N-point ASOM

Generally, the existing ASOM may be divided into two types:

  • Indirect ones: converting the description of boundary conditions to the description of a box boundary conditions around the supply opening.

  • Direct ones: describing boundary conditions in the vicinity of supply openings. Contrary to indirect methods, they need neither measurements nor empirical formulas. There are mainly two direct ASOMs:

    • Basic model that uses a simple opening with the same effective area as the complex diffuser. It may cause obvious error for a diffuser with small effective area.

    • Momentum model that describes velocity vectorbased on diffuser effective area. To keep the appropriate supply air mass flow and to introduce the same amount of air into the room, the boundary conditions for continuity equation and momentum equations have to be described separately.

In principle, direct ASOM can be applied for any case. Thus, it should be the first choice for engineering application.

«N-point ASOM» combines the positive features of both direct ASOM and momentum method.

The essential of N-point ASOM is to replace the real diffuser by several simple openings so as to reduce thenumber of grids for numerical calculation, while maintaining the inlet momentum and mass flows.

For a supply opening with one discharge direction, the actual inlet momentum flow is

\[J_{in} = mV_r = m\frac{L}{A_c}\]

  • \(J_{in}\) = momentum flux (kg.m/s²)

  • \(m\) = mass flow rate (kg/s)

  • \(V_r\) = velocity (m/s)

  • \(L\) = volume flow rate (m³/s)

  • \(A_c\) = effective area of the supply opening (m²)

To describe the right momentum flow while maintainingthe same mass flow rate, the effective area coefficient for calculating the inlet momentum source term in the CFD code is used. That is:

\[J_{in} = m\frac{L}{R_{fa}A}\]

  • \(A\) = gross area of the supply opening (m²)

  • \(R_{fa}\) = ratio of effectivearea to gross area of the supply opening (\(\leqslant 1\))

By this equation, inlet momentum flow can be correctly defined and the right inlet mass flow is also given at the same time. It is not necessary to describe boundary conditions for momentum and continuity equations separately.

The buoyancy inflow of the supply opening is

\[B = g\Delta\rho L\]

  • \(g\) = acceleration of gravity (m/s²)

  • \(\Delta\rho\) = difference of supply and indoor air density (kg/m³)

  • \(L\) = supply volume flow rate (m³/s)

For indoor air, we have

\[ \Delta\rho = -\Delta T\beta\rho,\\ \beta = \frac{1}{T_0}\]

where \(\Delta T\) is the difference of supply and indoor air temperature (K), \(\beta\) is the volumetric coefficient of expansion (K\(^{-1}\)) and \(T_0\) is the average temperature of indoor air (K).

Therefore,

\[B=−g\frac{\Delta T}{T_0}\rho L.\]

The \(N\)-point ASOM can ensure \(B\) if \(L\) is correctly defined. Therefore, it can be applied for both isothermal and non-isothermal air jets.
Some validation cases of \(N\)-point ASOM can be found in Ref. [5].

References

  • [5] Zhao Bin, Li Xianting. The \(N\)-point air supply opening model for indoor airflow simulation. Department of Building Science, School of Architecture, Tsinghua University, China, 2000.