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Reynolds time-averaged method:
Time dependent (instantaneous) = time averaged (Reynolds averaged) +
fluctuation.
"
"
u = u + u ≡ u + u
"
"
v = v + v ≡ v + v
T = T + T
"
≡ T + T
"
P = P + P
"
≡ P + P
"
"
"
ρ = ρ + ρ ≡ ρ + ρ
Since
t
t
+Δ �
u
" dt = 0
t
t+Δt
v
" dt = 0
t
t+Δt
P
" dt = 0
t
t+Δt
T
" dt = 0
t
Therefore,
v "
∼
= T " = ρ " = P " = 0
Substitute the above instantaneous quantities into the original conservation
of mass, momentum, and energy equation, respectively, and then performing
time average over a period of time.
10.1.1 Continuity Equation
197
Turbulent Flow Heat Transfer
�
�
Reynolds time-averaged method:
Time dependent (instantaneous) = time averaged (Reynolds averaged) +
fluctuation.
"
"
u = u + u ≡ u + u
"
"
v = v + v ≡ v + v
T = T + T
"
≡ T + T
"
P = P + P
"
≡ P + P
"
"
"
ρ = ρ + ρ ≡ ρ + ρ
Since
t
t
+Δ �
u
" dt = 0
t
t+Δt
v
" dt = 0
t
t+Δt
P
" dt = 0
t
t+Δt
T
" dt = 0
t
Therefore,
v "
∼
= T " = ρ " = P " = 0
Substitute the above instantaneous quantities into the original conservation
of mass, momentum, and energy equation, respectively, and then performing
time average over a period of time.
10.1.1 Continuity Equation
197
Turbulent Flow Heat Transfer