Detailed Description

These models estimate package kW and useful acfm from normalized curve anchors. Select the control actually active during the measured interval. Establish pressure-corrected capacity anchors first, then normalize the measured point, evaluate the appropriate segment, and use Dimensional Result Reconstruction to recover dimensional results.

Performance Curves

Normalized centrifugal load/unload curve; test fixture P_FL=452.3 kW, Q_FL=3138 acfm, P_NL=71.3 kW.

Normalized centrifugal blow-off curve; bypass flow is shown as an internal balance.

Normalized centrifugal modulation/unload curve with the unload transition labeled.

Inputs and Origins

Quantity	Origin	Unit
Full-load package power and airflow	measured test or manufacturer data	kW, acfm
No-load package power	measured unloaded operation or catalog	kW
Unload power and airflow	controller transition point or catalog	kW, acfm
Maximum airflow	manufacturer stonewall/full-flow point	acfm
Blow-off power and airflow	manufacturer map or measured bypass condition	kW, acfm
Capacity-pressure anchors	maximum surge, rated/full load, and minimum stonewall	acfm at psig

Pressure-Capacity Correction

Three catalog anchors define a quadratic capacity map:

\begin{equation}\label{eq:centrifugal-pressure-fit} Q(P_g)=aP_g^2+bP_g+c \end{equation}

where the three \((P_g,Q)\) pairs are maximum surge, rated/full load, and minimum stonewall. Evaluate this fit at the requested full-load pressure to replace \(Q_{FL}\). For modulation/unload, evaluate it again at maximum pressure to replace \(Q_{max}\). Pressure is gauge pressure because the empirical map is fitted directly to psig catalog points.

Load/Unload Curve

Linear interpolation between no-load and full-load anchors.

\begin{equation}\label{eq:centrifugal-load-unload-power-from-airflow} f_P=f_{P,NL}+(1-f_{P,NL})f_Q \end{equation}

\begin{equation}\label{eq:centrifugal-load-unload-airflow-from-power} f_Q=\frac{f_P-f_{P,NL}}{1-f_{P,NL}} \end{equation}

\(f_P\)	Package power divided by full-load package power \([\unit{ \unitless}]\)
\(f_Q\)	Delivered airflow divided by full-load airflow \([\unit{ \unitless}]\)
\(f_{P,NL}\)	No-load package power divided by full-load package power \([\unit{ \unitless}]\)

Fully Substituted Example: With \(P_{FL}=452.3\ \mathrm{kW}\), \(Q_{FL}=3138\ \mathrm{acfm}\), and \(P_{NL}=71.3\ \mathrm{kW}\), \(f_{P,NL}=71.3/452.3=0.1576\). For \(f_Q=0.24\), \(f_P=0.1576+(1-0.1576)(0.24)=0.3598\). Therefore \(P=0.3598(452.3)=162.7\ \mathrm{kW}\) and \(Q=0.24(3138)=753.1\ \mathrm{acfm}\).

Modulation/Unload Curve

Piecewise interpolation through no-load, unload, and maximum-flow anchors.

For an airflow input, use the low segment below unload and the high segment from unload to maximum airflow:

\begin{equation}\label{eq:centrifugal-mod-unload-capacity} f_P=\begin{cases} f_{P,NL}+\dfrac{f_{P,UL}-f_{P,NL}}{f_{Q,UL}}f_Q, & f_Q<f_{Q,UL}\\ f_{P,UL}+\dfrac{1-f_{P,UL}}{f_{Q,max}-f_{Q,UL}}(f_Q-f_{Q,UL}), & f_{Q,UL}\le f_Q<f_{Q,max}\\ 1, & f_Q\ge f_{Q,max} \end{cases} \end{equation}

For a power input, invert the same two segments. Every reported airflow fraction uses the full-load basis \(f_Q=Q/Q_{FL}\), including the segment above unload. Dimensional airflow is therefore always reconstructed as \(Q=f_QQ_{FL}\).

