FLOW DISTRIBUTION OF GAS AND LIQUID IN PARALLEL PIPES

FLOW DISTRIBUTION OF GAS AND LIQUID IN PARALLEL PIPES

 

Tshuva M., Taitel Y. and Barnea D.

Department of Fluid Mechanics and Heat Transfer

Faculty of Engineering

Tel-Aviv University

Ramat-Aviv 69978, ISRAEL

 

Abstract

The situation of two-phase flow in parallel pipes is associated with the application of  D.S.G (Direct Steam Generation) by solar heating. In this process boiling water is fed into many parallel pipes from a common manifold. Instability and non-uniformity of the flow in this case can be a major operational problem.

In this work the gas and liquid distribution in two parallel pipes is mapped experimentally. It is found that the flow distribution can be either symmetric or asymmetric depending on the flow conditions and pipe inclination. A model that explains the observed phenomena is proposed.

 

Introduction

The study of two-phase flow in parallel pipes where the feed is from a common manifold is an interesting problem as the two phases may split unevenly when entering the parallel piping. The main motivation for this work is related to the processes that take place in the application of direct steam generation by solar heating. Such flows can develop instability and/or uneven distribution of the flow rates in the parallel pipes which is usually an undesirable phenomenon.

Pederson and May (1982) and Murphy & May (1982) studied two-phase flow instabilities which may arise during the operation of parallel pipes that absorb focused solar energy and produce steam directly in the collectors. They investigated the hydrodynamic transient behavior of a two-phase boiling system. Five flow instabilities were identified as potentially harmful to the operation of a D.S.G. system, and generalized maps were drawn which estimate the stability of a parallel-channel solar system.

Jovic et al. (1994) investigated experimentally the onset of pressure drop oscillations in three parallel channel flow. It was shown that the inter channel interaction can lead to unstable two phase flow regime.

Experimental work has been done by Ozawa et al. (1979), Ozawa et al. (1982) and Ozawa et al. (1989). Their work was on parallel-channel two-phase flow systems in capillary pipes of 3.1 mm diameter. They attempted to simulate flow in boiling channels by the injection of air and water along the pipes. Their conclusion was that the injection of air has a destabilizing effect on the pressure drop oscillations. On the other hand, the injection of liquid has a stabilizing effect, but induces a small-amplitude oscillation in the liquid flow rates.

No work has been carried out on parallel two-phase flow in inclined pipes. The work of Reinecke et al. (1994), however, is similar to the approach used in this work. Their work focuses on flow reversal in vertical two-phase flow in parallel channels that is related to loss of coolant accident (LOCA) or to loss of pumping power accident (LOPP) in nuclear plants. Their experimental set up consists of six tubes with an inner diameter of 19.05mm and a length of 1.3m connecting between a top and bottom plenum. The two-phase mixture was fed into the bottom plenum and experiments were carried out to determine the boundaries of the reversal state. A model, based on pressure drop calculations was presented for the prediction of the reversal boundaries. The boundaries for reversal two-phase flow in multiple tube array were determined when the hydrostatic pressure drop exceeds the system pressure.

The principle objective of this research is to find those operational conditions which allow to avoid flow instability and uneven flow distribution in parallel pipe systems.

 

Experimental

A schematic diagram of the experimental system is shown in Fig. 1. The experimental apparatus consists of two parallel pipes in which parallel flow is established and a third control pipe. Each pipe has a diameter of 2.4 cm and is 3 meters in length. The pipes are constructed from Plexiglas to enable visual observations of the flow patterns. The system has controlled water and air supplies. The whole flow system can rotate within the range of 0 to 90 degrees. It is possible to inspect the flow patterns and to measure the void fraction in each pipe. The superficial gas velocities are in the range of 0.50-5.60 m/s. The superficial liquid velocities are in the range of 0.02-3.03 m/s. The test is performed for three angles of inclination 0⁰, 5⁰ and 10⁰. Non-uniform flow patterns and void fraction are observed in upward inclinations of 5⁰ and 10⁰ (see figures 5 and 6). Observations of the flow regimes show that the flow always starts out as symmetric flow, and only after a short time the flow may become asymmetrical. Asymmetrical flow observed in our experiments is always in the form that one pipe contains intermittent flow while the other pipe is partially filled with stagnant fluid. The height of this liquid column is determined by the pressure gradient which must exist in the other pipe to maintain the intermittent flow. The injection of small pulses of air into the standing column of water causes the flow pattern of the two pipes to interchange. For high gas or liquid flow rates the flow in the pipes is always symmetric.

 

Analysis

In the analysis we try to find all possible steady state solutions for any combination of total input of liquid flow rate, U_LS, and gas flow rate, U_GS.

