Performance analysis of a novel thermal transpiration vacuum cooling system

ABSTRACT

A novel vacuum cooling system, which mainly consists of a 49-stage thermal transpiration based vacuum pump and a 100 L vacuum vessel, is proposed. The novel system can directly be driven by heat, while its structure and operation are similar to those of traditional mechanical vacuum systems. Then, a mathematic model is established to predict the performance of the novel system. The cooling capacity and coefficient of performance of the novel system increase with the rises of both parameters related to vacuum pump (the temperature difference between cold and hot chamber and pressure difference coefficient) and parameters related to vacuum vessel (mass transfer coefficient, chilled water temperature and supplement water temperature). It is a feasible way to raise system performance by cooling cold chambers, while heating hot chambers except for enhancement of mass transfer. The novel vacuum cooling system can produce relatively large cooling capacity exceeding 10,000 W at chilled water temperature over 289 K, the coefficient of performance (ranges from 0.71 to 1.48) of which is still comparable to that of the existing absorption refrigeration. It is clear that the novel thermal transpiration vacuum cooling is competitive among lots of emerging refrigeration technologies.

KEYWORDS:

• Thermal transpiration effect
• vacuum cooling
• working conditions
• performance analysis
• system design

Nomenclature

A_m, A_C—cross-section area of the microchannel group and connecting passage group in each stage of the thermal transpiration based vacuum pump, respectively [m²]

A_m,i, A_C,i—cross-section area of the microchannel group and connecting passage group for the ith stage of the thermal transpiration based vacuum pump, respectively [m²]

A_vl—area of the gas–liquid interface [m²]

c_p,w—specific heat at constant pressure of the chilled water [kJ·kg⁻¹· K⁻¹]

C_t,i—total conductance of the gas in the ith stage of the thermal transpiration based vacuum pump [m³·s⁻¹]

COP—coefficient of performance [--]

k_m—mass transfer coefficient [m·s⁻¹]

k_p—pressure difference coefficient [--]

L_c,i, L_h,i—length of the cold and hot chamber for the ith stage of the thermal transpiration-based vacuum pump, respectively [m]

L_r,i, L_R,i—characteristic dimensions of the microchannel and connecting passage for the ith stage of the thermal transpiration-based vacuum pump, respectively [m]

L_w—width of the cold or hot chamber for each stage of the thermal transpiration-based vacuum pump [m]

L_x,i, L_X,i—length of the microchannel and connecting passage for the ith stage of the thermal transpiration-based vacuum pump, respectively [m]

M_in—air that permeates the system [kg·h⁻¹]

p—total pressure in the system[Pa]

P_c,r—actual pressure in the cold chamber [Pa]

p_c, p_h—pressure in the cold and hot chambers, respectively [Pa]

p_d—partial pressure of non-condensable gas (i.e. dry air) [Pa]

p_s—partial pressure of saturated water vapor [Pa]

Q₀—cooling capacity [W]

Q_g—total heat consumed by the thermal transpiration-based vacuum pump [W]

Q_l,i—heat lost to the environment from the ith stage of the thermal transpiration-based vacuum pump [W]

Q_mc,i—heat required to maintain the temperature differences between the cold and hot chambers for the ith stage of the thermal transpiration-based vacuum pump [W]

Q_T,i, Q_P,i—thermal transpiration flow coefficient and poiseuille flow coefficient of the microchannel for the ith stage of the thermal transpiration-based vacuum pump, respectively [--]

Q_T,C,i, Q_P,C,i—thermal transpiration flow coefficient and poiseuille flow coefficient of the connecting passage for the ith stage of the thermal transpiration-based vacuum pump, respectively [--]

R—universal gas constant [J·mol⁻¹·K⁻¹]

S_p,i—pumping speed of the ith stage of the thermal transpiration-based vacuum pump [m³·s⁻¹]

t_g—mixed gas (i.e. moist air) temperature in the given control volume [°C]

T_avg—average temperature of the cold and hot chamber [K]

T_c, T_h—temperature of the cold and hot chambers, respectively [K]

T_e—ambient air temperature [K]

T_g—mixed gas (i.e. moist air) temperature in the given control volume [K]

T_m—supplement water temperature [K]

T_s—equilibrium temperature at the gas-liquid interface [K]

T_s(p)—equilibrium temperature at the total pressure [K]

T_w—chilled water temperature [K]

GREEK

α_s—heat transfer coefficient [W·m⁻²· K⁻¹]

δ—thickness of the cavity wall [m]

λ_w—thermal conductivity of the cavity material [W·m⁻¹·K⁻¹]

λ_g,i—gas thermal conductivity in any state for the ith stage of the thermal transpiration-based vacuum pump [W·m⁻¹·K⁻¹]

μ_d—molar mass of non-condensable gas [kg·kmol⁻¹]

ρ_w—chilled water density [kg·m⁻³]

φ_i, φ_C,i—section area fraction of the microchannel group and connecting passage group for the ith stage of the thermal transpiration-based vacuum pump, respectively [--]

ΔT_s—chemical potential temperature difference [K]

ΔT—temperature difference between the cold and hot chamber for each stage of the thermal transpiration-based vacuum pump [K]

Article highlights

● A novel vacuum cooling system with a 49-stage thermal transpiration-based vacuum pump and a 100-L vacuum vessel is proposed and the corresponding mathematic model is developed to predict its operation characteristics.

● The novel system can directly be driven by heat, while its structure and operation are similar to those of traditional mechanical vacuum systems excluding the problem of cavitation.

● The cooling capacity and coefficient of performance of the novel system increase with the rises in the temperature difference between cold and hot chamber, pressure difference coefficient, mass transfer coefficient, chilled water temperature, and supplement water temperature.

● The ways to raise system performance are also discussed.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 52066002) and the Guangxi Natural Science Foundation (Grant No. 2019GXNSFAA185024). The authors acknowledge the National Natural Science Foundation of China and the Guangxi Natural Science Foundation.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [Grant No. 52066002]; the Guangxi Natural Science Foundation [Grant No. 2019GXNSFAA185024].