## Buildings.Fluid.BaseClasses.FlowModels

Flow models for pressure drop calculations

### Information

This package contains a basic flow model that is used by the various models that compute pressure drop.

#### Assumption and limitations

Because the density does not change signficantly in heating, ventilation and air conditioning systems for buildings, the flow models compute the pressure drop based on the mass flow rate and not the volume flow rate. This typically leads to simpler equations because it does not require the mass density, which changes when the flow is reversed. Although, for conceptual design of building energy system, there is in general not enough information available that would warrant a more detailed pressure drop calculation. If a more detailed computation of the flow resistance is needed, then a user can use models from the Modelica.Fluid library.

All functions have an argument `m_flow_turbulent`

that determines where the
flow transitions to fully turbulent flow. For smaller mass flow rates,
the quadratic relation is replaced by a function that has finite slope
near zero pressure drop. This is done for numerical reasons, and to approximate
laminar flow, although the implementation does not use a linear function.

#### Implementation

The two main functions are
Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_dp
and
Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_m_flow
that compute the mass flow rate or the pressure drop, respectively.
Both functions are two times continuously differentiable.
First and second order derivatives are provided
in the function that have the suffix `_der`

and `_der2`

.

Extends from Modelica.Icons.BasesPackage (Icon for packages containing base classes).

### Package Content

Name | Description |
---|---|

basicFlowFunction_dp | Function that computes mass flow rate for given pressure drop |

basicFlowFunction_dp_der | 1st derivative of function that computes mass flow rate for given pressure drop |

basicFlowFunction_dp_der2 | 2nd derivative of flow function2nd derivative of function that computes mass flow rate for given pressure drop |

basicFlowFunction_m_flow | Function that computes pressure drop for given mass flow rate |

basicFlowFunction_m_flow_der | 1st derivative of function that computes pressure drop for given mass flow rate |

basicFlowFunction_m_flow_der2 | 2nd derivative of function that computes pressure drop for given mass flow rate |

Validation | Collection of validation models |

## Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_dp

Function that computes mass flow rate for given pressure drop

### Information

Function that computes the pressure drop of flow elements as

ṁ = sign(Δp) k √ Δp

with regularization near the origin. Therefore, the flow coefficient is

k = ṁ ⁄ √ Δp

The input `m_flow_turbulent`

determines the location of the regularization.

### Inputs

Type | Name | Default | Description |
---|---|---|---|

PressureDifference | dp | Pressure difference between port_a and port_b (= port_a.p - port_b.p) [Pa] | |

Real | k | Flow coefficient, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2) | |

MassFlowRate | m_flow_turbulent | Mass flow rate where transition to turbulent flow occurs [kg/s] |

### Outputs

Type | Name | Description |
---|---|---|

MassFlowRate | m_flow | Mass flow rate in design flow direction [kg/s] |

### Modelica definition

## Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_dp_der

1st derivative of function that computes mass flow rate for given pressure drop

### Information

Function that implements the first order derivative of Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_dp with respect to the mass flow rate.

Extends from Modelica.Icons.Function (Icon for functions).

### Inputs

Type | Name | Default | Description |
---|---|---|---|

PressureDifference | dp | Pressure difference between port_a and port_b (= port_a.p - port_b.p) [Pa] | |

Real | k | Flow coefficient, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2) | |

MassFlowRate | m_flow_turbulent | Mass flow rate where transition to turbulent flow occurs [kg/s] | |

Real | dp_der | Derivative of pressure difference between port_a and port_b (= port_a.p - port_b.p) |

### Outputs

Type | Name | Description |
---|---|---|

Real | m_flow_der | Derivative of mass flow rate in design flow direction [kg/s2] |

### Modelica definition

## Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_dp_der2

2nd derivative of flow function2nd derivative of function that computes mass flow rate for given pressure drop

### Information

Function that implements the second order derivative of Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_dp with respect to the mass flow rate.

Extends from Modelica.Icons.Function (Icon for functions).

### Inputs

Type | Name | Default | Description |
---|---|---|---|

PressureDifference | dp | Pressure difference between port_a and port_b (= port_a.p - port_b.p) [Pa] | |

Real | k | Flow coefficient, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2) | |

MassFlowRate | m_flow_turbulent | Mass flow rate where transition to turbulent flow occurs [kg/s] | |

Real | dp_der | 1st derivative of pressure difference between port_a and port_b (= port_a.p - port_b.p) | |

Real | dp_der2 | 2nd derivative of pressure difference between port_a and port_b (= port_a.p - port_b.p) |

### Outputs

Type | Name | Description |
---|---|---|

Real | m_flow_der2 | 2nd derivative of mass flow rate in design flow direction |

### Modelica definition

## Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_m_flow

Function that computes pressure drop for given mass flow rate

### Information

Function that computes the pressure drop of flow elements as

Δp = sign(ṁ) (ṁ ⁄ k)^{2}

with regularization near the origin. Therefore, the flow coefficient is

k = ṁ ⁄ √ Δp

The input `m_flow_turbulent`

determines the location of the regularization.

### Inputs

Type | Name | Default | Description |
---|---|---|---|

MassFlowRate | m_flow | Mass flow rate in design flow direction [kg/s] | |

Real | k | Flow coefficient, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2) | |

MassFlowRate | m_flow_turbulent | Mass flow rate where transition to turbulent flow occurs [kg/s] |

### Outputs

Type | Name | Description |
---|---|---|

PressureDifference | dp | Pressure difference between port_a and port_b (= port_a.p - port_b.p) [Pa] |

### Modelica definition

## Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_m_flow_der

1st derivative of function that computes pressure drop for given mass flow rate

### Information

Function that implements the first order derivative of Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_m_flow with respect to the mass flow rate.

Extends from Modelica.Icons.Function (Icon for functions).

### Inputs

Type | Name | Default | Description |
---|---|---|---|

MassFlowRate | m_flow | Mass flow rate in design flow direction [kg/s] | |

Real | k | Flow coefficient, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2) | |

MassFlowRate | m_flow_turbulent | Mass flow rate where transition to turbulent flow occurs [kg/s] | |

Real | m_flow_der | Derivative of mass flow rate in design flow direction [kg/s2] |

### Outputs

Type | Name | Description |
---|---|---|

Real | dp_der | Derivative of pressure difference between port_a and port_b (= port_a.p - port_b.p) |

### Modelica definition

## Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_m_flow_der2

2nd derivative of function that computes pressure drop for given mass flow rate

### Information

Function that implements the second order derivative of Buildings.Fluid.BaseClasses.FlowModels.basicFlowFunction_m_flow with respect to the mass flow rate.

Extends from Modelica.Icons.Function (Icon for functions).

### Inputs

Type | Name | Default | Description |
---|---|---|---|

MassFlowRate | m_flow | Mass flow rate in design flow direction [kg/s] | |

Real | k | Flow coefficient, k=m_flow/sqrt(dp), with unit=(kg.m)^(1/2) | |

MassFlowRate | m_flow_turbulent | Mass flow rate where transition to turbulent flow occurs [kg/s] | |

Real | m_flow_der | 1st derivative of mass flow rate in design flow direction [kg/s2] | |

Real | m_flow_der2 | 2nd derivative of mass flow rate in design flow direction [kg/s3] |

### Outputs

Type | Name | Description |
---|---|---|

Real | dp_der2 | 2nd derivative of pressure difference between port_a and port_b (= port_a.p - port_b.p) |