Algorithm of thermo-gas dynamic end heat transfer modeling for turbine blades National Aviation Academy of Azerbaijan Republic Baku, 2013 This document has been prepared by the financial support of European Union Authors from National Aviation Academy of Azerbaijan Republic, National Aviation Academy of Azerbaijan Republic are responsible for the content of this document This publication reflects the views only of the authors, and it can not be regarded as the European Union's official position The book is developed in frame of project “Development of Training Network for Improving Education in Energy Efficiency” acronym: ENERGY, grant Nr 530379TEMPUS-1-2012-1-LVTEMPUS-JPCR Project was approved by the European Commission in frame of the Program Tempus IV – Fifth call for proposals (Programme guide EACEA/25/2011) Sub-programme: Joint Projects Action: Curricular Reform Deliverable: 2.1 Development and translation of study courses within the frame of direction “Thermo-gas dynamic end heat transfer modeling for turbine blades” Project coordinator: Leonids Ribickis Editors: Institution: Riga Technical University Contributors Adalat Samadov Soltan, vice-rector of Educational affairs of the National Academy of Aviation (Azerbaijan, Baku), Doctor of Technical Science, Associated professor of “Aircrafts and Aviation Engines” Department Author of many publications in the field of gas dynamics and heat transfer in gas turbines as well as cooling systems for high temperature gas turbine elements AZ1045, Baku city , Bina settlement., 25th km highway., National Aviation Academy Parviz Abdullayev Shahmurad, Assoc Prof DPh Eng Research interests: aircraft gas turbine engines condition monitoring methods on the basis of modern mathematical methods and techniques (neural networks, fuzzy logic) Present position: head of Aircrafts and Aviation Engines Department of the Azerbaijan National Academy of Aviation AZ1045, Baku city , Bina settlement., 25th km highway., National Aviation Academy Rzagulu Agaverdiyev Sultan, National Aviation Academy (NAA) « Aircraft and aviation engines » department lecturer and ph.d candidate, Azerbaijan Airlines (SilkWay Technics) airframe and power plant engineer AZ1045, Baku city , Bina settlement., 25th km highway., National Aviation Academy phone./fax: (+994 12) 497 28 29; 497 28 24; 497 28 38; 456 05 03 mail adress : Rz0gulu@gmail.com; RAgaverdiyev@swt.az; Introduction « Algorithm of thermo-gas dynamic end heat transfer modeling for turbine blades » NAA ‘Aircraft and aviation engines’ department lecturer, Azerbaijan Airlines (SilkWay Technics) airframe and power plant engineer: Agaverdiyev R.S ph.d candidate supervisor: Samadov A.S ph.d Abdullayev P.S ph.d This book is overview of existing Theoretical background of thermo-gas dynamic end heat transfer modeling principles for turbine blades The purpose of this book is the justification of scientific and modeling principles of the thermo-gas dynamic end heat transfer processes In this course we investigate the thermo-gazo dynamic end heat transfer processes and modeling principles in turbine blade cooling technology via Unigraphics, Ansys and Fluent software at aviation engines Primarily we analyze internal convective flows and film cooling methods Executive summary Algorithm of thermo-gas dynamic end heat transfer modeling for turbine blades Title 1: Eulerian models In Eulerian models the gas and the solid phases are treated as interpenetrating phases, and the theory behind such models is basically an extension of the classical kinetic theory that takes non- ideal particle-article collisions and gas-particle drag into account Title 2: Cooling via internal convective flows The purpose of cooling technology gas turbine components via internal convective flows is obtain the highest overall cooling effectiveness with the lowest possible penalty on the thermodynamic cycle performance Title 3: Fundamentals of Film Cooling Performance The purpose of film cooling is reduce the heat transfer to the wall is by reducing the gas temperature near the wall, i.e reducing the driving temperature potential for heat transfer to the wall Title 3.1 Correlations of Film Cooling Performance The primary measure of film cooling performance is the film effectiveness, η, since this has a dominating effect on the net heat flux reduction Title 4: A Conjugate Heat Transfer Method for Turbine Blade Cooling Conjugate heat transfer (CHT) is the process regarding the interaction between the heat conduction inside the solid