James D. Heidmann

Conjugate Heat Transfer Effects on a Realistic Film-Cooled Turbine Vane

A conjugate heat transfer solver has been developed and applied to a realistic film-cooled turbine vane for a variety of blade materials. The solver used for the fluid convection part of the problem is the Glenn-HT general multiblock heat transfer code. The solid conduction module is based on the Boundary Element Method (BEM), and is coupled directly to the flow solver. A chief advantage of the BEM method is that no volumetric grid is required inside the solid – only the surface grid is needed. Since a surface grid is readily available from the fluid side of the problem, no additional gridding is required. This eliminates one of the most time consuming elements of the computation for complex geometries. Two conjugate solution examples are presented - a high thermal conductivity Inconel nickel-based alloy vane case and a low thermal conductivity silicon nitride ceramic vane case. The solutions from the conjugate analyses are compared with an adiabatic wall convection solution. It is found that the conjugate heat transfer cases generally have a lower outer wall temperature due to thermal conduction from the outer wall to the plenum. However, some locations of increased temperature are seen in the higher thermal conductivity Inconel vane case. This is a result of the fact that film cooling is a two-temperature problem, which causes the direction of heat flux at the wall to change over the outer surface. Three-dimensional heat conduction in the solid allows for conduction heat transfer along the vane wall in addition to conduction from outer to inner wall. These effects indicate that the conjugate heat transfer in a complicated geometry such as a film-cooled vane is not governed by simple one-dimensional conduction from the vane surface to the plenum surface, especially when the effects of coolant injection are included.

A three-dimensional coupled internal/external simulation of a film-cooled turbine vane

A three-dimensional Navier-Stokes simulation has been performed for a realistic film-cooled turbine vane using the LeRC-HT code. The simulation includes the flow regions inside the coolant plena and film cooling holes in addition to the external flow. The vane is the subject of an upcoming NASA Lewis Research Center experiment and has both circular cross-sectional and shaped film cooling holes. This complex geometry is modeled using a multiblock grid, which accurately discretizes the actual vane geometry including shaped holes. The simulation matches operating conditions for the planned experiment and assumes periodicity in the spanwise direction on the scale of one pitch of the film cooling hole pattern. Two computations were performed for different isothermal wall temperatures, allowing independent determination of heat transfer coefficients and film effectiveness values. The results indicate separate localized regions of high heat flux in the showerhead region due to low film effectiveness and high heat transfer coefficient values, while the shaped holes provide a reduction in heat flux through both parameters. Hole exit data indicate rather simple skewed profiles for the round holes, but complex profiles for the shaped holes with mass fluxes skewed strongly toward their leading edges.

BEM/FVM conjugate heat transfer analysis of a three‐dimensional film cooled turbine blade

We report on the progress in the development and application of a coupled boundary element/finite volume method temperature‐forward/flux‐back algorithm developed to solve conjugate heat transfer arising in 3D film‐cooled turbine blades. We adopt a loosely coupled strategy where each set of field equations is solved to provide boundary conditions for the other. Iteration is carried out until interfacial continuity of temperature and heat flux is enforced. The NASA‐Glenn explicit finite volume Navier‐Stokes code Glenn‐HT is coupled to a 3D BEM steady‐state heat conduction solver. Results from a CHT simulation of a 3D film‐cooled blade section are compared with those obtained from the standard two temperature model, revealing that a significant difference in the level and distribution of metal temperatures is found between the two. Finally, current developments of an iterative strategy accommodating large numbers of unknowns by a domain decomposition approach is presented. An iterative scheme is developed along with a physically‐based initial guess and a coarse grid solution to provide a good starting point for the iteration. Results from a 3D simulation show the process that converges efficiently and offers substantial computational and storage savings.

An Experimental Study of the Effect of Wake Passing on Turbine Blade Film Cooling

