an improved method of simulating an atmospheric boundary layer

Atmospheric Environment Pergamon Press 1969. Vol. 3, pp. 197-214. Printed in Great Britain

AN IMPROVED METHOD OF SIMULATING AN ATMOSPHERIC BOUNDARY LAYER IN A WIND TUNNEL

J. COUNlHAN

Central Electricity Research Laboratories, Cleeve Road, Leatherhead, Surrey, England

(First received 9 September 1968 and in jinal form 9 December 1968)

Abstract-An experimental assessment of various types of turbulence generators has led to the adoption of a system of “elliptic wedge” generators and a castellated barrier to produce a simulated rough wall boundary layer.

The characteristics of this simulated boundary layer have been measured and exhibit no significant spanwise variations. They are also sensibly constant over that area of a wind tunnel working section which would be occupied by a model. A working section length of between four and five boundary layer heights is required to produce the simulated flow.

In all aspects considered the simulated boundary layer is comparable to a neutral atmospheric boundary layer.

1. INTRODUCTION

MANY wind tunnel experiments in the field of industrial aerodynamics require that the tests should be carried out in the environment of a simulated neutral atmsopheric or rough wall boundary layer. The necessity of having a correct representation of this boundary layer and the relative importance of simulating either correct velocity or turbulence profiles, or both, has previously been discussed by ARMITT and COUNIHAN (1968).

In the case of the CERL low speed wind tunnel a four foot high boundary layer was required. The length of working section required to grow such a boundary layer naturally was clearly prohibitive. Therefore an attempt was made to devise a method which would give an accelerated rate of growth and produce a fully developed boundary layer in a distance of from three to four times the required boundary layer height. The method chosen involved the use of triangular vortex generators and a barrier or wall positioned upstream of them on the floor of the wind tunnel.

Nomenclature: A = constant; B = constant; d = roughness physical height, in.; h = distance from tunnel floor, in.; H = generator height, in.; u 111.X = Free-stream velocity, ft/sec;

IJr = friction velocity, ft/sec; U = longitudinal velocity component, ft/sec; V = lateral velocity component, ft/sec; W = vertical velocity component, ft/sec.; r. = roughness length, in.;

: = height in boundary layer, in.; = boundary layer thickness, in. ;

A prime denotes a fluctuating contribution and a bar denotes an average with respect to time. 1 in. = 25.4 mm: 1 deg = 0.017453 rad.

197

198 J. COUNIHAN

The experimental testing and asessment of this system, carried out in the CERL low speed wind tunnel and previously reported by Armitt and Counihan, showed that there were some undesirable characteristics present in the flow produced. It was therefore decided to investigate this system and others in more detail at a smaller scale where generator and barrier wall alterations could more readily be made when required. These tests were therefore subsequently carried out in the CERL boundary layer wind tunnel.

It was thought that other systems to be examined shoufd consist of an ogive shaped generator or possibly pairs of triangular generators in tandem, one large and one small, set at incidences less than that of the generators in the original scheme. However, after further consideration, these methods were rejected as being unnecessarily complex.

TYPES OF GENERATORS WHOSE WAKE C~ARACTER}STlCS WERE INVESTIGATE0

SIDE VIEW OF TRIANGULAR AND CRANKED GENERATORS

1

*----I \x.___r -.- .--- PLARE ELLIPTIC GENERATOR

1

I I’ - I

I I

I -__-___ -

L ‘I*

+ NOTE: ‘THE WEDGE ANGLE IS A CONSTANT AT ANY

ELLIPTIC WEDGE GENERATOR HORIZONTAL SECTIO,,‘x.x’

SCALE: K

FIG. 1. Types of generators whose wake characteristics were investigated.

The characteristics of four simple generator shapes were examined in the boundary layer wind tunnel. These consisted of triangular, cranked triangular, plane elliptic and elliptic wedge generators (FIG. 1). As expected the former three produced similar wake patterns. Therefore it was decided to compare in more detail only the wakes of the

Simulating an Atmospheric Boundary Layer in a Wind Tunnel 199

triangular and elliptic wedge generators because of their different properties. The general shape of the triangular generator wake could be predicted at this stage from the original results (ARMITT and COUMHAN, 1968) but not, however, in sufficient detail and without the effects of the upstream barrier wall superimposed.

