Luca Andrei

Numerical Benchmark of Nonconventional RANS Turbulence Models for Film and Effusion Cooling

Over the course of the years, several turbulence models specifically developed to improve the predicting capabilities of conventional two-equations Reynolds-averaged Navier–Stokes (RANS) models have been proposed. They have, however, been mainly tested against experiments only comparing with standard isotropic models, in single hole configuration and for very low blowing ratio. A systematic benchmark of the various nonconventional models exploring a wider range of application is hence missing. This paper performs a comparison of three recently proposed models over three different test cases of increasing computational complexity. The chosen test matrix covers a wide range of blowing ratios (0.5–3.0) including both single row and multi-row cases for which experimental data of reference are available. In particular the well-known test by Sinha et al. (1991, “Film-Cooling Effectiveness Downstream of a Single Row of Holes with Variable Density Ratio,” J. Turbomach., 113, pp. 442–449) at BR = 0.5 is used in conjunction with two in-house carried out experiments: a single row film-cooling test at BR = 1.5 and a 15 rows test plate designed to study the interaction between slot and effusion cooling at BR = 3.0. The first two considered models are based on a tensorial definition of the eddy viscosity in which the stream-span position is augmented to overcome the main drawback connected with standard isotropic turbulence models that is the lower lateral spreading of the jet downwards the injection. An anisotropic factor to multiply the off diagonal position is indeed calculated from an algebraic expression of the turbulent Reynolds number developed by Bergeles et al. (1978, “The Turbulent Jet in a Cross Stream at Low Injection Rates: A Three-Dimensional Numerical Treatment,” Numer. Heat Transfer, 1, pp. 217–242) from DNS statistics over a flat plate. This correction could be potentially implemented in the framework of any eddy viscosity model. It was chosen to compare the predictions of such modification applied to two among the most common two-equation turbulence models for film-cooling tests, namely the two-layer (TL) model and the k–ω shear stress transport (SST), firstly proposed and tested in the past respectively by Azzi and Lakeal (2002, “Perspectives in Modeling Film Cooling of Turbine Blades by Transcending Conventional Two-Equation Turbulence Models,” J. Turbomach., 124, pp. 472–484) and Cottin et al. (2011, “Modeling of the Heat Flux For Multi-Hole Cooling Applications,” Proceedings of the ASME Turbo Expo, Paper No. GT2011-46330). The third model, proposed by Holloway et al. (2005, “Computational Study of Jet-in-Crossflow and Film Cooling Using a New Unsteady-Based Turbulence Model,” Proceedings of the ASME Turbo Expo, Paper No. GT2005-68155), involves the unsteady solution of the flow and thermal field to include the short-time response of the stress tensor to rapid strain rates. This model takes advantage of the solution of an additional transport equation for the local effective total stress to trace the strain rate history. The results are presented in terms of adiabatic effectiveness distribution over the plate as well as spanwise averaged profiles.

Performance Improvement of a Heavy Duty GT: Adiabatic Effectiveness Measurements on First Stage Vanes in Representative Engine Conditions

Nowadays total inlet temperature of gas turbine is far above the permissible metal temperature; as a consequence, advanced cooling techniques must be applied to protect from thermal stress and to reduce the risk of creep failure, oxidation and corrosion of components located in the high pressure stages, such as first vane. Film cooling has been widely used to control temperature of high temperature and high pressure vanes. In a film cooled vane the air taken from last compressor stages is ejected through discrete holes to provide a cold layer between hot mainstream and turbine components. A comprehensive understanding of phenomena concerning the complex interaction of hot gases with coolant flows in a vane passage plays a major role in the definition of a well performing film cooling scheme.The aim of this study is the measurement of adiabatic effectiveness on the first stage vane of a heavy duty GT by means of coolant concentration technique based on Pressure Sensitive Paint (PSP). The investigation of coolant distribution on airfoils and platforms was done in order to make feasible possible optimizations and to validate numerical design tools. The experimental analysis was performed on a static test article replicating an annular sector made up of two cooled airfoils and three passages. An actual first stage vane (scale 1:1) with complete internal cooling scheme has been tested at different coolant conditions and imposing two values of density ratio (DR = 1.0;1.5). Film protection was generated by a showerhead on the leading edge and by cylindrical holes on pressure and suction side and on the platforms; finally a cutback with elongated pedestals was employed for the protection of the pressure side trailing edge. Results, reported in terms of detailed 2D maps of film cooling effectiveness and averaged trends, point out the effect of coolant-to-mainstream mass ratio and density ratio. Beyond the results obtained in this specific vane geometry, the use of PSP was proven to be a promising technique for direct measurements on real geometries: as a matter of fact, the opportunity to get detailed results of pressure and adiabatic effectiveness distributions is of outstanding importance for the design and optimization of vanes and blades cooling systems.Copyright

Numerical Analysis of Effusion Plates for Combustor Liners Cooling With Varying Density Ratio

