Engee documentation

Pipe (MA)

Rigid piping for the flow of moist air.

blockType: AcausalFoundation.MoistAir.Elements.Pipe

pipe (ma)

Path in the library:

/Physical Modeling/Fundamental/Moist Air/Elements/Pipe (MA)

Description

Block Pipe (MA) simulates the dynamics of the flow of moist air in a pipe. The unit takes into account losses due to viscous friction and convective heat exchange with the pipe wall. There is a constant volume of moist air in the pipe. The pressure and temperature vary depending on the compressibility and heat capacity of this volume of moist air. The flow becomes critical when the velocity of the humid air at the outlet reaches the speed of sound.

Block Controlled Mass Flow Rate Source (MA) or a block Mass Flow Rate Source (MA), connected to the block Pipe (MA), cannot set a greater mass flow rate than the possible mass flow rate of the block.

The equations

The block’s equations use these symbols:

  • Lower indexes , , and indicate the properties of dry air, water vapor, impurity gas, and water droplets, respectively.;

  • Lower index indicates the water vapor saturation level;

  • Lower indexes , , and specify the appropriate port;

  • Lower index indicates the properties of the internal volume of humid air.

  • — mass consumption;

  • — energy consumption;

  • — heat consumption;

  • — pressure;

  • — density;

  • — universal gas constant;

  • — the volume of moist air inside the pipe;

  • — specific heat capacity at constant volume;

  • — specific heat capacity at constant pressure;

  • — specific enthalpy;

  • — specific internal energy;

  • — mass fraction ( — specific humidity, which is a synonym for the mass fraction of water vapor);

  • — molar fraction;

  • — relative humidity;

  • — humidity coefficient;

  • — the mass ratio of water droplets to moist air;

  • — temperature;

  • — the time.

Conservation of mass and energy

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









where

  • — condensation consumption;

  • — the rate of evaporation of water droplets;

  • — loss of energy by condensed water per unit of time;

  • — parameter value Fraction of condensate entrained as water droplets;

  • — energy per unit of time added by sources of moisture and impurity gases;

  • and — the mass consumption of water and gas, respectively, through the port S. Values , and They are determined by sources of moisture and impurity gases connected to the S port of the pipe.

The equation of conservation of mass of water vapor relates the mass flow rate of water vapor with 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 conservation of mass of water droplets relates the mass flow rate of water droplets to the dynamics of entrained water droplets 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:

Momentum Balance

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

  • — gas pressure at port A, port B or internal node I, as indicated by the subscript;

  • — density at port A, port B, or internal node I, as indicated by the subscript;

  • — the cross-sectional area of the pipe;

  • and — pressure loss due to viscous friction.

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

  • — hydraulic pipe diameter;

  • — dynamic viscosity in the inner node.

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

  • — parameter value Laminar friction constant for Darcy friction factor;

  • — parameter value Aggregate equivalent length of local resistances.

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



where

  • — the Darcy coefficient on port A or B, as indicated by the subscript.

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.

Convective heat exchange

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

  • — inlet temperature, depending on the flow direction;

  • — average mass flow rate from port A to port B;

  • — specific heat capacity calculated at an average temperature.

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.

Saturation and condensation

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

  • — relative humidity at saturation (usually 1);

  • — water vapor saturation pressure, estimated at .

The condensation consumption is equal to:

where — parameter value Water vapor condensation time constant.

The rate of evaporation of droplets is:

where — parameter value Water droplets evaporation time constant.

Condensation effects on the wall surface

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

where

  • — mass consumption of dry air and impurity gases at the inlet;

  • — the enthalpy of the mixture per unit mass of dry air and impurity gases at the wall;

  • — the enthalpy of the mixture per unit mass of dry air and impurity gases at the inlet.

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

  • — specific enthalpy of dry air and impurity gases at the inlet;

  • — specific enthalpy of water vapor at the inlet;

  • — humidity coefficient at the entrance.

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

where

  • — specific enthalpy of dry air and impurity gases at the wall;

  • — specific enthalpy of water vapor at the wall;

  • — the humidity coefficient at the wall, defined as

    where — moisture saturation coefficient based on the wall temperature.

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

  • When the wall temperature is higher than the dew point, then therefore, condensation does not occur, and the unit outputs only the temperature difference. .

  • When the wall temperature is below the dew point, therefore, condensation occurs and displays the difference in temperature and humidity.

