Abstract
A turbulence model is proposed for the prediction of inhomogeneous flows. A spectral closure is used to predict the energy transfer to the dissipative scales. The inhomogeneous transport terms are evaluated within the framework of one-point closures. Rough approximations are made concerning the anisotropy of turbulence. In the case of a flat plate boundary layer, the model is found to compare favorably with the experimental data. Possible improvements are discussed.
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Abbreviations
- < >):
-
Statistical average
- aKPQ):
-
\( = \frac{1}{2}({b_{KPQ}} + {b_{KQP}}) \)
- b):
-
Constant
- bKPQ):
-
Coefficient depending on the geometry of a triad in wave space
- D(K, X, t)):
-
Transport term in the energy spectrum equation
- E(K, X, t)):
-
Energy spectrum
- g(K, Kmax)):
-
Modeled spectral shape for the transport term D
- K):
-
Wave-vector
- K):
-
Wave-number, = |K|
- Kmin):
-
Infrared cutoff for the spectral computation
- Kmax):
-
Wave-number corresponding to the maximum of the energy spectrum
- k):
-
Turbulent kinetic energy
- K):
-
Constant
- L):
-
Integral length scale
- <q2>):
-
Twice the turbulent kinetic energy
- r):
-
Constant
- T(K, X, t)):
-
Energy transfer
- Ui(X, t)):
-
Velocity field
- u*):
-
Shear stress velocity
- δ):
-
Boundary layer thickness
- σ1, σ2):
-
Constants
- Фij(K, X , t)):
-
Spectral tensor, Fourier transform of the double velocity correlation at x and x′ with \(X = \frac{{x + x\prime }}{2}\)
- φij(k, X, t)):
-
Integral of Ф ij over a spherical shell of radius K
- φij,l):
-
Fourier transform of the triple correlation
- λ):
-
Constant
- ω):
-
Dimensionless stream function, \( = \frac{{\psi - {\psi _1}}}{{{\psi _E} - {\psi _1}}} \)
- πi):
-
Fourier transform of the pressure velocity correlation
- ψ):
-
Stream function
- µ):
-
Damping factor
- v):
-
Kinematic viscosity
- θKPQ):
-
E.D.Q.N.M. characteristic time
References
Bertoglio, J.-P. (1982): A model of three-dimensional transfer in non-isotropic homogeneous turbulence, in Turbulent Shear Flows 3, ed. by L. J. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt, J. H. Whitelaw (Springer, Berlin, Heidelberg) p. 253
Cambon, C., Jeandel, D., Mathieu, J. (1981 a): Spectral modeling of homogeneous non-isotropic Turbulence. J. Fluid Mech. 104, pp. 247–262
Cambon, C., Bertoglio, J.-P., Jeandel, D., (1981b); Spectral closure of homogeneous turbulence, AFOSR-HTTM-Stanford Conf. on Complex Turb. Flows, Sept. 1981
Dannevik, W., (1984): Two-point closure study of covariance budgets for turbulent Rayleigh-Benard convection, Ph. D. Thesis, St. Louis Univ., MO
Goldstein, M. E., Durbin, P. A. (1980): The effect of finite turbulence spatial scale on the amplification of turbulence by contracting stream. J. Fluid Mech. 98, (3), 473–508
Hamadiche, M. (1981): Modélisation spectrale des mécanismes linéaires dans les écoulements turbulents non homogènes. Thèse Univ. Cl. Bernard, Lyon I, Déc. 1981
Herring, J. R. (1985): Some contributions of two-point closure to turbulence, in Frontiers in Fluid Mechanics (Springer, Berlin, Heidelberg) p. 68
Hunt, J. C. R. (1978): A review of the theory of rapidly distorded turbulent flows and its applications. Fluid Dyn. Trans. 9, 121–152
Jeandel, D. (1976): Une approche phénoménologique des écoulements turbulents inhomogènes. Thèse Univ. Cl. Bernard, Lyon I, Juillet 1976
Jeandel, D., Brison, J. F., Mathieu, J. (1978): Modeling methods in physical and spectral space. Phys. Fluids 21, 169
Klebanoff, P. S. (1955): Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA Report 1247
Kraichnan, R. H. (1972): Test-field model for inhomogeneous turbulence. J. Fluid Mech. 56, 287–304
Lumley, J. L. (1983): Turbulence modeling, J. Appl. Mech. 50, 1097
Maxey, M. R. (1982): Distortion of turbulence in flows with parallel streamlines. J. Fluid Mech. 124, 261–282
Ménoret, L. (1982): Contribution à l’étude spectrale des écoulements turbulents faiblement inhomogènes et anisotropes. Thèse Univ. Cl. Bernard, Lyon I, Juin 1982
Ng, K. H., Spalding, D. B. (1972): Turbulence model for boundary layers near walls. Phys Fluids 15, 20
Ng, K. H., Spalding, D. B. (1976): Predictions of two-dimensional boundary layers on smooth walls with a two-equation model of turbulence. Int. J. Heat Mass Transf. 19, 1161–1172
Orszag, S. A. (1970): Analytical theories of turbulence. J. Fluid Mech. 41, 363–386
Patankar, S.V., Spalding, D. B. (1967): Heat and Mass Transfer in Boundary Layers (Morgan-Grampian, London)
Rodi, W., Spalding, D. B. (1970): Wärme Stoffübertrag. 3, 85
Weinstock, J. (1981): Theory of pressure-strain-rate correlation for Reynolds-stress turbulence closures, Part 1. Off-diagonal element. J. Fluid. Mech. 105, 369–396
Weinstock, J. (1982): Theory of the pressure-strain-rate. Part 2. Diagonal elements. J. Fluid. Mech. 116, 1–29
Wu, C. T., Ferziger, J. H., Chapman, D. R. (1985): Simulations and modeling of homogeneous, compressed turbulence, Fifth Symposium on Turbulent Shear Flows
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Bertoglio, JP., Jeandel, D. (1987). A Simplified Spectral Closure for Inhomogeneous Turbulence: Application to the Boundary Layer. In: Durst, F., Launder, B.E., Lumley, J.L., Schmidt, F.W., Whitelaw, J.H. (eds) Turbulent Shear Flows 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71435-1_3
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DOI: https://doi.org/10.1007/978-3-642-71435-1_3
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