CFD initial assessment of a protrusions based experimental facility

2.1 Experimental apparatus and data analysis

The experimental apparatus employed in this study is described in details in some recent papers [15-17]. The flow loop consists of a transparent test section and two supply lines of air and water, which converge into a horizontal pipe.

The test section (Fig. 1) consists of a horizontal distributor, which has a circular cross-section of 26 mm i.d., equipped with an interchangeable orifice plate with 16 orifices supplying an equal number of vertical channels. The channel dimensions (length, depth, width) are 500, 15, 18 mm respectively. The perforated plate has pass-through holes having a diameter (d_p) equal to 5 mm; inside each of them the protruding pipes have been inserted.

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Figure 1. Test section and channel pairs

Downstream of the test section, an array of valves is operated in order to extract the flow rate coming from a pair of vertical channels (channel pairs are numbered from j=1 to j=8), which carries the liquid and gas phases flow toward the corresponding flow meters.

The main and extracted (“separated”) gas streams are evaluated by two thermal mass flow meters (overall accuracy of ± 2% of the reading) and the ones for the main and extracted liquid are two magnetic devices with an overall accuracy of ±0.8% of the reading.

The gas superficial velocity is referred to the header diameter and inferred from a reference pressure and from temperature measurements (K-type thermocouples), both read just upstream the header.

Five pressure taps, named p₀ to p₄ along the flow direction, are connected to a differential pressure transducer and give the pressure values at the header inlet (p₀), and inside it (p₁ to p₄).

The operating conditions, evaluated at the distributor inlet covered the following ranges of gas and liquid superficial velocities: V_sg=1.50÷16.50 m/s and V_sl=0.20÷1.20 m/s, respectively. Intermittent and annular flows were visually observed by analysing the two-phase flow structure.

Experiments were carried out by protruding the vertical channels into the header by means of short pipes (external diameter 5 mm, internal one 4 mm).

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Figure 2. Variable protrusion depth configurations: (a) P3; (b) P2

These pipes have been changed initially according to 3 different configurations having a constant protrusion depth h equal to 13, 19.5 and 23.5 mm respectively. The corresponding h/D ratio is equal to 0.5, 0.75 and 0.90, respectively. Two new configurations have been here investigated: they are characterized by a variable protrusion depth along the distributor, as showed in fig. 2. In the first one (hereafter “P3”) the protrusion depth has 3 levels: it increases in the flow direction from h/D=0.50 (protrusions 1 and 2), to h/D=0.75 (protrusions 3, 4, 5 and 6), to h/D=0.90 (protrusions 7, 8, 9 and 10), then it symmetrically decreases to h/D=0.75 (protrusions 11, 12, 13 and 14) and to h/D=0.50 (protrusions 15, 16). The second configuration (hereafter “P2”) has only 2 depths: the protrusion depth is constant (h/D=0.90) except for the first 2 protrusions and the last two (protrusions 15, 16) for witch h/D=0.75.

The gas and liquid flow rates are reported in a non-dimensional way. For the generic phase k (k=g for the gas and k=l for the liquid) the dimensionless flow rate is defined as:

$\dot{m}_{k,j}^{*}=\frac{\dot{m}_{k,j}^{{}}}{\sum\limits_{i=1}^{N}{\dot{m}_{k,j}^{{}}/N}}$    (k= g, l)     (1)

where N is the total number of channel pairs and j refers to the channel pair under consideration.

Another synthetic representation of the phase distributions inside the channels is the standard deviation of the k-phase flow ratio, defined as follows:

$ST{{D}_{k}}={{\sqrt{{{\sum\limits_{j=1}^{N}{\left( \dot{m}_{k,j}^{*}-1 \right)}}^{2}}/N}}^{{}}}$   (2)

that represents a single-value index of liquid which expresses the distribution / maldistribution of the flow rate of the liquid or of the gas phase.

2.2 Experimental findings

In a first step the protrusion depth was held constant along the entire header length; the 3 different configurations analysed had the dimensionless depth h/D equal to 0.50, 0.75 and 0.90 respectively.

It can be observed that the protruded pipes can exert a positive influence on phase distribution provided that the dimensionless depth h/D is greater than 0.5. In fact either the gas or liquid distribution are very similar to the “ref” case (this condition refers to the header with no fittings inside the header) when the protrusion is too short: in this case most of the gas flows inside the first channels from header inlet, while the liquid migrates to the central/end channels.

The analysis of the measurements, gathered for other liquid velocities, leads to similar conclusions, even if the effect of the protrusion depth is less apparent.

Increasing the protrusion depth, the flow distribution improves considerably, with a typical trend: the liquid ratios in the central channels (j = 4, 5 and 6) are lower than those of other channels; the gas ratios exhibit the opposite behaviour, with low values in the first and last channels.

