W. Abou-Hweij and F.
Azizi / European Journal of Mechanics / B Fluids 84 (2020) 207–232 217
Fig. 7. Velocity contours through the 7th screen at various axial locations at
Reb = 20 for Mn = 20 and Mn = 80.
3.1. Model validation
In order to validate the model predictions, numerical simu-
lation results were compared to pressure drop data from the
literature. The overall pressure drop in the mixer is the result of
skin friction at the pipe wall in addition to losses resulting from
the flow through the screen. Hence, the pressure drop across a
screen element can be calculated using Eq. (4) [39]:
(Pin − Pout ) − ∆Po
∆Pscreen = (4)
Ns
where Pin and Pout are the area weighted average of the static
pressure at the inlet and outlet of the STSM, and ∆Po is the
pressure drop in an empty pipe having the same length as the
mixer, and Ns is the number of screen elements in the pipe.
Pressure drop across a screen (∆Pscreen ) is typically reported in
terms of a pressure loss coefficient, that is the equivalent of the
Fig. 8. Vorticity contours through the 7th screen at various axial locations at
Euler number (Eu). This number is the ratio of the pressure drop Reb = 20 for Mn = 20 and Mn = 80.
through the screen to the dynamic pressure (i.e. 1/2ρ U 2 ). For flows
through screens, Eu is typically a function of both the screen open
area, α , and the wire Reynolds number (Reb = ρ Ub/µ) as shown
against the values calculated using the aforementioned correla-
in Eqs. (5)–(7).
tions at pre-defined Reb values. Fig. 4 shows how the empirical
10.76 1 − α2
[ ( )] [ ]
Eu = 0.4537 + · (5) and simulated values compare against each other. It can be clearly
Re0.8213 α2
) ( b observed that the results obtained from the CFD simulations for
0.75
[( )
18
Eu = + Reb ≥ 10 are in close agreement with the correlation predictions
Reb log 10 (Reb + 1.25)
proposed by Azizi [27] (cf. Fig. 4a) with a maximum relative
1 − α2
] [ ]
+ (0.055 log 10 (Reb + 1.25)) · (6) error of 7.3%. Larger relative errors were calculated at Reb = 1,
α2
where they reached a maximum of 24.5%. This however is still
1−α
[ ] [ ]
49
Eu = 0.72 + · (7) acceptable for two reasons. First, the correlation of Azizi [27]
(Reb /α ) α2
was developed for the range of Reb ≥ 2, and second, while
Different correlations for the prediction of Eu have been proposed
Azizi correlated the data for a large number of experimental
in the open literature, the most recent being that presented
in Eq. (5) and reported by Azizi [27]. It was developed after ana- measurements, his correlation was reported to fall within ± 30%
lyzing more than thousand experimental measurements and cov- of these points. Similarly, the maximum relative error reaches a
ered a wide range of flow conditions (2 ≤ Reb ≤ 14,000). Eqs. (6) maximum of 13.9% for Reb ≥ 10 when comparing the CFD results
and (7) report the empirical correlations of Bailey et al. [29] and
Ehrhardt [30], respectively. These two correlations were selected to the correlation of Bailey et al. [29], but the error increases
in this work for validation purposes because of their different to 33.5% at Reb = 1. The relative error, however, was almost
algebraic form or varying dependency on the open area. A more constant at around 20% when comparing the simulation results
thorough analysis of these correlations can be found in the work
to the correlation of Ehrhardt [30].
of Azizi [27].
To validate the simulation results, the Euler number predic- It is worth mentioning that Eu values for Mn = 50 (α = 30.3%)
tions across one screen in a pipe were computed and compared and Mn = 80 (α = 31.4%) seem to be identical for the same Reb .
