flow through screens
TRANSCRIPT
Ann. Rev. Fluid Mech. 1978. 10: 247-66 Copyright © 1978 by Annual Reviews Inc. All rights reserved
FLOW THROUGH SCREENS
E. M. Laws and J. L. Livesey Department of Aeronautical and Mechanical Engineering, University of Salford,
Salford M5 4WT, England
INTRODUCTION
:-:8123
Control of the velocity distribution of a fluid flow is a fundamental problem In engineering fluid mechanics. The possible consequences for the operation and
efficiency of downstream components need no emphasis here. Ability to control the flow is also necessary in component testing where, for results to be meaningful, test conditions must reproduce the composite flow situation.
A screen may be used in both these operational modes to remove or create time-mean velocity nonuniformities, change the flow direction, and reduce or increase the scale and intensity of turbulence in a controlled manner.
A screen may be thought of as any distributed resistance that effects a change in flow direction and a reduction in pressure. Common examples of screens for aerodynamic applications are arrays of parallel rods, honeycombs, perforated plates, and wire-gauze screens. This review focusses on the wire-gauze screen, with brief consideration of other types of screen.
A survey of the available literature on the topic of flow through screens divides roughly into three categories:
CATEGORY I Investigations concerned principally with characterizing the flow properties of the screen.
CATEGORY 2 Investigations concerned with the effect of a screen on time-mean velocity distributions. In engineering applications there are two seemingly contradictory main objectives: the production of a uniform profile from arbitrary and nonuniform conditions upstream of the screen (e.g. in wind-tunnel applications) and the production of a specified velocity profile from arbitrary, though often uniform, conditions upstream of the screen (e.g. in simulating test conditions).
CATEGORY 3 Investigations concerned with the turbulence distribution downstream of gauze screens. This is the combination of three distinct turbulence profiles. The first is due to the passage of turbulence upstream of the screen through the screen, the second is due to turbulence generated by the screen itself, and the third is shear-generated turbulence produced by nonuniformities in the generated timemean profile as it decays. The interrelation ami interaction between these three
247 0066-4189/78/0115-0247$01.00
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248 LA WS & LIVESEY
effects leads to complications in flow prediction. Paradoxically, until simulation techniques are so refined that mean profile and turbulence structure can virtually be created independently, a concise experimental program covering all aspects of this category may be impossible to envisage.
In this review the literature covering these three categories is discussed. Because of the volume of literature involved no attempt is made to give au exhaustive survey; however, the reader is directed to the most pertinent sources df information wherever possible.
CATEGORY 1: SCREEN PROPERTIES
The weaving process of gauze manufacture is likely to contribute to inherent variations in screen dimensions that could lead to significant downstream effects, particularly for fine-mesh screens (Simmons & Cowdrey 1945). The screen in situ may also be liable to contamination from dust and dirt, which could also contribute to departurc from uniformity. Advances madc in thc analytical treatmcnt of flow through screens usually assume that the screen dimensions are uniform; however, Jackson (1972) has considered the effect of non uniformities in mesh sizes on screen coefficients.
In a sense the flow through the screen is modelled on actuator-sheet theory, the presence of the screen being regarded as a finite discontinuity in the flow. How far such a simple model can describe the flow through what is essentially, from the aerodynamic point of view, a complicated distribution of bluff bodies, is open to some doubt. Nevertheless, it is on the basis of this assumption that most previous work is developed.
Since the momentum normal to the screen is conserved, the drag D on the screen is due solely to the pressure loss through each orifice. Considering the flow through a single gauze element (Figure I), the nondimensional drag coefficient,
REGION I
Figure 1
REGION 2
Coordinate system for flow through gauze element.
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FLOW THROUGH SCREENS 249
CD, is given by D/t.pw2S, where w is the undisturbed velocity and S a typical gauze area.
For wire-gauze screens specified by wire diameter d and wire spacing I, the area usually taken as S i� the solid area of the mesh (1-f3)lz, where {3, the porosity, is defined as the ratio of open to total gauze area. For square-mesh wire screens fJ = (l-d/l)z. Pinker & Herbert (1967) have shown that fJ underestimates the effective area of the gauze and suggest a sinusoidal porosity, fJ*, based on the assumption that each wire forms a sine wave. Historically, however, fJ has been adopted as the describing parameter; therefore
CD = (Pz-pd/tpwi(! -f3). The resistance (or pressure loss) coefficient Ko at approach angle 8 is defined by
KO=CD(1-fJ);
thus
Ke = Ko cosz 8,
where Ko is the resistance coefficient at normal incidence (8 = 0). Some authors refer to a deflection force coefficient Fe, which is analogous to Ko, such that the tangential force component is given by tpuIFo; thus
jpuIFo = PUI cos 8(Ul sin 8 - Uz sin cp).
Hence,
Fo = 2cos o sec cpsin (e - cp).
The deflection coefficient B is defined by B = 1 -uzlu 1, so that B = sin (8 - cp)/ sin 0 cos cp.
