Flow Features in a Fully Developed Ribbed Duct Flow as a Result of MILES

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1 Flow Features in a Fully Developed Ribbed Duct Flow as a Result of MILES Máté Márton Lohász (lohasz@ara.bme.hu) Department of Fluid Mechanics, Budapest University of Technology and Economics Environmental and Applied Fluid Dynamics Department, Von Karman Institute for Fluid Dynamics Patrick Rambaud (rambaud@vki.ac.be) Environmental and Applied Fluid Dynamics Department, Von Karman Institute for Fluid Dynamics Carlo Benocci (benocci@vki.ac.be) Environmental and Applied Fluid Dynamics Department, Von Karman Institute for Fluid Dynamics Abstract. The present contribution describes the topology associated with the turbulent flow in a square duct partially blocked by a rib of square section mounted on a single wall. The flow is simulated by means of a MILES method and the resulting velocity fields are analysed using the concepts of streamsurface, vortex core detection, wall streamline and bifurcation line. Instantaneous and time averaged coherent structures are extracted applying the second scalar invariant of the velocity gradient tensor (so-called Q criterion) respectively to the instantaneous and time averaged velocity fields. This postprocessing reveals significant 3D effects induced by the geometry, namely the influence of the side walls, which is clearly identified. The combination of the different visualisation techniques offers a complement to the standard representation based on Eulerian statistics and contributes to a deeper understanding of this complex flow. Keywords: Ribbed Duct, MILES, Flow Topology, Q Criterion 1. Introduction Flow in ribbed ducts can be considered representative of the phenomenology found in the internal cooling channels within turbine blades. The presence of ribs increases turbulence levels and, as a result, it enhances heat transfer. Detailed knowledge of the heat transfer and the flow field is important for the blade designer to avoid material damage caused by overheating. In past years, this class of flow has been extensively investigated experimentally; in particular an in-depth investigation has been performed (and is still progressing) at the von Karman Institute for Fluid Dynamics (VKI) [31], [10], [7], [9], [6] and [8]. c 2006 Kluwer Academic Publishers. Printed in the Netherlands. ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.1

2 2 M. M. Lohász P. Rambaud C. Benocci The complex topology of the flow had already been demonstrated experimentally by [10] and studied in depth by [7], [9], [8] by means of Particle Image Velocimetry (PIV). These investigations demonstrated the complexity of the flow and its strong three dimensional nature, dominated by the effect of the side walls. The side wall effects have not yet been fully analysed using a numerical tool. The well-known limitations of Reynolds Averaged Navier-Stokes (RANS) for the investigated flow [29] led the authors to conclude that Large- Eddy Simulation (LES) would be the most suitable tool for a companion numerical research aiming at a complete understanding of this complex flow and especially the topological effect induced by the side walls. Indeed, the DNS or LES methodology have been extensively performed to reproduce the ribbed plane channel flow. In this simpler type of configuration, periodic conditions are usually adopted in the spanwise direction allowing a 2D-like description of the mean flow. A non-exhaustive bibliographic survey of this topic could list the first investigations by [13] and [41], as well the most recent contributions by [25], [15], [23], [3] and [28]. To the authors best knowledge, few ribbed duct simulations demonstrating the three-dimensional character of the mean flow have been performed at the present time. Among these, one may cite: [39], [26], [27], [1], [2], [34]. Nevertheless, in most of these investigations, the main interest was focused on reproduction and prediction of the Eulerian statistics (average) and of the resolved turbulent field, without a real topology analysis. The macroscopic quantities of engineering interest and Eulerian statistics of the averaged flow associated with the present flow have also been collected and presented [24], but the lack of a deep topological analysis justified the present contribution. In order to reach this goal, vortical structures embedded in the averaged flow field have been analysed together with their footprints on the different walls. Indeed, if different visualisation tools are available ([18] gives a summary), among them, the streamlines and streamsurfaces proved to give the most fruitful information. Further insights into the separation and reattachment regions have been gathered using wall streamlines and bifurcation lines. Furthermore, considering that the existence and the importance of coherent structures in separated wall flows have already been demonstrated ([16], [3], and [38]), the authors have applied the Q criterion [22] for the detection of coherent structures. It has to be noted that this criterion is here applied not only to the instantaneous field, where it reveals formation of the vortices on the leading edge of the rib and enables successful observation of their trajectories and ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.2

