Experimental Study of an Impinging Round Jet

Transcription

1 Marie Crie ay Final Report : Experimental dy of an Impinging Rond Jet BOURDETTE Vincent Ph.D stdent at the Rovira i Virgili University (URV), Mechanical Engineering Department. Work carried ot dring a six months training stay within the Marie Crie fellowships framework in the Institte of Chemical Process Fndamentals (ICPF) in Prage, Czech Repblic. Spervisor dring the stay : Jaroslav TIHON (ICPF) Ph.D spervisors : Jordi PALLARES (URV) Clara SALUEÑA (URV)

2 Contents Introdction 5 2 Constant temperatre anemometry (CTA): principle and calibration 6 3 Configration 7 4 Experimental reslts and discssion 7 4. Inlet profile Freqency response in the centerline and in the shear layer Excitation amplitde effect Spectral analysis Complete field Conclsions

3 List of Figres Configration Mean and rms vales of velocity at the nozzle exit for different excitation freqencies Jet centerline and shear layer freqency response at different locations from the nozzle Jet centerline freqency response at different locations from the nozzle band filtered with excitation freqency and half excitation freqency Jet shear layer freqency response at different locations from the nozzle band filtered with excitation freqency and half excitation freqency Effect of the excitation amplitde at the centerline X 0 5,X 5, X 3 (c), X 3 75 (d) Effect of the excitation amplitde at Y and at a distance from the plate of mm and 0 mm Non-excited jet velocity signal and the corresponding spectrm at X 0 and X 2 (c)(d) Excited case at 0 3. at X 0, X, X 2 (c), X 3 5 (d) on centerline Excited case at 0 3. FFT of velocity signal at X 0, X, X 2 (c), X 3 5 (d) at the centerline Excited case at 0 7. at X 0, X, X 2 (c), X 3 5 (d) at the centerline Excited case at 0 7. FFT of velocity signal at X 0, X, X 2 (c), X 3 5 (d) at the centerline Excited case at 7. at X 0, X, X 2 (c), X 3 5 (d) at the centerline Excited case at 7. FFT of velocity signal at X 0, X, X 2 (c), X 3 5 (d) at the centerline Non-excited impinging jet. Mean and rms velocity vales Excited impinging jet at 0 3 and Ae Mean and rms velocity vales Excited impinging jet at 0 7 and A e Mean and rms velocity vales Excited impinging jet at 7 and A e Mean and rms velocity vales

4 Nomenclatre δ ν θ Shear layer displacement thickness Air kinetic viscosity Shear layer momentm thickness A, B, M, N Calibration constants A e rms 0 0 D Amplitde of the excitation Diameter of the jet nozzle D w H h w k Wire diameter Distance nozzle to plate Local wire convection coefficient Air thermal condctivity mean x x Mean vale of a velocity signal t at a fixed position x mean 0 0 Mean vale of a velocity signal at the position X 0 and Y 0 N w h w D w k Wire Nsselt nmber Re 0 D ν Jet Reynolds nmber Re w 0 D w ν Wire Reynolds nmber rms x Root mean sqare vale of a velocity signal t at a fixed position x rms 0 Root mean sqare vale of a velocity signal at the position X 0 and Y 0 θ rohal nmber based on the jet diameter and on the velocity signal freqency Excitation rohal nmber based on the shear layer tickness and the lodspeaker freqency Excitation rohal nmber based on the jet diameter and on the lodspeaker freqency T m T air T hw 2 Mean wire bondary layer temperatre T air T hw Air temperatre ot of the wire bondary layer Hot wire temperatre 3

5 t max X Y Dration of the recorded velocity signal Velocity modle taking in accont the components normal to the wire Non-dimensional parallel to the plate distance from the jet centerline Non-dimensional normal to the plate distance from the jet center 4

