This article revisits the problem of indirect combustion noise in nozzles of finite length. The analytical model proposed by Moase et al. (JFM 2007) for indirect combustion noise is red-erived and applied to subcritical nozzles having shapes of increasing complexity. This model is based on the equations formulated by Marble & Candel (JSV 1977) for which an explicit solution is obtained in the subsonic framework. The discretization of the nozzle into n elementary units of finite length implies the determination of 2n integration constants for which a set of linear equations is provided in this article. The analytical method is applied to configurations of increasing complexity. Analytical solutions are compared to numerical results obtained using SUNDAY (a 1D non linear Euler solver in temporal space) and CEDRE (3D Navier-Stokes flow solver). An excellent agreement is found for all configurations thereby showing that acceleration discontinuities at the boundaries between adjacent elements do not influence the actual acoustic transfer functions. The issue of nozzle compactness is addressed. It is found that in the subcritical domain, spectral results should be nondimensionalized using the flow-through-time of the entire nozzle. Doing so, transfer functions of nozzles of different lengths are successfully compared and a compactness criterion is proposed that writes ω*∫0Ldζ/uζ<1 where L is the axial length of the nozzle. Finally, the EWG experimental setup of Bake et al. (JSV 2009) is considered. Analytical results are compared to the results reported by Howe (JFM 2010). Both models give similar trends and show the important role of the rising time of the fluctuating temperature front on the amplitude of the indirect acoustic emission. The experimental temperature profile and the impedance coefficients at the inlet and outlet provided by Bake et al. (JSV 2009) and Leyko et al. (JSV 2011) are introduced into the analytical formulation. Results show that the indirect combustion noise mechanism cannot be held responsible alone for the acoustic emission in the subcritical case.
{"title":"Analytical Analysis of Indirect Combustion Noise in Subcritical Nozzles","authors":"A. Giauque, M. Huet, F. Cléro","doi":"10.1115/1.4007318","DOIUrl":"https://doi.org/10.1115/1.4007318","url":null,"abstract":"This article revisits the problem of indirect combustion noise in nozzles of finite length. The analytical model proposed by Moase et al. (JFM 2007) for indirect combustion noise is red-erived and applied to subcritical nozzles having shapes of increasing complexity. This model is based on the equations formulated by Marble & Candel (JSV 1977) for which an explicit solution is obtained in the subsonic framework. The discretization of the nozzle into n elementary units of finite length implies the determination of 2n integration constants for which a set of linear equations is provided in this article. The analytical method is applied to configurations of increasing complexity. Analytical solutions are compared to numerical results obtained using SUNDAY (a 1D non linear Euler solver in temporal space) and CEDRE (3D Navier-Stokes flow solver). An excellent agreement is found for all configurations thereby showing that acceleration discontinuities at the boundaries between adjacent elements do not influence the actual acoustic transfer functions. The issue of nozzle compactness is addressed. It is found that in the subcritical domain, spectral results should be nondimensionalized using the flow-through-time of the entire nozzle. Doing so, transfer functions of nozzles of different lengths are successfully compared and a compactness criterion is proposed that writes ω*∫0Ldζ/uζ<1 where L is the axial length of the nozzle. Finally, the EWG experimental setup of Bake et al. (JSV 2009) is considered. Analytical results are compared to the results reported by Howe (JFM 2010). Both models give similar trends and show the important role of the rising time of the fluctuating temperature front on the amplitude of the indirect acoustic emission. The experimental temperature profile and the impedance coefficients at the inlet and outlet provided by Bake et al. (JSV 2009) and Leyko et al. (JSV 2011) are introduced into the analytical formulation. Results show that the indirect combustion noise mechanism cannot be held responsible alone for the acoustic emission in the subcritical case.","PeriodicalId":219275,"journal":{"name":"Volume 8: Turbomachinery, Parts A, B, and C","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131772614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
P. Jenny, R. Abhari, Martin George Rose, M. Brettschneider, K. Engel, J. Gier
The paper presents an experimental and computational study of the unsteady behavior of the rotor hub passage vortex in an axial low-pressure turbine. Different flow structures are identified as having an effect on the size, strength, shape, position and the unsteady behavior of the rotor hub passage vortex. The aim of the presented study is to analyze and quantify the sensitivities of the different flow structures and to investigate their combined effects on the rotor hub passage vortex. Particular attention is paid to the effect of the rim seal purge flow and of the unsteady blade row interaction. The rotor under investigation has non-axisymmetric end walls on both hub and shroud and is tested at three different rim seal purge flow injection rates. The rotor has separated pressure sides at the operating point under investigation. The non-dimensional parameters of the tested turbine match real engine conditions. The 2-sensor Fast Response Aerodynamic Probe (FRAP) technique and the Fast Response Entropy Probe (FENT) systems developed by ETH Zurich are used in this experimental campaign. Time-resolved measurements of the unsteady pressure, temperature and entropy fields between the rotor and stator blade rows are taken and analyzed. Furthermore, the results of URANS simulations are compared to the measurements and the computations are also used to detail the flow field. The experimental results show a 30% increase of the maximum unsteadiness and a 4% increase of the loss in the hub passage vortex per percent of injected rim seal cooling flow. Compared to a free stream particle, the rim seal purge flow was found to do 60% less work on the rotor.
{"title":"Unsteady Rotor Hub Passage Vortex Behavior in the Presence of Purge Flow in an Axial Low Pressure Turbine","authors":"P. Jenny, R. Abhari, Martin George Rose, M. Brettschneider, K. Engel, J. Gier","doi":"10.1115/GT2012-69256","DOIUrl":"https://doi.org/10.1115/GT2012-69256","url":null,"abstract":"The paper presents an experimental and computational study of the unsteady behavior of the rotor hub passage vortex in an axial low-pressure turbine. Different flow structures are identified as having an effect on the size, strength, shape, position and the unsteady behavior of the rotor hub passage vortex. The aim of the presented study is to analyze and quantify the sensitivities of the different flow structures and to investigate their combined effects on the rotor hub passage vortex. Particular attention is paid to the effect of the rim seal purge flow and of the unsteady blade row interaction. The rotor under investigation has non-axisymmetric end walls on both hub and shroud and is tested at three different rim seal purge flow injection rates. The rotor has separated pressure sides at the operating point under investigation. The non-dimensional parameters of the tested turbine match real engine conditions. The 2-sensor Fast Response Aerodynamic Probe (FRAP) technique and the Fast Response Entropy Probe (FENT) systems developed by ETH Zurich are used in this experimental campaign. Time-resolved measurements of the unsteady pressure, temperature and entropy fields between the rotor and stator blade rows are taken and analyzed. Furthermore, the results of URANS simulations are compared to the measurements and the computations are also used to detail the flow field. The experimental results show a 30% increase of the maximum unsteadiness and a 4% increase of the loss in the hub passage vortex per percent of injected rim seal cooling flow. Compared to a free stream particle, the rim seal purge flow was found to do 60% less work on the rotor.","PeriodicalId":219275,"journal":{"name":"Volume 8: Turbomachinery, Parts A, B, and C","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134314552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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