Film cooling on a convex surface: influence of external pressure gradient and Mach number on film cooling performance

 The film cooling performance on a convex surface subjected to zero and favourable pressure gradient free-stream flow was investigated. Adiabatic film cooling effectiveness values were obtained for five different injection geometries, three with cylindrical holes and two with shaped holes. Heat transfer coefficients were derived for selected injection configurations. CO₂ was used as coolant to simulate density ratios between coolant and free-stream close to gas turbine engine conditions. The film cooling effectiveness results indicate a strong dependency on the free-stream Mach number level. Results obtained at the higher free-stream Mach number show for cylindrical holes generally and for shaped holes at moderate blowing rates significant higher film cooling effectiveness values compared to the lower free-stream Mach number data. Free-stream acceleration generally reduced adiabatic film cooling effectiveness relative to constant free-stream flow conditions. The different free-stream conditions investigated indicate no significant effects on the corresponding heat transfer increase due to film injection. The determined heat flux ratios or film cooling performance indicated that coolant injection with shaped film cooling holes is much more efficient than with cylindrical holes especially at higher blowing rates. Heat flux penalties can occur at high blowing rates when using cylindrical holes. Received on 29 May 2000     

Film cooling effectiveness from trenched shaped and compound holes

This paper presents a comparative-numerical investigation on film cooling from a row of simple and compound-angle holes injected at 35° on a flat plate with four film cooling configurations: (1) cylindrical film hole; (2) 15° forward diffused film hole; (3) trenched cylindrical film hole; (4) trenched 15° forward-diffused film hole. All simulations are at fixed density ratio of 1.6, blowing ratio of 1.25, length-to-diameter L/D = 4 and pitch-to-diameter ratio of 3.0. The effect of length-to-diameter ratio on film cooling has been also investigated using L/D in the range of 1–8. Computational solutions of the steady, Reynolds-averaged Navier–Stokes equations have been obtained using a finite volume method. It has been found that the shape of the hole and the trenched holes can significantly affect the film cooling flow over the protected surface. Further, it has been shown that the film cooling effectiveness by trenched shaped holes is higher than all other configurations both in spanwise and streamwise specially downstream of the injection. Also, a trenched compound angle injection shaped hole produces much higher film cooling protection than the other configurations investigated in the present paper. The length-to-diameter ratio of trenched holes was found to have a significant effect on film cooling effectiveness and the spread of the coolant jets.     

Analysis of upstream,double-row,cylindrical holes on primary and secondary effects of endwall flow and film cooling

Flow features and film cooling performance of five configurations of double-row, cylindrical holes, upstream of an E3 vane, in a linear cascade are numerically investigated. This simulation is completed using a verified turbulence model at four blowing ratios (M = 0.5, 1.0, 1.5, 2.0). The first three configurations have two rows of cylindrical holes, each row with the same compound angle (β=-45°, 0° or 45°), while the other two have two rows with opposite compound angles (β=-45°, 45° and β=45°, -45°), which are also referred to as double-jet film cooling (DJFC) holes. The primary effects on the downstream endwall and the secondary effects on the nearby airfoil of the cooled passage are analyzed and discussed in detail. Results show that at low blowing ratios the movement of the coolant is denominated by the interaction between the jets and vortices resulting in similar film coverage on both the endwall and airfoil. The effect of vortices is reduced at high blowing ratios. It is also shown that the movement of the coolant is determined by the initial velocity direction, as well as the film cooling configuration.     

Heat transfer in film-cooled turbulent boundary layers at different blowing ratios as affected by longitudinal vortices

Effects of embedded longitudinal vortices on heat transfer in film-cooled turbulent boundary layers at different blowing ratios are discussed. These results were obtained in boundary layers at free-stream velocities of 10 and 15 m/s. Film coolant was injected from a single row of holes at blowing ratios of 0.47–1.26. A single longitudinal vortex was induced upstream of the film-cooling holes using a half-delta wing attached to the wind tunnel floor. Heat transfer measurements were made downstream of injection using a constant heat flux surface with 126 thermocouples for surface temperature measurements. For all blowing ratios examined, the embedded vortices cause significant alterations to wall heat transfer and to film cooling distributions. Measurrments of mean temperatures and mean velocities in spanwise planes show that high wall heat transfer regions are associated with regions of high near-wall longitudinal velocity where very little film coolant is present. In addition to high heat transfer regions associated with the vortex downwash, there are also secondary heat transfer peaks. These secondary peaks develop due to shear layer mixing and interaction between the vortex and cooling jets and become higher in magnitude and more persistent with downstream distance as the blowing ratio increases from 0.47 to 1.26.     

