IMPERIAL COLLEGE OF SCIENCE AND TECHNOLOGY 

DEPARTMENT OF AERONAUTICS 

Prince Consort Road, London, SW7 2BY 

Semi-Annual Status Report on Research Grant No. NAGW-581 

"Vortex/Boundary Layer Interact ion" 

Period 1 September 1986 - 28 February 1987 

P. Bradshaw, Principal Investigator 

IhASA-CB-180255) VORTEX/ECU tifAFiY LAYER N87-19646 

IETERAcTICN Seaiannnal Statas lieport, 1 

zep. 1986 - 28 EEL lfe7 (IBperial Coli, of 

Science and TEchaffogy) 18 I: CSCL 20D Unclas 

G3/34 43484 
1 

Summarv 

The three-year contract period is nominally finished, but we have 

already requested a I1no-costl1 extension for up to six months, because 

the research assistant, Dr.A.D. Cutler, did not comnence work until 

October 1984. We anticipate producing a final report well within this 

extra six month period: the present document summarizes progress over 

the last six months, with a brief view of the whole year's 

achievements. Data acquisition, and most of the analysis, are 

complete for the first test case, in which the trailing vortex pair 

from a delta wing merges with a turbulent boundary layer on a flat 

plate downstream of the delta wing, and data acquisition for the 

second case, where the vortices remains clear of the boundary layer 

but induce large crossflow in it is virtually complete. 

Present position 

Samples of analysed data for the first test case were presented 

in the last semi-annual progress report, and will not be repeated 

here. The data for the first test case are all recorded on disc in 

standard format, and the final passes through our data-analysis and 

computer graphics routines will be made simultaneously for both test 

cases. Data analysis for the first test case, already completed, 

includes evaluation of all the terms in the turbulent kinetic energy 

balance and the cross stream turbulence diffusion term in the 

transport equation for the longitudinal vorticity. 
2 

As usual, we began our investigation of the second test case 

(longitudinal vortex above, but not merging with, a turbulent boundary 

layer) with flow visualization studies, and a selection of photographs 

will be presented in the final report. The results of quantitative 

data acquisition for the non-merging test case are shown in figures 1 

to 8 of the present report. Only half of each cross-sectional plane is 

shown. The label "delta wing high" refers to the position of the 

vortex generator for the second case, the first being "delta wing 

lowll: as before, all results are made dimensionless with the span of 

the delta wing, s = 267 mm (10.5 in.), and a reference velocity Uref 

equal to the nominal undisturbed flow speed over the plate, about 

16 m/s. 

Figure 1 shows contours of axial velocity and vectors of the 

secondary flow velocity at a short distance downstream of the leading 

edge of the plate. The regular geometrical pattern in the vortex core 

is simply an artefact of the relatively coarse measurement grid and 

the lack of smoothing in the contour-plotting routine: in the present 

test case we are not interested in the details of vortex core, because 

it never interacts with the boundary layer. Essentially, this 

figure defines the vortex: note (1) the fairly accurate symmetry about 

the centre plane z = 0 (ii) the small but significant defect in 

velocity in the non-rolled-up part of the wake of the delta wing: the 

vertical strip on the centreline which is the wake of the delta-wing 

support strut. In the core of the vortex, the axial velocity is high, 

although the total pressure reaches a minimum there. Measurements in 
3 

I 

the boundary layer region were made separately, the traverse gear with 

4 automated degrees of freedom being replaced by a smaller one with y, 

yaw and roll movements but no pitch movement, since pitch angles near 

the surface are, by definition, small. Figure 2 shows mean velocities 

for the boundary layer region, and it can be seen that crossflow 

angles at the outer edge of the boundary layer are less than about 8 

degrees. The boundary layer thickness at this x position is only 

about 1 cm or 0.05 times the span of the delta wing. Figure 3 shows 

(unsmoothed) contours of turbulent kinetic energy in the delta-wing 

wake. Figure 4 shows the turbulent kinetic energy in the boundary 

layer region for the same case. 

