Skip to main content
SpringerLink
Log in

Large Eddy Simulations of Rough Turbulent Channel Flows Bounded by Irregular Roughness: Advances Toward a Universal Roughness Correlation

  • Published:
Flow, Turbulence and Combustion Aims and scope Submit manuscript

Abstract

The downward shift of the mean velocity profile in the logarithmic region, known as roughness function, \(\Delta U^+\), is the major macroscopic effect of roughness in wall bounded flows. This speed decrease, which is strictly linked to the friction Reynolds number and the geometrical properties which define the roughness pattern such as roughness height, density, shape parameters, has been deeply investigated in the past decades. Among the geometrical parameters, the effective slope (ES) seems to be suitable to estimate the roughness function at fixed friction Reynolds number, Re\(_{\tau }\). In the present work, the effects of several geometrical parameters on the roughness function, in both transitional and fully rough regimes, are investigated by means of large eddy simulation of channel flows characterized by different wall-roughness textures at different values of Re\(_{\tau }\) up to 1000. The roughness geometry is generated by the superimposition of sinusoidal functions with random amplitudes and it is exactly resolved in the simulations. A total number of 10 cases are solved. With the aim to find a universal correlation between the roughness geometry and the induced roughness function, we analyzed the effect of more than a single geometrical parameter, including the effective slope, which takes into account both the roughness height and its texture. Based on data obtained from our simulations and a number of data points from the literature, a correlation between the ES and the root mean square of the roughness oscillation, as well as between ES and the mean absolute deviation of the roughness, satisfactorily predicts the roughness function.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Busse, A., Thakkar, M., Sandham, N.: Reynolds-number dependence of the near-wall flow over irregular rough surfaces. J. Fluid Mech. 810, 196–224 (2017)

    MATH  MathSciNet  Google Scholar 

  • Chan, L., MacDonald, M., Chung, D., Hutchins, N., Ooi, A.: A systematic investigation of roughness height and wavelength in turbulent pipe flow in the transitionally rough regime. J. Turbul. 771, 743–777 (2015). https://doi.org/10.1017/jfm.2015.172

    Article  Google Scholar 

  • Cheng, H., Castro, I.P.: Near wall flow over urban-like roughness. Bound. Layer Meteorol. 104, 229–259 (2002)

    Google Scholar 

  • De Marchis, M.: Large eddy simulations of roughened channel flows: estimation of the energy losses using the slope of the roughness. Comput. Fluids 140, 148–157 (2016)

    MATH  MathSciNet  Google Scholar 

  • De Marchis, M., Napoli, E.: Effects of irregular two-dimensional and three-dimensional surface roughness in turbulent channel flows. Int. J. Heat Fluid Flow 36, 7–17 (2012)

    Google Scholar 

  • De Marchis, M., Napoli, E., Armenio, V.: Turbulence structures over irregular rough surfaces. J. Turbul. 11(3), 1–32 (2010)

    Google Scholar 

  • De Marchis, M., Ciraolo, G., Nasello, C., Napoli, E.: Wind-and tide-induced currents in the Stagnone lagoon (Sicily). Environ. Fluid Mech. 12(1), 81–100 (2012)

    Google Scholar 

  • De Marchis, M., Freni, G., Napoli, E.: Three-dimensional numerical simulations on wind- and tide-induced currents: the case of Augusta Harbour (Italy). Comput. Geosci. 72, 65–75 (2013)

    Google Scholar 

  • De Marchis, M., Milici, B., Napoli, E.: Numerical observations of turbulence structure modification in channel flow over 2D and 3D rough walls. Int. J. Heat Fluid Flow 56, 108–123 (2015)

    Google Scholar 

  • De Marchis, M., Milici, B., Napoli, E.: Large eddy simulations on the effect of the irregular roughness shape on turbulent channel flows. Int. J. Heat Fluid Flow 80, 1–15 (2019). https://doi.org/10.1016/j.ijheatfluidflow.2019.108494

    Article  Google Scholar 

  • Flack, K.A., Schultz, M.P.: Review of hydraulic roughness scales in the fully rough regime. J. Fluids Eng. 132, 1–10 (2010)

    Google Scholar 

  • Flack, K.A., Schultz, M.P.: Roughness effects on wall-bounded turbulent flows. Phys. Fluids 26(103105), 1–17 (2014)

    Google Scholar 

  • Forooghi, P., Stroh, A., Magagnato, F., Jakirlic, S., Frohnapfel, B.: Towards a universal roughness correlation. J. Fluids Eng. 139(12), 12121 (2017)

    Google Scholar 

  • Forooghi, P., Stroh, A., Frohnapfel, B.: A systematic study of turbulent heat transfer over rough walls. Int. J. Heat Mass Transf. 127(part c), 1157–1168 (2018)

    Google Scholar 

  • Hama, F.R.: Boundary layer characteristics for smooth and rough surfaces. Trans. Soc. Nav Arch. Mar. Eng. 62, 333–358 (1954)

    Google Scholar 

  • Jackson, P.S.: On the displacement height in the logarithmic profiles. J. Fluid Mech. 111, 15–25 (1981)

    MATH  Google Scholar 

  • Jelly, T.O., Busse, A.: Reynolds and dispersive shear stress contributions above highly skewed roughness. J. Fluid Mech. 852, 710–724 (2018)

    MATH  MathSciNet  Google Scholar 

  • Jimenez, J.: Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196 (2004)

    MATH  MathSciNet  Google Scholar 

  • Jimenez, J., Hoyas, S.: Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236 (2008)

    MATH  Google Scholar 

  • Kim, J., Moin, P., Moser, R.: Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166 (1987)

