TubeBase

Models the pressure drop in a fluid-carrying tube considering friction and optional inertia.

This component calculates the pressure drop ($\Delta p$) across a tube as a function of the mass flow rate (m_flow). The calculation includes frictional losses, represented by the sheer variable, based on the Darcy-Weisbach equation. The friction factor ($ff$) is determined from flow conditions, fluid properties (density $\rho$ and dynamic viscosity $\mu$), tube geometry (length length, cross-sectional area area, hydraulic diameter d_h), and a shape_factor. An additional head_factor can scale these frictional losses. Fluid density and viscosity are obtained from the medium properties at port_a. The hydraulic diameter is defined as:

$$d_h = \frac{4 \cdot \text{area}}{\text{perimeter}}$$

The fluid velocity is:

\[\text{velocity} = \frac{\text{m_flow}}{\rho \cdot \text{area}}\]

The pressure drop due to friction (sheer) is calculated as:

\[\text{sheer} = 0.5 \cdot \rho \cdot \text{velocity}^2 \cdot ff \cdot \text{head_factor} \cdot \frac{\text{length}}{d_h}\]

The total pressure drop ($\Delta p$) can optionally incorporate fluid inertia, adding a dynamic pressure component proportional to the rate of change of mass flow rate (der(m_flow)):

\[\Delta p = \text{sheer} + \begin{cases} \frac{\text{length}}{\text{area}} \frac{d(\text{m_flow})}{dt} & \text{if add_inertia is true} \\ 0 & \text{if add_inertia is false} \end{cases}\]

TwoPorts

Usage

TubeBase(area, length, perimeter, shape_factor, head_factor, add_inertia=false, d_h=4*area/perimeter, m_flow0)

Parameters:

Connectors

• port_a - (Port)
• port_b - (Port)

Variables

Behavior

Behavior of this component cannot be rendered because it includes path variables.

Source

# Models the pressure drop in a fluid-carrying tube considering friction and optional inertia.
#
# This component calculates the pressure drop ($\Delta p$) across a tube as a function of the mass flow rate (`m_flow`).
# The calculation includes frictional losses, represented by the `sheer` variable, based on the Darcy-Weisbach equation.
# The friction factor ($ff$) is determined from flow conditions, fluid properties (density $\rho$ and dynamic viscosity $\mu$),
# tube geometry (length `length`, cross-sectional area `area`, hydraulic diameter `d_h`), and a `shape_factor`.
# An additional `head_factor` can scale these frictional losses. Fluid density and viscosity are obtained from the medium properties at `port_a`.
# The hydraulic diameter is defined as:
# ```math
# d_h = \frac{4 \cdot \text{area}}{\text{perimeter}}
# ```
# The fluid velocity is:
# ```math
# \text{velocity} = \frac{\text{m_flow}}{\rho \cdot \text{area}}
# ```
# The pressure drop due to friction (`sheer`) is calculated as:
# ```math
# \text{sheer} = 0.5 \cdot \rho \cdot \text{velocity}^2 \cdot ff \cdot \text{head_factor} \cdot \frac{\text{length}}{d_h}
# ```
# The total pressure drop ($\Delta p$) can optionally incorporate fluid inertia, adding a dynamic pressure component
# proportional to the rate of change of mass flow rate (`der(m_flow)`):
# ```math
# \Delta p = \text{sheer} + \begin{cases} \frac{\text{length}}{\text{area}} \frac{d(\text{m_flow})}{dt} & \text{if add_inertia is true} \\ 0 & \text{if add_inertia is false} \end{cases}
# ```
component TubeBase
  extends TwoPorts
  # Cross-sectional area of the tube
  parameter area::Area
  # Length of the tube
  parameter length::Length
  # Wetted perimeter of the tube's cross-section
  parameter perimeter::Length
  # Factor accounting for non-circular cross-section in friction calculation
  parameter shape_factor::Real
  # Multiplier for head losses (e.g., minor losses, bends)
  parameter head_factor::Real
  # Flag to include (if true) or exclude (if false) fluid inertial effects
  parameter add_inertia::Boolean = false
  # Calculated hydraulic diameter of the tube
  final parameter d_h::Length = 4*area/perimeter
  # Density of the fluid
  variable rho::Density
  # Dynamic viscosity of the fluid
  variable mu::DynamicViscosity
  # Average velocity of the fluid in the tube
  variable velocity::Velocity
  # Pressure drop component due to frictional shear
  variable sheer::Pressure
  # Darcy friction factor
  variable ff::Real
  # Initial guess or value for the mass flow rate
  parameter m_flow0::MassFlowRate
relations
  initial m_flow = m_flow0
  rho = density(port_a.medium, port_a.p)
  mu = viscosity(port_a.medium)
  velocity = m_flow/(rho*area)
  ff = friction_factor(m_flow, area, d_h, mu, shape_factor)
  sheer = 0.5*rho*reg_pow(velocity, 2)*ff*head_factor*(length/d_h)
  Δp = if add_inertia then sheer+(length/area)*der(m_flow) else sheer
  m_flow = port_a.m_flow
end

