Numerical investigation of boiling heat transfer on hydrocarbon mixture refrigerant in vertical rectangular minichannel

Abstract

In order to investigate the characteristics of boiling heat transfer for hydrocarbon mixture refrigerant in plate-fin heat exchanger which is used in the petrochemical industry field, a model was established on boiling heat transfer in vertical rectangular channel. The simulated results were compared with the experimental data from literature. The results show that the deviation between the simulated results and experimental data is within ±15%. Meanwhile, the characteristic of boiling heat transfer was investigated in vertical rectangular minichannel of plate-fin heat exchanger. The results show that the boiling heat transfer coefficient increases with the increase in quality and mass flux and is slightly impacted by the heat flux. This is because that the main boiling mechanism is forced convective boiling while the contribution of nucleate boiling is slight. The correlation of Liu and Winterton is in good agreement with the simulation results. The deviation between correlation calculations and simulation results is mostly less than ±15%. These results will provide some constructive instructions for the understanding of saturated boiling mechanism in a vertical rectangular minichannel and the prediction of heat transfer performance in plate-fin heat exchanger.

Keywords

Plate-fin heat exchanger boiling heat transfer mixture model computational fluid dynamics

Introduction

In the recent years, compact heat exchangers with minichannel types are widely concerned, which present several advantages such as reduced size and higher efficiency, with the benefit of both cost and safety. Plate-fin heat exchangers (PFHE), as a type of compact exchangers with high performance, have been widely used in petrochemical industry field.^1–4 It consists of many rectangular minichannels. The gap size of rectangular minichannels is usually about 0.5–10 mm^5–7 in the PFHE. It is a key technology to predict the boiling heat transfer performance on hydrocarbon mixture refrigerant in a rectangular minichannel for the PFHE in petrochemical industry field.⁸ However, the realistic phenomena have scarcely been explored on boiling heat transfer for hydrocarbon mixture refrigerant in a rectangular minichannel until now.⁹

Although many investigations have been done to investigate the phenomena of boiling heat transfer in the minichannel of compact heat exchangers, there are many contradictions in the available literature on this subject.^10,11 Meanwhile, because of the complexity of the phenomenon of boiling heat transfer on hydrocarbon mixture refrigerant and the limitations of computational technology and measurements,^1,12–14 it is still under open discussion for the mechanism to dominate the boiling heat transfer in the vertical rectangular minichannel. For example, the boiling heat transfer coefficient is not dependent on vapor quality while dependent on heat flux according to Feldman et al.¹⁵ and Ma et al.¹⁶ In other words, the nucleate boiling and forced convection boiling are the main mechanisms for boiling heat transfer in the minichannel. According to the literature,^14,17–23 the heat flux and system pressure have a certain influence on the boiling heat transfer coefficient while the dependency on vapor quality and mass flux is insignificant. The above results show that the key mechanism for boiling heat transfer in the minichannel is nucleate boiling while the forced convective boiling is slight. At the same time, Sumith et al.¹⁰ also experimentally surveyed the boiling heat transfer on water in a vertical minichannel with 1.45 mm diameter under the atmospheric pressure. The results show that the main heat transfer mechanism for the saturated boiling heat transfer in a vertical minichannel is the liquid film evaporation. Most of the above investigations are mainly focused on the boiling heat transfer of simplex refrigerant in minichannel. At the same time, the understanding of the heat transfer mechanism is not clear on boiling heat transfer in the minichannel according to the above analysis.^24–26

At the same time, because of the practical significance of heat transfer coefficient correlation in the boiling heat transfer performance design of PFHE, many investigations have been made on correlating boiling heat transfer coefficient and many correlations have also been obtained on the basis of experimental data in the minichannel.^27,28 Nevertheless, it is very difficult to find a reasonable and accurate correlation to calculate the boiling heat transfer coefficient in the minichannel of PFHE.^29,30

In this article, a model on boiling heat transfer in vertical rectangular minichannel of PFHE was established and validated by the experiment data from literature. The characteristics of boiling heat transfer were investigated on hydrocarbon mixture refrigerant in vertical rectangular minichannel. A correlation was proposed to calculate the boiling heat transfer coefficient on hydrocarbon mixture refrigerant in a vertical rectangular minichannel.

Analysis of mathematic-physical mode

In this article, the characteristics of saturated boiling heat transfer was investigated on hydrocarbon mixture refrigerant in a vertical rectangular minichannel whose cross-section dimension is 1.6 × 6.3 mm and the length is 200 mm. The analysis model is depicted in Figure 1.

Figure 1.

The vertical rectangular minichannel model.

