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As described in the page on Settling Chambers and Contractions, a contraction in area of a stream reduces percentage variations in velocity over the cross section, by increasing the velocity without altering the total pressure. Since a screen or other uniform "hydrodynamic resistance" in a constant-area passage experiences a drag force and therefore reduces the total pressure of the flow passing through it without altering the average velocity locally, we expect velocity variations to be reduced in this case as well, because the drag force will be greater in regions where the velocity is higher than average, thus tending to equalize the total pressure over the cross-section. The analysis is more complicated than for a contraction.
A screen will in principle reduce the velocity defect in a turbulent boundary layer that passes through it. The boundary-layer edge remains on the same streamline but the profile becomes "fuller" (smaller shape parameter H) and the edge streamline is displaced slightly towards the surface. Screens which are not mounted taut can "belly" noticeably near the walls, disturbing the boundary layer. For a discussion of the effects of a screen on a boundary layer see the paper by Mehta, "A turbulent boundary layer perturbed by a screen", AIAA J., Vol. 23, p. 1335 (1985).
The simplified analysis in the section "Effect of a Screen on Mean Velocity", below, shows that the ratio of the excess velocity far downstream to the excess velocity far upstream is (2-K)/(2+K) where K is the screen pressure-drop coefficient. A more refined analysis by G.K. Batchelor, (Homogeneous Turbulence, Cambridge University Press, 1953: paperback in "Cambridge Science CLassics", 1982), treats a variation in mean velocity as a special case of turbulent flow, with infinitely long eddies, and takes account of the transverse velocities produced by the static-pressure disturbances. It predicts that the excess velocity will be eliminated for K approx. 2.8 rather than K = 2.
Pressure-drop Coefficients of ScreensR.C. Pankhurst & D.W. Holder, Wind-Tunnel Technique, Pitman, London, 1952 - an old but still valuable book - give the Borda-Carnot one-dimensional formula for screen pressure-drop coefficient K = (1 - To give the maximum reduction of turbulence, the aggregate pressure-drop coefficients of all the screens should be as high as possible: dense screens are sensitive to imperfections of weave and instabilities of flow through the pores, which cause variations of pressure-drop coefficient from point to point and can produce large variations in mean velocity.
In any case, the flow through a screen with a ratio of open area to total area less than about 0.58 (depending slightly on Reynolds number) suffers from a kind of instability. The jets coming through the holes in the screen stick together in irregular patterns by mutual entrainment, and actually produce flow nonuniformities of their own, triggered by otherwise-negligible imperfections of weave. Therefore screens of open-area ratio less than about 0.58 (pressure-drop coefficient greater than about 1.2 at typical settling-chamber speeds of a few m/s} should be avoided. See the paper by Mehta and Hoffmann, "Boundary layer two-dimensionality in wind tunnels," Experiments in Fluids, Vol. 5, p. 358 (1987) for a disscusion on the effects of screens on boundary layer two-dimensionality. Accordingly, several screens in series are needed to reduce turbulence to an acceptable level, and mean-velocity variations are therefore almost eliminated: those that do remain are largely the result of weaving imperfections or wrinkles in the last screen, or accumulated dirt. |
If a tunnel has no built-in filter, the screens (particularly the upstream-most screen) do the filtering. Not only does dirt buildup reduce the open-area ratio, perhaps below the 0.58 (approx. limit) but the dirt is densest near the bottom of the screen, leading to a vertical gradient of velocity in the test section. Therefore screens need cleaning at intervals, and some tunnels have a liquid-level manometer or other pressure transducer permanently installed to monitor the pressure drop across the first screen or the whole set of screens. A significant increase in the pressure drop indicates that the screens need cleaning.
Effect of a Screen on Mean VelocityThe 1953 analysis by G.K. Batchelor is a refinement of his earlier work "On the concept and properties of the idealized hydrodynamic resistance", Australian Council for Aeronautics Rept ACA-13 (1945) which neglected the refractive index of the screen. For present purposes the simpler 1945 analysis is adequate.
When a nonuniform flow in the x direction passes through a screen, the change in velocity can be attributed to the y-wise and z-wise vorticity created in the flow by the screen. The vorticity is convected downstream without change (except for viscous diffusion which we neglect). From this odd way of looking at the problem we can see that the x-component velocity induced by this trailing vorticity must be half as large at the screen as it is far downstream. This is because at the screen (x=0,say) the induced velocity depends on an integral of the vorticity from x=0 to downstream infinity, whereas "infinitely" far downstream the integrand is the same (the vorticity is unchanged) but the limits are in effect plus and minus infinity. (This is analogous to a basic result in the theory of induced drag of wings.)
Suppose that the nonuniformity is concentrated in a narrow stream tube as a small "top hat" increment u on the main stream speed U. With subscripts u, s and d for Upstream, Screen position and Downstream, the above argument says that uu - us = (uu - ud)/2 or simply us = (uu - ud)/2
Now if the screen has pressure-drop coefficient K (usual symbol) then the total-pressure drop in the non-uniform region is (1/2) There will be a small additional static-pressure perturbation in the region of the nonuniformity (to reduce uu to us by the time the flow arrives at the screen) but it will die out downstream. Therefore the final dynamic pressure drop in the nonuniform stream tube will be (1/2) (1/2) Simple algebra gives (ud / uu) = (2-K)/(2+K). This odd result that a screen with K = 2 eliminates (small) variations in velocity goes away when account is taken of the refractive index: then, ud/uu decreases more slowly with increasing K and reaches zero at K = 2.8 approx.
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)/ 
, i.e. based on the velocity through the
pores of the screen rather than the approach velocity U. Wieghardt's formula is based on data for Re between 60 and 600: it intersects the high-Re "Borda" formula at Re = 300 approx. For a given screen, either of the above conditions for elimination of disturbances in mean velocity could only be satisfied at one tunnel speed, and the arrangement of screens is usually decided by the need to reduce the turbulence generated in the return circuit.
K(U+us)2
whereas the total-pressure drop elsewhere is (1/2)