Buildings.Fluid.Movers.BaseClasses.Characteristics

Information

This package implements performance curves for fans and pumps, and records for parameter that can be used with these performance curves.

The following performance curves are implemented:

Independent variable	Dependent variable	Record for performance data	Function
Volume flow rate	Pressure	flowParameters	pressure
Relative volumetric flow rate	Efficiency	efficiencyParameters	efficiency
Volume flow rate	Power	powerParameters	power

Package Content

Name	Description
flowParameters	Record for flow parameters
flowParametersInternal	Record for flow parameters with prescribed size
efficiencyParameters	Record for efficiency parameters
powerParameters	Record for electrical power parameters
pressure	Flow vs. head characteristics for fan or pump pressure raise
flowApproximationAtOrigin	Approximation for fan or pump pressure raise at origin
power	Flow vs. electrical power characteristics for fan or pump
efficiency	Flow vs. efficiency characteristics for fan or pump

Buildings.Fluid.Movers.BaseClasses.Characteristics.flowParameters

Information

Data record for performance data that describe volume flow rate versus pressure rise. The volume flow rate V_flow must be increasing, i.e., V_flow[i] < V_flow[i+1]. Both vectors, V_flow and dp must have the same size.

Extends from Modelica.Icons.Record (Icon for records).

Parameters

Type	Name	Default	Description
VolumeFlowRate	V_flow[:]		Volume flow rate at user-selected operating points [m3/s]
Pressure	dp[size(V_flow, 1)]		Fan or pump total pressure at these flow rates [Pa]

Modelica definition

record flowParameters "Record for flow parameters"
  extends Modelica.Icons.Record;
  parameter Modelica.SIunits.VolumeFlowRate V_flow[:](each min=0) 
    "Volume flow rate at user-selected operating points";
  parameter Modelica.SIunits.Pressure dp[size(V_flow,1)](
     each min=0, each displayUnit="Pa") 
    "Fan or pump total pressure at these flow rates";
end flowParameters;

Buildings.Fluid.Movers.BaseClasses.Characteristics.flowParametersInternal

Information

Data record for performance data that describe volume flow rate versus pressure rise. The volume flow rate V_flow must be increasing, i.e., V_flow[i] < V_flow[i+1]. Both vectors, V_flow and dp must have the same size.

This record is identical to Buildings.Fluid.Movers.BaseClasses.Characteristic.flowParameters, except that it takes the size of the array as a parameter. This is required in Dymola 2014. Otherwise, the array size would need to be computed in Buildings.Fluid.Movers.BaseClasses.FlowMachineInterface in the initial algorithm section, which is not supported.

Extends from Modelica.Icons.Record (Icon for records).

Parameters

Type	Name	Default	Description
Integer	n		Number of elements in each array
VolumeFlowRate	V_flow[n]		Volume flow rate at user-selected operating points [m3/s]
Pressure	dp[n]		Fan or pump total pressure at these flow rates [Pa]

Modelica definition

record flowParametersInternal 
  "Record for flow parameters with prescribed size"
  extends Modelica.Icons.Record;
  parameter Integer n "Number of elements in each array";
  parameter Modelica.SIunits.VolumeFlowRate V_flow[n](each min=0) 
    "Volume flow rate at user-selected operating points";
  parameter Modelica.SIunits.Pressure dp[n](
     each min=0, each displayUnit="Pa") 
    "Fan or pump total pressure at these flow rates";
end flowParametersInternal;

Buildings.Fluid.Movers.BaseClasses.Characteristics.efficiencyParameters

Information

Data record for performance data that describe volume flow rate versus efficiency. The volume flow rate r_V must be increasing, i.e., r_V[i] < r_V[i+1]. Both vectors, r_V and eta must have the same size.

Extends from Modelica.Icons.Record (Icon for records).

Parameters

Type	Name	Default	Description
Real	r_V[:]		Volumetric flow rate divided by nominal flow rate at user-selected operating points
Real	eta[size(r_V, 1)]		Fan or pump efficiency at these flow rates

Modelica definition

record efficiencyParameters "Record for efficiency parameters"
  extends Modelica.Icons.Record;
  parameter Real  r_V[:](each min=0, each max=1, each displayUnit="1") 
    "Volumetric flow rate divided by nominal flow rate at user-selected operating points";
  parameter Real eta[size(r_V,1)](
     each min=0, each max=1, each displayUnit="1") 
    "Fan or pump efficiency at these flow rates";
end efficiencyParameters;

Buildings.Fluid.Movers.BaseClasses.Characteristics.powerParameters

Information

Data record for performance data that describe volume flow rate versus electrical power. The volume flow rate V_flow must be increasing, i.e., V_flow[i] < V_flow[i+1]. Both vectors, V_flow and P must have the same size.

