Pipe (MA)

Rigid conduit for moist air flow

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Libraries:
Simscape / Foundation Library / Moist Air / Elements

Description

The Pipe (MA) block models pipe flow dynamics in a moist air network due to viscous friction losses and convective heat transfer with the pipe wall. The pipe contains a constant volume of moist air. The pressure and temperature evolve based on the compressibility and thermal capacity of this moist air volume. Liquid water condenses out of the moist air volume when it reaches saturation. Choked flow occurs when the outlet reaches sonic condition.

Caution

Air flow through this block can choke. If a Mass Flow Rate Source (MA) block or a Controlled Mass Flow Rate Source (MA) block connected to the Pipe (MA) block specifies a greater mass flow rate than the possible choked mass flow rate, the simulation generates an error. For more information, see Choked Flow.

The block equations use these symbols. Subscripts a, w, g, and d indicate the properties of dry air, water vapor, trace gas, and water droplets, respectively. Subscript ws indicates water vapor at saturation. Subscripts A, H, and S indicate the appropriate port. Subscript I indicates the properties of the internal moist air volume.

$$\dot{m}$$	Mass flow rate
Φ	Energy flow rate
Q	Heat flow rate
p	Pressure
ρ	Density
R	Specific gas constant
V	Volume of moist air inside the converter
cp	Specific heat at constant volume
h	Specific enthalpy
u	Specific internal energy
x	Mass fraction (xw is specific humidity, which is another term for water vapor mass fraction)
y	Mole fraction
φ	Relative humidity
r	Humidity ratio
rd	Mass ratio of water droplets to moist air
T	Temperature
t	Time

Mass and Energy Balance

The net flow rates into the moist air volume inside the converter are

$$\begin{array}{l}{\dot{m}}_{net}={\dot{m}}_A-{\dot{m}}_{condense}+{\dot{m}}_{wS}+{\dot{m}}_{gS}+{\dot{m}}_{d,evap}\\ {\Phi }_{net}={\Phi }_A+Q_H+{\Phi }_S-(1-{\lambda }_d){\dot{m}}_{condense}{h}_d\\ {\dot{m}}_{w,net}={\dot{m}}_{wA}-{\dot{m}}_{condense}+{\dot{m}}_{wS}+{\dot{m}}_{d,evap}\\ {\dot{m}}_{g,net}={\dot{m}}_{gA}+{\dot{m}}_{gS}\\ {\dot{m}}_{d,net}={\dot{m}}_{dA}+{\dot{m}}_{dS}+{\lambda }_d{\dot{m}}_{condense}-{\dot{m}}_{d,evap}\end{array}$$

where:

• $$\dot{m}$$_condense is the rate of condensation.

• $$\dot{m}$$_d,evap is the rate of water droplet evaporation.

• Φ_condense is the rate of energy loss from the condensed water.

• λ_d is the value of the Fraction of condensate entrained as water droplets parameter.

• Φ_S is the rate of energy added by the sources of moisture and trace gas. $${\dot{m}}_{wS}$$ and $${\dot{m}}_{gS}$$ are the mass flow rates of water and gas, respectively, through port S. The values of $${\dot{m}}_{wS}$$, $${\dot{m}}_{gS}$$, and Φ_S are determined by the moisture and trace gas sources connected to port S of the converter.

Water vapor mass conservation relates the water vapor mass flow rate to the dynamics of the humidity level in the internal moist air volume

$$\frac{d{x}_{wI}}{dt}{\rho }_{I}V+x_{wI}{\dot{m}}_{net}={\dot{m}}_{w,net}$$

Similarly, trace gas mass conservation relates the trace gas mass flow rate to the dynamics of the trace gas level in the internal moist air volume

$$\frac{d{x}_{gI}}{dt}{\rho }_{I}V+x_{gI}{\dot{m}}_{net}={\dot{m}}_{g,net}$$

The water droplets mass conservation equation relates the water droplet mass flow rate to the entrained water droplet dynamics in the internal moist air volume

$$\frac{d{r}_{dI}}{dt}{\rho }_{I}V+r_{dI}{\dot{m}}_{net}={\dot{m}}_{d,net}.$$

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

$$\left(\frac{1}{p_I}\frac{d{p}_I}{dt}-\frac{1}{T_I}\frac{d{T}_I}{dt}\right){\rho }_{I}V+\frac{R_a-R_w}{R_I}\left({\dot{m}}_{w,net}-x_w{\dot{m}}_{net}\right)+\frac{R_a-R_g}{R_I}\left({\dot{m}}_{g,net}-x_g{\dot{m}}_{net}\right)+{\rho }_I\dot{V}={\dot{m}}_{net}$$

where $$\dot{V}$$ is the rate of change of the converter volume.