Effusion cooling technology has been assessed in past years as one of the most efficient methods to maintain allowable working temperature of combustor liners. Despite many efforts reported in literature to characterize the cooling performances of those devices, detailed analysis of the mixing process between coolant and hot gas are difficult to perform especially in case superposition and density ratio effects become important. Furthermore, recent investigations on the acoustic properties of these perforations pointed out the challenge to maintain optimal cooling performance also with orthogonal holes which showed higher sound absorption.This paper performs a CFD analysis of the flow and thermal field associated with adiabatic wall conditions to compute the cooling effectiveness. The geometry consists of an effusion cooling plate drilled with 18 holes and fed separately with a cold and hot gas flow. Two types of perforations equivalent in porosity and pitches are investigated to assess the influence of the drilling angle between 30 and 90 deg. The reference conditions considered in this work comprehend an effective blowing ratio ranging between 1 and 3 at isothermal conditions (reaching a maximum hole Reynolds number of 10000) and high inlet turbulence intensity (17%). This set of conditions was exploited to perform a validation of the numerical procedure against detailed experimental data presented in another paper. Inlet turbulence effects highlighted by measurements for the slanted perforation were also investigated simulating a low turbulence condition corresponding to 1.6% of intensity. Furthermore the nominal DR = 1.0 was increased up to 1.7 to expand the available data set towards typical working conditions for aero-engines.Steady state RANS calculations were performed with the commercial code ANSYS® CFX, modeling turbulence by means of the k — ω SST. In order to include anisotropic diffusion effects due to turbulence damping in the near wall region, the turbulence model is corrected considering a tensorial definition of the eddy viscosity with an algebraic correction to dope its stream-span components. Computational grids were finely clustered close to the main plate and inside the holes to obtain y+ < 1, to maximize solver accuracy according to previous similar analysis.Copyright

Investigation on the Effect of a Realistic Flow Field on the Adiabatic Effectiveness of an Effusion-Cooled Combustor

Effusion cooling represents the state of the art of liner cooling technology for modern combustors. This technique consists of an array of closely spaced discrete film cooling holes and contributes to lower the metal temperature by the combined protective effect of coolant film and heat removal through forced convection inside each hole. Despite many efforts reported in literature to characterize the cooling performance of these devices, detailed analyses of the mixing process between coolant and hot gas are difficult to perform, especially when superposition and density ratio effects as well as the interaction with complex gas side flow field become significant. Furthermore, recent investigations on the acoustic properties of these perforations pointed out the challenge to maintain optimal cooling performance also with orthogonal holes, which showed higher sound absorption.The objective of this paper is to investigate the impact of a realistic flow field on the adiabatic effectiveness performance of effusion cooling liners to verify the findings available in literature, which are mostly based on effusion flat plates with aligned crossflow, in case of swirled hot gas flow. The geometry consists of a tubular combustion chamber, equipped with a double swirler injection system and characterized by twenty-two rows of cooling holes on the liner. The liner cooling system employs slot cooling as well: its interactions with the cold gas injected through the effusion plate are investigated too.Taking advantage of the rotational periodicity of the effusion geometry and assuming axisymmetric conditions at the combustor inlet, steady state RANS calculations have been performed with the commercial code ANSYS® CFX simulating a single circumferential pitch. Obtained results show how the effusion perforation angle deeply affects the flow-field around the corner of the combustor, in particular with a strong reduction of slot effectiveness in case of 90° angle value.© 2014 ASME

Film Cooling Modelling for Gas Turbine Nozzles and Blades: Validation and Application

The use of Computational Fluid Dynamics (CFD) for modern turbine blade design requires the accurate representation of the effect of film cooling. However, including complete cooling hole discretization in the computational domain requires a substantial meshing effort and leads to a drastic increase in the computing time. For this reason, many efforts have been made to develop lower order approaches aiming at reducing the number of mesh elements and therefore computational resources. The simplest approach models the set of holes as a uniform coolant injection, but it does not allow an accurate assessment of the interaction between hot gas and coolant. Therefore higher order models have been developed, such as those based on localized mass sources in the region of hole discharge.It is here proposed an innovative injection film cooling model (FCM), embedded in a CFD code, to represent the effect of cooling holes by adding local source terms at the hole exit in a delimited portion of the domain, avoiding the meshing process of perforations. The goal is to provide a reliable and accurate tool to simulate film-cooled turbine blades and nozzles without having to explicitly mesh the holes.The validation campaign of the proposed model is composed of two phases. During the first one, results obtained with the film cooling model are compared to experimental data and to numerical results obtained with the full meshing of the cooling holes on a series of test cases, ranging from single row to multi row flat plate, at varying coolant conditions (in terms of blowing and density ratio). Though details of the flow structure downstream of the holes cannot be perfectly captured, this method allows an accurate prediction of the overall flow and performance modifications induced by the presence of the cooling holes, with a strong agreement to complete hole discretization results. In the second phase, a complete film-cooled vane test case has been studied, in order to consider a real injection system and flow conditions. In this case, film cooling model predictions are compared to an in-house developed correlative approach and full CHT 3D-CFD results.Finally, a comparison between film cooling model predictions and experimental data was performed on an actual nozzle of a GE Oil & Gas heavy-duty gas turbine as well, in order to prove the feasibility of the procedure.The presented film cooling model proved to be a feasible and reliable tool to evaluate adiabatic effectiveness, simplifying the design phase avoiding the meshing process of perforations. Also, refining the mesh near the hole exit, FCM results well approximate the solution coming from a full CHT calculation.Copyright

