Applied Thermal Engineering 117 (2017) 468–480
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Numerical simulation of three dimensional two-phase flow and prediction of oil retention in an evaporator of the automotive air conditioning system Vladimir D. Stevanovic a,⇑, Pega Hrnjak b,c a b c
University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, 11120 Belgrade, Serbia Air Conditioning and Refrigeration Center, Department of Mechanical Engineering, University of Illinois at Urbana Champaign, 1206 West Green Street, Urbana, IL 61801, USA CTS, 2209 Willow Rd., Urbana, IL, USA
h i g h l i g h t s Three-dimensional model of refrigerant-oil two-phase flow is developed. R134a and 1234yf two-phase flows with PAG oil in an evaporator are simulated. Oil retention and refrigerant mass in the evaporator are numerically predicted. Numerical results are validated against measured data. Locations of oil retention inside evaporator are predicted.
a r t i c l e
i n f o
Article history: Received 13 November 2016 Revised 18 January 2017 Accepted 5 February 2017 Available online 20 February 2017 Keywords: Oil retention Refrigerant Evaporator Numerical simulation
a b s t r a c t This paper presents a three-dimensional model of the refrigerant-oil two phase flow developed with the aim of predicting the oil retention in evaporators of air-conditioning systems. The developed model is based on the two-fluid model approach. The governing mass, momentum and energy balance equations are written for each phase. The gas phase is the refrigerant vapor, while the liquid phase is the mixture of liquid refrigerant and oil. The balance equation for the oil mass fraction in the mixture with liquid refrigerant is included. Transfer processes at the vapor-liquid interfaces and on the flow channel walls are predicted with closure laws. The model is solved by the in-house computer code based on the SIMPLE type numerical procedure. The model is validated by comparing numerically predicted refrigerant mass and oil retention data in a brazed plate and fin evaporator, typically used in automotive applications, against measured values. Two sets of experiments performed with refrigerants R134a and R1234yf in the mixture with PAG oil are simulated. The numerical results provide a complete picture of the two-phase flow structure in the evaporator. Model predicts that oil is mainly retained in the bottom header and in smaller amounts in the top header and in parallel evaporating channels with upward refrigerant flow. The developed three-dimensional modeling and numerical approach has the advantage of being more reliable for the prediction of oil retention than existing one-dimensional models. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Oil is added to refrigerant in vapor compression refrigerant systems in order to lubricate compressors. Some amount of oil is taken by the refrigerant vapor at the compressor outlet, circulates within the refrigerant system and retains in the system components. This effect is especially pronounced in automotive air condi-
⇑ Corresponding author. E-mail address:
[email protected] (V.D. Stevanovic). http://dx.doi.org/10.1016/j.applthermaleng.2017.02.027 1359-4311/Ó 2017 Elsevier Ltd. All rights reserved.
tioning systems with compressors that do not have an oil separator at the compressor outlet. The oil retention in refrigerant components reduces the oil amount for the compressor lubrication, which could cause the compressor failure if the sufficient amount of oil is not provided. In addition, the presence of oil in flow channels increases the hydraulic resistance, while in condensers and evaporators influences the heat transfer efficiency [1]. Therefore, the prediction of oil retention within refrigerant system components is very important for the safe and efficient refrigerant system operation.
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Nomenclature A CD cp D F G g h j k _ m OCR p p0 Pr Q_ q_ St T t u v x
surface, area interfacial drag coefficient specific heat diameter force per unit volume mass flux gravitational acceleration, mass faction specific enthalpy, heat transfer coefficient Colburn factor, Eq. (25) thermal conductivity mass flow rate oil in circulation ratio, Eq. (44) pressure pressure correction in SIMPLE method Prandtl number heat flow rate volume heat flux Stanton number, Eq. (25) temperature time velocity, velocity projection on x axis specific volume flow quality, Eq. (43)
l m q r
dynamic viscosity kinematic viscosity density surface tension
Indexes A air bub c e i i, j, k O p R r ref sat W 1 2 21
surface air parameter boiling parameter condensation evaporator liquid-vapor interface numerical grid indices oil phase index, particle refrigerant relative refrigerant parameter saturation wall liquid vapor interfacial
volume fraction evaporation, condensation rate thickness surface efficiency factor, Eq. (23)
Abbreviations OCR oil in circulation ratio PAG Polyalkylene glycol POE Polyol ester SIMPLE Semi-Implicit Method for Pressure-Linked Equations
Greek
a C d
e
Both non-intrusive and intrusive experimental methods have been used for the measurement of oil retention in components of refrigerant systems [2]. The components of interest are evaporators, condensers or pipes with refrigerant-oil single or two-phase flows. The non-intrusive method was used by Lee [3] and Cremaschi [4] to measure oil retention in the components of air conditioning systems. They injected oil upstream of the component initially filled with pure refrigerant and separated oil downstream by using the oil separator. The difference between injected and separated oil represented the oil retention. The estimated relative error of oil retention predictions by this method was 12%. The intrusive methods are based on the trapping of the refrigerant and oil mixture in the component of the refrigerant system by the simultaneous closure of the inlet and outlet valves and the removal of the component from the system. Afterwards, the trapped refrigerant is flashed carefully from the component, while the oil remains in it. A difference of the mass of component after flashing and the mass of the clean component is the mass of retained oil. This method was applied by Zoellick and Hrnjak [5], Sethi and Hrnjak [6,7] and Ramakrishnan and Hrnjak [8] for the investigation of oil retention in horizontal and vertical suction lines. The flashing technique and sophisticated mix and sample technique were introduced by Peuker and Hrnjak [9] and used by Jin and Hrnjak [10] for the measurement of refrigerant and oil distribution in air conditioning systems. The achieved relative errors of these predictions were below 2%. Calculations of the oil retention in refrigerant systems have been limited to the application of one-dimensional models. The current status of these one-dimensional models is represented here by the models developed by Radermacher et al. [11], Sethi and Hrnjak [12] and Jin and Hrnjak [13]. Radermacher et al. [11]
applied a one-dimensional model of oil film and vapor core flow in a suction line towards the compressor. A new empirical correlation for the prediction of the vapor core-oil film interfacial friction in annular flow was derived based on the available experimental data. This correlation shows a rapid increase of the interfacial friction coefficient with the liquid film decrease in annular flow, which is opposite to the well-known Wallis correlation that predicts a decrease of the interfacial friction coefficient (f) with the film thickness (d) decrease in the form f ¼ 0:005½1 þ 75ð1 a2 Þ [14], where f is written in the Fanning form and d ð1 a2 Þ. Cremaschi [4] and Radermacher et al. [11] also predicted oil retention in the evaporator. Each evaporator tube was discretized into certain number of control volumes along its length. The liquid refrigerant and oil mixture were calculated for each control volume based on empirical correlations for the prediction of refrigerant boiling heat transfer and liquid volume fraction in the two-phase mixture. The effects of oil on the boiling temperature were predicted by the thermodynamic approach, as presented by Thome [15]. Basic assumptions of the one-dimensional modeling of the evaporator two-phase flow were presented by Jin and Hrnjak [13]: the twophase flow distribution from evaporator headers towards parallel evaporating channels is uniform and bottom headers have liquid level filled up to the channel inlets. These assumptions are the main drawbacks of the one-dimensional modeling approaches. The liquid and vapor phase distribution from the header towards the parallel evaporating channels, as well as the liquid level in a horizontal header are highly non-uniform, as shown by Vist and Pettersen [16] and by Stevanovic et al. [17]. Jin and Hrnjak [13] predicted the refrigerant and oil content in the evaporator by using the one-dimensional model with the deviation of 20% from measured values. Li and Hrnjak [1] improved their one-dimensional