Finally, energy conservation relates the energy flow rate to the dynamics of the pressure, temperature, and mass fractions of the internal moist air volume:

$$\left(c_{pI}-R_I+r_d{c}_{pd}\right)V{\rho }_I\frac{d{T}_I}{dt}+u_{aI}{\dot{m}}_{MA,net}+\left(u_{wI}-u_{aI}\right){\dot{m}}_{w,net}+\left(u_{gI}-u_{aI}\right){\dot{m}}_{g,net}+h_d{\dot{m}}_{d,net}={\Phi }_{net}-p_I\dot{V}$$

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

$$p_I={\rho }_I{R}_I{T}_I$$

The mixture specific gas constant is

$$R_I=x_{aI}{R}_a+x_{wI}{R}_w+x_{gI}{R}_g$$

Momentum Balance

The momentum balance for each half of the pipe models the pressure drop due to momentum flux and viscous friction:

$$\begin{array}{l}{p}_A-p_I={\left(\frac{{\dot{m}}_A}{S}\right)}^2\cdot \left(\frac{T_I}{p_I}-\frac{T_A}{p_A}\right)R_I+\Delta p_{AI}\\ p_B-p_I={\left(\frac{{\dot{m}}_B}{S}\right)}^2\cdot \left(\frac{T_I}{p_I}-\frac{T_B}{p_B}\right)R_I+\Delta p_{BI}\end{array}$$

where:

• p is the pressure at port A, port B, or internal node I, as indicated by the subscript.

• ρ is the density at port A, port B, or internal node I, as indicated by the subscript.

• S is the cross-sectional area of the pipe.

• Δp_AI and Δp_BI are pressure losses due to viscous friction.

The pressure losses due to viscous friction, Δp_AI and Δp_BI, depend on the flow regime. The Reynolds numbers for each half of the pipe are defined as:

$$\begin{array}{l}{\mathrm{Re}}_A=\frac{\left|{\dot{m}}_A\right|\cdot D_h}{S\cdot {\mu }_I}\\ {\mathrm{Re}}_B=\frac{\left|{\dot{m}}_B\right|\cdot D_h}{S\cdot {\mu }_I}\end{array}$$

where:

• D_h is the hydraulic diameter of the pipe.

• μ_I is the dynamic viscosity at the internal node.

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

In the laminar flow regime, the pressure losses due to viscous friction are:

$$\begin{array}{l}\Delta p_{A{I}_{lam}}=f_{shape}\frac{{\dot{m}}_A\cdot {\mu }_I}{2{\rho }_I\cdot D_h^2\cdot S}\cdot \frac{L+L_{eqv}}{2}\\ \Delta p_{B{I}_{lam}}=f_{shape}\frac{{\dot{m}}_B\cdot {\mu }_I}{2{\rho }_I\cdot D_h^2\cdot S}\cdot \frac{L+L_{eqv}}{2}\end{array}$$

where:

• f_shape is the value of the Shape factor for laminar flow viscous friction parameter.

• L_eqv is the value of the Aggregate equivalent length of local resistances parameter.

In the turbulent flow regime, the pressure losses due to viscous friction are:

$$\begin{array}{l}\Delta p_{A{I}_{tur}}=f_{Darc{y}_A}\frac{{\dot{m}}_A\cdot \left|{\dot{m}}_A\right|}{2{\rho }_I\cdot D_h\cdot S^2}\cdot \frac{L+L_{eqv}}{2}\\ \Delta p_{B{I}_{tur}}=f_{Darc{y}_B}\frac{{\dot{m}}_B\cdot \left|{\dot{m}}_B\right|}{2{\rho }_I\cdot D_h\cdot S^2}\cdot \frac{L+L_{eqv}}{2}\end{array}$$

where f_Darcy is the Darcy friction factor at port A or B, as indicated by the subscript.

The Darcy friction factors are computed from the Haaland correlation:

$$\begin{array}{l}{f}_{Darc{y}_A}={\left[-1.8{\log }_{10}\left(\frac{6.9}{{\mathrm{Re}}_A}+{\left(\frac{{\epsilon }_{rough}}{3.7D_h}\right)}^{1.11}\right)\right]}^{-2}\\ f_{Darc{y}_B}={\left[-1.8{\log }_{10}\left(\frac{6.9}{{\mathrm{Re}}_B}+{\left(\frac{{\epsilon }_{rough}}{3.7D_h}\right)}^{1.11}\right)\right]}^{-2}\end{array}$$

where ε_rough is the value of the Internal surface absolute roughness parameter.

When the Reynolds number is between the Laminar flow upper Reynolds number limit and the Turbulent flow lower Reynolds number limit parameter values, the flow is in transition between laminar flow and turbulent flow. The pressure losses due to viscous friction during the transition region follow a smooth connection between those in the laminar flow regime and those in the turbulent flow regime.

