Numerical simulation of flow boiling in microchannels

Numerical simulation of flow boiling in microchannels during maneuvering flight Yu Xu, Guohua Li

Weiwei Chen

College of Aerospace Engineering Nanjing University of Aeronautics and Astronautics Nanjing, China [email protected]

School of Energy and Mechanical Engineering Nanjing Normal University Nanjing, China

Abstract—Two-dimensional numerical investigations of flow boiling of R134a in micro-channels during maneuvering flight with hypergravity levels of 1–15 g and directions of 0º–180º were conducted. Flow patterns, temperature and pressure fields of the simulation domain are obtained, and the effects of hypergravity on flow boiling characteristics are analyzed. The results indicate that the flow boiling characteristics during maneuvering flight are significantly different from those on ground. When the hypergravity has the same direction as the flow (ș = 0º), the heat transfer coefficient remains basically invariable, while the frictional pressure drop decreases. When the hypergravity is perpendicular to the flow (ș = 90º), the heat transfer coefficient decreases with the increasing hypergravity and the frictional pressure drop decreases slightly. When the hypergravity has the opposite direction with the flow (ș = 180º), the heat transfer coefficient keeps almost unchanged, while the frictional pressure drop increases. Since the flow evolves into a quasi-stratified flow at ș = 90º, the heat transfer deterioration occurs due to dryout. Keywords—numerical simulation, flow boiling, hypergravity, maneuvering flight, micro-channels

inner diameter (ID) horizontal tube agreed with those captured in experiments [6]. The simulated flow dynamics and heat transfer of slug flow of R245fa in a 0.5 mm ID micro-channel indicated that the characteristics of continuous bubbles were quite different from those of a single bubble [7]. The simulated flow boiling characteristics of water in a 6 mm ID helically coiled tube with uniform and one-side heating showed that the vapor was mainly distributed on the inner side due to the effect of the centrifugal force [8]. For subcooled flow boiling, the simulated bubble behaviors of water in a vertical square pipe were consistent with the experimental results [9]. The experimental and numerical studies of subcooled boiling of water in segmented ¿nned micro-channels showed that the simulated Àow patterns were similar to the observations while the bubble growth rate and heat transfer coe cient were over-predicted [10]. The simulated flow patterns, void fraction and total pressure drop of subcooled boiling of HFE-7100 in a 6 mm ID vertical channel under normal gravity (1 g) and microgravity (0.05 g) agreed well with the experimental data [11].

I. INTRODUCTION With the rapid increase of heat loads of electronic devices in modern high-performance flight vehicles, the phase change cooling method are demanded. Due to the harsh requirements of small volume and lightweight, the compact heat exchangers with micro-channels are preferred as evaporators. Moreover, some flight vehicles are often subjected to hypergravity during maneuvering flight. Therefore, it is necessary to study the flow boiling characteristics in micro-channels under hypergravity.

For adiabatic two-phase flow, the numerical studies of air– water flow in horizontal pipes with IDs of 7 and 10 mm under 1 g, 0.38 g, 0.17 g and 10–4 g indicated that the simulated flow patterns were consistent with the experimental results and the gravity played a signi¿cant role in Àow patterns and void fraction [12]. The numerical investigations of air–water and R134a flows in a rectangular pipe with a hydraulic diameter of 12 mm under 1 g and 10–4 g showed that the flow patterns under different gravities had differences [13].

Investigations on flow boiling in micro-channels conducted on ground or space environment has been increasing rapidly in recent year. However, flow boiling studies during maneuvering flight are still few. The hypergravity levels of previous studies [1-5] were low, because reaching high hypergravity levels in experiments and conducting visualizations under these cases are still difficult. The numerical simulation of flow boiling under normal or micro gravity has attracted many attentions and has great potential in obtaining flow boiling characteristics under hypergravity.

The above literature survey indicates that the numerical simulation of two-phase flow was feasible. Although the characteristics of two-phase flow were affected by the gravity, simulations of flow boiling under hypergravity is still rare. In this paper, Two-dimensional simulations of flow boiling of R134a in a 1.002 mm micro-channel under hypergravity are conducted, and the effects of hypergravity are analyzed.