Numerical modelling of film cooling with and without mist injection

Two-phase CFD calculations, using a Lagrangian model and commercial code Fluent 6.2.16, were employed to calculate the gas and droplet flows and film cooling effectiveness with and without mist on a flat plate. Two different three dimensional geometries are generated and the effects of the geometrical shape, size of droplets, mist concentration in the coolant flow and temperature of mainstream flow for different blowing ratios are studied. A cylindrical and laterally diffused hole with a streamwise angle of 30° and spanwise angle of 0° are used. The diameter of film cooling (d) hole, and the hole length to diameter ratio (L/d) for both of geometries are 10 mm and 4, respectively. Also the blowing ratio ranges from 1.0 to 2.0, and the mainstream Reynolds number based on the mainstream velocity and hole diameter (Re _d) is 6,219. The results are shown for different droplets diameters (1–10 μm), concentrations (1–5%) and mainstream temperatures (350–500 K). The centreline effectiveness and distribution of effectiveness on the surface of cooling wall are presented.     

Coherent structures in unsteady swirling jet flow

An LDA technique and phase-averaging analysis were used to study unsteady precessing flow in a model vortex burner. Detailed measurements were made for Re=15,000 and S=1.01. On the basis of the analysis of phase-averaged data and vortex detection by the λ₂-technique of Joeng and Hussain (1995), three precessing spiral vortex structures were identified: primary vortex (PV), inner secondary vortex (ISV), and outer secondary vortex (OSV). The PV is the primary and most powerful structure as it includes primary vorticity generated by the swirler; the ISV and OSV are considered here as secondary vortical structures. The jet breakdown zone is the conjunction of a pair of co-rotating co-winding spiral vortices, PV and ISV. The interesting new feature described is that the secondary vortices form a three-dimensional vortex dipole with a helical geometry. The effect of coupling of secondary vortices was suggested as a mechanism of enhanced stability reflected in their increased axial extent.     

In-hole and mainflow velocity measurements of low-momentum jets in crossflow emanating from short holes

Discrete hole film cooling utilizes jet-in-crossflow geometry where the jet is supplied through a short hole which may be pitched relative to the main flow. Typically, the velocity ratio is near one. Under these conditions, the mean flow structure of the jet/mainstream interaction may be strongly affected by the characteristics of the flow within the hole. Magnetic resonance velocimetry (MRV) is used to measure the 3-dimensional mean velocity field for various jets in crossflow with short holes of varied inclination angles and blowing ratios typically of gas turbine applications. Novel measurements of the flow within inclined feed holes are captured using MRV. Secondary flows within the hole are found to be strongly dependent on the inclination of the hole. The traditional counter-rotating vortex pair is observed in the mainstream, as well as high levels of wall-normal vorticity. The 3D vorticity field is used to modify traditional jet-in-crossflow vortex ring theory to apply to low-momentum jets which remain attached to the ejection surface.     