Experimental evidence suggests that cpl8 tends to a finite limit, ex, as 8 tends to zero (Taylor & Batchelor 1949) and also that a flow approaching at an angle 8 will be deflected towards the normal to the screen on passing through the screen. Thus 0 � ex � 1.
For small angles of e, therefore,
B = 1 - ex = F 0128 and 0 � B � 1.
On the basis of an actuator sheet the boundary conditions at the screen are described in terms of the resistance and deflection coefficients of the mesh, and therefore it is important that these parameters be capable of accurate prediction or measurement.
Resistance Coefficient
Most previous work, which falls in Category 1, has concentrated on the behavior of Ko. This may be because of early engineering interest in losses and in damping screens in which K 0 is the dominant parameter, or possibly because it was considered relatively easy to measure; however, see Morgan (1959) and Pinker & Herbert (1967).
It is well documented that Ko is a function of porosity, Reynolds number, and
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250 LA WS & LIVESEY
Mach number. The reader is directed to the paper by Pinker & Herbert (1967), who reviewed the literature on this topic. Many of the suggested correlations of earlier workers (e.g. Glauert et al 1933, Collar 1939, Taylor & Davies 1944) have been compared with their own detailed experimental results; these correlations are based on a variety of flow models, discussions of which, for compactness, cannot be included in this review.
The variation of Ku(fJ,Rd,M) is such that for incompressible flow (strictly zero Mach number) Ko decreases with Rd (Reynolds number based on the gauze-wire diameter and approach-flow velocity) until Rd> 250, after which point Ku is a function of porosity only.
The optimum expression for this functional relationship has been found by Pinker & Herbert (1967) and Reynolds (1969) to be
Ku = 0.52(1-f32)/fV
The fact that Ko would also vary with Reynolds number was first suggested by Collar (1939). The resistance coefficient was shown to decrease with Reynolds number, until a limiting value was attained. Annand (1953), from data due to Simmons & Cowdrey (1945) and Cornell (1958), suggested that a further increase in Reynolds number should result in an increase in K u; however, Pinker & Herbert (1967) doubted the evidence for this conclusion.
Pinker & Herbert (1967) carried out a very detailed experimental program in which the variation of Ko for a range of Reynolds number at fixed Mach numbers was obtained. They observed no tendency for Ku to subsequently increase with Reynolds number, and after reviewing the literature (e.g. Taylor & Davies 1944, Jonas 1957 and Davis 1957) concluded that the optimum description for the variation of Ko with Reynolds number was given by
Ko = At(Re)(I-f32)jfJ2.
Figure 2 shows the dependence of AI on Reynolds number.
0·7
0·6
0·4
0·3
,
� ........ � � 0
2 3 4
Ia _v 0 1-' 0 o 0"
0
2 34 R�/ft
Figure 2 Variation of At with Reynolds number.
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FLOW THROUGH SCREENS 251
At higher Mach numbers the resistance coefficient increases at a rate strongly dependent on the screen porosity until choking occurs. The choking Mach number, Meh, was shown by Adler (1946) to satisfy the simple one-dimensional expectation
fJ = A*/A = f(Mch).
Pinker & Herbert (1967) showed that a more accurate determination of Mch was given if [J* replaced [J, which suggests that [J* is a more practical parametric description. They suggested a method of extrapolating data obtained for incompressible flow to higher Mach numbers.
The conclusion that can be drawn . from the literature is that the resistance coefficient can be evaluated with a fair degree of accuracy (within the limitations previously mentioned). However, for high accuracy it may still be necessary to determine the value experimentally.
For perforated plates information may be found in Baines & Peterson (1951), Rice (1954), and Budoff & Zorumski (1971).
Deflection C oe./Jicient
The evaluation of the deflection coefficient presents considerable difficulties, which arise because the screen is not plane as assumed but actually rippled. This results in highly irregular variations in local transverse velocity that may defy any analytical treatment. The rippled nature of the gauze makes the deflection coefficient difficult to measure and possibly accounts for the scatter in experimental results. Gauze anisotropy is also likely to affect measurement of the deflection coefficient since a definite variation is noted when flow incidence to the mesh is maintained constant and the gauze orientation to the flow varied.
A connection between the resistance and deflection coefficients has been noted.
However, though both theoretical and semi-empirical attempts have been made to establish the exact form of this relationship, no entirely satisfactory form has been established.
Taylor & Batchelor (1949), Schubauer et al (1950), Elder (1959), and more recently Reynolds (1969) and Gibbings (1973) have all developed correlations for the relationship between Ke and B. The basis of these various flow models cannot be included here, nor can individual comparisons with experimental data.
Observations from such a comparison indicate that the expression due to Gibbings (1973) gives the best overall agreement, particularly for Ko < 3. Since in most aerodynamic applications screens with resistance coefficients well below three will be used, this suggested expression should yield reasonably accurate values for general applications.
If an experimental evaluation is indicated care must be taken and the screen orientation carefully controlled.
