1、z ,_._ Iw-b hi_ s1- o aNATIONAL ADVISORY COMMITTEE FOR AERONAUTICAS STUDYTECHNICAL NOTE 3696OF THE HIGH-SPEED PERFORMANCEByCHARACTERISTICSOF 90 BENDS IN CIRCULAR DUCTSJames T. Higginbotham, Charles C. Wood,and E. Floyd ValentineLangley Aeronautical LaboratoryLangley Fieldj Va.WashingtonJune 1956.-.
2、. . . . . . . . . -. - . . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARY KAFB,NM.sNATIONAL ADVISORY COMMITTEEr=,with4.00IllllllllllllllllllllllllllFOR AERONAUTICS00bb370TECHNICAL NOTE 3696A STUDY OF THE HIGH-SPEED PERFORMANCE CHARACTE
3、RISTICSOFBy James90 BENDS IN CIRCULAR DUCTST. Higginbotham, Charles C. Wood,and E. Floyd ValentineSUMMARYme performance of four 90 bends in ducts Of constant diameterratios of radius of curvature to diameter of 0.75, 1.00, .2.50jandwas investigatedover a range of inlet Mach numbers extendingup tothe
4、 choking condition for both a thin and a thick inlet boundary lay consequently, t was obtainedby adifferent procedure from that just described. For these three elbows,t was calculatedfrom one-dimensionalrelationships, elbow cros-sectionalarea, snd measured values of mass flow, total pressure %,C)tot
5、al temperature Tt,and the static pressure at station 1.5. Thedyntic pressure ,o used to obtain the nondimensional coefficientsG/Fc,o d =t/%,o is based on the weighted mean total pressuret,o, a rectangular velocity distribution,and the mass flow. The veloc- ,ity distributionsat stations e and 1.5 in.
6、the horizontalplane areavailable for the r/d = 1.00 elbow only and are presented in terms of,/5- , a quantitywhich approximatesthe local velocity divided by the %,0mean velocity at station O. A straight-line static-pressuregradientwas assumed from the inner to the outer duct wall at station e for th
7、epurpose of calculatingthe local impact pressure, while an average staticpressure obtained from the four static-pressureorifices at station 1.5was assumed for the downstream station. Both experimentalsmd theoret-ical longitudinal static-pressuredistributionsalong the wall are pre-sented for each elb
8、ow. The theoretical distribution correspondstopotential incompressibleflow and is obtainedby a relaxationproceduredescribed in references 8 and 9. The distributionsare presented interms of l,o along the inner and outer wall for each elbow. Themeasured distribution is presented in the same terms for
9、several low-speed runs for comparisonpurposes.distributionsalong each of the fourouter) are presented in terms of thepressure to the upstream center-lineeral values of .For high inlet speeds the pressurewalls (top,bottom, inner, and/ratio p pt,v of the local staticreference total pressure for sev-Pr
10、ovided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3696. RESULTS AND DISCUSSION7Inlet ConditionsThe velocity profiles for two inlet Mach numbers (approximately0.4and 0.8) at each of two differentboundary-layer conditionsare presentedin figure 4. T
11、he profiles, as measured along four radii, were symmet.rical so that an average is presented. The boundary-layerparametersare tabulated in this figure for the thick boundary layer. The thinboundary layers were too small for accurate determination of the boundary-layer parameters with the instrumenta
12、tionused. Decreases in theboundary-layer thickness were noted with increase in the Mach number forboth boundary-layer cases. From the velocity profiles given in figure 4it will be noted that the inlet conditions correspondedto roughly thethinnest and thickest layers obtainablepractically.I Choking M
13、ach Number.,. The Mach number at station O for each of the elbows is presentedin figure 5 as a function of the ratio Pr for the two boundary-layerconditions. For each elbow, the highest value of reached when is plotted against Pr is defined as the choking Mach nuder h. Itis observed from these curve
14、s that the elbows which had the largestchoking Mach number required less total pressure to attain it and lesspressure to attain any Mach number below the choke value.A cross plot of the choking Mach number fich,ojas a function of theelbow radius-diameterratio r/d.is shown in figure 6 for both bounda
15、ry-layer test conditions. Also included in this figure are the results ofreference 7 for square and rectangular elbows with a thin inlet boundarylayer. The data show that somewhathigher choking Mach numbers wereachieved for the circular elbows than for the square or rectangulsx ones.Whether this res
16、ult indicates a fundamental difference in the flow devel-opment or a lack of comparabilityof the two sets of test data is unlmown.For circular elbows, an increase in the inlet boundary-layer thicknessdecreased the choking Mach number slightly: The elbow with r/d = 2.50is shown to produce the highest