Previous numerical studies related to two-phase flow under different gravities are briefly summarized here. For saturated flow boiling, the simulated flow patterns of R134a in a 0.5 mm

II.

NUMERICAL METHOD

A. Mathematical model The VOF model was adopted to simulate the flow patterns. The volume fraction (Į) defined as the ratio of the volume of the target fluid to that of the computational cell was introduced.

This study is supported by National Natural Science Foundation of China (51576099).

The condition of Į = 1 means the cell is full of the target fluid, Į = 0 means the cell is empty of the target fluid, and 0 < Į < 1 means the cell contains the interface between the target fluid and other fluid. The governing equations could be written as: ∂α k ρ k ∂t + ∇ ⋅ (α k ρ k v ) = Sα k

(1)

The velocity inlet and pressure outlet boundary conditions were applied at the inlet and outlet. The simulation domain was full of saturated liquid R134a at the beginning. Predictions of flow patterns are conducted with the flow pattern map proposed by Wojtan et al. [19] to determine suitable simulation conditions. The determined conditions are G = 500 kg/m2 s, p = 0.71 MPa, q = 13.9, 27.7, and 55.4 kW/m2, xin = 0, xout = 0.041, 0.082, and 0.164, ah = 1, 3, 6, 9, 12, and 15 g, and ș = 0º, 90º, and 180º.

∂ρ v ∂t + ∇ ⋅ ( ρ vv ) = −∇p + ∇ ⋅ ª¬ μ ( ∇v + ∇v T ) º¼ + ρ ah + Fvol (2)

∂ρ E ∂t + ∇ ⋅ ¬ªv ( ρ E + p ) º¼ = ∇ ⋅ ( λ∇T ) + Q

(3)

where v is the fluid velocity, S is the mass source term, a h is the hyper-gravitational acceleration, Fvol is the body force, E is the energy, Q is the heat source term, and the subscript k = l and v represent liquid phase and vapor phase, respectively. The physical properties (e.g., density) and energy of the mixture could be computed as the average values of the liquid and vapor phases, weighted by Į.

ρ = ¦αk ρk E = ¦ α k ρk Ek

(4)

¦α ρ k

(5)

k

Figure 1. Schematic of physical model.

C. Mesh and solution As shown in Figure 2, two-dimensional structured mesh was generated. The edge ratios of the grid cells should be close to 1, in order to ensure the simulation accuracy of various bubble behaviors. Considering both the computation load and accuracy, the edge ratios from the wall to the axis were set from 2.5 to 1. The independence of mesh size was examined by comparing the outlet void fraction and pressure drop. The differences were found to be less than 3% when the mesh size was greater than or equal to 140,400. Since finer mesh means both more simulated small bubbles and longer computation time, the above mesh size was picked.

The surface tension force could be formulated according to the continuum surface force model [14]. Fvol = σρκ∇α ª¬0.5 ( ρl +ρv )º¼

(6)

where ı is the surface tension coefficient, and ț is the local surface curvature. The mass source term could be determined by the Lee model [15], and then the energy source term could be obtained based on it and the latent heat of vaporization (hlv). ° rα ρ (T − Tsat ) Tsat Sαv = − Sαl = ® l l l °¯rvαv ρv (Tsat − T ) Tsat

Q = Sαv hlv

T ≥ Tsat T < Tsat

(7) (8)

where rl and rv are the evaporation frequency and condensation frequency, which should be fine set. B. Physical model The simulations of flow boiling were conducted in a 1.002 mm ID micro-channel heated uniformly with a working fluid of R134a according to our previous experimental studies [16]. A length-diameter ratio of about 65 was taken. The ratios in the previous simulations of two-phase refrigerant flow were less than 60 [17, 18]. The schematic of the physical model is shown in Figure 1, form which it can be seen that the hypergravity can be perpendicular to the flow (ș = 90º), or has the same (ș = 0º) or opposite (ș = 180º) directions with the flow. A non-slip and constant heat flux boundary condition was applied to the wall.

Figure 2. Computational mesh.