Figure 5 shows the primary and secondary velocity components in 

the boundary layer region far downstream, where the spanwise variation 

of the crossflow due to the vortex has resulted in a strong spanwise 

variation of boundary layer thickness and the formation of a ridge at 

about z/s = 1 (in the first, Vnerging", test case this ridge was more 

concentrated and was lifted out of the boundary layer by the vortex as 

a Iltongue" of fluid). Figure 6 shows the corresponding turbulent 

kinetic energy contours, which, as always, are distorted in roughly, 

but by no means exactly, the same way as the velocity contours. 

The outer part of the "boundary layer" is undoubtedly so 

distorted by the vortex that the conventional boundary-layer 

approximation (that streamwise and spanwise gradients of mean velocity 

shall be small compared to normal gradients) is not satisfied: 

however, we may still hope that the inner layer of the boundary layer 
4 

(y < 0.16, say) will obey the same simple scaling laws as in a 

conventional three-dimensional wing boundary layer. Figure 7 shows 

semi-logarithmic plots of the resultant velocity with the flow 

measured with a 3-hole pitot probe locally aligned in yaw. If it is 

assumed that these profiles follow the conventional "law of the wall" 

a skin-friction coefficient can be deduced: these values of skin 

friction has been used to produce the plots shown in figure 8. This 

is a partly, but not entirely, circular process: if the law of the 

wall does not hold, then the profiles in figure 7 would s mply 

intersect the logarithmic law (shown dotted) at the value of yt at 

which they were forced to match it: however, the profiles follow the 

logarithmic law over the whole of the expected range, between yt = 40 

and y/6 = 0.1. 

Figure 8 shows skin-friction vectors for both test cases: in 

figure 8(a), for the present test case, the spanwise variations of 

skin-friction magnitude cover a range of roughly 1.5 as in the first, 

merged-vortex, test case shown in figure 8(b): however, crossflow 

angles in the present case are barely half those in the first test 

case. 

Hot-wire data acquisition in the boundary layer region and in the 

vortex region has been completed for planes at x = 16, 34, 52, 61 and 

70 inches as have measurements of total pressure using the 3-hole 

pitot at x = 16, 34, 52 and 70 inches. As in the first test case, a 

group of three closely-spaced stations have been measured so that 

x-derivatives can be accurately evaluated for use in the transport 

equations. All that remains are a few check measurements. 
5 

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-, 

Other work in progress includes further flow-visualization of the 

delta-wing wake, as part of an undergraduate project. As mentioned in 

previous reports, the present work seems to be almost the first 

detailed investigation of the wake of a delta wing, and the flow has 

been found to be much more complicated than is implied by the use of 

simple concentrated-vortex models. We are also devoting considerable 

effort, at no cost to the present contract, to the development of 

graphical output routines for this and other three-dimensional 

experiments. like that of figure 1, in which there is no room 

for labels on each contour, are much easier to read if the contours 

are intelligently smoothed, and coloured or separated by colour 

infill. Work on graphics routines is being assisted by Professor J.K. 

Eaton of Stanford University, sabbatical visitor at Imperial College, 

January - June 1987. 

Plots 

Publications 

A review of work on vortex flows in the Principal Investigator's 

group has been written, by invitation, for presentation at the 

symposium on Perspectives in Turbulence Studies, Gottingen, May 1987. 

The present experiments are described, without full detail. The data 

have already appeared in our progress reports to NASA but a copy of 

the symposium paper is attached for information. 

i 
6 

Further plans 

We expect all data-taking and the final analysis of the data, 

including evaluation of terms in the transport equations,to be 

complete within about two months from now. The principal investigator 

regards the data taken by the research assistant as being of 

exceptionally high quality, forming a solid basis for further 

interpretation and calibration of turbulence models. Draft journal 

papers on both test cases should be complete before the research 

assistant leaves, and will form the basis of the final report which we 

expect to submit by the end of the six-month extension period in 

September 1987. 
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