PIV and LDV measurements behind a backward facing step

Transcription

1 PIV and LDV measurements behind a backward facing step M.T. Pilloni, C. Schram, M.L. Riethmulle/^ ^ Mechanical Engineering Department, Cagliari, Italy ^ von Karman Institute for Fluid Dynamics, 1640 Rhode St-Genese, Belgium Abstract This experimental work is the result of a collaboration between the Mechanical Engineering Department of Cagliari, Italy, and the von Karman Institute for Fluid Dynamics, Brussels. Here the flow field downstream of a backward facing step in a low speed wind tunnel was experimentally studied by means of a PIV system, and series of images of the instantaneous flow were acquired and averaged to obtain the mean flow field and turbulence information. The same flow region in similarity conditions was experimentally investigated by an optic fibre LDV system, in a similar test facility in Cagliari university. The averaged flow field is characterised by a principal recirculation region downstream of the step, together with a secondary vortex located between the main bubble and the step, while the instantaneous flow field is characterised by a very complicated system of vortices, and a shear layer develops from the backward facing step corner and reaches the bottom wall at the reattachment length. The comparison of LDV and PIV experiments results is quite good, especially for what the horizontal mean velocity component is concerned. The test performed showed that PIV and LDV information should be integrated to give both a temporal and a spatial information for the whole measurement field, which is fundamental for a correct evaluation of the complex atmospheric flows, and allows the analysis of the time evolution of the main flow patterns.

2 634 Air Pollution VIII 1 Introduction Separated flow regions are of very great importance both in urban and industrial air pollution applications. Industrial applications of atmospheric separated flows cover a wide range of engineering problems; their knowledge is of fundamental importance, and for that tests on industrial complexes have to be performed. In particular, the knowledge of recirculating flow regions around isolated buildings or groups of buildings is very important for a proper position and design of air conditioning and ventilation systems. To reach this goal the flow around basic simple models should be investigated both in numerical and experimental way, in order to analyse and understand more complex phenomena. Moreover, at the present time, the cost involved in a reliable numerical simulation (Direct Numerical Simulation) of such complex flows is still prohibitive. Nowadays, the most commonly used tools for experimentally investigate recirculating flow regions are LDV and PIV systems. LDV is a well established technique, used for a wide range of applications, for almost thirty years, but for ten years, PIV has been the emerging technique. The combination of the two techniques allows to obtain more complete and extensive information. In this frame, the complicate pattern of the flow field behind a backward facing step was analysed. This flow has been extensively studied in the past (see Armaly et al 1983) and is still investigated both experimentally and numerically (see Le et al. 1997). Despite the simplicity of its geometry, that allows the assumption of a 2-D averaged flow field, the complexity of the flow structure still justifies further works. The analysis was performed in the mid-plane of a low speed wind tunnel test section, by means of an LDV and a PIV system. The first one gives the information on the variation with time of the velocity in a single point of the flow field; the second one gives the instantaneous picture of the whole two dimensional flow field. The results of the two measurements, therefore, put together, should allow to account at the same time for the variations of the flow in both space and time. This paper is mainly concerned with the first aspect of the problem. After describing the experimental set-up and how the LDV and PIV measurements were performed, the mean velocity flow field obtained by both LDV and PIV together with RMS values and the velocity profiles at some locations from the obstacle are shown. This gives the picture of the main patterns of the flow field. Moreover a detailed analysis of the information obtainable from the two systems together with the comparison between the results obtained from the measurements is illustrated.

3 Air Pollution VIII Experimental set-up 2.1 LDV experiments LDV tests were performed at the Mechanical Engineering Department of Cagliari University. The experimental set-up includes both the wind tunnel and the measuring system. The first is a low speed wind tunnel, with a 1000mm long plexiglas test section, with an area of 200*200mml It is divided in two parts by a horizontal plexiglas plate, thus forming a 200*100mnf useful test section. The wind tunnel is composed of a diffuser (with a honeycomb at the entrance and two screens for turbulence control), a stagnation chamber (with another honeycomb and three screens), a convergent and the test section; it is driven by an axial fan positioned upstream of the stagnation chamber and moved by a 0.95kW asynchronous motor; the velocity can be continuously changed by means of a frequency controller. Figure 1 shows a sketch of the upper part of the test section and the measurements region. Figure 1: Upper part of the test section and measurements region. A plexiglas plate with the thickness of 20mm is used to realise a 20mm backward facing step geometry, leading to a 80mm height upstream channel, followed by a 100mm height channel. The expansion ratio, defined as the ratio between the channel height downstream and upstream of the step, was The measurement chain includes a 6W Argon LASER (Spectra-Physics), the optics (beam splitter, beam displacer, Bragg cell, optic fibre manipulators, etc.) (Dantec), the LASER probe, the Burst Spectrum Analyser, the PC and the traversing system. The whole system is software controlled. The measurements were performed using incense seeding particles, introduced at the inlet of the fan, thus producing a seeding of the entire flow.

