Mitsubishi Heavy Industries Technical Review Vol. 57 No. 1 (March 2020)
1

Development of Numerical Simulation Method for
Evaluation of Gas-Liquid Two-Phase Flow Distribution

MASAYUKI SAKAI*1

ATSUSHI ENYA*2

YASUTAKA AOKI*2

Mitsubishi Heavy Industries Group provides heat exchangers used in chemical plants,boilers, air conditioners, etc. In heat exchangers, gas-liquid two-phase flow is distributed tomultiple heat transfer tubes by a cone-type or header-type distributor. To predict the flow
distribution characteristics, we need to consider not only the behavior of the gas-liquid two-phaseflow in the distributor, but also the pressure drop in the heat transfer tubes on the downstreamside. Therefore, we developed a flow distribution prediction method by coupling numerical analysis
for the flow in a distributor and a one-dimensional model for the pressure drop in heat transfertubes. The results obtained by the developed prediction method were compared with theexperimental results, and it was verified that regardless of the presence or absence of phasechange due to heat exchange in heat transfer tubes, the developed method could predict theliquid-phase distribution ratio with practical accuracy.

|1. Introduction
In heat exchangers used in chemical plants or air conditioners, gas-liquid two-phase flow isdistributed to multiple heat transfer tubes through cone-type or header-type distributors. If the flow
distribution becomes extremely uneven, some parts of the heat exchanging area are not usedeffectively, resulting in the degradation of the heat exchanging performance. In addition, heattransfer tubes with a low flow rate may be excessively heated and damaged. Therefore, it isnecessary to accurately evaluate the flow distribution characteristics from the perspective ofensuring the performance and reliability of heat exchangers.
Generally, the flow distribution to multiple heat transfer tubes is affected by the flow state ina distributor and the pressure drop in the downstream heat transfer tubes. Therefore, for predictionof the flow distribution, in addition to the distributor, the downstream heat transfer tubes must also
be integrally modeled. The gas-liquid two-phase flow presents various flow regimes depending on
the flow rate, quality or heat load, however, and it is still difficult to accurately evaluate thepressure drop in heat transfer tubes by numerical analysis, even with today’s advanced numericalanalysis technologies for the gas-liquid two-phase flow. Therefore, we developed a new flow
distribution prediction method by coupling one-dimensional evaluation equations for which theaccuracy has already been verified to determine the pressure drop in heat transfer tubes andunsteady numerical analysis to analyze the behavior of the gas-liquid two-phase flow in a
distributor. This paper introduces an overview of the prediction method and describes theverification results for the prediction accuracy through comparison with the experimental results.

|2. Prediction method
An overview of the developed prediction method is shown in Figure 1. The behavior ofgas-liquid two-phase flow in the distributor was simulated by three-dimensional unsteadynumerical analysis, while each downstream heat transfer tube was divided into multiple elements inthe flow direction, and the heat exchange rate and the pressure drop were calculated by
one-dimensional evaluation equations. The details of the numerical analysis method and theone-dimensional model, as well as the coupling method, are explained below.
*1

Heat Transfer Research Department, Research & Innovation Center*2

Research Manager, Heat Transfer Research Department, Research & Innovation CenterMitsubishi Heavy Industries Technical Review Vol. 57 No. 1 (March 2020)
2Figure 1

2.1

Overview of prediction method

Numerical analysis method

The two-fluid model, by which the gas phase and the liquid phase are treated by separate
equations, was adopted to evaluate the flow regime in the distributor and the gas-liquid separation
due to gravity. The generalized thermal-hydraulics analysis software "ANSYS Fluent" was used as
the solver. The governing equations for the two-fluid model (mass conservation, momentum
conservation and energy conservation) are given as follows:+∇∙(1)=+∇∙ℎ+∇∙ℎ=−∇ +∇∙()+=−++:∇++ℎ+(2)(3)

is the volume fraction of thephase,is the phase change rate from the pwherephase to thephase,is the momentum generation term of thephase,is the term of external
force that acts on thephase, andis the heat input to the q phase. Equations (1) - (3) represent thegoverning equations of the gas phase when = and = , and the governing equations of theliquid phase when = and = .
The momentum transfer terms caused by velocity difference between the gas phase and liquid
and the lift force
phase were calculated by equations (4) and (5), with the gas-liquid interfacial dragthat acts on bubbles taken into account, respectively. In equations (4) and (5), ，and CL are
the gas-liquid interfacial area concentration, drag coefficient and lift coefficient, respectively. The flow
regime was judged by physical properties, void fraction, flow rate, etc., and appropriate constitutive
equations were applied. For the details, refer to the previously published technical reviews(1),(2).
=1
8=−

2.2

∙∙−−

∙−× ∇×(4)(5)

One-dimensional model for inside of heat transfer tubes

The heat transfer tubes were divided into multiple elements along the flow direction and thepressure drop in each element was calculated by one-dimensional evaluation equations. Since thepressure drop changes due to not only the flow rate but also the quality, the gas-liquid phase change
caused by heat exchange with outside-tube fluid was also considered.
The friction loss in heat transfer tubes was given by the following equations based on theLockhart-Martinelli correlation(3).

Mitsubishi Heavy Industries Technical Review Vol. 57 No. 1 (March 2020)
3∆=∆=1+(6)+1χ(7)whereis the Lockhart-Martinelli parameter,is the Chisholm parameter, and ∆ isthe pressure drop when only the liquid phase flows. For the Chisholm parameter , different
correlations were used according to the size of the heat transfer tubes or channel type, and theLi-Hibiki correlation(4) was used for mini-channels.

