# Single Impinging Slot Jet on a Concave Surface: Inlet/Outlet Influence

Laurent-Emmanuel Brizzi, Thi Kim Dung Hoang, Eva Dorignac, Matthieu Fénot

► To cite this version:

Laurent-Emmanuel Brizzi, Thi Kim Dung Hoang, Eva Dorignac, Matthieu Fénot. Single Impinging Slot Jet on a Concave Surface: Inlet/Outlet Influence. ASME 2008 Heat Transfer Summer Conference collocated with the Fluids Engineering, Energy Sustainability, and 3rd Energy Nanotechnology Conferences, Aug 2008, Jacksonville, United States. 10.1115/HT2008-56279. hal-00403614

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SINGLE IMPINGING SLOT JET ON A CONCAVE SURFACE: INLET/OUTLET INFLUENCE

Brizzi L.-E.

Laboratoire d'Etudes Aérodynamiques – Bât K,
40 avenue du recteur pineau POITIERS Cedex,
86022, France

Hoang T.K.D.

Laboratoire d'Etudes Aérodynamiques – Bât K,
40 avenue du recteur pineau POITIERS Cedex,
86022, France

Dorignac E.

Laboratoire d'Etudes Thermiques – ENSMA,
Futuroscope Chasseneuil Cedex, 86961,
France

Fénot M.

Laboratoire d'Etudes Thermiques – ENSMA,
Futuroscope Chasseneuil Cedex, 86961,
France

ABSTRACT

An experimental study of fluid flow and heat transfer has been carried out for a single slot jet impinging on a concave surface. Experiments have been conducted with nozzle exit Reynolds number (Re<sub>b</sub>=3200), dimensionless impinging height (H/b=7) and relative curvature (D<sub>c</sub>/b=5) to determine the heat transfer coefficients under a constant heat flux condition by infrared thermography (≈ 500 samples). The distributions of mean velocity and velocity fluctuation on the concave surface have been measured by using classical Particle Image Velocimetry (≈ 5000 samples).

The presence of an oscillatory impinging jet around three different positions has been observed. This type of behavior modifies considerably the impinging jet structure and the turbulence values which results in a modification the cooling efficiency. In order to use this type of jet for the optimization of the cooling of a concave surface, we propose to study, in this present study, the effect of Inlet/Outlet condition (riblets and obturator).

The results underline the strong effect of outlet condition (e
varies from 0 to 10 mm) for a single slot impingement jet on a
concave surface. The flow is characterized by an oscillatory jet
when the exit is totally opened (e=10 mm) while the jet is
stabilized at the opposite part for the closed exist (e=0 mm).
Therefore, the oscillatory impinging jet generated a uniform and
symmetric heat transfer area while the stabilized impinging jet
causes a dissymmetrical heat transfer.

INTRODUCTION

One of the means frequently used by the manufacturers
to cool overheated surfaces is the impinging jets technique. This
process improves thermal exchanges between walls and fluid
but jet dynamics and flow structures must be studied more to
understand and optimize the heat transfer obtained with
impinging jets.

Most of the studies on impinging jets have focused first on impingement on flat surfaces but recently, the interest moved on impingement in the presence of curved surfaces (convex/concave, [1, 2 & 3]). Indeed, the exact role of the curvature on the mass and/or heat transfer remains still unknow. To approach this problem we have chosen to study the influence of several characteristic parameters of jets impinging on a curved wall: the radius of curvature of the wall, the impingement height (jet exit-to-surface spacing) and the Reynolds number.

For a slot jet, Gilard & Brizzi [4] have noted the presence
of three semi-stable flow regimes in the vicinity of the concave
wall. This flow transformation involves a modification of the
temporal structure of the slot jet flow and of course the heat
transfer and it could be interesting to generate/annihilate this
behaviour.

In order to see if this type of jet can be use to optimize the
cooling of a concave surface, we propose to study, in this paper,
the effect of the inlet/outlet conditions. In fact, a review of the
previous studies indicates that some points seem to have a very particular importance:

* The boundary conditions seem to be important. For example, Gau & Chung [1] show clearly that the flow after the impact can disturb the jet flow near the nozzle and then modify the generation of the vortices in the shear layer. In these conditions, the shape of the cavity seems to have a considerable effect on the structure of the flow. On the other hand, Yang et al. [5] show that the nozzle geometry influences the characteristics of the jet (turbulence level) and modifies the heat transfer at the stagnation point even if it always corresponds to the location where the turbulence intensity is maximal.

* The eddies seem to be important: Many vortical structures develop in the vicinity of the impact (shear layer vortices and other secondary structures close to the wall) and if their role in the heat transfer is not in doubt (Thomann [6]), the modifications which involve on the aerodynamic field seem relatively misunderstood.

To answer to this question it is necessary to know the unsteady structure of the flow and for this reason the jet dynamics and flow structure will be encountered by using classical PIV, and an infrared thermography will be used to carry out the thermal transfer.

## NOMENCLATURE

b [m] Slot height

$D_c$ [m] Diameter of concave wall

e [m] Obturator height

$h$ [$W/m^2\cdot{}^\circ C$] Local heat transfer coefficient

H [m] Impinging height

L [m] Slot width

$Q_j$ [$m^3\cdot{}s^{-1}$] Flow rate

s [m] Curvilinear coordinate

U, V [$m\cdot{}s^{-1}$] Streamwise & transverse mean velocity

u', v' [$m\cdot{}s^{-1}$] Streamwise & transverse velocity fluctuation

$U_j$ [$m\cdot{}s^{-1}$] Jet velocity

x, y, z [m] Coordinates

v [$m^2\cdot{}s^{-1}$] Kinematic viscosity

$Re_b$ [–] Reynolds number ($Re_b=U_j\cdot{}b/v$)

## EXPERIMENTAL APPARATUS

The slot jet is supplied by a right-angled parallelepiped channel (955 mm long, 300 mm wide and 10 mm high). A grid and a honeycomb are placed upstream in order to obtain a “fully developed” velocity profiles at the jet exit. According to Rajaratnam [7], the aspect ratio ($L/b=30$) must be higher than 20 to obtain a quasi two-dimensional flow.

<figure><img src="image_2.png" /><figcaption>**Figure 1** Experimental set-up</figcaption></figure>

a) Inlet condition (colored zone)

b) Riblets detail

c) Outlet condition (colored zone)

The impingement surface (c.f. Figure 1) consists of three parts: The first one is semi-cylindrical (450 mm long and 50 mm in diameter), simple geometry for modeling, and corresponds to the concave part of the curved surface; the others are straight (450 mm long and 150 mm wide) and are used as higher and lower boundaries. All these elements are transparent (Altuglas) to allow measurements by classical Particle Image Velocimetry (PIV). For the thermal measurement these are replaced by heating plates (epoxy/copper 0.2 mm thick, whose thermal conductivity is $0.29\pm0.02 \text{ Wm}^{-1}\text{K}^{-1}$ in the thickness direction) to allow the use of various thermal measurement techniques (thermocouple, infrared thermography).
For both cases, the impingement surface is closed laterally by transparent plates (thickness of 10 mm) in order to avoid the external disturbances which would contaminate the jet

The complete device is fixed on a moving system making it possible to vary impinging height H (H is defined as the distance between the exit of the channel and the center of the impact surface).

This testing apparatus is generated by a fan F 802 (2 m³/min under 1000 mm EC, 3.9 kW, 2910 tr/min) or a centrifugal fan HP APE 801C (3 m³/min, 11368 Pq 5.3 kW, 2900 RPM) respectively in dynamic and thermal measurements.

The air flow rate $Q_j$ is controlled using manual valves and three different flowmeters (Fischer & Porter) connected in parallel, these flowmeters have different measurement ranges in order to optimize the accuracy of the aerodynamic measurements. A venturi is used for the thermal measurements. The venturi is equipped with two pressure sensors (a differential pressure (0-5 mbar), and a static pressure (800-1200mbar)) and a thermocouple (K type) to measure flow temperature through the venturi. This temperature is controlled by a heat exchanger placed between the flowmeters and the channel. Finally, all elements of this feeding system (fan, valves, flowmeters and thermal regulator) are connected using pipe (PVC or flexible plastic) 80 mm in diameter. The feeding system is connected to the channel by a diffuser.

To modify the inlet conditions, we use “riblets” pasted on the upper part of the exit section (c.f. Figure 1b).

Outlet condition is obtained using an obturator at the right exit of the surface impact (c.f. Figure 1c). The height of this obstruction (e) can be adjustable from 0 to 10 mm (e=0 corresponds to a total obstruction of the right exit, e=10 mm with a maximum opening).

To summarize, the three main parameters of this study are:

* The Reynolds number based on the jet mean flow velocity $U_j$ ($U_j=Q_j/(b \cdot L)$) and the jet height b ($Re_b=U_j \cdot b / v = Q_j / Lv$, $Re_b=1400$, 3200 and 6400).

* The dimensionless impinging height ($H/b=3$, 5 and 7).

* The relative curvature of the wall ($D_c/b=5.2$, 9.4)

Since the same flow structure and the same effect of the curvature radius were observed for each impinging height (H/b) higher than 4, only the results for the configuration ($Re_b=3200$; $D_c/b=5.2$, $H/b=7$) will be presented.

# MEASUREMENTS TECHNIQUES

## 1) CLASSICAL PIV

The quantitative description of the mean flow is obtained from velocity measurements carried out by PIV technique (LAVISION technology). A Nd-Yag double cavities QUANTEL laser source (2*120 mJ, 10 Hz and 532 nm) is used to illuminate the flow in the plane of interest and obtain a relatively fine light sheet (≈1.5mm). The flow is seeded with

olive oil droplets using an atomizer (laskin nozzle). The mean size of the particles is less than 1 µm.

Pictures are taken using a Hi-sense CCD camera working in cross-correlation mode (12 bits, 1376x1040 pixels² double frames, 4-5 Hz). The recorded images are analyzed in order to obtain the displacement of the tracers, and then the velocity. In our configuration we used a multi-pass adaptative cross-correlation technique (4 passes, the last being doubled, start by 128x128 and finish by 32x32), with an overlap 50%×50%.

As a preliminary, and in order to minimize the influence of the light reflections, a "basic image" is subtracted from each image before the computation of the vectors. This "basic image" is obtained before the recording of the sequence under the same experimental conditions as for measurements but without seeding.

All the measurements are realized in the symmetry plane (z=0) of the slot jet for several experimental configurations. For each configuration, 5000 independent samples of measurements are recorded at 4-5Hz, divided into 25 packages of 200 recordings. From the instantaneous fields, a validation and a statistical process are used to obtain the mean velocity ($\overline{U}$, $\overline{V}$) and the Reynolds stresses ($\sqrt{u'^2}$, $\sqrt{v'^2}$, $u'^v$) values. However for the areas where there are less than 1000 validated vectors, no result is presented.

A 5% convergence is obtained from 150 samples for the mean value and from 1300 for fluctuations of the longitudinal component. Then, the acquisition of 2000 instantaneous velocity fields is thus largely sufficient to obtain enough statistical convergence.

**Velocity measurement uncertainty:** The errors inherent in the PIV measurements were quantified according Westerweel [8] with a 95% confidence level. The errors of the method mainly depend on the scale calibration (≈ 0.65%), the pixel displacement (≈ 1.04%) and the time interval between the two images (negligible uncertainty). To obtain the uncertainty of measurement, it is necessary to add to the precision the various biases of this technique. There are many biases and some of them are not easily quantifiable. For example, we will note the bias related to interpolation sub-pixel (Westerweel [8]) or the bias due to the zones with strong velocity gradient (Keane [9]). However if we assure that the biases are less the twice of the uncertainty allotted to the precision, the uncertainty is estimated at 3% for the mean values and at 6% for RMS.

