Effect of the geometrical configuration of wall-reattachment fluidic device on the switching dynamics, the switching time, and its dispersion, was investigated experimentally by using a large scale model. The results obtained can be summarized as follows: 1) The switching time, its dispersion, and switching probability depend upon the connection of the input to the control port. 2) Effect of the vent and splitter on the jet in dynamic switching is explained commonly by using the margin of a given control flow rate to the switching control flow rate. 3) The switching time ,decreases as input increases, whereas its dispersion remains constant except for small input

Dohta, Shujiro

Shimizu, Akira

Wada, Tsutomu

Okayama University Scientific Achievement Repository

Memoirs of the School of Engineering,Okayama University Vol. 14·1, November 1979Dynamic Switching of Wall-ReattachmentFluidic DeviceTsutomu WADA*, Akira SHIMIZU*, and Shujiro DOHTA**(Received October 31, 1979)SynopsisEffect of the geometrical configuration of wall-reattach-ment fluidic device on the switching dynamics, the switchingtime, and its dispersion, was investigated experimentally byusing a large scale model.The results obtained can be summarized as follows:1) The switching time, its dispersion, and switching probabilitydepend upon the connection of the input to the control port.2) Effect of the vent and splitter on the jet in dynamic switchingis explained commonly by using the margin of a given controlflow rate to the switching control flow rate.3) The switching time ,decreases as input increases, whereas itsdispersion remains constant except for small input.1. IntroductionDesigning fluidics circuits by using the wall-reattachment fluidic device, it***Department of Industrial Science.Okayama College of Science.2930 Tsutomu WADA, Akira SHIMIZU, and Shujiro DOHTAis important to grasp the dynamics of the device. Many investigations have beenperformed on the dynamics experimen~ally and theoretically 1),2),3),4). Most ofthem present comprehensive results on the measurement of switching time and thetheoretical analysis based on the assumption of quasi-steady process. Howeverfew paper investigated systematically on the effects of the geometrical configura-tion of the device on the switching time and its dispersion 5), 6) Thus, it isnecessary to make clear these effects for designing the reliable device.In this paper, therefore~ the effects of the geometrical configuration on theswitching dynamics, especially the switching time and its dispersion are experi-mentally made clear.Then, it is shown that these effects can be commonly explained by using themargin of a given control flow rate to the statical switching control flow rate.2. Experimental Setup and ProcedureFig.l shows the large scale model of wall-reattachment fluidic device used forexperiments. Main nozzle width was 8 mm, and aspect ratio was 5.9. All experimentswere carried out using the air. Reynolds number of the jet was 1.36xl04 based onthe main nozzle width as the characteristic length. The model was the symmetricalbistable type, the offset D/bs = I and the inclined wall angle a = IS°. Wall lengthor vent distance, and splitter distanceFig.l Large scale modelIIIlrIFig.2 Experimental setupInput) :I-<r------ts ---..0switching timesoIeooid valveOUIPU~III310150--r--+---r+----r------~ hot-wirean"''imeter_-:::::::.d;:~were variable.Dynamic Switching of Waif- Reattachment Fluidic DeviceFor simplicity, the width of the side wall vent was the same as the output ductwidth, and the vent distance along main nozzle axis was equal to the splitterdistance.The experimental setup is shown in Fig.2. A stepwise input was generated bythe solenoid 3-way valve, and supplied to the control port through the small tank( volume = 2500 cm 3 ). The switching time, defined as the time required from 10 %31of input velocity change to 90 % of output, was measured with the electronic digitalcounter, and the velocity by the hot-wire anemometer. Input pulse duration was 5seconds, which was about 30 times the average switching time. From twenty datameasured for each input, the average of switching time and its dispersion wereevaluated. The dispersion was represented by the range ( the difference between themaximum switching time and the minimum ).3. Results and Discussion3.1 Input PressureFig.3 (a) and (b) show the shapes and amplitudes of the input pressure andvelocity in two cases: (a) the input is applieddirectly and (b) through the tank. The velocitychanges at the control nozzle exit Uc are similarin two cases. While, the pressure chnges in thecontrol port Pc are quite different; the pressurechange in case (a) shows the large overshoot. Foreach input, the switching time, its histogram, andswitching probability are shown in Fig.4 (a) and(b). In Fig.4 (a), the control flow rate was chosenas input magnitude. In the statical switching, itis not a serious problem which is chosen contrl flowrate or control pressure as an input magnitude.But in dynamic switching, the switching can occurmmAq10'L..........