An experimental investigation on passive scalar mixing due to the interaction of a synthetic jet with a thermal boundary layer is presented. From velocity measurements, performed by particle image velocimetry, two jet behaviours were identified. For jet to crossflow velocity ratios less than 1.2, the velocity fluctuations due to the jet/crossflow interaction stayed close to the wall. At higher ratios, the fluctuations moved away from the wall. The thermal mixing was examined using laser induced fluorescence. During expulsion, the thickness of the downstream thermal boundary layer increased whilst the thermal boundary layer was annihilated immediately downstream of the jet during entrainment

Bénard, Emmanuel

Cooper, Richard K.

Mitchell, Glen

Uruba, Vaclav

English

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Passive Scalar Mixing Downstream of aSynthetic Jet in CrossflowGlen Mitchell1, Emmanuel Benard1, Vaclav Uruba2, and Richard .K. Cooper11 School of Mechanical and Aerospace Engineering, Queen’s University Belfast,Belfast, UK2 Institute of Thermomechanics, The Academy of Sciences of the Czech Republic,Prague, Czech RepublicAbstract. The abstract should summarize the contents of the paperusing at least 70 and at most 150 words. It will be set in 9-point fontsize and be inset 1.0 cm from the right and left margins. There will betwo blank lines before and after the Abstract. . . .1 IntroductionSurface heat transfer is important in many engineering applications, e.g. energy,aerospace and automotive. For a crossflow, it is possible to increase surfaceheat transfer through the use of vortex generators upstream of the heat transfersurface [1, 2] and by injecting continuous jets into the flow [3]. In both cases,heat transfer enhancement is obtained by altering the thermal mixing near thesurface. It is possible that a synthetic jet could also be used to improve crossflowsurface heat transfer.The synthetic jet actuator consists of a cavity with an oscillating surfaceacting as one wall and an orifice in another wall. During the forced oscillationof the surface, fluid is alternately entrained into and expelled from the cavitycreating a series of vortex pairs that coalesce to form a jet. In a cross-flow, thevortex generated travels downstream of the orifice and at low ratios of jet tocrossflow velocity, the vortex remains close to the wall. This vortex influencesthe transport of fluid within the boundary layer and, when the wall is heated,the thermal mixing.The current study aims at investigating the influence of a 2D synthetic jet onpassive scalar mixing in a turbulent boundary layer, with temperature acting asthe passive scalar. An initial particle image velocimetry (PIV) study is used tostudy the hydrodynamics of the jet/crossflow interaction and proper orthogonaldecomposition (POD) of the flow field is used to identify the conditions for nearwall mixing. A laser induced fluorescence (LIF) study is then conducted in orderto examine the thermal mixing due to the jet/crossflow interaction.2 Water channel and synthetic jet actuatorThe experiments were conducted in a closed circuit horizontal water channel witha test section of length 1000mm and cross-section 60mm wide by 360mm high.The channel has a maximum test section velocity of 40cm/s with a freestreamturbulence intensity of less than 1.5%. The flow along the sidewall of the channelwas tripped just after the contraction using cylindrical roughness elements togenerate a turbulent boundary layer. The boundary layer can be heated by a400mm long copper plate. The plate is located 600mm downstream from the startof the test section and has two uniform heat flux electrical heaters at the rear.A radiator in the settling chamber of the channel ensures the water temperaturefluctuates by less than 0.1◦C.The synthetic jet was generated by a mechanical piston/cylinder arrangementconnected to a cavity with a slot type orifice of width 0.75mm and length 105mm.The jet orifice is located in the heated copper plate, 130 slot widths downstreamfrom the start of the thermal boundary layer and is orientated so the long axisof the orifice is perpendicular