THE BASIC THEORY OF GRAVITATIONAL FLOWS THROUGH SINGLE OPENINGS CONSIDERING ROOM TEMPERATURE CHANGE

Abstract

 The purpose of this paper is to derive the numerical expressions on the air velocity and the neutral plane height at the indoor and outdoor boundary area from the theory of gravitational flows through a single opening.

 In Chapter 2, we examined the relation between steady-state condition and mass flow balance in gravitational ventilation through opening. From the consideration based on the formula which is expressing the air volume difference in gravitational ventilation, it was shown that steady state conditions both of flow rate and temperature are necessary for the assumption of mass flow balance in the same space volume. This condition is not general as a condition of a room where ventilated by gravitational flows. Thus, the numerical expression that simply assuming mass flow balance cannot be adopted to general conditions. In this paper, we derived the mass conservation formula (4) corrected with the coefficient rm in order to apply the mass conservation law to the same space volume, assuming that the room temperature changes due to gravitational flows.

 In Chapter 3, we applied the energy conservation law to the area through which air flows by gravitational ventilation, and derived the basic formula (6) considering mass flow correction and discharge coefficient. The formula (7) for obtaining the boundary air velocity, and the formula (10) to determine the neutral plane height are also shown. And the conventional numerical expression of gravitational ventilation can be considered as a formula assuming an external reference point where the windward dynamic pressure is 0. We also corrected the conventional formula obtaining neutral plane height, and derived the formula (11). The inclination of the neutral plane height which appears in the calculation result of CFD was explained by this formula.

 In Chapter 4, in order to verify the theory of gravitational ventilation shown in Chapter 3, numerical experiments using CFD and calculation results of each formula in Chapter 3 were compared. As a result, the air velocity distribution and the neutral plane height calculated from the equations shown in this paper coincided with CFD and the theoretical validity was proved. On the other hand, in the conventional numerical expressions, since the dynamic pressure distribution at the boundary area was ignored, there was an error in the neutral plane height and the air velocity distribution.