ShaftConnectedCompressor1Phase

This component models a compressor that is connected to a Shaft for the single-phase flow model. The compressor formulation is based off the model described in INL (2018). The user supplies performance curves that give the pressure ratio and isentropic efficiency as functions of shaft speed and mass flow rate. The compressor then applies a pressure rise and work to the working fluid, according to the current flow conditions.

Usage

The parameter "volume" specifies the volume of the junction, and the parameter "position" specifies the spatial location of the center of the junction, which is used for plotting purposes only.

Initial conditions are specified with the following parameters:

"initial_T": temperature
"initial_p": pressure
"initial_vel_x": x-velocity
"initial_vel_y": y-velocity
"initial_vel_z": z-velocity

This component must be must be connected to a Shaft component, which controls the compressor rotational speed. The user must specify which flow channel boundaries are connected to the compressor with the "inlet" and "outlet" parameters.

The user assigns values for several compressor rated conditions: "omega_rated", "mdot_rated", "rho0_rated", and "c0_rated". These rated conditions, along with the user-supplied data "Rp_functions", "eff_functions", "speeds", define the compressor performance model.

The parameter speeds is a list of relative corrected speeds $var element = document.getElementById("moose-equation-ecc6d69b-5a0e-4024-bcb2-226fcc35ff4c");katex.render("\\alpha", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ (see Eq. (6)) in increasing order. The parameters parameters Rp_functions and eff_functions define curves for the pressure ratio $var element = document.getElementById("moose-equation-8e92d562-8ee1-4f20-85ec-28efef2628b3");katex.render("r_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ (see Eq. (2)) and isentropic efficiency $var element = document.getElementById("moose-equation-ee9fc854-ab4a-4e13-8368-de4fb86f1c81");katex.render("\\eta", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ (see Eq. (4)), respectively, as Functions for each entry in speeds, where the time value in the function corresponds to the relative corrected mass flow rate $var element = document.getElementById("moose-equation-bade3ef5-d84a-404d-89d2-9322632856e7");katex.render("\\nu", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ (see Eq. (5)). Further discussion on these equations and the input data used in them is found in Compressor performance data.

The user inputs values for "tau_fr_coeff", "tau_fr_const", and "speed_cr_fr" that are used to compute friction torque as defined in Friction torque.

The compressor moment of inertia contributes to the total moment of inertia of the shaft, which represents the resistance to acceleration of the shaft speed. The user inputs values for "inertia_coeff", "inertia_const", and "speed_cr_I" that are used to compute the compressor moment of inertia as defined in Moment of inertia.

The parameter "A_ref" corresponds to the reference area $var element = document.getElementById("moose-equation-7ff3b28e-69b4-458c-b18c-89b8fa10516a");katex.render("A_\\text{ref}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ (see Eq. (1)). It should generally be assigned a value between the inlet area and outlet area. A_ref can act as a means to scale the compressor head and can also be used in combination with "K" to apply a pressure drop due to form loss.

Input Parameters

A_refReference area [m^2]
C++ Type:double
Controllable:No
Description:Reference area [m^2]
Rp_functionsFunctions of pressure ratio versus relative corrected flow. Each function is for a different, constant relative corrected speed. The order of function names should correspond to the order of speeds in the `speeds` parameter [-]
C++ Type:std::vector<FunctionName>
Controllable:No
Description:Functions of pressure ratio versus relative corrected flow. Each function is for a different, constant relative corrected speed. The order of function names should correspond to the order of speeds in the `speeds` parameter [-]
c0_ratedRated compressor stagnation sound speed [m/s]
C++ Type:double
Controllable:No
Description:Rated compressor stagnation sound speed [m/s]
eff_functionsFunctions of adiabatic efficiency versus relative corrected flow. Each function is for a different, constant relative corrected speed. The order of function names should correspond to the order of speeds in the `speeds` parameter [-]
C++ Type:std::vector<FunctionName>
Controllable:No
Description:Functions of adiabatic efficiency versus relative corrected flow. Each function is for a different, constant relative corrected speed. The order of function names should correspond to the order of speeds in the `speeds` parameter [-]
inertia_coeffCompressor inertia coefficients [kg-m^2]
C++ Type:std::vector<double>
Controllable:No
Description:Compressor inertia coefficients [kg-m^2]
inertia_constCompressor inertia constant [kg-m^2]
C++ Type:double
Controllable:No
Description:Compressor inertia constant [kg-m^2]
inletCompressor inlet
C++ Type:BoundaryName
Controllable:No
Description:Compressor inlet
mdot_ratedRated compressor mass flow rate [kg/s]
C++ Type:double
Controllable:No
Description:Rated compressor mass flow rate [kg/s]
omega_ratedRated compressor speed [rad/s]
C++ Type:double
Controllable:No
Description:Rated compressor speed [rad/s]
outletCompressor outlet
C++ Type:BoundaryName
Controllable:No
Description:Compressor outlet
positionSpatial position of the center of the junction [m]
C++ Type:libMesh::Point
Controllable:No
Description:Spatial position of the center of the junction [m]
rho0_ratedRated compressor stagnation fluid density [kg/m^3]
C++ Type:double
Controllable:No
Description:Rated compressor stagnation fluid density [kg/m^3]
speed_cr_ICompressor speed threshold for inertia [-]
C++ Type:double
Controllable:No
Description:Compressor speed threshold for inertia [-]
speed_cr_frCompressor speed threshold for friction [-]
C++ Type:double
Controllable:No
Description:Compressor speed threshold for friction [-]
speedsRelative corrected speeds. Order of speeds needs correspond to the orders of `Rp_functions` and `eff_functions` [-]
C++ Type:std::vector<double>
Controllable:No
Description:Relative corrected speeds. Order of speeds needs correspond to the orders of `Rp_functions` and `eff_functions` [-]
tau_fr_coeffCompressor friction coefficients [N-m]
C++ Type:std::vector<double>
Controllable:No
Description:Compressor friction coefficients [N-m]
tau_fr_constCompressor friction constant [N-m]
C++ Type:double
Controllable:No
Description:Compressor friction constant [N-m]
volumeVolume of the junction [m^3]
C++ Type:double
Controllable:No
Description:Volume of the junction [m^3]