The results illustrated the difficulties introduced in using a system involving triangular generators and are discussed in Section 3. It was therefore decided to use a com- bination of elliptic wedge generators and a barrier wall in further tests to produce a simulated boundary layer (FIG. 2). The characteristics of the flow produced by this system were measured and are presented in this paper. The more relevant data only of the generator assessment tests are presented here. Full details are included in COUNIHAN (1968).

2. THE PRINCIPLE OF THE TRIANGULAR GENERATOR

Before referring to some relevant facts arising from recent investigations into the physics of boundary layer flow it is necessary to restate in detail some of the reasons for originally adopting a triangular generator.

The method chosen was intended to produce an accelerated version of a model of the flow processes in a natural turbulent boundary layer as proposed by TOWNSEND (1957). This concept implies the existence of sets of large eddies both in the inner or constant shear section of the boundary layer and in the outer layer. However the two sets of eddies are not necessarily of similar structure. It is assumed that these large eddies are of comparable size to the respective sections of the boundary layer in which they exist and are relatively slow motions.

Thus the pairs of generators at alternate incidences were intended to produce large scale eddies or vortices of opposite sign and of the type envisaged by Townsend. At the same time they maintained the nett streamwise vorticity of the flow at zero. The action of these vortices should then accelerate the outward diffusion of the high intensity turbulence produced at ground level, It is necessary to diffuse this turbulence, created by surface roughness, outwards in order to overcome the initial lack of turbulence in the outer section of the simulated boundary layer.

The results of a more recent study of boundary layer flow (?kI'ITON, 1967), however, are not consistent with the above concept of a large eddy structure existing in the boundary layer and suggests that separate descriptions of large eddies for both boundary layer regions may be inappropriate, Further work (KLINE, REYNOLDS, SCHRAUB and RUSTADLER, 1967) has shown the existence of secondary vorticity, presumably the large scale eddies described by Townsend, in the inner region of the boundary layer. It is suggested that the action of these secondary vortices on the spanwise vorticity gives rise to the formation of wall streaks. The subsequent ejection of fluid away from the wall is then considered to be the main mechanism for the transfer of energy, momentum and vorticity between the inner and outer regions of the boundary layer. Therefore it seems that the present knowledge on the physics of the flow in a boundary layer is inconclusive concerning the existence of large scale eddies. If they do exist they are more likely to be a result of outward diffusion of turbulence rather than its cause. It is also assumed that the boundary layers studied by the above investigations were those associated with a smooth wall, whereas the structure of a rough wall boundary layer might be slightly different.

200 J. CWNEHAN

FindIy it is considered that by the use of triangular generators some degree of asymmetry would still exist in the flow due to the alternate incidence settings of the generators,

3. THE PRfNCIPLE OF THE ELLIPTXC WEDGE GENERATOR

The design of the elliptic wedge generators is based on the following concepts. It was assumed that, since the lower region of the boundary layer is the more important, this should be left todevelop freely and that the turbulence needed for the outer layers should be produced by the generators. It was assumed that eventually the two sections would blend together to form a complete boundary layer.

In accordance with the shape of the vertical distribution of turbulence eventually required it was decided that a generator was needed in whose wake either the turbulence remained constant with height or, more acceptable, whose turbulence decayed from some maximum value at or near ground level to approximately zero at the top of the generator.

The tests using the triangular generator had indicated a tendency for an excessive momentum loss in the inner region of the boundary layer and insufficient loss in the outer section. Hence the elliptic shape was chosen as a method of area redistribu- tion in an attempt to overcome this. The resultant generator design, which it was

thought could produce the above wake flow, is called an elliptic wedge vorticity generator.

The side view of the elliptic wedge is a quarter ellipse whose major axis is twice its minor axis. In plan view the section is wedge shaped, the wedge angle being a constant at any plan section. The apex of the wedge faces into the flow direction and hence there is no asymmetry introduced into the system. Therefore the characteristics of the elliptic wedge wake should be identical at equal distances either side of its centre line.

It was considered that a low wedge angle would be beneficial in producing a vertical distribution of vorticity rather than a vortex in the wake. From this point of view a semi-wedge angle of 5 to 6” seemed reasonable. Higher wedge angles might also have produced a section having excessive base drag but test results indicated later that this may not have been significant. A constant wedge angle was maintained at all sections of the generator as it was fett that this was needed for the production of turbulence or vorticity over the complete generator height.