3 Flow Features in A Fully Developed Ribbed Duct Flow 3 deformation, but also to the time-averaged field where it underlines the complexity of the mean flow Description of the Studied Configuration The present authors have studied the flow in a square-section duct (with four side walls) where successive ribs of square cross-section are mounted on one wall, placed normal to the stream direction. The value of the Reynolds number is 40000, based on the hydraulic diameter (D) and the bulk velocity (U). The geometry is defined, in dimensionless units, by the rib size (h/d =0.3) and the pitch distance (p/h = 10) between the successive ribs. In [7] and [9], it has been experimentally found that, for such a configuration, the flow starts to repeat itself every pitch length after the fourth rib. Therefore, the simulation is confined to one pitch length and periodic boundary conditions are applied in the streamwise direction. The fluid is treated as incompressible. 2. Numerical Solution 2.1. Numerical Solution of the Transport Equations The flow field is simulated using Fluent 6.1, a general-purpose commercial code for fluid dynamics simulation produced by Fluent Inc. The Large Eddy Simulation (LES) approach is applied to model the turbulent field. The relevant transport equations are discretised in space with the Finite Volume approach, implemented in a cell-centred collocated variable arrangement for unstructured grids. The equations for the three components of the momentum are solved sequentially and the pressure-velocity coupling is performed by applying the wellknown SIMPLE algorithm [17]. Time integration is performed by the second-order Gear s method in an implicit formulation. The solid walls are modelled using the classical linear-logarithmic law condition for velocity, while, as already stated, a periodic condition is imposed for the streamwise direction together with a forcing term added to the streamwise momentum equation to maintain constant mass flux in time The choice of the MILES approach The LES approach is based upon the hypothesis that the turbulent field can be separated, by the application of a spatial filter, in the large, energy-containing eddies, to be explicitly resolved by means of a time-marching calculation, and the small-scale eddies, to be modelled ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.3

4 4 M. M. Lohász P. Rambaud C. Benocci with an adequate sub-grid stress model (SGS). A complete survey of this technique can be found in [32]. An alternative approach is to make use of an implicit SGS model, as proposed by Boris [5] with the monotonically integrated LES (MILES) concept. This approach relies on the fact that any high-order upwind scheme coupled to a non-linear limiter produces a numerical dissipation of order O( 2 ), proportional to the grid size ( ) and, hence, proportional to the size of the spatial filter applied by the LES approach. Therefore, this numerical term is formally analogous to the explicit sub-grid diffusivity of classical SGS models and could replace it. Different examples in the literature ([19] and [37]) show that this approach is capable of yielding results comparable to the ones of classical LES. In the present study, the relatively high Reynolds number and complexity of the flow make it, in any case, mandatory to apply a monotonic discretisation to avoid the presence of aliasing errors, making MILES a cost-effective approach. Therefore, the present simulation is performed applying a second-order upwind scheme, limited by a slope limiter, for the momentum fluxes of the convection term, while the pressure in the momentum equation is interpolated with a second-order interpolation scheme. The validity of the present approach has been checked by a control simulation, performed by adding to the MILES dissipation an explicit SGS diffusivity (Smagorinsky model with a coefficient C s =0.1 [32]). As will be shown in the following, it has yielded comparable results, validating the use of MILES for the present investigation Grid The presents simulations were performed over a hybrid grid. In the near wall regions, a structured layer with a thickness of 0.08D is used. The size of the first inner cell is 0.003D and the cell-to-cell ratio is 1.09 when moving away from the wall. The wall layer spans respectively 8 cells on the lateral side walls, 14 cells over the top of the rib and 10 cells above all other walls. The typical distance from the wall of the first cell centre is about y + = 5 in wall units based on an instantaneous wall shear velocity. While this resolution is not adequate for a fully resolved LES, it is sufficient to ensure that the first inner grid point falls within the viscous sub-layer and, then, provides a satisfactory reproduction of the wall shear stress. The cell sizes in the directions parallel to the walls are one order of magnitude larger than the size in the wall normal direction. Outside the wall regions, the grid is unstructured in the X Y planes and structured in the spanwise direction, with a typical cell size in the order of 0.02D. ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.4