17、 value of Mch for both bounda-layer(%conditions h = 0.77 for the thin boundary layer and ch = 0.75 forthe thick one). The value of ch = 0.77 correspondsto 95 percent ofthe air flow obtainable at a Mach nuniberof 1.00. A brief investigation. of the use of vortex generators and vanes for increasing fi
18、c was unpro-uctive. More information is needed on control devices in elbows athigh subsonicMach numbers. For mechanical reasons, investigationsof this nature should be made on elbows of larger scale. . . ._ _ _ ._._=Provided by IHSNot for ResaleNo reproduction or networking permitted without license
19、 from IHS-,-,-8 NACA TN 3696Static-PressureDistributions and Static-Pressure-DropCoefficientsThe static-pressurevariation along the inner, outer, top, andbottom walls is presented in figure 7 for each elbow_at both boundary-layer conditionsfor a range of inlet lkch numbers “fromO.20 tochoke. The cur
20、ves of static-pressuredistributionthrough each elbowremain similar as the inlet Mach nuniberis increased up to the Ich num-ber where local shock waves (as indicatedby the static-pressuredistri-bution) occur in or downstre however, inall cases, the influence of the elbow does not extend as far as the
21、 ref-erence station O.The cuxvespermit some conclusionsrelative to the point in theduct where choke occurred. The curcvesfor tlie r/d = 0.75 and 1.00elbows (top,bottom, and outer walls) indicate that sonic velocity wasnot reached in the elbow with either boundary layer. The values ofp/pt for the inn
22、er-wall curve for these two SlbOWS dO not COrreSpOndto arepresentativelocal Mach numiberbecause of the high total-pressureloss along this wall. It is evident from these curves that chokingmust occur at the elbow exit or downstream of it. The high-speed curvesindicate that the region do%mstream of th
23、e exit contains a mixture ofsubsonic and supersonicflow. At the 0.50-diameter location downstreamof the exit, supersonicflow is present along the four walls for ther/d = 0.75 and the r/d = 1.00 elbow for both inlet boundary-layerconditions. It would be expected that choking would occur prior to thee
24、stablishment of the supersonic flow that is noted at the 0.50-diameterdownstream location. Also, it would seem logical for the choke locationto correspondto a section which contains slightly subsonic and slightlysupersonicflow in order to pass a maximum flow in a mixed flow stream.The approximate lo
25、cation of such sections falls between the elbow exitand the 0.50-diameterdownstream location for each case. The curves forthe elbows of r/d = 2.50 and 4.00 indicate that no sectionproduced aMach nuniberof 1.00; therefore, it is concludedthat choke occurred atthe tailpipe exit of these elbows. These
26、observationslead to the con-clusion that the chokingMach numibersmeasured for the r/d . 0.75 and1.00 elbows are representativebecause the choking sectionwas closeto the exit. However, the chokingMach numbers observed for ther/d = 2.50 and r/d = 4.00 elbows were determinedyartiallyby thelength of the
27、 downstream straight section, so that shorter lengths might have produced slightlyhigher chokingMach nunibers.LProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-sNACA TN 3696 9.The static-press however, it may be stated that theeffect is small. The sam
28、e trends are noted for the total-pressure-losscoefficientas for the static-pressure-dropcoefficient;that is, theloss increaseswith Mach number increase,the smallest loss being. . _ . . -.- . _ _ _ _-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10
29、NACA TN 3696realized for the r/d = 2.50 elbow. The r/d = 0.75 elbow producedthe highest losses and the most severe Mach number effect. At thechoke condition,the elbow with r/d . 2.50 produced a total-pressure-10SS coefficient of 0.16 as comparedwith 0.69 for the elbow withr/d = 0.75. The loss throug
30、h the r/d = 0.75 elbow, 0.6920 or0.136t o, is equivalentto that through a normal shock at = 1.68.YThe longitudinal static-pressuredistributions indicate thatchoking occurred downstream of the elbows. This result suggests thatchoking is obtainedbecause of the loss in total pressure and the con-sequen
31、t change in density, in a manner similar to that for a longstraightpipe. In order to check this hypothesis, the choking Machnumiberfor the r/d = 1.00 elbow was calculatedby using the measuredloss coefficientat choke (fig. 10), one-dimensionalcompressible-flowequations, and the assumptionthat sonic v
32、elocity occurred at station1.5. The resulting theoretical choking Mach puniberis shown in figure 10and agrees closely with the thin-boundary-layerdata. Unfortunatelyjthe measured loss coefficientsfor the other elbows are not available;thus an adequate check of the above hypothesis is not possible. A
33、gree-ment of the theoreticalMach nuniberwith the measured value for ther/d = 1.00 elbow, however, suggests the possibility of estimatingthechoking Mach number for a pmticular elbow design from a low-speed valueof loss coefficientand an assumption regarding the effect of inletspeed on loss coefficien