Simulation mechanism

In order to investigate the boiling heat transfer in a vertical rectangular minichannel, the inhomogeneous two-fluid model and thermal phase change model are used. For conservation of mass, momentum, energy, and turbulent quantities for the study in a Cartesian coordinate system, the Reynolds-averaged governing equations can be written as follows:

Mass conservation

\frac{\partial}{\partial t} (r_{g} ρ_{g}) + \nabla \cdot (r_{g} ρ_{g} U_{g}) = Γ_{gl}

(1)

\frac{\partial}{\partial t} (r_{l} ρ_{l}) + \nabla \cdot (r_{l} ρ_{l} U_{l}) = Γ_{\lg}

(2)

where r, ρ, and U represent the volume fraction, density, and velocity, respectively. Subscripts g and l denote vapor phase and liquid phase, respectively. $Γ_{gl}$ is the mass flow rate from liquid phase to vapor phase in per unit volume. It can be written as

Γ_{gl} = {\overset{\cdot}{m}}_{gl} A_{gl}

(3)

where ${\overset{\cdot}{m}}_{gl}$ represents the mass flow rate from liquid phase to vapor phase in per unit interfacial area. $A_{gl}$ is the interfacial area density between liquid phase and vapor phase. It can be calculated based on the thermal phase change model.

For the mixture model in CFX, $A_{gl}$ can be written as

A_{gl} = \frac{r_{g} r_{l}}{d_{gl}}

(4)

where $d_{gl}$ represents the interfacial length scale between vapor phase and liquid phase.

According to equations (3) and (4), the mass flow rate in per unit volume is related to the interfacial length scale and the interphase mass flux. The interfacial length scale between liquid phase and vapor phase can be written as

d_{gl} = \sqrt{\frac{{\bar{r}}_{g} {\bar{r}}_{l} {\bar{λ}}_{gl} N u_{gl} (1 - γ) l}{2 m x_{out} C_{pg}}}

(5)

where $γ$ , $C_{pg}$ , $x_{out}$ , and m are the vaporization rate, the mixture heat capacity, the quality in outlet, and the mass flow rate, respectively. The vaporization rate can be calculated in terms of the literature.³¹

Momentum conservation

\begin{matrix} \frac{\partial}{\partial t} (r_{g} ρ_{g} U_{g}) + \nabla \cdot (r_{g} (ρ_{g} U_{g} \otimes U_{g})) \\ = \nabla \cdot (r_{g} (μ_{g} + μ_{tg}) (\nabla U_{g} + {(\nabla U_{g})}^{T})) \\ - r_{g} \nabla p'_{g} + r_{g} (ρ_{g} - ρ_{ref}) g + M_{g} \end{matrix}

(6)

\begin{matrix} \frac{\partial}{\partial t} (r_{l} ρ_{l} U_{l}) + \nabla \cdot (r_{l} (ρ_{l} U_{l} \otimes U_{l})) \\ = \nabla \cdot (r_{l} (μ_{l} + μ_{tl}) (\nabla U_{l} + {(\nabla U_{l})}^{T})) \\ - r_{l} \nabla p'_{l} + r_{l} (ρ_{l} - ρ_{ref}) g + M_{l} \end{matrix}

(7)

where p, µ, and µ_t represent pressure, viscosity, and turbulent viscosity, respectively. M represents the total of interfacial forces taking on a phase as a result of the existence of other phase, that is, momentum transfer and drag forces with interphase mass transfer and so on. The $(\nabla U)^{T}$ is the transpose of a matrix $\nabla U$ and operator ⊗ is a tensor product.

In this article, the standard k-ε turbulent model is used in vapor phase and liquid phase, respectively. For the liquid phase, the turbulent viscosity is modeled as

μ_{tl} = C_{μ} ρ_{l} (\frac{k_{l}^{2}}{ε_{l}})

(8)

where C_µ is a constant given as 0.09. ε and κ represent turbulence dissipation rate and turbulence kinetic energy of vapor phase, respectively. Turbulent kinetic energy and turbulence dissipation rate transmission equation for vapor phase can be written as

\frac{\partial}{\partial t} (r_{l} ρ_{l} k_{l}) + \nabla \cdot (r_{l} (ρ_{l} U_{l} k_{l} - (μ_{l} + \frac{μ_{t l}}{σ_{k}}) \nabla k_{l})) = r_{l} (P_{k l} - ρ_{l} ε_{l})

(9)

\begin{matrix} \frac{\partial}{\partial t} (r_{l} ρ_{l} ε_{l}) + \nabla \cdot (r_{l} (ρ_{l} U_{l} ε_{l} - (μ_{l} + \frac{μ_{tl}}{σ_{ε}})) \nabla ε_{l}) \\ = r_{l} \frac{ε_{l}}{k_{l}} (C_{ε 1} P_{kl} - C_{ε 2} ρ_{l} ε_{l}) \end{matrix}

(10)

where C_ε₁, C_ε₂, σ_k, and σ_ε are 1.44, 1.92, 1.3, and 1.0, respectively. According to viscous and buoyancy forces modeled, the vapor phase turbulence production $P_{kl}$ can be written as