to the flow. An electromagnetic shaker is used toexcite the piston with a sinusoidal oscillation. The cylinder is connected to thecavity by a flexible hose to isolate the vibration of the shaker from the channel.Using this arrangement, jets can be generated with Reynolds number rangingfrom 20 to 1000 and Strouhal numbers in the range 0.001 to 0.2.3 PIV/LIF techniqueThe PIV/LIF system consists of a 15Hz double pulsed Nd:YAG (532nm wave-length) laser and a CCD camera with a resolution of 2048 × 2048pixels2 and amaximum frame rate of 15 frames per second. The laser light sheet was adjustedso it was located along the orifice centreline parallel to the flow and the flow wasseeded with hollow glass spheres for PIV and Rhodamine B fluorescent dye forthe LIF temperature measurements.For both the PIV and LIF experiments phase and ensemble averaged resultswere obtained. The image acquisition was phase-locked to the actuator motionwith images acquired at 24 equally spaced intervals during the actuator cycle.For PIV, 150 double framed images were acquired for each phase of the cy-cle. These images were analysed using a multi-pass cross-correlation techniqueproducing vector fields with a resolution of 0.22 × 0.22mm2. For LIF, 40 singleframe images were taken at each phase. For each image, the florescence inten-sity was averaged over cells of 10 × 10pixels2 to maximise the signal to noiseratio resulting in a spatial resolution of 0.16 × 0.16mm. The intensity distribu-tion across the light sheet varies for each laser shot. This intensity variation wascorrected by a procedure similar to the correction method of Seutie¨ns et al [4].The final temperature field was calculated from the florescence intensity using apre-determined calibration relationship.4 Proper orthogonal decompositionThe POD provides an energy efficient decomposition of the fluctuating part ofthe velocity field. The instantaneous velocity field is decomposed into a timeaveraged component and a fluctuating component:−→u (−→x , t) = −→U (−→x ) +N∑n=1an(t)φn(−→x ) (1)where the fluctuating component is described by a linear combination of modes, φ.The modes are organised so the first mode contain the most energy and the lastmode the least energy. This makes POD a useful tool for identifying dominant co-herent flow patterns. In this paper, the POD has been performed by the methodof snaphots [5].5 Hydrodynamic effectsTo investigate the hydrodynamic effects of the interaction of the synthetic jetwith a crossflow, eight different cases were studied. Only two representative casesare presented here. Case 1 has a low jet to crossflow velocity ratio and case 2has a high velocity ratio. The parameters for both jets are given in Table 1. Forboth cases, the boundary layer had the following parameters at the jet orifice;Reθ = 760, δ = 21mm and H = 1.3. To confirm that the boundary layer wasturbulent, the velocity profile was compared to the logarithmic law of the walland the turbulence intensity profile was examined.The first three POD modes for each case are shown in Figure 1. It can beseen that modes 1 and 2 are similar for each case. The first mode has as structuresimilar to the ejection portion of the jet cycle, with a large velocity magnitudeat the orifice exit and a vortex immediately downstream. The structure of thesecond mode resembles the suction portion of the cycle, with a smaller velocityaround the orifice and the vortex further downstream. A closer look at the rela-tionship between these two modes shows a 90◦ phase difference between them.Reconstructions of the flow field using these two modes are similar to the phaseaveraged flow, as demonstrated in Figure 2 for case 2. It should be noted thatthis is not valid for the start of the expulsion cycle. At this point, the two modereconstruction differs significantly from the phase averaged flow field in the re-gion of the orifice as modes 1 and 2 do not contain enough detail to reconstructthe complex flowfield in this area. The first two modes combined contain over30% of the energy with subsequent modes having less than 5% each.After the first two modes, the modes for the two jet cases