Flow Instability Downstream of Screens
Corrsin (1944), Baines & Peterson (1951), Morgan (1960), Bradshaw (1964), and Patel (1966) all describe a flow instability that occurs downstream of low-porosity screens.
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Baines & Peterson (1951) observed the instability by noting appreciable and unsteady differences between measured and expected downstream profiles. They attributed this to local minute variations in wire diameter and spacing producing significant local variations in velocity and pressure so that the jet flow through each element of the screen could either coalesce or diverge with its neighbor in a fairly random manner. This effect occurred only in screens with fJ < 0.5.
Both Morgan (1960) and Bradshaw (1964) suggest that in this jet coalescence it is possible for the jets not to emerge orthogonal to the screen. This, as illustrated in Bradshaw (1963), gives rise to a pattern of trailing vortices of various sizes in the downstream flow. These vortices can persist for appreciable distances downstream of the screen and can have a significant effect on downstream flow parameters, causing a spanwise variation in skin-friction coefficient. Bradshaw (1964) found that screens with porosities less than 0.57 could exhibit this phenomenon and therefore recommended that such screens should be avoided in wind-tunnel applications, since they could cause serious effects due to boundary-layer disturbance on flow models. Since such a porosity would imply a screen with a resistance coefficient appreciably less than the K:>o 2.8 required to produce uniformity, Bradshaw (1964) suggested that multiple screens should be used to reproduce the required pressure loss.
Patel (1966) conducted an experimental investigation into this instability and found that the span wise variations in skin-friction coefficient could almost be eliminated by the addition of a deep-�ell, good-quality honeycomb downstream of the offending screen.
Cowdrey (1968), investigating self-excited oscillations in tube banks, carried out some experimental work using single rows of closely spaced rods at right angles to an air stream. He varied the number of rods in order to produce flow instability and found that in certain cases the instability could be eliminated by displacing certain rods a small distance downstream. A definite preferred pattern was founp for stable flow which could be obtained by judicious choice of the number of rods in the grid.
In the choice of screen for a particular application the possible consequences of flow instability for low-porosity screens must be considered.
CATEGORY 2: EFFECT OF SCREENS ON THE TIME-MEAN
VELOCITY DISTRIBUTION
Early methods of profile generation and flow control were mainly by trial and error, the profile being produced downstream of some distribution of blockages the precise shape of which was determined by laborious experimental work. This method was not only time consuming but also limited since it afforded little or no control of the turbulence structure, and generated profiles suffered from rapid decay rates and often involved large secondary flows.
The first major attempt at a theoretical design of a generating grid to produce a specified velocity profile was made by Owen & Zienkiewicz (1957), who concentrated on the design of a two-dimensional grid of parallel rods of variable spacing such that the velocity profile downstream of the grid was a linear shear.
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FLOW THROUGH SCREENS 253
By describing the flow through the grid in terms of resistance and deflection coefficients, they were able to obtain a relationship between the downstream profile and the rod spacing on the assumption that the upstream profile was uniform and that flow departures from uniformity were small.
They tested the design method by producing a grid to generate a shear with parameter }"LjU of 0.45 and obtained good agreement with experiment. They also found that there was no evidence of any large-scale secondary flows and that the profile showed no tendency to decay as the distance from the generator increased. A minimum value of loss coefficient was found for a given shear parameter.
Livesey & Turner (1964a) and Cockrell & Lee (1966) applied the method of Owen & Zienkiewicz (1957) to the design of generating grids for specific applications. Cockrell & Lee (1966) produced a modified method that was later improved by Durgin (1970).
The analytical treatment of Owen & Zienkiewicz (1957) was followed by a method due to Elder (1959). Elder (1959) focused attention on the flow downstream of shaped wire-gauze screens and linearized the equations of motion for flow through
the screen on the basis of certain assumptions. By describing the flow conditions at the screen in terms of a resistance coefficient, K, and deflection coefficient, B, he obtained a relationship between the velocity profiles upstream and downstream of the screen, the screen shape, and the span wise variation of resistance coefficient across the screen.
Adopting the notation of Figure 3 we may summarize the results of this analysis by the equations
u*-J = A(u-I)-O.S(l-A)s(y)+EIlXncos(nnyjL),
B tan 0 = I IXn sin (nny/L),
where
y = K cos2 () = yo[l +s(y)J,
with
[ s(y) ely = 0, I s(y) I <'i 1,
and
E = Yo/(2+Yo-B), A = l-yo(1-E).
U Lx
CD
I \ I , I '� I \ I 1 / 9 1// n
x=O
Lu
®
u*
Figure 3 Coordinate system for flow through a shaped-gauze screen.
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Nondimensional profiles far upstream and downstream of the screen (theoretically at x = ± 00) are denoted by u and u*.
Though in its stated form the two-dimensional case is considered, the theory can also be applied to axisymmetric flows in pipe and annulus and to flows in converging and diverging ducts. Elder (1959) also gave the solution to flow through multiple screens with interference, though this particular aspect has been considered in more detail by Davis (1957).
