1、, .- ,%. ,. ,.-,.,.,*TECHi?ICAL MEMORANDUMS. -,., ,. ,! . . . . .NAT IOtiALADVISORY “COMMIT;E “FORA-E-RONA”UIGSI1,-4-.- No . 1003- ,.TilzREs ISTANOE COEFFIC TENT OF cOMMERC I.JLLROUND WIRE., . ,., -.-, . .,.,ByB. Ec!kert and E: Pfidger. ,.”,. . .,.,Luftfahrtforschungvol. 18, no”. 4, April 22, 1941.V
2、erlag Von R. Qldenbour, Miinchen und -B-rln.,; ,. .,.,., ,.WashingtonJanuary 1942,.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.,11111111. -=-,. - ., ., TECHNICAL MFJMORANDUM1?OR.,A,ER,AUTICS.o.o oo3,. . . . . . .,. . ., - -i . . . . . . . . .THE
3、 RES ISTAItCtiCOEFFICIENT 031COMMEi CTAL hOUND WIRE GRIDS *., ,.,. . .By B, Eckert and F. Pflger,., . . . .SGMMARY.The resistance. Coefficients of CornmerCial tYpf3S of.,round wire grids” were examined for the purpose of obtaining the necessary data on supercharger test stands forthrottling the indu
4、cted a“ir to a pressure correspondingto a V i.stherefore independent of the operating height.To illustrate: If a supercharger designed for 8kilometers critical altitude is tested under sealevelconditions (1.033 k.g/cma and t = 15 C, point A infig. 1), the supercharger power required amounts to.,. .
5、1.226 mkg o km = InL s ,1as compared to. .N 0.525 p mkg Bkm= ! -;- In L. . ,”for instance, before the supercharger entrance openingt produces an air density corresponding to the criticalaltitude. Applied to the foregoing example, the power(point C, fig. 1) then amounts to.,. ,. .-, .,. u.O.525 o,t.h
6、rotted = ,n, s.,.,. . . .:., . .:.?!). ,-.,. ,. ,.-,-.,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 NACA Technical Memorandum No. 1OO3A .pr.e,ssuredrop across the grid from D to C (fig. .1) is:-thereby achieved. With Cw as the resistance coeffic
7、ientof the throttle, the pressure drop isAp = Q V2 Cw2 (2)Superficial investigations indicated that the air densityP prevailing behind the throttling point would be prac-tible in equation (2). Applied to the example shown infigure 1, the air density iven for point C should then beused as a basis for
8、 the solution,The simplest throttling ineans are wire grids.EXP13R.IMENTAL PROCEDUREThe resistance coefficients of the different roundwire grids were determined in a supercharger test standof the Stuttgart Research Institute, admittedly at suchlow air speed,that the density vari.ationsrelative tothe
9、 experimefits,levaluation could be disregarded. Theexperimental setup along with the test stations is shown.in figure 2. .An axial blower sucks the air through the entrancecone ; the grids of varying solidifies mounted between twbflanges were tested between “entrance cone and blower. Theair leaves t
10、he test section by way”of a fine throttling .device (Prasil type) which was kept wide open during theresistance measurements. By varying the engine speed theair speed could be increased to 30 meters per second.To determine the air speed the static pressure wasrecorded at the entry (test station 1, f
11、ig. 2);while therecording of the pressure upstream (test station 2) anddownstream (statien 3) from the grid afforded the pressure drop across the grid. Betz micromanometers wereused.TEST GRIDSThe experiments extended to commercial round wiregrids with square mesh; The wire gage of all grids wasthe s
12、ame, except one, grid no, XVI, which disclosed twodifferent gages in its texture.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.NACA.Technical Memorandum No. 100s 5-. .- Wire gage”-and mesh were measured very carefully andthe solidity of the separa
13、te grids defined accordingly.In some tests the number of grids was doubled; in othersdifferent grids were arranged in tandem and their resist-ance coefficients defined. Table 1 contains a list ofthe explored grids and grid combinations with their .char-acteriitie data.On two “grids a and b arranged
