfoil [25] and (b) end wall vortices [39]

Fig. 4

Typical gas turbine blade squealer tip cooling configuration [33]

Fig. 5

Typical turbine blade internal cooling channel with rotation-induced vortices [96]

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