body and the heat transfer in the surrounding fluid In real problems, the near wall flow is highly influenced by the solid thermal status Title Eulerian models In Eulerian models the gas and the solid phases are treated as interpenetrating phases, and the theory behind such models is basically an extension of the classical kinetic theory that takes non- ideal particle-article collisions and gas-particle drag into account In this scheme, collections of particles are modelled using continuous medium mechanics The solid particles are generally considered to be identical having a representative diameter and density, meaning that the particle phase is volume averaged The general idea in formulating such a multi-fluid model is to treat each phase as an interpenetrating continuum and therefore to construct integral balances of continuity, momentum and energy for both phases with appropriate boundary conditions and jump conditions for the phase interfaces Since such a resulting continuum approximation for the solid phase has no equation of state and obviously lacks variables such as viscosity and normal stress, certain averaging techniques and assumptions are required to obtain a momentum balance for the solid phase Figure shows a snapshot of liquid fuel spray coming out of an injector nozzle in a realistic gas-turbine combustor Here the spray atomization was simulated using a stochastic secondary breakup model (Apte et al 2003a) with point-particle approximation for the droplets Very close to the injector, it is observed that the spray density is large and the droplets cannot be treated as point-particles The volume displaced by the liquid in this region is significant and can alter the gas-phase flow and spray evolution In order to address this issue, one can compute the dense spray regime by an Eulerian Eulerian technique using advanced interface tracking/level-set methods (Sussman et al 1994; Tryggvason et al 2001; Herrmann 2003) This, however, is computationally intensive and may not be viable in realistic complex configurations We therefore plan to develop a methodology based on Eulerian-Lagrangian technique which will allow us to capture the essential features of primary atomization using models to capture interactions between the fluid and droplets and which can be directly applied to the standard atomization models used in practice The numerical scheme for unstructured grids developed by Mahesh et al (2003) for incompressible flows is modified to take into account the droplet volume fraction The numerical framework is directly applicable to realistic combustor geometries Our main objectives in this work are: Develop a numerical formulation based on Eulerian-Lagrangian techniques with models for interaction terms between the fluid and particles to capture the KelvinHelmholtz type instabilities observed during primary atomization Validate this technique for various two-phase and particulate flows Assess its applicability to capture primary atomization of liquid jets in conjuction with secondary atomization models Figure Snapshot spray from a gas-turbine fuel-injector Although constitutive relations according to the kinetic theory of particle flow have been incorporated into recent models, pure CFD models for fluid bed granulation still suffer from the fact that the contact between fluid, particles and boundary surfaces is not considered explicitly with respect to particle inertia and the mechanical properties of the particles This limits the ability of CFD multiphase models to adequately represent particle-particle and fluid-particle interactions thereby reducing the accuracy of the prediction of both the fluid and the particle dynamics Considering the required computational power and complexity, gas-particle flow fields calculated with the multifluid interpenetrating approach of the Eulerian granular multi-phase model is still a fast method to calculate flow fields, as it is well known from simple particle systems as spraydrying and conveying systems etc Due to the obvious need for accounting precise particle level properties into fluid bed hydrodynamic models, pure Eulerian CFD models must be regarded as inappropriate even in an industrial context Title Cooling via internal convective flows The purpose of cooling technology of Aviation Engines Gas Turbine components via internal convective flows is obtain the highest overall cooling effectiveness with the lowest possible penalty on the thermodynamic cycle performance The coolant is extracted from