Instabilities in multi-hole converging flow of viscoelastic fluids

Studies of the onset of instabilities were conducted on single hole and multi-hole contractions using laser speckle visualization. A well characterized elastic fluid was used with constant viscosity of 13.1 Pa · s and elasticity characterized by a longest relaxation time constant of 2.233 s. The onset of instabilities was characterized in terms of the Deborah number and the contraction ratio. Three types of instabilities were observed: pulsing vortices, azimuthally rotating vortices, and swirling vortices. For the single hole contractions the critical Deborah number for instability increased from 4.4 to 5.07 to 5.25 as the contraction ratio increased from 4: 1 to 8: 1 to 12: 1. The magnitude of the instabilities was much greater for the 4: 1 contraction than for the other two contraction ratios. For the multi-hole contraction a square array of nine holes was used and the ratio of the hole diameter to hole spacing was varied. The height of the vortices is very similar for the single hole and multi-hole contractions at low Deborah numbers. At high Deborah numbers the effect of adjacent holes is to reduce the height of the vortices by a factor of three. For the 4: 1 spacing no secondary vortex was observed below a Deborah number of De = 3.7. Secondary vortices occurred for the 8:1 and 10:1 spacing at all Deborah numbers. Unstable pulsing vortices appeared for all spacings at a critical Deborah number around 5.5. Adjacent holes decreased the strength of the unsteady vortex motions. The centerline velocities were measured for the multi-hole contraction at shear rates of 5, 30, and 300 s^–1. The elongational strain rates are similar at a low shear rate of 5 s^–1. As shear rate is increased the onset of stretching occurs closer to the plane of the contraction for the smaller contraction ratios.     

Flow visualisation of the external flow from a converging slot-hole film-cooling geometry

This paper presents flow visualisation experiments for a novel film-cooling hole, the converging slot-hole or console for short. Previously published experimental results have demonstrated that the console improved both the heat transfer and the aerodynamic performance of turbine vane and rotor blade cooling systems. Flow visualisation data for a row of consoles were compared with that of cylindrical and fan-shaped holes and a slot at the same inclination angle of 35° to the surface, on a large-scale, flat-plate model at engine-representative Reynolds numbers in a low speed tunnel with ambient temperature mainstream flow. In the first set of experiments, the flow was visualised by using a fine nylon mesh covered with thermochromic liquid crystals, allowing the measurement of gas temperature contours in planes perpendicular to the flow. This data demonstrated that the console film was similar to a slot film, and remained thin and attached to the surface for the coolant-to-mainstream momentum flux ratios of 1.1 to 40 and for a case with no crossflow (infinite momentum flux ratio). A second set of flow visualisation experiments using water/dry-ice fog have confirmed these results and have shown that the flow through all coolant geometries is unsteady.     

Experimental investigation of vortex rings impinging on inclined surfaces

Vortex–ring interactions with oblique boundaries were studied experimentally to determine the effects of plate angle on the generation of secondary vorticity, the evolution of the primary vorticity and secondary vorticity as they interact near the boundary, and the associated energy dissipation. Vortex rings were generated using a mechanical piston-cylinder vortex ring generator at jet Reynolds numbers 2,000–4,000 and stroke length to piston diameter ratios (L/D) in the range 0.75–2.0. The plate angle relative to the initial axis of the vortex ring ranged from 3 to 60°. Flow analysis was performed using planar laser-induced fluorescence (PLIF), digital particle image velocimetry (DPIV), and defocusing digital particle tracking velocimetry (DDPTV). Results showed the generation of secondary vorticity at the plate and its subsequent ejection into the fluid. The trajectories of the centers of circulation showed a maximum ejection angle of the secondary vorticity occurring for an angle of incidence of 10°. At lower incidence angles (<20°), the lower portion of the ring, which interacted with the plate first, played an important role in generation of the secondary vorticity and is a key reason for the maximum ejection angle for the secondary vorticity occurring at an incidence angle of 10°. Higher Reynolds number vortex rings resulted in more rapid destabilization of the flow. The three-dimensional DDPTV results showed an arc of secondary vorticity and secondary flow along the sides of the primary vortex ring as it collided with the boundary. Computation of the moments and products of kinetic energy and vorticity magnitude about the centroid of each vortex ring showed increasing asymmetry in the flow as the vortex interaction with the boundary evolved and more rapid dissipation of kinetic energy for higher incidence angles.     

A broad reconsideration of anti-vortex film cooling method using numerical optimization and an improved heat-flux model