6 Introdction An impinging jet flow (IJF) is a simple configration in which a flid issing from a nozzle impinges with a normal incidence on a plate. The technical applications of impinging jets concern cooling, drying, heating of srfaces becase they prodce high heat and/or mass transfer rates. From a scientific point of view IJF incldes several interesting effects. The formation of a shear layer near the nozzle edge is associated to a Kelvin-Helmholtz instability with the corresponding vortex formation. Under some conditions the interaction between vortices can occr (vortex pairing). Near the plate, the vortices are deflected and they interact with the wall bondary layer. Trblent IJF is a challenging test case for nmerical simlations and for sb-grid scale models sed in large eddy simlation (LES) (see Sagat [2000], Olsson and Fchs [998]). My PhD thesis is related to the nmerical simlation of a forced rond impinging jet flow and the main objectives of my stay in the Institte of Chemical Process and Fndamentals of the Academy of Science of Czech Repblic in Prage were : to carry ot an investigation of the effects of the inlet velocity excitation (its amplitde and freqency) on the flow strctres inside a trblent impinging jet at low Reynolds nmber to identify which excitation freqencies prodce characteristics flow regimes and conseqently which freqencies are relevant for nmerical simlation of IJF to collect a set of experimental data sefl in order to set the bondary conditions and to validate reslts of the nmerical simlation. Experiments were done sing the experimental setp bilt by Vejrazka [2002]. The applied constant temperatre anemometry techniqe is briefly described in the second section of this report. The third section describes the jet configration and the experimental conditions sed for the measrements. The forth section presents and discsses the reslts obtained dring the stay. The freqency response measrement consists in pnctal recording of the velocity for different excitation freqencies. The complete field measrements were carried ot for selected excitation conditions over a dense grid covering the whole zone of interest. 5

7 2 Constant temperatre anemometry (CTA): principle and calibration The CTA techniqe measres is sed for local velocity measrements. The working principle of CTA is based on the cooling effect of a flow on a heated body (here a thin wire of 5 µm diameter). The convective heat transfer from a wire (related to the wire Nsselt nmber N w ) is a fnction of the mean wire bondary layer temperatre T m and of the velocity component normal to the wire (related to the wire Reynolds nmber Re w ). The anemometer system provides the vales of N w and T m and the Collis-William s law (see Collis and Williams [959]) gives a relation between N w and Re w : N w T m T air M A BRe N w () Where A, B, M and N are constants which are set by the calibration procedre. The calibration consists on positioning the hot wire at the jet nozzle center where the velocity (and so Re w ) is compted according to the Bernolli s eqation from the pressre measred in the settling chamber. Then a set of N w and corresponding Re w vales is fitted by Eq to find the for constants A, B, M and N. More information on CTA principles can be fond in Goldstein [983]. The measred velocity time series are processed to compte the mean and rms vales. The mean and the rms vales of a velocity signal t at a fixed position x 0, are defined as: mean x 0 x 0 rms x 0 t max t max tmax 0 t dt (2) 0 t x 0 2 dt (3) In the present stdy, the sampling rate 2 khz (6 khz for complete field measrement) was sed to record (6392 for complete field) samples at each measring point. As an example, this setting yields approximately 50 samples per a excitation period (at 85 Hz i.e 0 7) and a record covers at least 200 excitation periods. In all the cases (i.e. for all excitation freqencies) these settings were satisfactory to prodce consistent statistics. 3 Configration Experiments were carried ot in an impinging rond jet with a nozzle diameter (D) of 25mm (see Fig.). The plate was located normally to the symmetry axis of the rond nozzle at a distance H 4D. The Reynolds nmber (Re 0 D ν ) was based on the jet nozzle diameter 6