    MATH  Google Scholar 

  • Leonardi, S., Orlandi, P., Antonia, R.A.: Properties of d- and k-type roughness in a turbulent channel flow. Phys. Fluids 19, 1–6 (2007)

    MATH  Google Scholar 

  • Maas, C., Schumann, U.: Direct numerical simulation of separated turbulent flow over a wavy boundary. In: Hirschel, E.H. (ed.) Flow Simulation with High Performance Computers. Notes on Numerical Fluid, vol. 52, pp. 227–241. Springer, Berlin (1996)

    Google Scholar 

  • MacDonald, M., Chan, L., Chung, D., Hutchins, N., Ooi, A.: Turbulent flow over transitionally rough surfaces with varying roughness densities. J. Fluid Mech. 804, 130–161 (2016)

    MathSciNet  Google Scholar 

  • Mejia-Alvarez, R., Christensen, K.T.: Wall-parallel stereo particle-image velocimetry measurements in the roughness sublayer of turbulent flow overlying highly irregular roughness. Phys. Fluids 25, 115109 (2013)

    Google Scholar 

  • Milici, B., De Marchis, M.: Statistics of inertial particle deviation from fluid particle trajectories in horizontal rough wall turbulent channel flow. Int. J. Heat Fluid Flow 60, 1–11 (2016)

    Google Scholar 

  • Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to \(Re_{\tau }\) = 590. Phys. Fluids 11(4), 943–945 (1999)

    MATH  Google Scholar 

  • Napoli, E., Armenio, V., De Marchis, M.: The effect of the slope of irregularly distributed roughness elements on turbulent wall-bounded flows. J. Fluid Mech. 613, 385–394 (2008)

    MATH  Google Scholar 

  • Perry, A.E., Schofield, W.H., Joubert, P.N.: Rough wall turbulent boudary layers. J. Fluid Mech. 37, 383–413 (1969)

    Google Scholar 

  • Rao, V.N., Jefferson-Loveday, R., Tucker, P.G., Lardeau, S.: Large eddy simulations in turbines: influence of roughness and free-stream turbulence. Flow Turbul. Combust. 92(1–2), 543–561 (2014)

    Google Scholar 

  • Schlichting, H.: Experimental investigation of the problem of surface roughness. Ing. Arch. 7, 1–34; Translation from German published 1937 as NACA Tech. Memo. 823 (1936)

  • Schmid, M.F., Lawrence, G.A., Parlange, M.B., Giometto, M.G.: Volume averaging for urban canopies. Bound. Layer Meteorol. 173, 349–372 (2019)

    Google Scholar 

  • Schultz, M.P., Flack, K.A.: Turbulent boundary layers on a systematically varied rough wall. Phys. Fluids 21(015104), 1–9 (2009)

    MATH  Google Scholar 

  • Thakkar, M., Busse, A., Sandham, N.: Surface correlations of hydrodynamic drag for transitionally rough engineering surfaces. J. Turbul. 18(2), 138–169 (2017). https://doi.org/10.1080/14685248.2016.1258119

    Article  MathSciNet  Google Scholar 

  • Wu, Y., Christensen, K.T.: Outer-layer similarity in the presence of a practical rough-wall topography. Phys. Fluids 19, 1–15 (2007)

    MATH  Google Scholar 

  • Wu, Y., Christensen, K.T.: Spatial structure of a turbulent boundary layer with irregular surface roughness. J. Fluid Mech. 655, 380–418 (2010)

    MATH  Google Scholar 

  • Yuan, J., Piomelli, U.: Estimation and prediction of the roughness function on realistic surfaces. J. Turbul. 15(6), 350–365 (2014)

    MathSciNet  Google Scholar 

  • Zang, Y., Street, R.L., Koseff, J.R.: A dynamic mixed subgride-scale model and its application to turbulent recirculating flows. Phys. Fluids 12, 3186–3196 (1993)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Facolta’ di Ingegneria e Architettura, Universita’ degli Studi di Enna “Kore”, Cittadella Universitaria, Enna, Italy

    Mauro De Marchis, Domenico Saccone & Barbara Milici

  2. Dipartimento di Ingegneria Civile, Ambientale, Aerospaziale, dei Materiali, Universita’degli Studi di Palermo, Viale delle Scienze, Palermo, Italy

    Enrico Napoli

Authors
  1. Mauro De Marchis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Domenico Saccone
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Barbara Milici
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Enrico Napoli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mauro De Marchis.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Appendix: Details of the Sinusoidal Functions Used to Generate the Irregular Rough Surfaces

Appendix: Details of the Sinusoidal Functions Used to Generate the Irregular Rough Surfaces

In the following are reported the data of the amplitude, \(A_i\) and \(B_j\), and the wave length \(L_{x_1}/2i\), in the streamwise direction, and \(L_{x_2}/2j\), in the spanwise direction, for each sinusoid. In Table 3 are reported the wave amplitude and wave length of the upper and lower two-dmensional roughness. See Fig. 1 of Napoli et al. (2008) and De Marchis et al. (2010). In Table 4 are reported the data to reproduce the irregularity of 3D rough walls in the streamwise direction. In Table 5 are reported the data to reproduce the irregularity of 3D rough walls in the spanwise direction.

Table 3 Data of the wall oscillations
Full size table
Table 4 Data of the wall oscillations
Full size table
Table 5 Data of the wall oscillations
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

De Marchis, M., Saccone, D., Milici, B. et al. Large Eddy Simulations of Rough Turbulent Channel Flows Bounded by Irregular Roughness: Advances Toward a Universal Roughness Correlation. Flow Turbulence Combust 105, 627–648 (2020). https://doi.org/10.1007/s10494-020-00167-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10494-020-00167-5

Keywords

Search

Navigation