4. CONVENTIONAL AND ECO-INNOVATIVE QUALITY PRESERVATION
4.2. Microwave treatment
4.1 Results in Test Section I (R = 0.14 m)
4.1.1 Introductory observations
A wide range of experimental measurements were carried out in test section I described in section 3.2.2; the radius of curvature was R = 0.14 m. The flows varied from Re = 1,800 to 20,000 (V = 35
-a
170 £/min) covering fully laminar (up to Re cl = 8,900), transitional (Re = 8,900 - 16,600) and fully turbulent (Re > 16,600) conditions.ct cl
Before each measurement, the precise spanwise location of a vortex pair was located using visualisation; then simultaneous LDA and hot film measurements were carried out.
Mainly cross-sectional and also streaklines visualisation (see also section 3.4.1) revealed the existence of natural Gortler vortices of various sizes, wavelengths and strengh across the span of the water channel. Uneven spacing was observed between successive troughs and crests corresponding to the regions of the
flow where the fluid moves towards and away from the surface respectively.
These regions will be called regions of downwash and upwash.
The development of a vortex pair at Re = 14,200 (V = 120 £/min)
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will be considered, as it represents a typical case for the development of a vortex through transition. The first indications of the counter
rotating motion of the fluid appear early in the bend (<j> H 5°).
The vortices appear to be in the linear stage of amplification, the flow pattern corresponding with solutions of the linearised
equations of motion and the centre of rotation of each vortex coincides
with the geometric centre of the vortex cross-sections. A few degrees further downstream (<J> ^ 1 0°) the cross-sectional shape
of the vortices distorts, the circular cross sections become elliptic, perhaps skewed, and for a vortex pair the vortex centres move closer
together nearer to the upwash region. This is the non-linear phase.
By (j) = 15-20° the first signs of unsteadiness are observed; the
vortices appear to meander in the spanwise direction, at an apparently fixed frequency. The flow at this point is still laminar. The
next stage following the meandering motion, is an intermittent
flow breakdown with turbulent spot production. In a short streawise distance (approx. 7° in angle) the turbulent spots populate rapidly until the flow becomes fully turbulent. This region is the transition region, and is investigated further in the next section.
The spanwise location of a vortex pair remains constant with streamwise distance, and so does the vortex wavelength. However the vortex dimension normal to the wall increases, and the centre
of the vortex moves away from the surface. For instance at V = 120 £/min and z = 77 mm the vortex centre moves from y = 3 mm at <j> = 15°
to y = 10 mm at <p = 75°. Upwash and downwash locations can be
distinguished everywhere in the streamwise direction (for a specific vortex pair), the discrimination between them decreasing as the vortex becomes turbulent after the transition end. Boundary layer
thickness variation in the spanwise direction is significant and
irregular, being the result of the coexistence of vortices of different size (Sabzvari, 1984). The reason for this irregularity may be
related to the random and uneven disturbances, present in the flow upstream. In any case, these disturbances, originating from' surface irregularities or other upstream flow perturbation, as for instance
from the final screen in the settling chamber, are the primary reason for the initiation of the Gortler vortices.
All the above observations are demonstrated in the next section, through the LDA and hot film measurements.
4.1.2 Description, characteristics and analysis of the flow
The experimental measurements revealed the complex characteristics of the concave wall boundary layer. The vortex pair chosen for
the LDA and hot film measurements, was situated with its upwash
region at approximately 77 mm from the channel bottom. This location varied by ± 2 mm from day to day, but was maintained with varying
flow rate.
Two mean velocity profiles were measured in the straight section preceeding the bend, at x = -5 mm and x = -25 mm (x = 0 at <f> = 0°). The results shown in figures 4.1a,b, indicate that the flow cannot be considered as parabolic, since the velocity does not attain a constant value outside the boundary layer, but
increases with y due to the upstream influence of the bend. This is most apparent at Re = 20,200, corresponding to the highest
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of flow rates (V = 170 &/min) in the present tests.
The streamwise development of the mean and fluctuating velocity profiles is shown in figures 4.2 to 4.6 for five different flows, namely 35, 75, 95, 120 and 170 £/min (Re = 4,200, 8,900, 11,300,cL
14,200, 20,200) covering flows from fully laminar to fully turbulent.
Plotted points pointing upwards correspond to upwash locations;
those pointing downwards correspond to downwash locations.
At Re^ = 4,200, (fig. 4.2) the flow is fully laminar throughout the bend as far as cf> = 75° where upwash and downwash velocity profiles
are easily distinguished. Core flow turbulence intensity is below 1%, with the maximum intensity near the wall. The vortex pattern is steady, and remains so until the end of the bend. The vortex half wavelength appeared to vary between 8 and 1 0 mm, but evidence from flow visualisation would imply that it is reasonable to assume that the vortex wavelength remains constant with streamwise distance, the small variations in half-wavelength being attributed to the
uncertainty in pinpointing the exact centre of the downwash region.