\(f_{P,NL}\)	No-load power divided by full-load power \([\unit{ \unitless}]\)
\(f_{P,UL}\)	Unload power divided by full-load power \([\unit{ \unitless}]\)
\(f_{Q,UL}\)	Unload airflow divided by full-load airflow \([\unit{ \unitless}]\)
\(f_{Q,max}\)	Maximum airflow divided by full-load airflow \([\unit{ \unitless}]\)
\(f_P\)	Package power fraction \([\unit{ \unitless}]\)
\(f_Q\)	Airflow fraction \([\unit{ \unitless}]\)

Fully Substituted Example: For \(P_{FL}=452.3\ \mathrm{kW}\), \(Q_{FL}=3138\ \mathrm{acfm}\), \(P_{NL}=71.3\ \mathrm{kW}\), \(P_{UL}=411.9\ \mathrm{kW}\), \(Q_{UL}=2731\ \mathrm{acfm}\), and \(Q_{max}=3005\ \mathrm{acfm}\), the unload fractions are \(f_{P,UL}=0.9107\) and \(f_{Q,UL}=0.8703\). At \(f_Q=0.8693\), the low segment gives \(f_P=0.9098\); at exactly \(f_Q=0.8703\), both segments give \(f_P=0.9107\). At \(f_P=0.94\), inversion of the high segment gives \(f_Q=0.8990\) and \(Q=0.8990(3138)=2821.0\ \mathrm{acfm}\). Passing \(f_Q=0.8990\) back through the capacity calculation returns \(f_P=0.94\), demonstrating that the two paths use the same basis. The transition is continuous.

Blow-Off Curve

Separate useful airflow from the bypass flow needed to hold the compressor stable.

\begin{equation}\label{eq:centrifugal-blowoff-low} f_Q=f_{Q,BO}-f_{BO}\quad\text{for }f_P\le f_{P,BO} \end{equation}

\begin{equation}\label{eq:centrifugal-blowoff-high} f_Q=\frac{1-f_{Q,BO}}{1-f_{P,BO}} \left[f_P-1+\frac{1-f_{P,BO}}{1-f_{Q,BO}}\right] \end{equation}

\begin{equation}\label{eq:centrifugal-blowoff-bypass} Q_{BO}=(f_{Q,BO}-f_Q)Q_{FL} \end{equation}

\(f_{P,BO}\)	Blow-off package power divided by full-load package power \([\unit{ \unitless}]\)
\(f_{Q,BO}\)	Blow-off airflow divided by full-load airflow \([\unit{ \unitless}]\)
\(f_{BO}\)	Bypass airflow divided by full-load airflow \([\unit{ \unitless}]\)
\(Q_{BO}\)	Calculated bypass or blow-off airflow \([\unit{ \acfm}]\)
\(Q_{FL}\)	Full-load airflow \([\unit{ \acfm}]\)
\(f_P\)	Package power fraction \([\unit{ \unitless}]\)
\(f_Q\)	Useful delivered airflow fraction \([\unit{ \unitless}]\)

Fully Substituted Example: With \(P_{FL}=452.3\ \mathrm{kW}\), \(Q_{FL}=3138\ \mathrm{acfm}\), \(P_{BO}=370.9\ \mathrm{kW}\), \(Q_{BO,anchor}=2510\ \mathrm{acfm}\), and a bypass fraction 0.6798, \(f_{P,BO}=0.8200\) and \(f_{Q,BO}=0.7999\). Because the measured power fraction 0.82 is at the blow-off anchor, \(f_Q=0.7999-0.6798=0.1201\). Thus useful airflow is \(0.1201(3138)=376.8\ \mathrm{acfm}\) and the bypass intermediate is \(0.6798(3138)=2133.2\ \mathrm{acfm}\).

Assumptions and Limits

Piecewise segments are used only between their defining anchors; extrapolation beyond a manufacturer map is not a validated centrifugal performance prediction.
Capacity-based modulation/unload evaluation changes segments at the unload airflow fraction, not at the unload power fraction.
Blow-off airflow is a bypass-flow intermediate retained by the library. Useful delivered airflow and package power are the assessment outputs normally presented to users.

Modules
	Centrifugal Load/Unload Calculation
	Linear interpolation between no-load and full-load anchors.

	Centrifugal Modulation/Unload Calculation
	Piecewise interpolation through no-load, unload, and maximum-flow anchors.

	Centrifugal Blow-Off Calculation
	Separate useful airflow from the bypass flow needed to hold the compressor stable.

Files
file	centrifugal_compressor.h
	Centrifugal compressor assessment model declarations.