The effect of upstream blade row wake passing on the showerhead film cooling performance of a downstream turbine blade has been investigated through a combination of experimental and computational studies. The experiments were performed in a steady-flow annular turbine cascade facility equipped with an upstream rotating row of cylindrical rods to produce a periodic wake field similar to that found in an actual turbine. Spanwise, chordwise, and temporal resolution of the blade surface temperature were achieved through the use of an array of nickel thin-film surface gauges covering one unit cell of showerhead film hole pattern. Film effectiveness and Nusselt number values were determined for a test matrix of various injectants, injectant blowing ratios, and wake Strouhal numbers. Results indicated a demonstratable reduction in film effectiveness with increasing Strouhal number, as well as the expected increase in film effectiveness with blowing ratio. An equation was developed to correlate the span-average film effectiveness data. The primary effect of wake unsteadiness was found to be correlated well by a chordwise-constant decrement of 0.094-St. Measurable spanwise film effectiveness variations were found near the showerhead region, but meaningful unsteady variations and downstream spanwise variations were not found. Nusselt numbers were less sensitive to wake and injection changes. Computations were performed using a three-dimensional turbulent Navier-Stokes code which was modified to model wake passing and film cooling. Unsteady computations were found to agree well with steady computations provided the proper time-average blowing ratio and pressure/suction surface flow split are matched. The remaining differences were isolated to be due to the enhanced mixing in the unsteady solution caused by the wake sweeping normally on the pressure surface. Steady computations were found to be in excellent agreement with experimental Nusselt numbers, but to overpredict experimental film effectiveness values. This is likely due to the inability to match actual hole exit velocity profiles and the absence of a credible turbulence model for film cooling.

Film Cooling Analysis Using DES Turbulence Model

The complex dynamic nature of the spanwise vortices in film cooling of turbine blades makes it necessary to accurately model the flow field temporally and spatially using detailed simulation techniques like direct numerical simulation or large eddy simulation of turbulence. Although, the later requires less computational effort and thus can simulate flows at higher Reynolds number than direct simulation, both these methods remain very expensive. As a viable alternative, this paper presents a Spalart-Allamaras based detached eddy simulation (DES) that is applied to a film cooled flat plate for the first time. The numerical model uses an unstructured grid system to resolve the dynamic flow structures on both sides of the plate as well as inside the hole itself. Detailed computation of a single row of 35 degree round holes on a flat plate has been obtained for blowing ratio of 1.0, and a density ratio of 2.0. The DES solution is also benchmarked with Reynolds averaged Navier-Stokes formulation for the same blade-hole configuration. The comparison shows that the DES simulation, which makes no assumption of isotropy downstream of the hole, greatly enhances the realistic description of the dynamic mixing processes.Copyright

A Numerical Study of Anti-Vortex Film Cooling Designs at High Blowing Ratio

A concept for mitigating the adverse effects of jet vorticity and lift-off at high blowing ratios for turbine film cooling flows has been developed and studied at NASA Glenn Research Center. This “anti-vortex” film cooling concept proposes the addition of two branched holes from each primary hole in order to produce a vorticity counter to the detrimental kidney vortices from the main jet. These vortices typically entrain hot freestream gas and are associated with jet separation from the turbine blade surface. The anti-vortex design is unique in that it requires only easily machinable round holes, unlike shaped film cooling holes and other advanced concepts. The anti-vortex film cooling hole concept has been modeled computationally for a single row of 30 degree angled holes on a flat surface using the 3D Navier-Stokes solver Glenn-HT. A modification of the anti-vortex concept whereby the branched holes exit adjacent to the main hole has been studied computationally for blowing ratios of 1.0 and 2.0 and at density ratios of 1.0 and 2.0. This modified concept was selected because it has shown the most promise in recent experimental studies. The computational results show that the modified design improves the film cooling effectiveness relative to the round hole baseline and previous anti-vortex cases, in confirmation of the experimental studies.

Detached Eddy Simulation Of Turbine Blade Cooling

Implementation of direct numerical simulation or large eddy simulation for turbomachinery applications is very expensive with present day computational power. Present work explores the possibility of detached eddy simulation (DES) for the film cooled flat plate. A geometry of single row of 35 degree round holes on a flat plate is used for the blowing ratio of 1.0 and density ratio of 0.5. Use of symmetry boundary condition is avoided to capture threedimensional, unsteady, turbulent nature of the flow. Present simulation uses unstructured grid and parallel algorithm to perform DES. Implicit time -stepping is used for the CFL number upto one million. Presence of asymmetry in the DES solution is documented by plotting the temperature and velocity profiles at various streamwise locations. Numerical calculation of effectiveness is validated with reported experimental results.

