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3.2 Sub-group 1.2 in which one differential equation is used

3.2.1 Prandtl energy with prescribed length scale

(a) The effective viscosity

Prandtl, in 1945, generalised his hypothesis regarding the effective viscosity of a turbulent fluid, giving it the form:

EV = const1 * LM * SQRT (KE)

where: LM is a prescribed length scale, which may vary from place to place; and KE is the kinetic energy of the turbulent motion, deducible from the velocity fluctuations in the three directions u', v' and w'

Thus: KE = 0.5 * ( u'**2 + v'**2 + w'**2 )

(b) The source of information about KE


Prandtl postulated that the turbulence energy obeyed a transport equation of the form:

term representing

D(KE)/Dt time-dependence & convective transport = div( const2*EV* grad(KE)) turbulent diffusion + EV*(vel_grad)**2 kinetic-energy generation by shear - const3*k**1.5/LM kinetic-energy disipation

Thus:

(c) Advantages and disadvantages

(d) Activation in PHOENICS

In order to activate the PEM in PHOENICS, the PIL command TURMOD needs to be inserted in the Q1 file with the argument KLMODL. TURMOD(KLMODL) is equivalent to the following PIL commands:

SOLVE(KE) ENUT=GRND3;KELIN=0 PATCH(KESOURCE,PHASEM,1,NX,1,NY,1,NZ,1,LSTEP) COVAL(KESOURCE,KE,GRND4,GRND4);GENK=T

Then the choice of LM formula is made by the setting of further parameters such as EL1, EL1A, etc (see the HELP file entry EL1).

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