The above discussion has in effect decided the &ape of the generator and, assuming that it would prove satisfactory, the only important factor remaining is the spacing of the generators relative to each other.

4. THE EXPERIMENTAL ASSESSMENT OF THE GENERATORS

This assessment was carried out in the CERL boundary layer wind tunnel which has a working section 24 in. wide, 7-30 in. high and 5 ft long. The tests were made at a free stream velocity of 30 ft/sec and without the presence of a barrier or surface roughness. It was intended to produce a 6 in. thick boundary layer in the wind tunnel and therefore the generators were 6 in. high.

In accordance with the arguments of Section 3 it was decided that the assessment should be based upon m~~ments of the distribution of longitudinal turbulence in the wake of single generaturs over a section 18 in., i.e. three boundary layer heights,

FIG. 2. Arrangement of barrier and generators in the boundary layer wind tunnel.

(Facing page 200)

Simulating an Atmosp~ric Boundary Layer in a Wind Tunnel 201

.3.0 -2.0 -1.0 0 il.0 +z.o +3.0 in DISTANCE FROM GENERATOR'%

FIG. 3, Contours of constant lon~~din~ turbulence in the wake of a triangular generator at BII incidence of 10”.

T 10

aI= SEMI-WEOGEANGLEV SEMI.WEDGEANGLESO

TURBULENCES

f ,

I I I I I 43.0 42.0 l l.O 0 +I.0 +2.0 +3.0in

DISTANCE F~MGENERATOR~

FIG. 4. Contours of constant ion~tudinal turbulence in the wake of elliptic wedge generators.

202 J. COUNIHAN

downstream of the generators. This section was chosen as it included the position equivalent to the turntable leading edge in the CERL low speed with tunnel.

The more relevant results of the tests are shown in FIGS. 3 and 4. The considerable extent of the triangular generator wake is clearly evident, At this distance downstream there is still no indication of break-up of the vortex and quite severe turbulence gradients exist, The asymmetry of the wake on either side of the generator centre-line is also very pronounced.

In contrast the elliptic wedge produces a vertical distribution of turbulence in its wake of the type postulated in Section 3 as being of the required form. The second significant characteristic of this generator wake is that at any given height the spanwise turbulence intensity is sensibly constant over a good proportion of the spanwise extent of the wake. Clearly at any particular section the wake of the 6” generator will be wider than that of the 5” generator. In other words, the 5” generators would have to be positioned closer together than the 6” generators to obtain a similar degree of lateral ~ifo~ty of the wake flow.

Therefore, having thus found the properties of the elliptic wedges to be satisfactory, a suitable arrangement of the generators and barrier in the tunnel had to be determined.

5. OPTIMIZATION OF THE GENERATOR/BARRIER ARRANGEMENT IN THE WIND TUNNEL

The points which were investigated in determining the final layout in the tunnel are briefly commented on here. Note is also made of the extent to which they are considered to be of importance relative to the characteristics of the boundary layer to be finally produced in the wind tunnel.

1.0

h - 0.6

~ELLIPTICWE~EG~E~TO~S (SEMMNGLE 5c)

SPAN in. 50.6

0 4.0 80 120 16.C

1.0

0 4.0 8.0 12 0 16.0

FIG. 5. The effect of generator spacing on the wake distribution of longitudinal turbulence.

Simulating an Atmospheric Boundary Layer in a Wind Tunnel

5.1. Generator angle and ~pa~~~g

203

It is clear that the spanwise uniformity of the flow finally produced is of importance and is dependent on the spacing of the generator,. 0 In which case it is necessary to define what one considers to be an acceptable degree of lateral non-uniformity. It was decided that a spanwise variation of turbulence of the order of 1 per cent would be tolerable at any given height in the boundary layer. It was also considered that the generator spacing should be as wide as possible, consistent with the above limits, as it was felt that too close a spacing might have some effect on the frequency spectra of the turbulence.

Consequently, the variation of turbulence with height was determined at positions in line with the generator centre line and at mid-span of the generators for a number of different generator spacings. All of the m~urements were made 18 in., i.e. three boundary layer heights, downstream of the generator trailing edges. The measurements at these positions indicate the maximum lateral variations of the longitudinal turbulence intensity.

The results of these tests on elliptic wedge generators of semi-angle 5 and 6” are shown in FIG. 5. Based on the above arguments it was decided that the generator of 6” semi-wedge angle at a spacing of between 3 and 33 in., i.e. between O-5 and O-6 boundary layer heights, was the most acceptable.