the internal channel for impingement and pin fin cooling Jet impingement is a very aggressive cooling technique which very effectively removes heat from the vane wall However, this technique is not readily applied to the narrow trailing edge The blade trailing edge is cooled using pin-fins (an array of short cylinders) Figure1 Aviation Engine Cross Section The pin-fins increase the heat transfer area while effectively mixing the coolant air to lower the wall temperature of the vanes After impinging on the walls of the airfoil, the coolant exits the vane and provides a protective film on the blade external surface Similarly, the coolant traveling through the pin-fin array is ejected from the trailing edge of the airfoil The importance of improving the cooling of gas turbine blades have seen an increasing demand of, initially experimental evidences, and now well validated numerical methods for use as optimization tools The effect of variating rib-sizes, Reynolds number etc have been documented in both numerical simulations and experimentally Figure Turbine blade cooling Although the many merits of experimental evidence, there is a problem that should be recognize when performing experiments: it is very difficult to achieve conditions which enable measured data to be dependent on only a single parameter In many investigations the data is obscured by slight perturbations in Reynolds number, different heating, rotation number etc These unknowns add up to a level of uncertainty in the measured data, which should be considered when making comparisons to the predicted result In numerical simulations on the other hand it is very easy to ensure an exact Reynolds number or that the flow is incompressible, or that the temperature behave as a passive scalar etc., all conditions which can only be an approximation of the real world It is thus important that both measurements and predictions are made under as identical conditions as possible, to 10 as 25% at the optimum blowing ratio, but increased film effectiveness as much as 50% at higher blowing ratios The decrease in film effectiveness at the optimum blowing ratio was primarily due to the roughness upstream of the coolant holes The upstream roughness doubled the boundary layer thickness and significantly increased turbulence levels which resulted in more separation of the coolant jets and increased dispersion of the coolant Figure Effect of convex and concave curvature on film effectiveness (reproduced with permission from Journal of Turbomachinery) There are a number of mainstream factors that can affect film cooling performance including approach boundary layers, turbulence levels, Mach number, unsteadiness, and rotation [David G Bogard Dr David Bogard is a Professor of Mechanical Engineering at the University of Texas at Austin : pages 314-316; total pages 320; printed date 07.11.2002] Because of the very high levels of mainstream turbulence exiting the combustor and entering the turbine section, turbulence levels have the largest 54 effect on film cooling performance Mainstream turbulence levels exiting the combustor can be higher than Tu = 20% and have been found to be nominally isotropic in simulated combustor studies Furthermore the integral length scale of the turbulence is large relative to the coolant hole diameters, i.e Λf/d > 10 (based on Λf values given in Radomsky and Thole) Primarily due to the acceleration of the mainstream as it passes around the first vane, the local turbulence levels reduce to less than 5% on the suction side of the vane, and to about 10% for much of the pressure side These are still relatively high turbulence levels, and it is important to recognize the effects on film cooling performance High mainstream turbulence levels degrade film cooling performance by increasing heat transfer coefficients and generally decreasing film effectiveness Simulations of the large scale turbulence with levels of Tu = 10% to 17% showed an increase in heat transfer coefficient of 15% to 30%, respectively The effects of high mainstream turbulence levels on film effectiveness are shown by the laterally averaged film effectiveness levels for Tu = 0.3%, 10%, and 20% shown in figure Results in figure were obtained using a flat surface test facility with a row of cylindrical holes spaced 6.5d apart, with an injection angle of 30º and aligned with the mainstream direction Smooth and rough surfaces were tested The coolant density ratio was DR = 2.0 For a smooth surface with low turbulence levels the