5 Flow Features in A Fully Developed Ribbed Duct Flow 5 The resulting mesh contains cells. The grid in the X Y plane is presented in Figure 1. Figure 1. Grid in the X Y plane Simulations and Validation In the present simulations, the time step was fixed at 0.005D/U, which approximately corresponds to an average CFL (Courant, Friedrichs, Lewy number) value of 0.3 over the whole domain. Even if maximum values of the order of 3 are found in some small, high-velocity cells, this average value respects the criteria proposed by [12] to ensure accuracy in time for LES. The averaging time of the present simulations is equivalent to 47 times the time necessary for a fluid particle to be transported through the complete duct at the bulk velocity (141D/U) assuring convergence of the corresponding statistics. As already stated, detailed analysis of the Eulerian statistics of mean and resolved turbulent quantities lies outside the purpose of the present article and only some basic results are presented here, to prove that the flow has been satisfactorily simulated and the present analysis is therefore valid. Detailed results and comparison with the corresponding measurements can be found in [24]. From the engineering viewpoint, the average pressure drop over one pitch interval ( P ) is one of the most important integral parameters characterising the performance behaviour of the set-up. This pressure drop can be linked to the friction factor (f) by the following relation: f = D P 2pρU 2 (1) In present calculations, the average value of f is obtained averaging over the time span of the calculation, while information about its determination in the companion experiment can be found in [7]. The ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.5

6 6 M. M. Lohász P. Rambaud C. Benocci relative effect of the presence of the rib can be assessed by comparing the present friction factor with the one for a smooth pipe with the same hydraulic diameter and the same Reynolds number. This last case can be expressed with the following correlation [4]: f 0 = 0.046Re 0.2 (2) The ratio f/f 0 computed both for the experiments and the simulations are proposed in Table I. The difference found between measurement and Table I. Enhancement of the friction factor compared to a smooth pipe at the same Reynolds number. f/f 0 From measurement [7] 12.3 ± 0.25 From MILES with C s = From MILES with C s = simulation is of the order of 5% and represents a rather encouraging validation. The difference between the two LESs shows that the simulation is still sensitive to the presence of an explicit SGS model, a result which would confirm that MILES might be, by itself, insufficient to totally take into account the interchange between resolved and sub-grid scales, as found by [14], while it provides a satisfactory reproduction of the macroscopic effects. Figure 2. Flow structures in the symmetry plane (Z = 0); average streamlines. The topology of the average flow in the symmetry plane can be seen from the streamlines in Figure 2. Four main regions are easily recognised where the flow exhibits a strong rotating nature. The largest ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.6

7 Flow Features in A Fully Developed Ribbed Duct Flow 7 region corresponds to the main separation downstream of the rib. The other regions, labelled V 1, V 2andV 3 correspond, respectively to the recirculation; at the downstream corner of the bottom wall (V 1), on the top rib (between the leading and trailing edges, V 2) and at the upwind corner of the bottom wall (V 3). The associated lengths in the streamwise direction are respectively labelled as: L Big, L V 1, L V 2 and L V 3. In the present work, the values of these lengths are evaluated by applying the criterion defined in the companion experimental study [8] to allow a direct comparison. They are therefore not measured on the wall itself but at a small distance above it [8]. The results are presented in Table II. It can be remarked that the two simulations agree quite Table II. Streamwise sizes of the recirculating regions in the symmetry plane, see: Figure 2. L Big L V 1 L V 2 L V 3 C s =0 3.34h 0.52h 0.91h 1.62h C s = h 0.5h 0.91h 2.14h Exp. [6] 3.76h 3.84h 0.255h 0.28h 0.6h 0.9h 1.04h 1.5h well with the experimental result for the main separation (L Big ). For the smaller detached regions the difference is greater and it can be concluded that the explicit sub-grid dissipation has a clear effect only on the L V 3 length. Figure 3 presents the average in-plane velocity components for the symmetry plane X Y. Except for some small differences in the streamwise velocity, the agreement for averaged velocities is satisfactory. This conclusion, together with the previously discussed results, enables us to conclude that the large-scale flow field is well reproduced and can be used to study and reconstruct the topology of the flow. 3. Results 3.1. Topology of the averaged flow The general phenomenology of the present flow is shown in Figure 2. Although the mean flow in the symmetrical plane seems similar to the one which could be found in a 2D situation (i.e. ribbed channel), outside the symmetrical plane, the effect of the side wall is strong and the flow is entirely 3D. This is already noticeable from the streamlines in the main recirculation bubble that are not closed (see Figure 2). ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.7