5.2. Position and height of the barrier will It was thought that, if the barrier wall was placed at the intersection of the working

section and contraction, it could influence the flow through and from the contraction. In the case of a wind tunnel in which there is no contraction before the working section the point to be considered is that there will be a relatively thick floor boundary layer and that the momentum loss due to this will have to be taken into account when deciding on the height of the barrier wall.

A brief investigation showed that the barrier wall could be positioned 2 in., i.e. one third of the boundary layer height, from the contraction in the CERL boundary layer wind tunnel. However, if the working section length of a wind tunnel is short, the barrier wall could be moved closer to the contraction without seriously affecting the end results.

The barrier wall used for these tests was a scaled down version of that used in the original tests and was O-75 in., i.e. one-eighth of the boundary layer height, high. Some tests on other barriers showed that the turbulence intensity and velocity defects increased on increasing the barrier wall height.

5.3. Position of the generators relative to the barrier wall This was determined by varying the position of the generators from the barrier wall

which was fIxed at the position stated above and making similar measurements to those indicated in Section 5.1. These showed that the determination of the position of the generators was to some extent arbitrary, as in the case of the barrier. In this case, where it was positioned was based on what it was thought the shape and magnitude of the final vertical distribution of turbulence should assume. What these should be was in turn based on an assessment of existing measurements in natural turbulent boundary layers and predicted or measured values of turbulence intensity at or near ground level in full scale conditions.

204 J. COUN~HAN

In this case it was decided to position the leading edge of the generators 5 in., i.e. five- sixths of the boundary layer height, from the barrier wall. If the generators are closer to the barrier than the intensities of turbulence at the same measuring position will clearly be lower. Therefore, as in the case of the barrier, if the wind tunnel working section is short and a lower turbulence level can be tolerated, the generators can be moved closer to the barrier without seriously affecting the shape of the vertical distribution of turbulence.

6. EXPERIMENTAL WORK WITH THE COMPLETE BOUNDARY LAYER SIMULATION METHOD IN THE WIND TUNNEL

The barrier and generators were positioned in the wind tunnel as indicated in Section 5 and “Leg,” baseboards were fitted to the tunnel floor to represent surface roughness. The mean velocity profile, turbulence components and Reynolds stresses were then measured at various spanwise positions 18 in., i.e. three boundary layer heights, downstream of the generators. Initially, the generators were set 33 in. apart, i.e. three-fifths of the boundary layer height, and the barrier was 0.75 in., i.e. one- eighth of a boundary layer height, high.

The mean velocity profiles and Reynolds stresses measured at the above conditions are shown in FIG. 6. The turbulence components were also measured and were sensibly close to the tolerance given in Section 5, regarding lateral uniformity. It was then considered desirable to reduce the difference between the velocity profiles measured at the two spanwise positions.

The first step was to reduce the generator spacing to 3 in., i.e. one-half of a boundary layer height (FIG. 7). Then, since the mean measured velocity defect was stiil less than that for a 1/7th Power Law profile, the height of the barrier was increased to O-875 in., i.e. one-seventh of boundary layer height. (FIGS. 8 and 9). An improvement was obtained in the velocity profiles in the first instance and in the Reynolds stresses in the second. The turbulence profiles were also acceptably uniform.

It was thought that a further momentum loss was needed in the region of the generator centre span. This was effected by locally increasing the barrier height immediately upstream of the generator centre line. It was assumed that the wake produced by this height increase interacted with the generator wakes to induce earlier coalescence of these. This alteration is referred to as Mod. A. and the relevant test results are shown in FIGS. 10, 11 and 12. The mean of the velocity profiles then approximated to the lf7th Power Law and all of the other components were within acceptable limits. The frequency spectra were also measured at this section and are shown in FIG. 13 and are clearly not affected by the close generator spacing.

Finally the velocity, turbulence intensities and Reynolds stress were measured at a section 27 in. (i.e. four and one half boundary layer heights) downstream of the generator trailing edges (FIGS. 14 and 15) and here the lateral uniformity has increased particularly in the case of the velocity profiles. This section coincides with a position equivalent to the centre of the turntable in the CERL Low Speed Wind Tunnel.