2.3

Coupling of numerical analysis and one-dimensional model

The one-dimensional evaluation equations for calculating the heat exchange rate and thepressure drop in heat transfer tubes were incorporated in ANSYS Fluent as user defined functions(UDFs), so that the numerical analysis for the distributor section and the one-dimensional modelfor the heat transfer tube section were coupled. The information exchange between theone-dimensional model and the solver is shown in Figure 2. With reference to the information suchas flow rate, void fraction and physical properties that the solver has, the heat exchange rate and thepressure drop were calculated by the one-dimensional model and returned to the solver as the phasechange ratein equation (1) and the external force termin equation (2), respectively.

Figure 2

Exchange of information between one-dimensional model and solver|3. Verification calculation
This section describes a calculation example for a header-type distributor of a parallel-flowheat exchanger for air conditioning products such as car air conditioners.
The heat exchanger to be calculated is shown in Figure 3. It consists of two headers that arevertically elongated, multiple flat heat transfer tubes and fins, and heat exchange is performed
between the fluid in the tubes and air passing between the fins. Both ends of each tube are inserted
into the respective headers so that the gas-liquid two-phase flow that enters the lower part of theinflow header is distributed to each tube. In this verification, the calculation was performed undercondition (1): non-heating condition using air and water and under condition (2): heating condition
involving phase change in heat transfer tubes with the fluorocarbon refrigerant to be used in theactual equipment, and the flow distribution to each heat transfer tube was predicted.
The flow distribution ratio of the liquid phase is shown in Figure 4. Concerning condition(2), the calculation result for the case where the developed method was not used (that is, in the caseone-dimensional pressure drop evaluation model for heat transfer tubes was not applied) was alsodescribed. The tendencies of the flow distributions under both conditions predicted by thedeveloped method reproduced the flow distributions of the experimental results well. When theflow distribution prediction accuracy ε defined by equation (8) was introduced, = 18% undercondition (1) and = 27% under condition (2) ( = 67% before the developed method isapplied). It was verified that by the developed method, the liquid phase flow rate into each heattransfer tube could be predicted within ±30%.

Mitsubishi Heavy Industries Technical Review Vol. 57 No. 1 (March 2020)
4Figure 3

Heat exchanger to be calculated

Figure 4 Comparison of liquid-phase distribution ratio

1=∑,−,(8)̅(: Number of heat transfer tubes,
̅ : Average flow rate of liquid phase in each heat transfer tube,: Flow rate of liquid phase in heat transfer tube
[Calculation] ): Experiment,:Figure 5 shows the photo of the visualized inside of the header in condition (2) (experiment)
and the contour map of the void fraction (calculation) and Figure 6 shows the pressure drop
between the inlet and the outlet of the heat exchanger in condition (2). Gas-liquid flow state,
distribution of void fraction in the header determined by gravity and gas-liquid interfacial drag, andthe pressure drop in the heat transfer tubes are in good agreement with those in the experimentalresults. This shows that the coupling of numerical analysis and the one-dimensional model has
achieved the desired effect. The high void fraction region near the inlet tube leads to reduce theliquid phase inflow into the No. 7 tube, while the liquid phase inflow into the No. 4 to 6 tubes
increases due to the formation of a low void fraction region in the middle stage of the header. Theseflow distribution characteristics, which are difficult to explain by gravity effect, could be predicted
only by using the developed method.

Mitsubishi Heavy Industries Technical Review Vol. 57 No. 1 (March 2020)
5

As described above, we applied the developed prediction method to a header type distributorof a parallel-flow heat exchanger to confirm that the distribution of gas-liquid two-phase flow canbe predicted with practical accuracy. Thus, flow distribution characteristics under different flowrate conditions or with different distributor shapes can be quantitatively predicted so that it ispossible to design the distributor shape for optimizing the flow distribution.

Figure 5Comparison of flow state in header

Figure 6 Comparison of pressure drop inheat exchanger|4. Conclusion
We developed a method for predicting the gas-liquid two-phase flow distribution in a heatexchanger by coupling numerical analysis for evaluation of flow behavior in a distributor andone-dimensional model for pressure drop in heat transfer tubes. We performed the verification
calculation for a parallel-flow heat exchanger for air conditioners and confirmed that the flow
distribution in each heat transfer tube can be accurately predicted. Using this method, we will makeefforts to improve the design of heat exchangers and optimize the shapes of distributors toward
improvement of the performance and reliability of heat exchangers.

References(1)(2)

Kondo, Y. et al., Development of Two-phase Flow Numerical Simulation Platform for Evaluating Boiling
Heat Exchanger Design, Mitsubishi Heavy Industries Technical Review Vol. 55 No. 2 (June 2018), p.1～5
Komuro, Y. et al.，Development of Numerical Evaluation Method for Unsteady or Phase-changing
Gas-liquid Two-phase Flow, Mitsubishi Heavy Industries Technical Review Vol. 56 No. 1 (March 2019),p.1～5

Mitsubishi Heavy Industries Technical Review Vol. 57 No. 1 (March 2020)
6(3)(4)Lockhart, R. W. et al., Proposed correlation of data for isothermal two-phase, two-component flow inpipes, Trans. ASME, Vol.66No.2 (1945), p.39～48
Li, X. et al., Frictional pressure drop correlation for two-phase flows in mini and micro multi-channels,
Applied Thermal Engineering, Vol.116 (2017), p.316～328