Extends from Modelica.Icons.Record (Icon for records).

Parameters

Type	Name	Default	Description
VolumeFlowRate	V_flow[:]	{0}	Volume flow rate at user-selected operating points [m3/s]
Power	P[size(V_flow, 1)]	{0}	Fan or pump electrical power at these flow rates [W]

Modelica definition

record powerParameters "Record for electrical power parameters"
  extends Modelica.Icons.Record;
  parameter Modelica.SIunits.VolumeFlowRate V_flow[:](each min=0)= {0} 
    "Volume flow rate at user-selected operating points";
  parameter Modelica.SIunits.Power P[size(V_flow,1)](
     each min=0) = {0} "Fan or pump electrical power at these flow rates";
end powerParameters;

Buildings.Fluid.Movers.BaseClasses.Characteristics.pressure

Information

This function computes the fan static pressure raise as a function of volume flow rate and revolution in the form

Δp = r_N²   s(V/r_N, d) - Δp_r ,

where Δp is the pressure rise, r_N is the normalized fan speed, V is the volume flow rate and d are performance data for fan or pump power consumption at r_N=1. The term

Δp_r = V   Δp_max ⁄ V_max   δ

models the flow resistance of the fan, approximated using a linear equation. This is done for numerical reasons to avoid a singularity at r_N=0. Since δ is small, the contribution of this term is small. The fan and pump models in Buildings.Fluid.Movers modify the user-supplied performance data to add the term Δp_r prior to computing the performance curve. Thus, at full speed, the fan or pump can operate exactly at the user-supplied performance data.

Implementation

The function s(·, ·) is a cubic hermite spline. If the data d define a monotone decreasing sequence, then s(·, d) is a monotone decreasing function.

For r_N < δ, the polynomial is replaced with an other model to avoid a singularity at the origin. The composite model is once continuously differentiable in all input variables.

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

Inputs

Type	Name	Default	Description
flowParametersInternal	data		Pressure performance data
VolumeFlowRate	V_flow		Volumetric flow rate [m3/s]
Real	r_N		Relative revolution, r_N=N/N_nominal [1]
VolumeFlowRate	VDelta_flow		Small volume flow rate [m3/s]
Pressure	dpDelta		Small pressure [Pa]
VolumeFlowRate	V_flow_max		Maximum volume flow rate at r_N=1 and dp=0 [m3/s]
Pressure	dpMax		Maximum pressure at r_N=1 and V_flow=0 [Pa]
Real	d[:]		Derivatives at support points for spline interpolation
Real	delta		Small value used to transition to other fan curve
Real	cBar[2]		Coefficients for linear approximation of pressure vs. flow rate
Real	kRes		Linear coefficient for fan-internal pressure drop [kg/(s.m4)]

Outputs

Type	Name	Description
Pressure	dp	Pressure raise [Pa]

Modelica definition

function pressure 
  "Flow vs. head characteristics for fan or pump pressure raise"
  extends Modelica.Icons.Function;
  input Buildings.Fluid.Movers.BaseClasses.Characteristics.flowParametersInternal
                                                                                  data 
    "Pressure performance data";
  input Modelica.SIunits.VolumeFlowRate V_flow "Volumetric flow rate";
  input Real r_N(unit="1") "Relative revolution, r_N=N/N_nominal";
  input Modelica.SIunits.VolumeFlowRate VDelta_flow "Small volume flow rate";
  input Modelica.SIunits.Pressure dpDelta "Small pressure";

  input Modelica.SIunits.VolumeFlowRate V_flow_max 
    "Maximum volume flow rate at r_N=1 and dp=0";
  input Modelica.SIunits.Pressure dpMax(min=0) 
    "Maximum pressure at r_N=1 and V_flow=0";

  input Real d[:] "Derivatives at support points for spline interpolation";
  input Real delta "Small value used to transition to other fan curve";
  input Real cBar[2] 
    "Coefficients for linear approximation of pressure vs. flow rate";
  input Real kRes(unit="kg/(s.m4)") 
    "Linear coefficient for fan-internal pressure drop";
  output Modelica.SIunits.Pressure dp "Pressure raise";