This paper represents the detailed results of an evolutionary optimization framework towards the exploration of vortex mechanisms leading to effective anti-vortex film cooling. In this regards, several arrangements of triple cooling holes were studied on flat and curved geometries using differential-evolution optimization algorithm and a modified Reynolds-stress based flow solver. Depending on the flow and geometric parameters, four distinct types of vortex interaction with different cooling mechanisms were identified. The vortex-trapping mechanism, observed in the optimized upstream arrangement acts through imposing a mild downwash over the main counter-rotating vortex pair and provides the best cooling effectiveness for the low injection angle (less than 30°) cases. The vortex-suppression and -balancing are the optimal possible solutions of the adjacent arrangement. The latter is the classic well-known type of anti-vortex cooling, while the former provides a sudden strong controlling potential for high blowing ratios (higher than 1.0) and high injection angle film cooling. For the non-flat surfaces the triple holes effectively perform up to blowing-ratio of 2.0. However, the reverse-vortex-trapping mechanism occurring in the downstream arrangement is recommended for convex surfaces, while the adjacent arrangement is the choice for concave regions. In general, there is a possibility of reducing the coolant consumption about 30% through increasing the pitch-to-diameter ratio, while the values of cooling-effectiveness still remain in an acceptable range.     

Effects of injection angle orientation on concave and convex surfaces film cooling

The present study employs a transient liquid crystal thermography to measure film cooling performance over constant curvature of concave and convex surfaces. This work investigates detailed distributions of both film cooling effectiveness and heat transfer coefficient on concave and convex surfaces with one row of injection holes inclined stream-wise at 35° at four blowing ratios (0.5, 1.0, 1.5 and 2.0) on four test pieces with different hole configurations. All test models have a row of discrete holes with a stream-wise injection angle (γ of 35° and a pitch-to-diameter ratio (P/d) of 3. The current work examines four different injection configurations, one with simple and three with 8° forward-expanded holes. Three compound angles of 0, 45 and 90° with air (ρ_c/ρ_m = 0.98) as coolants are tested under the mainstream Reynolds number (Re_d) of 2300 on concave surface, and 1700 on convex surface. Measured results of the concave surface show that both the span-wise averaged heat transfer coefficient and film cooling effectiveness increase with blowing ratios for all tested models. Higher heat transfer levels induced by large flow disturbance of compound-angle injection also lead to poorer overall film cooling performance, especially at high blowing ratio and large span-wise injection angle. Present results show that the best surface protection on the concave surface over the widest range of M can be provided by the forward-expanded holes with β = 0° (Model-B), followed by the forward-expanded holes with β = 45° (Model-C). Convex surface results show that the compound-angle injection indicates increases in both film cooling effectiveness and heat transfer at moderate and high blowing ratios. The forward-expanded hole with simple-angle injection provides the best film performance because of high film cooling effectiveness and low heat transfer coefficient at blowing ratio of 0.5.     

Hybrid LES-RANS study of an effusion cooling array with circular holes

A multi-row effusion cooling configuration with scaled gas turbine combustor conditions is studied numerically, using a novel wall-proximity-based hybrid LES-RANS approach. The distribution of the coolant film is examined by surface adiabatic cooling effectiveness (ACE). Simulation results have shown that the accuracy of cooling effectiveness prediction is closely related to the resolution of turbulent flow structures involved in hot-cold flow mixing, especially those close to the plate surface. The formation of the coolant film in the streamwise direction is investigated. It is shown that the plate surface directly downstream the coolant holes are covered well by the coolant jets, while surface regions in between the two columns of the coolant holes could not be protected until the coolant film is developed sufficiently in the spanwise direction in the downstream region. More detailed study has also been carried out to study the time-averaged and time-dependent flow fields. The relation between the turbulent flow structures and coolant film distribution are also examined. The Kelvin–Helmholtz instability in the upper and lower coolant jet shear layer, is found to have the same frequency of around 8000 Hz, and is independent of the coolant hole position. Additionally, it is suggested by the spectral coherence analysis that those unsteady flow structures from the lower shear layer are closely related to the near wall flow temperature, and such effect is also independent of the coolant hole position.     