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model predictions by incorporating analytical description of experimentally observed non-uniformity of liquid and vapor phase distributions towards parallel evaporating tubes. Oil might be miscible or immiscible with liquid refrigerant under operating conditions of air conditioning systems. For instance the naphthenic type mineral oil is miscible with refrigerant R22, while it is immiscible with R134a [18]. Mineral oil is not miscible with current HFC-based refrigerants [19]. The miscibility and better transport of oil through components of the air conditioning system, back to the compressor, are achieved by synthetic lubricants, such as PAG (Polyalkylene glycol) and POE (Polyol ester) [19]. The miscibility of liquid refrigerant and oil depends also on their mass fractions in the mixture and temperature. In addition, refrigerant vapor might be soluble in oil, as in case of R744 solubility in PAG oil [20]. Regardless of the oil miscibility with the liquid refrigerant, the transport of oil in tubings and other components of the air conditioning system depends on the liquid refrigerant and miscible or immiscible oil transport in the two-phase flow with refrigerant vapor. Therefore, the proper prediction of two-phase flow of refrigerant vapor and liquid refrigerant-oil miscible or immiscible mixture is crucial for the reliable prediction of oil retention in components of air-conditioning systems. Numerical simulations of multidimensional refrigerant twophase flows and heat transfer conditions have been applied with the aim of overcoming shortcomings of one-dimensional models and providing an improved support for efficient and reliable operation of refrigerant system components. Numerical multidimensional investigations have been directed towards refrigerant twophase flows in components of simpler geometry, such as tubes, T-junctions and two-dimensional flow distributors. An overview of such results was presented by Li et al. [21] and they were obtained with commercial CFD codes based on the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) type numerical algorithm [22]. A stratified flow of supercritical CO2 and oil in a horizontal channel was numerically simulated by Dang et al. [23]. Simulations were conducted by using a commercial CFD software and the volume-of-fluid (VOF) model was applied to capture the oil and CO2 interface. Recently, refrigerant two-phase flows in more complex geometry of evaporators and condensers were numerically investigated. An operation of the two-phase flow distributor in the plate-fin heat exchanger was investigated with a commercial CFD code by Yuan et al. [24]. A performance of a condenser of an automotive air conditioner with maldistribution of inlet air was simulated by Datta et al. [25] with the special purpose software based on a technique called ‘‘junction-tube connectivity matrix”. In the present paper, the shortcomings of one-dimensional model predictions of refrigerant and oil two-phase flows in the evaporator are overcome by the application of the threedimensional modeling of two-phase flow. The developed model is based on the two-fluid model approach [26], which means that the mass, momentum and energy balance equations are derived for each phase. The liquid phase is the mixture of liquid refrigerant and oil, while the gas phase is the pure refrigerant vapor. The interfacial transfer processes at the liquid and vapor interface surfaces are described and predicted by closure laws [26]. The calculation domain is discretized by the control volume approach presented by Patankar [22] and the governing equations are solved by the SIMPLE type method [22], which was extended for the conditions of two-phase flow, as presented by Stosic and Stevanovic [27] and Stevanovic [28]. The same numerical approach was successfully applied for the prediction of refrigerant maldistribution in the evaporator’s header [17] and two-phase flows on the shell side of the nuclear steam generators [29] and the kettle reboilers [30]. The prediction of oil retention in a complex geometry of the evaporator is the outcome of the three-dimensional numerical simula-
tion. The modeling approach presented previously in [17,27–30] is upgraded in order to take into account the presence of oil in the mixture with liquid refrigerant, as well as to predict the oil retention. The development and application of the three dimensional numerical simulation approach, presented in this paper for the oil retention prediction is an innovation regarding previously developed and applied one-dimensional models. The obtained results of numerical predictions of refrigerant content and mass of retained oil in the evaporator of an automotive airconditioning system show a good agreement with measured data for experiments performed with two refrigerants R134a and R1234yf and PAG oil. The mathematical model of evaporator two-phase flow conditions and oil retention is presented in Section 2. The developed model validation and results of the two-phase flow simulations and oil retention in the evaporator are presented in Section 3. Conclusions are outlined in Section 4. 2. Modeling approach The applied three-dimensional model of refrigerant-oil twophase flow is based on the following assumptions: the liquid is the two-component mixture of refrigerant and miscible oil, the gas phase is formed only by the refrigerant vapor and the same pressure holds both in the liquid and gas phase. The gas and liquid mixture in the two-phase flow is observed as an interpenetrating media in space and each fluid stream is described with the mass, momentum and energy balance equation. The transport phenomena at the gas and liquid interfaces are predicted with appropriate closure laws. Such a model is known as the two-fluid model [26] and the appropriate balance equations and closure laws are written as follows. 2.1. Balance equations The following system of governing balance equations is applied. Mass balance of vapor and liquid refrigerant-oil mixture
@ðap qp Þ ! þ r ðap qp u p Þ ¼ ð1Þp ðCe Cc Þ @t
ð1Þ
Volume balance
a1 þ a2 ¼ 1
ð2Þ
Momentum balance !
@ðap qp u p Þ ! ! ! þ r ðap qp u p u p Þ ¼ ap rp þ r ½ap qp mp ðr u p @t !
T
!
!
þ ðr u p Þ Þ þ ap qp g ð1Þp F 21 !
ð1Þpþ1 ðCe Cc Þu 1i
ð3Þ
Energy balance
@ðap qp hp Þ ! @p ð1Þpþ1 ðCe Cc Þh2;sat þ q_ wp þ r ðap qp hp u p Þ ¼ ap @t @t ð4Þ Balance of refrigerant mass fraction in liquid mixture with oil
@ða1 q1 g R;1 Þ ! þ r ða1 q1 g R;1 u 1 Þ ¼ Ce þ Cc @t
ð5Þ
Balance of mass fractions of liquid phase components
g R;1 þ g O;1 ¼ 1
ð6Þ
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In the above equations indices 1 and 2 denote the liquid and the vapor respectively, where in Eqs. (1), (3) and (4) p = 1 or p = 2, index e denotes the evaporation, c denotes the condensation, while refrigerant and oil parameters have indices R and O respectively. The following dependent parameters are applied both for liquid !
and gas phase: the volume fraction a, the velocity u , the enthalpy h, and the pressure p. Also, dependent variables are the refrigerant and oil mass fractions in the liquid phase gR,1 and gO,1 respectively. Independent variables are the time t and the spatial coordinates that figure in the differential operator nabla. Other parameters and terms are as follows: q is the density, C is the evaporation or condensation rate, m is the kinematic viscosity, g is the acceler-
Surface tension is calculated as [31]
r ¼ rR;1 þ ðrO;1 rR;1 Þg 0:5 O;1
ð11Þ
Eqs. (10) and (11) were used in [4] for several refrigerant-oil mixtures, such as R22-mineral oil, R410A-mineral oil, R410A-POE oil, R134a-POE and R134a-PAG oil mixtures. In [13] Eq. (10) was applied for R134a-PAG and R1234yf-PAG oil mixtures, while in [36] for R113-oil mixture. Although Eqs. (7)-(11) were generally adopted in the literature as appropriate for the prediction of thermophysical properties for various refrigerant-oil mixtures, there is still a need for the experimental prediction of refrigerant-oil mixture thermophysical properties and validation of these correlations.
