In this article we will discuss about:- 1. Introduction to the Physical Modelling of ABL 2. Primary Features of the Atmospheric Boundary Layer (ABL) 3. Similarity Criteria 4. The Meteorological Wind Tunnel (MWT).
Introduction to the Physical Modelling of ABL:
Efforts to determine wind effects on objects and dispersion of air pollutants using small-scale models in air flows generated by various means are reported in publications dating back to the decade of 1750-1760. Two centuries elapsed before serious efforts were made to produce air flows that modelled characteristics of natural wind in the ABL.
However, measurement of wind pressures on buildings by Irminger (1893) and Irminger (1930 and 1936) in Denmark, at the National Physical Laboratory by Stanton (1924) and Bailey et al (1943), development of a warm-cold air tunnel (16 m long, 1 m wide, 0.25 m high) at the Kaiser Wilhelm Institute for Flow Research by Prandtl et al (1934), studies of dispersion of stack effluent at the University of Michigan by Sherlock et al (1941), and studies of evaporation from plane boundaries at the University of Iowa and Colorado State University by Albertson (1948) and Cermak (1952), respectively, clearly demonstrated that the ABL should be modelled for wind-effect studies. During the two centuries, 1750-1950, laboratory flow facilities for such studies evolved from the rotating arm of Robins (1742) and Smeaton (1759) shown in Fig. 1 to the type shown in Fig. 2 which was constructed by the writer in 1949.
Although the wind tunnel shown in Fig. 2 was designed for studies of heat and mass transfer by forced convection in which simulation of the ABL was of no concern, significant information for modelling of the ABL was obtained, Cermak et al (1956). A historical summary of the foregoing developments is given by Cermak (1975) and examples of wind tunnel use for industrial aerodynamics studies, the precursor of wind engineering, are presented by Scruton (1960).
Following a summary description of primary features of the ABL, similarity criteria for modelling the ABL are presented. Wind-tunnel characteristics needed to satisfy the dominant similarity criteria are discussed and a boundary-layer wind tunnel (BLWT) having these characteristics, the Colorado State University meteorological wind tunnel (MWT), is described. Confirmation of similarity is shown by comparisons of flow measurements in the MWT with micrometeorological data.
During the last decade BLWTs with multiple and/or special capabilities have been designed and constructed. Several wind tunnels that mark significant advances in the evolution of natural wind modelling for wind-engineering purposes are described.
Primary Features of the Atmospheric Boundary Layer (ABL):
Wind in the planetary boundary layer (PBL) is driven primarily by horizontal pressure differences caused by non-uniform solar heating of Earth’s surface. Vertical distributions of mean velocities and turbulence in the PBL are determined by the surface shear stress, vertical gradients of temperature and rotation of Earth.
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A model developed by Lettau (1962), based on Reynolds equations for turbulent boundary layers, and predicts vertical distributions of mean wind velocity. Numerical integration for an atmosphere that is steady, horizontally homogeneous, dry, adiabatic, and without vertical motion gives a vertical distribution shown in Fig. 3 when the surface roughness length zo is 1 m, the geostrophic wind speed Ugeo is 34.5 ms-1, and the latitude is 30° north.
Mean Wind Speeds Distributions:
The ABL is defined for wind-engineering purposes to be a region between the surface and the gradient wind height zg where the mean wind speed U becomes a maximum Ug. During strong winds (neutral thermal stratification) the vertical distribution of U is closely approximated by a “power-law”.
Both the power-law exponent 1/n and the gradient wind height zg depend upon the surface-roughness length zo as indicated by Fig. 4.
A more detailed gradation of zo with respect to surface type developed by Wieringa (1992) is given in Table 1.
Low wind speeds must be considered in the lower part of the ABL, the atmospheric surface layer (ASL) shown in Fig. 1, when dispersion of air pollutants is considered.
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Thermal stratification then perturbs the logarithmic distribution for neutral flows to give mean distributions of wind speed U and temperature T that can be expressed by log-linear relationships according to Monin and Obukhov (1954) similarity as follows:
In Eqs. 2 and 3 the shear velocity u., friction temperature T. and Monin-Obukhov length L are defined as follows:
Equations 2 and 3 provide a basis for comparison of mean wind speed and temperature distribution in the ASL for wind-tunnel and field measurements.
Turbulence Characteristics in the ABL:
For wind-engineering applications turbulence measures of primary concern are the turbulence intensities, spectra, length scale and turbulent fluxes. The following expressions for these quantities over flat uniformly rough surfaces when the flow is near neutral give a framework for evaluation of the ABL and ASL models.
A simple form for intensity of the longitudinal component of turbulence Iu in the ASL is given by Tieleman (1991) as:
where ᴋ = 0.4 (von K arman constant) and Au = 2.5. Accordingly, a determination of zo from Table 1 provides a direct estimate of Iu. Upon matching scaling laws for the “inner” and “outer” layers of the ABL Harris et al (1980) have developed equations for Iu that are applicable throughout the ABL.
Olesen et al (1984) have presented two models for the turbulence spectra- a “pointed” model for flat uniformly rough surface and a “blunt” model for upwind approach with small perturbations of flatness and/or roughness. These models have been developed by Tieleman (1992) to provide spectral forms for all three turbulence components within the ASL which are listed in Table 2.
Widely used spectral models of von Karman (1948) and Davenport (1961) are discussed in a report by Tieleman (1991). The strong dependence of velocity spectra on thermal stratification of the ASL is evident in data reported by Kaimal et al (1972) as shown in Fig. 5.
A distinguishing feature of the neutral ASL is near constancy of the turbulent shear stress — the “constant” flux layer indicated in Fig. 3. Data in Fig. 6 extracted from a report by Izumi (1971) on the 1968 Kansas field program illustrate this property.