optimum momentum flux ratio was I = 0.3 At this momentum flux ratio, a turbulence level of Tu = 17% caused a factor of two decrease in film effectiveness near the hole, and almost a complete loss of cooling for x/d > 25 The optimum momentum flux ratio for high mainstream turbulence conditions was about I = 1.1, substantially higher than would have been expected from low mainstream turbulence tests At this higher momentum flux ratio the film effectiveness for the high mainstream turbulence case was higher than for the low mainstream turbulence case 55 Figure Effect of freestream turbulence level on laterally averaged effectiveness as a function of momentum flux ratio for a smooth surface and low free-stream turbulence This difference was attributed to the higher mainstream turbulence mitigating the effect of coolant jet separation by returning some of the coolant towards the surface with the increased coolant dispersion caused by the higher turbulence levels These results show the importance of accounting for realistic mainstream turbulence levels when predicting film cooling performance [David G Bogard Dr David Bogard is a Professor of Mechanical Engineering at the University of Texas at Austin : pages 314-316; total pages 320; printed date 07.11.2002] 56 Title A Conjugate Heat Transfer Method for Turbine Blade Cooling In general, the study of heat transfer gives useful information to provide efficient solutions to many common engineering problems, as heating in circuits, heat exchanger or gas turbines For instance, modern turbines reach temperatures which exceed the melting point of the blade material Conjugate heat transfer (CHT) is the process regarding the interaction between the heat conduction inside the solid body and the heat transfer in the surrounding fluid In real problems, the near wall flow is highly influenced by the solid thermal status In the external blade cooling, cold air is injected through the film cooling holes on the external blade surface in order to create a thin film cooling layer (figure1) In the internal method, the heat is removed by a variation of convection and impingement cooling configurations, where high velocity air flows and hits the inner surfaces of the turbine vanes and blades Conjugate heat transfer (CHT) boundary conditions determine by the interface fluid temperature is known from the previous step, the temperature can be calculated at the fluid interface cells After grid generation, normal vectors and distances along the normal have been calculated for each interface cell 57 Figure Turbine blade surface and cooling holes As a result of the conjugate calculation approach, the surface temperatures and temperature fields in the nozzle solid body can be determined Figure shows the external surface temperature distribution on the nozzle vanes pressure side and shrouds, and Figure on the suction side and shrouds, respectively The damage to the nozzle was evaluated based on the analysis by Mazur et al [Article of Zdzislaw Mazur, Alejandro Herna´ndez-Rossette, Rafael Garcı´a-Illescas,Alberto Luna-Ramı´rez (Journal Volume 26, Issue 16 November 2006 Pages 1796-1806 ; Editor-inChief: D.A Reay link:http://www.journals.elsevier.com/applied-thermal-engineering; http://www.sciencedirect.com/science/journal/13594311/26/16)] 58 Figure External surface temperature distribution on the nozzle vanes pressure side and shrouds The maximum temperature (934 _C) on the pressure side is localized at the central part of the vane airfoil (50% height) on the leading edge and decreases gradually in a direction perpendicular to the vane axis, reaching a local minimum at the film cooling ducts (640.5 _C) Next the metal temperature is increasing at trailing edge and reaching a local maximum (853.9 _C) Similarly, the maximum temperature (934 _C) on the suction side is localized at the central part of the vane airfoil (50% height) on the leading edge Then the temperature decreases gradually in a direction perpendicular to the nozzle axis, and drops abruptly at the two rows of film cooling ducts, near the vane leading edge until it reaches a local minimum (640.5 _C) 59 Figure External surface temperature distribution on the nozzle vane suction side and shrouds Afterwards, the temperature increases at the trailing edge, reaching a local maximum of 853.9 _C Fig gives the distribution of internal vane temperatures in the cutting plane at 50% height (section of maximum temperature) As it can be appreciated, due to relatively thin vane walls, the