Improved Film Cooling Effectiveness by Placing a Vortex Generator Downstream of Each Hole

Calculations are presented demonstrating the effect of placing a delta vortex generator downstream of a film cooling hole. The effects of blowing ratio, density ratio, and spanwise pitch are included in the study. Flow over a flat plate with film cooling holes oriented at a 30 degree angle was investigated. The Reynolds numbers based on the freestream velocity and the hole diameter was 11,300. The simulation was performed using the Glenn-HT code, a full three-dimensional Navier-Stokes solver using the Wilcox k-ω turbulence model. A structured multi-block grid was used with approximately one million cells, and average y+ values on the order of unity. Local and span averaged effectiveness are presented. Analysis and visualization of the flow are presented as well as a discussion on the mechanisms which contribute to the dramatic improvement in effectiveness. The results demonstrate that the delta vortex generator was able to annihilate the up-wash vortex pair produced by the film hole and produce a down-wash pair downstream.

First Hybrid Turbulence Modeling for Turbine Blade Cooling

Introduction G AS turbines require proper cooling mechanisms to protect the airfoils from thermal stresses generated by exposure to hot combustion gases. The problem becomes aggravated by the growing trend to use higher turbine inlet temperatures to generate more power. Thus, film cooling is used as a cooling mechanism, and it works in the form of row of holes located in the spanwise direction, through which cold jets are issued into the hot crossflow. The penetration of cold jets into the main flow creates a complex flowfield. Systematic investigation of such flowfield started in late 1950s. Figure 1 shows the schematic of a single round jet injected in the crossflow at an angle α = 35 deg. The figure also describes the boundary conditions applied at different faces. Even though use of symmetry boundary condition at the hole centerline would reduce the computational time by half, its use is avoided as it prevents the possibility of capturing the unsteady asymmetric vortical flow patterns. This geometry is well accepted by the gas-turbine community and has been extensively studied1 for cooling performance for a wide range of blowing ratios, M = ρ j Vj/ρfsVfs, where ρ and V are density and normal velocity, respectively, for jet j and freestream fs. Goldstein2 correlated film cooling effectiveness η = (Tfs − T )/ (Tfs − Tj ) with the parameter x/Mb, where x is the downstream distance; M is the blowing ratio; b is the slot width; and Tfs, T , and Tj are the temperatures of crossflow, blade, and jet, respectively. Sinha et al.1 carried out experimental work to study the relationship between the fluid-thermal parameters of jet and film cooling effectiveness using a row of inclined holes. The mixing of a jet in a cross stream is a fully three-dimensional phenomenon.3 Amer et al.4 pointed out that the flow predictions are greatly affected by the selection of the turbulence model. Roy5 documented the cooling performance of 12 different arrangements of holes with a combination of blowing ratio M , distance between the holes L , and jet angle α using a upwind-biased finite volume code and standard k–ω turbulence closure model. Garg and Rigby6 resolved the plenum and hole pipes for a three-row showerhead film cooling arrangement with Wilcox’s k–ω turbulence model. Heidmann et al.7 used Reynolds-averaged Navier–Stokes (RANS) to compute the heat transfer for a realistic turbine vane with 12 rows of film cooling holes with shaped holes and plena resolved. Though these studies provide good details of the flow, the anisotropic dynamic nature of the spanwise vortices that affect the film cooling process are more complex than that can be captured by the mixing models used in aforementioned papers. Acharya8 compared the re-

Unsteady Analysis of Blade and Tip Heat Transfer as Influenced by the Upstream Momentum and Thermal Wakes

The effect of the upstream wake on the blade heat transfer has been numerically examined. The geometry and the flow conditions of the first stage turbine blade of GE s E3 engine with a tip clearance equal to 2 percent of the span was utilized. Based on numerical calculations of the vane, a set of wake boundary conditions were approximated, which were subsequently imposed upon the downstream blade. This set consisted of the momentum and thermal wakes as well as the variation in modeled turbulence quantities of turbulence intensity and the length scale. Using a one-blade periodic domain, the distributions of unsteady heat transfer rate on the turbine blade and its tip, as affected by the wake, were determined. Such heat transfer coefficient distribution was computed using the wall heat flux and the adiabatic wall temperature to desensitize the heat transfer coefficient to the wall temperature. For the determination of the wall heat flux and the adiabatic wall temperatures, two sets of computations were required. The results were used in a phase-locked manner to compute the unsteady or steady heat transfer coefficients. It has been found that the unsteady wake has some effect on the distribution of the time averaged heat transfer coefficient on the blade and that this distribution is different from the distribution that is obtainable from a steady computation. This difference was found to be as large as 20 percent of the average heat transfer on the blade surface. On the tip surface, this difference is comparatively smaller and can be as large as four percent of the average.