The heat exchanged with the pipe wall through port H is added to the energy of the moist air volume represented by the internal node via the energy conservation equation (see Mass and Energy Balance). Therefore, the momentum balances for each half of the pipe, between port A and the internal node and between port B and the internal node, are assumed to be adiabatic processes. The adiabatic relations are:

$$\begin{array}{l}{h}_A-h_I={\left(\frac{R_I{\dot{m}}_A}{S}\right)}^2\left[{\left(\frac{T_I}{p_I}\right)}^2-{\left(\frac{T_A}{p_A}\right)}^2\right]\\ h_B-h_I={\left(\frac{R_I{\dot{m}}_B}{S}\right)}^2\left[{\left(\frac{T_I}{p_I}\right)}^2-{\left(\frac{T_B}{p_B}\right)}^2\right]\end{array}$$

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

Convective Heat Transfer

The convective heat transfer equation between the pipe wall and the internal moist air volume is:

$$Q_H=Q_{conv}+\frac{k_I{S}_{surf}}{D_h}\left(T_H-T_I\right)$$

S_surf is the pipe surface area, S_surf = 4SL/D_h. If Condensation on wall surface is off, and assuming an exponential temperature distribution along the pipe, the convective heat transfer is

$$Q_{conv}=\left|{\dot{m}}_{avg}\right|c_{p_{avg}}\left(T_H-T_{in}\right)\left(1-\exp \left(-\frac{h_{coeff}{S}_{surf}}{\left|{\dot{m}}_{avg}\right|c_{p_{avg}}}\right)\right)$$

where:

• T_in is the inlet temperature depending on flow direction.

• $${\dot{m}}_{avg}=\left({\dot{m}}_A-{\dot{m}}_B\right)/2$$ is the average mass flow rate from port A to port B.

• $$c_{p_{avg}}$$ is the specific heat evaluated at the average temperature.

The heat transfer coefficient, h_coeff, depends on the Nusselt number:

$$h_{coeff}=Nu\frac{k_{avg}}{D_h}$$

where k_avg is the thermal conductivity evaluated at the average temperature. The Nusselt number depends on the flow regime. The Nusselt number in the laminar flow regime is constant and equal to the value of the Nusselt number for laminar flow heat transfer parameter. The Nusselt number in the turbulent flow regime is computed from the Gnielinski correlation:

$$N{u}_{tur}=\frac{\frac{f_{Darcy}}{8}\left({\mathrm{Re}}_{avg}-1000\right){\mathrm{Pr}}_{avg}}{1+12.7\sqrt{\frac{f_{Darcy}}{8}}\left({\mathrm{Pr}}_{avg}^{2/3}-1\right)}$$

where Pr_avg is the Prandtl number evaluated at the average temperature. The average Reynolds number is

$${\mathrm{Re}}_{avg}=\frac{\left|{\dot{m}}_{avg}\right|D_h}{S{\mu }_{avg}}$$

where μ_avg is the dynamic viscosity evaluated at the average temperature. When the average Reynolds number is between the Laminar flow upper Reynolds number limit and the Turbulent flow lower Reynolds number limit parameter values, the Nusselt number follows a smooth transition between the laminar and turbulent Nusselt number values.

Saturation and Condensation

The equations in this section account for the condensation that happens when the volume of moist air becomes saturated. For additional equations that account for wall surface condensation, when the Condensation on wall surface check box is selected, see Effect of Condensation on Wall Surface.

When the moist air volume reaches saturation, condensation may occur. The specific humidity at saturation is

$$x_{wsI}={\phi }_{ws}\frac{R_I}{R_w}\frac{p_{wsI}}{p_I}$$

where:

• φ_ws is the relative humidity at saturation (typically 1).

• p_wsI is the water vapor saturation pressure evaluated at T_I.

The rate of condensation is

$${\dot{m}}_{condense}=\{\begin{array}{ll}0,\hfill & \text{if }{x}_{wI}\le x_{wsI}\hfill \\ \frac{x_{wI}-x_{wsI}}{{\tau }_{condense}}{\rho }_{I}V,\hfill & \text{if }{x}_{wI}>x_{wsI}\hfill \end{array}$$

where τ_condense is the value of the Water vapor condensation time constant parameter.

The rate of evaporation is

$${\dot{m}}_{d,evap}=\frac{x_{wsI}-x_{wI}}{x_{wsI}{\tau }_{evap}}{r}_{dI}{\rho }_{I}V,$$

where τ_evap is the value of the Water droplets evaporation time constant parameter.

Effect of Condensation on Wall Surface

Moist air blocks that contain an internal volume of fluid (such as chambers, converters, and so on) model water vapor condensation when this volume of fluid becomes fully saturated with water vapor, that is, at 100% relative humidity. However, water vapor can also condense on a cold surface even if the volume of air as a whole has not yet reached saturation. The ability to model this effect in Pipe (MA) blocks is important because many HVAC systems contain pipes and ducts. If these pipes and ducts are not well insulated, their surface could get cold, and condensation on wall surface occurs. Note that this effect does not replace the condensation that occurs when the bulk moist air volume reaches 100% relative humidity, both effects can occur simultaneously.