~(a) without tanku,--~ :~:_~;c:-, Q ~(b) with tankFig.3 Input pressure andvelocity32 Tsutomu WADA, Akira SHIMIZU, and Shujiro DOHTA0.3 0.4 0.5 Qc/Q.Switching time VB. controlflow rate with tank"'C'Ly /b.=12 "'C'80 800» with vent and600 1.0,., l --._- splitter 1.0 ».,-l ,..-' 600,..; ,.,-ri I .,-l~ / ,..;I .,-l400 tlIl,o I bD~i 40005 I:: 2 i J~ 05 1::,0:a Pi J .,-l a.<:l I-t200 t.> : 200 t.> P,,., I ,.,~ ~ c:9 .,-l! :.:III ! IIIOl-() 03 04 05 Q.I Qso .....0Fig.4(a) Switching time VB. control Fig.4(b)flow rate without tankJi!: t"i!jIILv/b.=! 2with ventandsplitter0.2 0.4 0.5Qc IQscontrol fl.ow·rateFig.5 switching probability.ed that the effect of the control flowcompared with the no overshoot case.even when the applied control flow rateis less than the statical one as shownThis fact is explained as follows: theactual resultant input is very large duerate on the switching time is small inin Fig.4 (a) when the input pressure'has large overshoot. It must be notic-to the overshoot, so the switching is not almost affected by the control flow rate.Fig.S shows the switching probability for the various inactive offset DN/bs ' Thus,when the impedance is mismatched in contrOl port, it is difficult to estimate thedynamic switching from the statical one. This mismatching may cause the hazard inthe fluidics circuits.In following experiments such an overshoot was removed with the tank.3.2 Effects of Initial Control FlowIn the practical fluidic device, the control pressure in no input state is theambient pressure due to the control or output vents of the preceeding element. Thisinduces the inflow into the control port before the input is applied. In thissection, the switching dynamics in such a situation is discussed.DyoomicSwitching oj Wall"Reattnchment Fluidic Device 33Fig.6 shows the switching time and its disper-sion for some initial control flow rates. The switch-ing time and its dispersion are not affected by theinitial control flow rate.3.3 Effects of the SplitterThe statical switching control flow rates areplotted for each geometrical configuration in Fig.7.Here, the device with the splitter only was investi-gated to make clear the effect of splitter. Fig.8shows the relationships between the splitter distanceLs/bs and the switching time and its dispersion. The1:"~ 1600 •0 Q"/Qo,= Oct.,-1 8 0.25 •+> -0 0.5 0be 1400 0.75.~ •.,-1.<:1 1200()+>0,-1-Go~ 1000 0I800•600:9 0d • D0 • e.,-1 400 ~'"•~QJ•PI 200 -0'":l: e.,-1 ~ 8'd o~0 0.4 0.5Gc IGscontrol flow rateFig06 Effect of initialcontrol flow rateswitching time and its dispersion vary, with the splitter distance. This is due tothe shrinkage effect 7) of the splitter in statical switching. The shrinkage effecthas been explained as follows: when the jet begins to interact the splitter, thepressure lowering in the flow passage formed by the splitter and the side wall makesthe pressure in reattaching bubble decrease and the reattachment point of the jetmoves upstream in compared with the case where the splitter is faraway. That is,the bubble shrinks. But when the splitter is located extremely upstream, such ashrinkage has a limit because the jet flows separately.Of, /Y--.~ 1000 l\ l\t1:" I..s/bs= 6x80 ~\1\1;1 • 800 10·/,9:......... QJ 12ct \""1& a 200 \ \ \100 .,-1 \ \', "91' +> 600 ~,~~0 " be. ,, '" ~0 0,-1...... Ii .<:1 400J ()with splitter~-~- +>Q2 .,-1l3=vent L. --------'"200~~ttero--0 I 1. 6 8 10 12 14 16 18 20 Lv,hs l..sjbs 0 0.'2 0.3 OJ. 0;5.Gc IGsFig07 Switching control flow rate Fig08 Effect of splitter34 Tsutomu WADA. Akira SHIMIZU. and Shujiro DOHTA1000-r3.4 Effects of the Side Wall VentsIn order to make clear theeffects of the side wall vents, theexperimental model with the ventsonly is dealt with. Fig.9 shows theswitching time and its dispersion~ 800.r<...,bD 600I:l.r<.Q~400~01200for various vent distance Lv/bs .This figure shows that the shrinkageeffect of the wall end 7) appears inoFig.9 Effect of vents05O</Giadynamic switching as well as in statical one. This effect has been explained asfollows: when a part of the jet flows out of the vent, the pressure in the reattch-ing bubble lowers and consequently the radius of jet curvature decreases. Fig.7shows the relationship between the statical switching control flow rate Qcso/Qs andthe vent distance Lv/b s '3.5 Effects of the Splitter and VentsFig.IO shows the switching dynamics for various geometrical configurations withthe splitter and vents.The statical switching control flow rate for each configuration is shown inFig.7. The interaction between the splitter and vents has been explained asfollows: if the splitter is located near the vent, the pressure drop in output ductis not remarkable. This means that the shrinkage effect of the splitter will bereduced by the presence of the vent.On the other hand, for small Lv/bsand large vent width, the splittereffect is strongly reduced, the venteffect becomes dominant. Fig.IOshows that such a interaction exists1000't'~ 800...,bD 600I:l......