P_{k l} = μ_{t l} \nabla U_{l} \cdot (\nabla U_{l} + \nabla U_{l}^{T}) - \frac{2}{3} \nabla \cdot U_{l} (3 μ_{t l} \nabla \cdot U_{l} + ρ_{l} k_{l}) + P_{k b l}

(11)

where $P_{kbl}$ is the vapor phase buoyancy production term. For the full buoyancy model, it can be written as

P_{kbl} = - \frac{μ_{tl}}{\Pr_{tl}} g \cdot \nabla ρ_{α}

(12)

Energy conservation

\frac{\partial}{\partial t} (r_{g} ρ_{g} H_{g}) + \nabla \cdot (r_{g} ρ_{g} U_{g} H_{g}) = \nabla \cdot (r_{g} λ_{g} T_{g}) + Q_{g} + Γ_{g l} H_{g s}

(13)

\frac{\partial}{\partial t} (r_{l} ρ_{l} H_{l}) + \nabla \cdot (r_{l} ρ_{l} U_{l} H_{l}) = \nabla \cdot (r_{l} λ_{l} T_{l}) + Q_{l} + Γ_{l v} H_{l s}

(14)

where H and λ represent the enthalpy and thermal conductivity, respectively. Q represents the interphase sensible heat transfer to one phase across interfaces with the other phase. $Γ_{gl} H_{gs}$ represents heat transfer induced by interphase mass transfer into vapor phase. $H_{gs}$ represents interfacial values of enthalpy passed to vapor phase due to phase change. According to the thermal phase change model, the total heat transfer produced by interphase mass transfer is equal to the total interphase sensible heat transfer. Therefore, it can be given as

Q_{g} + Q_{l} = - (Γ_{gl} H_{gs} + Γ_{\lg} H_{ls})

(15)

Substituting equation (3) in equation (15), the interphase mass flux from liquid phase to vapor phase, ${\overset{\cdot}{m}}_{gl}$ , can be given as

{\overset{\cdot}{m}}_{gl} = \frac{Q_{g} + Q_{l}}{A_{gl} (H_{ls} - H_{gs})}

(16)

Based on the two resistance models in CFX, the sensible heat transfer process is achieved by defining two heat transfer coefficients on each side of the phase interface. Therefore, the interphase sensible heat transfer to liquid phase and that to vapor phase can be expressed as, respectively

Q_{l} = h_{l} A_{gl} (T_{s} - T_{l})

(17)

Q_{g} = h_{g} A_{gl} (T_{s} - T_{g})

(18)

where $h_{l}$ and $h_{g}$ represent the heat transfer coefficient of liquid phase and vapor phase on one side of the phase interface between vapor phase and liquid phase, respectively. T_s is the interfacial temperature. By considering thermodynamic equilibrium and ignoring effects of surface tension on pressure, the interfacial temperature can be written as

T_{s} = T_{sat}

(19)

where $T_{sat}$ represents the saturation temperature.

In this study, a zero resistance condition is adopted for the liquid phase on one side of the phase interface, which is to make the interfacial temperature have the same temperature with the liquid phase, $T_{s} = T_{l}$ . For the vapor phase, the heat transfer coefficient $h_{g}$ can be written as

h_{g} = \frac{λ_{g} N u_{g}}{d_{gl}}

(20)

where $N u_{g}$ is a dimensionless Nusselt number on vapor phase side of the phase interface.

Analytical methods

The components and physical property vary with temperature for hydrocarbon mixture refrigerant. Meanwhile, the characteristics of boiling heat transfer on hydrocarbon mixture refrigerant in the vertical rectangular minichannel are obviously impacted by the components and physical property. Therefore, based on Soave equation (SRK equation), the components and physical property are calculated on hydrocarbon mixture refrigerant at different operation pressure and temperature. The calculation is listed in Table 1.

Table 1.

The properties of mixture refrigerant (methane, propane, and ethylene) at different temperatures.