protected 
   Integer dimD(min=2)=size(data.V_flow, 1) "Dimension of data vector";

  function performanceCurve "Performance curve away from the origin"
    input Modelica.SIunits.VolumeFlowRate V_flow "Volumetric flow rate";
    input Real r_N(unit="1") "Relative revolution, r_N=N/N_nominal";
    input Real d[dimD] "Coefficients for polynomial of pressure vs. flow rate";
    input Buildings.Fluid.Movers.BaseClasses.Characteristics.flowParametersInternal
                                                                                    data 
      "Pressure performance data";
    input Integer dimD "Dimension of data vector";

    output Modelica.SIunits.Pressure dp "Pressure raise";

  protected 
    Modelica.SIunits.VolumeFlowRate rat "Ratio of V_flow/r_N";
    Integer i "Integer to select data interval";
  algorithm 
    rat := V_flow/r_N;
    i :=1;
    // Since the coefficients for the spline were evaluated for
    // rat_nominal = V_flow_nominal/r_N_nominal = V_flow_nominal/1, we use
    // V_flow_nominal below
    for j in 1:dimD-1 loop
       if rat > data.V_flow[j] then
         i := j;
       end if;
    end for;
    // Extrapolate or interpolate the data
    dp:=r_N^2*Buildings.Utilities.Math.Functions.cubicHermiteLinearExtrapolation(
                x=rat,
                x1=data.V_flow[i],
                x2=data.V_flow[i + 1],
                y1=data.dp[i],
                y2=data.dp[i + 1],
                y1d=d[i],
                y2d=d[i+1]);
  end performanceCurve;

algorithm 
  if r_N >= delta then
     dp := performanceCurve(V_flow=V_flow, r_N=r_N, d=d,
                            data=data, dimD=dimD);
  elseif r_N <= delta/2 then
    dp := flowApproximationAtOrigin(r_N=r_N, V_flow=V_flow,
                                    VDelta_flow=  VDelta_flow, dpDelta=dpDelta,
                                    delta=delta, cBar=cBar);
  else
    dp := Modelica.Fluid.Utilities.regStep(x=r_N-0.75*delta,
                                           y1=performanceCurve(V_flow=V_flow, r_N=r_N, d=d,
                                                               data=data, dimD=dimD),
                                           y2=flowApproximationAtOrigin(r_N=r_N, V_flow=V_flow,
                                                   VDelta_flow=VDelta_flow, dpDelta=dpDelta,
                                                   delta=delta, cBar=cBar),
                                           x_small=delta/4);
  end if;
  dp := dp - V_flow*kRes;
end pressure;

Buildings.Fluid.Movers.BaseClasses.Characteristics.flowApproximationAtOrigin

Information

This function computes the fan static pressure raise as a function of volume flow rate and revolution near the origin. It is used to avoid a singularity in the pump or fan curve if the revolution approaches zero.

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

Inputs

Type	Name	Default	Description
VolumeFlowRate	V_flow		Volumetric flow rate [m3/s]
Real	r_N		Relative revolution, r_N=N/N_nominal [1]
VolumeFlowRate	VDelta_flow		Small volume flow rate [m3/s]
Pressure	dpDelta		Small pressure [Pa]
Real	delta		Small value used to transition to other fan curve
Real	cBar[2]		Coefficients for linear approximation of pressure vs. flow rate

Outputs

Type	Name	Description
Pressure	dp	Pressure raise [Pa]

Modelica definition

function flowApproximationAtOrigin 
  "Approximation for fan or pump pressure raise at origin"
  extends Modelica.Icons.Function;
  input Modelica.SIunits.VolumeFlowRate V_flow "Volumetric flow rate";
  input Real r_N(unit="1") "Relative revolution, r_N=N/N_nominal";
  input Modelica.SIunits.VolumeFlowRate VDelta_flow "Small volume flow rate";
  input Modelica.SIunits.Pressure dpDelta "Small pressure";
  input Real delta "Small value used to transition to other fan curve";
  input Real cBar[2] 
    "Coefficients for linear approximation of pressure vs. flow rate";
  output Modelica.SIunits.Pressure dp "Pressure raise";
algorithm 
  dp := r_N * dpDelta + r_N^2 * (cBar[1] + cBar[2]*V_flow);
end flowApproximationAtOrigin;

Buildings.Fluid.Movers.BaseClasses.Characteristics.power

Information

This function computes the fan power consumption for given volume flow rate, speed and performance data. The power consumption is

P = r_N³   s(V, d),

where P is the power consumption, r_N is the normalized fan speed, V is the volume flow rate and d are performance data for fan or pump power consumption at r_N=1.

