The proper orthogonal decomposition (v. Lumley 1967) is utilized to provide one mode estimates of various turbulence quantities in tile ,mar-wall region of the turbulent bound-ary layer. The experimental data of Herzog (1986) and the direct numerical simulation (DNS) results of Zang (1991) provide the two-point correlation tensor. The correlation tensor is then used as the kernel in the integral eigenvalue problem from which the proper orthogonal nmdes arc obtained. The one mode estimates of the turbulent kinetic energy, dissipation, and triple moments all exhibit the proper asymtotic behavior near the wall. As a validation test, a model for the triple moments is developed and its near-wall behavior is studied. This information can then be used to obtain an estimate of the damping function near the wall, which is then compared to known existing behavior. Since this is an initial investigation the streamwise and spanwise dependence is sur-pressed and only the wall normal direction (y+) behavior of various turbulence statistics near the wall is studied. Before examining one mode estimates of the triple moments and the dissipation (on which the model is based), second order moments are exam-ined. If these do not exibit proper the wall seem the one mode
{"title":"Turbulence Modeling","authors":"D. Roychowdhury","doi":"10.1201/9780367809171-9","DOIUrl":"https://doi.org/10.1201/9780367809171-9","url":null,"abstract":"The proper orthogonal decomposition (v. Lumley 1967) is utilized to provide one mode estimates of various turbulence quantities in tile ,mar-wall region of the turbulent bound-ary layer. The experimental data of Herzog (1986) and the direct numerical simulation (DNS) results of Zang (1991) provide the two-point correlation tensor. The correlation tensor is then used as the kernel in the integral eigenvalue problem from which the proper orthogonal nmdes arc obtained. The one mode estimates of the turbulent kinetic energy, dissipation, and triple moments all exhibit the proper asymtotic behavior near the wall. As a validation test, a model for the triple moments is developed and its near-wall behavior is studied. This information can then be used to obtain an estimate of the damping function near the wall, which is then compared to known existing behavior. Since this is an initial investigation the streamwise and spanwise dependence is sur-pressed and only the wall normal direction (y+) behavior of various turbulence statistics near the wall is studied. Before examining one mode estimates of the triple moments and the dissipation (on which the model is based), second order moments are exam-ined. If these do not exibit proper the wall seem the one mode","PeriodicalId":297608,"journal":{"name":"Computational Fluid Dynamics for Incompressible Flows","volume":"126 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133064492","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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