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# Relative Humidity

Humidity is the term used to describe the amount of water vapor that is present in the air. It is expressed in terms of the concentration of the vapor to the amount of air. The level of humidity is related to the occurrence of dew, fog, and precipitation phenomena. Humidity modeling is possible in SimScale.

As wet air is lighter than dry air (humidity affects the fluid density), the level of humidity can have an impact on the flow patterns. This is most important in heat, ventilation, and air conditioning (HVAC) systems where variations in humidity are to be expected across the analyzed domain.

When enabled, SimScale computes the variations in the density of air due to the humidity alongside its diffusion and conduction with the airflow. Humidity sources and sinks are also defined alongside the flow inlet and outlet boundary conditions.

## Simulation Setup for Modeling Humidity

### Global Settings

The computation of the humidity effects and result fields are activated in the global settings panel for the Conjugate Heat Transfer v2 simulation. Please be aware that the Compressible toggle must be enabled before Relative humidity can be:

### Model

The Model panel includes the Turbulent Schmidt number, which is used to compute the ratio of turbulent transport of momentum to the turbulent transport of humidity in the fluid. It appears as a parameter in the transport equation for the specific humidity:

$$\frac{ \partial \rho \xi }{ \partial t} + \nabla\cdot ( \rho U \xi ) = \nabla \cdot ( \mu_{eff} \nabla \xi ) + S_{\xi}, \tag{1}$$

$$\mu_{eff} = \mu_{lam} + \frac{ \mu_{turb} }{ Sc_t }, \tag{2}$$

Where:

• $$\rho$$ is the fluid density
• $$\xi$$ is the specific humidity
• $$t$$ is time
• $$U$$ is the velocity vector
• $$\mu$$ is the dynamic viscosity, subscripts refer to effective, laminar and turbulent
• $$Sc_t$$ is the turbulent Schmidt number

### Boundary Conditions

An additional parameter to specify the source/sink of humidity is present in some boundary conditions such as velocity inlets, pressure inlets, and pressure outlets. This allows the user to indicate the percentage of relative air humidity at the assigned surfaces.

The level of humidity present in the air is measured in three principal forms:

• Relative humidity: It is the ratio of the amount of water vapor present in the atmosphere to the maximum amount of water vapor that air can hold before precipitation occurs (at a given temperature). These concepts are quantified respectively as the partial pressure of water vapor and the equilibrium vapor pressure of water. The field is unitless and is often presented as a percentage. We can express this ratio as:

$$\phi = \frac{ p_{H_2O} }{ p_{sat} }$$

• Absolute humidity: It is the mass of water vapor present in a given volume of wet air (air mixed with water vapor). It has units of mass per volume, and can be computed as:

$$AH = \frac{ m_{H_2O} }{ V_{mixture} }$$

• Specific humidity: Also known as the moisture content, it is the mass of water vapor present in a given mass of air/water mixture. It has units of mass per mass, expressed as $$g/kg$$ or as $$kg/kg$$. Can be computed as:

$$\xi = \frac{ m_{H_2O} }{ m_{H_2O} + m_{air} }$$

These three fields are used to compute the effects of humidity in the flow, and will also be delivered for post-processing as part of the result fields.

## Limitations

The main limitation in the current humidity modeling inside SimScale is the lack of condensation and evaporation processes.

Condensation occurs when the relative humidity reaches a value of 100%. In this case, the consequent effect on the humidity level and temperature would not be taken into account. It is up to the user to verify that the relative humidity level at any point does not surpass the limit value of 100%.

Last updated: March 7th, 2023