!
ation of gravity, F 21 is the interfacial force between the liquid and gas phase. The heat exchange per unit volume of flow channel between the fluid phase p and the flow channel wall (denoted with w) is q_ wp . 2.2. Thermo-physical parameters of the liquid refrigerant and the miscible oil
2.3. Closure laws Closure laws define transfer processes between the liquid and vapor phase. The evaporation and condensation rates are defined by the empirical non-equilibrium model [38]
Ce ¼
a1 q1 h1 h1;sat se h2;sat h1;sat
ð12Þ
Cc ¼
a1 q1 h1;sat h1 sc h2;sat h1;sat
ð13Þ
The density of liquid refrigerant and oil mixture is calculated as
1
q1 ¼ ð1gO;1 Þ qR;1
g O;1
þq
ð7Þ
O;1
where qR,1 and qO,1 are the densities of the liquid refrigerant and the oil at the pressure and temperature of the liquid mixture. Eq. (7) is derived directly from the expression for the prediction of mixture specific volume v 1 ¼ ð1 g O;1 Þv R;1 þ g O;1 v O;1 and by writing each specific volume as the reciprocal of corresponding density. Thome and co-workers [31] suggested the application of Eq. (7) without any comment that it might deviate from real values for some types of refrigerant-oil mixture. In contrast, Conde [32] introduced a correction into Eq. (7) based on the empirical data by Jaeger [33] for refrigerants of the methane and ethane series. For refrigerants of the ethane series (to which, for instance, R134a belongs) the maximum deviation of the refrigerant-oil mixture specific volume from the measured value is in the range from 1% to 3% for the mixture temperature respectively between 0 °C and 40 °C and the oil mass fraction about 0.3 [32]. Regarding these low discrepancy values and the limited available other information on the subject, it is assumed that Eq. (7) is general enough for any refrigerant-oil mixture. The dynamic viscosity of the liquid refrigerant and the oil mixture is calculated as gO O;1
gR R;1
l1 ¼ l l
ð8Þ
and the kinematic viscosity is m = l/q. Eq. (8) is based on the Arrhenius mixing law [34], which assumes the ideal liquid mixtures and solutions, and the application of Eq. (8) was recommended for instance in [31,32]. According to Schroeder’s study [35], Eq. (8) is the most practical equation that provides the least deviation from the measured values for various refrigerant-oil mixtures. The specific heat of the liquid mixture is calculated as the mass average of the specific heats of its constituents
cp;1 ¼ g R;1 cp;R;1 þ g O;1 cp;O;1
ð9Þ
As it was suggested by Jensen and Jackman [36] and assumed as acceptable for any refrigerant-oil mixture in [31,32]. Thermal conductivity is calculated with the following correlation proposed by Filippov and Novoselova [37]
k1 ¼ g R;1 kR;1 þ g O;1 kO;1 0:72g R;1 g O;1 ðkO;1 kR;1 Þ
ð10Þ
This correlation was also recommended in [31,32] without mentioning its limitations regarding the refrigerant-oil mixture type.
where se and sc are respectively the relaxation times of evaporation and condensation, which are defined as the experimental constants. The enthalpy of saturated refrigerant vapor is h2,sat and it is a function of local pressure, while the enthalpy of saturated liquid phase is calculated as
h1;sat ¼ g R;1 hR;1 ðT bub Þ þ g O;1 hO;1 ðp; T bub Þ
ð14Þ
where hR;1 ðT bub Þ and hO;1 ðp; T bub Þ are enthalpies of the liquid refrigerant and the oil that depend on the local pressure p and the bubble point temperature Tbub. The bubble point temperature depends on the oil mass fraction in the mixture with the liquid refrigerant and according to Thome [15] it is calculated as
T bub ¼
A lnðpÞ B
ð15Þ
where p is the local pressure in (MPa) and Tbub is calculated in (K). The parameters A and B in Eq. (15) depend on the oil mass fraction in the mixture with refrigerant and they are predicted by the empirical expressions
A ¼ a0 þ 182:5g O;1 724:2g 3O;1 þ 3868g 5O;1 5269g 7O;1
ð16Þ
B ¼ b0 0:722g O;1 þ 2:39g 3O;1 13:78g 5O;1 þ 17:07g 7O;1
ð17Þ
where the parameters a0 and b0 are predicted for the pure refrigerant and the local pressure p. !
Calculation of the interfacial drag force (F 21 ) is a crucial step for the proper prediction of the relative velocities between the vapor and liquid phase, and consequently the prediction of the void fraction. The interfacial drag force per unit volume of the computational cell, which is filled with liquid and vapor is calculated as !
F 21 ¼
! ! ! 3 C ! a2 q1 D ju 2 u 1 jðu 2 u 1 Þ; 4 Dp
ð18Þ
where CD is the interfacial drag coefficient, and Dp is the diameter of the dispersed particle. For bubbly two-phase flow the modified Ishii-Zuber correlation is used for the calculation of CD [30].