The pressure-based solver was applied for transient simulations. The vapor phase was defined as the primary phase. The explicit Geo-Reconstruction scheme was used for the discretization of volume fraction. The implicit body force treatment was employed. The PISO scheme was adopted for the pressure–velocity coupling. The PRESTO! scheme was used for the discretization of pressure. The second order upwind scheme was employed for the discretization of momentum and energy. A time step of 10–5 s was selected for lower hypergravity, while 10–6 s for higher hypergravity. D. Validation Revellin et al. [20] measured the void fractions during flow boiling of R134a in a 0.5 mm ID horizontal micro-channel with a length of 70.7 mm. The conditions of G =1000 kg/m2 s, T sat = 30 , and ǻTsub = 3 were used to validate the numerical method. The comparison of the simulated and experimental void fractions is shown in Figure 3, from which it can be seen that the simulated void fractions are quite close to the experimental ones with absolute deviations less than 9%, indicating that the above numerical method is suitable for the flow boiling in micro-channels during maneuvering flight.

with the increasing hypergravity, the vapor phase gets longer and changes into elongated slugs. This is due to the gradually weakened effect of inertia force and the gradually enhanced effect of shear force, leading to the head of vapor phase sharp and the tail curve as well as the contact and coalescence of the upstream and downstream vapor phases.

Figure 3. Comparison of simulated and experimental void fractions.

III.

RESULTS AND DISCUSSION

A. Flow patterns of flow boiling during maneuvering flight Flow patterns of flow boiling during maneuvering flight at ș = 0º are shown in Figure 4, from which it can be seen that the vapor phase is getting shorter and shorter and trends to a quasiellipsoidal/spherical shape with the increasing hypergravity. This is because of the gradually enhanced effect of inertia force and the gradually weakened effect of shear force, leading to the head of vapor phase dull and the tail flat.

Figure 6. Flow patterns at ș = 180º.

B. Heat transfer of flow boiling during maneuvering flight The heat transfer coefficients (Į) of flow boiling during maneuvering flight are shown in Figure 7, from which it can be seen that at ș = 90º, the heat transfer coefficient decreases gradually with the increasing hypergravity. This is because the flow patterns change from plug/slug flow into quasi-stratified flow, leading to the dryout and heat transfer deterioration. At ș = 0º and 180º, the heat transfer coefficient remains basically unchanged. This is because the flow patterns still belong to plug/slug flow and the probability of dryout keep unchanged, although the vapor phases transform into other shapes.


Flow patterns of flow boiling during maneuvering flight at ș = 90º are shown in Figure 5, from which it can be seen that the flow evolves into a quasi-stratified flow with the increasing hypergravity. This is because the vapor phase moves to the upper side of the micro-channel by the increasing buoyancy, then it is elongated by the inertia and shear forces with the shape turning to sloped and slender, and finally the adjacent slender vapor phases contact and coalesce with each other.


Flow patterns of flow boiling during maneuvering flight at ș = 180º are show in Figure 6, from which it can be seen that

Figure 7. Heat transfer coefficient.

C. Pressure drop of flow boiling during maneuvering flight The frictional pressure drop of flow boiling during maneuvering flight are shown in Figure 8, from which it can be seen that at ș = 0º, the frictional pressure drop decreases with the increasing hypergravity, because the vapor phase is shortened and its velocity decreases. At ș = 90º, the frictional pressure drop decreases quite slightly, because the vapor phase starts to contact with the wall during this period. At ș = 180º, the frictional pressure drop increases basically, because the vapor phase is elongated and its velocity increases.

ACKNOWLEDGMENT Y. X. thanks the help of Prof. Xiande Fang of NUAA. REFERENCES [1] [2]

[3]

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[13] Figure 8. Frictional pressure drop.

IV.

CONCLUSIONS

Two-dimensional numerical simulations of flow boiling of R134a in a 1.002 mm micro-channel during maneuvering flight were conducted with ah = 1–15 g and ș = 0º–180º. The effects of hypergravity on flow patterns, heat transfer, and pressure drop are significant. At ș = 0º, the vapor phase trends to a quasi-ellipsoidal/spherical shape with the increasing hypergravity, the heat transfer coefficient keeps invariable, while the frictional pressure drop decreases. At ș = 90º, the flow evolves into a quasi-stratified flow, the heat transfer coefficient decreases due to dryout, and the frictional pressure drop decreases slightly. At ș = 180º, the vapor phase changes into an elongated slug form, the heat transfer coefficient remains unchanged, while the frictional pressure drop increases.

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