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 during 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.

Current at the speed of sound

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 , may not 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 pulse balance, assuming that the exit velocity is equal to the speed of sound:



Assumptions and limitations

  • The pipe wall is absolutely rigid.

  • The stream is fully developed. Friction losses and heat transfer do not include input effects.

  • The effect of gravity is negligible.

  • The inertia of the air is negligible.

  • This block does not simulate supersonic flow.

  • The equations of wall condensation are based on the analogy between thermal and mass transfer and, therefore, are valid only when the Lewis number close to 1.

Variables

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.

Ports

Conserving

# B — input or output port
humid air

Details

The humid air port corresponds to the inlet or outlet of the pipe. This block has no internal orientation.

Program usage name

port_b

# H — pipe wall temperature
warm

Details

A thermal port related to the temperature of the pipe wall. This temperature may differ from the temperature of humid air.

Program usage name

thermal_port

# S — adding or removing moisture and impurity gases
humid air

Details

Connect this port to the S port of the library block Moist Air: Sources for adding or removing moisture and impurity gases.

Dependencies

To use this port, set the parameter Moisture and trace gas source meaning Controlled.

Program usage name

source_port

# A — input or output port
humid air

Details

The humid air port corresponds to the inlet or outlet of the pipe. This block has no internal orientation.

Program usage name

port_a

Output

# W — condensation rate
scalar

Details

The output port that contains the value of the condensation flow rate in the pipe. If the parameter Condensation on wall surface When switched on, this port reports the total steam condensation rate, which includes condensation from the volume of saturated humid air, as well as condensation on the pipe wall.

Data types

Float64
Complex numbers support

No

# F — data on pressure, temperature, humidity and amount of impurity gases
vector

Details

The output port is a vector with the following elements: pressure, temperature, humidity level and the amount of impurity gases inside the component. A block is used to decompress the vector signal Measurement Selector (MA).

Data types

Float64
Complex numbers support

No

Parameters

Initial Conditions

# Initial trace gas mass fraction — the amount of impurity gas in the humid air channel

Details

The amount of impurity gas in moist air by mass fraction at the beginning of the simulation. The mass fraction is determined relative to the total mass of water vapor, impurity gas, and dry air.

The block ignores this parameter if for the parameter Trace gas model in the block Moist Air Properties (MA) the value is set None.

Dependencies

To use this parameter, set for the parameter Initial trace gas specification meaning Mass fraction.

Default value

0.001
Program usage name

x_g_start
Evaluatable

Yes

# Initial relative humidity — relative humidity at the beginning of the simulation

Details

The relative humidity of the humid air at the beginning of the simulation. Relative humidity is the ratio of the partial pressure of water vapor to the saturation pressure of water vapor, or the ratio of the molar fraction of water vapor to the molar fraction of water vapor at saturation.

Dependencies

To use this parameter, set for the parameter Initial humidity specification meaning Relative humidity.

Default value

0.5
Program usage name

RH_start
Evaluatable

Yes

# Initial temperature — temperature at the beginning of the simulation
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

The initial temperature of the humid air.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

293.15 K
Program usage name

T_start
Evaluatable

Yes

# Initial specific humidity — specific humidity at the beginning of the simulation

Details

The specific humidity of the humid air at the beginning of the simulation. Specific humidity is the mass fraction of water vapor relative to the total mass of water vapor, impurities, and dry air.

Dependencies

To use this parameter, set for the parameter Initial humidity specification meaning Specific humidity.

Default value

0.01
Program usage name

x_w_start
Evaluatable

Yes

# Initial wet-bulb temperature — the temperature according to the wet thermometer at the beginning of the simulation
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

The temperature according to the wet thermometer at the beginning of the simulation. The unit uses this value to calculate humidity.

Dependencies

To use this parameter, set for the parameter Initial humidity specification meaning Wet-bulb temperature.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

287 K
Program usage name

T_wb_start
Evaluatable

Yes

# Initial humidity ratio priority — priority of the humidity coefficient parameter
None | Low | High

Details

The priority that the solver assigns to the parameter Initial humidity ratio during block initialization.

Set this parameter to High to determine the initial conditions. You may need to set this parameter to Low or None if this initial condition conflicts with the initial conditions of another block.

Dependencies

To use this parameter, set for the parameter Initial humidity specification meaning Humidity ratio.