Numerical Benchmark of Non-Conventional RANS Turbulence Models for Film and Effusion Cooling

In the course of the years several turbulence models specifically developed to improve the predicting capabilities of conventional two-equations RANS models have been proposed. However they have been mainly tested against experiments only comparing with standard isotropic models, in single hole configuration and for very low blowing ratio. A systematic benchmark of the various non-conventional models exploring a wider range of application is hence missing.This paper performs a comparison of 3 recently proposed models over three different test cases of increasing computational complexity. The chosen test matrix covers a wide range of blowing ratios (0.5–3.0)including both single row and multi-row cases for which experimental data of reference are available. In particular the well known test by Sinha and Bogard [1] at BR = 0.5 is used in conjuction with two in-house carried out experiments: a single row film-cooling test at BR = 1.5 and a 15 rows test plate designed to study the interaction between slot and effusion cooling at BR = 3.0.The first two considered models are based on a tensorial definition of the eddy viscosity in which the stream-span position is augmented to overcome the main drawback connected with standard isotropic turbulence models that is the lower lateral spreading of the jet downwards the injection. An anisotropic factor to multiply the off-diagonal position is indeed calculated from an algebraic expression of the turbulent Reynolds number developed by Bergeles [2] from DNS statistics over a flat plate. This correction could be potentially implemented in the framework of any eddy viscosity model. It was chosen to compare the predictions of such modification applied to two among the most common two-equation turbulence models for film-cooling tests, namely the Two-Layer (TL) model and the k–ω Shear Stress Transport (SST), firstly proposed and tested in the past respectively by Azzi and Lakeal [3] and Cottin at al. [4].The third model, proposed by Holloway et al. [5], involves the unsteady solution of the flow and thermal field to include the short-time response of the stress tensor to rapid strain rates. This model takes advantage of the solution of an additional transport equation for the local effective total stress to trace the strain rate history.The results are presented in terms of adiabatic effectiveness distribution over the plate as well as spanwise averaged profiles.Copyright

Numerical Analysis of Heat Transfer in a Leading Edge Geometry With Racetrack Holes and Film Cooling Extraction

A numerical study of a state of the art leading edge cooling scheme was performed to analyze the heat transfer process within the leading edge cavity of a high pressure turbine airfoil. The investigated geometries account a trapezoidal supply channel with a large racetrack impingement holes. The coolant jets, confined among two consequent large fins, impact the leading edge internal surface and it is extracted from the leading edge cavity through both showerhead holes and film cooling holes. The CFD setup has been validated by means of the experimental measurements performed on a dedicated test rig developed and operated at University of Florence. The aim of this study is to investigate the combined effects of jet impingement, mass flow extraction and fins presence on the internal heat transfer of the leading edge cavity. More in details, the paper analyses the impact, in terms of blade metal temperature, of large fins presence and positioning. Jet’s Reynolds number is varied in order to cover the typical engine conditions of these cooling systems (Rej = 20000 – 40000).Copyright

Heat Transfer Measurements in a leading Edge Geometry with racetrack Holes and Film Cooling Extraction

An experimental survey on a state of the art leading edge cooling scheme was performed to evaluate heat transfer coefficients (HTC) on a large scale test facility simulating an high pressure turbine airfoil leading edge cavity. Test section includes a trapezoidal supply channel with three large racetrack impingement holes. On the internal surface of the leading edge, four big fins are placed in order to confine impingement jets. The coolant flow impacts the leading edge internal surface and it is extracted from the leading edge cavity through 24 showerhead holes and 24 film cooling holes. The aim of the present study is to investigate the combined effects of jet impingement and mass flow extraction on the internal heat transfer of the leading edge. A non uniform mass flow extraction was also imposed to reproduce the effects of pressure side and suction side external pressure. Measurements were performed by means of a transient technique using narrow band Thermo-chromic Liquid Crystals (TLC). Jet Reynolds number and crossflow conditions into the supply channel were varied in order to cover the typical engine conditions of these cooling systems (Rej = 10000–40000). Experiments were compared with a numerical analysis on the same test case in order to better understand flow interaction inside the cavity. Results are reported in terms of detailed 2D maps, radial-wise and span-wise averaged values of Nusselt number.Copyright