7. COMPARISON WITH THEORETICAL AND OTHER DATA

A theoretical assessment has been made in Appendix 1 of the extent to which the simulated boundary layer compares with a naturally grown boundary layer of similar

1.0

0.8

0.6

5 1

il.4

a.2

a

BARRIER USin: E.O. GENERATORS 60 3%$in APART: ‘LEGa’ 6A~~R~A~S AS R~uGH~~ESS

PLANE OF TRAVERSE. EQUiVALENT TO TURNTABLE L.E. TRAVERSES WITH SURFACE ROUGHNESS ADDED

BARRIER 0.75in: E.W. GENERATORS So 3in APXlf: ‘LEGD’ BASE8OARClS AS ROUGHNESS PLANE Of TRAYERSE + EQIJIVALUYT TO TURNTABLE LE.

TRAYERSES WITH SURFACE RQUGMESS AOOED

206 J. COUNIHAN

BARRlER0.875in: E.W. GENERATORS6°3inAPART PLANEOFTRAVERSEEQUlVALENTT0TURNTABLEL.E.

TRAVERSESWITHSURFACE ROUGtdESSADDED

1.0 r

0.8 1 0.6 t

h ’ s

0.4 -

0.2 -

0

GENR.1 - f SPAN!_ -l-

!;thPOWERLAW -

0.2!l 0.40 0.60 0.60 1.W

ii/u H*x

0 om2 O.DM 0866

mvnrx

FIG. &Velocity and Reynolds Stress profiles with 0.875 in. barrier and generators 3 in. apart, 18 in. from generators.

BARRlER0.675in:E.W.GENERATORS6°3in:APA~

PLANE0FTRAVERSEEQUlVALENTT0TURNTABLEL.E.

TRAVERSESWlTHSURFACEROUGHNES3ADDEO

GENR.'L -

SPANC -x-

1.0

0.8

0.6 I > I

>

0.4

0.2

-IO 0 5 m!6M,,10 15 10 0 5 10

mh,

FIG. 9. Turbulence profiles with 0.875 in. barrier and generators 3 in. apart, 18 in. from generators.

10 -

0.8 :

I = 0.6 !- 1 I

0.4 -

0.2 -

Simulating an Atmospheric Boundary Layer in a Wind Tunnel

ELLIPTIC WEDGE 6OV.G. SPACING fin: BARRIER HEIGHT O.E?Sin + MOD. A TRAVERSE AT lain FROM V.G.TRAlLlNG EDGE TRAVERSESWITHSURFACE ROUGHNESSADDED

HARRlS(FULLSCALE

207

FIG. 10. Velocity and Reynolds Stress profiles with O-875 in. barrier f Mod. A. and generators 3 in. apart, 18 in. from generators.

ELLIPTIC WEDGE60 V.G. fPAClNG 3in:BARRlER HEIGHT 0.87Sin * Y0D.A TRAVERSEATl5iaFRWV.G. TRAILINGEDGE TRAYERfEtWi~MRF~EROUMRSE~ADDW

0.8 -

FIG. 11. Turbulence prof%s with 0475 in. barrier+Mod. A. and generators 3 in. apart, 18 in. from generators.

208

1.5

/_ 0.8 r

x 1

0.6

0.4

0.2

0

EtCIPTJC #EDGE 6* V.G. SPACING 3in: BARRtEA HEIGHT Q.@Sis + MQQ. A TRAYERSES AT lia FROM V.G. TRAMHG EDGL T%AVE%~S i@TH SURFACE ~QG~~SS ADQEQ

1.0

0.73in FRQM. i 1,Wn FRQM.

HARRIS {FULL SCALE

T%R%ULE%C~~ %

1.0

0.8

0.6

I

0.4

0.1

0

1.0

il.8

0.6

_= .z

0.4

0.2

0


ELLIPTIC WEDGE 60 V.G. SPACING 3in: BARRIER HEIGHT 0.875in + MOD. A TRAVERSE 27 in FROM V.G. TRAILING EDGE TRAVERSES WITH SURFACE ROUGHNESS ADDED

0.2 0.4 0.6 0.8 1.0 a o.Ofl2 0.064 O.OC§

vu “AX im,,,

1.0

0.8

0.6

t 1

0.4

0.2

0

FIG. 14. Velocity and Reynolds Stress pro&s 27 in. from generators.