As a result of the linearization procedure the expression for the downstream profile is composed of three terms. The first term represents the attenuation of the upstream flow variation by a uniform plane gauze of equivalent resistance coefficient normal to the flow; the second term describes the effect of a span wise variation in resistance coefficient; and the final term accounts for the variation in screen angle, f}.
The screens of common practical interest are the shaped gauze screen of uniform resistance and the screen of nonuniform resistance placed normal to the flow (cf Owen & Zienkiewicz 1957). The analysis can be applied to both of these situations with ease.
The formulation of Elder (1959) becomes identical with that of Owen & Zienkiewicz (1957) when (J = 0 and K is variable, say, K(y). When the screen is plane and of uniform resistance, the method describes the effect of such a screen on a nonuniform upstream profile [u*-1 = A(u-l)J.
When A = 0 the value of K "" 2.8 and thus a scrcen with this value of K will produce a uniform downstream profile no matter what the upstream profile. A screen with K > 2.8 will reverse upstream velocity variations. This result is in agreement with the findings of Taylor & Batchelor (1949); prior to their paper it was thought K = 2 was the required value since the deflection coefficient had been neglected.
Thus, using a range of screens with K "" 2.8 but with varying wire. diameter gives a means of producing a variation of grid-generated turbulence intensity while maintaining a uniform time-mean profile. Unfortunately, there are definite limits to the range of turbulence intensities that can be produced in this way, 10% being a typical maximum value for longitudinal turbulence intensity.
Elder (1959) contains some comparison with experimental results and also the design of a screen to produce a linear shear. Some errors in this paper have been pointed out by Lau & Baines ( 1968) and Turner (1969).
Livesey and Laws used Elder's method to generate axisymmetric pipe profiles and results obtained during the course of their investigation can be found in Livesey & Laws (1973a, 1973b). Discrepancies between measured and calculated profiles lead to a re-examination of the original linearization described in Elder (1959). One of the basic assumptions of this linearization was that the screen angle was small, and Livesey & Laws (1973b) have shown that differences between profiles arise because Elder (1959) retained a second-order term [namely sly)] in a first-order theory.
Since this violation occurs only when (j is variable, the theory applied to the plane grid with resistance variation is valid.
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FLOW THROUGH SCREENS 255
When (J is variable as in the shaped, uniform K gauze screen, the s-term must be neglected since it is second-order and thus
u* -I = A(u-I)+E I exn cos (nnyjL).
If a shaped screen also had variable K the full equation would be valid:
u*-1 = A(u-1)-O.5(1-A)s(y)+ E I ex" cos (nny/L),
but in this case the s-term would be due solely to the variation in K. Thus the original formulation due to Elder (1959) contained a fundamental error.
The corrected theory shown above is the correctly linearized first-order theory. The correct second-order theory would include not only the s-term but also other second-order terms that have been neglected earlier in the analysis. Elder's (1959) original solution is in general a mixture of first- and second-order terms and is referred to here as a "pseudo" solution.
In a particular experiment designed to demonstrate the error in Elder's solution, a two-dimensional profile was produced downstream of a sinusoidal gauze screen. The results of the investigation are shown in Figure 4 in which the experimental profile is compared with both the original and modified theory.
As the linearized theory is formulated there are two possible ways in which the theory can be applied. These ways are referred to as the direct and indirect methods.
1·1
,... I ,
I , I \
\ \
/ ..... I \
I \ I \
\ \ ,
I·'
\ \ .g.u 1·0 f::o�.o=---C.-\--r----'L---,""""'----'<o!r----L-\--x-If-'----'1----''-'-:-:--+lI·O .!!.
'·0 ii
0·9
I \J
x I I
,./ SOLUTION INCLUDING S - TERM.
SOLUTION OMITTING S - TERM.
X EXPERIMENTAL POINTS.
0'9
Figure 4 Velocity profile measured downstream of screen compared with theoretical profiles.
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In the direct method the upstream velocity profile, the screen shape, and the screen properties are specified and the downstream profile calculated. In the indirect method the upstream profile, the required downstream profile, and the screen properties are specified, and the required screen shape is calculated.
In the "pseudo" solution the indirect method involved an iterative technique because of the interrelation between the three terms composing the downstream profile. Turner (1969) tackled the indirect method using Elder (1959) and experienced difficulties in obtaining convergence. He tested a grid designed to produce a linear shear and commented that there was only a slight change in the screen shape if the s-term was neglected. This may account for the reasonable agreement between experiment and theory that he obtained with this screen.
Lau & Baines (1968) in an independent analysis considered the flow of a stratified fluid through a shaped-gauze screen. This method is capable of modification to nonstratified flows, but the resulting analysis is more complex and calculations more tedious than that due to Elder (1959). Lau & Baines ( 1968) also investigated the effect of screens on the boundary-layer region of the upstream flow. Owen & Zienkiewicz (1957) observed that the profiles they produced departed from linearity near the walls where a bulge in the downstream profile occurred. This was attributed to the fact that the fluid in the boundary layer suffered a smaller loss in total head than the fluid outside the layer in passing through the screen.
