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[Reprinted from THE AERONAUTICAL JOURNAL OF THE ROYAL AERONAUTICAL SOCIETY, November 1979] Technical Notes Design rules for small low speed wind tunnels R. D. MEHTA and P. BRADSHAW Technical Notes Design rules for small low speed wind tunnels 1. INTRODUCTION Even with today's computers, a wind tunnel is an essential tool in engineering, both for model tests and basic re- search. Since the 1930s, when the strong effect of free- stream turbulence on shear layers became apparent, emphasis has been laid on wind tunnels with low levels of turbulence and unsteadiness. Consequently most high performance wind tunnels were designed as closed-circuit types (Fig. 1(a)) to ensure a controlled return flow. How- ever, as will be seen below, it is possible with care to achieve high performance from an open-circuit tunnel, thus saving space and construction cost. 'Blower' tunnels (with the fan at entry to the tunnel, Fig. 1(b)) facilitate large changes in working section arrangements; to cope with the resulting large changes in operating conditions, a centrifugal fan is preferable to an axial one. For case of changing working sections the exit diffuser is often omitted from small blower tunnels, at the cost of a power factor greater than unity. This paper concentrates on the design of small blower tunnels but most of the infor- mation is applicable to wind tunnels in general. A large open-circuit tunnel would be of rather incon- venient dimensions, mainly in length. Also, an open- circuit tunnel requires enough free room around it so that the quality of the return flow is not affected signifi- cantly (remember that an open-circuit tunnel in a room is really a closed-circuit tunnel with a poorly-designed re- turn leg). The choice may also be restricted by the maxi- mum available blower size. A working section Re per metre of more than about 3x 10º (a speed of about 40 ms-?) is rare in blower tunnels of whatever size, and commercial blowers capable of producing such a speed in a section more than about 1 mê in area are also rare. The main advantage of open-circuit tunnels is in the saving of space and cost. They also suffer less from temperature changes (mainly because room volume 5 tunnel volume) and the performance of a fan fitted at the upstream end is not affected by disturbed flow from the working section. One disadvantage of any open- circuit tunnel with an exit diffuser is that the pressure is always less than atmospheric and so spurious jets issue from holes left unpatched, although this can be remedied by obstructing the tunnel outlet and creating an over- pressure in the working section. The main advantage of a centrifugal blower, as distinct from an axial fan, is that it performs well over a large range of loads (the whole blade being at the same incidence and hence operating at the same lift coefficient). The only advantage of a suction tunnel, with a centrifugal or axial fan at exit, is the dubious one that air coming from the tunnel room may be less disturbed than that coming from a fan. It is difficult and unwise to lay down firm design rules mainly because of the wide variety of requirements and especially the wide variety of working-section configura- tions. An attempt is made here to present design guide- Aeronsutical Journal November 1979 Mehta and Bradshaw R. D. MEHTA and P. BRADSHAW lines for the main components of a wind tunnel—the fan, wide-angle diffuser, corner vanes, settling chamber, con- traction and exit diffuser (Fig. 1)—based on data from successful designs and some original experiments. For details of the data correlations see Mehta (1977) and for complete details of the experiments and design procedure see Mehta (1978). 2. FANS 2.1. Axial flow fans The usual arrangement in a closed-circuit tunnel is a stator ('pre-rotation vanes') upstream of the rotor (the fan proper), designed so that the swirl at exit is zero. In the case of an open-circuit tunnel, swirl present in the flow out of the fan may be dissipated before the flow reaches the intake, but a remaining advantage of pre- rotation vanes is that the flow velocity relative to the fan blades is larger than if the stator is absent or located downstream of the fan. 24.1. Fan solidity The design procedure outlined by Bradshaw and Pank- hurst (1964) is still an adequate guide. The only serious problem found in fan design that is not found in the design of wings for low-speed aircraft is the interference between the flow fields of the blades. This interference depends mainly on the “solidity”, the ratio of blade chord to the gap between blades (measured around the cireum- ference). Providing that the solidity is less than unity approximately, interference is small enough to be treated as a small correction to the performance of an isolated aerofoil; for higher solidities the flow cannot be accur- ately related to that round an isolated aerofoil, and data for “cascades' (rows of aerofoils arranged in the same manner as corner vanes) must be used instead. The solidity varies with radius, and in order to use the same The Authors: Dr. R. D. Mehta and Professor P. Bradshaw, BA, Department of Aeronautics, Imperial College of Science and Technology, London. Paper No 718. 