The wavelength was also checked by measuring the distance between two upwash regions, and the values were similar.
At Re = 8,900, (fig. 4.3) the vortex pattern is still well
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defined, and steady in the early stages of the bend (<j> < 25°), becoming unsteady around <J> = 27°, where the film probe picks up the first signs of turbulence in the flow, resulting in non-zero intermittency, which increases from then onwards to a maximum at
<p = 45°. This can be seen in the plots of the streamwise distribution of the maximum values of intermittency for all flows (figure 4.7).
As indicated by the plots, y attains the value of 30% at upwash at <f> = 45° but only 7% downwash; for <j> > 45°, intermittency decreases and reaches zero at <J> = 75°. The fluctuation velocity profiles indicate a shift of the maximum r.m.s. value from the point nearest to the wall, to a point away from the wall, where the shear is
at a maximum by way of the nature of the upwash region of the boundary- layer at that point. This is observed at higher flows as well.
This region of high shear away from the wall might be the location where transition is initiated and turbulent spots first appear;
Van Driest and Blumer (1962) suggest that flat surface transition initiates from a point away from the wall where the shear!?4^ is
a maximum. The above phenomenon is not observed at the downwash locations. Both the upwash and downwash velocity profiles are distorted, implying a skewed vortex, making the accurate evaluation of integral boundary layer parameters almost impossible (figure 4.8). Half wavelength was similar to Re = 4,200.cl
When Re is increased to 11,300, transition is more advanced but still incomplete, intermittency attaining y = 63% at upwash,
y = 33% at downwash at <f> = 45° and then drops as <f> increases (figure 4.7). The fluctuating velocity shows an increase at the high shear region as before, and this is the location where y is maximum.
Half wavelength was 6-9 mm, following no specific trend with increasing angle (<j>). Similar behaviour is at Re = 14,200, the flow getting
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nearer fully turbulent conditions, and after attaining y = 72%
at upwash and <j) = 45°, y then drops slowly. Half wavelength in this case varied between 7-8 mm.
The highest Re attained in the experiments, is 20,200. In
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this case (fig. 4.6) the flow is fully turbulent (y > 90%) after
$ =27°, but possibly earlier, a fact which may not have been
detected because of the relatively large separation between streamwise stations where measurements were taken. The cross stream point
of maximum intermittency has now shifted to the wall (y = 2 mm).
However, upwash and downwash regions can still be distinguished eve at <f> > 45°. Half wavelength varied between 6-9 mm. Elaborate methods had to be devised to carry out the hot film tests at this high flow rate because the probe stem was vibrating violently, thus corrupting the anemometer output signal. For example a 10 mm- chord splitter plate was glued onto the trailing side of the probe stem all along its length, in order to reduce the creation of vortices
by the stem itself, and hence reduce the induced vibrations.
Overall, the intermittency factor was consistently less at downwash compared to upwash. This, together with the cross stream distribution of r.m.s velocity which peaked at the high shear region at upwash, seems to support the theory of Van Driest and Blumer,
that the production of turbulent spots and the mechanism of transition originates at a fixed distance from the wall where the shear is
a maximum and which in the present case is situated at the spanwise location of upwash (for a fixed vortex).
Another characteristic present in all flows where y > 0 ie V > 75 £/min is that intermittency drops after attaining a maximum at <J> = 45°. This drop is more significant at the lower flows, becoming less significant with increasing flow. This is explained by observing figure 4.9 which shows the streamwise variation of the potential wall velocity u through which the pressure gradient variation is estimated. u^w was approximated using the LDA measurements of mean velocity outside the boundary layer, and extrapolating
to the wall, as shown in figure 4.9a$ (presently used me£/ie>cU, As seen from figure 4.9a the free stream velocity u^ does
not attain a constant value outside the boundary layer, thus introducing a complication in evaluating the potential wall velocity u . To
avoid this problem another method was tried for evaluating u .
According to this (Jeans and Johnston, 1982), the velocities measured were normalised according to the relation
u = u [ ~ _ y ] where
n R
R is the radius of curvature. The attempt however proved unsuccessful
and the method was abandoned.
Figure 4.9 shows that for <f> > 30°, the pressure gradient becomes favourable and hence accelerates and tends to relaminarise
the flow to a certain degree, and consequently lowers the intermittency.