8 8 M. M. Lohász P. Rambaud C. Benocci Figure 3. Comparison between computed (Circle for C s = 0, Triangle for C s =0.1) and PIV result of [6] (solid line). In the symmetry plane (Z/h =0)a)X velocity, b) Y velocity. Streamlines in the Z = 0 plane are not closed due to the fact that the symmetry condition requires U/ Z = 0, V/ Z = 0 and W = 0, while W/ Z = 0 is not a property of a symmetry (mirroring) plane. The three-dimensional character of the flow will be progressively demonstrated with different visualisation methods in the following subsections Wall Streamlines Figure 4, 5 show the wall streamlines for the entire flow field. It appears that the flow trapped in the upstream separation region escapes upward in the area with low streamwise momentum, formed by the side wall boundary layer. The traces of the flow on the sidewalls are characterised by bent wall streamlines. Figure 4, 5 also display bifurcation lines (thick white/black lines), defined as borders where the streamsurfaces detach or reattach themselves from/to the walls ([21]). As a matter of fact, for a general 3D flow a wall shear stress component exists aligned in the direction of the bifurcation line, making arbitrary and useless the classical definition of the separation and reattachment point for 2D flow (zero wall shear stress). Therefore, the authors adopt the extraction method proposed in [20] to remove this arbitrariness and use the cell size to mark the bifurcation line. Unfortunately, this representation is still subject to computational noise due to the level of convergence, which may appear on the figures as white ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.8

9 Flow Features in A Fully Developed Ribbed Duct Flow 9 Figure 4. Wall streamlines and bifurcation lines; positive ( separation ) white lines, negative ( reattachment ) black lines. and/or black points. These series of points have to been seen (when possible) as continuous lines Secondary Flow Figure 6 displays four spanwise planes holding unclosed streamlines giving a first confirmation of the presence of strong secondary flows. As an interpretation, it may be proposed that the blockage induced by the rib forces the flow (in front of the rib) to escape along the side wall and over the rib in an upward motion. This upward motion is compensated for by a downward motion in the central part of the duct, leading to a couple of streamwise elongated counter-rotating structures in the upper part of the duct (Figure 6). In Figure 7, the presence of the high spanwise velocity regions, due to the blockage effect of the rib, is underlined by isosurfaces of relatively high spanwise velocity component value Side Wall Effect on the Recirculation Regions It can be concluded that the side walls have a strong influence on the separated region located on the windward side of the rib. This effect is linked to the secondary flow induced by a spanwise pressure gradient. The presence of this gradient can be deduced from Figure 8, which shows the static pressure for, respectively, the symmetry plane Figure 8 (upper) and the side wall Figure 8 (lower). It can be seen ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.9

10 10 M. M. Lohász P. Rambaud C. Benocci Figure 5. Wall streamlines (arrows lines) and bifurcation lines; positive ( separation ) white dotted lines, negative ( reattachment ) black dotted lines. Figure 6. Secondary flow patterns in time-averaged flow (black lines), wall streamlines (white lines). that, around the stagnation corner of the rib, a region of high pressure is present on the side wall and in the symmetrical plane, resulting in a spanwise pressure gradient which drives the fluid toward the side wall. One may also remark that an opposite pressure gradient region exists downstream of the rib. This pressure gradient induces a motion away from the side walls toward the symmetrical plane. This swirl away from the wall was already visible through its footprint on the wall streamlines of Figure 4, 5 and is confirmed by the pattern of the single streamline ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.10

11 Flow Features in A Fully Developed Ribbed Duct Flow 11 Figure 7. Streamsurface starting from X = 2, Y = 0.02 (yellow); 3D Streamline trapped in the main recirculation and reaching the bottom wall at X =5,Z = 0.3 (black line); isosurfaces of regions of high (0.3U) spanwise velocity (blue surface: W = 0.3U, red surface: W =0.3U); bifurcation lines as in Figure 4, 5 drawn in the wake of the rib in Figure 7. From the spanwise direction point of view, the recirculation before and after the rib is driving the flow in the opposite sense: from the symmetrical plane towards the side walls for the recirculation upstream the rib, from the side walls towards the symmetrical plane for the recirculation downstream the rib Vortical Structures and Stream Surfaces A consequence of the upstream separation is the production of a high level of vorticity. Experimental investigation performed at VKI by [7], [9] and [8] gave indication that a major part of the vorticity field is induced by the side walls: the boundary layer on the wall displaced by the rib produces extra vorticity in the streamwise direction. These rotation-dominated regions can be visualised as isosurfaces of the second scalar invariant (Q) of the velocity gradient tensor ([22]): Q. = 1 2 (Ω ijω ji S ij S ji ) (3) where Ω and S are the anti-symmetrical and the symmetrical part of the velocity gradient tensor. Q is nowadays a commonly accepted and applied criterion for visualising the coherent structures embedded in the instantaneous field ([16]) as it will be used in the next section. Nevertheless, such a detection tool can also be applied to the averaged ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.11

