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Dynamic simulation and performance investigation of no-frost refrigerator: Part I mathematical model

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Abstract

A dynamic approach for the modeling, simulation and analysis of no-frost Refrigerator (RF) is discussed. In Part I, the complex interactions among the components in the cooling system are analyzed in detail, based on which the modeling simplifications are proposed. Then, the mathematical models for the evaporator, cabinet and duct-fan are presented. The whole system is divided into two subsystems—refrigerant cycling system and air cycling system. In order to simplify the model, two closed-loop systems are broken into the compressor component and the evaporator component, respectively. A general distributed parameter model is employed for evaporator with homogeneous flow to simplify the two-phase evaporating flow region. The z-transfer function model is used to describe the cabinet load. Computational fluid dynamics (CFD) method is employed to obtain the pressure drop and flow rate curve of the duct-fan model.

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Abbreviations

a, a i :

Coefficient of the equations

A :

Area, m2

b, b i :

Coefficient of the equations

c p :

Specific heat capacity at constant pressure, J/(kg·K)

C :

Thermal capacity, J/K

D :

Diameter, m

h :

Specific enthalpy, J/kg

L :

Length or thickness, m

p :

Pressure, Pa

q m :

Mass flow rate, kg/s

Q :

Heat transfer rate, W

T :

Temperature, K

u :

Velocity, m/s

V :

Volume, m3

-x :

Average mass quality

α :

Heat convection coefficient, W/(m2.K)

β :

Thermal leakage factor, W/(m.K)

η :

Length along the air flow direction, m

θ :

Temperature, °C

µ :

Dynamic viscosity, kg/(m·s)

ξ :

Length along the tube, m

ρ :

Density, kg/m

τ :

Time, s

a, as:

Air, air side

am:

Ambient

eff:

Effective

f:

Refrigerant, refrigerant side

in:

Inside

l:

Liquid

v:

Vapor

w:

Tube wall

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Authors and Affiliations

  1. Institute of Refrigeration and Cryogenics, Shanghai Jiaotong University, Shanghai, 200240, China

    Xiu-ping Su  (苏秀平), Jiang-ping Chen  (陈江平) & Zhi-jiu Chen  (陈芝久)

  2. BSH Bosch and Siemens Cooling Appliances Co., Ltd., Chuzhou, 239016, Anhui, China

    Xiao-tian Zhou  (周小天)

Authors
  1. Xiu-ping Su  (苏秀平)
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  2. Jiang-ping Chen  (陈江平)
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  3. Zhi-jiu Chen  (陈芝久)
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  4. Xiao-tian Zhou  (周小天)
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Correspondence to Xiu-ping Su  (苏秀平).

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Su, Xp., Chen, Jp., Chen, Zj. et al. Dynamic simulation and performance investigation of no-frost refrigerator: Part I mathematical model. J. Shanghai Jiaotong Univ. (Sci.) 14, 40–44 (2009). https://doi.org/10.1007/s12204-009-0040-4

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  • DOI: https://doi.org/10.1007/s12204-009-0040-4

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