2023 Asia Pacific Mathematical Modeling Competition Question B

Microclimate regulations in glass greenhouses

The yield of greenhouse crops is affected by various climatic factors, including temperature, humidity and wind speed [1]. Among them, suitable temperature and wind speed are the keys to plant growth [2]. In order to adjust the temperature, wind speed and other climate factors in the glass greenhouse, the design of the greenhouse usually uses a ventilation system with a greenhouse fan, as shown in Figure 1. The position of the greenhouse fan and the speed of the warm air outlet affect the distribution and uniformity of the velocity field and temperature field in the greenhouse. So how to optimize your greenhouse fan

, obtaining appropriate wind speed and temperature and improving their uniformity are important issues that need to be solved in the current glass greenhouse design.

Glass greenhouses are sealed and placed indoors without considering external factors such as greenhouse doors, ventilation strips, solar radiation and other environmental factors. The size of the glass greenhouse currently designed is 10 meters! 3m! 2 meters (length! width height) and the size of the greenhouse fan is 0.5 meters! 0.5 meters, located on the left side of the greenhouse. The center of the greenhouse fan is located 1.3 meters above the ground, as shown in Figure 2. The boundary conditions on the fan side of the greenhouse are set as velocity inlet conditions, blowing warm air at 40" in the horizontal direction, with an average speed of 2 m/s. The outer glass and subsoil of the greenhouse are set as wall conditions, which mainly exchange energy with the entire greenhouse. Convection heat transfer and conduction [3]. Initial temperature is set to 20". When crops are grown in a greenhouse, it is necessary to consider the canopy resistance of the crop. The crop model can be simplified to porous media with dimensions of 8 meters! 2 m! 0.5 meters (length! width height) [4], placed in the center of the greenhouse. The suitable wind speed for crop growth in the greenhouse is

0.31m/s, suitable temperature is 23-26”.

Question 1: Please establish a mathematical model of temperature and wind speed distribution in a glass greenhouse without crops. Displays the cross-sectional wind speed and temperature distribution at greenhouse height 0. 5 meters.

Question 2: Please establish a mathematical model of the temperature and wind speed distribution in a glass greenhouse where crops are grown. The wind speed and temperature distributions are presented for two cross-sections in the greenhouse: one at a height of 0.5 m (crop canopy level) and the other at a height of 0.1 m (within the crop canopy). Analyze whether these conditions are suitable for crop growth.

Question 3: Please provide the temperature and wind speed distribution in the glass greenhouse for the following two situations and compare with the solution proposed in the second question. In option 1, increase the speed of the warm air outlet from 2 m/s to 3 m/s. In option 2, the greenhouse fan is lowered by moving it from 1.3 meters to 1 meter.

Question 4: Can your team further optimize the greenhouse fan design of the glass greenhouse in terms of the number, location, wind speed, blowing temperature, specifications, different crops and other factors of the greenhouse fans?

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