Temperature (K)	Pressure (MPa)	Density (kg/m³)		Specific heat (kJ/(kg K))		Quality	Conductivity (mW/(m K))		Viscosity (µPa s)
Temperature (K)	Pressure (MPa)	Liquid	Vapor	Liquid	Vapor	Quality	Liquid	Vapor	Liquid	Vapor
150	0.2	608.19	2.82	2.27	2.06	0.35	194.84	16.49	305.11	5.79
168		607.99	2.78	2.21	1.86	0.50	177.98	18.87	278.43	6.36
177		608.28	2.77	2.18	1.78	0.59	168.97	19.43	273.86	6.63
186		607.16	2.75	2.17	1.72	0.67	160.61	19.62	267.03	6.89
195		603.82	2.75	2.17	1.68	0.76	153.17	19.40	255.02	7.11
204		598.68	2.81	2.18	1.64	0.88	146.49	18.67	239.61	7.26
150	0.32	590.11	4.83	2.34	1.94	0.40	193.95	16.31	257.99	6.58
162		593.25	4.61	2.29	1.86	0.49	184.36	18.11	245.75	6.89
174		594.78	4.52	2.25	1.77	0.61	173.08	19.55	239.27	7.16
186		596.81	4.42	2.21	1.70	0.72	161.58	20.32	239.34	7.46
198		594.88	4.34	2.20	1.66	0.82	151.39	20.52	231.71	7.74
210		588.99	4.37	2.21	1.63	0.96	142.53	19.93	216.35	7.93
211		588.37	4.38	2.214	1.63	0.97	141.84	19.84	214.88	7.94
150	0.4	572.57	5.66	2.39	2.23	0.23	194.84	16.49	232.44	5.81
168		586.98	5.34	2.29	2.04	0.38	177.98	18.87	231.59	6.45
177		587.80	5.31	2.26	1.94	0.46	168.97	19.43	225.36	6.73
186		588.30	5.29	2.24	1.86	0.55	160.61	19.62	221.58	7.01
195		587.90	5.27	2.23	1.80	0.63	153.17	19.40	217.73	7.26
204		585.65	5.26	2.23	1.76	0.72	146.49	18.67	211.00	7.49
213		581.56	5.32	2.24	1.72	0.82	140.54	20.65	201.39	7.67
150	0.5	549.47	7.15	2.49	2.30	0.15	183.54	16.77	197.56	5.82
168		577.44	6.64	2.32	2.11	0.35	175.54	19.25	215.49	6.47
177		579.57	6.56	2.29	2.02	0.42	168.71	20.47	210.79	6.77
186		580.44	6.54	2.27	1.93	0.50	161.37	21.34	206.92	7.05
195		580.70	6.51	2.25	1.85	0.59	154.00	21.78	203.98	7.31
204		579.49	6.49	2.25	1.80	0.67	147.01	21.86	199.45	7.55
213		576.39	6.52	2.26	1.77	0.76	140.50	21.56	192.22	7.76

Meanwhile, the characteristics of boiling heat transfer on hydrocarbon mixture refrigerant in a vertical rectangular minichannel are investigated by ANSYS-CFX. In order to guarantee the grid arrangement with fine meshes quality, the fluid area is discretized into hexahedral finite control volumes by the ICEM software. The simulations were performed with three different meshes: 711,000, 1,400,000, and 2,830,000 cells. The simulation results show that the calculation results become mesh independent when the mesh amount exceeds 1,400,000 cells. At the same time, the computation efficiency and mesh sensitivity were considered in this article. Therefore, the total number of mesh cells applied in the article was 1,400,000. The diffusion terms are solved by the central differential scheme. The convection terms are solved using the high-resolution scheme, which is second-order accurate. The transient term is solved by the first-order backward Euler scheme. The mass flow, vapor volume fraction, and temperature boundary are adopted at inlet. Outlet is set by the static pressure and the constant heat flux is used in the wall of vertical rectangular minichannel.

In order to facilitate the convergence, the steady-state solution in a vertical rectangular minichannel is obtained first and then it is used as the initial condition for other cases.

Results and discussion

Comparison between simulation results and experimental data

In order to validate the model on boiling heat transfer of hydrocarbon mixture refrigerant in a vertical rectangular minichannel, Figure 2 depicts the relation between the simulation results and the experimental data from literature² at different vapor quality for heat flux q = 1.1 kW/m², the mass flux m = 50 kg/(m² s) and heat flux q = 6 kW/m², the mass flux m = 215 kg/(m² s). The results show that the deviation between the simulated results and experimental data obtained from literature² is within ±15% (h_SIM is the simulated results and h_EXP is the experimental data from literature²).

Figure 2.

Comparison between simulation results and experiment at different mass fluxes and heat fluxes.

For the sake of further verifying the rationality of the model on boiling heat transfer of hydrocarbon mixture refrigerant in a vertical rectangular minichannel, the boiling heat transfer in a vertical rectangular minichannel is simulated at the condition of different heat flux. At the same time, the simulation results are compared with the experiment data. Figure 3 is the relation between simulation results and experimental data from literature.² The results show that the simulation results are consistent with experimental data from literature and the deviation is within ±15% between the simulation results and experimental data at different heat flux for the mass flux m = 215 kg/(m² s), the vapor quality x = 0.5 and the mass flux m = 215 kg/(m² s), the vapor quality x = 0.25.

Figure 3.

Comparison between simulation results and experiment at different vapor quality.