) 1=2 ( 6=7 2 2 g Dq 1 þ 17:67ðf ða2 ÞÞ r C D ¼ Dp 3 rH 2 0 r 18:67f ða2 Þ
ð19Þ
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Stair ¼ jair Prair
where 1:5
f ða2 Þ ¼ ð1 a2 Þ ;
ð20Þ
and rH2 O is the water surface tension at the same temperature as the temperature of the liquid refrigerant-oil mixture. For churnturbulent flows, the following correlation is used [30]
C D ¼ 1:487Dp
1=2 g Dq
r
ð1 a2 Þ3 ð1 0:75a2 Þ2
r rH2 0
ð21Þ
The pure water surface tension rH2 O is determined for the same temperature as the refrigerant temperature. It is assumed that bubbly flow holds for void fraction less or equal to 0.3, while churn-turbulent flow takes place for higher voids. In case when the heated wall is in contact with the two-phase mixture, the heat transferred from the wall to the two-phase mixture is used for the liquid evaporation. Therefore, the volumetric heat flux from the heated wall to the vapor is q_ w2 ¼ 0 in Eq. (4), while its value to the liquid phase is calculated as q_ w1 ¼ q_ Aw1 =Dl, where q_ Aw1 is the wall heat flux and Dl is the thickness of the calculation control volume in the direction normal to the wall. The heat flux is calculated as
q_ Aw1 ¼ hðT air T bub Þ
ð22Þ
where T air is the outside air temperature, the two-phase mixture temperature T bub is calculated with Eq. (15) and the overall heat transfer coefficient h is calculated by taking into account the thermal resistances of convection on both air and refrigerant sides and the conduction thermal resistance through the wall. Following the same procedure as applied by Jin and Hrnjak [13], the overall heat transfer coefficient is calculated as
h¼
1 Aref eair hair Aair
þ kdww þ h1
ð23Þ
ref
where Aref and Aair are the heat transfer areas respectively on the refrigerant and the air side, eair is the surface efficiency factor [39] that takes into account the heat transfer enhancement on the air side by fins, dw and kw are respectively the thickness of the evaporator plate wall and its thermal conductivity, and hair and href are the heat transfer coefficients on the air side and the refrigerant side, respectively. The heat transfer coefficient on the air side is calculated as
hair ¼ Gair cp;air St ir
ð24Þ
where Gair is the air mass flux, cp,air is the specific heat of air and the Stanton number is calculated as
ð25Þ
Prair is the Prandtl number for air, while the Colburn j-factor is calculated by the Park and Jacobi correlation [40]. The heat transfer coefficient for the boiling on the refrigerant side href is calculated by the Yan and Lin correlation [41], which is developed for the R134a evaporation in a small brazed plate evaporator, i.e. for the conditions that correspond to the experiments simulated in this paper. 2.4. Numerical solution The governing scalar Eqs. (1), (4) and (5) and projections of the momentum vector Eq. (3) for the liquid and vapor phase onto the three coordinate axes of the Cartesian system result into a set of 9 scalar partial differential equations. The tenth scalar equation is derived for the calculation of the pressure field according to the SIMPLE type pressure-correction method [22], which is extended for the conditions of two-phase flow, as presented in [27,28]. These partial differential equations are discretized by integrating them over rectangular control volumes of variable size in the 3D Cartesian coordinate system (Fig. 1) [22]. Fully implicit time integration is applied [22]. The scalar parameters, i.e. the pressure, the enthalpy, the liquid volume fraction and the mass fraction are calculated for the basic (scalar) control volumes that are depicted with the full lines in Fig. 1, while the velocity components are calculated for the staggered control volumes depicted with dashed lines. The convective and diffusive terms at the control volume boundaries are determined with the power low numerical scheme [22]. The extension of the SIMPLE method [22] to the conditions of two-phase flows is briefly outlined as follows. The pressure filed is calculated from the so-called pressure-correction equation by taking into account the presence of two phases – the liquid and gas phase [27,28]. The derivation of this equation is adjusted to the iterative method of solution. The velocity components of the phase p at the n-th iteration are calculated as
upðnÞ ¼ upðn1Þ þ u0p ;
ðn1Þ v ðnÞ þ v 0p ; p ¼ vp
ðn1Þ wðnÞ þ w0p p ¼ wp
ð26Þ
and pressure as
pðnÞ ¼ pðn1Þ þ p0
ð27Þ
The velocity component correction u0p and pressure correction p0 are connected through the reduced form of the momentum difference equations [22]
Fig. 1. Three-dimensional numerical grid in Cartesian coordinates.
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ciþ1=2;j;k ðu0p Þiþ1=2;j;k ¼ ðap Þiþ1=2;j;k ðp0iþ1;j;k p0i;j;k ÞDyj Dzk
ð28Þ
or
ðu0p Þiþ1=2;j;k ¼ ðdp Þiþ1=2;j;k ðp0iþ1;j;k p0i;j;k Þ
ð29Þ
where
ðdp Þiþ1=2;j;k ¼
ðap Þiþ1=2;j;k Dyj Dzk
ð30Þ
ciþ1=2;j;k
and the coefficient ciþ1=2;j;k results from the discretization of the momentum balance equation projected along x coordinate as presented in [22]. By combining Eq. (26) for the velocity component ðnÞ
up and Eq. (29) it follows that the velocity component ðup Þiþ1=2;j;k at the n-th iteration is calculated from the values of the previous (n-1) iteration as
bi;j;k ¼
ða1 q1 þ a2 q2 a01 q01 a02 q02 Þi;j;k Dxi Dyj Dzk
Dt h ðn1Þ ðn1Þ ða1 q1 u1 þ a2 q2 u2 Þiþ1=2;j;k ðn1Þ ðn1Þ þ a2 q2 u2 Dyj Dzk a1 q1 u1 i1=2;j;k h ðn1Þ ðn1Þ ða1 q1 v 1 þ a2 q2 v 2 Þi;jþ1=2;k ðn1Þ ðn1Þ a1 q1 v 1 þ a 2 q2 v 2 D z k D xi i;j1=2;k ðn1Þ ðn1Þ a1 q1 w1 þ a2 q2 w2 i;j;kþ1=2 ðn1Þ ðn1Þ þ a2 q2 w2 Dxi Dyj a1 q1 w1 i;j;k1=2
ð38Þ
aiþ1;j;k ¼ ða1 q1 d1 þ a2 q2 d2 Þiþ1=2;j;k Dyj Dzk
ð39aÞ
ð31Þ
ai1;j;k ¼ ða1 q1 d1 þ a2 q2 d2 Þi1=2;j;k Dyj Dzk
ð39bÞ
This shows that the velocity at the (n-1)-th iteration is corrected in response to the pressure corrections to produce the velocity component at the n-th iteration. The correction formulas for the velocity components in other directions can be written similarly as
ai;jþ1;k ¼ ða1 q1 d1 þ a2 q2 d2 Þi;jþ1=2;k Dzk Dxi
ð39cÞ
ai;j1;k ¼ ða1 q1 d1 þ a2 q2 d2 Þi;j1=2;k Dzk Dxi
ð39dÞ
ai;j;kþ1 ¼ ða1 q1 d1 þ a2 q2 d2 Þi;j;kþ1=2 Dxi Dyj
ð39eÞ
ai;j;k1 ¼ ða1 q1 d1 þ a2 q2 d2 Þi;j;k1=2 Dxi Dyj
ð39fÞ