To model the effect of wall condensation on a cold pipe surface in contact with a moist air volume, select the Condensation on wall surface check box. In this case, the convective heat transfer equation needs to account for both sensible and latent heat, and the block has an additional equation that calculates the rate of water vapor condensation on the surface.

If Condensation on wall surface is on, the combined convective heat transfer is

$$Q_{combine{d}_{conv}}=\left|{\dot{m}}_{ag}\right|\left({\overline{h}}_H-{\overline{h}}_{in}\right)\left(1-\exp \left(-\frac{h_{coeff}{S}_{surf}}{\left|{\dot{m}}_{avg}\right|c_{p_{avg}}}\right)\right)$$

where:

• $${\dot{m}}_{ag}$$ is the mass flow rate of dry air and trace gas at the inlet.

• $${\overline{h}}_H$$ is the mixture enthalpy per unit mass of dry air and trace gas at the wall.

• $${\overline{h}}_{in}$$ is the mixture enthalpy per unit mass of dry air and trace gas at the inlet.

This equation is similar to the equation in Convective Heat Transfer, but the temperature difference has been replaced by the mixture enthalpy difference. Because the mixture enthalpy depends on both the temperature and the composition of the moist air, the mixture enthalpy difference accounts for both a change in temperature and a change in the moisture content. In other words, it captures both sensible and latent heat effects. The exponent term and the correlations that go into computing the heat transfer coefficient remain the same as before because the model is derived based on the analogy between heat and mass transfer. For more information, see [3].

To simplify the derivations, the equation uses the mixture enthalpy per unit mass of dry air and trace gas, as opposed to the mixture enthalpy per unit mass of the mixture, because the amount of dry air and trace gas does not change during the water vapor condensation process. To ensure that the equation remains consistent, the mixture enthalpy difference is multiplied by the mass flow rate of dry air and trace gas, $${\dot{m}}_{ag}$$, as opposed to the total mixture mass flow rate, $$\dot{m}$$.

The mixture enthalpy per unit mass of dry air and trace gas at the inlet is

$${\overline{h}}_{in}=h_{a{g}_{in}}+W_{in}{h}_{w_{in}}$$

where:

• $$h_{a{g}_{in}}$$ is the specific enthalpy of dry air and trace gas at the inlet.

• $$h_{w_{in}}$$ is the specific enthalpy of water vapor at the inlet.

• W_in is the humidity ratio at the inlet.

The mixture enthalpy per unit mass of dry air and trace gas at the wall is

$${\overline{h}}_H=h_{a{g}_H}+W_H{h}_{w_H}$$

where:

• $$h_{a{g}_H}$$ is the specific enthalpy of dry air and trace gas at the wall.

• $$h_{w_H}$$ is the specific enthalpy of water vapor at the wall.

• W_H is the humidity ratio at the wall, defined as

  $$W_H=\min \{W_{in},W_{sH}\}$$

  where W_sH is the saturation humidity ratio based on the wall temperature.

The min function in the previous equation provides the switch between “dry” and “wet” heat transfer:

• When the wall temperature is above the dew point, then W_sH > W_in, therefore, condensation is not occurring and $$\left({\overline{h}}_H-{\overline{h}}_{in}\right)$$ represents difference in temperature only.

• When the wall temperature is below the dew point, then W_sH < W_in, therefore, condensation is occurring and $$\left({\overline{h}}_H-{\overline{h}}_{in}\right)$$ represents difference in both temperature and humidity content.

The rate of water vapor condensation on the wall surface is

$${\dot{m}}_{condens{e}_H}=\left|{\dot{m}}_{ag}\right|\left(W_{in}-W_H\right)\left(1-\exp \left(-\frac{h_{coeff}{S}_{surf}}{\left|{\dot{m}}_{avg}\right|c_{p_{avg}}}\right)\right)$$

This equation is similar to the combined convective heat transfer equation because the amount of water vapor condensing on the wall is the same as the convective mass transfer from the moist air to the pipe wall. The exponent term is also the same because of the heat and mass transfer analogy used. For more information, see [3].

The energy associated with the water condensed on the pipe wall is

$${\Phi }_{condens{e}_H}={\dot{m}}_{condens{e}_H}\left(h_{wH}-\Delta h_{vapH}\right)$$

where Δh_vapH is the specific enthalpy of vaporization at the wall temperature.

The sensible portion of the convective heat transfer between the pipe wall and the moist air is

$$Q_{conv}=Q_{combine{d}_{conv}}+{\Phi }_{condens{e}_H}$$

This equation has a plus sign because Q is negative when it is cooling the moist air. Therefore, adding $${\Phi }_{condens{e}_H}$$, which is a positive value, removes the latent portion of the heat transfer.