Values

None | Low | High
Default value

High
Program usage name

HR_priority
Evaluatable

No

# Initial water vapor mole fraction — molar fraction of water vapor at the beginning of the simulation

Details

The molar fraction of water vapor in a moist air channel at the beginning of the simulation. The molar fraction of water vapor is determined relative to the total molar amount of water vapor, impurities, and dry air.

Dependencies

To use this parameter, set for the parameter Initial humidity specification meaning Mole fraction.

Default value

0.01
Program usage name

y_w_start
Evaluatable

Yes

# Initial temperature priority — priority of the temperature parameter
None | Low | High

Details

The priority that the solver assigns to the parameter Initial temperature during block initialization.

Set this parameter to High to determine the initial conditions. You may need to set this parameter to Low or None if this initial condition conflicts with the initial conditions of another block.

Values

None | Low | High
Default value

High
Program usage name

T_priority
Evaluatable

No

# Initial humidity ratio — humidity coefficient at the beginning of the simulation

Details

The humidity coefficient in the humid air channel at the beginning of the simulation. The humidity coefficient is the ratio of the mass of water vapor to the mass of dry air and impurity gases.

Dependencies

To use this parameter, set for the parameter Initial humidity specification meaning Humidity ratio.

Default value

0.01
Program usage name

HR_start
Evaluatable

Yes

# Initial trace gas mole fraction — molar fraction of impurity gas at the beginning of the simulation

Details

The amount of impurity gas in the moist air channel by molar fraction at the beginning of the simulation. The molar fraction is determined relative to the total molar amount of water vapor, impurity gas, and dry air.

The block ignores this parameter if for the parameter Trace gas model in the block Moist Air Properties (MA) the value is set None.

Dependencies

To use this parameter, set for the parameter Initial trace gas specification meaning Mole fraction.

Default value

0.001
Program usage name

y_g_start
Evaluatable

Yes

# Initial specific humidity priority — priority of the specific humidity parameter
None | Low | High

Details

The priority that the solver assigns to the parameter Initial specific humidity during block initialization.

Set this parameter to High to determine the initial conditions. You may need to set this parameter to Low or None if this initial condition conflicts with the initial conditions of another block.

Dependencies

To use this parameter, set for the parameter Initial humidity specification meaning Specific humidity.

Values

None | Low | High
Default value

High
Program usage name

x_w_priority
Evaluatable

No

# Initial mass ratio of water droplets to moist air — the ratio of water droplets to moist air

Details

The initial mass ratio of water droplets to moist air.

Default value

0
Program usage name

r_d_start
Evaluatable

Yes

# Initial trace gas specification — type of impurity gas measurement
Mass fraction | Mole fraction

Details

The type of impurity gas measurement.

Values

Mass fraction | Mole fraction
Default value

Mass fraction
Program usage name

trace_gas_type
Evaluatable

No

# Initial pressure priority — priority of the pressure parameter
None | Low | High

Details

The priority that the solver assigns to the parameter Initial pressure during block initialization.

Set this parameter to High to determine the initial conditions. You may need to set this parameter to Low or None if this initial condition conflicts with the initial conditions of another block.

Values

None | Low | High
Default value

High
Program usage name

p_priority
Evaluatable

No

# Initial mass ratio of water droplets to moist air priority — the priority of the parameter of the ratio of the mass of water droplets to moist air
None | Low | High

Details

The priority that the solver assigns to the parameter Initial mass ratio of water droplets to moist air during block initialization.

Set this parameter to High to determine the initial conditions. You may need to set this parameter to Low or None if this initial condition conflicts with the initial conditions of another block.

Values

None | Low | High
Default value

High
Program usage name

r_d_priority
Evaluatable

No

# Initial trace gas mole fraction priority — priority of the parameter of the molar fraction of the impurity gas
None | Low | High

Details

The priority that the solver assigns to the parameter Initial trace gas mole fraction during block initialization.

Set this parameter to High to determine the initial conditions. You may need to set this parameter to Low or None if this initial condition conflicts with the initial conditions of another block.

Dependencies

To use this parameter, set for the parameter Initial trace gas specification meaning Mole fraction.

Values

None | Low | High
Default value

High
Program usage name

y_g_priority
Evaluatable

No

# Initial wet-bulb temperature priority — the priority of the temperature parameter according to the wet thermometer
None | Low | High

Details

The priority that the solver assigns to the parameter Initial wet-bulb temperature during block initialization.