ai;j;k ¼ aiþ1;j;k þ ai1;j;k þ ai;jþ1;k þ ai;j1;k þ ai;j;kþ1 þ ai;j;k1
ð39gÞ
ðnÞ
ðn1Þ
ðup Þiþ1=2;j;k ¼ ðup Þiþ1=2;j;k ðdp Þiþ1=2;j;k ðp0iþ1;j;k p0i;j;k Þ
ðv p Þi;jþ1=2;k ¼ ðv p Þi;jþ1=2;k ðdp Þi;jþ1=2;k ðp0i;jþ1;k p0i;j;k Þ ðnÞ
ðn1Þ
ðnÞ
ðn1Þ
ðwp Þi;j;kþ1=2 ¼ ðwp Þi;j;kþ1=2 ðdp Þi;j;kþ1=2 ðp0i;j;kþ1 p0i;j;k Þ
ð32Þ ð33Þ
Further, the liquid and vapor mass conservation equations, represented by Eq. (1), are summed ! ! @ða1 q1 þ a2 q2 Þ þ r ða1 q1 u 1 þ a2 q2 u 2 Þ ¼ 0 @t
ð34Þ
and obtained Eq. (34) is discretized as
½ða1 q1 þ a2 q2 Þi;j;k ða01 q01 þ a02 q02 Þi;j;k Dxi Dyj Dzk
Dt þ ½ðða1 q1 u1 Þiþ1=2;j;k þ ða2 q2 u2 Þiþ1=2;j;k Þ ðða1 q1 u1 Þi1=2;j;k þ ða2 q2 u2 Þi1=2;j;k ÞDyj Dzk þ ½ðða1 q1 v 1 Þi;jþ1=2;k þ ða2 q2 v 2 Þi;jþ1=2;k Þ ðða1 q1 v 1 Þi;j1=2;k þ ða2 q2 v 2 Þi;j1=2;k ÞDzk Dxi
þ ½ðða1 q1 w1 Þi;j;kþ1=2 þ ða2 q2 w2 Þi;j;kþ1=2 Þ ðða1 q1 w1 Þi;j;k1=2 þ ða2 q2 w2 Þi;j;k1=2 ÞDxi Dyj ¼ 0
ð35Þ
where superscript 0 denotes a value from the initial (previous) time level, while all parameters without superscript are taken at the new time level. Volume fractions and densities at the scalar control volumes boundaries are determined with the upwind scheme, for example
( ðap Þiþ1=2;j;k ¼
ðap Þi;j;k ;
if
ðup Þiþ1=2;j;k > 0
ðap Þiþ1;j;k ; if
ðup Þiþ1=2;j;k < 0
ð36Þ
Dimensions of the control volume are calculated as Dxi ¼ xiþ1=2 xi1=2 , Dyj ¼ yjþ1=2 yj1=2 , and Dzk ¼ zkþ1=2 zk1=2 . Finally, velocity Eqs. (31)-(33) are introduced into the discterized mass balance Eq. (35) and the pressure-correction equation is derived as
ai;j;k p0i;j;k ¼ aiþ1;j;k p0iþ1;j;k þ ai1;j;k p0i1;j;k þ ai;jþ1;k p0i;jþ1;k þ ai;j1;k p0i;j1;k þ ai;j;kþ1 p0i;j;kþ1 þ ai;j;k1 p0i;j;k1 þ bi;j;k where
ð37Þ
The resulting discretized equations are solved iteratively with the line-by-line method and with the application of the TreeDiagonal-Matrix-Algorithm (TDMA) procedure [22]. For the calculation of a steady-state condition, the transient calculation procedure is performed with constant boundary conditions, in the following steps: 1. The liquid volume fraction, the liquid enthalpy and the oil mass fraction are calculated for the scalar control volumes from the set of difference equations resulting from Eqs. (1), (4) and (5) respectively. 2. The liquid and gas phase velocity components are calculated for the staggered momentum control volumes, from projections of Eq. (3). 3. The pressure equations, obtained by combining the mass and momentum conservation equations, are solved for the scalar control volumes. 4. The time is increased and the new values are taken as the initial ones for the new time step of integration. 5. Steps 1 to 4 are repeated until the two-phase mixture mass conservation is achieved within a specified relative error for every scalar control volume. The satisfaction of the two-phase mixture mass conservation for every scalar control volume, step 5, implies also that the overall mass balance, for the whole flow domain is achieved in the steadystate conditions. The relative error of the mass balance for each control volume is calculated as
er;CV i;j;k ¼
jbi;j;k jDt ða1 q1 þ a2 q2 Þi;j;k Dxi Dyj Dzk
ð40Þ
The accuracy of calculation is also quantified by the relative error of the integral mass balance for the whole flow domain, which is calculated as the absolute value of the difference of inlet
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and outlet two-phase mixture mass flow rates divided by the inlet two-phase mixture mass flow rate
er;INT
! !
R R ! ! ! !
ð a q u þ a q u Þ d A ð a q u þ a q u Þ d A 2 2 2 1 1 1 2 2 2
Ainlet 1 1 1
Aoutlet ¼ ! R ! ! ða1 q1 u 1 þ a2 q2 u 2 Þ d A Ainlet ð41Þ
The relative error of dependent flow parameter U (the liquid volume fraction, enthalpy, oil mass fraction and the liquid and vapor phase speed) is calculated as
er;U ¼
jU U 0 j jUj
ð42Þ
3. Results and discussion The validation of the developed three-dimensional model for the prediction of refrigerant and oil two-phase flow and oil retention in the evaporator was performed for experimental conditions presented by Jin and Hrnjak [10,42]. The four pass plate and fin evaporator used in the test facility is shown in Fig. 2. The refrigerant and oil two-phase mixture inflows the top header on the right. The top header is partitioned into three parts denoted in Fig. 2 as header #1, #3 and #5, while the bottom header is portioned into headers #2 and #4. The first pass of the refrigerant and oil two-
phase mixture is directed downwards from the top header #1 to the header #2, the second flow pass is directed upwards from the header #2 to the header #3 and so forth through the third and the fourth pass till the outlet on the left end of the top header. The refrigerant and oil mixture is heated by the outside air flow, the liquid refrigerant evaporates and depletes in the mixture with oil along the flow path, and the two-phase mixture of vapor and liquid with a high concentration of oil outflows from the evaporator towards the compressor. At the evaporator outlet the refrigerant is superheated. The measured and numerically simulated operating conditions of the evaporator are presented in Table 1. One set of experiments was performed with the refrigerant R134a and the other with R1234yf, while PAG oil was used as lubricant in both experimental sets. The refrigerant pressure at the evaporator inlet was approximately 3.0 bar in experiments with R134a, while it was approximately 3.3 bar in case of experiments with R1234yf. The refrigerant vapor superheating at the evaporator outlet was in the range from 13.9 to 15.7 °C. The vapor flow quality at the evaporator inlet was approximately 0.24 in experiments with R134a and 0.33 in experiments with R1234yf. The vapor flow quality in the two-phase refrigerant and oil mixture is defined as
_ R;2 =ðm _ Rþm _ OÞ x¼m
ð43Þ
_ R;2 is the refrigerant vapor mass flow rate, while m _ R and m _O where m are the total (vapor and liquid) refrigerant and oil mass flow rates respectively.
a)
Posion of channel inlets
b) Fig. 2. Plate and fin evaporator: (a) a view of the evaporator with indicated refrigerant flow passes – top (width height depth = 254.6 mm 228.6 mm 73 mm, header diameter = 33 mm), (b) a view of the evaporator header inside – bottom [42].