The block then uses this Q_conv value in the first equation in Convective Heat Transfer to calculate the heat transfer at thermal port H.

Choked Flow

The unchoked pressure at port A or B is the value of the corresponding Across variable at that port:

$$\begin{array}{l}{p}_{A_{unchoked}}=\text{A}\text{.p}\\ p_{B_{unchoked}}=\text{B}\text{.p}\end{array}$$

However, the port pressure variables used in the momentum balance equations, p_A and p_B, do not necessarily coincide with the pressure across variables A.p and B.p because the pipe outlet may choke. Choked flow occurs when the downstream pressure is sufficiently low. At that point, the flow depends only on the conditions at the inlet. Therefore, when choked, the outlet pressure (p_A or p_B, whichever is the outlet) cannot decrease further even if the pressure downstream, represented by A.p or B.p, continues to decrease.

Choking can occur at the pipe outlet, but not at the pipe inlet. Therefore, if port A is the inlet, then p_A = A.p. If port A is the outlet, then

$$p_A=\{\begin{array}{ll}A.p,\hfill & \text{if }A.p\ge p_{A_{choked}}\hfill \\ p_{A_{choked}},\hfill & \text{if }A.p<p_{A_{choked}}\hfill \end{array}$$

Similarly, if port B is the inlet, then p_B = B.p. If port B is the outlet, then

$$p_B=\{\begin{array}{ll}B.p,\hfill & \text{if }B.p\ge p_{B_{choked}}\hfill \\ p_{B_{choked}},\hfill & \text{if }B.p<p_{B_{choked}}\hfill \end{array}$$

The choked pressures at ports A and B are derived from the momentum balance by assuming the outlet velocity is equal to the speed of sound:

$$\begin{array}{l}{p}_{A_{choked}}-p_I=p_{A_{choked}}\left(\frac{p_{A_{choked}}{T}_I}{p_I{T}_A}-1\right)\frac{c_{p_A}}{c_{v_I}}+\Delta p_{AI}\\ p_{B_{choked}}-p_I=p_{B_{choked}}\left(\frac{p_{B_{choked}}{T}_I}{p_I{T}_B}-1\right)\frac{c_{p_B}}{c_{v_I}}+\Delta p_{BI}\end{array}$$

Assumptions and Limitations

• The pipe wall is perfectly rigid.

• The flow is fully developed. Friction losses and heat transfer do not include entrance effects.

• The effect of gravity is negligible.

• Fluid inertia is negligible.

• This block does not model supersonic flow.

• The equations for wall condensation are based on the analogy between heat and mass transfer, and are therefore valid only when the Lewis number (Le) is close to 1. This is a reasonable assumption for a moist air mixture. For more information, see [3].

Examples

Aircraft Environmental Control System

Models an aircraft environmental control system (ECS) that regulates pressure, temperature, humidity, and ozone (O3) to maintain a comfortable and safe cabin environment. Cooling and dehumidification are provided by the air cycle machine (ACM), which operates as an inverse Brayton cycle to remove heat from pressurized hot engine bleed air. Some hot bleed air is mixed directly with the output of the ACM to adjust the temperature. Pressurization is maintained by the outflow valve in the cabin. This model simulates the ECS operating from a hot ground condition to a cold cruise condition and back to a cold ground condition.

• Open Model

Medical Ventilator with Lung Model

Models a positive-pressure medical ventilator system. A preset flow rate is supplied to the patient. The lungs are modeled with the Translational Mechanical Converter (MA), which converts moist air pressure into translational motion. By setting the Interface cross-sectional area to unity, displacement in the mechanical translational network becomes a proxy for volume, force becomes a proxy for pressure, spring constant becomes a proxy for respiratory elastance, and damping coefficient becomes a proxy for respiratory resistance.

• Open Model

Pneumatic Actuator with Humidity

How the Simscape™ Foundation Library moist air components can be used to model a pneumatic actuator operating in a humid environment. The Directional Valve is a subsystem composed of four Variable Local Restriction (MA) blocks, and the Double-Acting Actuator is a subsystem composed of two Translational Mechanical Converter (MA) blocks in opposite mechanical orientation.

• Open Model

Ports

Output

W — Rate of condensation leaving system, kg/s

physical signal

Physical signal output port that measures the rate of condensation that leaves the system. If you select Condensation on wall surface this port reports the total rate of water vapor condensation, which includes the condensation from a saturated moist air volume as well as the condensation on the pipe wall. This value does not include the portion of condensation that is entrained as water droplets.