The pressure gradient is more dominant at lower flows where boundary layer thickness is larger compared to higher flows, whereas the channel width remains constant throughout the bend. At Re = 8,900,
3
(V = 75 £/min) the velocity gradient parameter K is estimated as
-6
. . .approximately 5 x 10 which exceeds the Launder relaminansation criterion (Launder and Jones, 1972) of 2.5 x 10 6 . At the higher flow of Re = 12,500 (V = 105 £/min) where the intermittency approaches
3
50% (maximum), K is estimated at 3 x 10 comparable to the Launder value. At the highest of flow rates (Re = 20,200) where transition
3
is completed (Y > 90% throughout for <j> > 27°) K is only around 1 x 10 6.
The structure of the transitional boundary layer with respect to turbulence is examined by inspecting the profiles of intermittency
(y direction), which are shown for four flows, all stations, upwash and downwash, in figure 4.10. As a general characteristic the
peak of intermittency moves away from the wall, as the flow progresses downstream. This is consistent with the development of the boundary layer in the y direction (growth), and also with the variation
of the maximum r.m. s velocity with y and x. In particular, for the regions of upwash, the maximum u m g value shifts from y = 2 mm at <J> = 15° to y = 6 mm at <j> = 27° then to y = 8-10 mm at cf> = 45°.
Further downstream, wall generated turbulence, which once it appeared increased with streamwise distance, mixed with turbulence generated at the high shear region, slowly shifted the location of the maximum ur m s back to y = 4 mm at <j) = 60° and y = 2-3 mm at <j> = 75°. This
was true for all flows except Re = 20,200, where the flow is fully cl
turbulent throughout, and the maximum u ir .m. s always occurs at y = 2 mm (point nearest to the wall). At downwash, where no high
shear region exists, the maximum ar m s always occurs near the wall (y = 2 mm). At <p = 45° where the intermittency at upwash attains a maximum and influences the downwash values, the location of the maximum is shifted to y = 4-6 mm. Figure 4.11 shows the streamwise variation of (u /u, .. ) for four flows,
r.m.s Dulk max
Wall shear generated turbulence becomes apparent after the appearance of turbulence at the upwash high shear locations but
as Re increases, becomes the dominant source of turbulence production, a
and together with the high shear region turbulence production, tends to flatten out the peaks of the intermittency profiles at upwash, whereas pointed peaks occur at downwash.
An alternative way to examine laminar-to-turbulent transition, is to fix the location and vary the flow rate. Figure 4.12 shows the variation of intermittency with Re^ for all streamwise stations, for (a) y = 4 mm, always within the boundary layer, and (b) y = 1 2 mm, near the edge of the boundary layer, for both upwash and downwash regions, for 7 flows (Re = 8,900 to 20,200). When transitioncl is viewed in this manner, the phenomena are very similar to those seen by changing streamwise locations at fixed flow rate. The variation of Y with flow rate appears to follow an exponential
like distribution in most cases.
The variation of integral boundary layer parameters, namely Re , G and H, is shown in figures 4.13 a,b,c for 3 flows
0 0
(Re = 8,900, 12,500, 20,200). The variations of Re and G with x
ot 0 0
do not seem to follow a pattern common to all 3 flows. Values of Gq as low as 2 for downwash regions and as high as 40 for upwash regions occur. However the number of streamwise stations (5) where measurements, were taken, was not enough to obtain a reliable assessment
of the behaviour of Re , G , etc with streamwise distance. The slightly adverse pressure gradient at the early stages of the bend, followed by a favourable one at <j) > 30° makes the present problem even more complicated. The shape factor H attains values of up to 4 in the laminar region, a value which is consistent with Riley
(1986), and then appears to converge down to approximately 1.1, irrespective of flow, and spanwise position, at the fully or partly turbulent flow region at bend exit. This behaviour is similar to flat plate boundary layers, but the present range (4 to 1.1) is outside the H = 2.6 to H = 1.3 band encountered on flat plates.
The inaccuracies introduced in estimating 6* and 0 from the small number of data points in the boundary layer, especially at downwash positions, and the line fit through the core flow points to evaluate u should also be borne in mind,
pw
Turbulence intensity Tu = u /u in the core flow was r.m.s mean
in the range of 0.8% to 2.1%, for Re varying from 20,200 to 8,900cL (where Y £ 0). This is shown in figure 4.14, and it will be used in the next section to compare with existing transition criteria.
Slight variation of Tu with streamwise distance is observed, as for instance at Re = 16,600, Tu varies between 1% and 1.4%. This
a
variation appears to be random. Overall, the higher the flow, the lower the core flow turbulence intensity; at Re = 8,900
Tu » 2.1, whereas at Re = 20,200, Tu = 0.9%. Furthermore, intermittency
cL
in the core flow was zero which indicates that fluctuations outside
the boundary layer are all at low frequencies, and in the curved section of the duct are probably associated with the unsteady motion of the vortices.