temperature gradients in the solid hollow body of the vane are not too high 60 Figure Temperature distribution on the nozzle vane transversal section in the cutting plane at 50% height (section of maximum temperature) 61 The diagram of the temperature distribution on the external surface of the nozzle vane transversal section in the cutting plane at 50% height is shown in Fig As it can be seen in Figs 2, and 4, the temperature gradients in the film cooling ducts regions are very high and these zones must be taken into account in a succeeding thermal stress analysis Fig shows the same temperature distribution on the external surface of the nozzle vane transversal section in the cutting plane at 50% height varying cooling air flow rate and temperature For the nominal cooling flow rate of 4% (related to the principal gas flow) the nozzle metal maximum temperature is 934 _C (see pink curve) Increasing air flow rate to 8%, the maximum nozzle metal temperature is reduced to 860 _C (navy-blue curve) Increasing nominal air flow temperature by 100 _C and maintaining nominal air flow rate, the maximum metal temperature is increased to 950 _C (red curve) Figure External surface temperature distribution on the nozzle vane transversal section in the cutting plane at 50% height for varying cooling air flow rate and temperature Finally, increasing air flow temperature by 200 _C for increased air flow rate of 8%, it gives metal maximum temperature of 975 _C (green curve) [Article of Zdzislaw Mazur, Alejandro Herna´ndez-Rossette, Rafael Garcı´a-Illescas, Alberto Luna-Ramı 62 ´rez (Journal Volume 26, Issue 16 November 2006 Pages 1796-1806 ; Editor-in-Chief: D.A Reay link: http://www.journals.elsevier.com/applied-thermal- engineering; http://www.sciencedirect.com/science/journal/13594311/26/16)] As it can be appreciated, the cooling air flow rate and temperature influence significantly the heat transfer in the nozzle solid body and results in metal maximum temperature and temperature profile As a result of this investigation, the predicted nozzle temperature distribution made it possible to numerically analyse the thermal stresses and creep loads on the nozzle in steadystate operation of the gas turbine The damage to the nozzle was evaluated based on the analysis by Mazur et al Steady-state analyses of conjugate heat transfer of a first stage nozzle were conducted in order to predict the temperature distribution during continuous load operation In order to simulate the actual nozzle, the ejection of the internal cooling air into the gas path, the distribution of the bulk temperature of the cooling air in the internal passage, and the inlet distribution of gas temperature were integrated into the computational model As a result, the computations were able to simulate the heat transfer in the nozzle during steady-state operation The conducted investigation shows that the cooling air flow rate and temperature influence significantly the heat transfer in the nozzle solid body and, as a result, the metal maximum temperature and temperature profile Also, the assessment of service induced degradation of cobalt base alloy FSX-414 of the nozzle, after 24,000 h of operation at high temperature was carried out Temperature distribution on the nozzle vane (Figs 2,3,4 and 5), it is confirmed that a direct relation between the degree of alloy deterioration and metal temperature exists It is note worthy that the largest grain size and volume fraction of carbides corresponds to 63 the highest metal temperature zones This is one of the most of important facts found in this investigation The present predictions made it possible to estimate stress and creep strain loaded on the nozzle and to assess the nozzle remaining life based on the evaluation of the damage 64 References [1] Leontiev, A.I., Osipov, M.I., Ivanov, V.L., Manushin, E.A., (2004), «Heat exchange apparatus and cooling systems of gas turbine and combined arrangements », Moscow, MGTU nam N.E Bauman, pages 592 [2] Zisina-Molojen, L.N and etc (1974), «Heat exchange in turbomachines», Leningrad, Mashinostroeniye, 1974, pages 336 [3] Pashayev, A.M., Askerov, D.D., Sadiqov, R.A., Samedov, A.S (2005), «Numerical modeling of gas turbine cooled blades», International Journal of Aviation of Vilnius Gediminas, Technical University., vol 9, № 3, 2005, pages.9-18 [4] A.M.Pashaev, R.A.Sadiqov, C.M.Hajiev, (2002), «The BEM Application in development of Effective Cooling Schemes of Gas Turbine Blades» th Bienial Conference on Engineering Systems