14、in tandem the meanwire gage 8m was determined at a rsa+ zb bb6m = .-z +Za bINTERPRETATIONa) Determination of Undi hence the pressure loss across the grid.-Numb er- -.1234567891011121314.15161?181920212223+_Table l.- Grids and CombinationsGrid number-.JIIIIIIVL“vVIVII “VIIIIXx.X1XIIXIIIXIVxvXVIXIII +
15、 VXII + VIXII + VIIXII + VIIIXII + IXXII + XV2 x XIII.-_ _,-!,!eshpercentimeter,-1.52,23.04.6?;?9.514.518.522.525.528.029.031.534.037.042.038.738.543.547.557.066%63.0.- -_- -Wire gage(mm).-_-_0,?.6.45a713.25,25.2:;.14,12lv:Y5%:.26.p.1918:166.1455.131.15_ -_- - .Solidity)?v=- -0.212.265.252.25?.328.4
16、19.-.496.505.53.58?.559.743723:564603:957.882.92,951.955.962982:997- -C) Definition of Projected Area of Grid and SolidityWith R as projected area of wire exposed to airstream and F as area of grid boundary, the solidity(reference 1) is:FRcp=%-(8). . .-. . - - . IProvided by IHSNot for ResaleNo repr
17、oduction or networking permitted without license from IHS-,-,-“NACA Technics.i Memorandum No. 1003 7*. hence. .c#:isa.m.eas-.ur.e,.f.o,r-th.egid.d.en.s.i.t.y.The .t.otal. projected area of the grid follows as.the sum of the pro- “ject ions of all wires. Referred to unit area Al? (10 mmx10 mm = 100 r
18、nm2) the projected area for z wires of 10 mmeach and ,a wire gage 6 is:A R= 10 Z6 + 10 2:6 - (28)2 .,. .A “R “= 20 26 “(z8)2 = 26.(20 - 28) mm (9),.-.“hene the solfdit,y: .:. ,. ., . ,:,. . ,”. !AF!Z6 ( 2.6) . . . . . . .,.4,v,=% ; = ., ,L-. .(8,)”Al? 100 ,The minor di”scre”pancies at the pipe circu
19、mferencecanbe disregarded;. . .,., ,.,RESULTS OF.TESTS;.,. , ., .,: , ,Figure .3.!shows the .r:sistance .qef.fici.ent .Of.w.the .round,.wire grids listed in table 1 plotted against theundisturbed flow velocity. “ “: “:” ,:,., ,. . . . ,.,The resstanhe Coefficients” ofseveral grfds with,!. small soli
20、dity as obtained by measurement are presented in,-.,; figure 4; whereas in figure 5 the resistance coefficientsare plotted against the Reynolds number. Re, wheretie= 5;:” “;”,!“:. ,:.,(M)Corresponding to the mean test condition, the kine-I, matic viscosity was based on 750 millimeters mercury and -2
21、00 c, that is . . .:. ,.*:”i.nc,”e”asein.Reynolds number ,is accompanied by a drop In resistancecoefficient. he .thi,ncylindrical, wiyes,.of which the”grids are manufact,ured disclose a relationship with theReynolds number similar to the cylinder tests in windtunnels. Because of the wellrounded, bel
22、 mouth and theshort distance of the grid away from it the inflow is largely laminar. An increase; in air speed, that is, aProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 NACA Techtii”cal?lemorandurn.No; .20.03resistance measurement” at.Reynolds num
23、,b.ersof Re 1.000.was experimentally impossible. , .,.,The experiments with double grids showed that, whenarranged close together without intermediate space, thetotal resistance coefficient is lower than the 6um of thetwo separate resistance coefficients. This.phenomenon isattributable to the fact t
24、hat the solidity of the twogrids is unable to become fully effective, that is, somewire overlap exists - even if only partial+ On verynarrow-mesh grids the mutual spacing is of less Lmportan.cefor the total resistance coefficient. The total resist-ance coefficients of two grids spaced 10 millimeters
25、 apartapproximately equals the sum of the separate resistancecoefficients.Figure 6 shows the resistance coefficients Cw Of the explored grids plotted against the solidity p atRe = 200. From the data provided, it is easy to computethe necessry solidity q for a desired Cw or the num-ber of meshes z fo
26、r a given wire gage 8.Example: Suppose the necessary resistance coeffi-cient cw for the required throttling is 13.Figure .6 gives for Re + 200 and Cw = 13 a solid-ity tf of 0.78. ith a reference area AF = 100 squaremillimeters , the necessary projected area AFR of thewires isAFR=cpAF=78mm2The mesh r