Characteristic of boiling heat transfer

In this part, the characteristics of saturated boiling heat transfer are investigated based on the above model validated by the experimental data from literature.² The vapor quality is independent on the saturation temperature and pressure for the boiling heat transfer on simplex refrigerant. However, for the boiling heat transfer on hydrocarbon mixture refrigerant in PFHE, the vapor quality is dependent on the saturation temperature and pressure. Therefore, the influence of saturation temperature and pressure is a necessity for this study.

Figure 4 presents the heat transfer coefficient as a function of saturated temperature at different heat fluxes with mass flux m = 250 kg/(m² s) and at different mass fluxes with heat flux q = 20 kW/m². The results show that the heat transfer coefficient increases with the increase in saturated temperature. The influence of mass flux is obvious for the heat transfer coefficient while that is slightly impacted by the heat flux. Specifically, the heat transfer coefficient rises gradually with the mass flux. According to Table 1, the vapor quality increases as the saturated temperature increases. Therefore, the above results further indicate that the forced convection boiling is the main mechanism for boiling heat transfer on hydrocarbon mixture refrigerant in a vertical rectangular minichannel. At the same time, the change of components and physical property of vapor or liquid phase is also a major influence factor for hydrocarbon mixture refrigerant.

Figure 4.

The heat transfer coefficient versus saturated temperature.

Figure 5 illustrates the variation of the heat transfer coefficient with saturated temperature at different pressures with mass flux m = 250 kg/(m² s), heat flux q = 20 kW/m². The results show that the heat transfer coefficient also increases as the saturated temperature increased. The influence of pressure is obvious for the heat transfer coefficient when the saturated temperature is less than 203 K. Meanwhile, the higher the pressure, the larger the heat transfer coefficient. When the saturated temperature is more than 203 K, the heat transfer coefficient is slightly impacted by the pressure.

Figure 5.

The heat transfer coefficient versus saturated temperature at different pressures.

Figure 6 depicts the relation between the heat transfer coefficient and mass flux at different saturated temperatures with heat flux q = 20 kW/m², pressure P = 0.32 MPa and at different heat fluxes with saturated temperature T = 195 K, pressure P = 0.32 MPa. The results show that the heat transfer coefficient is obviously impacted by the mass flux and linearly increases with its increase. Also, the higher the saturated temperature, the larger the heat transfer coefficient. The influence of the heat flux is slight for the heat transfer coefficient.

Figure 6.

The heat transfer coefficient versus mass flux.

The influence of mass flux for heat transfer coefficients at different pressures is also analyzed in Figure 7. The plots are drawn at different pressures for heat flux q = 20 kW/m², saturated temperature T = 195 K. The results also indicate that the heat transfer coefficient is obviously impacted by the mass flux and linearly increases with its increase. Meanwhile, the higher the pressure, the larger the heat transfer coefficient.

Figure 7.

The heat transfer coefficient versus mass flux.

To sum up, for the boiling heat transfer of hydrocarbon mixture refrigerant in a vertical rectangular minichannel, the heat transfer coefficient increases as the saturated temperature and the mass flux increased because the forced convection boiling mechanisms enhance with the increase of that for boiling heat transfer on hydrocarbon mixture refrigerant in a vertical rectangular minichannel. Meanwhile, the heat transfer coefficient is obviously impacted by the pressure while the influence of heat flux is minimal for that.

Comparison between simulation results and existing correlation calculations

At present, many correlations on heat transfer coefficient for boiling heat transfer in a vertical rectangular minichannel have been given in terms of experimental data based on single-component refrigerant. It is very difficult to select an appropriate correlation for the design in engineering. At the same time, it is necessary to verify the rationality of the heat transfer coefficient correlations based on the experimental data of single-component refrigerant to predict the boiling heat transfer of hydrocarbon mixture refrigerant in a vertical rectangular minichannel. Therefore, the correlation calculations from different studies are compared with the simulation results at the temperature T = 150–215 K, mass flux m = 100–400 kg/(m² s), pressure P = 0.2–0.5 MPa, and heat flux q = 5–20 kW/m². The optimal correlation is recommended to predict the heat transfer coefficient on the boiling heat transfer of hydrocarbon mixture refrigerant in a vertical rectangular minichannel. Table 2 lists the correlations used in this article.

Table 2.

Common correlation on boiling heat transfer coefficient.

