Exponential roughness layer and analytical model for turbulent boundary layer flow over rectangular-prism roughness elements

Xiang Yang, Jasim Sadique, Rajat Mittal, Charles Meneveau

    Research output: Contribution to journalArticle

    40 Citations (Scopus)

    Abstract

    We conduct a series of large-eddy simulations (LES) to examine the mean flow behaviour within the roughness layer of turbulent boundary layer flow over rough surfaces. We consider several configurations consisting of arrays of rectangular-prism roughness elements with various spacings, aspect ratios and height distributions. The results provide clear evidence for exponential behaviour of the mean flow with respect to the wall normal distance. Such behaviour has been proposed before (see, e.g., Cionco, 1966 Tech. Rep. DTIC document), and is represented as U(z)/Uh = exp[a(z/h - 1)], where U(z) is the spatially/temporally averaged fluid velocity, z is the wall normal distance, h represents the height of the roughness elements and Uh is the velocity at z = h. The attenuation factor a depends on the density of the roughness element distribution and details of the roughness distribution on the wall. Once established, the generic velocity profile shape is used to formulate a fully analytical model for the effective drag exerted by turbulent flow on a surface covered with arrays of rectangular-prism roughness elements. The approach is based on the von Karman-Pohlhausen integral method, in which a shape function is assumed for the mean velocity profile and its parameters are determined based on momentum conservation and other fundamental constraints. In order to determine the attenuation parameter a, wake interactions among surface roughness elements are accounted for by using the concept of flow sheltering. The model transitions smoothly between 'k' and 'd' type roughness conditions depending on the surface coverage density and the detailed geometry of roughness elements. Comparisons between model predictions and experimental/numerical data from the existing literature as well as LES data from this study are presented. It is shown that the analytical model provides good predictions of mean velocity and drag forces for the cases considered, thus raising the hope that analytical roughness modelling based on surface geometry is possible, at least for cases when the location of flow separation over surface elements can be easily predicted, as in the case of wall-attached rectangular-prism roughness elements.

    Original languageEnglish (US)
    Pages (from-to)127-165
    Number of pages39
    JournalJournal of Fluid Mechanics
    Volume789
    DOIs
    StatePublished - Feb 1 2016

    Fingerprint

    boundary layer flow
    Boundary layer flow
    turbulent boundary layer
    Prisms
    prisms
    Analytical models
    roughness
    Surface roughness
    large eddy simulation
    Large eddy simulation
    drag
    Drag
    velocity distribution
    attenuation
    surface geometry
    flow separation
    shape functions
    Geometry
    Flow separation
    predictions

    All Science Journal Classification (ASJC) codes

    • Condensed Matter Physics
    • Mechanics of Materials
    • Mechanical Engineering

    Cite this

    @article{ac19adfdbc9d454880e8c7a200486ac2,
    title = "Exponential roughness layer and analytical model for turbulent boundary layer flow over rectangular-prism roughness elements",
    abstract = "We conduct a series of large-eddy simulations (LES) to examine the mean flow behaviour within the roughness layer of turbulent boundary layer flow over rough surfaces. We consider several configurations consisting of arrays of rectangular-prism roughness elements with various spacings, aspect ratios and height distributions. The results provide clear evidence for exponential behaviour of the mean flow with respect to the wall normal distance. Such behaviour has been proposed before (see, e.g., Cionco, 1966 Tech. Rep. DTIC document), and is represented as U(z)/Uh = exp[a(z/h - 1)], where U(z) is the spatially/temporally averaged fluid velocity, z is the wall normal distance, h represents the height of the roughness elements and Uh is the velocity at z = h. The attenuation factor a depends on the density of the roughness element distribution and details of the roughness distribution on the wall. Once established, the generic velocity profile shape is used to formulate a fully analytical model for the effective drag exerted by turbulent flow on a surface covered with arrays of rectangular-prism roughness elements. The approach is based on the von Karman-Pohlhausen integral method, in which a shape function is assumed for the mean velocity profile and its parameters are determined based on momentum conservation and other fundamental constraints. In order to determine the attenuation parameter a, wake interactions among surface roughness elements are accounted for by using the concept of flow sheltering. The model transitions smoothly between 'k' and 'd' type roughness conditions depending on the surface coverage density and the detailed geometry of roughness elements. Comparisons between model predictions and experimental/numerical data from the existing literature as well as LES data from this study are presented. It is shown that the analytical model provides good predictions of mean velocity and drag forces for the cases considered, thus raising the hope that analytical roughness modelling based on surface geometry is possible, at least for cases when the location of flow separation over surface elements can be easily predicted, as in the case of wall-attached rectangular-prism roughness elements.",
    author = "Xiang Yang and Jasim Sadique and Rajat Mittal and Charles Meneveau",
    year = "2016",
    month = "2",
    day = "1",
    doi = "10.1017/jfm.2015.687",
    language = "English (US)",
    volume = "789",
    pages = "127--165",
    journal = "Journal of Fluid Mechanics",
    issn = "0022-1120",
    publisher = "Cambridge University Press",

    }

    Exponential roughness layer and analytical model for turbulent boundary layer flow over rectangular-prism roughness elements. / Yang, Xiang; Sadique, Jasim; Mittal, Rajat; Meneveau, Charles.

