Boundary Lyer Theory

770 XXV. Determination of profile drug e. Lomen in the flow through cascndca 771
Pig. 25.7. Prcssrlrc clist,rihulion nnd position of point of scpnrntion or n tnrhnlcnt, houndery
l:rycr 011 tho I)lntlo of n 1.urlho mscntlo for two tlilTercnt nnglca of inflow, afler F.W. Iticgcla [44]
The work ill rnf. [4G] shows how t,o employ the method outlined in Sec. XXVtl
it\ ortler t,o c.nlt:nl:~tc thr. losscs of n two-clirncrmsionnl cascade at varying angles of
illllow. N. Srllolz allti I,. Spcitlel 1601 syst,cmatixecl such calculntio~ls ancl comparctl
tht!n~ wit.l~ rxlwrin~cntal results.
'I'ltn vrloc.it,y tlisl.ril)t~t,ion irnn~rrlintcly Idtirlc\f the exit plane of the cascnrle
shows stmng tlc~~,rrssions wllicl~ st.cnl from t,hc bountlary layers of the iutlivitl~lal
l~l:~.rins. 'I'url)ulrnlf ntixing rausrs t.I~csc velocity tliffernnce~ to sn~oofh out further
clownbl.rrnm, thl~s giving rise to an ntltlitionnl loss of energy. 'l'l~c amount of los.9
tlltc lo n,il:ing r:in IIC t:v:~.I~t:~,,c.tl wit.11 tltc nit1 of t.hn ~nomtmtum tl~rorrm. When
tlt+~rmi~~i~~g the t.ot:l.l loss it1 the flow tl~ro~lgl~ cascncl~s, it is necessary t,o take Chis
mixing loss into account in atltlit,ion to the loss of rnergy in the 11ountl:ar.y layers
of the individual blades. Thus a calculation of losses in n casc:dc cot&trs of the
following three partial calculations: 1. 1)eternmination of the ideal, potrnti:tl prcssure
distribution around tho contour of the blacles. 2. Calculations of t,lw (1:rminar or
turl)rrlont) hountlary layer at a blntlc. 3. DcLcrrninat.ion of the losses clrle to mixing
in t.hc wake bchintl the cnscadc.
The tot,al amount, of losscs nssociated with a cascade is best spccifictl by intlicatjing
thc tliffcrcncc Ag in t h total prcss~~rcs between the nnclisturbctl flow in front
of IJtc rascnclo rind Lhc "srnoot,llctl out" nclunl flow far bol~ind it. 'Jll~us
where p2' and wz' denote the pressure and vclocit,~~ in the real (i. e. alfcctctl I1.y
losses) flow far bchintl the cascatlr, respcctivcly. 'rhcsc sl~ould bo clist.ingrtisl~otl from
thc values p, and iuZ, respcctivcly, wltich refer to ideal (losslcss) flow. It is convenient
to render thn Lotd loss Ag tlimensionlcss with reference to thc dynnmio Ilond
formed with the axial velocity component w,, = wl sin P, = toz sin P,, as it tlct.crmines
the mass of fluid which passes through the cnscadc. For reasons of rontillttit,y
iB vnluc must be tho same in front of ns bclti~~tl tltc cascade. We tlto~ il~l.rotlttc:c
the following coefficient:
t, = - -9 -
few,," '
Some results of the systematic invest,igntions on cnscntles, rarrircl o~tl :it t he
Braunschweig Engineering University 1601, alao [49], are shown in Fig 25.8 These
represent a comparison between measured and calculated values of the loss coefficient.
All blades were derived from the aerofoil NACA 8410. The variable parameters
Fig. 2.5.8. LORS co~flicicnt tt from eqn.
(25.33) in terma of the deflexion coefficient,
dn = '~tl$f/W,, for turbine cascndes 8..
with difircnt solidity ratios t/1, after
[49J. Men.911rc1ncnta and calculntio~~a by
N. Scllolz nnd L. Speiclrl [GO]
Itlarlr prolllc. NArA RllO
Rcyeolds na~olrer R = w,llr - h x 10'
.- .- -. . -~ -
t In t,hc dmign of stcnru turbines it is 11sun1 to employ n aelocit?y coc//icient, 111, wl~icll
is clrlincd
as the ratio of thc rod exit vclociLy to its veluc in ideal flow, so tllet y, -- tu',/tc~,. Co:~srq~~rn(ly,
thc two cocflieicnh snlisfy the rcl:~tion Lt = (I -i/~2)/sinZ
P2.