Correlation name	Heat transfer coefficient correlation	Database range
Correlations by Tran et al.²⁰	$h_{tp} = 8.4 \times 10^{5} {(B o^{2} W e_{lo})}^{0.3} {(\frac{ρ_{g}}{ρ_{l}})}^{0.4}, Bo = \frac{q}{m i_{\lg}}, W e_{lo} = \frac{m^{2} D}{ρ_{l} σ}$	m (kg/(m² s)): 44–832 q (kW/m²): 7.5–129 D (mm): 2.4–2.92 x: 0.2–0.8
Correlation by Bertsch et al.³¹	$h_{tp} = E h_{sp} + S h_{nb}, E = 1 + 80 (x^{2} - x^{6}) e^{- 0.6 Co}$ $S = f (x) = 1 - x, h_{sp} = h_{sp, l} (1 - x) + h_{sp, g} x$ $h_{nb} = 55 {P_{r}}^{0.12 - 0.2 lo g_{10} R_{z}} \cdot (- lo g_{10} P_{r})^{- 0.55} {\bar{M}}^{- 0.5} {(q)}^{\frac{2}{3}}, P_{r} = \frac{P_{sat}}{P_{cr}}$ $h_{sp, l} = \frac{λ_{l}}{D} (3.66 + \frac{0.0668 \frac{D}{L} R e_{lo} P r_{l}}{1 + 0.04 \cdot {[\frac{D}{L} \cdot R e_{lo} \cdot \Pr]}^{2 / 3}}), P r_{l} = \frac{c_{p} μ_{l}}{λ_{l}}$	m (kg/(m² s)): 20–3000 q (kW/m²): 4–1150 D (mm): 0.16–2.92 x: 0–1
Correlation by Gungor and Winterton³⁰	$h_{tp} = E \cdot h_{sp} + S \cdot h_{nb}, R e_{lo} = \frac{mD}{μ_{l}}$ $E = 1 + 24, 000 B o^{1.16} + 1.37 {(\frac{1}{X_{tt}})}^{0.86}, X_{tt} = {(\frac{μ_{l}}{μ_{g}})}^{0.1} {(\frac{1 - x}{x})}^{0.9} {(\frac{ρ_{g}}{ρ_{l}})}^{0.5}$ $S = (1 + 1.15 \times 10^{- 6} E^{2} {Re}_{l}^{1.17})^{- 1} h_{sp} = 0.023 {Re}_{l}^{0.8} \Pr_{l}^{0.4} \frac{λ_{l}}{D}$ $h_{nb} = 55 P_{r}^{0.12} (- lo g_{10} P_{r})^{- 0.55} {\bar{M}}^{- 0.5} (q)^{2 / 3}$	m (kg/(m² s)): 67–61,518 q (kW/m²): 1.1–2280 D (mm): 2.95–32 x: 0–1
Correlation by Liu and Winterton¹	$h_{tp}^{2} = (F h_{cl})^{2} + (S h_{nb})^{2}, F = {[1 + xP r_{l} (\frac{ρ_{l}}{ρ_{g}} - 1)]}^{0.35}$ $S = (1 + 0.055 F^{0.1} {Re}_{lo}^{0.16})^{- 1}, h_{cl} = 0.023 {Re}_{l}^{0.8} \Pr_{l}^{0.4} \frac{λ_{l}}{D}$ $h_{nb} = 550 P_{cr}^{0.25} T_{cr}^{- 0.875} {\bar{M}}^{- 0.125} q^{0.75} R_{z}^{0.2} (0.14 + 2.2 \frac{P}{P_{cr}})$	m (kg/(m² s)): 12.4–8179.3 q (kW/m²): 0.35–2620 Re: 568.9–875,000 D (mm): 2.95–32 x: 0–0.948
Correlation by Kandlikar and colleagues^32,33	$h_{tp} = MAX (h_{tp, NBD}, h_{tp, CBD})$ $h_{tp, NBD} = [0.6683 C o^{- 0.2} + 1058.0 B o^{0.7} F_{fl}] {(1 - x)}^{0.8} h_{sp, lo}$ $h_{tp, CBD} = [1.136 C o^{- 0.9} + 667.2 B o^{0.7} F_{fl}] (1 - x)^{0.8} h_{sp, lo}$ $h_{sp, lo} = {\begin{matrix} \frac{{Re}_{lo} \Pr_{l} (\frac{f}{2}) (\frac{λ_{l}}{D})}{1 + 12.7 (\Pr_{l}^{2 / 3} - 1) \sqrt{\frac{f}{2}}}, \begin{matrix} {Re}_{lo} > 10^{4} \end{matrix} \\ \frac{({Re}_{lo} - 1000) \Pr_{l} (\frac{f}{2}) (\frac{λ_{l}}{D})}{1 + 12.7 (\Pr_{l}^{2 / 3} - 1) \sqrt{\frac{f}{2}}}, \begin{matrix} 1600 < {Re}_{lo} < 10^{4} \end{matrix} \end{matrix}$	m (kg/(m² s)): 13–8179 q (kW/m²): 0.3–2280 D (mm): 4–32 x: 0.001–0.987
Correlation by Sun and Mishima³⁴	$h_{tp} = \frac{6 {Re}_{lo}^{1.05} B o^{0.54}}{{We}_{lo}^{0.191} {(ρ_{l} / ρ_{g})}^{0.142}} (\frac{λ_{l}}{D})$	m (kg/(m² s)): 44–1500 q (kW/m²): 5–109 D (mm): 0.21–6.5 x: 0–1