Effect of an Exit-Wedge Angle on Pinch-off and Mass Entrainment of Vortex Rings in Air

The effects of exit-wedge angle on evolution, formation, pinch-off, propagation and diffusive mass entrainment of vortex rings in air were studied using digital particle image velocimetry. Vortex rings were generated by passing a solenoid-valve-controlled air jet through a cylindrical nozzle. Experiments were performed over a wide range of exit-wedge angles (10° ≤ α ≤ 90°) of the cylindrical nozzle, initial Reynolds numbers (450 ≤ Re ≤ 4,580) and length-to-diameter ratios (0.9 ≤ L/D ≤ 11) of the air jet. For sharp edges (α ≤ 10°), a secondary ring may emerge at high Reynolds numbers, which tended to distort the vortex ring if ingested into it. For blunt edges (α ≥ 45°), by contrast, stable vortex rings were produced. The formation phase of a vortex ring was found to be closely related to its evolution pattern. An exit-wedge angle of 45° was found to be optimal for rapid pinch-off and faster propagation and better stability of a vortex ring. Diffusive mass entrainment was found to be between 35% and 40% in the early stages of a vortex ring propagation and it gradually increased throughout the course of vortex ring propagation. Entrainment fraction was found to be sensitive to the L/D ratio of the initial jet and decreases when the L/D ratio is increased.     

Numerical study on film cooling effectiveness from shaped and crescent holes

This paper presents a comparative numerical investigation on film cooling from a row of holes injected at 35° on a flat plate with three film cooling configurations, including cylindrical hole, 15° forward diffused shaped hole, and new crescent hole. All simulations are conducted at blowing ratio of 0.6 and 1.25, length-to-diameter ratio of four and pitch-to-diameter ratio of three. Computational solutions of the steady, Reynolds averaged Navier–Stokes equations are obtained using a finite volume method. Previous successful application of a two-layer turbulence model to cylindrical hole is extended to predict film cooling for the different hole geometries. It has been found that the film cooling effectiveness of cylindrical holes obviously declined along with increasing the blowing ratio. While the forward diffused shaped hole presents a marked improvement, with a higher effectiveness at the lateral area between adjacent holes. By comparison, the crescent hole exhibits the highest film cooling effectiveness among the three configurations both in spanwise and streamwise especially downstream of the intersection of the two holes. Also, the crescent hole can restrain the vortex intensity, and then enhance the film cooling effectiveness.     

Measurement of the temperature field downstream of simulated leading-edge film-cooling holes

Experiments to measure the temperature field downstream of simulated leading-edge-region film-cooling holes were performed in an 11 m/s wind tunnel flow. Heated air was passed to a hollow 140 mm diameter cylinder in which three 10.5 mm diameter, spanwise-inclined, film-cooling holes had been machined. A fine nylon mesh, coated with encapsulated thermochromic liquid crystals, was used to measure temperature contours downstream of the holes by moving the mesh relative to the holes and adjusting the power to the air heater. The measurements indicate the extent of the lateral spreading of the coolant gas and show the influence of hole location and coolant mass flow rate on film trajectory and spreading. Received: 5 February 1998/ Accepted: 22 October 1998     

The effect of turbulence intensity on film cooling of gas turbine blade from trenched shaped holes

This paper reports a computational investigation on the effects of mainstream turbulence intensity on film cooling effectiveness from trenched holes over a symmetrical blade. Computational solutions of the steady, Reynolds-Averaged Navier–Stokes equations are obtained using a finite volume method with k − ε Turbulence model. Whenever possible, computational results are compared with experimental ones from data found in the open literature. Computational results are presented for a row of 25° forward-diffused film hole within transverse slot injected at 35° to AGTB symmetrical blade. Four blowing ratios, M = 0.3, 0.5, 0.9 and 1.3 are studied together with four mainstream turbulence intensities of Tu = 0.5, 2, 4 and 10%. Results indicate that the trenched shaped holes tend to give better film cooling effectiveness than that obtained from discrete shaped holes for all blowing ratios and all turbulence intensities. The trenching of shaped holes has changed the optimum blowing ratio and also the location of re-attachment of separated jet at high blowing ratios. Moreover, it has been found that the effect of mainstream turbulence intensity for trenched shaped holes is similar to that obtained for discrete shaped holes with the exception that the sensitivity of film cooling effectiveness to turbulence intensity has decreased for trenched shaped holes.     