## 2) INFRARED THERMOGRAPHY

Infrared thermography combines the advantage of being non-intrusive and allows a continuous measurement of the considered surface. This technique is carried out with an infrared matrix camera CEDIP Jade MWIR (InSb, 3.6-5.1 µm, 320x240 pixels²). The infrared camera counts the photons, transforms them into electric power (V) then into digital level
(DL) and finally the calibration transforms these results into temperature (K). A series of 500 images is recorded using the software Altaïr during a lap of 10 seconds (the data frequency remains 50 Hz) and then an average is calculated by the software SAPHIR. From the acquisition of 5 different fluxes, convective heat transfer coefficient h is calculated according to a linear regression method (Fenot [10]). In these conditions, the values of h are obtained with an accuracy of ±12%.

Although the reflective stick-on allows a precise location, the change of location of the camera involves a shift for the same scene taken with different flows. This involves uncertainties on the curvilinear position (S=±1 mm).

The ambient temperature was encountered by averaging temperature measurement of two thermocouples.

## RESULTS

### Without any device

The influence of the inlet/outlet conditions are analyzed from a comparison with the reference case (Reh=3200; H/b=7; Dc/b=5). Figure 2 shows the mean and RMS velocity field obtained by PIV for this reference case. We observe that the jet issuing from the left does not impact directly the centre of the curved wall (x/b=7 and y/b=0). Indeed, there is a triangular area in the vicinity of this impingement point where the velocities are very low. The mean flow is always symmetrical about the x-axis, but there seems to be a “dead fluid” area which prevents the jet from impacting with the curved wall. Thus, the fluid makes a half-turn and comes out at the top and bottom of the figure.

For the horizontal component (RMSu), figure 2 also shows two zones with high intensity (≈ 0.6 Uj) located symmetrically about the jet axis in x/b=4 and y/b=±2.5. For the vertical component, we find a single zone of maximum in the vicinity of (x/b=7 and y/b=0). However, we can notice that the level reached is very high (≈ 0.5 Uj).

At first sight, this behavior can appear surprising since there is no direct impact in this case (lower relative curvature Dc/b=5.2). A more detailed analysis indicates that the histograms of the two components of the velocity for this configuration show three distinct peaks, centred around the values: (-3 m/s, 0 m/s and 3 m/s) for the vertical component and (-2.3 m/s; 0 m/s; +2 m/s) for the horizontal component. This can be explained by the superposition of three distinct behaviors (cf. Figure 3):

For the first mode (cf. figure 3-a) we observe, contrary to the mean velocity field, that the jet impacts the higher part of the curved surface (x/b = 4; y/b = 2.6) and then separates in two parts. A significant part of the jet skirts the curved wall to the bottom and another smaller part sets out again directly towards the left. In this case, the flow is no longer symmetrical about the horizontal axis.

For mode 2 (cf. figure 3-b), we notice that the jet impacts the centre of the curved wall at (x/b = 7; y/b = 0). The jet separates and each part follows the curved wall on both sides of

the stagnation point (cf. figure 3-b). Then we find a symmetrical flow about the horizontal axis.

Finally, figure 3-c shows the mean velocity field for the third mode which is the symmetric of the first mode.

These results indicate that the flow oscillates between three semi-stable positions: For example, the jet remains directed to the top a few seconds then it moves towards another position (bottom or middle) to be stabilized again. A few seconds later, it starts again. This phenomenon which modifies significantly (in level and position) the turbulent values is a fluidic instability governed by the pressure field. Of course, this flow transformation involves a modification of the heat transfers.

<figure><img src="image_3.png" /><figcaption>Figure 2: Streamlines and RMSu values</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 3: Scheme of the flow.</figcaption></figure>

### With riblets

When we apply “riblets” on the upper part of the exit section, the flow is highly modified (cf. Figure 4). In this case, the jet is stabilized on the lower part of the device (x/b=3 and y/b=-2.5). A significant part of the jet follows the curved surface to the top and a smaller part leaves directly on the left. In this case, the flow is not symmetrical any more according to the horizontal axis.

On the instantaneous field, most of the time, we can see a weak oscillation of the jet around this mean position but few times the jet goes upward and quickly comes back down. From this point of view, we can assume that the riblets stabilize the plane jet.

We observe on the case with riblets important modifications for the locations and the levels of RMSu
compared to the reference case. Indeed, for the reference case, two zones of strong intensity (RMSu ≈ 0.63Uj) are symmetrically placed compared to the x-axis at (x/b=4.5; y/b=±2.5) (cf. figure 2), while only one zone of strong longitudinal fluctuations (RMSu ≈ 0.9Uj) located around (x/b=3.8; y/b=-2.5) is observed (cf. figure 4) for the case with riblets. This difference can be explained because the riblets create longitudinal structures whose fluctuations increase the turbulence intensity of the jet flow. It is thus seen that the jet control (with a transfer enhancement) is possible by this device.

However the implementation and the real time control of this kind of device (e.g. by changing the riblets geometry and/or their location) seem relatively complex.

<figure><img src="image_5.png" /><figcaption>**Figure 4:** Streamlines and RMS values with « riblets »</figcaption></figure>

### With an obturator

On the other hand, the outlet condition is easier to realize and manage. Thus, in order to have several outlet conditions, we use an obturator with different thickness placed in the higher exit.

Figure 5 presents the streamlines and the RMSu values obtained at different outlet condition.

A sensitive change of the outlet condition can strongly modify the structure of the jet and the position of the stagnation point. We observe two types of impact: *stabilized* (Figure 5 a, b & c) or *oscillatory* impinging jet (Figure 5 d, e & f).

### e=0 (totally closed):

When the higher part is closed (e=0 mm, Figure 5a), the mean flow looks like to the “riblets” case: the jet is “stabilized” (because the very low turbulence intensity ≈ 0.3Uj) on the lower part of the device (x/b=1.6 and y=-2.45). A small part of the jet leaves directly on the left and a significant part of the flow follows the curved surface to the top. At this place and because of the exit closure, the flow separates and generates a new vortex. Most of the fluid is then attracted by the main jet. Choi et al. [11], Gau & Chung [1] and Lee et al. [12] also observed this phenomenon (fluid coming from the wall jet involved in the main jet) and indicate that this recirculating flow disturbs the vortex formation in the shear layer. Thus, the probability of obtaining stable vortices in the main jet is somewhat reduced.

For the thermal point of view, we can notice that, the heat transfer at the left part is always higher than at the right part. The stabilized location of impinging jet presents a maximum heat transfer (Figure 6). In fact, if the stagnation point is closer to the non-blocked exit, the jet velocity at this point is higher, it mixes significantly with the entrained air, and induces turbulence and eddy activity, all of which enhance h, hence its high value. On the opposite side the 3rd vortex (Vortex A on figure 5a) causes a minimum heat transfer. Kornblum & Goldstein [13] suggest that a recirculation would cause the increase in fluid temperature close to the wall. The heat transfer coefficient being calculated from nozzle exit temperature, this rise in jet temperature would cause a drop of heat transfer.

### e∈[0; 6]:

The more e increases, the more the part of the “reverse flow” is reduced. Following to the streamlines issuing from the jet, we observe that, the location of stagnation point on the mean flow field progresses towards a symmetrical position (x/b=7 and y/b=0) at the center of curved wall when the outlet condition e increases from 0 to 10mm.

For the stabilized jet case (e=0 to 4 mm), only one zone with high turbulence intensity (≈0.37 Uj) is found at the vicinity of the stagnation point. This stabilized impact leads to a maximum heat transfer at this stagnation point. The heat transfer of the blocked part is always lower than at the other part because of the more exit flow at the non-blocked part, and the jet always dominates at the non-blocked part of the wall.

