Advanced k-epsilon modeling of heat transfer

This report describes two approaches to low Reynolds-number k-epsilon turbulence modeling which formulate the eddy viscosity on the wall-normal component of turbulence and a length scale. The wall-normal component of turbulence is computed via integration of the energy spectrum based on the local dissipation rate and is bounded by the isotropic condition. The models account for the anisotropy of the dissipation and the reduced mixing length due to the high strain rates present in the near-wall region. The turbulent kinetic energy and its dissipation rate were computed from the k and epsilon transport equations of Durbin. The models were tested for a wide range of turbulent flows and proved to be superior to other k-epsilon models, especially for nonequilibrium anisotropic flows. For the prediction of airfoil heat transfer, the models included a set of empirical correlations for predicting laminar-turbulent transition and laminar heat transfer augmentation due to the presence of freestream turbulence. The predictions of surface heat transfer were generally satisfactory

The Influence of Leading Edge Diameter on Stagnation Region Heat Transfer Augmentation Including Effects of Turbulence Level, Scale, and Reynolds Number

Stagnation region heat transfer measurements have been acquired on two large cylindrical leading edge test surfaces having a four to one range in leading edge diameter. Heat transfer measurements have been acquired for six turbulence conditions including three grid conditions, two aero-combustor conditions, and a low turbulence condition. The data have been run over an eight to one range in Reynolds numbers for each test surface with Reynolds numbers ranging from 62,500 to 500,000 for the large leading edge and 15,625 to 125,000 for the smaller leading edge. The data show augmentation levels of up to 110% in the stagnation region for the large leading edge. However, the heat transfer results for the large cylindrical leading edge do not appear to infer a significant level of turbulence intensification in the stagnation region. The smaller cylindrical leading edge shows more consistency with earlier stagnation region heat transfer results correlated on the TRL parameter. These results indicate that the intensification of approaching turbulence is more prevalent with the more rapid straining of the smaller leading edge. The downstream regions of both test surfaces continue to accelerate the flow but at a much lower rate than the leading edge. Bypass transition occurs in these regions providing a useful set of data to ground the prediction of transition onset and length over a wide range of Reynolds numbers and turbulence intensity and scales. Introduction Cooling the stagnation region of a turbine airfoil has always been an important consideration in hot section design. Depending on the performance and operation considerations of the engine as well as the fuel and air quality, the leading edge of turbine airfoils can either be internally cooled or rely on showerhead type film cooling arrays. New land based gas turbines are becoming larger producing higher chord and leading edge Reynolds numbers. At high Reynolds numbers stagnation heat transfer levels on a vane are expected to be much lower than the turbulent regions of flow found over the suction surface and much of the pressure surface. However, current land based machines have leading edge Reynolds numbers exceeding 300,000. Depending on the combustion system, inlet turbulence levels could be 20% or higher. At the same time, industry trends show larger leading edge diameters in first vanes. Currently, designers simply do not have a reliable data base at the most aggressive stagnation region conditions expected for land based gas turbines. The present study has been designed to extend the parameter range for stagnation region heat transfer to encompass the range expected for modern engines. This research will also investigate the effects of larger stagnation regions on heat transfer augmentation due to the response of turbulence in the leading edge strain field. The experimental data also include heat transfer distributions downstream from the stagnation region, which show transitional and fully turbulent flow behavior

Complementary Aerodynamic Performance Datasets for Variable Speed Power Turbine Blade Section from Two Independent Transonic Turbine Cascades

Two independent experimental studies were conducted in linear cascades on a scaled, two-dimensional mid-span section of a representative Variable Speed Power Turbine (VSPT) blade. The purpose of these studies was to assess the aerodynamic performance of the VSPT blade over large Reynolds number and incidence angle ranges. The influence of inlet turbulence intensity was also investigated. The tests were carried out in the NASA Glenn Research Center Transonic Turbine Blade Cascade Facility and at the University of North Dakota (UND) High Speed Compressible Flow Wind Tunnel Facility. A large database was developed by acquiring total pressure and exit angle surveys and blade loading data for ten incidence angles ranging from +15.8deg to 51.0deg. Data were acquired over six flow conditions with exit isentropic Reynolds number ranging from 0.05106 to 2.12106 and at exit Mach numbers of 0.72 (design) and 0.35. Flow conditions were examined within the respective facility constraints. The survey data were integrated to determine average exit total-pressure and flow angle. UND also acquired blade surface heat transfer data at two flow conditions across the entire incidence angle range aimed at quantifying transitional flow behavior on the blade. Comparisons of the aerodynamic datasets were made for three "match point" conditions. The blade loading data at the match point conditions show good agreement between the facilities. This report shows comparisons of other data and highlights the unique contributions of the two facilities. The datasets are being used to advance understanding of the aerodynamic challenges associated with maintaining efficient power turbine operation over a wide shaft-speed range