12 12 M. M. Lohász P. Rambaud C. Benocci Figure 8. Pressure contours on symmetrical plane (upper) and on sidewall (lower). field, where it is very useful for investigating rotation-dominated regions [30]. It is also used in this section, associated with the traditional stream surfaces. For this purpose, the composite Figure 9 presents, in a single frame, the information given by a Q visualisation of the averaged flow field as well as the traditional stream surfaces. The left part of this figure displays the stream surface passing through the line (X/h = 1.08; Y/h = 0.05; 1.6 <Z/h<0). This stream surface helps to visualise the active recirculation tube which drives the flow arriving on the rib in a swirling movement towards the side walls. This observation is in agreement with previous experimental interpretations ([10], [7], [9], [6]). The right part of Figure 9 shows the Q isosurface associated with the value 0.2U 2 /h 2. Both representations underline the structure resulting from the upstream separation on the ribbed wall, the path of the flow which is lifted up close to the sidewall by the upward motion and is arched over the rib. One can note that the Q isosurface also highlights the attached recirculation structure on the top of the rib and the streamwise-oriented structures on the upper corners of the duct, which were already visible in Figure 6. Despite the usefulness of the information yielded by the Q field, the traditional stream surfaces remain a powerful tool for demonstrating the high mixing introduced by the rib obstacle. In Figure 10, such surfaces are created from line (X/h = 3.8; Y/h =0.5; 1.6 <Z/h< ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.12

13 Flow Features in A Fully Developed Ribbed Duct Flow 13 Figure 9. Left side (Z < 0): streamsurface released from location X/h = 1.08, Y/h =0.05 (blue). Right side (Z >0): Q =0.2 (U 2 /h 2 ) isosurfaces (red); streamlines bounding these isosurface (black lines) and wall streamlines (black lines); vortex cores (thick white lines). 0) and from line (X/h = 3.8; Y/h =0.25; 0 <Z/h<1.6). It appears that the flow belonging to stream surfaces released with Y < 0.25 is lifted up at the side wall or trapped in the recirculation located in the wake of the rib. This wake structure downstream of the rib is better visualised by Figure 11, which shows the details of the separation region on the top of the rib. It may be noted that the top rib structure is weakly influenced by the side walls. This is demonstrated by the streamlines forming the stream surface, which are almost parallel to the streamwise direction, shown in Figure 11. In contrast, it appears that the wake structure (whose shape and position is controlled by the rib geometry) has a strong influence on the wall streamlines on the side walls, as is shown in Figure 12 where one may see 3D streamlines flowing over the rib before entering the wake recirculation from the side to move toward the symmetrical plane. The vortex cores of the recirculation regions, detected by the method proposed in [36], are also shown in Figure 12 as a bold line. It can be noted that the core of the wake is displaced towards the side wall near the rib, while the strength and persistence of the corner streamwise vortex are also evident. ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.13

14 14 M. M. Lohász P. Rambaud C. Benocci Figure 10. Streamsurface of time averaged field released from a line at X/h = 3.8, Y/h =0.5 andx/h = 3.8, Y/h = Coherent structures in the instantaneous realisations The presence of regions of high vorticity in the mean flow is matched and related to the presence of vortical structures in the instantaneous fields, which can be considered as instantaneous realisations of coherent structures. These structures are created by the separation at the upstream corner of the rib and undergo complex development over the length of the rib (rollers, Λ vortices, vortex pairing), before being transported downstream of the obstacle. It must be noted that the present high blockage (h/d =0.3) gives the rib a predominant role in the creation of the coherent structures. In agreement with other related studies, it is found that the presence of the vortex structures is driven by the formation of a shear layer on the leading edge of the rib. This shear layer is subject to Kelvin Helmholtz instability and rolls up to form rollers dominated by spanwise vorticity. Typical rollers are visualised by Figure 13, using Q isosurfaces. Approximately half way between separation and reattachment, the effects of stretching in the streamwise direction and tearing in the spanwise direction are visible on the wavy rollers. These effects cause the formation of disconnected asymmetric vortex structures, named as ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.14