start to deviate asshown in Figure 1(c). For case 1, the third mode consists of a series of vorticalTable 1. Parameters for the three jet cases considered.Case ReU0 StU0 U∞ [cm/s] U0/U∞1 278 0.0277 40.0 0.832 556 0.0089 40.0 2.223 278 0.0089 40.0 1.110 10 20 300510152025x/hy/hCase 10 10 20 300510152025x/hy/hCase 2(a)0 10 20 300510152025x/hy/h0 10 20 300510152025x/hy/h(b)0 10 20 300510152025x/hy/h0 10 20 300510152025x/hy/h(c)Fig. 1. Visualisation of the first three POD modes for cases 1 and 2: (a) mode 1,(b) mode 2, (c) mode 3.structures, located close to the wall whereas case 2 has a horizontal fluctuationlocated away from the wall. Although not presented here, subsequent modes forcase 2 tend to consist of a series of vortical motions moving away from the wallwhilst, for case 1, the fluctuations in higher modes remain close to the wall.For all eight of the jet cases studied, the POD modes followed the same pat-tern as cases 1 and 2. The first two modes were similar for all cases. For mode3 and higher, the two different behaviours described above were observed. Thetype of behaviour the jet displays was found to be dependant on the jet to cross-flow velocity ratio. For U0/U∞ < 1.2 the fluctuations remain close to the wallwhilst they move away from the wall for U0/U∞ > 1.6.0 10 20 300510152025x/hy/h(a)0 10 20 300510152025x/hy/h(b)Fig. 2. The synthetic jet flowfield during the suction cycle for case 1: (a) phase-averaged, (b) 2 mode reconstruction.6 Passive Scalar EffectsTo investigate the scalar effects, a jet similar to case 1 is considered, i.e. thefluctuations in the higher modes of the POD remain close to the wall. Theparameters for this jet are once again given in Table 1 (case 3). The results ofthe LIF study are shown in Figure 3 for two different phases of the jet cycle;half way through the ejection cycle and the midpoint of the suction cycle.During the expulsion cycle, the jet pushes warm fluid away from the wallincreasing the thickness of the thermal boundary layer downstream of the jet.Upstream of the orifice, the thermal boundary layer is unchanged from the nojet condition. During the suction cycle, the thermal boundary layer downstreamof the orifice is annihilated as the jet sucks in the warm fluid close to the wallupstream of the orifice as observed in Figure 3(b). Comparing the upstreamthermal boundary layers in Figures 3(a) and 3(b), it can be seen that the en-trainment of the near wall fluid into the cavity also causes the upstream thermalboundary layer to become thinner.(a) (b)Fig. 3. Thermal mixing between the synthetic jet and a heated crossflow: (a) t/T = 1/4,(a) t/T = 3/4.7 ConclusionsReferences1. Tiggelbeck, S., Mitra, N., Fiebig, M.: Experimental investigations of heat transferenhancement and flow losses in a channel with double rows of longitudinal vortexgenerators. International Journal of Heat and Mass Transfer 36 (1993) 2327–23372. Jacobi, A., Shah, R.: Heat transfer surface enhancement through the use of longitu-dinal vortices: A review of recent progress. Experimental Thermal and Fluid Science11 (1995) 295–3093. Zhang, X., Collins, M.: Flow and heat transfer in a turbulent boundary layer throughskewed and pitched jets. AIAA Journal 31 (1993) 1590–15994. Seutie¨ns, H., Kieft, R., Rindt, C., van Steenhoven, A.: 2D Temperature Measure-ments in the Wake of a Heated Cylinder using LIF. Experiments in Fluids 31 (2001)588–5955. Sirovich, L.: Turbulence and the dynamics of coherent structures. Part I: Coherentstructures. Quarterly of Applied Mathematics 45 (1987) 561–571

A.: 2D Temperature Measurements in the Wake of a Heated Cylinder using LIF.

Experimental investigations of heat transfer enhancement and ﬂow losses in a channel with double rows of longitudinal vortex generators.

Flow and heat transfer in a turbulent boundary layer through skewed and pitched jets.

Heat transfer surface enhancement through the use of longitudinal vortices: A review of recent progress.

Turbulence and the dynamics of coherent structures. Part I: Coherent structures.

Passive scalar mixing downstream of a synthetic jet in crossflow

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