From  the  literature  review,  it  can  be  seen  that  the    indoor

environment not only affects the performance of air curtains,    but

also   determines  the  energy  consumption   of   the   supermarket

When the entire discharged air from the DAG is drawn back into

HVAC  system。  However,  few  studies  have  gave   comprehensive

details on the heat transfer and fluid flow characteristics   coupling

,  the infiltration air flow  goes to zero,   which

the supermarket HVAC system and the VORDC, and the influence of the HVAC system on the thermal performance of VORDC。 In fact, the heat transfer and fluid flow characteristics include multiple length scales from the supermarket HVAC system to the products in the VORDC [26], as is show in Fig。 1。 Therefore, the work described in this paper intends to evaluate the influence of super- market HVAC system (such as air temperature, relative humidity and velocity, et al。) on the thermal performance and energy con-

sumption of VORDC based on a multi-scale   approach。

represents the best insulating performance of air  curtains。

Considering the influence of the PBP airflow, the NIR formula can be defined in Eq。  (2)

NIR ¼ ð1 — bÞNIR0  þ bNIR0NIRPBP ð2Þ

where, b is the mass flow ratio from PBP which can be obtained based on Eq。 (3)  and NIRPBP  is  the NIR  for  PBP airflow given  by Eq。 (4)

The previous work has proved the feasibility of the    multi-scaleapproach which couples the supermarket HVAC system and the VORDC。 The fluid flow and heat transfer process for different scales

models are assumed as a 3D steady-state model。 The basic govern- ing  equations  are  continuity,  momentum  and  energy equations。

The turbulence is modeled by the standard j–e two-equation model。  Considering  the  mixing  fluid  of  dry  bulb  air  and   water

vapor and the heat gain of products through radiation, a species transfer model and the discrete ordinates model are used, respec- tively。 The SIMPLE algorithm is employed to deal with the pres- sure–velocity coupling。 The convection term is  discretized using the second order upwind scheme。

2。Parameter definitions

Due to the fluctuation in the air curtains, the ambient warm air is entrained throughout the entire height of the display cabinet opening and mixed with the air curtains。 A portion of the mixed ambient air will enter the return air grille, which is defined as infil- tration。 The rest spills into ambient at the bottom of the opening。 Generally, the non-dimensional form of the infiltration rate with- out perforated back papal (PBP)  airflow,  NIR0,  is  defined  as Eq。 (1) [27]。

The ambient measurement point of a VORDC is midway along

the cabinet length in accordance with the EN 441-4。 The point loca- tion is shown in Fig。  2。

The cooling load of refrigerated display cabinets mainly consists of the heat transfer between the fabric of the cabinet and the ambi- ent air, radiation between the products and surrounding surfaces, heat gains from fan motor and lights and infiltration of ambient air across the air curtains [28]。 The total cooling loads can be calcu- lated simply by Eq。 (5)。 It can be pided into sensible Eq。 (6) and latent Eq。 (7) components [2,29]。 Thus, the electricity consumption can be obtained by cooling load pided by the coefficient of per- formance (COP) of refrigeration system。 Commonly, the COP of a middle typical temperature VORDC is 2   [30]。