    In: Journal of Fluid Mechanics, Vol. 789, 01.02.2016, p. 127-165.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Exponential roughness layer and analytical model for turbulent boundary layer flow over rectangular-prism roughness elements

    AU - Yang, Xiang

    AU - Sadique, Jasim

    AU - Mittal, Rajat

    AU - Meneveau, Charles

    PY - 2016/2/1

    Y1 - 2016/2/1

    N2 - We conduct a series of large-eddy simulations (LES) to examine the mean flow behaviour within the roughness layer of turbulent boundary layer flow over rough surfaces. We consider several configurations consisting of arrays of rectangular-prism roughness elements with various spacings, aspect ratios and height distributions. The results provide clear evidence for exponential behaviour of the mean flow with respect to the wall normal distance. Such behaviour has been proposed before (see, e.g., Cionco, 1966 Tech. Rep. DTIC document), and is represented as U(z)/Uh = exp[a(z/h - 1)], where U(z) is the spatially/temporally averaged fluid velocity, z is the wall normal distance, h represents the height of the roughness elements and Uh is the velocity at z = h. The attenuation factor a depends on the density of the roughness element distribution and details of the roughness distribution on the wall. Once established, the generic velocity profile shape is used to formulate a fully analytical model for the effective drag exerted by turbulent flow on a surface covered with arrays of rectangular-prism roughness elements. The approach is based on the von Karman-Pohlhausen integral method, in which a shape function is assumed for the mean velocity profile and its parameters are determined based on momentum conservation and other fundamental constraints. In order to determine the attenuation parameter a, wake interactions among surface roughness elements are accounted for by using the concept of flow sheltering. The model transitions smoothly between 'k' and 'd' type roughness conditions depending on the surface coverage density and the detailed geometry of roughness elements. Comparisons between model predictions and experimental/numerical data from the existing literature as well as LES data from this study are presented. It is shown that the analytical model provides good predictions of mean velocity and drag forces for the cases considered, thus raising the hope that analytical roughness modelling based on surface geometry is possible, at least for cases when the location of flow separation over surface elements can be easily predicted, as in the case of wall-attached rectangular-prism roughness elements.

    AB - We conduct a series of large-eddy simulations (LES) to examine the mean flow behaviour within the roughness layer of turbulent boundary layer flow over rough surfaces. We consider several configurations consisting of arrays of rectangular-prism roughness elements with various spacings, aspect ratios and height distributions. The results provide clear evidence for exponential behaviour of the mean flow with respect to the wall normal distance. Such behaviour has been proposed before (see, e.g., Cionco, 1966 Tech. Rep. DTIC document), and is represented as U(z)/Uh = exp[a(z/h - 1)], where U(z) is the spatially/temporally averaged fluid velocity, z is the wall normal distance, h represents the height of the roughness elements and Uh is the velocity at z = h. The attenuation factor a depends on the density of the roughness element distribution and details of the roughness distribution on the wall. Once established, the generic velocity profile shape is used to formulate a fully analytical model for the effective drag exerted by turbulent flow on a surface covered with arrays of rectangular-prism roughness elements. The approach is based on the von Karman-Pohlhausen integral method, in which a shape function is assumed for the mean velocity profile and its parameters are determined based on momentum conservation and other fundamental constraints. In order to determine the attenuation parameter a, wake interactions among surface roughness elements are accounted for by using the concept of flow sheltering. The model transitions smoothly between 'k' and 'd' type roughness conditions depending on the surface coverage density and the detailed geometry of roughness elements. Comparisons between model predictions and experimental/numerical data from the existing literature as well as LES data from this study are presented. It is shown that the analytical model provides good predictions of mean velocity and drag forces for the cases considered, thus raising the hope that analytical roughness modelling based on surface geometry is possible, at least for cases when the location of flow separation over surface elements can be easily predicted, as in the case of wall-attached rectangular-prism roughness elements.

    UR - http://www.scopus.com/inward/record.url?scp=84955087865&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84955087865&partnerID=8YFLogxK

    U2 - 10.1017/jfm.2015.687

    DO - 10.1017/jfm.2015.687

    M3 - Article

    AN - SCOPUS:84955087865

    VL - 789

    SP - 127

    EP - 165

    JO - Journal of Fluid Mechanics

    JF - Journal of Fluid Mechanics

    SN - 0022-1120

    ER -