34、t. According to the data of figure 10 for thethin boundary layer, increasingthe inlet Mach number from 0.3 to chokeincreasesthe loss coefficient for elbows with r/d = 075,1.00, 2.50,and 4.00 by 114, 33, 31, and 7 percent, respectively. ,Downstream Velocity DistributionsFor the r/d = 1.00 elbow, tota
35、l-pressure surveys were made in thehorizontalplane at stations e and 1.5 and the resulting data ue pre-sented in the form of velocity distributions in figure 11. As pointedout previously, a linear static-pressuredistribution from the inner tothe outer wall was assumed at station e and an average of
36、four static-pressure readings about the elbow was used for station 1.5 in order tocompute the velocity ratios at these stations. At the elbow exit(station e), separation is noted over about 12 to 15 percent of thediameter. The remainder of the flow is at an approximately constanttotal pressure, the
37、velocity gradient being produced by the static-pressure variation. The flow at this point for high inlet Mach nuaibersconsists of a mixture of subsonic and supersonic flow with a Mach nuniberrange from O to approximately1.25. At station 1.5 the flow is consid-erably more uniform amd all subsonic. Th
38、e effect of the thick inletboundary layer is shown most clearly at this station,where the lowvelocity region is more extensive than for the thin boundary layer.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.NACATN 3696 U.The general increase in the
39、 relative velocity with increasing inlet Machnuniber,as shown in the distribution, is the primary result of theincreasing difference in density between stations O-and eincreasingMach nuniber.Theoretical and ExperimentalLongitudinalPressure Distributionsor 1.5 withThe theoretical distributions along
40、the inner and outer walls ofeach elbow were calculatedaccording to the relaxation method (refs. 8and 9) for two-dimensional,incompressible,potential flow, and are pre-sented in figure 12. These theoretical curves indicate normal pressurechanges for such elbow designs, that is, an acceleration follow
41、ed by anexpansion along the inner wall and an expansion followed by m acceler-ation along the outer wall. The curves also indicate that the pressuregradient extends beyond the elbow inlet and exit both upstream and down-stream. The radius-diameterratio of the bends determines the magnitudeof the tra
42、nsverse gradient in the bend since, owing to the centri-force relationship,pressure differences across the bend are roughlyinverselyproportional to the radius-di%meterratio.A comparison of the theoretical and experimental distributionsforthe thin-boundary-layercase is shown in figure 13. Only the th
43、in-boundsry-layer case is shown because it most closely approximatespoten-tial flow. The figure indicates excellent agreement on the outer wallfor the r/d = 0.75, 1.00, and 2.50 elbows, where the boundary layer iscontinuouslyremoved by the secondary flow, up to a point near the exitwhere the effects
44、 of the losses through the elbow sre noted. Agreementwas less satisfactoryon the inner wall where the boundary layer accu-mulated as a result of the secondary flow and separation;however, thedifferencesbetween the theoretical and experimentalvalues follow thesame trends, the actual flow producing ro
45、ughly 75 percent more maximumpressure variation for the bends of small radius-diameterratio. Itshould be noted that some of the differencesbetween the theoretical andmeasured values may be accounted for by the fact that the theoreticaldistributionwas computedby using the assumption of two-dimensiona
46、lflow, which would not apply accurately to a circular elbow.CONCLUSIONSFour 90 constant-diametercircular-arcelbows with a straightpipe2.67 diameters long attached to the exit were tested up to choking Machnuribersfor a very thin and a very thick inlet boundary layer. The.-. ._._ _Provided by IHSNot
47、for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 NACATN 3696ratio of the radius of curvatureto the diameter (r/d) of the elbowswas from 0.75 to 4.00 and the Reynolds number range was from 0.53 x 106to 1.30 x 106. The following conclusionsare derived:1. The elbow with
48、 r/d = 2.50 produced the best performance withrespect to total-pressure-losscoefficient, static-pressuredrop, andchoking Mach number. For the thin-boundary-layercase, the elbowattained a chokingMach number of 0.77 which correspondsto 95 percentof the maximum theoretical air flow obtainable.2. Thickening the inlet boundaiy layer produced somewhat less uni-form flow distributionsdownstream of the elbows but did not affectappreciablythe pressure losses and chokingMach nuniber.3. Longitudinalwall static-pressuregradients indicate that theelbows with r/d = 0.75 md 1.00 choked in the tailpipe
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