Incompressibletterodynamic tenso
linearitygnon
Notation fhoh lqqalanh.ly
EIEEanEauaantigs
7 3 tuf fi rzui
TEyie
expensive
sink
donettaeniy J
summation
simulationcomplexityscaleswithReY't
i L 2,3 Over
3 spatial coordinates apearstuice
inthetenm JU oEEtuihFiotk
zz z.io p.u
3
itmmttiwi
KtYemea
ou xtEftw a
EE iaIe
We assume
steadyflowagundofonsiderfirstly permutation
velocity tensorGjik
1 cyclicaltourist
Vorticity is
definedas 1 17 1 intensornotation wi Eiji.BY 1
icydicaltou3 0
srepeatedindex
Reynolds Decomposition Edean
actual
Untie where
fluctuation
ltnhif.IN Udt and whiffudt o
µ
Considertwoquantities F Ttt and 5 Sts a
TimeAveraged
theaveragedtheproductdfluctuations It E
yYpafiYe
z BE.de
it Utu
mihwmi.me
EEII Ithuffnohame am
8 st 0
give sI 0
uncorrelated sandt
steady
2jUtUt tVYy
p xtM decomposing
UtuHf Vtv HYtyI tp2 vD4Utu ytimeaveraging
U3 tu eu xtuExivFyvfZytvFyirfZy fHIxt3Htr3 tn tfIyt2fy4
uafziFE.tv ytvIfy
yaf vPIYi2Iydz
ufI EFFIE FI
, UF.tv uIa Ey o
ytfI
continuity.fr
vTIy tpfIxtvpgUz 2jyU
uY uzy uT uTEy
UF.eu
ytfIi uEytFfy tp3IxtvPYfrtZdg
Egg'd'd
u
tvFyt tafify.I.gg rpzu zyuyHNSEgnaIfEyI
shearstresses aka
uiuj LEIEIFI.IT
Turbulent
Terms
putandput arecalledReynoldstresses ynormalstresses stresses
ThinShearLagerApproximation weassumezEe2 a0
cozy
We assume thatflouisstatistically 2D uiuj EuEE
ForinviscidandirrotationalflourtheRANSequationbecomes UF tV tp
andassumesmallperturbations thinaerofoil AUatuandV T y
we arrive atLaplace'sEquation 2 linearPDE
0 23 ttgyz 0 u Uttuctux
y
T lFtt0ct0x
Contributions fromthickness incidence x andcambered
can be individuallydeterminedandthen summed q.yzg.ec
quasinati
r
Uaocosain
I u Thickness
t
U BEgnuoayfi.sn
yg
TI t v
y'ttu2gIy
pootlzpUB pttzplllloocosxtuftllloosinxi.TT
smalla n t
sQawmdi q Incidences
Ej
1.2vsun.at
Cp fzppq
ga
2uiqsfa lu2u
au atuffy
v t
2
i Cp 2uI u.FI Camber c
LinearisedImpermeabilityBoundary Condition 4 f
snetu.FI
y dfg Va a
Iu a tufty
µjev
GOVERALI
, horizontalvelocity SurfaceSingularity Methods
out
componentscancelvelocities
normal
givingpurely
a sour.es iyhtE.otagtE.ngfhdinanfe.y.hiohcmbeafunokon
uppserurface
IF I
mW t2UayiE t
ace
inducedvelocity mangy
atpoint no circulation nonliftingbody
u fjz.ru dx
LumpedVortexModel
Circulation T fo x dx and he pilot
circulation
intensity
lumpedvortexplacedat 44 cop
TT
72222v fItIIxd
Yr
Faathinplate
Ce2Ta 2TLa T TLU cx x Zqisthe
collocationpoint
Collocationpointx'canbe
found BC xtIu O uto
using at2 a O
linearitygnon
Notation fhoh lqqalanh.ly
EIEEanEauaantigs
7 3 tuf fi rzui
TEyie
expensive
sink
donettaeniy J
summation
simulationcomplexityscaleswithReY't
i L 2,3 Over
3 spatial coordinates apearstuice
inthetenm JU oEEtuihFiotk
zz z.io p.u
3
itmmttiwi
KtYemea
ou xtEftw a
EE iaIe
We assume
steadyflowagundofonsiderfirstly permutation
velocity tensorGjik
1 cyclicaltourist
Vorticity is
definedas 1 17 1 intensornotation wi Eiji.BY 1
icydicaltou3 0
srepeatedindex
Reynolds Decomposition Edean
actual
Untie where
fluctuation
ltnhif.IN Udt and whiffudt o
µ
Considertwoquantities F Ttt and 5 Sts a
TimeAveraged
theaveragedtheproductdfluctuations It E
yYpafiYe
z BE.de
it Utu
mihwmi.me
EEII Ithuffnohame am
8 st 0
give sI 0
uncorrelated sandt
steady
2jUtUt tVYy
p xtM decomposing
UtuHf Vtv HYtyI tp2 vD4Utu ytimeaveraging
U3 tu eu xtuExivFyvfZytvFyirfZy fHIxt3Htr3 tn tfIyt2fy4
uafziFE.tv ytvIfy
yaf vPIYi2Iydz
ufI EFFIE FI
, UF.tv uIa Ey o
ytfI
continuity.fr
vTIy tpfIxtvpgUz 2jyU
uY uzy uT uTEy
UF.eu
ytfIi uEytFfy tp3IxtvPYfrtZdg
Egg'd'd
u
tvFyt tafify.I.gg rpzu zyuyHNSEgnaIfEyI
shearstresses aka
uiuj LEIEIFI.IT
Turbulent
Terms
putandput arecalledReynoldstresses ynormalstresses stresses
ThinShearLagerApproximation weassumezEe2 a0
cozy
We assume thatflouisstatistically 2D uiuj EuEE
ForinviscidandirrotationalflourtheRANSequationbecomes UF tV tp
andassumesmallperturbations thinaerofoil AUatuandV T y
we arrive atLaplace'sEquation 2 linearPDE
0 23 ttgyz 0 u Uttuctux
y
T lFtt0ct0x
Contributions fromthickness incidence x andcambered
can be individuallydeterminedandthen summed q.yzg.ec
quasinati
r
Uaocosain
I u Thickness
t
U BEgnuoayfi.sn
yg
TI t v
y'ttu2gIy
pootlzpUB pttzplllloocosxtuftllloosinxi.TT
smalla n t
sQawmdi q Incidences
Ej
1.2vsun.at
Cp fzppq
ga
2uiqsfa lu2u
au atuffy
v t
2
i Cp 2uI u.FI Camber c
LinearisedImpermeabilityBoundary Condition 4 f
snetu.FI
y dfg Va a
Iu a tufty
µjev
GOVERALI
, horizontalvelocity SurfaceSingularity Methods
out
componentscancelvelocities
normal
givingpurely
a sour.es iyhtE.otagtE.ngfhdinanfe.y.hiohcmbeafunokon
uppserurface
IF I
mW t2UayiE t
ace
inducedvelocity mangy
atpoint no circulation nonliftingbody
u fjz.ru dx
LumpedVortexModel
Circulation T fo x dx and he pilot
circulation
intensity
lumpedvortexplacedat 44 cop
TT
72222v fItIIxd
Yr
Faathinplate
Ce2Ta 2TLa T TLU cx x Zqisthe
collocationpoint
Collocationpointx'canbe
found BC xtIu O uto
using at2 a O
