Predicting fully-developed channel flow with zero-equation model

  • Md Mizanur Rahman Hangzhou Dianzi University, China
  • Khalid Hasan Hangzhou Dianzi University, China
  • Wenchang Liu Hangzhou Dianzi University, China
  • Xinming Li Hangzhou Dianzi University, China
Keywords: y-phrases, Algebraic model, SED theory, Stress length, Stress-intensity parameter, Wall turbulence


A new zero-equation model (ZEM) is devised with an eddy-viscosity formulation using a stress length variable which the structural ensemble dynamics (SED) theory predicts. The ZEM is distinguished by obvious physical parameters, quantifying the underlying flow domain with a universal multi-layer structure. The SED theory is also utilized to formulate an anisotropic Bradshaw stress-intensity factor, parameterized with an eddy-to-laminar viscosity ratio. Bradshaw’s structure function is employed to evaluate the kinetic energy of turbulence k and turbulent dissipation rate epsilon  . The proposed ZEM is intrinsically plausible, having a dramatic impact on the prediction of wall-bounded turbulence. 


Download data is not yet available.


Bradshaw P, Ferriss DH, Atwell NP: Calculation of boundary layer development using the turbulent energy equations. Journal of Fluid Mechanics, 23:3164;1967. DOI: 10.1017/S0022112067002319

Champagne FH, Harris VG, Corrsin S: “Experiments on nearly homogeneous turbulent shear flow.” Journal of Fluid Mechanics, 41:81139; 1970. DOI: 10.1017/S0022112070000538

Durbin PA: Some recent developments in turbulence closure modeling. Annual Review of Fluid Mechanics, 50:77-103; 2018. DOI: 10.1146/annurev-fluid-122316-045020

Kawamura H, Abe H, Matsuo Y: DNS of turbulent heat transfer in channel flow with respect to Reynolds and Prandtl number effect. International Journal of Heat and Fluid Flow, 20(3):196-207;1999. doi:10.1016/S0142-727X (99)00014-4. DOI: 10.1016/S0142-727X(99)00014-4

Menter FR: Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32(8):1598-1605; 1994. DOI:

Mansour NN, Kim J, Moin P: Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. Journal of Fluid Mechanics, 194:15-44;1988. DOI: 10.1017/S0022112088002885

Prandtl L: Bericht uber Untersuchungen zur ausgebildeten Turbu- lenz. Zeitschrift fur angew. Math. u. Mechanik. 5:136-139; 1925. (in German) DOI: 10.1007/978-3-662-11836-8_57

Rahman MM, Keskinen K, Vuorinen V, Larmi M, Siikonen T: Consistently formulated eddy-viscosity coefficient for k-equation model. Journal of Turbulence, 19(11-12):959- 994; 2019.

Rahman MM, Miettinen A, Siikonen T: Modified SIMPLE formulation on a collocated grid with an assessment of the simplified QUICK scheme. Numerical Heat Transfer, Part B, 30(3):291-314; 1996.

Rahman MM, Siikonen T, Miettinen A: A pressure-correction method for solving fluid flow problems on a collocated grid. Numerical Heat Transfer, Part B, 32(1): 63-84; 1997.

Schlatter P, Orlu R: Assessment of direct numerical simulation data of turbulent boundary layers. Journal of Fluid Mechanics, 659:116126;2010. DOI: 10.1017/S0022112010003113

Segalini A, Orlu R, Alfredsson PH: Uncertainty analysis of the von Karman constant. Experiments in Fluids, 54:1460, 2013. DOI: 10.1007/s00348-013-1460-3

She Z-S, Chen X, Wu Y, Hussain F: New perspective in statistical modeling of wallbounded turbulence. Acta Mechanica Sinica, 26(6):847-861; 2010. DOI: 10.1007/s10409-010-0391-y

She, Z-S, Chen X, Hussain F: Quantifying wall turbulence via a symmetry approach: a Lie group theory. Journal of Fluid Mechanics, 827:322-356; 2017. DOI: 10.1017/jfm.2017.464

She Z-S, Hu N, Wu, Y: Structural ensemble dynamics-based closure model for wall bounded turbulent flow. Acta Mechanica Sinica 25:731-736;2009. DOI: 10.1007/s10409-009-0282-2

Townsend AA: The Structure of Turbulent Shear Flow, 2nd edition,1976. Cambridge University Press.

Wilcox DC: Turbulence Modeling for CFD, vol. 2. La Canada, DCW industries (2006).

How to Cite
Rahman, M. M., Hasan, K., Liu, W., & Li, X. (2021). Predicting fully-developed channel flow with zero-equation model . MIST INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY, 9(2), 17-22.