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V.D. Stevanovic, P. Hrnjak / Applied Thermal Engineering 117 (2017) 468–480 Table 1 Measured and simulated operating conditions [42]. Experiment
E1
E2
E3
E4
E5
E6
E7
Refrigerant Oil Inlet pressure (bar) Outlet superheat (°C) Inlet flow quality, x OCR (%) Inlet oil mass fraction, g O;1 _ (g/s) Refrigerant and oil mass flow rate, m Air inlet temperature (°C) 3 Air flow rate (m /h)
R134a PAG 3.0 14.5 0.24 2.1 0.028 25.45 35 489 3.99/4.05
R134a PAG 3.0 13.9 0.24 3.3 0.043 25.45 35 489 3.92/3.98
R134a PAG 3.0 15.7 0.24 3.8 0.05 25.45 35 489 3.95/3.99
R1234yf PAG 3.3 15.7 0.33 2.3 0.034 34.72 35 489 4.19/4.14
R1234yf PAG 3.3 15.5 0.33 3.8 0.057 35.04 35 489 4.22/4.08
R1234yf PAG 3.3 15.6 0.33 4.0 0.060 34.79 35 489 4.26/4.04
R1234yf PAG 3.3 15.7 0.33 2.9 0.043 51.4 35 489 6.06/6.08
Measured / calculated heat flow to refrigerant, Q_ e (kJ/s)
Three experiments with R134a and three experiments with R1234yf were performed with lower refrigerant and oil mixture mass flow rates equal to approximately 25.45 g/s and 35 g/s respectively, while one experiment with R1234yf was performed with the higher mass flow rate of 51.4 g/s. The oil in circulation ratio (OCR) values ranged from 2.1 to 4.0, as presented in Table 1, where
_ O =ðm _ Rþm _ OÞ OCR ¼ m
ð44Þ
The oil mass fraction in the mixture with liquid refrigerant is calculated as
g O;1 ¼ OCR=ð1 xÞ;
ð45Þ
and the corresponding values at the evaporator inlet are presented in Table 1. The last row in Table 1 presents the measured and calculated heat flow rate from the air to the refrigerant in the evaporator. The calculated values are predicted by the following Eq. (46) based on the results of the numerical simulations
Q_ e ¼
Z
!
Aoutlet
!
!
ða1 q1 h1 u 1 þ a2 q2 h2 u 2 Þ d A !
!
þ a2 q2 h2 u 2 Þ d A
Z
Ainlet
defined by SAE standard [45]. It is usually regarded as the ‘‘design condition”, which has to prove the sufficient cooling capacity of the system. The experiment E7 corresponds to L35 condition with higher compressor speed [45]. The refrigerant and oil masses in the evaporator were measured by the intrusive method. The evaporator content was trapped by instantaneous closing of the inlet and outlet valves after a longer period of steady state operation, and its content was directly measured, as described by Jin and Hrnjak [10]. The high accuracy below 2% was achieved in the refrigerant and oil mass measurements [10]. The presented operating conditions of the evaporator were simulated with the developed three-dimensional model for the following boundary conditions: (a) The homogeneous two-phase flow at the top header inlet was assumed. The inlet void fraction is calculated according to [46] as
a2 ¼
!
ða1 q1 h1 u 1 ð46Þ
As presented, a good agreement is obtained between measured and calculated values, with the relative error smaller than 6% for experiments E5 and E6 and smaller than 2% for all other experiments. The heat flow to the refrigerant is approximately 4 kJ/s for six experiments (from E1 to E6), which were performed both with R134a (experiments E1, E2, and E3) and R1234yf (experiments E4, E5 and E6). It should be mentioned that the nearly constant heat flow to both refrigerants and different inlet flow qualities, together with different heat of evaporation of R134a and R1234yf are the cause of different refrigerants mass flow rates between experiments performed with R134a and experiments with R1234yf. As mentioned above, in the experiments E1, E2 and E3 with R134a, the mass flow rate is 25.45 g/s and the inlet flow quality is 0.24, while in the experiments E4, E5 and E6 with R1234yf these values are greater, approximately 35 g/s and 0.33 respectively. In addition, the heat of evaporation of these two refrigerants are different - the heat of evaporation of R134a is 198.2 kJ/kg at the evaporator operating inlet pressure of 3 bar [43] and the value for R1234yf is smaller, 161.4 kJ/kg at the inlet pressure of 3.3 bar [44]. Therefore, the mass flow rate is greater in experiments with R1234yf in order to achieve the same heat flow rate as in the experiments with R134a that has the greater heat of evaporation and which inlet flow quality is lower 0.24. The heat flow in the experiment E7 is greater, approximately 6 kJ/s, and consequently the refrigerant mass flow rate is greater 51.4 g/s. The experiments from E1 to E6 correspond to the idle condition (I35) of the automotive air conditioning system operation, as
1 1 þ 1x x
q2 q1
ð47Þ
where the inlet flow quality values x are presented in Table 1. The inlet liquid and vapor velocities are calculated from the prescribed mass flow rates as
u1 ¼ u2 ¼
_ m ½ð1 a2 Þq1 þ a2 q2 A
ð48Þ
where A is the cross sectional area of the inlet tube and the mass flow rate values are presented in Table 1. The inlet enthalpy is predicted with Eq. (14) for the inlet pressure presented in Table 1 and the bubble point temperature calculated with Eqs. (15)-(17). The inlet oil mass fraction is presented in Table 1, as well as the air inlet mass flow rate and temperature. It should be mentioned that the two-phase flow pattern at the inlet of the header might have the influence on the liquid and vapor flow distribution from the header towards the parallel flow channel. For instance, in [17] the annular flow pattern is prescribed in order to achieve a good agreement between calculated and measured liquid refrigerant distribution from the header towards parallel channels of an evaporator. But, in here performed experiments the inlet part of the header is short, it is partitioned from the rest of the header (the header #1 in Fig. 2) and the refrigerant-oil mixture is distributed only to four downward channels. Hence, the simulations performed with the homogeneous inlet flow conditions and the annular flow pattern at the header inlet showed that there was no practical difference between results obtained for these two different inlet conditions. (b) The applied evaporator model also comprises the evaporator outlet pipe in the length of 0.05 m and the constant pressure
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boundary condition was applied at this outlet boundary. The constant pressure at the evaporator outlet is applied by setting to zero the pressure correction p0 at the outlet boundary volumes, as presented in [47]. (c) The no-slip velocity conditions were applied at the flow channel walls. (d) The heat flux from the hotter air stream to the colder refrigerant-oil flow inside the evaporator is calculated according to Eqs. (22)-(25). The grid refinement tests were performed in order to determine the sensitivity of the calculated mass of retained oil on the number of control volumes (CVs), as presented in Table 2. It was shown that the relative difference between the results obtained with grids 32 68 68 and 32 136 134 is less than 2%. Due to the long calculation time of the oil accumulation transients in the evaporator, the adopted grid for the simulations of the evaporator operating conditions has 32 68 68 = 147,968 control volumes. The first simulation was started with the evaporator filled only with vapor, and the transient calculation was performed until the steady state condition was achieved. The simulation time period was 300 s with the grid 32 68 68. Due to the required low time step of integration in the range from 0.0004 s till 0.0008 s, the calculation time on the PC computer with i7 2.6 GHz processor was approximately 20 days, while in case with 32 136 134 control volumes the calculation time was almost two times longer. In order to speed up the simulations, the initial states for other simulations with different OCR and/or other different operational parameters, but the same geometry of the evaporator and the same number of control volumes, were defined as calculated steadystate conditions of the previous simulations, which resulted in the substantial reduction of the simulation time regarding the first simulation. Fig. 3 shows the transients of oil retention predicted with different numerical grids. The prediction with the fine grid with 32 136 134 control volumes (CVs) shows slower increase of oil retention than results obtained with the coarser grids. This effect was caused by the application of the greater time step of integration in case of the fine grid, which was done in order to speed up the calculation. It should be mentioned that in case with the fine grid the calculation was stable with the time step up to 0.0008 s, while in cases with the coarser grids the stability of the simulation transients was jeopardized with time steps greater than 0.0004 s. The relative error of the mass balance for each control volume, calculated with Eq. (40), was lower than 104 during the transient accumulation of oil and refrigerant for all simulations presented in this paper, while its value was order of magnitudes lower upon reaching the steady-state conditions (approximately after 150 s for all performed simulations, as presented in Fig. 3). The relative error of all dependent parameters, calculated with Eq. (42), was below 105. A difference between the refrigerant and oil inflow and outflow from the evaporator exists during the transient accumulation of liquid, while the relative error of the integral mass balance for the whole flow domain, as defined with Eq. (41), was satisfied with the value below 0.01 upon reaching the steady-state conditions. Fig. 4 shows the dependence of the calculated and measured refrigerant and oil masses in the evaporator on OCR value. The relative differences between the calculated and measured masses of
60 50
Mass (g)
40 30
32x136x134 CVs 32x68x68 CVs 16x68x68 CVs 16x34x68 CVs Measured
20 10 0 0
100
200
Time (s) Fig. 3. Transient oil accumulation in the evaporator for different grid refinements.
