It is attempted to explain the effects of oil by investigating the fluid proper-ties. The pure R134a properties are obtained in EES [61]. The liquid density, liquid viscosity, and surface tension of R134a and PAG oil mixture are cal-culated in Eq. 4.2, Eq. 4.3, and Eq. 4.4, respectively. These equations were generated based on the curve-fit of the experiment results in Seeton and Hrn-jak [77]. Bowers and HrnHrn-jak [75] used these equations in their study on the two-phase flow in horizontal tubes with the same refrigerant and lubricant combination. The coefficients in Eq. 4.2 and Eq. 4.3 are listed in Table 4.1, which are also from Seeton and Hrnjak [77].
ρl,mix =a1+ a2T + a3T2 + ω(a4+ a5T + a6T2)
Table 4.1: Coefficients for Eq. 4.2 and Eq. 4.3 a1 3.403743 b1 8.656882
a2 -0.010897 b2 -3.009702 a3 0.000006 b3 0.000000 a4 -3.55165 b4 5.213823 a5 0.013753 b5 -1.17072 a6 0.000006 b6 0.000000 a7 1.424533 b7 3.450021 a8 0.000591 b8 -0.84431 a9 -0.000024 b9 0.000000
The results from Eq. 4.2, Eq. 4.3, and Eq. 4.4 at min = 6.25 g s−1 and xin = 0.2 are presented inTable 4.2as an example. They are compared with pure R134a properties. To explore the effects of these fluid properties, based on the Buckingham PI theorem analysis in Section 3.2, the liquid Froude number in Eq. 3.3, liquid Reynolds number in Eq. 3.5, and liquid Weber number in Eq. 3.7 are examined since oil affects only liquid properties.
Table 4.2: Difference of R134a and PAG 46 oil mixture properties from pure R134a
min = 6.25g s−1
xin = 0.2 Liquid density Liquid viscosity Surface tension
OCR = 0.5% −0.01% 124.30% 17.31%
OCR = 2.5% −0.03% 138.30% 48.88%
OCR = 4.7% −0.05% 163.50% 68.90%
When the header geometry is fixed and the inlet mass flow rate and quality are the same, only fluid properties affect the distribution. It is found that the liquid density of the mixture does not change significantly even if OCR is increased to 4.7%. However, with a small amount of oil (i.e. OCR = 0.5%), the liquid viscosity is already increased by over 100%; therefore, the liquid Reynolds number is half of that for pure R134a. Oil makes it harder for liquid to flow up and reach the top tubes, worsening the distribution. On the other hand, as OCR increases over 2.5%, the surface tension is increased by 50%.
The higher surface tension generates more bubbles/droplets of smaller size in the churn flow region so that improves the mixing in this region. This helps to improve distribution at both low and high inlet qualities.
Oil also affects the flow patterns in the header by creating a layer of foam at the interface between liquid and vapor at high OCR as shown in Figure 4.6.
This layer of foam increases the size of churn flow region, which is another reason for improved distribution at high OCR. It is noticed that pure liquid does not foam. Synthetic oil, such as PAG oil, usually contains some surface-active additives (surfactant). Foam is created because of the accumulation of these surfactant at the interface. Foam is essentially unstable and tends to collapse to liquid (which is the lowest energy state) if left to rest. The surface-active additives, which tend to stay at the wall of foam, oppose the collapse of foam. The stirring or mixing of vapor and liquid in the header also help to maintain the foam at liquid-vapor interface. The foam generation and
stability is affected by viscosity, dynamic surface tension, Gibbs elasticity and interfacial shear, and dilatational viscosity, according to Randles and Rudnick [78]. Among these parameters, the Gibbs elasticity, which is related to surface tension gradients and Maragnoni effects, is believed to be most important. The distribution of surface-active additives on the foam wall creates the surface tension gradients in the liquid layer where some locations have high surface tension and other locations have low surface tension. When the rate of surfactant diffusion is just right, the thin spots on the foam wall (points of likely bursting) can be repaired. More detailed analysis about foam generation and stability was presented in Joseph [79]. Although the exact values of some properties relating to foam generation and stability are not available for R134a and PAG oil mixture, it is speculated that as PAG oil amount increases, the viscosity, Gibbs elasticity and interfacial shear also increase; thus, the foam is more stable.
Hewitt and Roberts [65] flow regime map for the vertical tube is used to generalize the flow regimes of pure refrigerant in the vertical header in Figure 2.24. The same method is used to generalize the flow regimes in this chapter when there is oil. The superficial momentum fluxes of liquid and vapor phases are used as in the horizontal and vertical axises, respectively, in Figure 4.8. It is observed that the presence of oil does not significantly affect the transition between churn and semi-annular flow.
Figure 4.8: Flow regime map of R134a and PAG 46 oil in the vertical header
However, oil affects flow patterns in terms of liquid reach and liquid sepa-ration height. The relative liquid reach H/L is related to the liquid mass flux in the header inFigure 4.9, where it is observed that the liquid reach is influ-enced by the amount of oil. At OCR = 0.5%, the liquid reach is below pure R134a case. As OCR further increases, the liquid reach is higher because of the layer of foaming at the interface. At OCR = 4.7%, the liquid reach is above pure R134a case. The effect of oil on liquid reach is also manifested by plotting the liquid reach against OCR in the example in Figure 4.10. The high enough liquid reach is necessary for the top tube to receive liquid. In churn flow, distribution is mainly affected by liquid reach; thus, the distribu-tion is worse at OCR = 0.5% and it is better as OCR further increases. The liquid separation height, as a function of vapor mass flux, is also affected by OCR, as shown in Figure 4.11. As OCR increases, the liquid separa-tion height is lower so that fewer tubes are bypassed by the liquid film and the distribution may be improved. In semi-annular flow, at OCR = 0.5%, the distribution is worse than pure R134a because the liquid reach is lower though the liquid separation height is also lower. As OCR increases to 2.5%
and 4.7%, the liquid reach is higher and the liquid separation height is lower.
Both liquid reach and liquid separation height cause the enlargement of the churn flow region; thus, improves the distribution in semi-annular flow.
Figure 4.9: Effect of oil on liquid reach (R134a and PAG 46 oil) Figure 4.12presents the coefficient of variation as a function of the liquid mass flux Gl = Gin(1 − xin) in the middle of the header. The value of σ
Figure 4.10: Liquid reach vs. OCR at min = 6.25 g s−1 and xin = 0.2
Figure 4.11: Effect of oil on liquid separation (R134a and PAG 46 oil)
reduces as liquid mass flux increases, i.e. the distribution is better. When oil is present, at OCR = 0.5%, the curve is above that of pure R134a, i.e.
the distribution is worse than pure R134a at low OCR. At OCR = 2.5%
and 4.7%, the curves are below the curve of OCR = 0.5% and also below the pure R134a curve, especially at high liquid mass flux, i.e. the distribution is improved at high OCR. The curve-fit correlations are presented in Eq. 4.6.
Eq. 4.7 obtained by using least square curve-fit method in Matlab is used to generalize the effects of oil on maldistribution at all OCR conditions.
Figure 4.12: σ as a function of liquid mass flux at different OCR for R134a
Figure 4.13: Generalization of the effects of oil on distribution
σ =
1.360 exp[−0.041Gin(1 − xin)] at OCR = 0.5%
1.188 exp[−0.053Gin(1 − xin)] at OCR = 2.5%
0.889 exp[−0.049Gin(1 − xin)] at OCR = 4.7%
(4.6)
σ = 0.544 exp[−0.0444Gin(1 − xin)]OCR−0.1897 for all three OCR (4.7)