443 vibration mountings and connected to me tunnel with a flexible coupling to reduce vibration. Double-inlet blowers (air entering the impeller from both sides) tend to produce a uniformly inclined flow (without a vortex) which takes a longer distance to re- attach to the bottom wall downstream of the tongue, One should therefore be more conservative in' designing wide-angle difíusers for double-inlet blowers. On the whole, commercially available single-inlet centrifugal blowers with backward-facing impellers are adequate for driving blower tunnels. Once the maximum required fan static pressure and volume fow rate have been estimated, the makers' per- formance charts can be consulted. Optimisation between the efficiency, rpm and required power leads to the blower choice (see section 10). 3. SCREENS Wind tunnel screens are normally made of metal wires interwoven to form square or rectangular meshes. Screens woven from nylon or polyester threads are also now being used when the wind loads are not expected to be very high (UTS of nylon = 70, steel = 1100, bronze =700-1100 MNm* and E of nylon P 3, steel=-200, bronze — [00 GNm-?. The action of the gauze is described in terms of two parameters: the pressure drop coefficient, K=f. (8, R., 89) and the deflection coefficient, a=F: (BB, K, 8), where £ is the screen open-area ratio and 6 is the flow incidence angle, measured from the normal to the screen. 3.1. Main effects for detailed explanations see Mehta 1978) Screens make the flow velocity profiles more uniform by imposing a static pressure drop proportional to (speed) and thus reduce the boundary layer thickness so that the ability to withstand a given pressure gradient is increased. A screen with a pressure drop coefficient of about 2 removes nearly all variation in the longitudinal mean velocity. A screen also refracts the incident flow towards the local normal and reduces the turbulence intensity in the whole flow-fleld. For a given open-area ratio, it is better to have a smaller mesh for the reduction of pre-existing turbulence. Plastic screens tend to yield à more uniform flow beyond the boundary layer edge, mainly due to the weaving properties, and produce an “overshoot' in the velocity profile near the edge, mainly caused by screen deflection angle which is a maximum at the wall. In terms of tackling a given pressure gradient or avoiding separation, this overshoot could be bencficial. 3.2. Open-area ratio (8) Metal screens with very low /3 (0-3) also produce an overshoot but this is caused by streamiine inclination near the boundary layer edge. Low 8 (<0:57) screens also produce instabilities resulting from a random cealition of eMadial-vana biouer + Bacaware sorotol lower é Becxard Sotypo biouor Figure 2. Different Impeller types used in centrifugal blowers Aeronamical Journal November 1979 Mehta and Bradshaw jets and presumably amalgamating to form longitudinal vortices which persist through the contraction. The coali- tion process is enhanced by variations in f (ie. non- uniform weave) and by irregularities in the sereen shape (ie, wrinkles). It is therefore essential to inspect and clean wind tunnel screens regularly 3.3. Determination of K (ratio of pressure drop to dynamic pressure) Although there is no wholly satisfactory method, Wicg- hardts (1953) formula (K=6:5 [1- 8/8] [Ud/ Bv"), where d is wire diameter, predicts the right trend; K decreases with increasing speed up to about Ud/fBv= 600, after which it is independent of Re. Collar's (1939) formula (K=0:9(1- 8/9) usually over-estimates K in the high Re limit. One needs to be more careful in pre- dicting K-values for plastic screens since, K=f(8, Ro 8... coplanarity. o). where Q is angle of screen to incident flow. For 60 use Ks=K cos" 6, with m=1-0 for screens with [0-6 and mm 1-4 for 8--0:3, 3.4. Determination of a ratio of outlet angle to inlet angle) For a the form: B v (1+K) where 4, B are empirical constants, is a better fit than the generally accepted form: 11 v (1+K) Note that the refractive index of a screen (ju) defined as in opties is equal to 1/a for small 6. For larger 6 use Q=A + = 8, - Pole-ro au= q tan (tan O Be [ “à 3] E FO) €, D, E and F are empirical constants. Values suggested for the empirical constants by some limited experiments (Mehta, 1978) are: 4=0:66, B= 0:31, C=0-68, D=0:62, 1:0, P=1+5: A more complete analysis of the flow through screens can be found in Mehta (1978). 