Figure 8 depicts the relation between simulation results and correlation calculations on the boiling heat transfer coefficient of hydrocarbon mixture refrigerant in a vertical rectangular minichannel. Here, h_SIM and h_COR represent the simulation results and correlation calculations, respectively. The results in Figure 8(a) show that the deviations are more than 15% in most cases and the calculations by the Tran’s correlation are much larger than the simulation results. Figure 8(b) shows that the deviations are more than −15% in most cases and the calculations by the correlation of Bertsch et al. are less than the simulation results. In other words, it is still very difficult to accurately predict the boiling heat transfer of hydrocarbon mixture refrigerant in a vertical rectangular minichannel by the correlation of Tran et al. and Bertsch et al. Figure 8(c) indicates that the calculations by correlation of Gungor and Winterton are much larger than the simulation results in most case and the deviations are less than ±15% in most cases. But the deviations between the simulation results and correlation calculations are still more than 15% in many cases. According to Figure 8(d) and (e), the calculations by correlation of Kandlikar and Sun and Mishima are less than the simulation results in most cases. The relation between the calculations by correlation of Liu and Winterton and the simulation results is shown in Figure 8(f). The results show that the deviations between the simulation results and the correlation calculations are less than ±15% at most conditions though the calculations by correlation of Liu and Winterton are less than the simulation results. At the same time, the calculations by correlation of Liu and Winterton have much better agreement with the simulation results compared with the above other models.

Figure 8.

Comparison between simulation results and correlation calculations: (a) comparison between simulation results and correlation of Tran et al.; (b) comparison between simulation results and correlation of Bertsch et al.; (c) comparison between simulation results and correlation of Gungor and Winterton; (d) comparison between simulation results and correlation of Kandlikar; (e) comparison between simulation results and correlation of Sun and Mishima; and (f) comparison between simulation results and correlation of Liu and Winterton.

Conclusion

In this article, a model was established to investigate the characteristics of boiling heat transfer on hydrocarbon mixture refrigerant in a vertical rectangular minichannel. ANSYS-CFX simulation was done on the boiling heat transfer. The simulation results were compared with the existing correlations of heat transfer coefficient developed in the literature. The following conclusions can be drawn from this study:

The results obtained by numerical simulations on heat transfer coefficient in a vertical rectangular minichannel show that the simulation results are consistent with the experiment data from the literature. Simultaneously, the deviations are within ±15% between simulation results and experiment data from the literature.

Due to the influence of the forced convection boiling mechanisms, the heat transfer coefficient increases with the increase in saturated temperature and the mass flux. The influence of the pressure is obvious for the boiling heat transfer of hydrocarbon mixture refrigerant in a vertical rectangular minichannel when the saturated temperature is less than 203 K.

The calculations of heat transfer coefficient by correlation of Liu and Winterton are in good agreement with the simulation results compared with other correlations though the calculations by correlation of Liu and Winterton are less than the simulation results. At the same time, the deviations between the simulation results and correlation calculations are less than ±15% in most cases at the temperature T = 150–215 K, mass flux m = 100–400 kg/(m² s), pressure P = 0.2–0.5 MPa, and heat flux q = 5–20 kW/m².

Footnotes

Appendix 1

Academic Editor: Mohammad Reza Salimpour

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (51378318).

References

Liu

Winterton

A general correlation for saturated and subcooled flow boiling in tubes and annuli, based on a nucleate pool boiling equation. Int J Heat Mass Tran 1991; 34: 2759–2766.

Kuznetsov

Shamirzaev

AS.

Boiling heat transfer for Freon R21 in rectangular minichannel. Heat Transfer Eng 2007; 28: 738–745.

Jiang

Gong

. Effect of geometric conditions on residual stress of brazed stainless steel plate-fin structure. Nucl Eng Des 2008; 238: 1497–1502.

Cai

Zheng

. Stress characteristics of plate-fin structures in the cool-down process of LNG heat exchanger. J Nat Gas Sci Eng 2014; 21: 1113–1126.

Peng

Ling

Optimal design approach for the plate-fin heat exchangers using neural networks cooperated with genetic algorithms. Appl Therm Eng 2008; 28: 642–650.

Jiang

Gong

. A comparison of brazed residual stress in plate-fin structure made of different stainless steel. Mater Design 2009; 30: 23–27.

Cai

Yao

. Investigation on stress characteristics of plate-fin structures in the heat-up process of LNG heat exchanger. J Nat Gas Sci Eng 2016; 30: 256–267.

Chen

Cai

. The influence of operation parameters on stress of plate-fin structures in LNG heat exchanger. J Nat Gas Sci Eng 2015; 26: 216–228.

Jemni

Kantchev

Abid

MS.