8 D, 0 is the mean velocity at the nozzle center and ν is the kinematic viscosity of air. For all measrements the Reynolds nmber was keep constant Re This vale is a qite low, bt still ensres trblent flow conditions inside the impinging jet. It was choosen to keep the nmerical simlation at an acceptable level in respect to CPU reqirements. The plate was placed ot of the core jet. Sch a configration lets to develop the shear layer instability and prodces a resolvable (nmerically) bondary layer at the plate. The flow was excited with a lodspeaker located in of the settling chamber. The nondimensional excitation freqency can be expressed as the rohal nmber f e D 0, where f e is the freqency of the sinsoidal lodspeaker signal. The excitation amplitde level is determine here by the amplitde defined as A e rms 0 0. A traverse system moved the single hot wire probe in two directions (X and Y ). The plane of measrement contains the symmetry axis of the jet (Fig.). Two types of single probes were sed: the bondary layer probe in the wall region and the bended probe in the jet region. The active wire was always placed perpendiclary to the mean flow direction to measre the absolte vale of the local velocity. In the following, all variables are non-dimensional. Relations between non-dimensional and dimensional variables sed are : d t t d D 0 X X d D Y Y d D (4) f f d D 0 (5) 0 rms rms d 0 (6) Where the sbscript d denotes a dimensional variable and the sbscript 0 denotes vales measred at the center of the nozzle orifice (for X 0 and Y 0). 4 Experimental reslts and discssion 4. Inlet profile Figres 2 and 2 show the profiles of the velocity mean and rms at the nozzle lip for the excited and the non-excited cases. The excitation amplitde was mainteined at Ae 5% by adjsting the power signal for the lodspeaker. The excitation at different freqencies affect only slightly the mean velocity profile compared with the jet observed at natral flow conditons (see Fig.2). The rms velocity is 0 4% at the jet potential core and % near the nozzle lip in the non-excited case (see Fig.2). In all the cases, the pertrbations (natral or artificial) affect more the bondary layer near the lip 7

9 than the central part of the jet where the flow can be considered as potential. Profiles are flat inside the jet core for 0 and 0 3, bt slightly crve for 0 6 and 7. It can be de to an effect of nozzle shape observed at high freqencies. The non-dimensional displacement thickness of the non-excited case was δ D and the non-dimensional momentm thickness was θ D 0 0. The ratio δ θ 2 36 is a characteristic of the laminar flow according to Zaman and Hssain [980a]. The non-excited inlet velocity profile was fond to be in a good agreement with the laminar Blasis profile. 4.2 Freqency response in the centerline and in the shear layer This section concerns a forced jet with an excitation of amplitde A e 5%. The centerline of the jet is the line Y 0 and the shear layer line is located at Y according to the position of the maxima of the rms vales shown in Fig.2. Figre 3 shows the velocity rms for different excitation rohal nmbers at different X positions along the centerline. It can be seen in Fig.3 that two velocity rms peaks are located at 0 3 and 0 7 at X 3. The first peak is also clearly seen in Fig.3 which correspond to the measrement in the shear layer. The intensity vale of this first peak increases to X 3 and decreases for X 3, this is explained by the presence of the stagnation zone forcing the rms velocity and the mean velocity to vanish at the centerline near the plate. Conseqently the effects of the plate are observed for X 3 which is in agreement with the nmerical simlation of Olsson and Fchs [998] and the experiments of Giralt and Trass [977]. The freqency response shown in Figs.3 and 3 have been filtered sing the excitation freqency and are plotted in Figs.4 and 5. The first peak is present and of the same order as in Fig.3 and Fig.3 implying a velocity signal with a strong component at the excitation freqency. Figres 4 and 5 are the velocity rms in the centerline and in the shear layer for different excitation freqencies which have been band filtered with half of the excitation freqency. A second peak appears in these figres and indicates a velocity signal with a strong component at a half of the excitation freqency for arond 0 7. Ths 0 3 and 0 7 prodce periodic response of the jet. Excitation at 0 3 prodces the maximm growth of velocity rms band filtered by the excitation freqency in the centerline and in the shear layer (Fig.4 and 5). The peaks occr at a higher freqency near the nozzle. The maximm vale of the velocity rms is fond for for the measrement at few millimeters from the nozzle lip. The excitation corresponds to θ e θ d f which is the most nstable mode of shear layer instability (see Zaman and Hssain [980a] and Zaman and Hssain [980b]). Going downstream to the plate, the first peak is shifted to 0 3 and the second to 0 7 at X 3. This shift is associated with two modes of instability in the jet as explained in Zaman 8