Set this parameter to High to determine the initial conditions. You may need to set this parameter to Low or None if this initial condition conflicts with the initial conditions of another block.

Dependencies

To use this parameter, set for the parameter Initial humidity specification meaning Wet-bulb temperature.

Values

None | Low | High
Default value

High
Program usage name

T_wb_priority
Evaluatable

No

# Initial trace gas mass fraction priority — priority of the parameter of the mass fraction of impurity gases
None | Low | High

Details

The priority that the solver assigns to the parameter Initial trace gas mass fraction during block initialization.

Set this parameter to High to determine the initial conditions. You may need to set this parameter to Low or None if this initial condition conflicts with the initial conditions of another block.

Dependencies

To use this parameter, set for the parameter Initial trace gas specification meaning Mass fraction.

Values

None | Low | High
Default value

High
Program usage name

x_g_priority
Evaluatable

No

# Initial water vapor mole fraction priority — priority of the parameter of the initial molar fraction of water vapor
None | Low | High

Details

The priority that the solver assigns to the parameter Initial water vapor mole fraction during block initialization.

Set this parameter to High to determine the initial conditions. You may need to set this parameter to Low or None if this initial condition conflicts with the initial conditions of another block.

Dependencies

To use this parameter, set for the parameter Initial humidity specification meaning Mole fraction.

Values

None | Low | High
Default value

High
Program usage name

y_w_priority
Evaluatable

No

# Initial relative humidity priority — priority of the initial relative humidity parameter
None | Low | High

Details

The priority that the solver assigns to the parameter Initial relative humidity during block initialization.

Set this parameter to High to determine the initial conditions. You may need to set this parameter to Low or None if this initial condition conflicts with the initial conditions of another block.

Dependencies

To use this parameter, set for the parameter Initial humidity specification meaning Relative humidity.

Values

None | Low | High
Default value

High
Program usage name

RH_priority
Evaluatable

No

# Initial pressure — humid air pressure at the beginning of the simulation
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

The pressure of humid air at the beginning of the simulation.

Units

Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg
Default value

0.101325 MPa
Program usage name

p_start
Evaluatable

Yes

# Initial humidity specification — the method of setting humidity
Relative humidity | Specific humidity | Mole fraction | Humidity ratio | Wet-bulb temperature

Details

A method for determining the initial humidity of humid air.

Values

Relative humidity | Specific humidity | Mole fraction | Humidity ratio | Wet-bulb temperature
Default value

Relative humidity
Program usage name

moisture_type
Evaluatable

No

Moisture and Trace Gas

# Added trace gas temperature specification — the method of determining the temperature of the impurity gas
Atmospheric temperature | Specified temperature

Details

Choose a method for determining the temperature of the impurity gas:

  • Atmospheric temperature — Use the ambient temperature.

  • Specified temperature — specify the value using the parameter Temperature of added trace gas.

Dependencies

To use this parameter, set for the parameter Moisture and trace gas source meaning Constant.

Values

Atmospheric temperature | Specified temperature
Default value

Atmospheric temperature
Program usage name

trace_gas_temperature_type
Evaluatable

No

# Temperature of added trace gas — impurity gas temperature
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

Enter the desired temperature of the added impurity gas. This temperature remains constant during the simulation. The unit uses this value only to estimate the specific enthalpy of the added impurity gas. The specific enthalpy of the impurity gas removed depends on the temperature of the connected volume of humid air.

Dependencies

To use this parameter, set for the parameter Added trace gas temperature specification meaning Specified temperature.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

293.15 K
Program usage name

T_g_const
Evaluatable

Yes

# Relative humidity at saturation — relative humidity, above which moisture condensation occurs

Details

The relative humidity above which condensation occurs.

Default value

1
Program usage name

RH_ws
Evaluatable

Yes

# Fraction of condensate entrained as water droplets — the proportion of condensate in water droplets

Details

The proportion of condensate in moist air that is entrained in the form of water droplets.

Default value

1
Program usage name

condensate_droplets_fraction
Evaluatable

Yes

# Rate of moisture added — constant mass consumption of humidity
kg/s | kg/hr | kg/min | g/hr | g/min | g/s | t/hr | lbm/hr | lbm/min | lbm/s

Details

The mass flow of water vapor through the unit. A positive value increases the amount of moisture in the pipe volume. A negative value extracts moisture from this volume.

