Document 5kxaYM8NkxybbKXk60dRg62Ve

676 CHAPTER 41 . B gas constant for air, -*.533',ft:lb per (lb) (Ranking degree). .. r. " compressor (or fan) pressure ratio (greater than 1.0), ' HimnniftnlA-- *' r( turbine pressure ratio (greater than 1.0), dimensionless. T a total temperature of air, Ranldne. T -- average total temperature of air between.'two' points in the system, Rahkinel ` Wb " flow rate of bleed air, pounds per'minute. Wc B flow rate of cooling air (basic system), pounds per minute. 17c a flow rate of cooling air in primary heat exchanger (boot strap system), pounds per minute. Wei B flow rate of cooling air in secondary' beat.ezchanger (bootstrap system), pounds per ininute. Yt " compressionfactor -- .1, dimensionless, v Y, a expansion factor -- 1 --. ' . dimensionless. r fjC-nrr AP pressure difference, inches Hg- : s.. . ..... > AT a temperature difference, Fahrenheit degrees. ATv a isentropic temperature difference of air across turbine, . Fahrenheit degrees.' . y a ratio of specific heat at constant pressure to specific heat at constant ..volume,- dimensionless;- For -air, r - 1.395. - >. v, a isentropic efficiency of compressor, dimimi<2nt<HM , . y, -- mechanical efficiency of cooling turbine , ' ... fan or compressor power 1 ----------- ---.. - - dimensionless. , turbine power Vi a isentropic efficiency of turbine,'dimensionless.. r a ratio of any air density to standard air density, dimen- Subecripts 1,_ 2, 3, . denote locations in the refrigeration sys tems'shown m Figs. 15 and 23. Example 1: For the basic system and conditions shown in Fig. 15, determine: (a) the flow rate of bleed air Wb, (b) the.flow rate of cooling air. Wc, and (c) turbine discharge air temperature TV The effective area of the turbine nozsle is 0.328 eqm-.Note that all temperatures and pressures are total values otherwise stated.Thy air, is assumed throughout the analysis. > Satuixon: A trial-and-error solution is necessary. Values are assumed for the bleed and cooling air flow rates Wb and Wc, and the turbine meed N. !. Assume Wb * 20 lb per inin., Wc -- 56 U> per min, and N - 67,000 rpm. 1965 Guide And Data Book Bleed-Air Circuit' . .From Fig. 10, using the assumed values for Wb and Wc, read B 0.932. . 'B ^ Ti - Tt ; ' triu * B(Ti - T<y =. 0.932(877 - 596) - 262 F deg ' T, . Ti - Ar,Ii - 877 - 262 - 615 R ` The average temperature between points ! and 2 is ' Ti + Tt 877 +615 (IW.-, 746 R ^.From Big. 11, for Wb " 20 lb per min, read *aP -- 123 in. Hg.- 17.35 (fW.1. where-1735 is the-ratio of-stain.dard temperature to standard pressure (519/29,92). . (vAPt-,)^.^,^; (12.3)(746) , ;.,.i7.3s(i>, -4^)!: 17.35(108 --'5in. Hg. '' (Note that this equation is arranged in a form convenient for solution on'1a Hide rule, but requires a trial-ahd-error process. It can be rearranged in quadratic-form and-solved directly for APu*) ' ....... ' ' ' """ ' Pi' - Pi - APi_a - lfl -- 5 = 103 in. Hg abs. The turbine pressure ratio'r, Pt/Pi = 103/33 = 3.12. ' The expansion factor is Y. - r,(T~tm 1 <3.12)*-***^^ , '; Isentropic temperature drop *. . (ATiHl* - r,K.'-.615(0.275) -169Fdeg. 'h 4^ <, M \ \ 20 n/Vr^ \ s root3 >5 01 201 NOTE' THE NOZZLE IS A FULL-ACM1SS1 OH PEB1PNERAL-TYPE UNIT. ' EFFECTIVE-AREA ^*0320 SQ IN. reaaiNE PRCsame-ratio ` For Turbm Noaxfe of Cooling-.Torbim^a. iotk Air-Cyd*, Rrfrigmfo- e Unit. \ ' 12____ Test Peirforrndnce.Curve--How Factor' vs Pressure Ratio* -v Rg'.'l 3 iVVVTest Performance'Girve-^-EfFiciency ' vs Velocity Fador*' Air-Cyde Equipment 677 For the assumed turbine 6peed N of 67,000 rpm. N/Vf, - 67,000/ vfll - 2700. From Fig.-12, read the turbine flow factor Frr = 0.94. WBVt ' Frr 15.63P*A. takers Vf. '<Frr>15.63P*A, ;T_* ' . (15.63)(103)(0.328X0.94) ------------- -- 20.01 lb per mid., The calculated v&lue.offFi'checks with the original assumed value. If the-calculated -value had not cheeked, a second trial solution would have been necessary. The turbine velocity factor; r N ; ., Ft KvWi)x-i 1 where \ * /r ,/12 X60\* -Fig. 15-;... Basic Air-Cyde Refrigeration System' ` for Example h* *.5111 rpm per. VTt deg. A Therefore,: ' ; . 5111V169 From Fig. 13, read the turbine,efficiency vi * 79.6 percent. The.turbine.discharge air temperature is ,v,[ Tt - Tt - A7W- 615 - 13.45 - 480.5 R (20.5 F).