The results discussed above suggested that, in order to decrease the liquid flow ratio in the first and last channels, the size of protrusion may be different along the distributor: a shorter protrusion depth in the initial and ending part of the header may penalize the liquid ratio in these regions, hence increasing the distribution in the central channels.

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Figure 3. Gas and liquid flow ratios for different protrusion configurations, V_sl=0.45 m/s, V_sg=9.0 m/s

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Figure 4. Gas and liquid flow standard deviations inside parallel channels: effect of the protrusion depth, V_sl=0.45 m/s

Fig. 3 shows the effect of the variable protrusion depth for the condition V_sl=0.45 m/s, V_sg=9.0 m/s. The behaviours of P3 and P2 configurations are very different: in the first channel P3 increases the gas flow ratio (Fig. 3(a)) and decreases the liquid flow ratio (Fig. 3(b)); at the same time liquid ratio of the last channel is significantly larger than those of other channels, yielding worse flow distribution even than with short protrusions (h/D=0.50). An excellent uniform distribution was obtained with P2 configuration: more liquid was supplied to upstream channels (Fig. 3(b)), while the gas was fairly uniformly distributed to inner channels, as for h/D=0.75÷0.90.

To quantify the flow distribution, standard deviations were calculated by Eq. (2), and are showed in Fig. 4. The graphs in Fig. 4a and 4b show the profiles of the gas and liquid standard deviations for V_sl=0.45 m/s, as a function of the gas superficial velocity. The typical trends are opposite: as the gas flow rate is increased, the gas distribution inside channels gets better, while the liquid one worsens. Inspection of Fig. 4 reveals that increasing the protrusion depth the phase standard deviations have significant benefits in comparison with the reference situation.

The liquid distribution is more uniform with the highest protrusion depth h/D=0.90 and with P2 configuration, except for the highest gas velocity. The singular behaviour of STD_l for V_sg=1.5 m/s is due to the strong decrease of the liquid phase in channels 7 and 8, which leads to a less uniform flow distribution.

Similar STD profiles were also observed at higher liquid velocities (V_sl=0.80 and 1.20 m/s). Either the gas or liquid distribution are very similar or even worse to the “ref” case when the protrusion is short: in this case most of the gas flows inside the first channels from header inlet, while the liquid goes to the central/end channels. The P3 configuration has a similar behaviour, probably because the first two short protrusions are not able to catch enough liquid phase. The best observed liquid phase distribution have been obtained for P2 configuration.

4.1 Steady-state analysis

Fig. 9 shows the results obtained with the flow rate of 860 l/h; Tab. 5 reports the percentage error (with reference to the experimental conditions) obtained by the simulations. Because in the experimental facility there are only 8 mass flow meters each of them collect a couple of protrusions: for this reason the results of the CFD analysis reports the aggregate value of pairs of two consecutive protrusions (e.g. the value n. I is referred to the protrusions n. 1 and 2, the value n. II to the protrusions n. 3 and 4, etc.).

All the turbulence models predict the value of the mass flow rate evolved in each couple of protrusions with a similar average percentage error (around 3%); the minimum error corresponds to the II and VIII couples of protrusions while the maximum to the III. The results obtained by CFD calculations are very similar, and for all the models the results trends are smoothed if compared to the experimental ones; particularly, the first and the third couples of protrusions show the higher percentage errors, due to the deviation of the experimental results from a “regular” trend.

Table 5. Errors [%] at 860 l/h

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Figure 9. CFD vs. experimental mass flow rates comparison at 860 l/h

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Figure 10. CFD vs. experimental mass flow rates comparison at 1530 l/h

The reasons of the smoothing in the CFD calculations could be due to the numerical “forcing” of the solver to reach a steady-state solution; the absence of the time-dependent terms could lead the solver to underestimate the effects of time-dependent instabilities and to calculate a smoother velocity field.

Fig. 10 shows the results obtained with the flow rate of 1530 l/h and Tab. 6 reports the percentage error (with reference to the experimental conditions) obtained in the simulations.

In this case, the maximum errors is placed near the inlet, probably due to the flow instabilities localized around the I and II couples of protrusions, instead very low errors are found in the last couple of protrusions. Differently from the results of the analysis at 860 l/h, the percentage errors (although higher) strongly depend on the turbulence models, which were used, and the SST k-ω model shows the highest average error, that reaches 10% in the first couple of protrusions. This error is probably determined by the complexity of the pattern of the flow impingement upon the first protrusion.

Table 6. Errors [%] at 1530 l/h

Unlike the numerical results trend at 860 l/h, the CFD curves have a much more uneven trend than experimental ones, in particular in the I, II, III and IV couple of protrusions; additionally, in the CFD results a rising mass flow rate value in each model appears, differently from the very smooth variations of the experimental data. Similarly to the previous considerations on the steady-state solution, we have a quasi-linear increment in the mass flow rate value, without noticeable instabilities between two consecutive couple of protrusions.