F — Vector physical signal containing pressure, temperature, humidity, and trace gas levels data

physical signal vector

Physical signal output port that outputs a vector signal. The vector contains the pressure (in Pa), temperature (in K), humidity level, and trace gas level measurements inside the component. Use the Measurement Selector (MA) block to unpack this vector signal.

Conserving

A — Inlet or outlet

moist air

Moist air conserving port associated with the inlet or outlet of the pipe. This block has no intrinsic directionality.

B — Inlet or outlet

moist air

Moist air conserving port associated with the inlet or outlet of the pipe. This block has no intrinsic directionality.

H — Temperature of pipe wall

thermal

Thermal conserving port associated with the temperature of the pipe wall. The block includes the convective heat transfer between the moist air mixture inside the pipe and the pipe wall.

S — Inject or extract moisture and trace gas

moist air source

Connect this port to port S of a block from the Moisture & Trace Gas Sources library to add or remove moisture and trace gas. For more information, see Using Moisture and Trace Gas Sources.

Dependencies

This port is visible only if you set the Moisture and trace gas source parameter to Controlled.

Parameters

Main

Pipe length — Length of the pipe

5 m (default)

Length of the pipe along the direction of flow.

Cross-sectional area — Internal area of the pipe

0.01 m^2 (default)

Internal area of the pipe normal to the direction of the flow.

Hydraulic diameter — Diameter of an equivalent cylindrical pipe with the same cross-sectional area

0.1 m (default)

Diameter of an equivalent cylindrical pipe with the same cross-sectional area.

Friction and Heat Transfer

Aggregate equivalent length of local resistances — Combined length of all local resistances present in the pipe

0.1 m (default)

Combined length of all local resistances present in the pipe. Local resistances include bends, fittings, armatures, and pipe inlets and outlets. The effect of the local resistances is to increase the effective length of the pipe segment. This length is added to the geometrical pipe length only for friction calculations. The moist air volume depends only on the pipe geometrical length, defined by the Pipe length parameter.

Internal surface absolute roughness — Average depth of all surface defects on the internal surface of the pipe

15e-6 m (default)

Average depth of all surface defects on the internal surface of the pipe, which affects the pressure loss in the turbulent flow regime.

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

2000 (default)

Reynolds number above which flow begins to transition from laminar to turbulent. This number equals the maximum Reynolds number corresponding to the fully developed laminar flow.

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

4000 (default)

Reynolds number below which flow begins to transition from turbulent to laminar. This number equals to the minimum Reynolds number corresponding to the fully developed turbulent flow.

Shape factor for laminar flow viscous friction — Effect of pipe geometry on the viscous friction losses

64 (default)

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

Nusselt number for laminar flow heat transfer — Ratio of convective to conductive heat transfer

3.66 (default)

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

Moisture and Trace Gas

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

Off (default) | On

Select this check box to model the effect of wall condensation on a cold pipe surface in contact with a moist air volume. For more information, see Effect of Condensation on Wall Surface. In default configuration, the block does not model this effect and accounts for water vapor condensation only at 100% relative humidity, as described in Convective Heat Transfer and Saturation and Condensation.

Relative humidity at saturation — Relative humidity above which condensation occurs

1 (default)

Relative humidity above which condensation occurs.

Water vapor condensation time constant — Time scale for condensation

1e-3 s (default) | positive scalar

Characteristic time scale at which an oversaturated moist air volume returns to saturation by condensing out excess moisture.

Water droplets evaporation time constant — Time scale for evaporation

1e-3 s (default) | positive scalar

Characteristic time scale at which water droplets evaporate to vapor.

Fraction of condensate entrained as water droplets — Fraction of condensate in water droplets

1 (default) | scalar in the range [0,1]

Fraction of the condensate in the moist air that is entrained as water droplets.

Moisture and trace gas source — Model moisture and trace gas levels

None (default) | Constant | Controlled

This parameter controls visibility of port S and provides these options for modeling moisture and trace gas levels inside the component:

• None — No moisture or trace gas is injected into or extracted from the block. Port S is hidden. This is the default.

• Constant — Moisture and trace gas are injected into or extracted from the block at a constant rate. The same parameters as in the Moisture Source (MA) and Trace Gas Source (MA) blocks become available in the Moisture and Trace Gas section of the block interface. Port S is hidden.

• Controlled — Moisture and trace gas are injected into or extracted from the block at a time-varying rate. Port S is exposed. Connect the Controlled Moisture Source (MA) and Controlled Trace Gas Source (MA) blocks to this port.

Moisture added or removed — Select whether the block adds or removes moisture as water vapor or water droplets

Water vapor (default) | Water droplets

Select whether the block adds or removes moisture as water vapor or water droplets.

Dependencies

To enable this parameter, set Moisture and trace gas source to Constant.

Water vapor evaporated from liquid or condensed to liquid — How the block adds or removes water vapor

off (default) | on

Select how the block adds or removes water vapor. If you clear this check box, the enthalpy of the added or removed moisture corresponds to the enthalpy of water vapor, which is greater than that of liquid water.