oil and refrigerant in the evaporator, calculated as ðmcalc mmeas Þ=mmeas ), are shown in Fig. 5. In cases with greater OCR values, i.e. the experiment E3 with refrigerant R134a and OCR equal to 3.8 and the experiments E5 and E6 with refrigerant 1234yf and OCR equal respectively to 3.8 and 4.0, the relative difference between the calculated and measured mass of retained oil is greater, in the range from 13% to 22%. For the same experiments the relative difference between calculated and measured refrigerant mass is small, below 3%. In cases of other experiments E1 and E2 with R134a and E4 and E7 with 1234yf and respective OCR values 2.1, 3.3, 2.3 and 2.9, the relative difference between the calculated and measured masses of retained oil is in the range from 3% for E7 to 11% for E4. The relative differences of calculated and measured refrigerant masses for these experiments (E1, E2, E4 and E7) are in the range from 6% (E1) to 14% (E7). The obtained relative differences between the calculated and measured oil and refrigerant masses are smaller than ±15% for all experiments, except in case of the retained oil prediction for experiment E6. The achieved relative difference with the one-dimensional model for the same experimental conditions was ±20%, as reported in [13]. It should be mentioned that the one-dimensional model prediction is based on the assumption that the liquid refrigerant and oil mixture level in the bottom header is located at the inlets of the evaporating channels, as indicated in Fig. 2, whereas in case of the three-dimensional model simulation the position of the liquid layer is predicted by the model itself and it completely differs from the one-dimensional model assumption, as presented in Figs. 7 and 14 below. In [4,11] the reported relative difference between calculated and measured mass of retained oil in the evaporator is ±29%. Therefore, the three-dimensional model provides more reliable predictions of oil and refrigerant masses in the evaporator than the one-dimensional models. In cases of E1, E2 and E3 experiments with R134a the calculated and measured values show the same trend in Fig. 4. The mass of retained oil slightly increases with the increase of OCR, while the mass of refrigerant in the evaporator is practically constant. In cases of E4, E5 and E6 experiments with 1234yf, the calculated values of oil retention show a smaller increase with the increase of OCR than the measured data (Fig. 4). Both the measured and calculated values of refrigerant
Table 2 Dependence of the calculated oil retention on the applied grid (simulated experiment is E1 from Table 1, refrigerant and oil mass flow rate = 25.45 g/s, inlet pressure = 0.3 MPa, inlet quality = 0.24, OCR = 2.1%, refrigerant outlet temperature 13 °C). Grid (number of control volumes)
16 34 68 = 36,992 CVs
16 68 68 = 73,984 CVs
32 68 68 = 147,968 CVs
32 136 134 = 583,168 CVs
Mass of retained oil (g)
51.5
46.9
42.3
41.5
V.D. Stevanovic, P. Hrnjak / Applied Thermal Engineering 117 (2017) 468–480
Mass (g)
140
477
Measured oil (R134a exp.)
120
Calculated oil (R134a exp.)
100
Measured R134a
80
Calculated R134a Measured oil (1234yf exp.)
60
E7
40
Calculated oil (1234yf exp.) Measured 1234yf
20
E1
E3 E5 E6
E2 E4
0 1.5
2
2.5
3
3.5
4
Calculated 1234yf
4.5
OCR (%) Fig. 4. Measured and calculated refrigerant and PAG oil content in the evaporator versus OCR (E1 till E7 label experimental conditions as presented in Table 1).
150
Calculated (g)
Fig. 7. Void fraction in the vertical plane of symmetry (experiment E1 with R134a).
100
+15% 50
0
-15% Oil (R134a exp.) Oil (1234yf exp.) R134a 1234yf
0
50
100 Measured (g)
150
Fig. 5. Comparison of measured and calculated refrigerant and PAG oil content in the evaporator.
Fig. 6. 3D view of void fraction in the evaporator (experiment E1).
