A multi-length-scale theory of the anomalous mixing-length growth for tracer flow in heterogeneous porous media

1992 ◽  
Vol 66 (1-2) ◽  
pp. 485-501 ◽  
Author(s):  
Qiang Zhang
Keyword(s):  
Porous Media ◽  
Heterogeneous Porous Media ◽  
Length Scale ◽  
Mixing Length ◽  
Scale Theory ◽  
Length Growth

Fundamentals of Transport Equation Formulation for Two-Phase Flow in Homogeneous and Heterogeneous Porous Media

1999 ◽  
Author(s):  
Michel Quintard ◽  
Stephen Whitaker
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Practical Importance ◽  
Volume Averaging ◽  
Heterogeneous Porous Media ◽  
Homogenization Theory ◽  
Length Scale ◽  
Two Phase ◽  
The Hierarchical Structure ◽  
Method Of Volume Averaging

Most porous media of practical importance are hierarchical in nature; that is, they are characterized by more than one length-scale. When these length-scales are disparate, the hierarchical structure can be analyzed by the method of volume averaging (Anderson and Jackson, 1967; Marie, 1967; Slattery, 1967; Whitaker, 1967). In this approach, macroscopic quantities at a given length-scale are defined in terms of a boundary value problem that describes the phenomena at a smaller length-scale, and information is filtered from one scale to another by a series of volume and area integrals. Other methods, such as ensemble averaging (Matheron, 1965; Dagan, 1989) or homogenization theory (Bensoussan et al, 1978; Sanchez-Palencia, 1980), have been used to study hierarchical systems, and developments specific to the problems under consideration in this chapter can be found in Bourgeat (1984), Auriault (1987), Amaziane and Bourgeat (1988), and Sáez et al. (1989). The transformation from the Darcy scale to the large scale is a recurrent problem in reservoir and aquifer engineering. A detailed description of reservoir properties is available through geostatistical analysis (Journel, 1996) on a fine grid with a length-scale much smaller than the scale of the blocks in the reservoir simulator. “Effective” or “pseudo” properties are assigned to the coarse grid blocks, while the forms of the large-scale equations are required to be the same as those used at the Darcy scale (Coats et al., 1967; Hearn, 1971; Jacks et al., 1972; Kyte and Berry, 1975; Dake, 1978; Killough and Foster, 1979; Yokoyama and Lake, 1981; Kortekaas, 1983; Thomas, 1983; Kossack et al., 1990). A detailed discussion of the comparison between the several approaches is beyond the scope of this chapter; however, one can read Bourgeat et al. (1988) for an introductory comparison between the method of volume averaging and the homogenization theory, and Ahmadi et al. (1993) for a discussion of the various classes of pseudofunction theories.

scholarly journals Turbulence Characteristics Across a Range of Idealized Urban Canopy Geometries

2021 ◽  
Author(s):  
Lewis P. Blunn ◽  
Omduth Coceal ◽  
Negin Nazarian ◽  
Janet F. Barlow ◽  
Robert S. Plant ◽  
...  
Keyword(s):  
Momentum Flux ◽  
Mixing Layer ◽  
Urban Canopy ◽  
Turbulence Closure ◽  
Length Scale ◽  
Good Representation ◽  
Mixing Length ◽  
Turbulence Characteristics ◽  
First Order ◽  
Turbulent Momentum

AbstractGood representation of turbulence in urban canopy models is necessary for accurate prediction of momentum and scalar distribution in and above urban canopies. To develop and improve turbulence closure schemes for one-dimensional multi-layer urban canopy models, turbulence characteristics are investigated here by analyzing existing large-eddy simulation and direct numerical simulation data. A range of geometries and flow regimes are analyzed that span packing densities of 0.0625 to 0.44, different building array configurations (cubes and cuboids, aligned and staggered arrays, and variable building height), and different incident wind directions ($$0^\circ $$ 0 ∘ and $$45^\circ $$ 45 ∘ with regards to the building face). Momentum mixing-length profiles share similar characteristics across the range of geometries, making a first-order momentum mixing-length turbulence closure a promising approach. In vegetation canopies turbulence is dominated by mixing-layer eddies of a scale determined by the canopy-top shear length scale. No relationship was found between the depth-averaged momentum mixing length within the canopy and the canopy-top shear length scale in the present study. By careful specification of the intrinsic averaging operator in the canopy, an often-overlooked term that accounts for changes in plan area density with height is included in a first-order momentum mixing-length turbulence closure model. For an array of variable-height buildings, its omission leads to velocity overestimation of up to $$17\%$$ 17 % . Additionally, we observe that the von Kármán coefficient varies between 0.20 and 0.51 across simulations, which is the first time such a range of values has been documented. When driving flow is oblique to the building faces, the ratio of dispersive to turbulent momentum flux is larger than unity in the lower half of the canopy, and wake production becomes significant compared to shear production of turbulent momentum flux. It is probable that dispersive momentum fluxes are more significant than previously thought in real urban settings, where the wind direction is almost always oblique.

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