Dependencies

To use this parameter, set for the parameter Moisture and trace gas source meaning Constant.

Units

kg/s | kg/hr | kg/min | g/hr | g/min | g/s | t/hr | lbm/hr | lbm/min | lbm/s
Default value

0 kg/s
Program usage name

mdot_moisture_const
Evaluatable

Yes

# Temperature of added moisture — temperature of added moisture
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

Enter the desired temperature of the added moisture. This temperature remains constant during the simulation. The unit uses this value only to estimate the specific enthalpy of the added moisture. The specific enthalpy of the removed moisture depends on the temperature of the connected volume of humid air.

Dependencies

To use this parameter, set for the parameter Added moisture temperature specification meaning Specified temperature.

Units

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

293.15 K
Program usage name

T_moisture_const
Evaluatable

Yes

# Water vapor condensation time constant — condensation time constant
s | ns | us | ms | min | hr | d

Details

A time scale factor that characterizes the time period for the oversaturated volume of humid air to return to saturation level due to condensation of excess moisture.

Units

s | ns | us | ms | min | hr | d
Default value

0.001 s
Program usage name

condensation_time_constant
Evaluatable

Yes

# Rate of trace gas added — mass consumption of added impurity gas
kg/s | kg/hr | kg/min | g/hr | g/min | g/s | t/hr | lbm/hr | lbm/min | lbm/s

Details

Reflects the mass flow rate of impurity gas added or removed from the pipe. A positive value adds impurity gas to the pipe volume. A negative value removes impurity gas from this volume.

Dependencies

To use this parameter, set for the parameter Moisture and trace gas source meaning Constant.

Units

kg/s | kg/hr | kg/min | g/hr | g/min | g/s | t/hr | lbm/hr | lbm/min | lbm/s
Default value

0 kg/s
Program usage name

mdot_g_const
Evaluatable

Yes

# Moisture added or removed — adds or removes moisture in the form of water vapor or water
Water vapor | Water droplets

Details

Choose in which form the unit adds or removes moisture — in the form of steam or water:

  • Water vapor — the enthalpy of added or removed moisture corresponds to the enthalpy of water vapor, which is greater than the enthalpy of water.

  • Water droplets — the enthalpy of added or removed moisture corresponds to the enthalpy of water, which is less than the enthalpy of water vapor.

Dependencies

To use this parameter, set for the parameter Moisture and trace gas source meaning Constant.

Values

Water vapor | Water droplets
Default value

Water vapor
Program usage name

moisture_source_phase
Evaluatable

No

# Condensation on wall surface — the effect of condensate on the cold surface of a pipe in contact with a volume of moist air

Details

Setting this flag allows you to simulate the condensation effect on the cold surface of a pipe in contact with a volume of humid air.

Default value

false (switched off)
Program usage name

wall_condensation
Evaluatable

No

# Added moisture temperature specification — method for determining the temperature of added moisture
Atmospheric temperature | Specified temperature

Details

Choose a method for determining the temperature humidity:

  • Atmospheric temperature — Use the ambient temperature.

  • Specified temperature — specify the value using the parameter Temperature of added moisture.

Dependencies

To use this parameter, set for the parameter Moisture and trace gas source meaning Constant.

Values

Atmospheric temperature | Specified temperature
Default value

Atmospheric temperature
Program usage name

moisture_temperature_type
Evaluatable

No

# Water droplets evaporation time constant — evaporation time constant
s | ns | us | ms | min | hr | d

Details

The characteristic time it takes for water droplets to evaporate, turning into steam.

Units

s | ns | us | ms | min | hr | d
Default value

0.001 s
Program usage name

evaporation_time_constant
Evaluatable

Yes

# Moisture and trace gas source — source of moisture and impurity gases
None | Constant | Controlled

Details

This parameter controls the use of the S port and provides the following features for modeling moisture and impurity gas levels inside the unit:

  • None — no moisture or impurity gas is introduced into or extracted from the unit. The S port is hidden. This value is used by default.

  • Constant — moisture and impurity gases are introduced into the unit or extracted from it at a constant flow rate. The S port is not in use.

  • Controlled — moisture and impurity gases are introduced into or extracted from the unit at a time-varying flow rate. Port S is available. Connect blocks (or several blocks) from the library to this port Moist Air: Sources.

Values

None | Constant | Controlled
Default value

None
Program usage name

moisture_trace_gas_source
Evaluatable

No

# Water vapor evaporated from liquid or condensed to liquid — add or remove water vapor

Details

Select a method for adding or removing steam from the unit:

  • If unchecked, the enthalpy of added or removed moisture corresponds to the enthalpy of water vapor, which is greater than the enthalpy of water.

  • If this option is selected, the enthalpy of added or removed moisture corresponds to the enthalpy of water, which is less than the enthalpy of water vapor.

When water vapor is added, it evaporates from the liquid, and the latent heat is released by the bound volume of the liquid. When water vapor is removed, it condenses into a liquid, and latent heat is released to the associated volume of liquid.

Dependencies

To use this parameter, set for the parameter Moisture and trace gas source meaning Constant, and for the parameter Moisture added or removed meaning Water vapor.

Default value

false (switched off)
Program usage name

vapor_from_liquid
Evaluatable

No

Friction and Heat Transfer

# Laminar friction constant for Darcy friction factor — the effect of pipe geometry on viscous friction losses

Details

A dimensionless coefficient that determines the effect of the geometry of the pipe cross-section on viscous friction losses in the laminar flow regime. Typical values: 64 for circular cross-section, 57 for a square section, 62 for a rectangular section with an aspect ratio 2 and 96 for a thin annular section [1].

Default value

64
Program usage name

shape_factor
Evaluatable

Yes

# Nusselt number for laminar flow heat transfer — the ratio of convective heat transfer to conductive

Details

The ratio of convective to conductive heat exchange in the laminar flow regime. Its value depends on the geometry of the pipe’s cross-section and the thermal boundary conditions of the pipe wall, such as constant temperature or constant heat flow. Typical value 3.66 for a circular cross-section with a constant wall temperature [2].

Default value

3.66
Program usage name

Nu_laminar
Evaluatable

Yes

# Internal surface absolute roughness — the average depth of all surface defects on the inner surface of the pipe
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The average depth of all surface defects on the inner surface of the pipe that affect pressure losses in the turbulent flow regime.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

1.5e-5 m
Program usage name

roughness
Evaluatable

Yes

# Aggregate equivalent length of local resistances — the total length of all local resistances present in the pipe
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The total length of all local resistances present in the pipe. Local resistances include bends, fittings, fittings, pipe entrances and exits. The effect of local resistances is to increase the effective length of the pipe segment. This length is added to the geometric length of the pipe only to calculate the friction. The volume of humid air depends only on the geometric length of the pipe, determined by the parameter Pipe length.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

0.1 m
Program usage name

length_add
Evaluatable

Yes

# Laminar flow upper Reynolds number limit — the Reynolds number, above which the flow begins to transition from laminar to turbulent

Details

The Reynolds number, above which the flow begins to transition from laminar to turbulent. This number is equal to the maximum Reynolds number corresponding to a fully developed laminar flow.

Default value

2000
Program usage name

Re_laminar
Evaluatable

Yes

# Turbulent flow lower Reynolds number limit — the Reynolds number, below which the flow begins to transition from turbulent to laminar

Details

The Reynolds number, below which the flow begins to transition from turbulent to laminar. This number is equal to the minimum Reynolds number corresponding to a fully developed turbulent flow.

Default value

4000
Program usage name

Re_turbulent
Evaluatable

Yes

Main

# Hydraulic diameter — the diameter of an equivalent cylindrical tube with the same cross-sectional area
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The diameter of an equivalent cylindrical tube with the same cross-sectional area.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

0.1 m
Program usage name

hydraulic_diameter
Evaluatable

Yes

# Cross-sectional area — pipe cross-sectional area
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area of the pipe in the direction perpendicular to the flow direction.

Units

m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac
Default value

0.01 m^2
Program usage name

port_area
Evaluatable

Yes

# Pipe length — pipe length
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The length of the pipe along the flow direction.

Units

m | um | mm | cm | km | in | ft | yd | mi | nmi
Default value

5 m
Program usage name

length
Evaluatable

Yes

Literature

  1. White, F. M., Fluid Mechanics. 7th Ed, Section 6.8. McGraw-Hill, 2011.

  2. Cengel, Y. A., Heat and Mass Transfer — A Practical Approach. 3rd Ed, Section 8.5. McGraw-Hill, 2007.

  3. Mitchell, John W., and James E. Braun. Principles of Heating, Ventilation, and Air Conditioning in Buildings. Wiley, 2013.

Examples