15 Flow Features in A Fully Developed Ribbed Duct Flow 15 Figure 11. Streamsurface released from location X/h = 0.501, Y/h = 1.01 (light grey) and bounding streamlines (deep lines); bifurcation lines (thick black and white lines). Λ vortices for their characteristic shape. These small structures are usually arranged staggered with respect to each other (visualisations by [33] show the Λ-shaped structures take the staggered arrangement above a critical Reynolds number of 190 based on the rib height and 1900 based on the length of the separation bubble, which is much lower than the one in the present simulation). These structures interact with other structures further downstream to create more complex shapes. The reconnection of the Λ vortices results in a helical arrangement and occasionally pairing of the structure. (Helical pairing was firstly visualised and described by [11] and was identified in computational simulation of temporally evolving mixing layers, of which an example is given by [35]). For the present simulation, a realisation of this pairing is shown in Figure 13, where it is marked by hand drawn black and white solid lines. An interesting combination of time-averaged and instantaneous results is found in Figure 14 where the downstream entrainment of the vortices in the wake of the rib is shown. As this region is shear dominated, the approximate inclination of the streamwise vortices is determined by the eigenvectors of the rate of strain tensor (S ij ) [40]. The present results were post-processed under this point of view. Inclination angles were found in the range of (Figure 14), spreading around the theoretical value of 45 determined for 2D shear flows. ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.15

16 16 M. M. Lohász P. Rambaud C. Benocci Figure 12. Streamlines entering the downstream recirculation region (released only in the negative direction), vortex cores shown by thick black lines, wall streamlines shown by thin black lines. Figure 13. Helical arrangement of the vortices. Rendered Q =36U 2 /h 2 isosurfaces. Flow is from the left to the right. White and black solid lines highlight a helically arranged vortex pair. Left) Perspective view. Right) Shown from the positive Y direction. 4. Conclusion Results of Large Eddy Simulation have been used to investigate the topology of the flow in a ribbed duct. The flow field has been qualitatively analysed and the effect of the lateral walls has been found to be very important. It is observed that the mean flow becomes completely three-dimensional in the region close to the rib, which introduces a flow swirling towards the side walls before moving away from the rib. ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.16

17 Flow Features in A Fully Developed Ribbed Duct Flow 17 Figure 14. Inclined streamwise vortices in the wake of the rib. Rendered Q = 18U 2 /h2 isosurfaces. Flow is from the left to the right. Left) Black lines are the streamlines of the averaged flow in the symmetry plane (Z/h = 0). White lines indicate inclined vortices. The numbers indicate the inclination angle to the averaged streamline. Shown from the positive Z direction. Above the rib, a part of the flow continues to swirl in the direction of the upper corners when another part of it enters in the wake recirculation to swirl back to the symmetry plane. It is found out that the lateral swirls, which create the secondary flow, are associated with a spanwise pressure gradient. The interaction between the two horizontal walls (ribbed-not ribbed) is underlined by the evolution of the stream surfaces trapped in an upward motion. This phenomenon should be kept in mind when non-staggered face-to-face ribbed walls are chosen in the design process of cooling channels for actual turbines blades. The side walls, together with the rib, produce a vorticity which organises itself in rotating structures which arch over the rib close to the lateral wall. This phenomenon was also highlighted using isosurfaces of second scalar invariant of the velocity gradient tensor (Q). The separation at the leading edge of the rib creates a recirculation region on the top face of the rib and this remains almost two-dimensional in spite of the strong side wall effect on the windward side. Downstream of the rib, the form of wake of the rib is only slightly affected by the sidewalls: the region in the immediate vicinity of the lateral wall is, of course, affected, but the central region remains quasi-2d. The fluid can enter the wake only through the perturbed side region, a finding which might be important in the matter of heat transfer. Analysing the instantaneous flow field, it is found that the most relevant phenomenon is the creation of spanwise vortices on the leading edge of the rib, their deformation to form staggered Λ-shaped structures and their transport in the streamwise direction. The present method has been shown to be capable of reproducing known complex phenomena involving coherent ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.17