4. DIFFUSERS The flow through a diffuser depends on its geometry defined by the area ratio (4), diffuser angle (29), wall contour and diffuser cross-sectional shapes. Other para- meters like the initial conditions, boundary layer control method and the presence of separation could also affect the flow thus making it very difficult to predict. Almost all knowledge acquired about diffusers is empirical. There are two main types: 4.1. Exit diffusers These are fitted downstream of the working sections and have gentle expansions with a diffuser included angle usually not exceeding 5º (for best flow steadiness, although best pressure recovery is achieved at about 10º) and an area ratio not exceeding about 2-5, It is import- ant to have a reasonable degree of flow steadiness in the exit diffuser, since otherwise the pressure recovery tends to fluctuate with time, and, therefore, so does the tunnel speed if the input power is nearly constant. The design “as of these diffusers is well catered for by existing methods isee Cockrell and Markland, 1974). 4.2. Wide-angle difftuser This type is normally installed between the blower and settling chamber or between the fourth corner and settling chamber of a closed-circuit tunnel; the cross-sectional area increases so rapidly that separation can be avoided only by boundary layer control. A wide-angle diffuser is a means of reducing the length for a given area ratio rather than effecting a pressure recovery: generally the net pressure rise through a screened wide-angle diffuser is negative but small. 42.1. Boundary layer control methods The most popular means of boundary layer control is by installing gauze screens. A screen, besides removing the direct effects of layer growth and incipient separa- tion, gives the layer a new lease of life. In a wide-angle difiuser it is better to use several screens of relatively small K (less than about 1-5) because increasing K at one station has little effect on the skin friction at a station much further downstream. Other types of boundary layer control methods include splitters, suction slots, trapped vortices, vortex generators and vanes and may be preferable in diffusers with very severe geometries (ADS, 2050). For a review see Mehta (1977. 42.2. Design charts The four most important parameters in a wide-angle difluser are 4, 26, K and n, where m is the number of screens within the diffuser—this includes the screens in- stalled at the inlet and outlet, Data were collected from over a hundred vwide-angle diffuser designs, mostly “successful” (no separation, and uniform outlet flow with an acceptable turbulence level), and charts were plotted for relevant parameters, from which design rules have been derived. In Fig. 3, 4 is plotted against 28; the curves enclosing successful configurations have an ap- proximately hyperbolic shape. As n increases, the vertex moves to a higher value of 26 and, to a lesser extent, to a higher value of , thus implying a stronger dependence of required n on 20. Figure 4 is a plot of the sum of pressure drop coefficients of all the screens, Km=5 (4p/q), vs 4. The straight line EF (A =1-14 Km + 1"0) included the maximum number of successful configura- tions. 4.23. Overall design procedure For a diffuser design to operate successfully it must lie to the left of the relevant curve in Fig. 3, giving the mini- mum number of screens required in the diffuser, and 4 Satresatur ein , cessa 7 x E WE dE E Figure 3. Design boundaries for diffusers with screens. 