Complementary Aerodynamic Performance Datasets for Variable Speed Power Turbine Blade Section from Two Independent Transonic Turbine Cascades

Two independent experimental studies were conducted in linear cascades on a scaled, two-dimensional mid-span section of a representative Variable Speed Power Turbine (VSPT) blade. The purpose of these studies was to assess the aerodynamic performance of the VSPT blade over large Reynolds number and incidence angle ranges. The influence of inlet turbulence intensity was also investigated. The tests were carried out in the NASA Glenn Research Center Transonic Turbine Blade Cascade Facility and at the University of North Dakota (UND) High Speed Compressible Flow Wind Tunnel Facility. A large database was developed by acquiring total pressure and exit angle surveys and blade loading data for ten incidence angles ranging from +15.8deg to 51.0deg. Data were acquired over six flow conditions with exit isentropic Reynolds number ranging from 0.05106 to 2.12106 and at exit Mach numbers of 0.72 (design) and 0.35. Flow conditions were examined within the respective facility constraints. The survey data were integrated to determine average exit total-pressure and flow angle. UND also acquired blade surface heat transfer data at two flow conditions across the entire incidence angle range aimed at quantifying transitional flow behavior on the blade. Comparisons of the aerodynamic datasets were made for three "match point" conditions. The blade loading data at the match point conditions show good agreement between the facilities. This report shows comparisons of other data and highlights the unique contributions of the two facilities. The datasets are being used to advance understanding of the aerodynamic challenges associated with maintaining efficient power turbine operation over a wide shaft-speed range

CHARACTERIZATION OF CATALYTIC COMBUSTOR TURBULENCE AND ITS INFLUENCE ON VANE AND ENDWALL HEAT TRANSFER AND ENDWALL FILM COOLING

Endwall heat transfer distributions taken in a large-scale low speed linear cascade facility are documented for mock catalytic and dry low NOx (DLN) combustion systems. Inlet turbulence levels range from about 1.0 percent for the mock Catalytic combustor condition to 14 percent for the mock dry low NOx combustor system. Stanton number contours are presented at both turbulence conditions for Reynolds numbers based on true chord length and exit conditions ranging from 500,000 to 2,000,000. Catalytic combustor endwall heat transfer shows the influence of the complex three-dimensional flow field, while the effects of individual vortex systems are less evident for the mock dry low NOx cases. Turbulence scales have been documented for both cases. Inlet boundary layers are relatively thin for the mock catalytic combustor case while inlet flow approximates a channel flow with high turbulence for the mock DLN combustor case. Inlet boundary layer parameters are presented across the inlet passage for the three Reynolds numbers and both the mock catalytic and DLN combustor inlet cases. Both midspan and 95 percent span pressure contours are included. This research provides a well-documented database taken across a range of Reynolds numbers and turbulence conditions for assessment of endwall heat transfer predictive capabilities

Predictions for the Effects of Free Stream Turbulence on Turbine Blade Heat Transfer

An approach to predicting the effects of free stream turbulence on turbine vane and blade heat transfer is described. Four models for predicting the effects of free stream turbulence were in incorporated into a Navier-Stokes CFD analysis. Predictions were compared with experimental data in order to identify an appropriate model for use across a wide range of flow conditions. The analyses were compared with data from five vane geometries and from four rotor geometries. Each of these nine geometries had data for different Reynolds numbers. Comparisons were made for twenty four cases. Steady state calculations were done because all experimental data were obtained in steady state tests. High turbulence levels often result in suction surface transition upstream of the throat, while at low to moderate Reynolds numbers the pressure surface remains laminar. A two-dimensional analysis was used because the flow is predominately two-dimensional in the regions where free stream turbulence significantly augments surface heat transfer. Because the evaluation of models for predicting turbulence effects can be affected by other factors, the paper discusses modeling for transition, relaminarization, and near wall damping. Quantitative comparisons are given between the predictions and data