If you select this check box, the enthalpy of the added or removed moisture corresponds to the enthalpy of liquid water, which is less than that of water vapor. When water vapor is added, it evaporates from liquid and the latent heat is contributed by the connected fluid volume. When water vapor is removed, it condenses to liquid and the latent heat is released to the connected fluid volume.

Dependencies

To enable this parameter, set Moisture and trace gas source to Constant and Moisture added or removed to Water vapor.

Rate of moisture added — Constant mass flow rate through the block

0 kg/s (default)

Water vapor or water droplets mass flow rate through the block. A positive value adds moisture to the connected moist air volume. A negative value extracts moisture from that volume.

Dependencies

To enable this parameter, set Moisture and trace gas source to Constant.

Added moisture temperature specification — Select specification method for the temperature of added moisture

Atmospheric temperature (default) | Specified temperature

Select a specification method for the moisture temperature:

• Atmospheric temperature — Use the atmospheric temperature, specified by the Moist Air Properties (MA) block connected to the circuit.

• Specified temperature — Specify a value by using the Temperature of added moisture parameter.

Dependencies

To enable this parameter, set Moisture and trace gas source to Constant.

Temperature of added moisture — Moisture temperature

293.15 K (default)

Enter the desired temperature of added moisture. This temperature remains constant during simulation. The block uses this value to evaluate the specific enthalpy of the added moisture only. The specific enthalpy of removed moisture is based on the temperature of the connected moist air volume.

Dependencies

To enable this parameter, set Added moisture temperature specification to Specified temperature.

Rate of trace gas added — Constant mass flow rate through the block

0 kg/s (default)

Trace gas mass flow rate through the block. A positive value adds trace gas to the connected moist air volume. A negative value extracts trace gas from that volume.

Dependencies

To enable this parameter, set Moisture and trace gas source to Constant.

Added trace gas temperature specification — Select specification method for the temperature of added trace gas

Atmospheric temperature (default) | Specified temperature

Select a specification method for the trace gas temperature:

• Atmospheric temperature — Use the atmospheric temperature, specified by the Moist Air Properties (MA) block connected to the circuit.

• Specified temperature — Specify a value by using the Temperature of added trace gas parameter.

Dependencies

To enable this parameter, set Moisture and trace gas source to Constant.

Temperature of added trace gas — Trace gas temperature

293.15 K (default)

Enter the desired temperature of added trace gas. This temperature remains constant during simulation. The block uses this value to evaluate the specific enthalpy of the added trace gas only. The specific enthalpy of removed trace gas is based on the temperature of the connected moist air volume.

Dependencies

To enable this parameter, set Added trace gas temperature specification to Specified temperature.

Initial Conditions

Initial pressure — Moist air pressure at the start of simulation

0.101325 MPa (default) | positive scalar

Moist air pressure at the start of the simulation.

Initial pressure priority — Pressure parameter priority

High (default) | Low | None

Priority the solver assigns to the Initial pressure parameter when initializing the block.

Set this parameter to High to define your 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.

Initial temperature — Temperature at the start of simulation

293.15 K (default) | positive scalar

Initial moist air temperature.

Initial temperature priority — Temperature parameter priority

High (default) | Low | None

Priority the solver assigns to the Initial temperature parameter when initializing the block.

Set this parameter to High to define your 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.

Initial humidity specification — Humidity specification

Relative humidity (default) | Specific humidity | Mole fraction | Humidity ratio | Wet-bulb temperature

Method to specify the initial moist air humidity.

Initial relative humidity — Relative humidity at the start of simulation

0.5 (default) | scalar in the range of [0,1]

Relative humidity in the moist air at the start of the simulation. The relative humidity is the ratio of the water vapor partial pressure to the water vapor saturation pressure, or the ratio of the water vapor mole fraction to the water vapor mole fraction at saturation.

Dependencies

To enable this parameter, set Initial humidity specification to Relative humidity.

Initial relative humidity priority — Relative humidity parameter priority

High (default) | Low | None

Priority the solver assigns to the Initial relative humidity parameter when initializing the block.

Set this parameter to High to define your 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 enable this parameter, set Initial humidity specification to Relative humidity.

Initial specific humidity — Specific humidity at the start of simulation

0.01 (default) | scalar in the range of [0,1]

Specific humidity in the moist air at the start of simulation. The specific humidity is the mass fraction of water vapor to the combined total mass of water vapor, trace gas, and dry air.

Dependencies

To enable this parameter, set Initial humidity specification to Specific humidity.

Initial specific humidity priority — Specific humidity parameter priority

High (default) | Low | None

Priority the solver assigns to the Initial specific humidity parameter when initializing the block.

Set this parameter to High to define your 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 enable this parameter, set Initial humidity specification to Specific humidity.

