Pipe (MA)

The net consumption of moist air in the volume of the pipe is equal to:

,

,

,

,

where

The equation of conservation of mass of water vapor relates the mass flow rate of water vapor to the dynamics of the humidity level in the internal volume of humid air:

.

Similarly, the equation of conservation of impurity gas mass relates the mass flow rate of impurity gas to the dynamics of the impurity gas level in the internal volume of humid air.:

.

The equation of mass conservation of a mixture relates the mass flow rate of a mixture to the dynamics of pressure, temperature, and mass fractions of the internal volume of moist air.:

.

Finally, the energy conservation equation relates energy consumption to the dynamics of pressure, temperature, and mass fractions of the internal volume of humid air.:

.

The equation of state relates the density of a mixture to pressure and temperature:

.

The universal gas constant of the mixture is:

.

The momentum balance for each half of the pipe simulates a pressure drop due to the momentum of the gas flow and viscous friction:

,

,

where

Pressure loss due to viscous friction and they depend on the flow regime. The Reynolds numbers for each half of the pipe are defined as:

,

,

where

If the Reynolds number is less than the parameter value Laminar flow upper Reynolds number limit, then the flow is in laminar mode. If the Reynolds number is greater than the limit value of the parameter Turbulent flow lower Reynolds number limit, then the current is in a turbulent mode.

In the laminar flow regime, the pressure loss due to viscous friction is:

,

,

where

In the turbulent flow regime, the pressure loss due to viscous friction is:

,

,

where

The Darcy coefficients are calculated from the Haaland correlation:

,

,

where — parameter value Internal surface absolute roughness.

When the Reynolds number is between the upper limit of the Reynolds number for laminar flow and the parameter values of the lower limit of the Reynolds number for turbulent flow, the flow is in a transition state between laminar and turbulent flow modes. Pressure losses due to viscous friction in the transient mode follow a smooth relationship between losses in the laminar flow mode and losses in the turbulent flow mode.

The heat exchange with the pipe wall through the H port is added to the energy of the gas represented by the internal node through the energy conservation equation. Therefore, the pulse balance for each half of the pipe between port A and the inner node and between port B and the inner node is considered an adiabatic process. Adiabatic relations:

,

,

where — specific enthalpy at port A, port B, or internal node I, as indicated by the subscript.

The equation of convective heat transfer between the pipe wall and the internal gas volume:

,

where — pipe surface area, .

If no condensation forms on the wall surface, assuming an exponential temperature distribution along the pipe, the convective heat transfer is:

,

where

Heat transfer coefficient depends on the Nusselt number:

,

where — the coefficient of thermal conductivity calculated at an average temperature.

The Nusselt number depends on the flow regime. The Nusselt number in the laminar flow mode is constant and is equal to the value of the parameter Nusselt number for laminar flow heat transfer. The Nusselt number in the turbulent flow regime is calculated from the Gnelinsky equation:

,

where — the Prandtl number calculated at an average temperature.

The average Reynolds number is:

,

where — dynamic viscosity, estimated at an average temperature.

When the average Reynolds number is between the values of the parameters of the upper limit of the Reynolds number for laminar flow and the lower limit of the Reynolds number for turbulent flow, the Nusselt number corresponds to a smooth transition between the values of the Nusselt number for laminar and turbulent flows.

The equations in this section take into account condensation, which occurs when the volume of humid air becomes saturated.

When the volume of humid air reaches saturation, condensation may form. The specific humidity at saturation is:

,

where

The condensation consumption is equal to:

,

where — parameter value Condensation time constant.

Condensed water is subtracted from the volume of moist air, as shown in the equations of conservation of mass. The energy associated with condensed water is:

,

where — specific enthalpy of evaporation, estimated at .

The parameters of changes in the amount of moisture and impurity gases are related to each other as follows:

,

,

,

,

.

Humid air units that contain an internal volume of liquid (such as chambers, transducers, and so on) simulate the condensation of water vapor when this volume of liquid becomes completely saturated with water vapor, that is, at 100% relative humidity. However, water vapor can also condense on a cold surface, even if the air volume as a whole has not yet reached saturation. The possibility of modeling this effect in the block Pipe (MA) It is important because many HVAC systems contain pipes and ducts. If these pipes and ducts are poorly insulated, their surface may cool down and condensation will form on the wall surface. Please note that this effect does not replace condensation that occurs when the volume of humid air reaches 100% relative humidity, both effects can occur simultaneously.

To simulate the effect of condensation on the cold surface of a pipe in contact with a volume of humid air, check the box Condensation on wall surface. In this case, the convective heat transfer equation must take into account both visible and latent heat, and the unit has an additional equation that calculates the condensation rate of water vapor on the surface.

If the check box is Condensation on wall surface if established, then the combined convective heat transfer is:

,

where

This equation is similar to the convective heat transfer equation, but the temperature difference has been replaced by the difference in enthalpies of the mixture. Since the enthalpy of the mixture depends on both the temperature and the composition of the humid air, the difference in the enthalpy of the mixture takes into account both the change in temperature and the change in moisture content. The unit captures both explicit and hidden thermal effects. The parts of the equation related to the exponent and correlation, which are used in calculating the heat transfer coefficient, remain the same as before, since the model is derived based on the analogy between thermal and mass exchange.

To simplify the derivation, the equation uses the enthalpy of the mixture per unit mass of dry air and impurity gas, as opposed to the enthalpy of the mixture per unit mass of the mixture, since the amount of dry air and impurity gas does not change during the condensation of water vapor. In order for the equation to remain consistent, the enthalpy difference of the mixture is multiplied by the mass flow rate of dry air and impurity gases.

The enthalpy of the mixture per unit mass of dry air and impurity gases at the inlet is:

,

where

The enthalpy of the mixture per unit mass of dry air and impurity gases at the wall is:

,

where

Function in the previous equation, provides switching between dry and wet heat transfer:

The condensation rate of water vapor on the wall surface is equal to:

.

This equation is similar to the combined equation of convective heat transfer, since the amount of water vapor condensing on the wall is the same as convective mass transfer from moist air to the pipe wall. The exponential component of the equation is also the same because of the analogy used between thermal and mass exchange.

The energy associated with the water condensing on the pipe wall is equal to:

,

where — specific enthalpy of evaporation at wall temperature.

A significant part of the convective heat exchange between the pipe wall and the humid air is:

.

This equation has a plus sign because it is negative when cooling humid air. Thus, adding , which is a positive value, eliminates the hidden part of the heat transfer.

The block then uses this value. in the first convective heat transfer equation for calculating heat transfer at port H.

The pressure in the subsonic current at port A or B is equal to the value of the corresponding variable:

,

.

However, the variable port pressures used in the momentum balance equations, and , do not necessarily match the pressure in the variables and because the pipe outlet can reach the sound barrier in terms of speed. The sound barrier occurs when the outlet pressure is low enough. At this point, the flow rate depends only on the conditions at the entrance. Therefore, when the sound barrier is reached, the outlet pressure ( or , depending on what the output is) cannot decrease further, even if the pressure is downstream, represented by or , continues to decline.

A sound barrier may be present at the outlet of the pipe, but not at the inlet. Therefore, if port A is an intake port, then . If port A is an outlet, then:

Similarly, if port B is an intake port, then . If port B is an outlet, then:

The pressure at the sound barrier in the openings A and B is determined from the balance of pulses, assuming that the exit velocity is equal to the speed of sound:

,

.

Use the parameter group Initial Targets to set the priority and initial target values for the block parameter variables before modeling. For more information, see Configuring physical blocks using target values.