<:~ 400....>01200L./b.= 8 010 ..12 ~20 004 0.5O</Q.Effect of splitter and vent0.2Fig.100'also in the dynamic switching.Dynamic Switching oj WalE-' Reattachment Flu'idic Device 353.6 Relationships between Switching Time, Its Dispersion and GeometricalConfigurationsIn' this experiment the input pulse duration was less than that of staticalswitching, so the minimum control flow rate that made switching probability 100 %was greater than'the statical switching control flow rate Qcso. Hence, the minimumcontrol flow rate that makes switching probability 90 % is evaluated as switchingcontrol flow rate Qcs, considering experimental error. Fig.7 shows Qcs and Qcso forvarious geometrical configurations. As shown in this figure, the switching controlflow rate depends upon the geometrical configurations.In oder to estimate the switching dynamics on the common basis, the controlflow rate in excess of Qcs was introduced. Fig.ll (a), (b) and (c) show the switch-ing time by using the excess control flow rate, rearranged from Fig.B, 9, and 10,respectively. The dispersion of the switching time is normalized by the averageswitching time. These show that there is no significant difference among the geo-metrical configurations. In particular, Fig.ll (a), showing the splitter effects,shows such a tendency remarkably. In all cases, the dispersion decreases as thecontrol flow rate increases, but remains about 15 % of the average switching timefor Qc/Qcs > 1.2.In Fig.ll (c), for Lv/bs 12, the dispersion is remarkable as compared with100"1°680 ';ri~60 ~rJl40 :a20 ~t'Io '.-I~oI:lL./b.=8 010 A12 co2001.4 1.6 1.8Q.lQc"Effect of vent1.2Fig.ll(b)20091181s=6 x8010 A12 co20012 1.4 1.6~control flow ratenormalized by QcsFig.ll(a) Effect of splitter~ 800+'tlO 600I:l•.-1.l:l$~o'.-1~rJl36 Tsutomu WADA, Akira SHIMIZU, and Shujiro DOHTA200ol,:-~~:--:-~--,_~~.=--,-~-:-,.1.0 1.2 1.4 1.6 1.8Qc/Qcsother cases. This is considered to bedue to the wall end effect mentioned insection 3.5.Fig.11(c) Effect of splitterand vent4. Conclusionlvlbs= 8 010"12G200100·'· §..-/80 ~Ql60 f;..-/40 'd'020 ~..-/o ~os::Effects of the geometrical configuration of the wall-reattachment fluidicdevice on the switching time and its dispersion were investigated experimentally.The results are summarized as follows:(1) The switching time, its dispersion, and switching probability depend upon theconnecting situation of input duct to the control port (impedance matching).The mismatched impedance may cause the hazard in the fluidics circuits.(2) Effect of the vent and splitter on the jet in dynamic switching is similar tothat of statical one. Comparing some geometrical configurations in the switch-ing time and its dispersion, there is no significant difference among them.(3) The switching time decreases as the control flow rate increases, whereas thedispersion remains constant for Qc/Qcs > 1.2.AcknowledgementThe authors wish to thank Mr, K. Ohsaka, assistant professor at Okayama Collegeof Science, for his discussion and suport and Mr. K. Katayama and Mr. M. Mizuno fortheir assistance in experiments.References1) P.A. Lush: Investigation of the Switching Mechanism in Large Scale Model of aDynamic Switching oj Walr Reattachment Fluidic DeviceTurbulent Reattachment Amplifier, Proc. 2nd Cranfield Conference, Al (1967)2) M. Epstein: Theoretical Investigation of the Switching Mechanism in a BistableWall Attachment Fluid Amplifier, Trans. ASME, vol.93, Series D, 55/62 (1971)3) M.R. OzgU and A.H. Stenning: Theoretical Study of the Switching Dynamics of Bi-stable Fluidic Amplifier with Low Setbacks, ASME Paper 7l-WA/FLCS-6 (1971)4) T.M. Drzewiecki: The Design of Flueric, Turbulent, Wall Attachment Flip-Flops,Proc. HDL Fluidics State-of-the-Art Symposium, vol.3, 433/498 (1974)5) H. Hanafusa and K. Miyata: Accuracy of Switching Pressure of Fluidic OR-NORDevice, Proc. 2nd International JSME Symposium, Fluid Machinery and Fluidics,vol.3, 213/222 (1972)6) H. Hanafusa and K. Miyata: Investigation on Accuracy of the Switching Pressureof Fluidic Comparators, Trans. SICE, vol.lO, 546/551 (1974)7) T. Wada et al.: Effects of a Splitter and Vents on a Reattaching Jet and ItsSwitching in Wall Reattachment Fluidic Device, Proc. HDL Fluidics State-of-the-Art Symposium. vol.3, 499/553 (1974)37

Dynamic Switching of Wall-Reattachment Fluidic Device

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