Numerical Simulation of Flow and Heat Transfer Past a Turbine Blade With a Squealer-Tip

Numerical calculations are performed to simulate the tip leakage flow and heat transfer on the squealer (recessed) tip of GE-E3 turbine rotor blade. A squealer tip with a 3.77% recess of the blade span is considered in this study, and the results are compared with the predictions for a flat-tip blade. The calculations have been performed for an isothermal blade with an overall pressure ratio of 1.32, an inlet turbulence intensity of 6.1%, and for three different tip gap clearances of 1%, 1.5% and 2.5% of the blade span. These conditions correspond to the experiments reported by Azad et al. [1]. The calculations have been performed for three different turbulence models (the standard high Re k-ε model, the RNG k-ε and the Reynolds Stress Model) in order to assess the capability of the models in correctly predicting the blade heat transfer. The predictions show good agreement with the experimental data, with the Reynolds stress model calculations clearly providing the best results. Substantial reductions in the tip heat transfer and leakage flow is obtained with the squealer tip configuration. With the squealer tip, the heat transfer coefficients on the shroud and on the suction surface of the blade are also considerably reduced.

Unsteady Rotor Heat Transfer in a Transonic Turbine Stage

This experimental investigation reports the convective heat transfer coefficient around the rotor of a transonic turbine stage. Both time-resolved and time-averaged aspects are addressed. The measurements are performed around the rotor blade at 15%, 50% and 85% span as well as on the rotor tip and the hub platform. Four operating conditions are tested covering two Reynolds numbers and three pressure ratios. The tests are performed in the compression tube turbine test rig CT3 of the von Karman Institute, allowing a correct simulation of the operating conditions encountered in modern aero-engines. The time-averaged Nusselt number distribution shows the strong dependence on both blade Mach number distribution and Reynolds number. The time-resolved heat transfer rate is mostly dictated by the vane trailing edge shock impingement on the rotor boundary layer. The shock passage corresponds to a sudden heat transfer increase. The effects are more pronounced in the leading edge region. The increase of the stage pressure ratio causes a stronger vane trailing edge shock and thus larger heat transfer fluctuations. The influence of the Reynolds number is hardly visible.

Prediction and Measurement of the Flow and Heat Transfer Along the Endwall and Within an Inlet Vane Passage

Numerical simulations and laboratory measurements are performed to study the flow field and heat transfer in a linear cascade of turbine vanes. The vanes are scaled-up versions of a turbine engine inlet vane but simplified in that they are untwisted and follow the mid-span airfoil shape of the engine vane. The hub endwall is axially profiled while the tip endwall is flat. The hub endwall comprises the focus of the heat transfer investigation. Configurations are considered with and without air injection through three discrete angled (25 degrees to the main flow direction) slots upstream of each vane. The freestream turbulence intensity at the vane cascade inlet plane is 11 (± 2) percent, as measured by a single hot-wire placed perpendicular to the mean flow. The transient thermochromic liquid crystal technique is used to measure the convective heat transfer coefficient at the hub endwall for the baseline case (without air injection through the slots), and the heat transfer coefficient and cooling effectiveness at the same endwall for the cases with air injection at two blowing ratios. Miniature Kiel probes are used to measure the distribution of total pressure upstream of, within, and downstream of one vane passage. Numerical simulations are performed of the incompressible flow using unstructured grids. Hybrid meshes comprised of prisms near solid surfaces and tetrahedra away from the wall are used to resolve the solutions, with mesh refinement up to approximately 2 million cells. For all calculations, the first grid point is within one viscous unit of solid surfaces. A Boussinesq approximation is invoked to model the turbulent Reynolds stresses, with the turbulent eddy viscosity obtained from the Spalart-Allmaras one-equation model. The turbulent heat flux is modeled via Reynolds analogy and a constant turbulent Prandtl number of 0.9. The simulations show that endwall axial profiling results in flow reversal upstream of the vane, an effect that lowers the Stanton number for the baseline flow near the vane leading edge compared to our previous work in a flat-endwall geometry. Predictions of the total pressure loss coefficient show that the peak levels are higher than those measured.

The Measurement of Full-Surface Internal Heat Transfer Coefficients for Turbine Airfoils Using a Non-Destructive Thermal Inertia Technique

A new method has been developed and demonstrated for the non-destructive, quantitative assessment of internal heat transfer coefficient distributions of cooled metallic turbine airfoils. The technique employs the acquisition of full-surface external surface temperature data in response to a thermal transient induced by internal heating/cooling, in conjunction with knowledge of the part wall thickness and geometry, material properties, and internal fluid temperatures. An imaging Infrared camera system is used to record the complete time history of the external surface temperature response during a transient initiated by the introduction of a convecting fluid through the cooling circuit of the part. The transient data obtained is combined with the cooling fluid network model to provide the boundary conditions for a finite element model representing the complete part geometry. A simple 1D lumped thermal capacitance model for each local wall position is used to provide a first estimate of the internal surface heat transfer coefficient distribution. A 3D inverse transient conduction model of the part is then executed with updated internal heat transfer coefficients until convergence is reached with the experimentally measured external wall temperatures as a function of time. This new technique makes possible the accurate quantification of full-surface internal heat transfer coefficient distributions for prototype and production metallic airfoils in a totally non-destructive and non-intrusive manner. The technique is equally applicable to other material types and other cooled/heated components.