10 and Hssain [980a]. The two peaks remain at the same positions for X Excitation amplitde effect It is interesting to stdy how the different excitation amplitdes A e affect the freqency response of the jet. Figres 6 to 6(d) show measrements of the velocity rms vales at the centerline (Y 0) for different excitation amplitde A e as a fnction of the excitation freqencies. The two peaks in the velocity rms are present at X 3 for 0 3 and 0 7 as previosly reported for A e 5% (previos section). The peaks reach approximately the same vale independently of A e as shown in Fig.6(d) indicating a satration of the amplitde of the pertrbation. For 25 the velocity rms vale of Fig.6 decreases to reach the level of the non-excited jet at X 5 (Fig.6). Downstream (i.e increasing vales of X along the centerline) the velocity rms vale decreases mch more, and there is a redction of a 50% of velocity rms vales at X 3 75 in comparison with the non-excited case. It shold be note that this strong decrease of the velocity rms occrs in the range For 2 5 the level of the velocity rms is the same as in the non-excited case denoting that the flow does not respond to the excitation. From positions X 5 to X 3 at the centerline the vales of the two peaks increase (the stagnation zone not affects the flow at these positions) and the velocity rms vale for decreases drastically. This strong decrease of the velocity rms vales at the centerline can not be associated with the effect of the stagnation zone according to the fact that the vales of the peaks are increased from X 5 to X 3. Figre 7- displays the velocity rms vales as a fnction of excitation in the wall jet (i.e the zone near the plate). The band of excitation freqency acconting for a strong decrease of the velocity rms is mch more weak in the bondary layer indicating a particlar response of the bondary layer of the wall jet. 4.4 Spectral analysis The velocity time series for the non-excited case at X 0 and X 2 at the centerline are plotted in Figs.8 and 8(c). The corresponding spectra are shown in Figs.8 and 8(d) respectively. The spectrm of the velocity signal at X 0 shows a wide peak from 0 to 0 4 and an even more broad peak from 0 to 0 9 at X 2. Figre 9-(d) shows the velocity signals for different centerline locations in an excited jet at 0 3. At position X 0 the signal is periodic with a single freqency (see Figs.9 and 0) while at X it shows a complex periodic behavior as indicated by the harmonics in the spectrm (Fig.0). A sharp peak corresponding to the freqency of excitation 0 3 is present in the spectrm along all the X position of the centerline (see Fig.0-9

11 (d)). The vortices are formed at the excitation freqency in the shear layer as a conseqence of the Kelvin-Helmholtz instability. The jet responds with the same freqency as the excitation freqency and no pairing process occrs. Figres to (d) show the velocity signals for an excited jet at 0 7. It can be seen in Fig. that the signal presents intermittent periods at the excitation freqency and periods at a half of this freqency as can be inferred from the corresponding spectrm shown in Fig.2. Figres 2to 2(d) clearly exhibits a peak at the half of the excitation freqency which becomes dominant at X 2. The vortices initially formed in the shear layer at the excitation freqency are in this case enogh close to interact and the vortex pairing occrs between the positions X and X 2. The excited jet at the freqency 7 has a different behavior. The velocity flctations are strongly damped as X is increased (see Fig.3). A sharp peak corresponding to a freqency of excitation 7 is present near the nozzle. The intensity of this peak decreases very near the nozzle and disappears completely at X 3 5 (Fig.3(d)). It can be seen in Fig.4(d) that the spectrm at X 3 5 shows a broad peak centered at Complete field The fields of the rms and the mean velocity vales were measred for the non-excited case and for 0 3, 0 7 and 7. We divided the plane of measrement in two zones : the jet core and the wall jet zone points of measrement are arranged on each zone with a minimm spacing between two points of 0 25mm and a maximm spacing of mm. The points of measrement were concentrated in the shear layer and near the plate arond Y. The measres were taken with a banded probe in the jet core and with a bondary layer probe in the wall zone. The mean and the velocity rms vales of the non-excited impinging jet are displayed in Figs.5 and 5. The shear layer becomes thicker when going throgh the plate becase external pertrbations make it nstable. The rms velocity vale starts increasing at X. For 0 3 an abrptly growth of the shear layer thickness (Fig.6) and an increase of the rms velocity vale appears at X in the shear layer. This position corresponds to the one where the vortex roll-p begin. The region where the vortices interacted with the wall bondary layer is marked by a maximm in the vale of the rms velocity near the plate for Y (see Fig.6). The field of the mean velocity vale for the jet excited at 0 7 shows the same kind of shear layer thickness growth as described for the jet excited at the freqency 0 3. In the case of the jet excited at the freqency 0 7 this increase of the shear layer thickness occrs closer to the nozzle lip (see Fig.7). Apparently the vortices roll-p develops closer to the jet nozzle for the jet excited with freqency 0 7 than in the case of an excitation freqency of

12 In the jet excited at freqency 7 there is no abrpt variations in the shear layer thickness (see Fig.8). The level of rms velocity vale is globally lower compared to the other cases. It can be seen in Figs.8 and 8 that for the excited jet at 7 there is no bondary layer separation, in contrast to the non-excited jet and to the excited jet at 0 3 and Conclsions The response of an impinging rond jet to inlet velocity excitations has been experimentally stdied. The velocity rms measrements performed along the jet centerline and in the jet shear layer provided three distinct ranges of excitation freqencies that affect the jet flow field qite differently. The excitation arond 0 3 prodces a periodic flow response with a high increase of the velocity rms vale. This excitation initiates the roll-p of vortices at a distance of one diameter from the jet nozzle. The excitation arond 0 7 also yields high vales of the velocity rms. Howewer, the vortex rolling-p appears near the nozzle and the vortices are close enogh to interact and merge. Therefore the freqency of flow flctations observed in the near-wall region in this case is a half of the excitation one. The excitation arond 7 cases a strong decrease of the velocity rms vales and the wall jet behavior is different from the previos cases. As the excitation amplitde is increased the level of velocity flctations decreases everywhere inside the jet and the flow flctations does not respond with a clearly defined freqency. Acknowledgments This work was spported by the Marie Crie program. I thank Jaroslav Tihon for accepting me as a Marie Crie fellow and for helping me dring the experiments. I acknowledge several helpfl discssions concerning data post processing with Jiri Vejrazka. Finally I am gratefl to the PhD stdents of ICPF to bring me in the spirit of Czech Repblic and of Slovakia dring this stay. References D.C. Collis and M.J. Williams. Two-dimensional convection from heated wires at low reynolds nmbers. Jornal of Flids Mechanics, 6: , 959. C.-J. Giralt, F. Chia and O. Trass. Characterization of the impingement region in an axisymmetric trblent jet. Ind. Eng. Chem. Fndam., 6, 977.

13 R.J. Goldstein. Flid mechanics measrements. Hemisphere pblishing corporation, 983. M. Olsson and L. Fchs. Large eddy simlations of a forced semiconfined circlar impinging jet. Physics Flids, 0(2): , 998. P. Sagat. Introdction à la simlation des grandes échelles por les écolements de flide incompressible. Springer, J. Vejrazka. Experimental stdy of a plsating rond impinging jet. PhD thesis, Institt national polytechniqe de Grenoble, K.B.M.Q. Zaman and A.K.M.F. Hssain. Vortex pairing in a circlar jet nder controlled excitation. part. general jet response. Jornal of Flids Mechanics, 0:449 49, 980a. K.B.M.Q. Zaman and A.K.M.F. Hssain. Vortex pairing in a circlar jet nder controlled excitation. part 2. coherent strctre dynamics. Jornal of Flids Mechanics, 0: , 980b. 2

14 D=25mm Y Nozzle Re=5000 Plane of measrement X H/D=4 Plate Axis of symmetry Figre : Configration 3

15 Whitot excitation =0.3 =0.7 =.7 mean() 0.6 rms() Whitot excitation =0.3 =0.7 = Y Y Figre 2: Mean and rms vales of velocity at the nozzle exit for different excitation freqencies 4

16 X=0.75 X=.5 X=3 X=3, X=0.4 X= X=2 X= rms() 0.25 rms() Figre 3: Jet centerline and shear layer freqency response at different locations from the nozzle X=0.75 X=.5 X=3 X=3, X=0.75 X=.5 X=3 X=3, rms() 0.25 rms() Figre 4: Jet centerline freqency response at different locations from the nozzle band filtered with excitation freqency and half excitation freqency 5

17 X=0.4 X= X=2 X= X=0.4 X= X=2 X= rms() 0.25 rms() Figre 5: Jet shear layer freqency response at different locations from the nozzle band filtered with excitation freqency and half excitation freqency 6

18 )/ mean( o )=% )=5% )=7% )=9% no excited level )=% )=5% )=7% )=9% no excited level rms() rms() )=% )=5% )=7% )=9% no excited level )=% )=5% )=7% )=9% no excited level rms() rms() (c) (d) Figre 6: Effect of the excitation amplitde at the centerline X 0 5,X 5, X 3 (c), X 3 75 (d) 7

19 )=% )=3% )=5% )=7% )=9% no excited level rms() rms() )=% )=3% )=5% )=7% )=9% no excited level Figre 7: Effect of the excitation amplitde at Y and at a distance from the plate of mm and 0 mm 8

20 Energy t Energy (c) (d) Figre 8: Non-excited jet velocity signal and the corresponding spectrm at X 0 and X 2 (c)(d) 9

21 t t t t (c) (d) Figre 9: Excited case at 0 3. at X 0, X, X 2 (c), X 3 5 (d) on centerline 20

22 Londspeaker signal Lodspeaker signal Energy Energy Lodspeaker signal Lodspeaker signal Energy Energy (c) (d) Figre 0: Excited case at 0 3. FFT of velocity signal at X 0, X, X 2 (c), X 3 5 (d) at the centerline. 2

23 t t t t (c) (d) Figre : Excited case at 0 7. at X 0, X, X 2 (c), X 3 5 (d) at the centerline 22

24 Lodspeaker signal Londspeaker signal Lodspeaker signal Energy Energy Lodspeaker signal Lodspeaker signal Energy Energy (c) (d) Figre 2: Excited case at 0 7. FFT of velocity signal at X 0, X, X 2 (c), X 3 5 (d) at the centerline. 23

25 t t t t (c) (d) Figre 3: Excited case at 7. at X 0, X, X 2 (c), X 3 5 (d) at the centerline 24

26 Lodspeaker signal Lodspeaker signal Energy Energy Lodspeaker signal Lodspeaker signal Energy Energy (c) (d) Figre 4: Excited case at 7. FFT of velocity signal at X 0, X, X 2 (c), X 3 5 (d) at the centerline. 25

27 Figre 5: Non-excited impinging jet. Mean and rms velocity vales. Figre 6: Excited impinging jet at 0 3 and Ae Mean and rms velocity vales. 26

28 Figre 7: Excited impinging jet at 0 7 and A e Mean and rms velocity vales. Figre 8: Excited impinging jet at 7 and A e Mean and rms velocity vales. 27