A Study of the Flow Structure in the Near-wall Region of a Complex-shaped Channel using Liquid Crystals
In the present work, results are reported of a study of the structure of a forced convective flow in a complex-shaped channel performed using cholesteric liquid crystals (LC). The model under study was a channel formed by two corrugated surfaces pressed closely together. To measure the temperature fields on the model surface, a thermochromic LC coating was used. To visualize the shear-stress distribution over the model surface the texture transition method based on the use of LC insensitive to temperature was used. The obtained data permit reconstruction of the vortex flow pattern in the near-wall region.
The problem of heat-transfer intensification in various apparatus is a most important one from a practical viewpoint (1, 2). To make a proper choice of the method for raising the heat-transfer rate (or that of the configuration of the heat-exchanging surface for a particular application), it is necessary to possess exact information as to the flow structure and conditions in the channel. In many cases, most suitable surfaces have an intricate shape for which analytical design is impossible. The complexity and great diversity of the possible shape of heat-exchanging surfaces and channels formed by these surfaces require direct experimental studies of the flow structure in such channels to be carried out. The heat-transfer rate, hydraulic resistance, and efficiency of any surface of interest all are determined by the flow structure in the channel. A knowledge of the distribution over model surfaces of such quantities as shear stress and temperature allows one to reconstruct the panoramic pattern of the flow and make an optimal choice of model geometry.
In the present work, results are reported of a study of the structure of a forced convective flow in a complex-shaped channel performed using cholesteric liquid crystals (LC). These crystals are known to readily respond to the combined action of temperature and shear stress (3). By the proper choice of coating, eliminating other possible influences, one can visualize solely the shear-stress distribution. On the other hand, the use of thermochromic coatings on the base of LC encapsulated in to a polymeric matrix (4) makes it possible to exclude the effect due to the shear stress. In this manner, the LC method allows one to easily determine both local and integral heat-transfer characteristics, which substantially cuts the time required for performing experiments (5).
Experiments were carried out in a small subsonic wind tunnel with a closed working section of dimensions 15 × 80 × 250 mm. The model under study was a channel formed by two corrugated surfaces pressed closely together. One of the surfaces was made of an organic glass, and the other of a 0.15 mm-thick stainless steel. The angle between the plate ribs forming the surfaces was 90 degrees. The main geometry parameters of the plates are the following: pitch p = 10.5 mm and the internal height of corrugation h = 6.3 mm. Figures 13.1 and 13.2 show a model and a diagram of one elementary cell of the channel.
As it was known, in the range of Reynolds number studied in this work, turbulent flows in channels of intricate shapes possess a complex three-dimensional vortex flow structure. At the channel inlet, the incoming stream is divided into a large number of elementary jets, each of which change in direction and motion, and the flow core in each jet gets disturbed. As a result, the structure of the turbulent flow in the channel is determined by the flows in elementary channels (grooves) along the ribs of lower and upper corrugated plates and their interaction in the mixing zone. The type and details of the flow structure and, hence, the heat-transfer rate and hydraulic losses depend on both the flow structure and geometric parameters.
To measure the temperature fields, thermochromic LC coatings were used with the temperature range of selective reflection of light ΔT = 3 and 5 °C. The experiments were carried out under conditions of constant heat-flux density on the wall. In this case, the isotherms are simultaneously the curves of constant heat-transfer coefficient. The LC film was glued on to the outer side of the corrugated surface, and, therefore, on the images recorded by camera through the transparent window, the rib top on the outer surface corresponds to the valley on the flow side.
The optical response of the LC coating to the temperature field (colour images of the model surface) was recorded by a camera or immediately grabbed in to a PC. Then, using calibration dependencies ‘hue-temperature’, the colour pattern was converted in to the temperature field. Figure 13.3 shows the map of isothermal regions in colour representation. In this figure one can see periodic cellular structure, where areas with the higher surface temperature are consistent with lower heat exchange (separation zones, for example). Highly sensitive LC displayed small local temperature gradients. The temperature is gradually increased from the inlet to the outlet of the channel. For more detail, Fig. 13.4 shows the plot of temperature variation on one of the ribs in its central part. The heat-transfer rate on the lee side is seen to be less than that on the windward side, which results in a higher lee-side temperature. Besides, interchanging sections with reduced and elevated temperatures are observed along the contact line of the corrugated plates, which is indicative of the probable presence of local two-dimensional flow detachment regions formed in the flow over ribs, three-dimensional vortex structures, etc. At the same time, an increase in temperature along the rib length and downstream is observed.
To gain more information about the flow structure, we performed visualization of the shear-stress distribution over the channel wall using LC coatings insensitive to temperature but readily responding to shear stress.
13.3.2 Visualization of the shear-stress distribution by the method of texture transition in cholesteric LC
To visualize the shear-stress distribution over the model surface, we used the texture transition method based on the use of LC insensitive to temperature (in the given temperature range) but sensitive to shear stress. On spraying the LC coating on to the model surface, we obtained the so-called focal-conic texture. In this texture, the LC molecules are arranged at random, without any predominant direction of molecule alignment. On exposing such an LC film to white light, the surface appears colourless because of light scattering, see Fig. 13.5. However, under the action of a shear stress, a transition from the focal-conic to the so-called Granjean (planar) texture occurs in which the LC molecules are aligned along the direction of shear. Under these conditions, the LC film selectively reflects the incident light and looks coloured.
The LC coating was sprayed on to the model surface painted black. After a certain time of model flow (equal to 5 min in our experiments), the test section of the wind tunnel was dismounted. The non-reversible colour pattern obtained on the corrugated surface was recorded with a camera. The colourless, black regions correspond to the zones of zero shear stress or, more accurately, of stresses lower than a certain threshold value. The regions with shear stresses higher then the threshold look coloured due to texture transition.
Figure 13.6 shows the distribution of shear stress over the windward rib side. On this side, quite a uniform distribution of shear stress throughout the whole corrugated plate is observed. Two specific features are observed, the black region near the valley that becomes narrower when going from channel inlet to outlet and a coloured region on the remaining area of this part of the rib. The flow wake in the coloured (lighter) region resembles a fur-tree branch with the axis lying close to the rib crest.
Figure 13.7 shows the distribution of shear stress on the lee rib side. The white dashed lines show the rib direction of the opposite plate. A three-dimensional cellular structure is clearly seen which varies both along the test section and along the length of the rib (elementary channel). A rise in the shear-stress level from inlet to outlet is clearly seen. Just behind the crest of the rib, a semicircular wake of a vortex brought about by the interaction between the streams flowing in the upper and lower elementary channels is observed in each elementary cell. Closer to the valley, a wavy wake of vortices localized in this region is seen. These two regions are separated from each other by a narrow black strip with zero shear-stress level. Near the rib ends, within one or two elementary cells, edge effects caused by flow deflection are observed, see Fig. 13.7.
The data permits a reconstruction of the vortex flow pattern in the near-wall region shown in Fig. 13.8. In this figure the development of both plates with a qualitative sketch of the shear stress pattern is presented.
Measurements of temperature and shear-stress fields indicate that regions of low or zero shear stress correlates well with regions of decreased heat transfer.
The combined use of LC coatings sensitive either to temperature or shear stress permits easy determination of the flow-structure features on a complex-shaped model. The obtained data can be used for optimization of the geometry of heat-exchanging surfaces.
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G M Zharkova, V N Kovrizhina, and V M Khachaturyan
Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia