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Flow characteristics of a wall-attaching oscillating jet over single-wall and double-wall geometries
Journal Pre-proofs Flow Characteristics of a Wall-Attaching Oscillating Jet over Single-wall and Double-Wall Geometries Shabnam Mohammadshahi, Hadi Samsam-Khayani, Omid Nematollahi, Kyung Chun Kim PII: DOI: Reference:
S0894-1777(19)30898-2 https://doi.org/10.1016/j.expthermflusci.2019.110009 ETF 110009
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
4 June 2019 2 September 2019 22 November 2019
Please cite this article as: S. Mohammadshahi, H. Samsam-Khayani, O. Nematollahi, K. Chun Kim, Flow Characteristics of a Wall-Attaching Oscillating Jet over Single-wall and Double-Wall Geometries, Experimental Thermal and Fluid Science (2019), doi: https://doi.org/10.1016/j.expthermflusci.2019.110009
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© 2019 Published by Elsevier Inc.
Flow Characteristics of a Wall-Attaching Oscillating Jet over Single-wall and Double-Wall Geometries Shabnam Mohammadshahia, Hadi Samsam-Khayania, Omid Nematollahia, Kyung Chun Kima* a School
of Mechanical Engineering, Pusan National University, Busan 609-735, South Korea ⁎
Corresponding author, E-mail address: [email protected] (K.C. Kim).
Abstract This paper presents the experimental results of two-dimensional time-resolved particle image velocimetry (2D-TR-PIV) measurements for two external geometries of a sweeping jet: a singlewall geometry and a double-wall geometry. The single-wall geometry has a non-confined backward-facing step, and the double-wall geometry has a confined step with a sudden expansion domain. The effect of the Reynolds number based on the hydraulic diameter (D) and mean velocity of throat (U) was also studied in the range of 2,000 to 10,000. The results show that the frequency of the oscillating jet is almost independent of the shape of the external region and varies almost linearly with the Reynolds number. In contrast, the velocity distribution of the flow is controlled by the external domain. The time-averaged velocity and vorticity data were acquired for the highest Re in the double-wall geometry, and there were three main vortices in the external domain that control the velocity distribution and a clear difference is observed. Other fields of view were also investigated in three different sections and the reattachment locations measured at a distance of 0.05D from the wall. The time-averaged results show that for both geometries, reattachment length was observed to decrease to the increase on Reynolds number. Key words: Fluidic oscillator, Particle image velocimetry, backward facing step, sudden expansion.
1. Introduction Fluidic oscillator is a device that does not involve any moving part and can create an oscillating jet that is self-induced and self-sustained [1]. They are widely used because of their simple design and wide range of frequencies [2]. Fluidic oscillators can be divided into three main groups based on the number of feedback loops: feedback-free, single-feedback, and double-feedback jets. The use of two feedback channels (recirculators) was discovered in the mid-20th century [3]. Nowadays, 1
the most popular fluidic oscillators have two feedback channels to connect the upstream and downstream parts of a chamber. In the present study, the double feedback fluidic oscillator is studied and the schematic view of that is illustrated in Fig. 1. The flow in the feedback channels plays a significant role in producing an oscillating jet. When the fluid enters, the flow attaches to one wall of the mixing chamber because of the Coanda effect, which is the tendency of a jet to remain attached to a solid surface. In addition, a lowpressure region is created between the jet and an adjacent surface. As a result, the jet bends toward the wall, and a counter flow is created downstream. Because the jet bends, a part of the flow enters the recirculators and discharges into the mixing chamber. Thus, the jet at the power nozzle is deflected toward the opposite wall, and this process is repeated at a certain frequency [4]. The oscillation frequency of a jet depends on the internal region of the fluidic oscillator, and some numerical and experimental studies have analyzed the internal part of fluidic oscillator to identify the mechanisms that drive the jet to oscillate and characteristics which are associated with the oscillation frequency ([5]–[10]). External flow dynamics and oscillation characteristics of the fluidic oscillators have been studied widely. Wen and Liu [11] studied the effect of Reynolds numbers (Re) of 2,500 to 11,700 on different parameters like the size of separation bubbles and the spreading angle. The flow characteristics and turbulence structures have been also discussed by the unsteady behavior of oscillating jet for different Re numbers [12]. Additionally, Wen et al. [13] investigated the interaction of two fluidic oscillators impinging on a flat plate. Sang and Hyun [14] studied the three-dimensional features of a fluidic oscillator at Re=8,000 to 24,000 and calculated the frequency of the oscillation. They also investigated the cross-sectional planes of the fluidic oscillator. Various applications of fluidic oscillators have also been experimentally examined such as separation control by fluidic oscillators ([15]–[19]), bluff body drag reduction [20], combustion [21], and heat transfer enhancement ([22]–[24]). Thus, fluidic oscillators can be used for cooling turbine blades and the more velocity and turbulent fluctuations, the more convection and diffusion [25]. In addition, in some real-world applications, the surfaces are in confined spaces. Therefore, in this study, the effect of the external 2
region on an oscillating jet was experimentally examined. First, one wall at the bottom of the external region with a step was examined, and then two walls at external geometry as confined domain with a double-wall was studied. For both geometries, two-dimensional time-resolved particle image velocimetry (2D-TR-PIV) was used in two different planes and various sections. Time-averaged velocity components and vorticity field are examined and flow dynamics at Re=10,000 are discussed in terms of phase-averaged velocity fields. The results show that the external confinement has not significant effect on the oscillating frequency, even if the velocity distribution of the fluid flow is changed. In contrast, the spreading angle is different based on the external geometry and confining the domain decreases that angle at a constant Re number which can affect the heat transfer performance. Additionally, different Reynolds number from 2,000 to 10,000 were performed and investigation of Coanda effect on the reattachment length of the oscillating flow was carried out. Supply feedback channel power nozzle dh=10 mm
mixing chamber exit
Throat
Fig. 1 Current fluidic oscillator’s components
2. Experimental setup and PIV measurement In the non-intrusive PIV method, a seeding flow of tracer particles is illuminated by a laser sheet. Then, images are captured by a camera from the light scattered by the tracer particles. As a result, the displacement of particles can be calculated between two images, and the velocity vectors can be obtained from the time difference. The flow was seeded through a water tank with 11.7-µm silver-coated hollow spheres at a density of 1.1 g/cm3. The laser light sheet was generated by a 5W continuous-wave laser beam operating at a wavelength of 532 nm and passing through a cylindrical lens.
3
The images of the illuminated particles were captured using a high-speed camera (Photron FastCam SA1.1). The camera captures images with a resolution of 1024 by 1024 pixels, and image processing was performed with PIVLab software. A final interrogation window of 16 × 16 pixels with 50% overlap was used to satisfy the Nyquist criterion. Instantaneous and ensemble averaging of the flow velocity vectors was performed using a cross-correlation algorithm [26]. The timeaveraged of such quantities were obtained from 10,918 frames of instantaneous velocity field. The experimental setups are shown in Fig. 1 (a-b), in which the field of view was visualized at different planes. In Fig. 2 (a), the target view is parallel to the x-y plane and located at z/D=0. In Fig. 2 (b), the target view is parallel to the x-z plane and located at y/D=0. In addition, other sections were also visualized at y/D=1 and y/D=2, as shown in Fig. 2 (b). The experiments were done with both single-wall and double-wall geometries. The geometry of the fluid domain for the single-wall geometry is shown in Fig. 3, and the dimensionless values are listed in Table 1. The origin of the coordinate system is at the center of the outlet of the fluidic oscillator. For the doublewall geometry, another plate similar to the bottom plate of the single-wall geometry is placed on top of the geometry, and the external domain of fluidic oscillator is bounded in the z direction by no-slip walls. A pump injects water into the fluidic oscillator, and the flow rate of the supplied water is measured by a flow meter. The working fluid in the current study is water, and the tank is made of acrylic because its refraction index is similar to that of water. The oscillator was also made from acrylic using a CNC machine, similar to that used in previous studies of [11] and [14]. The crosssection area of the outlet throat is 10*10 mm2, and the hydraulic diameter is 10 mm. The outlet nozzle has a 90o divergence angle and length of 40 mm. Air bubbles in the jet pipes were removed before PIV measurements. The experiments were performed for different Re of 2000 to 10,000 based on the hydraulic diameter.
4
(a)
(b)
Fig. 2 Experimental setup for a) plane z/D=0, b) plane y/D=0.
h m (b) m h m m
(a)
10 mm (c)
Fig. 3 Diagrams of (a-b) single-wall and (c) double-wall geometries.
Table 1 Dimensions of the setups in Fig. 2. Parameter H/D h/D L1/D L2/D
dimension 1 0.4 4 16
Parameter L3/D L4/D L5/D
dimension 60 20 40
3. Results and Discussion The following sections present the results to get the flow dynamics of oscillating jet. First, the characteristic of fluid pattern for non-confined and confined geometries are compared on the plane of z/D=0. Then, the comparison of the flow on y/D=0, 1 , 2 planes is done for both geometries. 3.1 y Plane for z/D=0
5
The oscillating jet is generated by a fluidic oscillator. The sampling rates of the experiments are at least three orders of magnitude more than the frequency of the oscillation, so in order to find the oscillation frequencies, the velocity distributions of two specific locations are extracted (symmetrical points about the centerline of the jet) [11-12]. Then, the velocity differences of the two points are calculated because there is a 180o phase lag between the feedback channels and between the two symmetrical points. Finally, the oscillation frequency is found by using a lowpass filter and FFT analysis. As Schmidt et. al. [17] showed, there is a linear dependence of oscillation frequency on mass flow rate. In the current study, the dimensions of fluidic oscillator are fixed for all experiments (Table 1) and Re number is changed based on the supply rate. Thus, as illustrated in Fig. 4, the oscillation frequency of a fluidic oscillator depends on the Re number and is almost independent of the external domain geometry. In addition, the frequency for the non-bounded external domain for the same fluidic oscillator was also calculated by Sang and Hyun [14] and is compared with the frequencies of confinement external geometries via one plate or two plates. It can be concluded that because the oscillating jet is generated by the internal part of the fluidic oscillator, the external domain does not have any significant effect on the frequency.
1.1
Single-wall geometry Double-wall geometry Not bounded external domain [14]
1.0
F [Hz]
0.9 0.8 0.7 0.6 0.5 0.4 0.3 4000
5000
6000
7000
8000
9000
10000
Re
Fig. 4 The oscillation frequency of a fluidic oscillator (the uncertainty was estimated at around 2% [11]).
Although the frequency of the fluidic oscillator is almost independent of the external domain, the performance of the external flow field is different for the two geometries. The edges of the maximum dimensionless velocity magnitude based on the mean velocity of throat (U) for 6
different Re are shown in Fig. 5. For low Re, the continuous jet in the forward direction and the general pattern of the two geometries are the same, as shown in Fig. 5 (a-b) (Re=2000 and 3300). But for high Re numbers, the behavior of the fluid is different. When increasing Re, a kind of Vshaped distribution is formed for both geometries and the jet diffuses more in lateral direction (Fig. 5 (c)). For the single-wall geometry at Re=8250 and 10,000 (right-side of Fig. 5 (d-e)), the oscillation patterns are similar to each other. However, for the double-wall geometry, the V-shaped pattern of the single-wall geometry is modified, and a different pattern is generated with completely different jet movement. The jet deflection angle is extracted from the time-averaged velocity components in both streamwise and transverse directions of the peak velocity components near the exit region of jet and is shown in Fig. 6. The spreading angle is defined as the angle between the centerline and maximum velocity deflection. The maximum deflection angle is a function of Re number (or supply rate in this study) and increases when increasing Re number until Re=8250 for the singlewall geometry. After that, the angle is constant at 45o because the exit nozzle angle is 90o, and the maximum angle between the two maximum deflections is 90o. For the double-wall geometry, at all Re numbers, the angle is smaller than that of the single-wall geometry, and the exit nozzle’s angle does not have significant effects on the velocity pattern. Furthermore, for Re=10,000, the spreading angle is less than that at Re=8250. This is also confirmed in Fig. 5. At Re=10,000, the flow bends the jet and breaks down in comparison with Re=8250.
(a)
(b)
(c)
(d)
(e)
Fig. 5 Time-averaged maximum deflection of the jet for: a) Re=2000, b) Re=3300, c) Re=4600, d) Re=8250, and e) Re=10,000. The right side of the centerline is the single-wall geometry, and the left side is the double-wall geometry.
7
Spreading Angle
50
Single-wall geometry Double-wall geometry
40
30
20 4000
5000
6000
7000
8000
9000
10000
Re
Fig. 6 The time-averaged angle of the maximum velocity deflection for different Re.
With increasing Reynolds number, jet impact region is enlarged significantly due to the greater jet spreading angle and jet momentum shifts from an even spatial distribution concentrated along the middle centerline to a V-shape distribution. Thus, at higher Reynolds numbers, the jet momentum has peaks on the lateral sides (Fig.5). In order to find the reason for the jet breaking down, Fig. 7 illustrates the time-averaged velocity magnitude, streamlines, streamwise velocities, and transverse velocities for Re=10,000. The velocity contours are nondimensionalized with the averaged throat velocity estimated from the flow rate (U=Q/A throat) which A throat is the area of the nozzle throat and Q is the volumetric flow rate. The V-shaped velocity pattern can be seen for the single-wall case (Fig. 7 (a)). However, adding the top plate to the external domain of the fluid and creating the double-wall geometry causes the V-shaped pattern to change (Fig. 7 (b)). For the single-wall case, the jet generates a high concentration of fluid at its maximum deflection, and there is weak flow in the middle region of the maximum deflection. Thus, an inhomogeneous distribution is created in this case. In Fig. 7 (c), for the single-wall geometry, the flow moves without any distortion, but for the double-wall geometry (Fig.7 (d)), there are some strong vortices that control the emitted jet (saddle and nodal points). The formation of these structures is highly dependent on the jet entrainment of the ambient fluid and their rotation direction is clockwise and counterclockwise as illustrated in Fig.7 (d). These vortices prevent the high-velocity flow from moving freely like in the single-wall geometry. Thus, when the jet is discharged, the quiescent fluid in the external domain will be continuously entrained into the jet and the high-speed flow is concentrated at a small region at the outlet of the fluidic oscillator. The time-averaged of streamwise velocity (Fig. 7 (e - f)) and transverse velocity (Fig. 7 (g - h)) were also investigated. At Re=10,000, the maximum streamwise and transverse velocities are 8
almost equal for the single-wall geometry. For the double-wall geometry, the maximum streamwise velocity occurs just near the exit region and is about two times the maximum transverse velocity. But these velocities are almost equal at the positions where the maximum transverse velocity occurs. This behavior is also confirmed by the streamlines in Fig. 7 (c-d). The ratios of the maximum magnitude of the transverse to the streamwise velocities are plotted in Fig. 8. For both cases at Re=2000, the magnitude of the transverse velocity is less than 20% of the streamwise velocity near the exit region. This means that the jet is emitted in the streamwise direction, and there is a small spreading angle. By increasing the Re number, the ratio is increased, but for the double-wall geometry, the jet momentum is still more in the streamwise direction near the exit region in comparison with the single-wall geometry for high Re numbers.
(a)
(c)
(e)
(g)
(b)
(d)
(f)
(h)
Fig. 7 Time-averaged of velocity magnitude (a-b), streamlines (c-d), streamwise velocity (e - f), and transverse velocity (g - h) for single-wall (a,c,e,f) and double-wall (b,d,f,g) geometries at Re=10,000 and plane z/D=0 ( : saddle point, : Nodal point).
9
1.0
Single-wall geometry Double-wall geometry
0.8
u/v
0.6
0.4
0.2
0.0
2000
4000
6000
8000
10000
Re
Fig. 8 The ratio of transverse to streamwise velocities.
Fig. 9 shows the instantaneous velocity field for Re=10,000 when the jet is moving between its maximum deflection (during T/2). As showed in Fig. 7, there is a strong vortex between maximum deflection of jet that prevents the jet to emit flow in y-direction and leads to creating small spreading angle in comparison with single-wall geometry as compared in Fig.6. In order to get more details, Q-criterion will be calculated for vortex identification in next part. Phase averaging data processing is also done with technique of getting the frequency of oscillation (Fig. 4) based on the differential velocity signal from the two reference positions. All 10,918 snapshots are sorted in ascending order and a phase window size of 3 yields 120 phase angle windows in one oscillation period is assumed. Thus, each phase angle window contains 91 snapshots. More details of this method can be found in [5,12]. In this paper, the instant that the oscillating jet is deflected at the bottom-most position is arbitrarily called zero phase. The jet has a rapid switching process from one side of the exit to the other and at its maximum deflection position, because of attaching to the diverging exit wall and Coanda effect, stays for a longer time [12]. According to the phase-averaged velocity vector field (Fig. 10), the velocity magnitude of the jet flow is strong at phase of 0 and 180 and during the change of direction, to 90, remains strong in a short distance. In addition, the footprint of the previous cycle exists in the opposite direction in the phase-averaged velocity fields of double-wall geometry.
10
(a)
(b)
(c)
(d) (e) (f) Fig. 9 Instantaneous normalized velocity magnitude for (a-b-c) single-wall, (d-e-f) double-wall for Re=10000 on plane z/D=0.
0o
90o
180o
(a)
(b)
(c)
11
0o
90o
180o
(d)
(e)
(f)
Fig. 10 Phase-averaged velocity field of sweeping jet in the x-y plane at Re=10,000 for (a-c) single-wall (d-f) double-wall geometry.
As the jet is emitted in the external field and moves forward, the water right next to the boundary of the jet also moves with the jet because of friction. But the water far away from the jet does not move, and the difference between these velocities causes a shear force. As a result, the water starts spinning, and vortices form because of the velocity difference. The normalized timeaveraged vorticity contours for Re=10000 are shown in Fig. 11 for the single-wall and double-wall geometries. One of the main processes that can influence the dynamics of jet and heat transfer is the edge shear layer surrounding the jet [27]. In Fig. 12 (a-b-c) and (d-e-f) the instantaneous vorticity field during T/2 for Re=10000 is shown for single-wall and double-wall geometry, respectively. The interaction between the jet shear layer and the confining external domain is obtained and the vorticity field of the double-wall geometry differs from that of the single-wall geometry. For the double-wall geometry, when the jet is emitted in stationary fluid and oscillates, main vortices are generated which one of them is near the exit region between the maximum deflection of jets (Fig 12 (d-e-f)). Two other main vortices are formed far away from the exit region. As a result, the flow direction bends from x/D=5. This is the reason why the V-shaped pattern of the flow cannot be observed in the double-wall geometry. For the single-wall geometry, the emitted jet can move freely, and the movement of the fluid is damped soon as well. Thus, only the counter-rotating vortex pairs can be seen, and the V-shaped distribution of the vortex occurs. For the double-wall geometry, three main vortices lead to the whole domain of the fluid moving, and a different pattern 12
of oscillating flow is formed. In fact, for one plate geometry similar to non-bounded external geometry, as Ostermann et. al. [28] showed, the mass flow is entrained from the direction normal to the oscillation pattern (z direction in the current work) and the entrainment rate can increase as contact area between jet and surrounding fluid is enlarged. This increment also shows the mixing enhancement as a result of acceleration of ambient fluid due to the jet momentum. In contrast, for two plates geometry, such entrainment from z direction is inhibited and those three main vortices are created which are beneficial to enhance convective heat transfer for the bottom wall at the external region.
(a)
(b)
Fig. 11 Time-averaged of normalized vorticity for : a) Single-wall, b) Double-wall for Re=10,000.
(a)
(b)
13
(c)
(d)
(e)
(f)
Fig. 12 Instantenous normalized vorticity during T/2 for: (a-b-c) Single-wall, (d-e-f) Double-wall at Re=10,000.
For vortex identification, Hunt et al. [29] defined the Q-criterion as a quantitative way criterion to obtain more details about vortex boundaries (Eq. 1). They concluded that vortex regions occur where Q is positive, which means the vorticity magnitude is greater than the magnitude of the rate of strain. In the current work, the Q-criteria were first calculated, and vortex boundaries were specified for time-averaged results(Fig.13 shows an example of this process). Then, the circulation (Γ), which is the integral of z-component vorticity (Eq. 2), was calculated over an area with a positive value of the Q-criterion because the area with a positive value of the Q-criterion is in the vortex area as shown in Fig.13. Thus, to measure the exact area of the vortex, this criterion is used for integrating the area. Overall, the vortices cancel each other out, and the circulation for the whole domain is zero, so the mean magnitude of both vortex circulations was calculated. The results are listed in Table 2. For better visualization of the behavior of the larger vortices, we calculated the Q-criterion of the instantaneous flow field during T/2 at Re=10,000 which is illustrated at Fig. 14. When the jet is at its maximum deflection (a,c,d,f in Fig. 14) the concentration of maximumn Q occures at jet location for single-wall geometry. In contrast, for double-wall germetry, that distribution is more even and on the opposite side of the jet, some coherenet structure is still remained. In addition, when jet is at centerline, confining the external domain causes the oscillating jet stays near the exit region. That’s because of the vorticities which are trapped by confining the external domain (Fig. 7). For the single-wall geometry, the dimensionless circulation is almost constant. However, by increasing Re, the circulation over the area of Q>0 is also increased to about 10 times the 14
circulation for Re=8250. Therefore, for Re=10,000, the strong vortices in the domain bend the oscillating jet and even break it, as shown in Fig. 5. However, for Re=8250, these vortices are not strong enough, and the jet can be maintained. This phenomenon also affects the spreading angle and causes the results at Re=8250 to have a greater spreading angle in comparison with Re=10,000 (Fig. 5). 2
2
Q ( S ) 2
Eq. 1
.dS
Eq. 2
S
(a)
(b)
Fig. 13 Time-averaged contour of Double-wall at Re=10,000 for (a) Qcriterion and (b) Vortex area definition.
(a)
(b)
15
(c)
(d)
(e)
(f)
Fig. 14. Instantenous contour of Q-criterion during T/2 for: (a-b-c) Single-wall, (d-e-f) Double-wall at Re=10,000. Table 2 Comparison of the dimensionless circulation over the area of Q>0. Re 8250 10000
Single-wall 0.015 0.015
Γmean / UD Double-wall 0.043 0.14
3.2 x-z Planes for y/D=0,1,2 This section discusses the time-averaged results, so it is necessary to prove that the characteristic of oscillating jet is independent of number of snap shots. Therefore, time-averaged flow fields by 2000, 4000, and 10918 independent 2D-2C- PIV snapshots of Re=10,000 and one-plate geometry at section y/D=0 is compared (Fig. 15). It can be seen, the main recirculation region which plays a dominant role and is identified near the step, is almost constant. Then, time-averaged velocity magnitude fields and streamlines for two Re values at the plane y/D=0 are calculated and shown in Fig. 16. The flow behind the step is bounded by the separating and reattaching shear layer and by the wall, so the flow reattaches and forms a recirculation zone behind the step. In addition, the reattachment length measured at a distance of 0.05D from the wall and the reattachment length is decreased by increasing Re (Table 3), in contrast to the behavior of the free stream on the backward-facing step [30]. One for this reduction in the reattachment length can be that by increasing the Re number, the spreading angle is also increased. Therefore, the jet’s angular distance from the center line is increased, and as a result, the reattachment length decreases in different y-planes.
16
In addition, although the spreading angle for the double-wall geometry is less than that for the single-wall geometry, the double-wall geometry has a smaller reattachment region (at a constant Re number). The symmetrical distribution of the velocity field is also observed in the double-wall geometry. Moreover, Fig. 17 presents the instantaneous velocity field and streamlines of Re=10,000 for single-wall geometry. It shows that the instantaneous flow is more irregular than the time-averaged flow structure and vorticities are created near the shear layer and move while the jet moves forward. The dimensionless time-averaged streamwise velocity profiles are shown in Fig. 18. For the double-wall geometry, a symmetric profile is created because of the two recirculation zones, and the profile becomes flat as x/D increases. However, for the single-wall geometry, there is one velocity peak, and when enhancing x/D, the peak becomes smoother. For high values of z/D, the fluid remains stationary and does not move.
2000 snapshots
4000 snapshots
10918 snapshots
Fig. 15 Time-averaged of velocity field for Re=10,000 and Single-wall geometry at plane y/D=0.
supply
supply
(a)
(c)
17
supply
supply
(b)
(d)
Fig. 16 Time-averaged of velocity field and streamlines for: a) Re 5300 Single-wall, b) Re=10000 Single-wall, c) Re=5300 Double-wall, d) Re=10000 Double-wall at plane y/D=0.
supply
supply
(a)
(b)
Fig.17 Instantenous of velocity field and streamlines for single-wall geometry at Re=10,000.
Table 3 Comparison of the dimensionless reattachment length (xr/D) at plane y/D=0. xr/D Re 2000 5300 10000
Single-wall 3.5 3 2
Double-wall 2 1.4 1
50
Spreading Angle
Single-wall geometry
Double-wall geometry
40
30
20 4000
18 5000
6000
7000
Re
8000
9000
10000
1.5
1.0
One plate geo. Two plates geo.
1.5
1.5
0.5
0.5
0.5
0.5
0.0
0.0
0.0
0.0
-0.5
-0.5
-0.5
-0.5
0.0
0.2
0.4
0.6
-1.0 -0.2
0.0
0.4
-1.0 -0.2
0.6
0.0
x/D=0.5 One plate geo.
x/D=1
Two plates geo.
1.0
1.5
0.4
0.6
-1.0 -0.2
1.5
One plate geo. Two plates geo.
1.0
0.5
0.5
0.0
0.0
0.0
0.0
-0.5
-0.5
-0.5
-0.5
0.2
u/U
x/D=2.5
0.4
0.6
-1.0 -0.2
0.0
0.2
0.4
-1.0 -0.2
0.6
0.0
0.2
u/U
u/U
x/D=3
0.4
0.6
One plate geo. Two plates geo.
1.0
z/D
z/D
1.5
0.5
0.0
0.2
x/D=2
0.5
-1.0 -0.2
0.0
u/U
x/D=1.5
One plate geo. Two plates geo.
1.0
z/D
0.2
u/U
u/U
u/U
1.5
0.2
z/D
-1.0 -0.2
One plate geo. Two plates geo.
1.0
1.0
z/D
z/D
1.0
One plate geo. Two plates geo.
z/D
One plate geo. Two plates geo.
z/D
1.5
x/D=3.5
0.4
0.6
-1.0 -0.2
0.0
0.2
0.4
0.6
u/U
x/D=4
Fig. 18 Time-averaged dimensionless streamwise velocity profiles for Re=5300 at plane y/D=0.
The time-averaged dimensionless vorticity for Re=10,000 is shown in Fig. 19. For the single-wall geometry, there is a small region of negative vorticity in the recirculation region due to the revised flow and induced flow by the secondary recirculation at the step corner. Peak values of vorticity occur in the shear layer separation and this vorticity extends from the step edge. Subsequently, such vorticity weakens and grows in width more in the downstream direction and is predominantly distributed. For the double-wall geometry, the magnitude of the primary vortex is much higher than for the single-wall geometry and confining the external domain causes the vorticity to be much stronger with smaller region.
19
supply
(a)
supply
(b) Fig. 19 Time-averaged dimensionless vorticity for (a) singlewall and (b) double-wall geometry for Re=10,000 at y/D=0.
The flow was visualized at two other sections with similar distances from each other. The time-averaged velocity contours for both geometries at different sections are presented in Fig. 20. In order to compare the effect of Re on both geometries, the dimensionless streamwise velocities for different sections were calculated and are plotted in Figs. 21-22. For the center plane of the jet with a norm of y (plane Y/D=0), two velocity profiles are created at X/D=0.5 and X/D=1.5. Fig. 20 shows that the behavior of the flow at Re=2000 is like a laminar flow, but for other Re, a turbulent profile is obtained. In Fig. 20 (a) and (b), the peak of u/U for the single-wall geometry is located at z/D>0 for x/D=0.5 and then placed at z/D=0 for x/D=1.5. This means that as the flow bends, it tends to attach to the plate because of the Coanda effect as it moves. In addition, as the jet is emitted, the velocity magnitude is decreased for constant Re and constant geometry. However, the difference between these amounts is higher for the double-wall geometry in comparison with the single-wall geometry. For example, for Re=2000 and the single-wall geometry, the maximum value of u/U is decreased from 0.65 for x/D=0.5 to 0.57 for x/D=1.5 (a difference of 0.08). These values for the double-wall geometry are 0.95 and 0.79, respectively (a difference of 0.16). Furthermore, for constant Re and x/D, the amount for the double-wall geometry is more than that for the single-wall because of the continuity equation. 20
Fig. 22 shows the dimensionless streamwise velocity at the plane y/D=1 and the plane y/D=2. For Re=2000 in the single- wall geometry, the peak velocity is decreased when changing y/D from 0 to 2. This means that the jet’s spreading angle is small, and the jet flows more in the streamwise direction rather than the transverse direction, as discussed previously.
(a)
(b)
(c)
(d)
Fig. 20 Time-averaged dimensionless velocity magnitude for (a) single-wall, Re=2000, (b) double-wall, Re=2000, (c) single-wall, Re=10,000, (b-d) double-wall, Re=10,000.
1.5
1.2
Single-wall, Re = 2000 Single-wall, Re = 5300 Single-wall, Re = 10000 Double-wall, Re = 2000 Double-wall, Re = 5300 Double-wall, Re = 10000
0.9
0.9
u/U
u/U
1.2
Single-wall, Re = 2000 Single-wall, Re = 5300 Single-wall, Re = 10000 Double-wall, Re = 2000 Double-wall, Re = 5300 Double-wall, Re = 10000
0.6
0.6
0.3
0.3
0.0 -0.850
-0.425
0.000
0.425
0.850
z/D
0.0 -0.850
-0.425
0.000
z/D
21
0.425
0.850
(a)
(b)
Fig 21 Time-averaged streamwise velocity profiles at plane y/D=0 for a) x/D=0.5 and b) x/D=1.5.
0.4
Single-wall, Re = 2000 Single-wall, Re = 5300 Single-wall, Re = 10000 Double-wall, Re = 2000 Double-wall, Re = 5300 Double-wall, Re = 10000
0.3
Single-wall, Re = 2000 Single-wall, Re = 5300 Single-wall, Re = 10000 Double-wall, Re = 2000 Double-wall, Re = 5300 Double-wall, Re = 10000
0.20 0.16
u/U
u/U
0.12
0.2
0.08 0.04
0.1 0.00
0.0 -0.850
-0.425
0.000
0.425
-0.04 -0.850
0.850
-0.425
0.000
0.425
0.850
z/D
z/D
(a)
(b)
Fig 22 Time-averaged streamwise velocity profiles at x/D=1.5 for planes a) y/D=1 and b) y/D=2.
4. Conclusion The 2D-TR-PIV method was used to visualize the flow characteristics of an oscillating fluidic oscillator emitted in a stationary fluid. The single-wall geometry had a non-confined backwardfacing step, and the double-wall geometry was symmetrically confined with a sudden expansion domain. Experiments were done for two different fields of view (y and z plane) with different sections (y/D=0, 1, 2 and z/D=0). The most important findings are summarized as follows: 1) The flow pattern of oscillating jet is a function of flow rate, which in this study normalized
by Re number, and external domain geometry. 2) Jet momentum is mostly in the streamwise direction rather than the transverse for lower
supply rate or Re number. 3) At a constant supply rate (Re number), although the external domain of the fluidic oscillator
does not have a significant effect on the oscillating frequency, the spreading angle can be changed dramatically. Thus, spreading angle can be decreased because of confining the external domain by two symmetrical walls at the bottom and upper side of region. The difference between entrained flow is the main reason. For one plate geometry, flow was entrained from the normal direction of the oscillating pattern results flow structure 22
considerably different in comparison with two plates geometry at the same Re number. For instance, the ensemble-averaged oscillating flow from the fluidic oscillator at Re=10,000 in the single-wall geometry created a V-shaped velocity distribution. However, for the double-wall geometry, this pattern was changed, and three main vortices were generated in the external domain. These vortices can enhance the convective heat transfer on the bottom wall. 4)
Confining the external domain creates a shorter reattachment length at same Re number on plane y/D=0 which is due to the existence of a strong vortex between maximum deflection of oscillating jet which showed on plane z/D=0.
Acknowledgements This research was supported by the International Research and Development Program of the National Research Foundation of Korea (NRF), which is funded by the Ministry of Science and ICT of Korea (NRF-2017K1A3A1A30084513). This study was also supported by the National Research Foundation of Korea (NRF) grant, which is funded by the Korean government (MSIT) (No. 2011-0030013, No. 2018R1A2B2007117). References [1]
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25
Highlights: Oscillating frequency is almost independent of the external domain shape. Frequency is increased linearly with increasing Reynolds number. High Reynolds number causes lateral velocity and spreading angle to increase. Strong vortices for the double-step geometry decreases the spreading angle. Reattachment length is decreased with increasing the Reynolds number.
26
S0894-1777(19)30898-2 https://doi.org/10.1016/j.expthermflusci.2019.110009 ETF 110009
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
4 June 2019 2 September 2019 22 November 2019
Please cite this article as: S. Mohammadshahi, H. Samsam-Khayani, O. Nematollahi, K. Chun Kim, Flow Characteristics of a Wall-Attaching Oscillating Jet over Single-wall and Double-Wall Geometries, Experimental Thermal and Fluid Science (2019), doi: https://doi.org/10.1016/j.expthermflusci.2019.110009
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© 2019 Published by Elsevier Inc.
Flow Characteristics of a Wall-Attaching Oscillating Jet over Single-wall and Double-Wall Geometries Shabnam Mohammadshahia, Hadi Samsam-Khayania, Omid Nematollahia, Kyung Chun Kima* a School
of Mechanical Engineering, Pusan National University, Busan 609-735, South Korea ⁎
Corresponding author, E-mail address: [email protected] (K.C. Kim).
Abstract This paper presents the experimental results of two-dimensional time-resolved particle image velocimetry (2D-TR-PIV) measurements for two external geometries of a sweeping jet: a singlewall geometry and a double-wall geometry. The single-wall geometry has a non-confined backward-facing step, and the double-wall geometry has a confined step with a sudden expansion domain. The effect of the Reynolds number based on the hydraulic diameter (D) and mean velocity of throat (U) was also studied in the range of 2,000 to 10,000. The results show that the frequency of the oscillating jet is almost independent of the shape of the external region and varies almost linearly with the Reynolds number. In contrast, the velocity distribution of the flow is controlled by the external domain. The time-averaged velocity and vorticity data were acquired for the highest Re in the double-wall geometry, and there were three main vortices in the external domain that control the velocity distribution and a clear difference is observed. Other fields of view were also investigated in three different sections and the reattachment locations measured at a distance of 0.05D from the wall. The time-averaged results show that for both geometries, reattachment length was observed to decrease to the increase on Reynolds number. Key words: Fluidic oscillator, Particle image velocimetry, backward facing step, sudden expansion.
1. Introduction Fluidic oscillator is a device that does not involve any moving part and can create an oscillating jet that is self-induced and self-sustained [1]. They are widely used because of their simple design and wide range of frequencies [2]. Fluidic oscillators can be divided into three main groups based on the number of feedback loops: feedback-free, single-feedback, and double-feedback jets. The use of two feedback channels (recirculators) was discovered in the mid-20th century [3]. Nowadays, 1
the most popular fluidic oscillators have two feedback channels to connect the upstream and downstream parts of a chamber. In the present study, the double feedback fluidic oscillator is studied and the schematic view of that is illustrated in Fig. 1. The flow in the feedback channels plays a significant role in producing an oscillating jet. When the fluid enters, the flow attaches to one wall of the mixing chamber because of the Coanda effect, which is the tendency of a jet to remain attached to a solid surface. In addition, a lowpressure region is created between the jet and an adjacent surface. As a result, the jet bends toward the wall, and a counter flow is created downstream. Because the jet bends, a part of the flow enters the recirculators and discharges into the mixing chamber. Thus, the jet at the power nozzle is deflected toward the opposite wall, and this process is repeated at a certain frequency [4]. The oscillation frequency of a jet depends on the internal region of the fluidic oscillator, and some numerical and experimental studies have analyzed the internal part of fluidic oscillator to identify the mechanisms that drive the jet to oscillate and characteristics which are associated with the oscillation frequency ([5]–[10]). External flow dynamics and oscillation characteristics of the fluidic oscillators have been studied widely. Wen and Liu [11] studied the effect of Reynolds numbers (Re) of 2,500 to 11,700 on different parameters like the size of separation bubbles and the spreading angle. The flow characteristics and turbulence structures have been also discussed by the unsteady behavior of oscillating jet for different Re numbers [12]. Additionally, Wen et al. [13] investigated the interaction of two fluidic oscillators impinging on a flat plate. Sang and Hyun [14] studied the three-dimensional features of a fluidic oscillator at Re=8,000 to 24,000 and calculated the frequency of the oscillation. They also investigated the cross-sectional planes of the fluidic oscillator. Various applications of fluidic oscillators have also been experimentally examined such as separation control by fluidic oscillators ([15]–[19]), bluff body drag reduction [20], combustion [21], and heat transfer enhancement ([22]–[24]). Thus, fluidic oscillators can be used for cooling turbine blades and the more velocity and turbulent fluctuations, the more convection and diffusion [25]. In addition, in some real-world applications, the surfaces are in confined spaces. Therefore, in this study, the effect of the external 2
region on an oscillating jet was experimentally examined. First, one wall at the bottom of the external region with a step was examined, and then two walls at external geometry as confined domain with a double-wall was studied. For both geometries, two-dimensional time-resolved particle image velocimetry (2D-TR-PIV) was used in two different planes and various sections. Time-averaged velocity components and vorticity field are examined and flow dynamics at Re=10,000 are discussed in terms of phase-averaged velocity fields. The results show that the external confinement has not significant effect on the oscillating frequency, even if the velocity distribution of the fluid flow is changed. In contrast, the spreading angle is different based on the external geometry and confining the domain decreases that angle at a constant Re number which can affect the heat transfer performance. Additionally, different Reynolds number from 2,000 to 10,000 were performed and investigation of Coanda effect on the reattachment length of the oscillating flow was carried out. Supply feedback channel power nozzle dh=10 mm
mixing chamber exit
Throat
Fig. 1 Current fluidic oscillator’s components
2. Experimental setup and PIV measurement In the non-intrusive PIV method, a seeding flow of tracer particles is illuminated by a laser sheet. Then, images are captured by a camera from the light scattered by the tracer particles. As a result, the displacement of particles can be calculated between two images, and the velocity vectors can be obtained from the time difference. The flow was seeded through a water tank with 11.7-µm silver-coated hollow spheres at a density of 1.1 g/cm3. The laser light sheet was generated by a 5W continuous-wave laser beam operating at a wavelength of 532 nm and passing through a cylindrical lens.
3
The images of the illuminated particles were captured using a high-speed camera (Photron FastCam SA1.1). The camera captures images with a resolution of 1024 by 1024 pixels, and image processing was performed with PIVLab software. A final interrogation window of 16 × 16 pixels with 50% overlap was used to satisfy the Nyquist criterion. Instantaneous and ensemble averaging of the flow velocity vectors was performed using a cross-correlation algorithm [26]. The timeaveraged of such quantities were obtained from 10,918 frames of instantaneous velocity field. The experimental setups are shown in Fig. 1 (a-b), in which the field of view was visualized at different planes. In Fig. 2 (a), the target view is parallel to the x-y plane and located at z/D=0. In Fig. 2 (b), the target view is parallel to the x-z plane and located at y/D=0. In addition, other sections were also visualized at y/D=1 and y/D=2, as shown in Fig. 2 (b). The experiments were done with both single-wall and double-wall geometries. The geometry of the fluid domain for the single-wall geometry is shown in Fig. 3, and the dimensionless values are listed in Table 1. The origin of the coordinate system is at the center of the outlet of the fluidic oscillator. For the doublewall geometry, another plate similar to the bottom plate of the single-wall geometry is placed on top of the geometry, and the external domain of fluidic oscillator is bounded in the z direction by no-slip walls. A pump injects water into the fluidic oscillator, and the flow rate of the supplied water is measured by a flow meter. The working fluid in the current study is water, and the tank is made of acrylic because its refraction index is similar to that of water. The oscillator was also made from acrylic using a CNC machine, similar to that used in previous studies of [11] and [14]. The crosssection area of the outlet throat is 10*10 mm2, and the hydraulic diameter is 10 mm. The outlet nozzle has a 90o divergence angle and length of 40 mm. Air bubbles in the jet pipes were removed before PIV measurements. The experiments were performed for different Re of 2000 to 10,000 based on the hydraulic diameter.
4
(a)
(b)
Fig. 2 Experimental setup for a) plane z/D=0, b) plane y/D=0.
h m (b) m h m m
(a)
10 mm (c)
Fig. 3 Diagrams of (a-b) single-wall and (c) double-wall geometries.