# Models the pressure drop in a fluid-carrying tube considering friction and optional inertia.
#
# This component calculates the pressure drop ($\Delta p$) across a tube as a function of the mass flow rate (`m_flow`).
# The calculation includes frictional losses, represented by the `sheer` variable, based on the Darcy-Weisbach equation.
# The friction factor ($ff$) is determined from flow conditions, fluid properties (density $\rho$ and dynamic viscosity $\mu$),
# tube geometry (length `length`, cross-sectional area `area`, hydraulic diameter `d_h`), and a `shape_factor`.
# An additional `head_factor` can scale these frictional losses. Fluid density and viscosity are obtained from the medium properties at `port_a`.
# The hydraulic diameter is defined as:
# ```math
# d_h = \frac{4 \cdot \text{area}}{\text{perimeter}}
# ```
# The fluid velocity is:
# ```math
# \text{velocity} = \frac{\text{m_flow}}{\rho \cdot \text{area}}
# ```
# The pressure drop due to friction (`sheer`) is calculated as:
# ```math
# \text{sheer} = 0.5 \cdot \rho \cdot \text{velocity}^2 \cdot ff \cdot \text{head_factor} \cdot \frac{\text{length}}{d_h}
# ```
# The total pressure drop ($\Delta p$) can optionally incorporate fluid inertia, adding a dynamic pressure component
# proportional to the rate of change of mass flow rate (`der(m_flow)`):
# ```math
# \Delta p = \text{sheer} + \begin{cases} \frac{\text{length}}{\text{area}} \frac{d(\text{m_flow})}{dt} & \text{if add_inertia is true} \\ 0 & \text{if add_inertia is false} \end{cases}
# ```
component TubeBase
  # The first fluid port of the component
  port_a = Port()
  # The second fluid port of the component
  port_b = Port()
  # Pressure difference across the component, defined as port_a.p - port_b.p
  variable Δp::AbsolutePressure
  # Overall mass flow rate through the component
  variable m_flow::MassFlowRate
  # Cross-sectional area of the tube
  parameter area::Area
  # Length of the tube
  parameter length::Length
  # Wetted perimeter of the tube's cross-section
  parameter perimeter::Length
  # Factor accounting for non-circular cross-section in friction calculation
  parameter shape_factor::Real
  # Multiplier for head losses (e.g., minor losses, bends)
  parameter head_factor::Real
  # Flag to include (if true) or exclude (if false) fluid inertial effects
  parameter add_inertia::Boolean = false
  # Calculated hydraulic diameter of the tube
  final parameter d_h::Length = 4*area/perimeter
  # Density of the fluid
  variable rho::Density
  # Dynamic viscosity of the fluid
  variable mu::DynamicViscosity
  # Average velocity of the fluid in the tube
  variable velocity::Velocity
  # Pressure drop component due to frictional shear
  variable sheer::Pressure
  # Darcy friction factor
  variable ff::Real
  # Initial guess or value for the mass flow rate
  parameter m_flow0::MassFlowRate
relations
  continuity(port_a.medium, port_b.medium)
  port_a.m_flow+port_b.m_flow = 0
  Δp = port_a.p-port_b.p
  initial m_flow = m_flow0
  rho = density(port_a.medium, port_a.p)
  mu = viscosity(port_a.medium)
  velocity = m_flow/(rho*area)
  ff = friction_factor(m_flow, area, d_h, mu, shape_factor)
  sheer = 0.5*rho*reg_pow(velocity, 2)*ff*head_factor*(length/d_h)
  Δp = if add_inertia then sheer+(length/area)*der(m_flow) else sheer
  m_flow = port_a.m_flow
metadata {}
end

Test Cases

No test cases defined.

Related

• Examples
• Experiments
• Analyses
• Tests
  • FluidSystemTest