Implementation

The function s(·, ·) is a cubic hermite spline. If the data d define a monotone decreasing sequence, then s(·, d) is a monotone decreasing function.

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

Inputs

Type	Name	Default	Description
powerParameters	data		Pressure performance data
VolumeFlowRate	V_flow		Volumetric flow rate [m3/s]
Real	r_N		Relative revolution, r_N=N/N_nominal [1]
Real	d[:]		Derivatives at support points for spline interpolation

Outputs

Type	Name	Description
Power	P	Power consumption [W]

Modelica definition

function power 
  "Flow vs. electrical power characteristics for fan or pump"
  extends Modelica.Icons.Function;
  input Buildings.Fluid.Movers.BaseClasses.Characteristics.powerParameters data 
    "Pressure performance data";
  input Modelica.SIunits.VolumeFlowRate V_flow "Volumetric flow rate";
  input Real r_N(unit="1") "Relative revolution, r_N=N/N_nominal";
  input Real d[:] "Derivatives at support points for spline interpolation";
  output Modelica.SIunits.Power P "Power consumption";

protected 
   Integer n=size(data.V_flow, 1) "Dimension of data vector";

   Modelica.SIunits.VolumeFlowRate rat "Ratio of V_flow/r_N";
   Integer i "Integer to select data interval";

algorithm 
  if n == 1 then
    P := r_N^3*data.P[1];
  else
    i :=1;
    // Since the coefficients for the spline were evaluated for
    // rat_nominal = V_flow_nominal/r_N_nominal = V_flow_nominal/1, we use
    // V_flow_nominal below
    for j in 1:n-1 loop
       if V_flow > data.V_flow[j] then
         i := j;
       end if;
    end for;
    // Extrapolate or interpolate the data
    P:=r_N^3*Buildings.Utilities.Math.Functions.cubicHermiteLinearExtrapolation(
                x=V_flow,
                x1=data.V_flow[i],
                x2=data.V_flow[i + 1],
                y1=data.P[i],
                y2=data.P[i + 1],
                y1d=d[i],
                y2d=d[i+1]);
  end if;
end power;

Buildings.Fluid.Movers.BaseClasses.Characteristics.efficiency

Information

This function computes the fan or pump efficiency for given normalized volume flow rate and performance data. The efficiency is

η = s(r_V, d),

where η is the efficiency, r_V is the normalized volume flow rate, and d are performance data for fan or pump efficiency.

Implementation

The function s(·, ·) is a cubic hermite spline. If the data d define a monotone decreasing sequence, then s(·, d) is a monotone decreasing function.

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

Inputs

Type	Name	Default	Description
efficiencyParameters	data		Efficiency performance data
Real	r_V		Volumetric flow rate divided by nominal flow rate [1]
Real	d[:]		Derivatives at support points for spline interpolation

Outputs

Type	Name	Description
Real	eta	Efficiency [1]

Modelica definition

function efficiency 
  "Flow vs. efficiency characteristics for fan or pump"
  extends Modelica.Icons.Function;
  input Buildings.Fluid.Movers.BaseClasses.Characteristics.efficiencyParameters
    data "Efficiency performance data";
  input Real r_V(unit="1") "Volumetric flow rate divided by nominal flow rate";
  input Real d[:] "Derivatives at support points for spline interpolation";
  output Real eta(min=0, unit="1") "Efficiency";

protected 
  Integer n = size(data.r_V, 1) "Number of data points";
  Integer i "Integer to select data interval";
algorithm 
  if n == 1 then
    eta := data.eta[1];
  else
    i :=1;
    for j in 1:n-1 loop
       if r_V > data.r_V[j] then
         i := j;
       end if;
    end for;
    // Extrapolate or interpolate the data
    eta:=Buildings.Utilities.Math.Functions.cubicHermiteLinearExtrapolation(
                x=r_V,
                x1=data.r_V[i],
                x2=data.r_V[i + 1],
                y1=data.eta[i],
                y2=data.eta[i + 1],
                y1d=d[i],
                y2d=d[i+1]);
  end if;

end efficiency;