Table 1 Dimensions of the setups in Fig. 2. Parameter H/D h/D L1/D L2/D
dimension 1 0.4 4 16
Parameter L3/D L4/D L5/D
dimension 60 20 40
3. Results and Discussion The following sections present the results to get the flow dynamics of oscillating jet. First, the characteristic of fluid pattern for non-confined and confined geometries are compared on the plane of z/D=0. Then, the comparison of the flow on y/D=0, 1 , 2 planes is done for both geometries. 3.1 y Plane for z/D=0
5
The oscillating jet is generated by a fluidic oscillator. The sampling rates of the experiments are at least three orders of magnitude more than the frequency of the oscillation, so in order to find the oscillation frequencies, the velocity distributions of two specific locations are extracted (symmetrical points about the centerline of the jet) [11-12]. Then, the velocity differences of the two points are calculated because there is a 180o phase lag between the feedback channels and between the two symmetrical points. Finally, the oscillation frequency is found by using a lowpass filter and FFT analysis. As Schmidt et. al. [17] showed, there is a linear dependence of oscillation frequency on mass flow rate. In the current study, the dimensions of fluidic oscillator are fixed for all experiments (Table 1) and Re number is changed based on the supply rate. Thus, as illustrated in Fig. 4, the oscillation frequency of a fluidic oscillator depends on the Re number and is almost independent of the external domain geometry. In addition, the frequency for the non-bounded external domain for the same fluidic oscillator was also calculated by Sang and Hyun [14] and is compared with the frequencies of confinement external geometries via one plate or two plates. It can be concluded that because the oscillating jet is generated by the internal part of the fluidic oscillator, the external domain does not have any significant effect on the frequency.
1.1
Single-wall geometry Double-wall geometry Not bounded external domain [14]
1.0
F [Hz]
0.9 0.8 0.7 0.6 0.5 0.4 0.3 4000
5000
6000
7000
8000
9000
10000
Re
Fig. 4 The oscillation frequency of a fluidic oscillator (the uncertainty was estimated at around 2% [11]).
Although the frequency of the fluidic oscillator is almost independent of the external domain, the performance of the external flow field is different for the two geometries. The edges of the maximum dimensionless velocity magnitude based on the mean velocity of throat (U) for 6
different Re are shown in Fig. 5. For low Re, the continuous jet in the forward direction and the general pattern of the two geometries are the same, as shown in Fig. 5 (a-b) (Re=2000 and 3300). But for high Re numbers, the behavior of the fluid is different. When increasing Re, a kind of Vshaped distribution is formed for both geometries and the jet diffuses more in lateral direction (Fig. 5 (c)). For the single-wall geometry at Re=8250 and 10,000 (right-side of Fig. 5 (d-e)), the oscillation patterns are similar to each other. However, for the double-wall geometry, the V-shaped pattern of the single-wall geometry is modified, and a different pattern is generated with completely different jet movement. The jet deflection angle is extracted from the time-averaged velocity components in both streamwise and transverse directions of the peak velocity components near the exit region of jet and is shown in Fig. 6. The spreading angle is defined as the angle between the centerline and maximum velocity deflection. The maximum deflection angle is a function of Re number (or supply rate in this study) and increases when increasing Re number until Re=8250 for the singlewall geometry. After that, the angle is constant at 45o because the exit nozzle angle is 90o, and the maximum angle between the two maximum deflections is 90o. For the double-wall geometry, at all Re numbers, the angle is smaller than that of the single-wall geometry, and the exit nozzle’s angle does not have significant effects on the velocity pattern. Furthermore, for Re=10,000, the spreading angle is less than that at Re=8250. This is also confirmed in Fig. 5. At Re=10,000, the flow bends the jet and breaks down in comparison with Re=8250.
(a)
(b)
(c)
(d)
(e)
Fig. 5 Time-averaged maximum deflection of the jet for: a) Re=2000, b) Re=3300, c) Re=4600, d) Re=8250, and e) Re=10,000. The right side of the centerline is the single-wall geometry, and the left side is the double-wall geometry.
7
Spreading Angle
50
Single-wall geometry Double-wall geometry
40
30
20 4000
5000
6000
7000
8000
9000
10000
Re
Fig. 6 The time-averaged angle of the maximum velocity deflection for different Re.
With increasing Reynolds number, jet impact region is enlarged significantly due to the greater jet spreading angle and jet momentum shifts from an even spatial distribution concentrated along the middle centerline to a V-shape distribution. Thus, at higher Reynolds numbers, the jet momentum has peaks on the lateral sides (Fig.5). In order to find the reason for the jet breaking down, Fig. 7 illustrates the time-averaged velocity magnitude, streamlines, streamwise velocities, and transverse velocities for Re=10,000. The velocity contours are nondimensionalized with the averaged throat velocity estimated from the flow rate (U=Q/A throat) which A throat is the area of the nozzle throat and Q is the volumetric flow rate. The V-shaped velocity pattern can be seen for the single-wall case (Fig. 7 (a)). However, adding the top plate to the external domain of the fluid and creating the double-wall geometry causes the V-shaped pattern to change (Fig. 7 (b)). For the single-wall case, the jet generates a high concentration of fluid at its maximum deflection, and there is weak flow in the middle region of the maximum deflection. Thus, an inhomogeneous distribution is created in this case. In Fig. 7 (c), for the single-wall geometry, the flow moves without any distortion, but for the double-wall geometry (Fig.7 (d)), there are some strong vortices that control the emitted jet (saddle and nodal points). The formation of these structures is highly dependent on the jet entrainment of the ambient fluid and their rotation direction is clockwise and counterclockwise as illustrated in Fig.7 (d). These vortices prevent the high-velocity flow from moving freely like in the single-wall geometry. Thus, when the jet is discharged, the quiescent fluid in the external domain will be continuously entrained into the jet and the high-speed flow is concentrated at a small region at the outlet of the fluidic oscillator. The time-averaged of streamwise velocity (Fig. 7 (e - f)) and transverse velocity (Fig. 7 (g - h)) were also investigated. At Re=10,000, the maximum streamwise and transverse velocities are 8
almost equal for the single-wall geometry. For the double-wall geometry, the maximum streamwise velocity occurs just near the exit region and is about two times the maximum transverse velocity. But these velocities are almost equal at the positions where the maximum transverse velocity occurs. This behavior is also confirmed by the streamlines in Fig. 7 (c-d). The ratios of the maximum magnitude of the transverse to the streamwise velocities are plotted in Fig. 8. For both cases at Re=2000, the magnitude of the transverse velocity is less than 20% of the streamwise velocity near the exit region. This means that the jet is emitted in the streamwise direction, and there is a small spreading angle. By increasing the Re number, the ratio is increased, but for the double-wall geometry, the jet momentum is still more in the streamwise direction near the exit region in comparison with the single-wall geometry for high Re numbers.
(a)
(c)
(e)
(g)
(b)
(d)
(f)
(h)
Fig. 7 Time-averaged of velocity magnitude (a-b), streamlines (c-d), streamwise velocity (e - f), and transverse velocity (g - h) for single-wall (a,c,e,f) and double-wall (b,d,f,g) geometries at Re=10,000 and plane z/D=0 ( : saddle point, : Nodal point).
9
1.0
Single-wall geometry Double-wall geometry
0.8
u/v
0.6
0.4
0.2
0.0
2000
4000
6000
8000
10000
Re
Fig. 8 The ratio of transverse to streamwise velocities.
Fig. 9 shows the instantaneous velocity field for Re=10,000 when the jet is moving between its maximum deflection (during T/2). As showed in Fig. 7, there is a strong vortex between maximum deflection of jet that prevents the jet to emit flow in y-direction and leads to creating small spreading angle in comparison with single-wall geometry as compared in Fig.6. In order to get more details, Q-criterion will be calculated for vortex identification in next part. Phase averaging data processing is also done with technique of getting the frequency of oscillation (Fig. 4) based on the differential velocity signal from the two reference positions. All 10,918 snapshots are sorted in ascending order and a phase window size of 3 yields 120 phase angle windows in one oscillation period is assumed. Thus, each phase angle window contains 91 snapshots. More details of this method can be found in [5,12]. In this paper, the instant that the oscillating jet is deflected at the bottom-most position is arbitrarily called zero phase. The jet has a rapid switching process from one side of the exit to the other and at its maximum deflection position, because of attaching to the diverging exit wall and Coanda effect, stays for a longer time [12]. According to the phase-averaged velocity vector field (Fig. 10), the velocity magnitude of the jet flow is strong at phase of 0 and 180 and during the change of direction, to 90, remains strong in a short distance. In addition, the footprint of the previous cycle exists in the opposite direction in the phase-averaged velocity fields of double-wall geometry.