Near-ground tornado-like vortex structure resolved by particle image velocimetry (PIV)

The near-ground flow structure of tornadoes is of utmost interest because it determines how and to what extent civil structures could get damaged in tornado events. We simulated tornado-like vortex flow at the swirl ratios of S = 0.03–0.3 (vane angle θ_v = 15°–60°), using a laboratory tornado simulator and investigated the near-ground-vortex structure by particle imaging velocimetry. Complicated near-ground flow was measured in two orthogonal views: horizontal planes at various elevations (z = 11, 26 and 53 mm above the ground) and the meridian plane. We observed two distinct vortex structures: a single-celled vortex at the lowest swirl ratio (S = 0.03, θ_v = 15°) and multiple suction vortices rotating around the primary vortex (two-celled vortex) at higher swirl ratios (S = 0.1–0.3, θ_v = 30°–60°). We quantified the effects of vortex wandering on the mean flow and found that vortex wandering was important and should be taken into account in the low swirl ratio case. The tangential velocity, as the dominant velocity component, has the peak value about three times that of the maximum radial velocity regardless of the swirl ratio. The maximum velocity variance is about twice at the high swirl ratio (θ_v = 45°) that at the low swirl ratio (θ_v = 15°), which is contributed significantly by the multiple small-scale secondary vortices. Here, the results show that not only the intensified mean flow but greatly enhanced turbulence occurs near the surface in the tornado-like vortex flow. The intensified mean flow and enhanced turbulence at the ground level, correlated with the ground-vortex interaction, may cause dramatic damage of the civil structures in tornadoes. This work provides detailed characterization of the tornado-like vortex structure, which has not been fully revealed in previous field studies and laboratory simulations. It would be helpful in improving the understanding of the interaction between the tornado-like vortex structure and the ground surface, ultimately leading to better predictions of tornado-induced wind loads on civil structures.     

Effect of film cooling on the aerodynamic performance of an airfoil

The effect of film cooling on the aerodynamic performance of turbine blades is becoming increasingly important as the gas turbine operating temperature is being increased in order to increase the performance. The current paper investigates the effect of blowing ratio on the aerodynamic losses of a symmetric airfoil by pressure measurements and Particle Image Velocimetry (PIV). The test model features 4 rows of holes located on the suction side at 5%, 10%, 15% and 50% of the chord length. The Reynolds number based on the airfoil chord is 1.2 × 10⁵. Experiments are performed by varying the location of air injection, the angle of attack, and the mainstream velocity. The coolant air is injected at ambient temperature and the blowing ratio is varied from 0 to 1.91. It is observed that the losses due to film cooling increase with blowing ratio of 0 to 0.48, and the wake is shifted towards the suction side. Conversely, the aerodynamic losses decrease when the blowing ratio is increased further from 0.64 to 1.91. This trend has been observed for all the experimental configurations. The effect of blowing ratio on flow separation is investigated with the time-averaged velocity fields obtained from PIV measurements. It is observed that low blowing ratios, the separation point shifts upstream and at high blowing ratios the ejected coolant energizes the flow and delays separation. The pressure field around the airfoil is reconstructed from the integration of the Poisson equation based on the PIV velocity fields. The experimental results can be used for validation of numerical models for predicting losses due to film cooling.     

The effects of acceleration in jets: kinematics of the near field vortices

Direct and large-eddy simulations (DNS/LES) of accelerating round jets are used to analyze the effects of acceleration on the kinematics of vortex rings in the near field of the jet (x/D < 12). The acceleration is obtained by increasing the nozzle jet velocity with time, in a previously established (steady) jet, and ends once the inlet jet velocity is equal to twice its initial value. Several acceleration rates (α = 0.02–0.6) and Reynolds numbers (Re _D = 500–20000) were simulated. Acceleration maps were used to make a detailed study of the kinematics of vortex rings in accelerating jets. One of the effects of the acceleration is to cause a number of new primary and secondary vortex merging events that are absent from steady jets. As the acceleration rate α increases, both the number of primary merging events between rings and the axial position where these take place decreases. The statistics for the speed of the starting ring that forms at the start of the acceleration phase for each simulation, agree well with the statistics for the “front” speed observed by Zhang and Johari (Phys Fluids 8:2185–2195, 1996). Acceleration maps and flow visualizations show that during the acceleration phase the near field coherent vortices become smaller and are formed at an higher frequency than in the steady jet, and their (mean) shedding frequency increases linearly with the acceleration rate. Finally, it was observed that the acceleration decreases the spreading rate of the jet, in agreement with previous experimental works.