A similar occurrence was observed by Lau & Baines (1968) when fluid flows through a screen. They demonstrate that a screen with K > 1 would cause a bulge in the boundary layer and that the larger the values of K the larger the bulge. Because of this, they recommend that, if possible, screens with values of K higher than 4 should not be used.
In generating a time-mean profile by means of a shaped-gauze screen it is possible to generate the same profile by using a screen with a high value of K and low screen angle or a screen with a low K value and high screen angle. It is in this way that it is possible to control profile and grid-generated turbulence independently. The first method could produce excessive pressure loss, cause boundary-layer bulge, and also result in flow instability (see Category 1); the second could violate the limits of application of the linear theory. Thus caution is necessary in selecting screen coefficients.
An indication from Livesey & Laws (1973b) is that the linearized first-order theory, though strictly applicable to weakly sheared flows and for small screen angles, gives reasonable results up to 0 of at least 45°, and with severe profile departures from uniformity. Nevertheless, the theory is limited and cannot be applied to three-dimensional flows.
McCarthy ( 1964) considered the passage of moderately sheared three-dimensional flow through variable resistance screens and obtained a solution without having to impose any limits on the magnitude of the span wise resistance variation or on the velocity variation across the grid.
The method cannot cater for screens of arbitrary shape and is restricted to flows in which the velocity profile upstream of the grid is uniform. The generators
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FLOW THROUGH SCREENS 257
are plane screens of variable resistance formed by overlaying and combining screens to form the specified distribution of resistance. McCarthy's paper includes a comparison between experimental and theoretical profiles; the experimental profiles were measured one duct length from the screen.
For situations where high accuracy is not required Livesey & Laws (1974) have shown that an empirical extension to the three-dimensional case can be achieved using the approximation gauze-profile inverse.
With the same objective but along different lines Kotansky (1966) has used honeycombs with transversely varying stream lengths to produce specified velocity distributions. Sajben et al (1973) also designed variable K profile generators, which were fabricated from plane screens by an electro-plating process.
Flow Through Partial Screens
Taylor (1944) considered the flow through a screen in an external flow and developed equations which for K � 4 gave reasonable agreement with experiment.
Elder (1959) suggested that his linear theory could be applied to partial screens
in internal flow situations as long as the restrictions on spanwise resistance variation were satisfied and thus K <1; 1. Elder (1959) produced no experimental data to validate this statement. The method due to McCarthy (1964) may also be applied to flow through partial screens.
Koo & James (1973) devised a mathematical model for steady two-dimensional flow through a partial screen. In the model the screen is replaced by a source distribution and the stream function adjusted to give the correct mass and momentum flow across the screen. Reasonable accuracy was obtained with K values up to 10. Theoretical profiles produced using Elder (1959) were also compared with their experimental results and gave reasonable results for K < 2 with significant departures for higher values.
Graham (1976) extended the quasi-steady theories of Davenport (1961) and Vickery (1965) to the drag of plane lattice-like structures in a finite external flow. He used the method of Taylor (1944) and Blockley (1968) for the flow past and through the screen and a simplified version of the work of Hunt (1972, 1973) treating the turbulence in the linearized approach flow by a rapid distortion theory. Following Bearman (1969) and Roberts (1971), drag, admittance, and velocity spectra upstream of the screen are reasonably predicted for values of K < 4.
Flow Through Multiple Screens
Davis (1957) and Elder (1959) have considered flow through two shaped-gauze screens sufficiently close to each other to cause interference. (Though no experimental comparisons were included.)
For a single plane gauze screen it has been mentioned previously that a screen with K = (2- B)/(I- B) produced a uniform profile whatever the profile upstream of the screen. Davis (1957) has shown that two aerodynamically interfering plane screens cannot completely remove the upstream velocity variation. However, they can remove a particular harmonic component. Even if one of the screens has
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K � 2.8 the screen arrangement will not produce uniformity unless the screens are positioned sufficiently far apart (theoretically infinite spacing) for interference effects to be negligible.
For zero separation, in which case the screens are overlayed, the two values of K, K [, and K2 are related by
1 2(K1 + K2) = 1 + (1-Bd(l- 82)' Thus if two screens satisfy this relationship they will produce uniformity at zero separation, which will always incur a higher pressure loss than the single gauze screen. Therefore, in general, a single screen will be preferred for this application (see Category 3).
The advantage of using two screens lies in the fact that there is an extra parameter that may be varied. namely the spacing of the screens. With any two screens, no matter what the values of K, it will always be possible to space them such that they remove at least a particular harmonic component; with a single screen only K � 2.8 would produce uniformity.
It must be noted that in obtaining the resistance coefficient of an overlay of two gauze screens it is not sufficient to add the resistance coefficients of the individual screens. Indeed, in some circumstances it is possible for the resistance
coefficient of the combined screen to be less than that of either of the individual screens. Care must be taken in the orientation of wires in overlayed screens so that the combined screen porosity can be estimated.