10
(a)
(b)
(c)
(d) (e) (f) Fig. 9 Instantaneous normalized velocity magnitude for (a-b-c) single-wall, (d-e-f) double-wall for Re=10000 on plane z/D=0.
0o
90o
180o
(a)
(b)
(c)
11
0o
90o
180o
(d)
(e)
(f)
Fig. 10 Phase-averaged velocity field of sweeping jet in the x-y plane at Re=10,000 for (a-c) single-wall (d-f) double-wall geometry.
As the jet is emitted in the external field and moves forward, the water right next to the boundary of the jet also moves with the jet because of friction. But the water far away from the jet does not move, and the difference between these velocities causes a shear force. As a result, the water starts spinning, and vortices form because of the velocity difference. The normalized timeaveraged vorticity contours for Re=10000 are shown in Fig. 11 for the single-wall and double-wall geometries. One of the main processes that can influence the dynamics of jet and heat transfer is the edge shear layer surrounding the jet [27]. In Fig. 12 (a-b-c) and (d-e-f) the instantaneous vorticity field during T/2 for Re=10000 is shown for single-wall and double-wall geometry, respectively. The interaction between the jet shear layer and the confining external domain is obtained and the vorticity field of the double-wall geometry differs from that of the single-wall geometry. For the double-wall geometry, when the jet is emitted in stationary fluid and oscillates, main vortices are generated which one of them is near the exit region between the maximum deflection of jets (Fig 12 (d-e-f)). Two other main vortices are formed far away from the exit region. As a result, the flow direction bends from x/D=5. This is the reason why the V-shaped pattern of the flow cannot be observed in the double-wall geometry. For the single-wall geometry, the emitted jet can move freely, and the movement of the fluid is damped soon as well. Thus, only the counter-rotating vortex pairs can be seen, and the V-shaped distribution of the vortex occurs. For the double-wall geometry, three main vortices lead to the whole domain of the fluid moving, and a different pattern 12
of oscillating flow is formed. In fact, for one plate geometry similar to non-bounded external geometry, as Ostermann et. al. [28] showed, the mass flow is entrained from the direction normal to the oscillation pattern (z direction in the current work) and the entrainment rate can increase as contact area between jet and surrounding fluid is enlarged. This increment also shows the mixing enhancement as a result of acceleration of ambient fluid due to the jet momentum. In contrast, for two plates geometry, such entrainment from z direction is inhibited and those three main vortices are created which are beneficial to enhance convective heat transfer for the bottom wall at the external region.
(a)
(b)
Fig. 11 Time-averaged of normalized vorticity for : a) Single-wall, b) Double-wall for Re=10,000.
(a)
(b)
13
(c)
(d)
(e)
(f)
Fig. 12 Instantenous normalized vorticity during T/2 for: (a-b-c) Single-wall, (d-e-f) Double-wall at Re=10,000.
For vortex identification, Hunt et al. [29] defined the Q-criterion as a quantitative way criterion to obtain more details about vortex boundaries (Eq. 1). They concluded that vortex regions occur where Q is positive, which means the vorticity magnitude is greater than the magnitude of the rate of strain. In the current work, the Q-criteria were first calculated, and vortex boundaries were specified for time-averaged results(Fig.13 shows an example of this process). Then, the circulation (Γ), which is the integral of z-component vorticity (Eq. 2), was calculated over an area with a positive value of the Q-criterion because the area with a positive value of the Q-criterion is in the vortex area as shown in Fig.13. Thus, to measure the exact area of the vortex, this criterion is used for integrating the area. Overall, the vortices cancel each other out, and the circulation for the whole domain is zero, so the mean magnitude of both vortex circulations was calculated. The results are listed in Table 2. For better visualization of the behavior of the larger vortices, we calculated the Q-criterion of the instantaneous flow field during T/2 at Re=10,000 which is illustrated at Fig. 14. When the jet is at its maximum deflection (a,c,d,f in Fig. 14) the concentration of maximumn Q occures at jet location for single-wall geometry. In contrast, for double-wall germetry, that distribution is more even and on the opposite side of the jet, some coherenet structure is still remained. In addition, when jet is at centerline, confining the external domain causes the oscillating jet stays near the exit region. That’s because of the vorticities which are trapped by confining the external domain (Fig. 7). For the single-wall geometry, the dimensionless circulation is almost constant. However, by increasing Re, the circulation over the area of Q>0 is also increased to about 10 times the 14
circulation for Re=8250. Therefore, for Re=10,000, the strong vortices in the domain bend the oscillating jet and even break it, as shown in Fig. 5. However, for Re=8250, these vortices are not strong enough, and the jet can be maintained. This phenomenon also affects the spreading angle and causes the results at Re=8250 to have a greater spreading angle in comparison with Re=10,000 (Fig. 5). 2
2
Q ( S ) 2
Eq. 1
.dS
Eq. 2
S
(a)
(b)
Fig. 13 Time-averaged contour of Double-wall at Re=10,000 for (a) Qcriterion and (b) Vortex area definition.
(a)
(b)
15
(c)
(d)
(e)
(f)
Fig. 14. Instantenous contour of Q-criterion during T/2 for: (a-b-c) Single-wall, (d-e-f) Double-wall at Re=10,000. Table 2 Comparison of the dimensionless circulation over the area of Q>0. Re 8250 10000
Single-wall 0.015 0.015
Γmean / UD Double-wall 0.043 0.14
3.2 x-z Planes for y/D=0,1,2 This section discusses the time-averaged results, so it is necessary to prove that the characteristic of oscillating jet is independent of number of snap shots. Therefore, time-averaged flow fields by 2000, 4000, and 10918 independent 2D-2C- PIV snapshots of Re=10,000 and one-plate geometry at section y/D=0 is compared (Fig. 15). It can be seen, the main recirculation region which plays a dominant role and is identified near the step, is almost constant. Then, time-averaged velocity magnitude fields and streamlines for two Re values at the plane y/D=0 are calculated and shown in Fig. 16. The flow behind the step is bounded by the separating and reattaching shear layer and by the wall, so the flow reattaches and forms a recirculation zone behind the step. In addition, the reattachment length measured at a distance of 0.05D from the wall and the reattachment length is decreased by increasing Re (Table 3), in contrast to the behavior of the free stream on the backward-facing step [30]. One for this reduction in the reattachment length can be that by increasing the Re number, the spreading angle is also increased. Therefore, the jet’s angular distance from the center line is increased, and as a result, the reattachment length decreases in different y-planes.
16
In addition, although the spreading angle for the double-wall geometry is less than that for the single-wall geometry, the double-wall geometry has a smaller reattachment region (at a constant Re number). The symmetrical distribution of the velocity field is also observed in the double-wall geometry. Moreover, Fig. 17 presents the instantaneous velocity field and streamlines of Re=10,000 for single-wall geometry. It shows that the instantaneous flow is more irregular than the time-averaged flow structure and vorticities are created near the shear layer and move while the jet moves forward. The dimensionless time-averaged streamwise velocity profiles are shown in Fig. 18. For the double-wall geometry, a symmetric profile is created because of the two recirculation zones, and the profile becomes flat as x/D increases. However, for the single-wall geometry, there is one velocity peak, and when enhancing x/D, the peak becomes smoother. For high values of z/D, the fluid remains stationary and does not move.
2000 snapshots
4000 snapshots
10918 snapshots
Fig. 15 Time-averaged of velocity field for Re=10,000 and Single-wall geometry at plane y/D=0.
supply
supply
(a)
(c)
17
supply
supply
(b)
(d)
Fig. 16 Time-averaged of velocity field and streamlines for: a) Re 5300 Single-wall, b) Re=10000 Single-wall, c) Re=5300 Double-wall, d) Re=10000 Double-wall at plane y/D=0.
supply
supply
(a)
(b)
Fig.17 Instantenous of velocity field and streamlines for single-wall geometry at Re=10,000.