### e∈[6; 10]:

For the oscillatory impinging jet (e=6 to 10 mm) two zones with high turbulence intensity (≈0.6Uj) are observed. These differences can be explained because for e lower than 4 mm the jet is stabilized in lower position whereas it oscillates around three semi-stable points if e>6 mm.

The jet dynamics and the heat transfer in this case are not very different for the two (blocked/non-blocked) parts of the wall. We can not observe the flow recirculation at the blocked part like for the case of stabilized jet. It should be due to the fact that, either the flow recirculation is not present for this case (the recirculation is reduced at the minimum), or our experimental impinging surface is not enough large to observe this type of flow.

### e=10 (totally open):

For e=10 mm (Reference case), we observe a symmetrical heat transfer according to the jet axis Y=0. This heat transfer coefficient is quite uniform (about 60 W/m²K) with two small local maximums where we observe high turbulence intensity (X/b=4.5 and Y/b=±2.5). This can be explained because statistically the impinging jet impacts more frequently at these two points (X/b=4.5 and Y/b=±2.5) than at the center of curved wall.
<figure><img src="image_6.png" /><figcaption>a) e=0 mm</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>b) e=2 mm</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>c) e=4 mm</figcaption></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /><figcaption>d) e=6 mm</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>e) e=8 mm</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>f) e=10 mm</figcaption></figure>

<caption>**Figure 5 :** Streamlines and RMS values</caption>
<figure><img src="image_13.png" /><figcaption>**Figure 6:** Local heat transfer coefficient along the surface</figcaption></figure>

**Next step: Towards the control?**

In order to facilitate the comparison between the various studied configurations, the position of the stagnation point defined by the angle between the stagnation point and the longitudinal axis (the origin is chosen at the cylinder center (cf. figure 1)) is plotted figure 7. On this graph, we clearly observe the continuous influence of the outlet condition on the stagnation point. The more open the higher part is, the more the position of the stagnation point tends towards a null angle and we find a symmetrical flow compared to the horizontal axis. And more the higher part is blocked, the more the flow is dissymmetrical and the position of the stagnation point moves away from the position x/b=7 and y/b=0.

Then, we can conclude that, the outlet condition is very effective to modify the jet dynamics and has the advantage of being very simple to realize. Moreover, the tendency of the curve allows us to estimate the position of the stagnation point for a given outlet condition (i.e. a value of e).

<figure><img src="image_14.png" /><figcaption>**Figure 7:** Influence of the outlet condition on the stagnation point location</figcaption></figure>

The outgoing flow rate is also carried out in the plans $(x/b=0; y/b \in [-2.5;-1.5] \cup [1.5; 2.5])$. The flow rate in the top increases for $e=0$ to 4 mm and decreases gradually for $e=6$ mm to 10 mm. We observe that for $e=0$, the value of the flow rate is not equal to zero because the section of computation does not correspond to the blocked section (presence of a 3D recirculation zone). For $e=10$ mm, we don't obtain a symmetrical value of the flow rate top/bottom probably because of the measurements uncertainties (3%).

<figure><img src="image_15.png" /><figcaption>**Figure 8:** Top/bottom flow rate</figcaption></figure>

## CONCLUSION

Through this experimental study for single slot impinging jet on a concave surface, we can summarize our main conclusions as follows:

The input/output conditions have a strong influence on the jet dynamics. They can disturb the flow and strongly modify the location of the stagnation point.

For the small obturator heights, the jet is stabilized in a low position and the flow is not symmetrical. The more $e$ increases ($e$ from 6 to 10 mm), the more the jet oscillates around three semi-stable positions. In these conditions the mean flow tends to a symmetric behavior and the heat transfer becomes uniform.

We find that the outlet condition seems interesting to control and may be optimized by the heat transfer obtained with impinging jet on concave surface. In fact, this technique is easy to implement (e.g. flapping wings) and allows a progressive control of the jet.

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