Velocity Profile Decay
Baines & Peterson (1951) commented that 5-10 mesh lengths downstream of any screen were necessary
' to ensure reasonably good flow establishment. In most
experimental investigations, however, a duct diameter has been allowed before measurements have been made. Further from the screen the velocity distribution will decay as the shears within the generated profile establish a turbulence structure that interacts with the mean flow.
At the present time, when some sophistication in generating techniques is available, little is known about the profile decay rate. Livesey & Turner (1964b) have shown that the decay rate can have a significant effect on the behavior of downstream components, and therefore the simulation technique will have to reproduce the velocity distribution and additionally the complete turbulence structure of the flow.
The practical difficulties of achieving such a complete simulation will probably lead to a focus on the more easily measured feature, namely the decay rate of the velocity distribution, with some simple boundary conditions. It is quite clear that turbulence decay rates must also be considered.
An investigation undertaken by Lim (1977) under the supervision of the authors of this review will provide much useful insight into profile decay with associated turbulence structure.
If the features of profile decay were understood, the possibility of generating
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1·5
1·3
1·2 .!:!. Ii 1·1
1.0 r/R
0·6
0·0
x PARTIAL GAUZE o SHAPED GAUZE
(a) Nondimensional velocity distribution
1·5
1·3
1·2 u if
1·1
0·6
4
FLOW THROUGH SCREENS 259
x PARTIAL GAUZe: o SHAPED GAUZE
0�1.0=-r7./R��0�.5--�0�.�0----�0�.5�r/�R�'·0
(b) Longitudinal turbulence intensity
FilJure 5 Velocity and turbulence profiles measured downstream of different screens : X, 7.5D downstream of partial screen, 0, 5.5D downstream of shaped-gauze screen.
profile and turbulence structure independently could be achieved, not only using the methods previously described but in addition by using the decay phenomenon. Lack of space precludes further discussion on this point. However, as an example,
Figure 5a shows two practically identical profiles produced downstream of two entirely different generators. One profile was produced 7.5 diameter downstream of a partial gauze screen, the other 5.5 diameters downstream of a complete shaped-gauze screen. Figure 5b illustrates the longitudinal intensities /U2/UL measured at the same planes.
CATEGORY 3: SCREENS AND TURBULENCE
It is necessary to identify two basic roles for screens either as turbulence suppressors or turbulence generators. In the suppressor role the downstream turbulence, in both intensity and scale, is reduced from any upstream value. The screens are typically of very fine mesh, avoiding the introduction of turbulence due to the screen (by operation at low Reynolds number) or ensuring that the scale and intensity of such generated turbulence is small enough to guarantee its very rapid downstream decay. In the generator role the turbulence downstream is of high
intensity (typically 10 per cent or higher) and is often achieved deliberately with
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control of scale and intensity by choice of element width (wire or rod diameter), mesh size and Reynolds number with a typically coarser mesh, higher solidity and operating at higher Reynolds number. The generated turbulence, initially much higher in intensity than any upstream turbulence, decays giving in the decay (intensity falls, scale grows) a further control of intensity and scale.
Previously in this review the generation or suppression of turbulence by the screen has been largely ignored (but see Category 2: Velocity Profile Decay). Any arbitrary generated time-mean velocity profile, as well as containing possible turbulence originating from the screen elemel1ts, will immediately begin to establish a turbulence structure dependent on the shear distribution and varying with its interaction with the time-mean velocity profile, as affected by the boundary conditions. This review would not therefore be complete without a brief mention of the associated features of turbulence suppression and generation by screens. Here an up-to-date sketch with signposts to sources is all that is attempted.
For an introduction to concepts, terminology, and measurements see Bradshaw (1971) and Tennekes & Lumley (1972), and for the more specific basic physics and the historical context see Batchelor (1967), Townsend (1976), and Corrsin (1963). A recent relevant review with excellent sources in the references and bibliography is contained within Loehrke & Nagib (1972).
The General Downstream Flow
Some of the complicated features of the development of the time-mean velocity profiles and their inherent turbulent structures for arbitrarily generated velocity profiles have already been considered in relation to the decay processes (see Category 2). Features of simpler flows lead to a greater understanding. Owen & Zienkiewicz (1957) explained the relative permanence in the x-direction of a linear velocity profile (du/dy constant) in terms of a conjectured constant eddy viscosity expected downstream of a screen. Rose ( 1966), for a homogeneous turbulent shear flow obtained the result, predicted by Corrsin ( 1963), of uniform constant turbulence intensity and shear stress coupled with scale increasing with distance from the screen. Later, Rose (1970) demonstrated that the turbulence scale imposed initially by the screen fixed the level of the turbulence intensity. Below some minimum initial scale the turbulence always decayed. Richards & Morton (1976), investigating flows with quadratic time-mean velocity profiles [constant total strain (x/V) dV/dyJ, achieved sufficiently large strain magnitude (> 3) to demonstrate that the initial findings of Rose (1966) were appropriate to only low strains and that turbulence intensitics began to increase again at a certain distance from the screen. These results confirmed that states of equilibrium are not reached in these simple developing shear flows. In the references quoted very detailed measurements are available of intensities, stresses, scales and occasionally spectra.
The generated arbitrary time-mean velocity profile with its arbitrary initial turbulence structure is thus a truly complex turbulent flow. The description of these flows in experimentally measured forms is very complicated, and the prediction of their behavior awaits the further development of the turbulence modelling, closure, and prediction procedures surveyed by Reynolds (1976). An additional
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FLOW THROUGH SCREENS 261
feature adds to the complication. The generated shear flows are occasionally found to be unstable in the classical sense, relating to the origin of the turbulent nature of the flow, with characteristic, sometimes nearly periodic, large-scale energetic eddies. These narrow band-width instabilities do not appear to be capable of precise prediction. Clearly an average Reynolds number based on defect velocity and zone width defined in an integral manner should be kept high; values less than 500 might be regarded as indicative of these instability problems. These flows may involve acoustic interactions with noise and vibration of screen elements and adjacent boundaries (Loehrke & Nagib 1972). The interactions are predictable if the basic frequencies are available. The features are particularly evident in flow distributions that contain multiple adjacent shear layers.
Suppression of Turbulence
Good concise discussions concerning suppression of turbulence by screens are found in eorrsin (1963), Townsend (1961), and Bradshaw & Pankhurst (1964). Loehrke & Nagib (1972) list sources extensively, and although their discussion is instructive it is somewhat confused by its consideration of some unusual specific suppression devices.
The aim basically is to obtain as uniform a mean flow, spatially, as possible, in order to avoid further turbulence generation, and to remove existing turbulence or reduce it to an acceptable low level. The production of a uniform mean flow has already been discussed (see Category 2). If the local Reynolds number Ud/f3v of the wires is greater than 80 (the normal situation) the wire wakes will be turbulent and the screen will contribute turbulence to the flow. For sufficiently fine screens this turbulence is of small scale and decays, 500 mesh lengths being allowed for this process. The initial plane screen (K � 2.8), normal to the flow, producing a uniform flow implies a solidity greater than 0.45, and the occurrence of downstream instability (see Category 2). Again, with a sufficiently fine mesh screen, together with a decay length, the added turbulence will be small and any remaining spatial non uniformity may be dealt with by the later successive lower-solidity, stable-flow, turbulence-suppressing screens. Taylor & Batchelor (1949), using a linear theory for isotropic turbulence, indicated the selective effect of a screen on the longitudinal and lateral turbulence components. The isotropic turbulence becomes axisymmetric and the attenuation of the longitudinal component is much greater than that of the lateral component. The magnitudes of the attenuations are not well predicted and experimental values (Batchelor 1967, Townsend 1961) should be used in design. Attention need only be focused on the required reduction in the lateral component. The lateral component attcnuation varies like (1 + K) - 1/2, and therefore several screens are more efficient than one screen for the samc pressure drop. A final decay length will normally enable a final intensity of 0.2 per cent to be achieved, dependent upon the scale of the ducting and the influence of the turbulent boundary layers on the main flow. For ducts that are suitably large, a further order of magnitude reduction in intensity is possibly by use of a suitable contraction in duct area of carefully profiled design [see Corrsin ( 1963) and Bradshaw & Pankhurst ( 1964)].
The greatest uncertainty in the above is the effect of the small-scale turbulence
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added by the fine-mesh screens because of the impracticability of operation at low enough wire Reynolds number. A further difficulty is the effect of upstream turbulence on the performance of the screens. Both difficulties are identified as significant by Schubauer et al (1950) and Loehrke & Nagib (1972). The first difficulty is the more significant. The additional large wave-number energy should increase the spectral transfer rate of the existing smaller wave-number energy and increase its decay rate. What is unknown is the effect of the wave-number ratio, which could presumably be too large. The mesh sizes of the screens are therefore usually equal or in cascade, starting with the largest mesh first, with mesh size ratios, screen to screen, of approximately 2 and with adequate decay lengths between screens. Availability, strength, handling, fabrication and the feasibility of cleaning usually dictate the finest screen. Gauze screens may be inappropriate for high-density flows and liquid flows in particular. Here strength considerations dictate element diameters implying Reynolds numbers in the vortex shedding range and the higher dynamic loadings lead to fatigue failures. A solution is provided by the honeycomb type of screens, which is also generally useful if swirl or initiaIIy high transverse velocities are present. Lumley (1964) and Lumley & McMahon (1967) give a treatment parallelling the approach described above for gauze screens and provide systematic design information. The description of the downstream decay of the generated turbulence due to the honeycomb is the least satisfactory treatment of their work.
Generation of Turbulence
The simplest convenient method of generating turbulence is by means of screens of relatively coarse mesh and diameter (more commonly referred to as grids) of solidities typically OJ-O.4 placed normal to a uniform upstream flow of low turbulence. Parallel cylinder arrays and biplane orthogonal square grids, of either cylinders or square section bars, and commercial woven mesh grids as well as punched plates have all been used. At a sufficiently large distance downstream (40 mesh lengths), the turbulence is near to homogeneous and nearly isotropic [longitUdinal to transverse velocity ratio (rms) 1.15]' The intensity is highest near to the grid and usually the variation downstream has been expressed as
U2jUZ = b(x-xo)jMK,
where b is approximately 100 (biplane grid Mid � 5) or 50 for a single row of rods. The virtual origin Xo is approximately 10 M. The intensity and energy ratio are seen to be larger for larger K, but high K implies high solidity and possibly extreme downstream inhomogeneity of unacceptable magnitude for these coarse grids. The longitudinal integral length scale is typicaIIy like
Mid � 5.
Approximate representations of the longitudinal correlation coefficient and spectrum are
Rll(r, 0, 0) = ur exp (- rIL)
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FLOW THROUGH SCREENS 263
Choice of turbulence properties are thus available within the decay downstream of the grid. The above relationships are nearly independent of Reynolds number. For detailed consideration of appropriate turbulence Reynolds numbers see Corrsin (1963). It is difficult to generate intensities much higher than 10 per cent by grids alone. Significantly higher intensities approaching 50 per cent (questionably indicated by hot wire anemometer) may be obtained by diffusing the flow, by means of an area increase, lowering the time-mean velocity of the main flow. Control of uniformity of the flow and homogeneity are poor but are aided by the initially high turbulence levels of the grid-generated turbulence. Area divergence rates up to twice conventional values (10° rather than 5° included angle cones) may be used without separation of the duct boundary layers.
More recently jet grids have been used [Gad-el-Hak & Corrsin (1974)J with jet injection into the wakes of the grid elements, using both downstream and upstream injection. Coflow injection produces lower turbulence intensities and scales, counterflow injection gives higher intensities and scales. Associated with sufficiently high injection rates, both coflow and counterflow, but especially the latter, are instabilities like those obtained with high-solidity passive grids. The active jet grid gives more control of turbulence intensity and scale magnitudes but at the expense of control of homogeneity of both the turbulence and the mean flow. Gad-el-Hak & Corrsin (1974) give details of turbulence intensities, scales, decays and spectra for their jet grid. In the same paper are summarized the results, in tabular form, of no less than twelve previous papers on both passive and active grids giving the turbulence component magnitudes and decays in the different form
[or B(x/M)"J,
where x is the distance from the grid, which apparently described the results sufficiently well. Values of B, b, n for some or all of the component energies as well as the grid Reynolds number Rm are quoted together with the details of the grids employed.
SUMMARY
The wider engineering application of screens cannot be covered completely here, and no more than a few examples with pertinent references can be included.
Gauze screens have been used in diffusers to reduce flow separation and produce uniform exit flows (Schubauer & Spangenburg 1948). With a gauze screen in conjunction with a diffuser of specified wall design, wide-angle diffusion in a short overall length with little separation and uniform outlet profile is possible (Gibson 1959, Kachhara et aI1976). Gibbings (1973) has designed a pyramid gauze diffuser.
Carefully positioned screens in jet engines have been used as effective noise reduction devices (Callaghan & Coles 1955).
Aerodynamically designed sails (Barakat 1964) and fishing nets (Morgan 1966) are similar applications of the screen (porous sheet), as is the design of shaped filter bodies serving the dual role of flow conditioners.
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Future work that is needed in relation to this review and to which one might hopefully look forward includes:
CATEGORY 1 Systematic design of specific property actuator sheets glVlng independent control of K and B. The manufacturing problem would be difficult but is immediately feasible for two dimensions and axial symmetry, e.g. the low-loss high-deflection cascade, and the expanded metal plate with preferred deflection direction. For three dimensions new conceptions are required if we are to be limited by planar screens, but the possibility for uniform screens of low loss deformed out of the plane are clear.
CATEGORY 2 Generalization of the actuator sheet concept to cover arrays varying in form from different classes of bluff bodies through to specific property screens.
Higher-order extensions of existing theoretical models probably by wholly numerical methods.
Three-dimensional calculation methods, initially rotational and in viscid, modified by dissipation and possibly in appropriate cases treating the upstream and downstream turbulence by rapid distortion theory and eventually incorporating fuller turbulence modelling.
CATEGORY 3 Effect of wave-number ratio of added screen-generated turbulence on spectral transfer rates in relation to turbulence suppression and screen-to-screen in terference.
Prediction methods for the behavior (development/decay) of arbitrary time-mean profiles accounting for initial turbulence structure and development.
Considered separately would be instability onset predictions and the possibility . of high-energy stable arrays in general flows generated by screens.
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FLOW THROUGH SCREENS 265
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Mec
h. 1
978.
10:2
47-2
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