4 636 Air Pollution VIII 2.2 PIV experiments PIV tests were performed at the von Karman Institute for Fluid Dynamics, in Brussels. The wind tunnel is characterised by the same geometry as the one of the LDV experiments. Some differences have however to be noted. A 0.7KW asynchronous motor, regulated by a frequency controller, drives a centrifugal blower. The diffuser attached to the blower by a soft link contains two grids and ends in a settling chamber through a honeycomb. The area ratio of the 2D contraction that leads to the test section is roughly equal to 5.5. A plexiglas plate divides the height of the test section to provide the same step geometry than for the LDV measurements. In order to achieve the independence of the inlet flow with respect to ambient conditions (temperature, noise, oil particle deposits...), the transition of the boundary layer is triggered at the leading edge of the plexiglas plate by 10 centimetres of glued sandpaper. For what concerns the PIV measurement chain, a double-pulsed Nd:YAG laser, that provides 200mJ in 10ns for each pulse, was used to illuminate a thin sheet of the BFS flow, in the mid-plane of the test section. The flow is seeded by small droplets of oil (lum) at the entrance of the blower. The images of the particles illuminated at the two successive instants are recorded by a CCD camera having a resolution of (756x58 l)px\ and sampled to (512x256)px^. The PIV processing of the pairs of images is performed by WIDIM, a homedeveloped software (see Scarano [1]). The similarity in LDV and PIV experiments is kept for the Reynolds number (Reh=5000), based on the obstacle height and the free stream velocity, for the geometry of the test section (200x200x1000) mnf and for the expansion ratio (ER=1.25). 3 LDV measurements and results The measurements were performed at a free stream velocity of 3.75m/s. The flow region under investigation, represented in figure 1, lies on a vertical plane at the centre of the wind tunnel and extends over 150mm downstream of the backward facing step. The measurement grid consists of 19 velocity profiles, each one described by 32 points; in order to better resolve the velocity gradient, a stretching of the measurement grid was used, with denser measurements close to the bottom plate and to the step. In each point of the grid bursts were acquired; the time of acquisition varied with the data rate, ranging from 8-10 seconds for the grid points far from the wall, to 3 minutes for the measuring points close to the wall, for which the data rate was very low: in this case a maximum acquisition time of 3 minutes was stated by program, giving a number of samples lower than but always larger than

5 Air Pollution VIII 637 From the instantaneous data, for each point under investigation, the averaged velocity, the RMS, the turbulence intensity and other turbulence parameters were calculated, for both the horizontal and the vertical velocity components. Figure 2 shows the mean velocity flow field obtained from the LDV measurements, characterised by a main recirculation region and a smaller vortex close to the step wall. Uo=3.75m/s x/h Figure 2: mean velocity flow field obtained by the LDV tests. The reattachment length, measured at the reversal of the horizontal component at the wall, was found at XI h ~ 5. In figures 3 and 4 the contour plots for the mean horizontal and vertical velocity components obtained by the LDV tests are illustrated; they clearly show a shear layer developing from the backward facing step corner and reaching the bottom wall at the reattachment length. x/h Figure 3: horizontal mean velocity isolines obtained by LDV.

6 638 Air Pollution VIII x/h Figure 4: vertical mean velocity isolines obtained by LDV. 4 PIV measurements and results The PIV measurement region concerns roughly the same area as for the LDV measurements: 160mm downstream of the step, in the mid-plane of the test section. This region was covered by 3 series of acquisitions, at successive downstream positions of respectively 92, 74 and 53 pairs of images. Although this number of acquisitions does not satisfy the criteria of statistical convergence, a comparison with the LDV data could be done. The mean velocity field, averaged from the 3 regions and interpolated on a regular grid with the same spatial sampling, is shown on figure 5. The velocity field shown was undersampled by a factor 13 in the.x-direction, in order to see the evolution of the mean flow with the downstream distance. Figure 5: mean velocity flow field obtained by the PIV tests. The superposition of some streamlines, computed by integration of clearly shows the presence of the 2 recirculating regions. ~

7 Air Pollution VIII 639 The smaller one is located in the corner of the step and is roughly 0.5/z high and 0.75/z long (where h stands for the step height). The main recirculating bubble is comprised between the smaller one and the reattachment point. The abscissa of this reattachment point, evaluated at the reversal of u at the wall, was found at xlh ~ 5.1. Figure 6: RMS isolevels of u by PIV experiments. The fluctuations of the flow are represented in figures 6 and 7, where the RMS isolevels of u and v are reported. It appears that the fluctuations of u, contained in the incoming turbulent boundary layer, develop past the step under the action of turbulence, and fill the step height in approximately 3h. The fluctuations of v begin to develop at x=lh, and also fill the step height at x=3h. Figure 7: RMS isolevels of v by PIV experiments.