18 18 M. M. Lohász P. Rambaud C. Benocci structure, making it a promising tool for on-going similar studies of heat transfer. Acknowledgements The authors would like to acknowledge the contribution of their undergraduate student Péter Tóth who prepared the movies and participated in their postprocessing. M. M. Lohász also would like to say thank you for the support of the Hungarian National Fund for Science and Research under contract No. OTKA T References 1. Abdel-Wahab, S. and D. K. Tafti: 2004, Large Eddy Simulation of Flow and Heat Transfer in a 90 Ribbed Duct with Rotation - Effect of Coriolis Forces.. In: Proceedings of ASME Turbo Expo 2004 Power for Land, Sea, and Air. Vienna, Austria. 2. Ahn, J., H. Choi, and J. S. Lee: 2004, Large Eddy Simulation of Flow and Heat Transfer in a Channel Roughened by Square or Semicircle Ribs.. In: Proceedings of ASME Turbo Expo 2004 Power for Land, Sea, and Air. Vienna, Austria. 3. Ashrafian, A., H. I. Andersson, and M. Manhart: 2004, DNS of turbulent flow in a rod-roughened channel. International Journal of Heat and Fluid Flow 25, Bejan, A.: 1984, Convection Heat Transfer, Chapt. Wall Turbulence, p John Wiley & Sons. 5. Boris, J. P., F. F. Grinstein, F. F. Oran, and R. L. Kolbe: 1992, New insight into Large Eddy Simulation. Fluid dynamics research 10, Casarsa, L.: 2003, Aerodynamic performance investigation of a fixed ribroughened internal cooling passage. Ph.D. thesis, Von Karman Institute for Fluid Dynamics. 7. Casarsa, L. and T. Arts: 2002, Aerodynamic Performance of a Rib Roughened Cooling Channel Flow with High Blockage Ratio. In: 11th International Symposium on Application of Laser Techniques to Fluid Mechanics. Lisbon, Portugal, pp Casarsa, L. and T. Arts: 2005, Experimental Investigation of the Aerothermal Performance of a High Blockage Rib-Roughened Cooling Channel. Transactions of the ASME, Journal of Turbomachinery 127, Casarsa, L., M. Çakan, and T. Arts: 2002, Characterization of the velocity and heat transfer fields in an internal cooling channel with high blockage ratio. In: Proceedings of ASME TURBO EXPO. Amsterdam, The Netherlands. 10. Çakan, M.: 2000, Aero-thermal investigation of fixed rib-roughened cooling passages. Ph.D. thesis, Von Karman Institute for Fluid Dynamics. 11. Chandrsuda, C., R. D. Metha, A. D. Weir, and P. Bradshaw: 1978, Effect of free-stream turbulence on large structure in turbulent mixing layers. Journal of Fluid Mechanics 85, ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.18

19 Flow Features in A Fully Developed Ribbed Duct Flow Choi, H. and P. Moin: 1994, Effects of the Computational Time Step on Numerical Solutions of Turbulent Flow. Journal of Computational Physics 133, Ciofalo, M. and M. W. Collins: 1992, Large-eddy simulation of turbulent flow and heat transfer in plane and rib-roughened channels. International Journal for Numerical Methods in Fluids 15, Comte, P. and L. M.: 1998, Large-Eddy Simulations of Compressible Turbulent Flows. In: Advances in Turbulence Modelling, Vol of LS. L.E.G.I./Institut de mecanique de Grenoble, France. 15. Cui, J., V. C. Patel, and C. L. Lin: 2003, Large-eddy simulation of turbulent flow in a channel with rib roughness. International Journal of Heat and Fluid Flow 24, Dubief, Y. and F. Delcayre: 2000, On coherent-vortex identification in turbulence. Journal of Turbulence 1, Ferziger,J.H.andM.Perić: 2002, Computational Methods for Fluid Dynamics. Springer. 18. Garth, C., X. Tricoche, T. Salzbrunn, T. Bobach, and G. Scheuermann: 2004, Surface Techniques for Vortex Visualization. In: Joint EUROGRAPHICS - IEEE TCVG Symposium on Visualization. 19. Grinstein, F. F., C. Fureby, and C. R. DeVore: 2005, On MILES based on fluxlimiting algorithms. International Journal for Numerical Methods in Fluids 47, Haimes, R. and D. Kenwright: 1999, On the velocity gradient tensor and fluid feature extraction. In: AIAA Paper No Norfolk, VA. 21. Hornung, H. and A. E. Perry: 1984, Some aspect of three dimensional separation Part I.: Streamsurface bifurcations. Zeitschrift für Flugwissenschaften und Weltraumforschung 8, Hunt, J. C. R., A. A. Wray, and P. Moin: 1988, Eddies, Streams, and Convergence Zones in Turbulent Flows. In: Proceedings of the Summer Program. 23. Leonardi, S., P. Orlandi, L. Djenidi, and R. Antonia: 2004, Structure of turbulent channel flow with square bars on one wall. International Journal of Heat and Fluid Flow 25, Lohász, M. M., P. Rambaud, and C. Benocci: 2003, LES simulation of ribbed square duct flow with Fluent and comparison with PIV data. In: Conference on Modelling Fluid Flow CMFF03 The 12th International Conference on Fluid Flow Technologies. Budapest, Hungary. 25. Miyake, Y., K. Tsujimoto, and N. Nagai: 2002, Numerical simulation of channel flow with a rib-roughened wall. Journal of Turbulence 3, Murata, A. and S. Mochizuki: 2000, Large eddy simulation with a dynamic subgrid-scale model of turbulent heat transfer in an orthogonally rotating rectangular duct with transverse rib turbulators. International Journal of Heat and Mass Transfer 43, Murata, A. and S. Mochizuki: 2001, Comparison between laminar and turbulent heat transfer in a stationary square duct with transverse angled rib turbulators. International Journal of Heat and Mass Transfer 44, Nagano, Y., H. Hattori, and T. Houra: 2004, DNS of velocity and thermal fields in turbulent channel flow with transverse-rib roughness. International Journal of Heat and Fluid Flow 25, ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.19

20 20 M. M. Lohász P. Rambaud C. Benocci 29. Ooi, A., G. Iaccarino, P. A. Durbin, and M. Behnia: 2002a, Reynolds averaged simulation of flow and heat transfer in ribbed ducts.. International Journal of Heat and Fluid Flow 23, Ooi, A., B. A. Petterson Reif, G. Iaccarino, and P. A. Durbin: 2002b, RANS calculations of secondary flow structures in ribbed ducts. In: Center for Turbulence, Research Proceedings of the Summer Program. 31. Rau, G., D. Moeller, M. Çakan, and T. Arts: 1998, The Effect of Periodic Ribs on the Local Aerodynamic and Heat Transfer Performance of a straight Cooling Channel. ASME Journal of Turbomachinery 120, Sagaut, P.: 2002, Large Eddy Simulation for incompressible Flows. An Introduction. Springer, 2nd edition. 33. Sasaki, K. and M. Kiya: 1991, Three-Dimensional Vortex Structure in a Leading-Edge Separation Bubble at Moderate Reynolds Numbers. Journal of Fluids Engineering 113, Sewall, E. A. and D. K. Tafti: 2004, Large Eddy Simulation of the Developing Region of a Stationary Ribbed Internal Turbine Blade Cooling Channel. In: Proceedings of ASME Turbo Expo 2004 Power for Land, Sea, and Air. Vienna, Austria. 35. Silvestrini, J., E. Lamballais, and M. Lesieur: 1998, Spectral-dynamic model for LES of free and wall shear flows. International Journal of Heat and Fluid Flow 19, Sujudi, D. and R. Haimes: 1995, Identification of Swirling Flow in 3D Vector Fields. Technical report, Dept. of Aeronautics and Astronautics, MIT, Cambridge, MA. 37. Tucker, P. G.: 2004, Novel MILES computations for jet flows and noise. International Journal of Heat and Fluid Flow 25, Tyagi, M. and S. Acharya: 2005, Large Eddy Simulations of Flow and Heat Transfer in Rotating Ribbed Duct Flows. Journal of Heat Transfer 127, Watanabe, K. and T. Takahashi: 2002, LES simulation and experimental measurement of fully developed ribbed channel flow and heat transfer. In: Proceedings of ASME TURBO EXPO. Amsterdam, The Netherlands. 40. Wu, X. and P. A. Durbin: 2001, Evidence of longitudinal vortices evolved from distorted wakes in a turbine passage. Journal of Fluid Mechanics 446, Yang, K.-S. and J. H. Ferziger: 1993, Large-eddy simulation of turbulent obstacle flow using dynamic subgrid-scale model. AIAA Journal 32(8), ftac_lohasz_rambaud_benocci.tex; 3/04/2006; 17:27; p.20