mass in the evaporator show the same increase with the OCR increase in cases of E4, E5 and E6 experiments. The experiment E7 with refrigerant 1234yf is performed with the mass flow rate of 51.4 g/s, which is two times greater value than the mass flow rate of experiments E1, E2 and E3 with refrigerant R134a and approximately 47% greater than the mass flow rate of experiments E4, E5 and E6 with refrigerant 1234yf (Table 1). Hence, the mass of retained oil is lower in E7 experiment compared to other experiments, which is the result of a greater drag between the vapor and liquid fluid streams under the greater refrigerant mass flow rate. The calculated mass of refrigerant accumulated in the evapo-
rator in the case of E7 experiment is in line with the results obtained for other experiments with 1234yf refrigerant (experiments E4, E5 and E6), while the measured value of E7 shows a greater discrepancy from this trend. It might be concluded that the dependence of the calculated data on the OCR values is more consistent than in cases of the measured data, which indicates a greater scattering of measured data in performed experiments. Generally, the results presented in Fig. 4 show an overall agreement between calculated and measured values. In addition, it is observed that both the measured and calculated results show a greater refrigerant mass presence in the evaporator in experiments with R134a than in experiments with R1234yf in the range from approximately 35% (the comparison of E1 and E4 data) to approximately 21% (the comparison of E3 and E6 data), (in Fig. 4 the calculated R134 mass is approximately 120 g, while the calculated R1234yf mass ranges from 89 in E4 till 99 g in E6). The R1234yf mass in the evaporator is smaller since the inlet flow quality and the mass flow rate of R1234yf are greater than in experiments with R134a, i.e. the higher inlet quality means less refrigerant liquid inflow, while the greater mass flow rate results in greater velocities and greater interfacial shears between the liquid and vapor phase that leads to the smaller accumulation of liquid phase in ‘‘dead” flow zones in headers (this issue is further explained by Figs. 14 and 15 and discussion at the end of this section). The mass of retained oil in the experiments E1, E2 and E3 with R134a is also greater than in the experiments E4, E5 and E6 with R1234yf, but by smaller amounts than the ratio of refrigerant masses in E1, E2 and E3 and experiments E4, E5 and E6. The retained oil mass in the experiment E1 is 15% greater than in E4 and in the experiment E3 it is 22% greater than in E6. The three-dimensional view at the void fraction in the evaporator for experiment E1, together with indicated numerical mesh with 32 68 68 control volumes, is shown in Fig. 6. The void fraction in the two-phase mixture at the header inlet is about 0.96 according to Eq. (47) for the homogeneous two-phase mixture parameters at the evaporator inlet pressure of 0.3 MPa, the inlet two-phase mixture quality 0.24, the liquid density q1 ¼ 1281 kg m3 (calculated with Eq. (7) for OCR = 0.021, g O;1 ¼ 0:028, qR;1 ¼ 1291 kg m3 , qO;1 ¼ 1000 kg m3 ) and the vapor density q2 ¼ 14:8 kg m3 . Regarding this high inlet void fraction and the evaporation process in the evaporator, the evaporator flow channels are mostly filled with vapor, while the liquid phase is collected mainly in the bottom header and within some evaporating channels with upward flow, as presented in Fig. 6. The cross section in Fig. 7 shows that liquid layers are collected
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in the bottom header below the parallel channels with the upward flow and in the smaller amount in the top header above the parallel evaporating channels. A liquid film also flows at the bottom of the evaporator outlet tube and it mainly consists of oil. A two phase mixture with void fraction between 0.6 and 0.8 is observed in some evaporating channels with upward flow, while in the channels with downward flows the vapor void fraction is high with values above 0.9. This difference between the distribution of vapor and liquid volumes in the upward and downward flow channels is also shown in Fig. 8. As presented, the downward flow channel is almost empty of liquid and only a small amount of liquid film is collected in the top and bottom headers. On the contrary, the upward flow channel contains two-phase mixture with a higher liquid fraction and a thicker liquid film exists in the bottom header below this upward flow channel. The oil mass fraction in the mixture with the liquid refrigerant is shown in Fig. 9. The oil mass fraction gradually increases from the evaporator inlet towards the outlet. The highest oil mass fraction exists in the channels with the lowest liquid fraction, which means that the droplets or thin liquid films are formed mainly by oil as the result of intensive evaporation. The oil mass per unit volume of the flow channel is determined by the product a1 q1 g O;1 and it is presented in Fig. 10. The locations of oil retention presented in Fig. 10 are the same as the locations of liquid accumulation presented in Fig. 7. As shown, the oil retains within the liquid layers in the headers and in some amount in the upward flowing liquid lumps in the evaporating channels. The liquid and vapor velocity fields are shown in Figs. 11 and 12. The liquid speed is the highest in the downward flow in the evaporating channels, it is lower in the upward flow in the evaporating channels and the circulation is shown in the liquid layers in the headers. In the volumes filled only with vapor, the liquid velocity is zero. The vapor velocity field through the evaporator vertical plane of symmetry shows both the upward flow in upper parts of the evaporating channels and the downward flow in lower parts of the evaporating channels. This is the result of a complex flow filed with recirculation zones and with non-uniform velocity vectors along the channel width, as presented in Fig. 13. Fig. 14 shows the void fraction in the vertical plane of symmetry of the evaporator, obtained by the numerical simulation of experiment E4 that is performed with refrigerant R1234yf. Compared to Fig. 7, related to the experiment E1 with refrigerant R134a, it can be observed that the liquid accumulation in the corners of bottom header is lower in Fig. 14 (locations of the predominant
Fig. 9. Oil mass fraction in the mixture with liquid refrigerant in the vertical plane of symmetry (experiment E1).
Fig. 10. Oil concentration (kg m3) in the vertical plane of symmetry (experiment E1).
Fig. 11. Liquid velocity in the vertical plane of symmetry (experiment E1).
Fig. 8. Void fraction in vertical cross sections through the third plate channel from the inlet with downward flow (left) and seventh channel from the inlet with upward flow (right), (experiment E1).
refrigerant-oil liquid retention in the bottom header are circled with dashed lines both in Figs. 7 and 14 and a lower amount of liquid volume is observed in Fig. 14). As mentioned in the above discussion related to Fig. 4, which also shows the smaller mass of R1234yf compared to R134a mass in the evaporator, the smaller
V.D. Stevanovic, P. Hrnjak / Applied Thermal Engineering 117 (2017) 468–480
Fig. 12. Vapour velocity in the vertical plane of symmetry (experiment E1).
479
Fig. 15. Vapor velocity in the vertical plane of symmetry (experiment E4 with R1234yf).
velocity field in the evaporator in case of the experiment E4 with R1234yf is shown in Fig. 15. A somewhat greater vapor speed can be observed in Fig. 15 in case of R1234yf flow than in Fig. 12 in case of R134a flow both in upward and downward flows in vertical plate channels and in the bottom and top headers of the evaporator. Other three-dimensional characteristics of the refrigerant and oil two-phase flow in the evaporator in the experimental cases with R1234yf are similar to the results presented in Figs. 6–13. 4. Conclusions
Fig. 13. Vapor velocity vectors in the vertical cross sections through the second plate channel from the inlet with downward flow (left) and seventh channel from the inlet with upward flow (right), (experiment E1).
The numerical model for the simulation of three-dimensional liquid and oil two-phase flow in the components of the vapor compression refrigerant system is presented and it is applied to the simulation of seven operating conditions in the evaporator of the automotive air-conditioning system. Three simulated experiments were performed with refrigerant R134a and four experiments with R1234yf, while PAG oil was applied in all experiments. The obtained results provide the complete three-dimensional picture of the two-phase flow in the evaporator headers and evaporating channels. The major findings are: – Oil mainly retains in the liquid layers in the headers in the mixture with refrigerant, the greatest oil retention is in the bottom header, while lower amounts of oil retains in the top header and in parallel evaporating channels with upward refrigerant flow. – Liquid layers are non-uniformly distributed in the headers. The liquid layers are the greatest in the bottom headers below the evaporating channels with upward flow. – The evaporating channels with downward flow are almost empty of liquid phase, while liquid lumps exist in the upward flow in the evaporating channels. – The high non-uniformity of the refrigerant liquid and vapor phase distribution from the header towards the parallel evaporating channels is confirmed.
Fig. 14. Void fraction in the vertical plane of symmetry (experiment E4 with R1234yf).
content of R1234yf in the evaporator is the result of the higher inlet flow quality of the refrigerant and the greater refrigerant mass flow rate and liquid velocities in the evaporator. The vapor
The relative difference between calculated and measured oil and refrigerant masses in the evaporator is lower than ±15%, except in one experiment, which is more reliable prediction than previously obtained with the one-dimensional models presented in [11,13]. The developed numerical modeling method is a support to the design of refrigerant components and pre-validation of the required oil content within the refrigerant system.
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