The Effect of Freestream Turbulence on Film Cooling Adiabatic Effectiveness

The film-cooling performance of a flat plate in the presence of low and high freestream turbulence is investigated using liquid crystal thermography. High-resolution distributions of the adiabatic effectiveness are determined over the film-cooled surface of the flat plate using the hue method and image processing. Three blowing rates are investigated for a model with three straight holes spaced three diameters apart, with density ratio near unity. High freestream turbulence is shown to increase the area-averaged effectiveness at high blowing rates, but decrease it at low blowing rates. At low blowing ratio, freestream turbulence clearly reduces the coverage area of the cooling air due to increased mixing with the main flow. However, at high blowing ratio, when much of the jet has lifted off in the low turbulence case, high freestream turbulence turns its increased mixing into an asset, entraining some of the coolant that penetrates into the main flow and mixing it with the air near the surface.

Predicting Transition Without Empiricism or DNS

A numerical procedure for predicting the receptivity of laminar boundary layers to freestream turbulence consisting of vortex arrays with arbitrary orientation has been developed. Results show that the boundary layer is most receptivity to those vortices which have their axes approximately in the streamwise direction and vortex wavelengths of approximately 1.2 δ. The computed near wall gains for isotropic turbulence are similar in magnitude to previously published experimental values used to predict transition. The new procedure is therefore capable of predicting the development of the fluctuations in the laminar boundary layer from values of the freestream turbulence intensity and length scale and hence determining the start of transition without resorting to any empirical correlation.

Computation of Turbulent Heat Transfer on the Walls of a 180 Degree Turn Channel With a Low Reynolds Number Reynolds Stress Model

The Low Reynolds number version of the Stress-ω model and the two equation k-ω model of Wilcox were used for the calculation of turbulent heat transfer in a 180 degree turn simulating an internal coolant passage. The Stress-ω model was chosen for its robustness. The turbulent thermal fluxes were calculated by modifying and using the Generalized Gradient Diffusion Hypothesis. The results showed that using this Reynolds Stress model allowed better prediction of heat transfer compared to the k-ω two equation model. This improvement however required a finer grid and commensurately more CPU time.

Correlation of Film Cooling Effectiveness From Thermographic Measurements at Engine Like Conditions

Adiabatic film cooling effectiveness on a flat plate surface downstream of a row of cylindrical holes is investigated. Highly resolved two dimensional surface data were measured by means of infrared thermography and carefully corrected for local conduction and radiation effects [1]. These locally acquired data are laterally averaged to give the streamwise distributions of the effectiveness. An independent variation of the flow parameters blowing rate, density ratio, and turbulence intensity as well as the geometrical parameters streamwise ejection angle and hole spacing is examined. The influences of these parameters on the laterally effectiveness is discussed and interpreted with the help of surface distributions of effectiveness and heat transfer coefficients presented in earlier publications [1, 2]. Besides the known jet in cross-flow behavior of coolant ejected from discrete holes, these data demonstrate the effect of adjacent jet interaction and its impact on jet lift-off and adiabatic effectiveness. In utilizing this large matrix of measurements the effect of single parameters and their interactions are correlated. The important scaling parameters of the effectiveness are shaped out during the correlation process and are discussed. The resulting new correlation is designed to yield the quantitatively correct effectiveness as a result of the interplay of the jet in crossflow behavior and the adjacent jet interaction. It is built modularly to allow for future inclusion of additional parameters. The new correlation is valid without any exception within the full region of interest, reaching from the point of the ejection to far downstream, for all combinations of flow and geometry parameters.

Measurements of the Effects of Freestream Turbulence on Separation-Bubble Transition

In this paper, measurements are presented on the effects of freestream turbulence on laminar-to-turbulent transition in separation bubbles, and correlations are proposed for the locations of transition and reattachment on the basis of this data. The boundary layer development is measured on a smooth, flat plate upon which streamwise pressure gradients are imposed by a flexible, contoured wall opposite to the test plate. Two variations in the streamwise pressure distribution are investigated, and two Reynolds numbers are considered for each pressure-gradient setting. For each combination of pressure distribution and Reynolds number, the freestream turbulence intensity and length scale are adjusted systematically by varying the open-area-ratio and cell size of the grid installed at the test-section inlet. Measured quantities consist of velocity obtained with a single-hot wire probe and surface pressures measured through pressure taps.

Leading-Edge Film-Cooling Physics: Part II — Heat Transfer Coefficient

A comprehensive study of film cooling on a turbine airfoil leading edge was performed with a documented, well-tested computational methodology. In this paper, numerically predicted heat transfer coefficients on the film-cooled leading edge are compared with experimental data from the open literature. The results are presented as the ratio of heat transfer coefficient with film cooling to that without film cooling, and the physics behind the surface results are discussed. The leading edge model was a half-cylinder in shape with a bluff afterbody to match the validation experiment, and other geometric parameters matched those of Part I of this study. Coolant at a density equal to that of the mainstream flow was injected through three rows of cylindrical film-cooling holes. One row of holes was centered on the stagnation line of the cylinder, and the other two rows were located ±3.5 hole diameters off stagnation. The downstream rows were staggered such that they were centered laterally between holes in the stagnation row. The holes were inclined at 20° with the surface, and made a 90° angle with the streamwise direction (radial injection). Four average blowing ratios were simulated in the range of 0.75 to 1.9, corresponding to the same momentum flux ratios as in Part I of this work. The multi-block, unstructured numerical grid was characterized by high quality and density, especially in the near wall region, in order to minimize error in predictions of the heat transfer. A fully-implicit scheme was used to solve the steady Reynolds-averaged Navier-Stokes equations, and a realizable k-ε model provided turbulence closure. A two-layer near-wall treatment allowed the resolution of the viscous sublayer for maximum accuracy in the prediction of the wall heat transfer coefficient. The numerical predictions exhibited generally good agreement with experimental data. The heat transfer coefficient was observed to increase sharply aft of the holes in the downstream rows. When coupled with the adiabatic effectiveness results of the first paper in this series, it is evident that a systematic computational methodology may be effectively applied to investigate and understand the complicated leading edge film-cooling problem.