The liquid and the gas enters the two parallel pipes via a common manifold. The flow of the gas and the liquid is then split into the two pipes. U_LS1 and U_GS1 are the liquid and the gas flow rates (per unit area) that enters pipe No. 1. The flow rates in pipe No 2 will then be U_LS2= U_LS-U_LS1 for the liquid and U_GS2= U_GS-U_GS1 for the gas. A possible steady state solution is the one for which the split between the two pipes will result in an equal pressure drop for the two pipes.

The calculation of the pressure drop is performed using physical models. At first the flow pattern is determined using Barnea (1987) unified flow pattern model. Once the flow pattern is predicted the pressure drop for the specific flow pattern obtained is determined by physical models that simulate very closely the hydrodynamics of the flow (Taitel & Dukler, 1976, Taitel & Barnea, 1990).

The solution procedure starts by assuming gas flow rate in pipe No 1, U_GS1 and then scan all possible liquid flow rates, U_LS1, that will yield the same pressure drop in the two pipes, that is DP₁=DP₂. Figure 2 shows all possible steady state solutions where the pressure drop in the two pipes is equal for the case of total gas flow rate of U_GS=1 m/sec and three values of total liquid flow rate, U_LS= 0.2, 0.3 and 0.5 m/sec. In figure 2a the solutions are given for the relative liquid flow rate U_LS1/U_LS as a function of the relative gas flow rate U_GS1/U_GS. In figure 2b, below, we see the pressure drop that is associated with each solution. Thus, for example, for U_GS1/ U_GS = 0.20, U_LS1/ U_LS = 0.4; and for U_GS1/ U_GS = 0.80, U_LS1/ U_LS = 0.60. The required pressure drop is the same and it is DP=2800 Pa.

As can be seen, there is (theoretically) an infinite number of solutions that satisfies equal pressure drop for each total input of liquid and gas flow rates. In addition another steady state solution may be possible in which the total flow of liquid and gas takes place in one pipe while the other pipe contains a stagnant liquid column, as shown in figure 3. This solution is possible provided the pressure drop of the two phase flow in the pipe is less than the hydrostatic pressure exerted by the liquid when it fills the pipe.

Figure 4 maps the conditions for which the pressure drop of the two phase flow, flowing in one pipe is less than the hydrostatic pressure of a pipe, full of stagnant liquid. Since the pipe length is 3 meters, the circles represent the case where the single pipe two phase pressure drop is less that the hydrostatic pressure of 3 meters of liquid (taking into account the angle of inclination which is 5⁰). Likewise the squares represent the case where the single pipe pressure drop is larger than 3´sin(5⁰) meters. Obviously, when the length of the calculated stagnant liquid column is larger than the pipe length (3 m) the two phases cannot flow only in a single pipe. Thus the solution for a flow in a single pipe is possible only for relatively low liquid flow rates as shown in figure 4.

Out of all these solutions the question is what will be the physical case that will also match our experimental data.

We postulate that the physical solution will be the one in which the pressure drop is minimal. Observation of figure 2 shows that out of all possible solutions  the minimum pressure drop is associated with a symmetrical flow. That is, for the case where the gas and liquid split evenly in the two pipes. On the other hand it may be also possible that a stagnant liquid will be present in one pipe and that the pressure drop in this case will be less than the pressure drop of the minimal solutions presented in figure 2. In this case the real physical solution will be that of stagnant liquid in one pipe and the total flow of liquid and gas in the other pipe.

 

Comparison with experiments

The experimental data confirm our major hypothesis, that is, that out of the infinite numbers of solutions the physical case will be the one that exerts the minimal pressure drop and will be either in the form of a symmetrical flow or in the form of total flow in a single pipe and a stagnant liquid column in the other pipe.

Figures 5 and 6 show the comparison of our prediction with experiment for a wide range of total liquid flow rates, U_LS, and total gas flow rates, U_GS. The circles represent the solution for the case where the flow is asymmetric (in the form of a single pipe flow) and the pressure drop is less than the pressure drop for a symmetric flow. The solid squares are our theoretical calculated results for which the symmetric flow yields less pressure drop than the “single pipe flow”. The solid curve is the result of the experiment that demarcates the regions of asymmetric and symmetric flows. As can be seen there is a good agreement between our theoretical results and the experimental data. The experiment also verifies our model that the flow is either symmetric or all of it flows through one pipe only.

When the flow is asymmetric, in the form of a single pipe flow while a stagnant liquid column is present in the other pipe, one may ponder what determines the conditions in each pipe, namely, which pipe will be the “stagnant” one and which the “flowing one”. The experimental results show that this determination is random. Some time we get the stagnant liquid in pipe no. 1 and some time in pipe no. 2. In fact by perturbing the stagnant liquid in one pipe, by a pulse of  gas, the situation is interchanged and the stagnant liquid moves to the other pipe.