Similarity Criteria for Modelling the ABL:
General similarity criteria may be obtained directly by inspectional analysis, Ruark (1935), of the equations for conservation of mass, momentum and energy in turbulent flow.
By use of inspectional analysis the following non-dimensional equations are given by Cermak (1975) in which similarity parameters are contained in brackets:
The variables are scaled as follows to form the non-dimensional quantities:
Although Eqs. 5, 6 and 7 are very general, there are some restrictions. Because the temperature dependence of density has been linearized in Eq. 6 (Boussinesq approximation) flows are limited to cases with ΔT < To. This restriction does not impose serious limitations on the use of Eq. 6 for ABL flow. Equation 7 does not allow for an exchange of energy by radiation or phase changes of water. Therefore, a strict interpretation of Eq. 7 limits application to ABLs without cloud content or precipitation.
Equations 5, 6 and 7 give the requirements for kinematic, dynamic, and thermic similarity when proper boundary conditions are satisfied. Equation 5 is invariant for this transformation in which all lengths are scaled equally; i.e., xi* = xi/Lo.
Therefore, geometric similarity results in kinematic similarity.
Equation 6 states that dynamic similarity can be achieved if each of the following parameters is equal for two systems:
Uo/(LoΩo), Rossby number (Ro); (ΔTo/To(Logo/Uo2), Richardson number (Ri); and UoLo/vo, Reynolds number (Re).
Thermic similarity will be obtained if, according to Eq. 7, the following dimensionless groups are equal for two systems:
voρoCpo/ko, Prandtl number (Pr); Uo2/(Cpo To), Eckert number (Ec); and Re.
The foregoing requirements for geometric, dynamic, and thermic similarities must be augmented by boundary specifications to complete requirements for similarity.
These external conditions are:
(1) Similarity of surface roughness and temperature distributions;
(2) Similarity of flow structure above the ABL;
(3) Similarity of the horizontal pressure gradient; and
(4) Sufficient flow development to establish equilibrium of ABL for conditions (1) and (2).
Boundary-layer studies by Cermak et al (1956) and Peterka et al (1974) in the wind tunnel of Fig. 2 reveal the need for condition (4). These conditions motivate consideration of a long wind- tunnel test section with features shown in Fig. 7.
The foregoing requirements for “exact” similarity of the ABL, result in the necessity that physical modeling of the ABL in a wind tunnel be considered on the basis of “approximate” similarity. The primary compromises that must be made are relaxation of the requirements that (Re)m = (Re)p and (Ro)m = (Ro)p because the nominal length scale is 1:500. Since Ec is proportional to the Mach number squared, equality of Ec for model and prototype need not be satisfied for wind speeds experienced in the ABL.
For “aerodynamically rough” surfaces inequality of Re for model and prototype is not a deterrent to achievement of flow similarity provided Re exceeds a value that depends upon the relative surface roughness ka/Lf. Values of Re required for Reynolds-number independence (RNI) for neutral thermal stability are given by Fig. 8.
The “model law” established by Jensen (1958) gives a RNI criterion for mean pressures on low-rise buildings. This criterion requires equality of the ratio of building height to the aerodynamic roughness length H/zo for model and prototype. Further research is needed to establish RNI criteria for thermally stratified flow, particularly in stable conditions.
In wind tunnels or channels which do not rotate, (Ro)m will be approximately 500 times larger than (Ro)p; therefore turning of the mean flow velocity with height shown in Fig. 3 will not be replicated. Development of a technique to model Rossby-number effects and maintain RNI remain a challenge.
The approach used for studies of flow over obstacles by Alessio et al (1983), a water channel (8 m long x 2 m wide x 0.6 m depth) placed on the 14-m diameter rotating platform of the Institute de M6canique, University de Grenoble, offers an interesting concept.
The Meteorological Wind Tunnel (MWT):
Based on research in the wind tunnel shown in Fig. 2 by Cermak et al (1956) and the similarity considerations presented above, the design of a wind tunnel following the concept illustrated by Fig. 7 was reported by Cermak (1958). This BLWT, commonly identified as the MWT, is shown in Fig. 9 and described by Plate et al (1963) and Cermak (1981).
Special Features of MWT for ABL Simulation:
A major difference between the wind tunnel shown in Fig. 2 and the MWT is the test-section length. The long test section serves to increase the ranges of surface roughness and wind speed for which Reynolds-number independence can be achieved as indicated by Fig. 8, to produce significant distances over which the boundary layer is in statistical equilibrium (shown by constant shape factor H in Fig. 10), and to provide large boundary-layer thicknesses indicated in Fig. 11.
The requirement that the pressure gradient ∂P/∂x be zero for ABL similarity is met by vertical adjustment of the test-section ceiling. Continuous adjustment along the test-section length, as shown in Fig. 9, allows a maximum height increase of 0.5 m at the downwind end.
Matching of Richardson numbers for the ASL is made possible in the MWT by the heating and cooling systems indicated in Fig. 9. Large magnitudes of Ri are achieved for low wind speeds with large temperature differences. Values of Ri in the range -1 to 1 can be developed. This range includes most of the values found in field measurements such as those given in Fig. 5.
For studies of wind effects on low-rise buildings and/or low-level dispersion, depth of the simulated ASL should be increased to permit length scaling in the range of 1:50 to 1:100. This motivates partial modelling of the ABL in which the characteristic feature of “constant” shear stress (see Fig. 6) is generated over a depth of approximately 0.5 m.
The introduction of inclined horizontal vanes at the test- section shown in Fig. 12 promotes downward transport of the Reynolds stress -ρ u̅’w̅’ to produce the desired flow. Figure 13 gives a vertical distribution of shear stress for the horizontal vane configuration.