446 Ksum Successful Operation [he Kyo Ci E DI TILSETE SNI BA A Figure 4. Overall pressure drop coefficient requirements for a diffuser with screens. must be less than (1:14 Km + 1-0), giving the minimum required overall pressure drop cocfficient. A diffuser con- figuration satisfying both these curves should perform successfully provided that certain other design factors are kept in mind: () Inlet conditions: Thin boundary layers and steady flow at the inlet are obviously beneficial. (ii) Screen Positioning: The basic rule is to place screens where the difuser wall angle changes suddenly, since these are the points where the flow is most likely to separate. In diffusers where no obvious location is indicated screens should be equally spaced, remem- bering that a screen at the diffuser entry (with a relatively high resistance) is desirable becanse the - angle changes suddenly there. (iii) Wall shape: The number of screens required in a diffuser could well be reduced, and the efficiency increased, by employing curved walls. Potential flow methods are sometimes used to determine wall shapes but it is often easier to design wall shapes by eye. Straight-walled diffusers (often with curved screens) are, however, often employed, because they are easier and cheaper to constrnct. (iv) Screen shape: Tt is an advantage for the screen to intersect the diverging walls and streamlines at right angles, so that the refraction of the flow by the screens does not itself induce separation. Curved screens can be held in metal frames pressed into circular ares and lined with wooden strips so that the gauze may be firmly embedded between two frames. It could be more difficult to dish the more flexible plastic screens (see section 3) which may also tend to fuíter. Another alternative is to use a plane, “variable-K" screen comprising of one screen con- centrically superimposed on another. Mehta and Bradshow Aeronautical Journal November 1979 7.3. Installation of components Sereens are normally tacked onto wooden frames. More care is necessary when tacking on plastic screens since these, being more flexible, tend to wrinkle along the lines of tension. The honeycomb is usually just push-fitted into its own frame. A useful arrangement for small tunnels is to rest the wide-angle diffuser, screen frames and con- traction on a table and clamp them by drawbolts, so that frames can be withdrawn easily. On larger tunnels, it is advisable to equip the setiling chamber (and wide-angle diffuser) components with castors for ease of removal. Even in tunneis made of metal or concrete, the scrcens are normally installed in separate frames which can be withdrawn from the tunnel for cleaning or replacement. 8. CONTRACTIONS A contraction : (i) Increases the mean velocity which allows the honey- comb and screens to be placed in a low speed region, thus reducing pressure losses. (ii) Reduces both mean and fluctuating velocity variations to a smaller fraction of the average velocity. The most important single parameter in determining these effects is c, the contraction ratio. The factors of reduction, as derived by Batchelor (1970) for c>1, are: U-component mean velocity: 1/c V or W-component mean velocity: y/c “u-component rms intensity: 1/2c (3 (Ind — pe = or w component rms intensity: -(30)'*/2. (The factor of reduction of percentage velocity variation is given by multiplying the above expressions by 100/c). The design of à contraction centres on the production of a uniform and steady stream at its outlet, and requires the avoidance of flow separation. Two more desirable criteria include minimum exit boundary layer thickness and minimum contraction length. A design satisfying all criteria will be such that separation is just avoided and the exit non-uniformity is equal to the maximum tolerable level for a given application (typically +4+% velocity variation outside the boundary layers). 8.1. Contraction lengths It is always possible to avoid separation in the contraction by making it very long, but this results in an increase of tunnel length, cost and exit boundary layer thickness. 8.2. Contraction ratio Since the power factor contribution of sereens in the settling chamber varies as 1/c*, large contraction ratios are advantageous. But large contraction ratios mean higher construction and running costs besides possible problems of noise and separation near the ends. Therefore, contraction ratios between about 6 and 9 are normally used, at least for the smaller tunnels. 