8 640 Air Pollution VIII 5 Comparison LDV-PIV 5.1 Comparison of the technique LDV and PIV are at the present major tools in the study of complicated flow structures, like shear layers, recirculation regions, separated flows, and so on. Nevertheless, apart from some common features, the two systems give a very different kind of information. LDV, characterised by a very high spatial resolution, allows to detect the variation with time of the instantaneous velocity, but the spatial correlations in the flow field are lost. PIV, on the other side, gives the instantaneous picture of the two-dimensional flow field, thus allowing the detection of the spatial correlation between the flow structure, but losing the time information. In particular, basic PIV systems do not allow the evaluation of the spectrum, that is a very powerful tool for analysing complex flows. The above statements suggest that they have to be considered as two complementary velocity measurement techniques, with different fields of application: LDV is indispensable in all those cases in which non stationary phenomena are involved and a time investigation of the problems is required; PIV should be taken into account when the 2D structures have to be quantitatively visualised. From the point of view of the measurements, the present investigation allowed to extend the comparison between LDV and PIV systems to some other aspects of the problem. One is, for example, the data rate that is achievable, and which settles directly the time needed to compute a converged statistical moment. In that respect, the LDV is much faster than PIV for one spatial point, since LDV only needs to acquire series of points, while PIV needs to acquire series of images. At the opposite, to obtain field quantities, like the mean flow field, the PIV is much more practical, since it doesn't need any mobile device, as needed in LDV which must scan the area of concern. A typical time needed by LDV to obtain a two-dimensional mean flow field is roughly equal to 30 hours. With a well-synchronized PIV system, the acquisition time is of the order of 100s for 1000 images (at lohz), and the processing of these images requires less than 3 hours. But in this evaluation the number of information acquired by the LDV system has to be taken into account: sample for each of the 32 points of 19 velocity profiles for the two velocity components, that makes samples! 5.2 Comparison of the results Figures 8 and 9 respectively show the normalized mean u and v profiles at several positions downstream of the step: x/h-0.5\ 7; 2.5; 5 and 7.5. The continuous line stands for the PIV data, and the squares for the LDV data. The scale of the u-axis is represented for the last profile, at x/h-7.5.

9 Air Pollution VIII 641 o o U/U. Figure 8: horizontal mean velocity profiles at several locations from the step 2 - I 1 L_ v/u. Figure 9: vertical mean velocity profiles at several locations from the step obtained by LDV and PIV tests. For what concerns the mean u profiles, the agreement is quite good, especially near the step, where the small reversal of u due to the recirculation bubble can be seen. Further from the step (x/h=5 and 7.5), the LDV profiles exhibit the behaviour of a redevelopping boundary layer, while the shape of the PIV profiles seem to indicate a later reattachment. The reasons for the slight discrepancies concerning the reattachment length may be twofold, lying in the measurement or in the flow itself. For what concerns the measurement technique, it is doubtful that some uncertainty could play a role in the evaluation of the reattachment length. On the flow side, it is known that slight differences in the experimental arrangement can justify a different behaviour: nature of the triggering of the boundary layer, centrifugal blower or axial fan, external noise, etc. The choice of the seeding particles (incense particles for LDV, oil particles for PIV) may also interfere. The statistical convergence of the v-profiles seems worse than for the u- profiles. This is explained by the fact that the relative RMS is bigger for v than for u. Nevertheless, a good agreement can be found in the small VRMS regions. In

10 642 Air Pollution VIII the high VRMS regions (see figure 7), it is more difficult to infer whether the discrepancies come from the flow or from the lack of statistical convergence. A last comment can be done on the resolution of the measurement techniques near the wall. Since the resolution of the CCD camera is fixed, the spatial sampling of the PIV measurement varies as the inverse of the field of view. As the field of view of the camera was chosen relatively large in order to cover the recirculation region in only 3 steps, the spatial resolution was limited to 0.8mm, such that the full height of the velocity gradient of the boundary layer could not be resolved. LDV, in that purpose, is much more flexible since it allows to continuously scan all the positions of the flow, without any limitation: the spatial resolution is related only to the size of the probe volume, which is of the order of 0.08 mm both in the u and v directions. This allowed to refine the LDV measurements near the wall, and to accurately resolve the velocity gradient of the boundary layer. 6 Conclusions The tests performed downstream of a backward facing step clearly show the ability of both LDV and PIV systems to properly measure complex flows. Besides the same capacity to properly track the flow patterns, the experiments performed allowed to shed some light on some very important aspects of the two techniques. In particular, a very large difference was detected in the acquisition time for the LDV and for PIV. Moreover, PIV is inherently two-dimensional, while the basic LDV technique is one-dimensional. This does not prevent the two components of the flow to be acquired in different times, but this means that Reynolds stresses cannot be computed, unless to use a two component LDV system, which requires two signal processors and a much more complicated measurement chain. On the other side, some advantages came out from the tests for the LDV technique, mainly the very high data rate and the time series information. The combination of the two measurement systems allows a more extensive and complete information giving both the temporal and the spatial variation of the flow. References [1] Armaly B.F., Durst F., Pereira J.C.F. and Schonung B. (1983) Experimental and theoretical investigation of backward-facing step flow. Journal of Fluid Mechanics 127: [2] Le H., Moin P. and Kim J. (1997) Direct numerical simulation of turbulent flow over a backward-facing step. Journal of Fluid Mechanics 330: [3] Scarano F. (1999) Iterative multigrid approach in PIV processing with discrete window offset. Exp Fluids 26: