art%3A10.1134%2FS0869864313060073

705

Thermophysics and Aeromechanics, 2013, Vol. 20, No. 6

Experimental investigation of the effect of small-obstacle-induced vortex sheet on the separated flow in cavity*

A.Yu. D’yachenko, V.I. Terekhov, and N.I. Yarygina

Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, Russia

E-mail: [email protected]

(Received May 24, 2013)

In the present paper, we report results of an experimental study of the influence which a vortex-generating element installed upstream of the main obstacle has on the separated flow and heat transfer in a cross-flow cavity-trench. The element was a small cross-flow rib whose height was an order of magnitude smaller than the depth of the cavity. In the experiments, the variable parameters were the angle of inclination of the frontal and rear walls of the cavity, the rib height, and the rib-to-cavity distance. It is shown that the introduction of additional vortical perturbations into the recirculation zone leads to a substantial modification of both the vortex production process and the distributions of pressure and heat-transfer coefficients. Optimal height of the mini-turbulizer and its optimal location are defined by the fall of the re-attachment point of mini-rib-generated flow onto the rear wall of cavity. In the latter situation, the maximal value of the heat-transfer coefficient increases as compared to the case with no vortex generator used, the increase amounting to 30 %.

Key words: cross-flow cavity, separated turbulent flow, thermographic visualization, heat transfer, pressure coefficients, instability.

Introduction

Control of the heat- and mass-transfer processes in separated flows is an important trend in improving the performance and reliability characteristics of heat-and-power apparatuses [1−4]. To date, this matter has been addressed in scientific literature rather scantily in comparison with the traditional methods to control the dynamics of separated flows [5]. From the practical point of view, most acceptable here are passive control means for the transfer of heat in separation regions behind such obstacles as steps and cavities based on using, upstream of the separation region, an outside turbulence [6−8] or additional turbulizing elements much smaller in size than the primary obstacle [9−12].

In [7, 8], it was found that an external turbulence reduces the scale of vortical structures and the extension of separation region, and it also makes less pronounced the effect of butt walls on the recirculation zone yet intensifies the transfer of heat in the separation region. For instance, in a system of several ribs, an extremely unstable vortex production process was

* This work was financially supported by the Russian Foundation for Basic Research (Grant No. 12-08-00249) and by the Ministry of Science and Education of the Russian Federation (State Contract No. 14.518.11.7015).

© A.Yu. D’yachenko, V.I. Terekhov, and N.I. Yarygina, 2013


706

observed in the second cell due to the occurrence of a counter-flow moving in the direction opposite to that of the main stream from the third to second cell. Under the action of external turbulence, the flow in the second cell becomes more stable. Due to different flow prehistories, the effect of external turbulence on the characteristics of separated flows behind various obstacles is manifested in different ways. The tendency towards size reduction of the separation bubble behind an obstacle under high turbulence is due to a substantial growth of the mixing layer. A growth of mixing layer behind the rib is more pronounced in comparison with that behind the step, so that the extension of separation region in the former case turns out to be reduced by 30 %, the same reduction in the latter case being 20 % only. Accordingly, the intensification of the transfer of heat behind the rib is more pronounced in comparison with the step. Low-height obstacles also proved to be more advantageous when used as heat-transfer intensifiers. A most enhanced transfer of heat due to external turbulence was observed in a cross-flow cavity and in a system of ribs.

On the other hand, using mini-turbulizers installed in the upstream region of an obstacle is a simpler method to control the dynamic and thermal characteristics of separated flows. In the latter case, control of thermal characteristics of a separated flow is exercised via intro-duction, into the separation region, of an additional vortex sheet causing a dramatic modification of recirculation-zone structure, displacement of reattachment point and, hence, the redistribu-tion of pressure-, heat-, and mass-transfer coefficients. Interest in using vortex-sheet generators permanently increases. J. Neumann and H. Wengle have published a report on their numerical simulations of passively controlled turbulent separated flow past a backward-facing step per-formed using DNS and LES methods [9, 10]. Profiles of flow velocity and velocity fluctua-tions, and also the spectral density of those quantities, in a plane channel with a low-height rib installed upstream of a step at a given rib-to-step distance were calculated. The authors have demonstrated a considerable growth of mixing-layer thickness, reduction of recirculation zone, and instability of the flow as a whole. In [11], based on their experimental data, for given channel dimensions J. Miau et al. have proposed optimal sizes of a vortex generator formed by two ribs, one rib being a thin stationary rib and the other, an oscillating rib. According to the recommendations by J. Miau et al., the height of the intensifier should be one third of step height H, and the intensifier itself should be installed at an upstream distance of 4H. K. Isomoto and S. Honami examined the effect of an additional turbulence produced by a small turbulizer in the form of a rod or a cross-flow cavity on the flow re-attachment process behind a step [12]. They showed that at the point of flow separation in the profiles of turbulence inten-sity there arise small characteristic peaks pointing to the presence of the turbulizer. For the rod, a reduction in the extension of reattachment region was noted, and for the trench, its growth. For heat-transfer intensification purposes, of interest is the search for optimal dimensions of vortex-generating elements and for their optimal location with respect to the obstacle. Because of its complexity and involvement of many factors, the influence of vortex sheet on the transfer of heat in separated flow remains a poorly studied matter. Here, scarcity of experimental data is evident. Since all reported studies were performed for the backward-facing rib, it would be of interest to also address the influence of a mini-generator on the separated flow behind a different obstacle, e.g., a cavity. For cross-flow trenches, an interesting region affecting the transfer of heat is also the rear edge since the most pronounced heat-transfer intensification is observed on the rear wall of cavity.

In the present paper, we report on the results of an experimental study of vortex produc-tion and fields of pressure and temperature in a cross-flow cavity (trench) with varied angle of inclination of the frontal and rear walls in the presence, upstream of the separation region, of a low-height intensifier in the form of a cross-flow rib. Other variable parameters were the rib height and location. The purpose of the study was to gain data on the coefficients of pressure and heat-and-mass transfer under interference of two separated flows of different scales.

Thermophysics and Aeromechanics, 2013, Vol. 20, No.6

707

Experimental setup

The experiments were carried out in the wind-tunnel facility of the Institute of Thermo-physics, SB RAS [5]. The cross-sectional dimensions of the working channel of the wind tunnel were 200×200 mm, and the length of the channel was 1000 mm. On the bottom of the channel, a model with a cavity clamped in between two aerodynamic panels was installed. In the upstream region of the cavity, the length of the aerodynamic panels was 480 mm, and the length of the planar surface behind the cavity was 200 mm. We examined the flow past a cavity whose dimensions were as follows (Fig. 1): depth Н = 60 mm, bottom width (between the points В and С) L = 60 mm, length in the cross-flow direction W = 180 mm, so that we had the case of W/H = 3 and H/L = 1. The walls of the cavity were tight against the channel walls. All in all, three models were fabricated; one model was intended for ther-mographic visualization of the flow, and the two other models, for measuring, respectively, the pressure fields and the thermal characteristics. For measuring the rate of heat transfer with the help of thermocouples, the cavity walls were prepared from a 20-mm thick cloth laminate sheet. The experiments were carried out for the following values of the angle of inclination of the sidewalls of cavity: ϕ = 30°, 45°, 60°, 70°, 80°, and 90°. In variation of sidewall incli-nation angle, the height of cavity H and the width of cavity bottom in the direction of the flow L remained unchanged while the separation between the points А and D increased in value with decreasing the angle ϕ. In the latter situation, depending on the inclination angle, the length of cavity sidewalls Lw was a varied quantity.

Measurements were carried out in the range of free-stream velocities U0 = 5 ÷ 35 or

in the range of Reynolds numbers ReH = HU0/ν = 2⋅104 ÷ 1.4⋅105. The majority of experiments

with mini-turbulizers were performed at U0 = 20 m/s (ReH = 8⋅104). At all velocities U0, the boundary layer in the upstream region of cavity was a turbulent boundary layer. The boun-

dary-layer momentum thickness prior to separation 0 0 00

** 1U U

dyU U

δ ρδρ

⎛ ⎞= −⎜ ⎟

⎝ ⎠∫ was calculated

from experimental velocity profiles, and it varied, depending on the Reynolds number, in the interval 3.2 to 3.7 mm, which values corresponded to a boundary-layer thickness value δ ≈ 35 mm. The turbulence number of the free channel flow as measured by a DISA-55M hot-wire anemomenter was 1.2 %. In examining the distribution of static pressure in the cavity, the model was provided with 80 static-pressure orifices located on the frontal and rear sidewalls and on the bottom of the cavity in six sections, two orifices on each wall.

A ribbon heater wound from aluminum foil of thickness 36 μm with strip width 5 mm was used to heat the sidewall and the bottom of the cavity in the regime of constant heat flux. The trench surface was provided with 158 chromel-copel thermocouples located in three longi-tudinal sections on the bottom, in five longitudinal cross sections on the sidewalls and in four sections across the flow (one section on each sidewall, and the two others in two sections on the bottom of cavity). The leak of heat across the plate was evaluated using data measured by four thermocouples calked into the back side of each heated wall.

In thermographic experiments, the cavity with the heater was mounted on the sidewall of the wind tunnel flush with the channel wall. The opposite wall was prepared from optical glass; in some cases, it was replaced with polyethylene film. The cavity was heated during one hour

Fig. 1. Diagram of the flow past a cross-flow cavity with a vortex generator in the form of a cross-flow rib installed upstream of the cavity.


708

in a required velocity regime, and then the wall temperature was measured with a THERMO TRACER TH7102 IR Imager (Japan) whose spectral range was 8 to 14 μm. Digitization of measured temperature fields was performed using thermocouple data obtained with the help of at least two thermocouples. Thermograms were plotted using special software.

The vortex generator was a thin cross-flow rib of height hg ranging from 2.5 to 10 mm,

which was installed in the upstream region of the cavity at a distance 0 to 100 mm from its leading edge (point А in Fig. 1).

Results of experiments

Thermographic visualization of the flow

Thermographic visualization was performed in cavity for various heights of the small rib and different rib-to-leading edge distances. The height hg was either 2.5, 5, or 7.5 mm, and the distance Sg was varied from 0 to 100 mm. Тhe thermograms well reflect the soot-oil visua-lization data obtained for the flow over the cavity bottom [8]. The visualization has showed that the most dramatic modification of the flow and thermal patterns on increasing the height of the intensifier installed at the leading edge of rectangular cavity was observed in the region of secondary flow immediately behind the channel expansion (Fig. 2, the flow moves from left to right). Behind the frontal wall, in addition to corner vortices moving towards the butt walls, there arises a large vortex at the center of the region. The latter leads to flow instability and to a transition from the primary vortex structure involving one cell to a structure comprising two cells. In the absence of a vortex generator, such instability emerges in cavities with sidewall inclination angles φ < 70º [8]. For hg = 7.5 mm, the centers of the two cells become most heated regions, the latter pointing to a decrease of the rate of the transfer of heat in the cavity. This finding can be related to the fact that, here, the reat-tachment point of rib-generated flow, xr ~ 15 (hg = 112.5 mm), falls in the downstream region of cavity.

On increasing the rib-to-cavity distance (the rib is located in the upstream region of the cavity), the flow in cavity becomes a more and more low-scale one (see Fig. 3). A similar regularity is also observed on decreasing the angle φ. For φ ≤ 70° in the secondary zone, three vortices, two corner ones, and one at the center are observed; those vortices proved to be even more manifested in comparison with the case of φ = 90°. A decrease in the temperature of the secondary vortex indirectly points to an enhanced transfer of heat.

Pressure coefficients

In the rectangular cross-flow cavity in the central section along the stream and in three reference sections across the flow, the distributions of pressure in the presence of the vortex intensifier were measured. Also, pressures at a distance of 50 mm ahead of, and at a distance of 70 mm behind the cavity were measured. The distributions of pressure coefficients along the stream as dependent on the height of a generator installed at the leading edge of cavity are shown in Fig. 4. The distributions of pressure in the transverse sections were nearly iden-tical. The graph in Fig. 4 shows that, the higher is the obstacle, the more pronounced are the decrease of the pressure coefficient in cavity and the increase of this coefficient in the imme-diate proximity ahead of and behind the cavity. Yet, the rate of change slows down, and the distributions of pressure coefficients for hg = 7.5 and 10 mm turn out to be differing little.

On the other hand, the distributions of pressure show an ambiguous behavior as depen-dence on the rib-to-cavity distance Sg (see Fig. 5). As the distance Sg increases from 0 to 10 mm, the rarefaction in the cavity becomes more pronounced. A maximal reduction of the pressure coefficient was observed at Sg = 10 mm, i.e., at Sg = 2 hg. On further increase of Sg, the pressure coefficient in the cavity again starts increasing to reach a level typical of the case with no mini-obstacle installed.


709

Thus, the pressure coefficient in cavity remains rather low till the re-attachment point of mini-rib-generated flow enters the cavity.

Heat-transfer coefficients

The relative values of the cavity-surface-mean heat-transfer coefficient normalized by the mean Nusselt number in the rectangular cavity without a mini-turbulizer for three angles φ are

Fig. 2. Thermogram of the bottom of a rectangular cavity with a mini-turbulizer of variable height installed at the leading edge.

hg = 0 mm (a), 2.5 mm (b), and 7.5 mm (c); Sg = 0 mm (a−c).

Fig. 3. Thermogram for a rectangular cavity behind a rib of height 5 mm installed at different distances to the cavity.

hg = 5 mm; Sg = 0 mm (a), 5 mm (b), and 10 mm (c).


710

shown in Fig. 6. The dependence of the relative Nusselt number on the height of a mini-rib installed at the leading edge of cavity is shown in Fig. 6а, and the dependence on rib location (for the rib of height 5 mm), in Fig. 6b. Most pronounced heat-transfer intensification is ob-served for cavities with inclined walls; in the latter case, the heat-transfer intensification turns out to be almost independent of rib height because the re-attachment point of rib-generated flow for all examined rib heights falls into the cavity. For the rectangular cavity, the effect is much less pronounced, and at hg = 7.5 mm, when the re-attachment point of rib-generated flow

Fig. 5. Distribution of pressure coefficients in a rectangular cavity with a mini-turbulizer of height 5 mm installed at different rib-to-cavity distances.

hg = 0 mm (1); hg = 5 mm: Sg = 0 mm (2), 10 mm (3), 25 mm (4), 50 mm (5), and 100 mm (6).

Fig. 4. Distribution of pressure coefficients along a rectangular cross-flow cavity with a mini-turbulizer installed at the leading edge.

U = 30 m/s; hg = 0 mm (1), 2.5 mm (2), 5 mm (3), 7.5 mm (4), and 10 mm (5).


711

falls into the downstream region of cavity, such heat-transfer intensification is not observed at all. Nonetheless, the intensification of heat transfer in the rectangular cavity reaches 30 % at generator height 5 mm for a generator installed at the generator-to-trench distance 10 mm.

Conclusions

The complexity of processes proceeding during the interaction of two separated turbulent flows with two characteristic scales has been demonstrated. The performed study has revealed a pronounced effect of an enhanced-turbulence vortex sheet produced by a low-height obstacle that was installed in the upstream region of a cross-flow cavity on the formation of vortices and on the heat transfer in the separation region due to cavity.

The thermographic visualization data have demonstrated that, when the flow re-attachment point due to the low-height turbulizer (of height much smaller than the cavity depth) falls into the rectangular trench, an unstable flow arises in the cavity and the primary eddy disintegrates into two cells. In the absence of the mini-turbulizer, such a phenomenon arises only for angles of inclination of the frontal and rear wall of cavity ϕ < 90°.

The modification of the flow has an impact on the behavior of pressure coefficients. With the example of a rectangular cavity we show that with increasing the height of the mini-obstacle installed on the leading edge of the trench, the pressure coefficient in the regions up-stream of rib and downstream of cavity increases in value while it decreases in the detachment zone, so that the rarefaction level in cavity shows an increase. Simultaneously, the rate of the growth diminishes when the re-attachment point due to the small turbulizer falls into the cavi-ty. On increasing the mini-rib-to-cavity distance the pressure coefficient in trench remains ra-ther low unless the re-attachment point leaves the cavity and, over the downstream region of the rib of ten or more calibers in terms of rib height, the pressure coefficient in cavity again increases to a level observed in the absence of the small turbulizer.

Behind the vortex generator, the magnitude of the heat-transfer coefficient increases in comparison with the case of the absence of the vortex generator providing that the re-attachment point due to the small obstacle falls into the cavity. Yet, because of the finite width of cavity, the intensification in cavity is less pronounced in comparison with the case of the downward-facing step. Both the location and height of mini-obstacle have an impact on the characteristics of the transfer of heat. In a rectangular cavity, at rib height hg = 7.5 mm a small rib installed on the leading edge leads to a decrease of the heat-transfer coefficient. That is the case in which the re-attachment point due to mini-rib enters the region behind the cavity. The most pronounced increase of the mean heat-transfer coefficient (1.3 times) is observed when the vortex intensifier is located at a distance of two calibers in term of its height; this increase

Fig. 6. Relative Nusselt number in cavities with different angles φ and with a mini-turbulizer installed at the leading edge versus turbulizer height (а) and turbulizer-to-cavity distance (b).

ϕ < 45° (1), 70° (2), 90° (3).


712

is somewhat lower in a trapezoidal cavity. Such an effect due to mini-turbulizer is quite com-parable with the effect due to external turbulence, and it can be interpreted as the effect due to a low-scale turbulence induced by small intensifiers.

The experimental data suggest that the optimal height of small ribs falls in the interval from 1/5 to 1/3 of cavity depth. On the other hand, the location is defined by the condition that the re-attachment point of mini-rib-generated flow should fall into the recirculation region

of cavity.

Nomenclature

Cp ⎯ pressure coefficient, Cp = 2(pi-p0)/ρU

2,

H ⎯ depth of cavity, mm; hg ⎯ height of vortex generator, mm,

L ⎯ width of cavity at cavity bottom, mm, Lw⎯ length of cavity sidewall, mm, Nu ⎯ Nusselt number, Nu = α H/λ, p ⎯ pressure, N/m

2,

Re ⎯ Reynolds number, ReH = U⋅H/ν, Sg ⎯ vortex generator-to-cavity distance, mm,

U ⎯ flow velocity, m/s,

W ⎯ cavity length (close to channel width), mm, xR ⎯ position of flow re-attachment point,

α ⎯ heat-transfer coefficient, W/m2 K,

λ ⎯ thermal conductivity coefficient, W/m⋅K, ν ⎯ kinematic viscosity, m

2/s,

ρ ⎯ density, kg/m3,

φ ⎯ angle of inclination of cavity sidewalls, °.

Subscripts

0 ⎯ main-flow parameter, w ⎯ wall parameter.

References

1. I.A. Popov, Intensification of Heat-Transfer Processes: Physical Background and Industrial Applications, Tupolev Kazan State University, 2009.

2. A.I. Leontyev and V.V. Olimpiev, Thermophysics and heat technology of advanced heat-transfer intensifiers (review), Izv. Ross. Akad. Nauk, Ser. Energetika, 2011, No. 1, P. 7−31.

3. H. Togun, S.N. Kazi, and A.A. Badarudin, Review of experimental study of turbulent heat transfer in separated flow, Australian J. Basic and Applied Sciences, 2011, Vol. 5, Nо. 10, P. 489−505.

4. B.V. Perepelitsa, An experimental study of temperature-field evolution in a channel with corrugated wall at a step change of the heat flux, Thermophysics and Aeromechanics, 2012, Vol. 19, No. 6, P. 689−696.

5. M. Gad-el-Hak, Modern developments in flow control, Appl. Mech. Rev., 1996, Vol. 49, No. 7, P. 365−379. 6. I.P. Castro and A. Haque, The structure of a shear layer bounding a separation region, Part 2, Effects of free-

stream turbulence, J. Fluid Mech., 1988, Vol. 192, P. 577−595. 7. V.I. Terekhov, N.I. Yarygina, and R.F. Zhdanov, Heat transfer in turbulent separated flows in the presence

of high free-stream turbulence, Int. J. Heat Mass Transfer, 2003, Vol. 46, No. 23, P. 4535−4551. 8. A.Yu. D’yachenko, V.I. Terekhov, and N.I. Yarygina, Vortex formation and heat transfer in turbulent flow past

a transverse cavity with inclined frontal and rear walls, Int. J. Heat Mass Transfer, 2008, Vol. 51, No. 14, P. 3275−3286.

9. J. Neumann and H. Wengle, DNS and LES of passively controlled turbulent backward-facing step flow, Flow, Turbulence and Combustion, 2003, Vol. 71, P. 297−309.

10. J. Neumann and H. Wengle, Coherent structures in controlled separated flow over sharp-edged and rounded steps, J. Turbulence, 2004, Vol. 5, No. 22, P. 14.

11. J. Miau, K.C. Lee, M.H. Chen, and J.H. Chou, Control of separated flow by a two-dimensional oscillating fence, AIAA J., 1991, Vol. 29, P. 1140−1148.

12. K. Isomoto and S. Honami, The effect of inlet turbulence intensity on the reattachment processes over a back-ward-facing step, Trans. JSME, 1988, Vol. 54B, P. 51−58.

art%3A10.1134%2FS0869864313060073

Documents

Transcript of art%3A10.1134%2FS0869864313060073