8.3. Cross-sectional shape In any contraction with a non-circular cross-section, the flow near the walls tends to migrate laterally, especially near corners of a polygonal section. In any case the boundary layers near the corners will be more liable to separate. However, recent investigations (Mehta, 1978) show that this does not cause a problem in a well-designed square contraction; the effect of boundary layer migration in a contraction whose cross-sectional aspect ratio changes along its lengih can be reduced by adding small 45º 448 corner fillets, but rapid termination of these in the working section must be avoided. Two-dimensional contractions are sometimes preferred on tunnels used for boundary layer studies, where the working section is wide but shallow. However, if the boundary layers are thick, the plane walls tend to develop strong secondary flows. Also, 2-D contractions require about 25% more length to attain the same uniformity of pressure distribution as axisymmetric ones. 8.4. Wall shape 8.4.1. Theoretical design The solution of the Laplace equation or the Stokes- Beltrami equation is relatively easy for simple geometries and many analytical solutions have been derived. With the onset of computers many numerical schemes have also been proposed. For a review see Mehta (1978). There is no wholly satisfactory method of theoretical wall shape design, as distinct from analysis. The applica- tion of all these methods requires the establishment of some criteria and then the application of trial-and-error techniques for which limited guidance is given. 84.2. Design by eye Designers have often used the rather unscientific method of design by cye. Note that the actual form of a con- traction contour is not very important except near the ends, and that smoothness in contour shape is much more important than exact dimensions. In general the wall radii of curvature should be less at the narrow end and each end must join the parallel sections so smoothly that at least the first and second derivatives of the curve are zero (or very small) at the ends. 9. WORKING SECTIONS Working section design is totally dependent on the re- quirements of the individual experimenter. Blower tunneis are more flexible in accepting a variety of working sections (with and without exit diffusers). The flow out of a contraction often takes a distance equivalent to about 0-5 diameters before the non- uniformities are reduced below am acceptable level. Also, if a turbulence grid is installed, it may take up to 10-15 mesh lengths before a homogencous flow is obtained. These requirements often fix the minimum length of the working section. The streamwise pressure gradient is best controlled by installing tapered fillets. It is advisable to mount removable side panels on pinned hinges on large working sections which makes their 'single-handed” removal easier and safer. Drag forces, being proportional to (velocity), change by twice as large a fraction as the mean velocity; lift forces change because of the change in mean velocity and because of the influence of tunnel walls on the efective angle of incidence. Lift interference on a complete air- craft model in a rectangular-section tunnel is minimised if the ratio of working section breadth to height is 2 (with model span less than three-quarters of the breadth) so most general purpose aerospace tunnels are made with approximately this aspect ratio. However tunnels for measurements in boundary layers, growing on the tunnel floor say, have an optimum breadth-to-height ratio of about five since all that is necessary is that a reasonable thickness of irrotational flow shall remain between the roof and floor boundary layers at the end of the test section (a diffuser with such a non-uniform entry flow would not be very efficient). Tunnels for testing building complexes or natural terrain at model scale can also have a large breadth/height ratio; conversely, tunnels for test- ing isolated tower buildings or smokestacks can have a Mehta and Bradshaw Aeronautica! Journal November 1979 breadth-to-height ratio less than unity, although the ratio of model breadth to tunnel breadth must still be kept small to minimise interference. 10. ESTIMATICN OF TUNNEL POWER FACTOR Having decided the size and configuration of a wind tunnel, the next design step is to estimate the tunnel power factor, À (equal to H/kp,U/A,, where H is the shaft input power and subscript o refers to working sec- tion conditions) so that the fan and drive unit can be selected, Tt is difficult, but in fact not essential, to estimate the power factor very accurately: adequate extra power must be installed to cope with a variety of model or working section configurations, not known in advance. The pressure losses in a wind tunnel are due to diffuser losses, resistive components such as screens, and friction on the tunnel walls. The total pressure loss due to each component can be estimated separately, and then summed and divided by the blower efficiency m, typically 0:8, to give the tunnel power factor. Typical values for a tunnel similar to that shown in Fig. 1(b) are given below (7) Losses due to skin friction. 