ELLIPTIC WEDGE 60 KG. SPACING 3in: BARRIER HEIGHT 0.87Sin + MOD. A TRAVERSE 2Z in FRDM V.G. TRAlLiNG EDGE TRAVERSES WITH SURFACE ~UG~ESS ADDED

n

1

PI

P

s 0.2

FIG. 15. Turbulence pro&s 27 in. from generators.

H A

210 J. COKJNIHAN

height. This comparison was made using the velocity defect law in conjunction with some of the measurements made in a natural rough wail boundary layer. The natural boundary layer was grown on a length of “Lego” base board in the boundary layer wind tunnel. It is seen that the theoretical predictions for the wall shear stress and velocity ratios compare reasonably well with those measured under the simulated conditions. The discrepancies present could be due to the fact that neither the natural nor simulated boundary layers seems to have reached a complete state of equilibrium. Such conditions are acceptable since it can be assumed that the atmospheric boundary layer, being constantly subjected to changes in terrain roughness, does not always have sufficient length in which to reach a state of equilibrium appropriate to a particular roughness. The ratio of @,/a) has also been estimated from the velocity defect law and has an approximate mean value of l/13 in comparison with l/30 for sand roughened pipes.

The results have also been compared with the full scale data of HARRIS (1966) which include measurements of velocity and turbulence variations with height. (FIGS. 10 and 12). The agreement between the measured velocity profiles is not as close as desirable but is acceptable bearing in mind that the surface roughness of both tests may not be exactly comparable.

1.0

0.8

0.6

9 c

0.4

0.2

0

~OOTHWALLEOURDARYLAY~R 1.0

0.8

0.2

0 0

TURBULENCE,%

I I 5.0 10.0 15.0

TURBULENCE.06

FIG. 16. Smooth and rough wall boundary layer turbulence ~stributions

A comparison with results from natural boundary layers (HINZE, 1959) (FIG. 16) with those of FIG. 12 shows that the turbulence profiles are typical of those of a rough wall boundary layer. Similar profiles are also presented in SCHLICHTING (1961). Reference was also made to DAVENPORT’S (1963) paper where results are summarked for pipe flow and natural wind experiments. The summarised data give a power law exponent of 117th for a surface shear stress coefficient of 0.0025 which is in agreement with the simulated boundary layer results.

Finally, the frequency spectra are compared with the theoretical spectra as proposed


by HARRIS (1963) and PANOFSKY and MCCORMICK (1960) (FIG. 13). The agreement here is acceptable and the maximum energy frequencies also agree with those obtained previously by ARMITT and COUNIHAN (1968).

8. ASSESSMENT OF THE SYSTEM AS A WORKING METHOD FOR BOUNDARY LAYER SIMULATION

The simulated atmospheric boundary layer in its present form does not possess any signifi~nt spanwise variations of the measured parameters. It is also sensibly constant in a streamwise direction over that section of a wind tunnel, which it is anti- cipated would be occupied by the model under test.

The attainment of a velocity profile approximating to the 117th Power Law was not the sine qua non of the simulation but was merely chosen as a convenient basis on which to build the present simulation. This protile, however, is typical of that obtained over rural terrain. It is assumed that the principles of the system adopted here can be developed to include simulation of flow over a wide range of conditions varying from built-up areas to flat open country.

A review of the present methods of boundary layer simulation (LAWSON, 1968) suggests that the methods available do not achieve correct representation of all of the flow properties simul~neously, and in many cases reproduction of a velocity profile only is achieved. It is suggested that this method reproduces all of the known important parameters to a degree of accuracy that makes the simulated boundary layer comparable to a naturally grown rough wall boundary layer. The total working- section length required for this simulation is 4-5 boundary layer heights.

9. CONCLUSIONS

It cm be concluded that : (a) This system provides a suitable method for simulating a neutral atmospheric boundary layer in a wind tunnel. (b) The boundary layer so produced is comparable to a rough wall boundary layer.

10. FUTURE WORIC

The future programme of work will include some additional frequency spectra measurements together with intermittency factor and correlation coefficient measurements.

Following this it is hoped to develop the system to simulate boundary layers appropriate to various degrees of terrain roughness.

Ac&~~i~~e~nts-~e work was carried out at the Central JZkctricity Research Laboratories, Leatherhead, and the paper is published by permission of the Central Electricity Generating Board. Acknowledgements are also due to Mr. D. J. W. RICHARDS and Dr. D. J. Moore for their helpful comments during preparation of this paper.