Design and Analysis, Istanbul, Turkey, (2002 July, pages 8-11) [5] Pashayev, A.M., Sadiqov, R.A., Samadov, A.S., Mammadov, R.N., (2004), «The solution of fluid dynamics direct problem of turbomachines cascades with integral equations method», Baku, proceed NAA, vol 3, pages 28-56 [6] Beknev, V.S., Epifanov, V.M., Leontiyev, A.I., Osipov, M.I and ets., (1997), «Fluid dynamics A mechanics of a fluid and gas», Moscow, MGTU nam N.E Bauman, pages 671 [7] Launder, B.E., Spalding, D.B., (1974), «The Numerical Computation of Turbulent Flows», Journal of Computational Methods in Applied Mechanics and Engineering, vol 3, pages 269-289 65 [8] Spalart, P and Allmaras, S., (1992), «A one-equation turbulence model for aerodynamic flows», Technical Report AIAA-92-0439, American Institute of Aeronautics and Astronautics, 1992 pages.6-12 [9] Imgrund, M.C (1992), ANSYS® Verification Manual, Swanson Analysis Systems, Inc [10] Fluent Fluent Inc., (2001), Centerra Resource Park, Cavendish Court, Lebanon, NH 03766, USA [11] Galitseiskiy, G and etc., (1996), «A thermal guard of blades», Moscow, Moscow Aviation Institute, pages 356 [12] Kopelev, S.Z., Slitenko, A.F., (1994), «Construction and calculation of GTE cooling systems», Ukraina, Kharkov, Osnova, pages 240 [13] Arseniev, L.V., Mitryayev, I.B., Sokolov, N.P., (1985), «The flat channels hydraulic resistances with a system of jets in a main stream», Journal of Energetic, 1985, № 5, pages 85-89 [14] Article of Robert Kwiatkowski, Roman Doma´nski > Institute of Heat Engineering University of Technology, Warsaw (Journal of Power Technologies;Dec2012, Vol 92 Issue 4, pages 208) [15] D Kercher, and W Tabakoff, “Heat Transfer by a Square Array of Round Air Jets Impinging Perpendicular to a Flat Surface Including the Effect of Spent Air,” Journal of Engineering for Power, 92 (1970): pages 73-82 [16] Article of W Colban; K A Thol Mechanical Engineering Department, Virginia Tech, Blacksburg, VA; M Haendler Siemens Power Generation, Muelheim a d Ruhr, Germany (J Turbomach 129(1), 23-31 (Jan 29, 2006) (9 66 pages)doi:10.1115/1.2370747, January 12, 2006; Revised January 29, 2006 ; link: http://turbomachinery.asmedigitalcollection.asme.org/article.aspx?articleid=1467350) [17] Article of Zdzislaw Mazur, Alejandro Herna´ndez-Rossette, Rafael Garcı´a-Illescas, Alberto Luna-Ramı´rez (Journal Volume 26, Issue 16 November 2006 Pages 1796-1806 ; Editor-in-Chief: D.A Reay link: http://www.journals.elsevier.com/applied-thermal-engineering; http://www.sciencedirect.com/science/journal/13594311/26/16) [18] R J Goldstein, “Film Cooling,” Advances in Heat Transfer (1971): pages 321379; CRC Press, 27.11.2012 pages№887 [19] David G Bogard Dr David Bogard is a Professor of Mechanical Engineering at the University of Texas at Austin : pages 314-316; total pages 320; printed date 07.11.2002 [20] Bunker, R.S., GE Global Research One Research Circle, K-1 ES-104 Niskayuna, NY 12309 : “The Gas Turbine Handbook” pages 298-299; total pages 445; printed date 2006 [21] Je-Chin Han Department of Mechanical Engineering, Texas A&M University, College Station, Texas, USA>: International Journal of Rotating Machinery Volume 10 (2004), Issue 6, Pages 443-457; link: http://www.hindawi.com/journals/ijrm/2004/517231/abs/ [22] Experimental and Numerical Impingement Heat Transfer in an Airfoil Leading-Edge Cooling Channel With Cross-Flow Revised 26.09.2007; Published 26.11.2008 [23] Gas Turbine Heat Transfer and Cooling Technology, Second Edition september 2001 67 Content , (14) 25 where - number of segments of the outline partition of the blade cross-section; x, y coordinates of segments At finding of cooler T best values, is necessary to solve the inverse problem of heat conduction For it is necessary at first to find solution of the heat conduction direct problem with boundary condition of the III kind from a gas leg and boundary conditions I kinds from a cooling air leg 25 68 ... overview of existing Theoretical background of thermo-gas dynamic end heat transfer modeling principles for turbine blades The purpose of this book is the justification of scientific and modeling. .. modeling principles of the thermo-gas dynamic end heat transfer processes In this course we investigate the thermo-gazo dynamic end heat transfer processes and modeling principles in turbine blade... software at aviation engines Primarily we analyze internal convective flows and film cooling methods Executive summary Algorithm of thermo-gas dynamic end heat transfer modeling for turbine blades