4) Í f Crjdx, where S is the duct local perimeter and remember- ing that the area ratio is the reciprocal of the velocity ratio. It is normally only necessary to estimate skin friction losses in the working section (A/A,=1). Those in the diffusers are normally accounted for in the efficiency and the other components do not contribute significantly. Therefore, AA CjSL/A, where L is the work- ing section length. Typical value: mAh — 0:07, assuming C,— 0-003. (if) Losses due to screens, honeycomb and corner-vanes. E ES nar [É] . So for a tunnel with four screens (two in the wide- angle diffuser with A/4,=4 and 6 respectively) each with K=1-5 (for U=5-10 m/5), and a honey- comb with K=0-5 we have, taking c=9, typical value: nAA,—0-18 (the screen at A/A,=4 contri- butes 0-094). (Hi) Loss of total head in the exit diffuser. [4)]. where mp is the difiuser efficiency. This is a loss due to the inefficiency of the diffuser in transforming kinetic energy into “pressure energy” and is caused by boundary layer growth and non-uniformity of the flow. The efficiency of a wide-angle diffuser with screens is generally negative but Ap is small. For a conical diffuser with A-2:5 and 20--5º, Cockrell and Markland (1974) suggest np=0"8, but this may be lower for diffusers with rectangular cross-sections, typical value: nAA,—0:25 for qo =0"7 and 4=2-5. n4h=0 mp) [ ha Aeronauticol Journal November 1979 Mehta and Bradshaw (iv) Loss of total head at the exit of an open-circuit tunnel. Im an open-circuit tunnel, the amount of kinetic energy lost at the exit and dissipated into heat adds to the total losses. / [=1 for blower tunnels with no exit diffuser), typical value: nAM=0-16 for 4=2-5 Therefore the estimated overall tunnel power factor, = Tam ime<0825 for the (oii a an exit diffuser), taking 7 =0:8. tunnel considered Once the tunnel power factor has been estimated and the required fan static pressure rise determined, one can set about the selection of the optimum fan size. The dynamic pressure rise through a blower is usually ignored and can be thought of as a safety factor in the calculations. The fan outlet fow will be least turbulent when the fan is operating near maximum efficiency. Fan efficiency is a function of the dimensionless flow rate; the pressure rise coefficient is a (weak) function of the dimensionless flow rate also, so that requiring maximum efficiency specifies both dimensionless flow rate and pressure rise coeficient. So for a given required flow rate and pres- sure rise, two equations are obtained which can be solved to give the fan size and optimum operating rpm. In practice the manufacturer's performance charts should be searched for a fan size (and rpm) giving near maxi- mum efficiency for the required flow rate and pressure rise. ACKNOWLEDGMENTS We are grateful to R. W. F. Gould, National Maritime Institute, M. C. Welsh, CSIRO Melbourne, and a refere, for helpful comments on a draft of this paper. REFERENCES BatcHELOR, G. K. The theory of homogeneous turbulence. Cambridge University Press, pp 55-75, 1970. BraDSHaw, P. and PANKHURST, R. C. The design of low-speed wind tumnels. Prog Aerospace Sci, Vol 5, p 1, 1964. CockrELL, D. J. and MARKLAND, E. Diffuser behavionr—a review of past experimental work-relevant today. Aircr Engng, Vol ã6, p 16 (reprint of Vol 35, p 286), 1974. Coixar, À. R. The eifect of a gauze on the velocity distri- bution in a uniform duct. ARCR & M 1867, 1939, Ermsmaus, R, and NAUDASCHER, E, Der Niedergeschwindig- skeits-windkanal des Instituts Fr Fydromechanik an der Universitát Karlsruhe, Zeitschrift fúr Flugwissenschaften und Weltraumjorschung, Vol 1, p 419, 1977. KLINE, S. 1. Moore, C. À. and CocuranE, D. L. Wide-angle difiusers of high performance and difiuser flow mech- anisms, J dero Sei, Vol 24, p 469, 1957, Lorrmke, R. 1. and NaGig, H. M. Control of free-stream tur- bulence by means of honeycombs: A balance between sup- pression and generation. ASME J Finids Enee, Vol 981, p 342, Lumzey, J. L. and McMAzoN, J. F. Reducing water tunnel turbulence by means of a honeycomb. ASME 1 Basic Engg, Vol 89D, p 764, 1967. META, R. D. The aerodynamic design of blower tunels with wide-angle difusers. Prog Aerospace Sei, Vol 18, p 59, 1977. Mega, R. D. Aspects of the design and performence of blower tunnel components. PhD Thesis, Imperial College, University of London, 1978. ScHuBauER, G. B. and SPANGENBERG, W. G. Effect of screens in wide-angle diftusers. NACA TN-1610. 1948. Sourre, H. B, and Hocc, H. Diffuser-resistance combinations in gelation to ind tumnel desigo. RÃE Report No Aero 19535, WrgHarDT, K, E. G. On the resistance of screens. Aero Quarterly, Vol 4 p 186, 1953. 449 