Influence of intake manifold design on in-cylinder flow and engine performances in a bus diesel engine converted to LPG gas fuelled, using CFD analyses and experimental investigations. Energy 2011; 36: 2701–2715.

10.

Sumith

Kaminaga

Matsumura

Saturated flow boiling of water in a vertical small diameter tube. Exp Therm Fluid Sci 2003; 27: 789–801.

11.

Lucas

Frank

Lifante

. Extension of the inhomogeneous MUSIG model for bubble condensation. Nucl Eng Des 2011; 241: 4359–4367.

12.

Kuznetsov

Dimov

Houghton

. Upflow boiling and condensation in rectangular minichannels. In: Proceedings of the first international conference on microchannels and minichannels, Rochester, NY, 24–25 April 2003. New York: ASME.

13.

Pulvirenti

Matalone

Barucca

Boiling heat transfer in narrow channels with offset strip fins: application to electronic chipsets cooling. Appl Therm Eng 2010; 30: 2138–2145.

14.

Owhaib

Martin-Callizo

Palm

Evaporative heat transfer in vertical circular microchannels. Appl Therm Eng 2004; 24: 1241–1253.

15.

Feldman

Marvillet

Lebouche

Nucleate and convective boiling in plate fin heat exchangers. Int J Heat Mass Tran 2000; 43: 3433–3442.

16.

Cai

Chen

. Numerical investigation on saturated boiling and heat transfer correlations in a vertical rectangular minichannel. Int J Therm Sci 2016; 102: 285–299.

17.

Tran

Wambsganss

Chyu

. A correlation for nucleate flow boiling in small channels. In: Shah

(ed.) Compact heat exchangers for the process industries. Danbury, CT: Begell House, 1997, pp.353–363.

18.

Tran

Chyu

Wambsganss

. Two-phase pressure drop of refrigerants during flow boiling in small channels: an experimental investigation and correlation development. Int J Multiphas Flow 2000; 26: 1739–1754.

19.

Tran

Chyu

Wambsganss

. Two-phase pressure drop of refrigerants during flow boiling in small channels: an experimental investigation and correlation development. In: Shah

(ed.) Compact heat exchangers and enhancement technology for the process industries. Danbury, CT: Begell House, 1999, pp.293–302.

20.

Tran

Wambsganss

France

DM.

Small circular- and rectangular-channel boiling with two refrigerants. Int J Multiphas Flow 1996; 22: 485–498.

21.

Lazarek

Black

SH.

Evaporative heat transfer, pressure drop and critical heat flux in a small vertical tube with R-113. Int J Heat Mass Tran 1982; 25: 945–960.

22.

Bao

Fletcher

Haynes

BS.

Flow boiling heat transfer of Freon R11 and HCFC123 in narrow passages. Int J Heat Mass Tran 2000; 43: 3347–3358.

23.

France

Wambsganss

. Two-phase pressure drop, boiling heat transfer, and critical heat flux to water in a small-diameter horizontal tube. Int J Multiphas Flow 2002; 28: 927–941.

24.

Kandlikar

SG.

Fundamental issues related to flow boiling in minichannels and microchannels. Exp Therm Fluid Sci 2002; 26: 389–407.

25.

Mishima

Hibiki

Some characteristics of air-water two-phase flow in small diameter vertical tubes. Int J Multiphas Flow 1996; 22: 703–712.

26.

Zhang

Hibiki

Mishima

Correlation for flow boiling heat transfer in mini-channels. Int J Heat Mass Tran 2004; 47: 5749–5763.

27.

Kim

Choi

. Numerical simulation of subcooled flow boiling heat transfer in helical tubes. J Press Vess: T ASME 2009; 131: 011305.

28.

Koncar

Krepper

CFD simulation of convective flow boiling of refrigerant in a vertical annulus. Nucl Eng Des 2008; 238: 693–706.

29.

Chen

JC.

Correlation for boiling heat transfer to saturated fluids in convective flow. Ind Eng Chem Proc DD 1966; 5: 322–329.

30.

Gungor

Winterton

RHS

. A general correlation for flow boiling in tubes and annuli. Int J Heat Mass Tran 1986; 29: 351–358.

31.

Bertsch

Groll

Garimella

SV.

A composite heat transfer correlation for saturated flow boiling in small channels. Int J Heat Mass Tran 2009; 52: 2110–2118.

32.

Kandlikar

SG.

A general correlation for saturated two-phase flow boiling heat transfer inside horizontal and vertical tubes. J Heat Transf 1990; 112: 219–228.

33.

Kandlikar

Balasubramanian

An extension of the flow boiling correlation to transition, laminar, and deep laminar flows in minichannels and microchannels. Heat Transfer Eng 2004; 25: 86–93.

34.

Sun

Mishima

An evaluation of prediction methods for saturated flow boiling heat transfer in mini-channels. Int J Heat Mass Tran 2009; 52: 5323–5329.