Free Stream Turbulence

7.13 Free Stream Turbulence

Most of the relationships presented so far describe conductances one would measure in a carefully constructed wind tunnel which minimizes the turbulence in the air. When turbulence is induced in the air that flows over the object, the conductance increases, often dramatically. Conduc- tances in wind tunnels with turbulence generated by placing obstructions upwind of the object are sometimes twice those for laminar flow.

The outdoor wind is naturally turbulent, so the conductance of objects placed in natural wind is likely to be higher than would be predicted using the equations presented so far. The size of this enhancement is determined by the size of the object and the size of the eddies in the air. The eddy size increases with height in the atmosphere, so the enhancement should change with height. Mitchell (1976) measured convective heat transfer

spheres in the atmosphere and related the enhancement to the ratio of sphere diameter to distance above the ground. Mitchell's relation is shown in Fig. 7.4. For heights ranging from about 2 to 10 times the object

diameter the enhancement is around 1.4, and this is the value we use for all outdoor computations.

Summary of Formulae for Conductance

The formulae given in this chapter are used frequently throughout the rest of the book. It is therefore convenient to summarize them in a single location. This is done in Table 7.6.

10 Height Diameter

F IGURE 7.4. Enhancement of conductance by free stream turbulence for spheres

T A BLE 7.6. Formulae for calculating conductances (mol for diffusion, convection, and turbulent transport in air. Process

Other Mass Transfer conduction or

Heat

Vapor Transfer

Plane = (molecular processes)

Plane

= A2 Plane g, =

Cylinder g Cylinder

Forced convection (fluid

= moved past surface by

= external force)

Free convection (fluid flow

generated from temperature

gradients) Eddy diffision or turbulent

transport (wind over fields)

110 Conductances for Heat and Mass Transfer

References

I.R. (1972) Mass and heat transfer in laminar boundary layers with particular reference to assimilation and transpiration in leaves. Agric. Meteor.

11-329.

D.W. and P.J.H. Sharp (1973) An analysis of the mechanics of guard cell motion. J.

Biol.

Eckert, E.R.G. and R.M. Drake (1972) Analysis of Heat and Mass Transfer New York: McGraw-Hill. J.R., and B.B. Hicks (1973) Momentum, heat, and water vapor transfer to and from natural and artificial surfaces. Quart. J. Roy. Meteor.

P.D. (1974) The diffusion of carbon dioxide and water vapor through stomata. J. Exp. Bot. Kowalski, G.J. and J.W. Mitchell (1975) Heat transfer from spheres in

Mech. Eng. Paper No. Kreith, F. (1965) Principles of Heat Transfer. Scranton, Pa.: International Textbook Co. J.L., and H.A.

the naturally turbulent, outdoor environment. Arner.

(1964) The structure of Atmospheric Turbulence. New York: Wiley. Mitchell, J.W. (1976). Heat transfer from spheres and other animal forms. Biophysical Journal

1-569.

Monteith, J.L., and G.S. Campbell (1980) of water vapour through

confusion. J. Biol. Monteith, J.L. arid M.H.

(1990) Principles of Environmental Physics. 2nd ed. London: Edward Arnold. Nobel, P.S. (1974) Boundary layers of air adjacent to cylinders Plant Physiol. 54: D.F., P.R. Duncan, D.M. Gates, and F. Kreith (1968) Wind tunnel modeling of convection of heat between air and broad leaves of plants Agric. Meteor.

K.D., G.W and M.E. Patterson (1988) Cuticular diffusive resistance measurements: A technique for teaching and research in postharvest research in horticulture. Dept. of Horticulture, Wash. State Univ., Pullman, WA.

Yasuda, N. (1988) Turbulent and diurnal variations in the at-

mospheric boundary layer. Boundary-Layer Meteorol.

Problems

7.1. Maximum width of a leaf in the direction of wind flow is 5 cm. Leaf temperature is

C in a 1

wind when

C. Find d, Re,

Gr ,

and H. Is heat transfer mainly by forced or free convection?

7.2. The wind speed at a height of 2 m is 5.6 Find the boundary layer (turbulent transport) conductance for a potato canopy that is 50 cm

high. Assume neutral stability.

Problems

11 1

C, to room air at 22" C if there is no wind (free convection) and if the wind speed is

7.3. Find the heat flux density from your arm, at

2 mls.

7.4. Compute the heat loss from a sheep to the air if its fleece is 5 cm thick and the diameter of the sheep's body (inside the fleece) is 25 cm. Assume the fleece has twice the conductance of still air, the body temperature is

and the air temperature is C.

C, the wind speed is 4

7.5. Compare thermal conductance of clothing at sea level with conduc- tance at 5000 m elevation. Is elevation likely to have a noticeable effect on heat loss through clothing?

7.6. In Eq. (7.10) there is no minus sign as in Eq. (7.9). Based on the sign convention implied by Eq.

discuss the between fluctuations of w and T and identify what conditions are associated with a flux from the soil surface to the atmosphere.

Heat Flow in the Soil

When the sun shines on the soil surface, some of the energy is absorbed, heating the soil surface. This heat is lost from the surface through con- duction to lower layers of the soil, through heating the atmosphere, and through evaporation of water. Heat transport from the surface to the at- mosphere was discussed in Ch. 7. This chapter considers heat transport into the soil. Some of the results from an analysis of heat transport in soil are presented in Ch. 2 to show typical temporal and spatial patterns of soil temperature. Here we show how those equations are derived and how they depend on soil properties.