Initial water vapor mole fraction — Mole fraction of water vapor at the start of simulation

0.01 (default) | scalar in the range [0,1]

Mole fraction of the water vapor in the moist air channel at the start of simulation. The water vapor mole fraction is relative to the combined molar quantity of water vapor, trace species, and dry air.

Dependencies

To enable this parameter, set Initial humidity specification to Mole fraction.

Initial water vapor mole fraction priority — Water vapor mole fraction humidity parameter priority

High (default) | Low | None

Priority the solver assigns to the Initial water vapor mole fraction parameter when initializing the block.

Set this parameter to High to define your 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 enable this parameter, set Initial humidity specification to Mole fraction.

Initial humidity ratio — Humidity ratio at the start of simulation

0.01 (default) | scalar in the range [0,1]

Humidity ratio in the moist air channel at the start of the simulation. The humidity ratio is the ratio of the mass of water vapor to the mass of dry air and trace gas.

Dependencies

To enable this parameter, set Initial humidity specification to Humidity ratio.

Initial humidity ratio priority — Humidity ratio parameter priority

High (default) | Low | None

Priority the solver assigns to the Initial humidity ratio humidity parameter when initializing the block.

Set this parameter to High to define your 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 enable this parameter, set Initial humidity specification to Humidity ratio.

Initial wet-bulb temperature — Wet-bulb temperature at the start of simulation

287 K (default) | scalar in the range [0,1]

Wet-bulb temperature at the start of the simulation. The block uses this value to calculate humidity.

Dependencies

To enable this parameter, set Initial humidity specification to Wet-bulb temperature.

Initial wet-bulb temperature priority — Wet-bulb temperature parameter priority

High (default) | Low | None

Priority the solver assigns to the Initial wet-bulb temperature parameter when initializing the block.

Set this parameter to High to define your 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 enable this parameter, set Initial humidity specification to Wet-bulb temperature.

Initial trace gas specification — Measurement type of trace gas

Mass fraction (default) | Mole fraction

Measurement type of trace gas.

Initial trace gas mass fraction — Amount of trace gas in the moist air channel

0.001 (default) | scalar in the range [0,1]

Amount of trace gas in the moist air by mass fraction at the start of the simulation. The mass fraction is relative to the combined total mass of water vapor, trace gas, and dry air.

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

Dependencies

To enable this parameter, set Initial trace gas specification to Mass fraction.

Initial trace gas mass fraction priority — Trace gas mass fraction parameter priority

High (default) | Low | None

Priority the solver assigns to the Initial trace gas mass fraction priority parameter when initializing the block.

Set this parameter to High to define your 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 enable this parameter, set Initial trace gas specification to Mass fraction.

Initial trace gas mole fraction — Mole fraction of trace gas at the start of simulation

0.001 (default) | scalar in the range [0,1]

Amount of trace gas in the moist air channel by mole fraction at the start of the simulation. The mole fraction is relative to the combined molar total of water vapor, trace gas, and dry air.

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

Dependencies

To enable this parameter, set Initial trace gas specification to Mole fraction.

Initial trace gas mole fraction priority — Trace gas mole fraction parameter priority

High (default) | Low | None

Priority the solver assigns to the Initial trace gas mole fraction priority parameter when initializing the block.

Set this parameter to High to define your 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 enable this parameter, set Initial trace gas specification to Mole fraction.

Initial mass ratio of water droplets to moist air — Ratio of water droplets to moist air

0 (default) | positive scalar

Initial mass ratio of water droplets to moist air.

Initial mass ratio of water droplets to moist air priority — Mass ratio of water droplets to moist air parameter priority

High (default) | Low | None

Priority the solver assigns to the Initial mass ratio of water droplets to moist air priority parameter when initializing the block.

Set this parameter to High to define your 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.

References

[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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2018a

R2024b: Updated options for initial conditions

You can now specify initial conditions for the block as parameters.

R2024b: Model water droplets suspended in moist air flow

Blocks in the moist air domain can now model water droplets suspended in a moist air flow. To model water droplets, select Enable entrained water droplets in the Moist Air Properties (MA) block connected to your moist air network.

R2024a: Numerical improvement for low-flow computation in pipes

To improve accuracy for pressure drop inside the pipe at low-speed flows, the momentum balance computations in the Pipe (MA) block have been changed slightly. There may be slight differences in simulation results compared to previous releases, especially when Mach number is low.

R2022b: Model effect of condensation on wall surface

The block has a new parameter, Condensation on wall surface, that lets you model the effect of wall condensation on a cold pipe surface in contact with a moist air volume. For more information, see Effect of Condensation on Wall Surface. In the default configuration, with this parameter set to Off, the block functions as in previous releases.

In R2023b, this parameter has been replaced with a check box. The default value and block functionality are the same as in previous releases.