REFERENCES

m J. and C~UMRUN J. (1968) The simulation of the atmospheric boundary layer in a wind tunnel. Atmospheric Environment 2,49-71.

QUNIHAN 3. (1968) An improved method of simulating an atmospheric boundary layer. C.E.R.L. Rep. RDiL/R 1540.

212 J. COUNIHAN

DAVENPORT A. G. (1963) The relationship of wind structure to wind loading. Paper 2, Symposium 16, Int. Conf. on Wind effects on Buildings and Structures at NPL, H.M.S.O., London.

HARRIS R. I. (1963) ERA Rep. SPI/T14 (Unpublished). HARRIS R. I. (1966) ERA Rep. SPIjT2g (Unpublish~). H~NZE J, 0. (1959) Turbulence-An introduction to its Mechanism and Theory. McGraw-Hill, New

York. KLINE S. J., REYNOLDS W. C., SCHRAUB F. A. and RUNSTADLER P. W. (1967) The structure of tur-

bulent boundary layers. J. Fluid Mech. 30, (41, 741-773. LAWSON T. V. (1968) Methods of producing velocity proSles in wind tunneIs. Atmospheric Environ-

ment P&73-76. PAN~F~KY H, A. and McCo~r+nc~ R. A. (1960) The spectrum of vertical velocity near the s&face.

Q.Jl. R. met. Sot. 86,495-503. Scwcxnnw H. (1960) Bounakry layer theory. McGraw-Hill, New York. TOWNSEND A. A. (1957) The turbulent boundary layer. Proc. I.U.T.A.M. Symposium on Boundary

Luyer Research. Springer, Berlin. TR~TT~N D. J. (1967) Some new correlation measurements in a turbulent boundary layer J. Fluid

Mech. 28, (3), 439-462.

APPENDIX I

The velocity defect law for a flat plate equilibrium boundary layer is as follows:

where constants A and B are taken as 2+lO and 540 respectively. When 0 = 0, z = z.

u max = .4+B log,,(6/2,).

uz (A.21

The wall shear stress of a natural rough-wall boundary layer 6 in. thick, knowing the properties of this boundary iayer when it is @95 in. thick, can be predicted using equation (A.2).

Denoting the properties of the 6 in. boundary layer by the suflix (l), and those of the @95 in. boundary layer by the sufiix (2):

u urn,, max --- = B log(G,/S,). u,, u,, As& = 6 in. and & = O-95 in. equation (A.3) reduces to:

u ulll*, msx --- = 4.490. UT, UT,

Since the measured value of

(U*&U,,,)2 = (u’w’/uamsx)2 = 0.004

it follows that:

Urn,,, u,, = 4~49+(l@MO4)= 20-30

and

(A.31


(u’w’/UZ,& = O-0024.

This predicted value of the Reynolds stress coefficient agrees well with the measured values for the simulated boundary layer at the sections 18 in. and 27 in. downstream of the generators, namelY 0.0024 and OGO23 respectively.

The velocity ratios can be predicted for the 6 in. thick boundary layer using the data from the 0.95 in. thick natural rough-wall boundary layer :

From the above calculations,

(V&J = l-284.

Then, using equation (A.l), it follows that:

%&%_)_~(I_&)= B(log,, [~,/zJ -ho CW4 (A.41

Since the velocity ratios will be compared at conditions of

dl 82 -=-, Zl zz

it follows that equation (A.4) reduces to

(A.3

The predicted values of the velocity ratios, derived from equation (A.5) are compared below with those measured in the simulated boundary layer

Natural Predicted Simulated 0.95 in. thick 6 in. thick 6 in. thick

boundary layer boundary layer boundary layer

040 O-815 O-860 0.875 0.30 o-740 0*800 0840 0.20 O-650 0.730 O-805 o-10 0.515 O-620 0.730

The “Lego” baseboard z. can be predicted from the same data: From equation (A.2), for the natuallly grown boundary layer where:

6 = O-95 in. and U,,/Ut = 1582

it follows that ze = 0.004467 in. Since d = 0.0625 in., i.e. the roughness height:

z,/d = l/14

From equation (A.2), for the simulated boundary layer, where :

S = 6.00 in. and tJ,~lJ, = 20.0

214

ie follows that

J.CIO.INIHLN

and

z,ld = l/12-5.