Table 3 Comparison of the dimensionless reattachment length (xr/D) at plane y/D=0. xr/D Re 2000 5300 10000
Single-wall 3.5 3 2
Double-wall 2 1.4 1
50
Spreading Angle
Single-wall geometry
Double-wall geometry
40
30
20 4000
18 5000
6000
7000
Re
8000
9000
10000
1.5
1.0
One plate geo. Two plates geo.
1.5
1.5
0.5
0.5
0.5
0.5
0.0
0.0
0.0
0.0
-0.5
-0.5
-0.5
-0.5
0.0
0.2
0.4
0.6
-1.0 -0.2
0.0
0.4
-1.0 -0.2
0.6
0.0
x/D=0.5 One plate geo.
x/D=1
Two plates geo.
1.0
1.5
0.4
0.6
-1.0 -0.2
1.5
One plate geo. Two plates geo.
1.0
0.5
0.5
0.0
0.0
0.0
0.0
-0.5
-0.5
-0.5
-0.5
0.2
u/U
x/D=2.5
0.4
0.6
-1.0 -0.2
0.0
0.2
0.4
-1.0 -0.2
0.6
0.0
0.2
u/U
u/U
x/D=3
0.4
0.6
One plate geo. Two plates geo.
1.0
z/D
z/D
1.5
0.5
0.0
0.2
x/D=2
0.5
-1.0 -0.2
0.0
u/U
x/D=1.5
One plate geo. Two plates geo.
1.0
z/D
0.2
u/U
u/U
u/U
1.5
0.2
z/D
-1.0 -0.2
One plate geo. Two plates geo.
1.0
1.0
z/D
z/D
1.0
One plate geo. Two plates geo.
z/D
One plate geo. Two plates geo.
z/D
1.5
x/D=3.5
0.4
0.6
-1.0 -0.2
0.0
0.2
0.4
0.6
u/U
x/D=4
Fig. 18 Time-averaged dimensionless streamwise velocity profiles for Re=5300 at plane y/D=0.
The time-averaged dimensionless vorticity for Re=10,000 is shown in Fig. 19. For the single-wall geometry, there is a small region of negative vorticity in the recirculation region due to the revised flow and induced flow by the secondary recirculation at the step corner. Peak values of vorticity occur in the shear layer separation and this vorticity extends from the step edge. Subsequently, such vorticity weakens and grows in width more in the downstream direction and is predominantly distributed. For the double-wall geometry, the magnitude of the primary vortex is much higher than for the single-wall geometry and confining the external domain causes the vorticity to be much stronger with smaller region.
19
supply
(a)
supply
(b) Fig. 19 Time-averaged dimensionless vorticity for (a) singlewall and (b) double-wall geometry for Re=10,000 at y/D=0.
The flow was visualized at two other sections with similar distances from each other. The time-averaged velocity contours for both geometries at different sections are presented in Fig. 20. In order to compare the effect of Re on both geometries, the dimensionless streamwise velocities for different sections were calculated and are plotted in Figs. 21-22. For the center plane of the jet with a norm of y (plane Y/D=0), two velocity profiles are created at X/D=0.5 and X/D=1.5. Fig. 20 shows that the behavior of the flow at Re=2000 is like a laminar flow, but for other Re, a turbulent profile is obtained. In Fig. 20 (a) and (b), the peak of u/U for the single-wall geometry is located at z/D>0 for x/D=0.5 and then placed at z/D=0 for x/D=1.5. This means that as the flow bends, it tends to attach to the plate because of the Coanda effect as it moves. In addition, as the jet is emitted, the velocity magnitude is decreased for constant Re and constant geometry. However, the difference between these amounts is higher for the double-wall geometry in comparison with the single-wall geometry. For example, for Re=2000 and the single-wall geometry, the maximum value of u/U is decreased from 0.65 for x/D=0.5 to 0.57 for x/D=1.5 (a difference of 0.08). These values for the double-wall geometry are 0.95 and 0.79, respectively (a difference of 0.16). Furthermore, for constant Re and x/D, the amount for the double-wall geometry is more than that for the single-wall because of the continuity equation. 20
Fig. 22 shows the dimensionless streamwise velocity at the plane y/D=1 and the plane y/D=2. For Re=2000 in the single- wall geometry, the peak velocity is decreased when changing y/D from 0 to 2. This means that the jet’s spreading angle is small, and the jet flows more in the streamwise direction rather than the transverse direction, as discussed previously.
(a)
(b)
(c)
(d)
Fig. 20 Time-averaged dimensionless velocity magnitude for (a) single-wall, Re=2000, (b) double-wall, Re=2000, (c) single-wall, Re=10,000, (b-d) double-wall, Re=10,000.
1.5
1.2
Single-wall, Re = 2000 Single-wall, Re = 5300 Single-wall, Re = 10000 Double-wall, Re = 2000 Double-wall, Re = 5300 Double-wall, Re = 10000
0.9
0.9
u/U
u/U
1.2
Single-wall, Re = 2000 Single-wall, Re = 5300 Single-wall, Re = 10000 Double-wall, Re = 2000 Double-wall, Re = 5300 Double-wall, Re = 10000
0.6
0.6
0.3
0.3
0.0 -0.850
-0.425
0.000
0.425
0.850
z/D
0.0 -0.850
-0.425
0.000
z/D
21
0.425
0.850
(a)
(b)
Fig 21 Time-averaged streamwise velocity profiles at plane y/D=0 for a) x/D=0.5 and b) x/D=1.5.
0.4
Single-wall, Re = 2000 Single-wall, Re = 5300 Single-wall, Re = 10000 Double-wall, Re = 2000 Double-wall, Re = 5300 Double-wall, Re = 10000
0.3
Single-wall, Re = 2000 Single-wall, Re = 5300 Single-wall, Re = 10000 Double-wall, Re = 2000 Double-wall, Re = 5300 Double-wall, Re = 10000
0.20 0.16
u/U
u/U
0.12
0.2
0.08 0.04
0.1 0.00
0.0 -0.850
-0.425
0.000
0.425
-0.04 -0.850
0.850
-0.425
0.000
0.425
0.850
z/D
z/D
(a)
(b)
Fig 22 Time-averaged streamwise velocity profiles at x/D=1.5 for planes a) y/D=1 and b) y/D=2.
4. Conclusion The 2D-TR-PIV method was used to visualize the flow characteristics of an oscillating fluidic oscillator emitted in a stationary fluid. The single-wall geometry had a non-confined backwardfacing step, and the double-wall geometry was symmetrically confined with a sudden expansion domain. Experiments were done for two different fields of view (y and z plane) with different sections (y/D=0, 1, 2 and z/D=0). The most important findings are summarized as follows: 1) The flow pattern of oscillating jet is a function of flow rate, which in this study normalized
by Re number, and external domain geometry. 2) Jet momentum is mostly in the streamwise direction rather than the transverse for lower
supply rate or Re number. 3) At a constant supply rate (Re number), although the external domain of the fluidic oscillator
does not have a significant effect on the oscillating frequency, the spreading angle can be changed dramatically. Thus, spreading angle can be decreased because of confining the external domain by two symmetrical walls at the bottom and upper side of region. The difference between entrained flow is the main reason. For one plate geometry, flow was entrained from the normal direction of the oscillating pattern results flow structure 22
considerably different in comparison with two plates geometry at the same Re number. For instance, the ensemble-averaged oscillating flow from the fluidic oscillator at Re=10,000 in the single-wall geometry created a V-shaped velocity distribution. However, for the double-wall geometry, this pattern was changed, and three main vortices were generated in the external domain. These vortices can enhance the convective heat transfer on the bottom wall. 4)
Confining the external domain creates a shorter reattachment length at same Re number on plane y/D=0 which is due to the existence of a strong vortex between maximum deflection of oscillating jet which showed on plane z/D=0.
Acknowledgements This research was supported by the International Research and Development Program of the National Research Foundation of Korea (NRF), which is funded by the Ministry of Science and ICT of Korea (NRF-2017K1A3A1A30084513). This study was also supported by the National Research Foundation of Korea (NRF) grant, which is funded by the Korean government (MSIT) (No. 2011-0030013, No. 2018R1A2B2007117). References [1]
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25
Highlights: Oscillating frequency is almost independent of the external domain shape. Frequency is increased linearly with increasing Reynolds number. High Reynolds number causes lateral velocity and spreading angle to increase. Strong vortices for the double-step geometry decreases the spreading angle. Reattachment length is decreased with increasing the Reynolds number.
26