27、equirdof;2a wire gage z 0.1 can be compute-d from 0.?8 = . - z 0.1), that is: Z = 53 mesh percentimeter.THEORETICAL RiZSISTANC31 COEFFICIENT OF A GRIDWith the identification of figure 7 the continuityequation reads : ., ,.,Suppose thatFb =12;, po=,pl=, pa=p(11)(12)Then , for potential flow, the pres
28、sure equation would givet . . -.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.,NA”CA Technical. Memorandum. No. 1003 9a71(13)Upstream from the grid the flow can be summarily dealtwith as free from loss; thus the actualpressure be,comes,.“PO,= o id
29、” andpl=,pl id. ,.,Downstream from the grid” the flow ,i,enet fr,ee from losses,since it separates in vicinity of the narrowest cross. section. Behind the wires of the grid a dead air region, develops , which in the further course of the flow is,however , equalized again by mixing, so ,that the spee
30、d in( flow section 12 may be treated againas uniformly dis-tribute - Vo) (16),I_./+1Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 NA.CA Technical Memorandum No-”.1“003.Avp=vo(:-) (17)The total stream force I acting along the l)oundaryof zone I i
31、s also equal to zero. Hence the resistance Wacting on the grid is e“qua1to the product of the pressuredifference Av p between sections O and 2 and the cross-sectional areas .Fo and F2.w= AVPFO (38)For a resistance ,coefficient ofwCw = -.-v2Fn20it then affordsorF2- =I?l f Cw -1-1(19)(20)(21)With the
32、notationF2=F = area of grid boundaryFI =F-FR = free section of grid(F , 2 ( FR “Cw(-Y- ) 2- theor = F _ R )(Y-:-F;) = 1- q) (22)These theoretical values of Cw are shown as dashedcurve in figure 6. The agreement between theory and ex-periment is satisfactory, considering that the testswere made at co
33、mparatively low Reynolds numbers and thatthe basic assumptions are, after all, somewhat crude.For double grids (a and b) the theoreticalCwtheor was determined in correspondence with the meansolidity tot fromProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS
34、-,-,-NACA Technical Memorandum No, 1003“” . .Cwtot.theor -= -m, .“a -.-+ .Cwb -theor the”orand11(23)attot/( q?a z + wl “-)2(”;-z-;-) L-:-; )a= - - - - -/- .- - -Here also agreement with experimental values is obtained,provided the solidity for grids mounted ene behind theother is computed according
35、to equat ien (25)Translation by J. Vanier,National Advisory Committeefor Aeronautics.REFERENCE1. Plachsbart, O.: Widerstand von Seidengazefiltern.Runddraht- und Blechstreifens ieben mit quadratischenMaschen. Ergebn. Aerodyn. Versuchsanst. Gottingen, ,IV, Lfg. , Mnchen 19329 R. Oldenbourg., . .i,yI1A
36、_ .- . .-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-LM5“)Kg 0,4 Q45 0,5 at? 0,7 Q8 0,$ tow / / / r.,. / .- /. .- / -40 .N . tO En +ropy, SA 30 m/degrePFigureL- I-S diagramof atmosphericair.Provided by IHSNot for ResaleNo reproduction or networki
37、ng permitted without license from IHS-,-,-1NACA TechnicalMemorandum No.1003 Figs. 2.3- “ - “;JJ,Figure 2.- Test lay-out for measuring the resistance coefficientsof,.round-wire grids.(a) Bell mouth. (b) Test station 1.)(c Test station 2.(d) Grid. (e) Test station 3. (f Axial fan.(g) Throttling device
38、. (h) Driving motor.216cidlI.l!t(iOmm sw CIi? QridnG,;dL- -nd;=fucbed:ilow, Figure 3.- Resistance coefficient of grids listed $n table I plottedh against undisturbed axial velocity.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-., .NACA Technical Me
39、morandum No.1oo3 Figs. 4,5IFigure 4.-I75-t-=/=-.I2Undisturbed flow , 7YResistance coefficient of various grids with smallsolidity plotted against undisturbed axial velocity.Reynolds number ,PeFigure 5.- Resistance coefficient of grids otted againstReynolds number.$i!A ,. . . . . . ,-.-.- - . -.- -.-
40、. ,1Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TZJACACIUIiCSLlMemorandum Noe1003-. .,Figure 6.- Resistance coefficient of grids plotted against solidity(Re = 20). -.=.? 21,.I-1b? 2Figure 7 Illustration of throttlingprocess ina &ri&. ._ Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