Finally, a brief attempt was made to record the energy spectrum at a point in the flow, using a spectrum analyser coupled to the hot film anemometer. Figure 4.15 shows spectral plots at Re = 8,900,
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12,500 and 20,200. obtained with the probe positioned at <f> = 27°, at an upwash location and at y = 2 mm. the three spectra have flow frequency ranges of 0-39 Hz, 0-130 Hz and 0-310 Hz for the Re^ values above. The spectra are continuous and no preferred frequencies are observed. Examples of corresponding digitised hot film output are also presented, with each spectrum. This is but an example of a flow spectrum, since the chosen location may
have been the wrong one for detection of possible preferred frequencies as suggested by Aihara and Koyama (1981). For that reason a very-
extensive energy spectrum investigation is carried out in the test section with R = 0.5 m, which is described in section 4.3.
4.1.3 Discussion on results for test section with R = 0.14 m
Before initiating a discussion, it should be noted that the present results refer to a region of the span affected by only
one particular vortex pair, not necessarily representative of spanwise averaged quantities, as many vortex pairs of different strength,
size and stage of amplification can coexist at the same streamwise station (Crane and Sabzvari, 1982).
The highly three-dimensional nature of the present boundary layer in which Gortler vortex amplification has gone beyond the linear stage (Crane and Sabzvari, 1982) and the large velocity
profile distortion may render Reg, Gg and H inappropriate parameters to be used in a transition criterion. However their measured values in the present experiments are used in comparisons with existing transition criteria. Four cases, Re = 8,900, 11,300, 12,500 andcl 20,200 (V = 75, 95, 105 and 170 £/min) will be considered.
Since transition appears to originate at upwash positions only, these will be the ones mainly considered. For the first three cases, figures 4.7 and 4.13 suggest values for Regg at upwash of 250, 260 and 280 respectively (transition start is where y first becomes non-zero). Corresponding Gortler numbers vary from 19 to 22. Core flow intensities were 2%, 1.8% and 1.5% respectively, and using equation 2.29 (Abu-Ghannam and Shaw), the calculated
Regg would be 300, 330 and 380 respectively, overestimated by 15-35%.
On the contrary, calculated Gortler numbers G e (6, 6.5 and 7) using equation 2.40 (Forest, 1977), are underestimated by up to three times. For the fourth case where Re = 20,200 and Tu = 0.9%
a
the flow is already 25% turbulent at $ = 15°. Differences between upwash and downwash are small. Re^ at that point is around 130
and Gq approximately equal to 5. Predicted Reg for similar conditions exceeds 300 and G is 7.5. However, at these conditions where
e
the flow is mostly turbulent, and the distortion of the profiles smaller, it is unlikely that the effect of the Gortler vortices would be a dominant one. I f .transition start is taken as the point where Y = 10% instead of 0-1% then the values of ReQ_ would come
closer to the calculated values as discussed above, the overestimating error falling to between 1 0-2 0%. Ggg values however would become an extra 3-6% more inaccurate because they would increase slightly.
The above results indicate that transition begins sooner
(at the upwash locations) compared to a flat plate, and that existing predictions for the start of transition through Reg are no longer valid. It should be noted that if the measured values of Re
ob are averaged between upwash and downwash, then Re in the present
0 b
case will be even smaller, and the consequent differences with
existing criteria even larger. Furthermore, in view of the contribution of the vortex unsteadiness to the local fluctuation: intensities,
it may be more appropriate to compare the present results with flat plate cases at lower turbulence levels. In this case, the differences between predicted and measured Reg will be even greater, and the transition criteria would then become highly inaccurate.
Transition length behaviour cannot be analysed using Reynolds numbers based on momentum thickness 0 because Reg exhibits a non
monotonic variation with streamwise distance (Sabzvari, 1984),
in contrast to flat plates where 0 and Re_ do increase monotonicallyu with distance; Reynolds numbers based on length - usually the distance
from the leading edge - can be used instead. Two cases will be considered for comparison, those of Re = 12,500 and 16,600. Theci experimental transition start Reynolds number will be assumed as correct, and transition length will be calculated using equation 2.38. For the first case, transition end is predicted at <J> = 58°
whereas the experimental intermittency curve attains its maximum
at <j> = 45° and in the second case the predicted end is at <J> = 32°
whereas the experimental one is at cj> = 27°. Cases at lower flows cannot be tested because the flow never reaches a fully turbulent
whereas the experimental one is at cj> = 27°. Cases at lower flows cannot be tested because the flow never reaches a fully turbulent