The theoretical calculation of the pressure drop still suffers from limited accuracy. This is probably the reason why the comparison with the experimental results, shown in figure 5 and 6, is not perfect. For the case where we have a stagnant liquid in one pipe we can use the liquid is the stagnant pipe as a manometer to check and verify our theoretical pressure drop calculations. Some of the results are summarized in table 1. For similar total flow rates of liquid and gas the height of the stagnant liquid is shown experimentally and theoretically. As can be seen the agreement is quite satisfactory.

 

Table 1.  Length  of  the stagnant  liquid column.

 

Also note in figure 2b, experimental data of the pressure drop are added for the case of liquid flow rate of U_LS=0.3 m/s. The agreement is not perfect, yet it is acceptable and it clearly shows experimentally that the minimum pressure drop occurs when the flow is symmetric.

 

Conclusions

The uneven distribution of gas-liquid two phase flow in 2 parallel pipes with common inlet and outlet manifolds is studied.

It is observed that two possible configurations can take place: (1) symmetric flow of liquid and gas in the two pipes and (2) asymmetric flow in which the two phases flow in one single pipe and a stagnant liquid column is present in the other pipe. The non symmetric configuration is observed in upward inclined parallel pipes at low flow rates. For the horizontal case the flow is symmetric for all flow conditions.

It is postulated that the flow configuration will be the one that results in a minimal pressure drop. The two phase pressure drop in the pipe is calculated by first identifying theoretically the flow pattern and then calculating the pressure drop using physical models.

Maps of superficial gas velocities versus superficial liquid velocities can be prepared for various operating conditions (length and diameter of the pipe, upward inclination angle, liquid and gas physical properties), which allow to determine the transition from the symmetric to asymmetric flow pattern.

 

Nomenclature

L          - stagnant liquid column length

U         - velocity

P          - pressure

 

Subscripts

G         - gas

L          - liquid

S          - superficial

 

References

 

Barnea, D. A., Unified model for prediction flow pattern transitions in the whole range of pipe inclination, Int. J. Multiphase flow, 13, 1-12 (1987).

 

Jovic, V., Afgan, N., Jovic, L. and Spasojevic, D., An experimental study of the pressure drop oscillations in three parallel channel two phase flow, Proceedings of the Internationa Heat Transfer conference Brighton UK. Ed. G.F. Hewitt,  6, 193-198, Paper 14-TP-9 (1994).

 

Murphy, L.M. and May, E.K., Steam generation in line-focus solar collectors: a comparative assessment of thermal performance, operating stability, and cost issues, SERI/TR- 632-1311. Golden, CO: Solar Energy Research Institute (1982).

 

Ozawa, M., Akagawa, K., Sakaguchi, T., Tsukahara, T. and Fujii, T., Oscillatory flow instabilities in air-water two-phase flow systems-1st report. pressure drop oscillation. Bull. JSME, 22, 1763-1770 (1979).

 

Ozawa, M., Akagawa, K., Sakaguchi, T. and Suezawa, T., Oscillatory flow instabilities in a gas-liquid two-phase flow system, heat transfer in nuclear reactor safety, 379-390, Hemisphere, Washington, D.C., (1982).

Ozawa, M., Akagawa, K. and Sakaguchi, T., Flow instabilities in parallel-channel flow systems of gas-liquid two-phase mixtures, Int. J. Multiphase Flow, 15, 639-657 (1989).

 

Pederson, R.J. and May, E.K., Flow instability during direct steam generation in a line - focus solar collector system, SERI/TR- 632-1354 .Golden, CO: Solar Energy Research Institute (1982).

 

Reinecke, N., Griffith, P. and Mewes, D., Flow-reversal in vertical, two-phase, two-component flow in parallel channels, 32rd  Meeting of the European Two-Phase Flow Group (1994).

 

Taitel, Y. and Dukler, A.E., A model for prediction flow regime transitions in horizontal and near horizontal gas-liquid flow, AIChE J., 22, 47-55 (1976).

 

Taitel Y. and Barnea D., Two phase slug flow, Advances in Heat Transfer, Hartnett J.P. and Irvine Jr. T.F. ed., 20, 83-132, Academic Press (1990).

 

 

 

 

 

 

 

 

 

 

 

 

                (a)

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                (b)

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(a) Liquid and gas flow rate distribution for equal pressure drop in the two parallel pipes.

(b) The solution of the pressure drop

U_GS = 1 m/s, upward inclination angle 5°.

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Fig. 4:    The regions for which the calculated length of the stagnant liquid column is smaller than 3 m. The square symbols correspond to symmetric flow and the circles correspond to asymmetric flow.

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Comparison with experiment. Upward inclination angle 5°.

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Comparison with experiment. Upward inclination angle 10°