Table 7. Errors [%] at 2300 l/h

Fig. 11 shows the results obtained with a flow rate of 2300 l/h and tab. 7 reports the percentage errors (with reference to the experimental conditions) obtained in the simulations.

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Figure 11. CFD vs. experimental mass flow rates comparison at 2300 l/h

In this set of simulations, the average percentage errors are very low and the profile of mass flow rates is very similar to the experimental one; like the previous showed results, there are relatively bigger errors only for the I and the III couples of protrusions. In these cases, there are very similar trends in both the numerical and experimental results; however, in the first and third couple of protrusions experimental instabilities of the mass flow rate distributions (unseen in the CFD results) appears. In the last three couples of protrusions the SST k-ω and the RNG k-ε models show uneven trends; particularly, in the VII protrusions couple there is a lower mass flow rate value than those in the surrounding couples of protrusions couple (i.e. VI and VIII); this behaviour is similar to that one experimentally measured in the II and IV protrusions couples.

4.2 Transient Analysis

A further set of simulations, by means of pisoFOAM transient solver, has been performed In order to evaluate the effect of time-dependent instabilities on the extent of maldistribution of the mass flow rate. The imposed BCs are obviously the same already adopted for the simulations by simpleFOAM solver. For the LES based solver two different grids (respectively composed by 1.7 and 3.4 M of cells) have been tested.

The obtained results are reported in fig. 12, 13 and 14 and Tab. 8, 9 and 10, respectively for 860, 1530 and 2300 l/h tests.

Table 8. Errors [%] at 860 l/h (transient solver)

Table 9. Errors [%] at 1530 l/h (transient solver)

Table 10. Errors [%] at 2300 l/h (transient solver)

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Figure 12. CFD vs. experimental mass flow rates comparison at 860 l/h (transient solver)

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Figure 13. CFD vs. experimental mass flow rates comparison at 1530 l/h (transient solver)

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Figure 14. CFD vs. experimental mass flow rates comparison at 2300 l/h (transient solver)

All the simulations have achieved stationary values after 1÷1.5 s, as it can be seen in Fig. 15.

Fig. 15 shows the temporal trend of the mass flow rate detected through the channel 4, 8, 12 and 16 at 860 l/h and with SST k-ω model (all the transient simulations showed similar results

The results of the transient  analysis, at 860 and 2300 l/h, do not give a substantial reduction in the mean error trends, in comparison with the steady state analysis presented in the previous paragraph.

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Figure 15. Mass flow rate temporal trends at 860 l/h (k-ω SST turbulence model)

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Figure 16. CFD vs. experimental mass flow rates comparison at 860 l/h with LES turbulence model (transient solver)

However, some interesting results were obtained at 1530 l/h: in addition to a very low average percentage errors, the mass flow rate distribution with both turbulence models seems virtually specular to the experimental one, between the II and V protrusions couples (in particular with the SST k-ω turbulence model). Similar results have been obtained with the LES Spalart-Allmaras isochoric turbulence model with 1.7 Mnodes at 860 l/h (Fig. 16): in this case, the virtually specular (to the experimental data) trend was obtained between I and VI protrusions couples.

Despite the (relatively) high percentage errors (see Tab. 10 and 11) in the specular part, the transient pisoFOAM k-ω solver and the pisoFOAM Spalart-Allmaras isochoric LES model can predict an instable behaviour, unlike the other tested models.

Table 10. Errors [%] at 2300 l/h (transient solver)

Table 11. Errors [%] at 860 l/h (transient solver with LES)

A CFD analysis of a multiport distributor has been accomplished and results were compared with available experimental data. The results shows a good agreement with the experimental data, with very low deviations which, in the worst case, do not reach the 10% for a single protrusions couple and 5% (as an averaged value) for all the protrusions couples. Furthermore, many different turbulence models have been used and they did not show any significant differences from the point of view of both the percentage deviations and the distribution profiles in steady-state solutions; the transient solvers show in some case a good prediction of mass flow distribution trend, without appreciable improving of the accuracy and increasing the calculation time by a factor larger than 7. Substantially the tested LES turbulence model does not lead to an appreciable improvement in the results; on the contrary we note a significant increase in the calculations times.

Then we can say that OpenFOAM predicts properly mass flow rates distributions (at least in the analysed range of Reynolds numbers).

This preliminary code-to-experiment comparison has provided very interesting results, also in view of a future further development of numerical models able to simulate even multiphase flow distributions within the different protrusions. Then, as a further future potential development, it could be also possible to (even only) computationally optimize (in terms of flow distribution uniformity) the collector geometrical configuration.