Required Parameters

K0Form loss factor [-]
Default:0
C++ Type:double
Controllable:No
Description:Form loss factor [-]
initial_TInitial temperature [K]
C++ Type:FunctionName
Controllable:No
Description:Initial temperature [K]
initial_pInitial pressure [Pa]
C++ Type:FunctionName
Controllable:No
Description:Initial pressure [Pa]
initial_vel_xInitial velocity in x-direction [m/s]
C++ Type:FunctionName
Controllable:No
Description:Initial velocity in x-direction [m/s]
initial_vel_yInitial velocity in y-direction [m/s]
C++ Type:FunctionName
Controllable:No
Description:Initial velocity in y-direction [m/s]
initial_vel_zInitial velocity in z-direction [m/s]
C++ Type:FunctionName
Controllable:No
Description:Initial velocity in z-direction [m/s]
max_pressure_ratio50Maximum pressure ratio
Default:50
C++ Type:double
Controllable:No
Description:Maximum pressure ratio
min_pressure_ratio0Minimum pressure ratio
Default:0
C++ Type:double
Controllable:No
Description:Minimum pressure ratio
scaling_factor_rhoEV1Scaling factor for rho*E*V [-]
Default:1
C++ Type:double
Controllable:No
Description:Scaling factor for rho*E*V [-]
scaling_factor_rhoV1Scaling factor for rho*V [-]
Default:1
C++ Type:double
Controllable:No
Description:Scaling factor for rho*V [-]
scaling_factor_rhouV1Scaling factor for rho*u*V [-]
Default:1
C++ Type:double
Controllable:No
Description:Scaling factor for rho*u*V [-]
scaling_factor_rhovV1Scaling factor for rho*v*V [-]
Default:1
C++ Type:double
Controllable:No
Description:Scaling factor for rho*v*V [-]
scaling_factor_rhowV1Scaling factor for rho*w*V [-]
Default:1
C++ Type:double
Controllable:No
Description:Scaling factor for rho*w*V [-]
treat_as_turbineFalseTreat the compressor as a turbine?
Default:False
C++ Type:bool
Controllable:No
Description:Treat the compressor as a turbine?

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(modules/thermal_hydraulics/test/tests/problems/brayton_cycle/closed_brayton_cycle.i)
(modules/thermal_hydraulics/test/tests/components/shaft_connected_compressor_1phase/jac.test.i)
(modules/thermal_hydraulics/test/tests/problems/brayton_cycle/open_brayton_cycle.i)
(modules/thermal_hydraulics/test/tests/components/shaft_connected_compressor_1phase/shaft_motor_compressor.i)

Formulation

The compressor is modeled as a 0-D volume based on the VolumeJunction1Phase component, which has conservation of mass, momentum, and energy equations in the volume, but with the addition of source terms to the momentum and energy equations:

var element = document.getElementById("moose-equation-63764994-7eca-434a-a6d1-08a21e2ca493");katex.render("\\ddt{\\rho V} = \\dot{m}_\\text{in} - \\dot{m}_\\text{out} \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

(1)var element = document.getElementById("moose-equation-cef46018-38f4-423e-85d8-bb16e3b2a7f8");katex.render("\\ddt{\\rho u V} = \\pr{(\\rho u^2 + p) A}_\\text{in} - \\pr{(\\rho u^2 + p) A}_\\text{out} + \\Delta p_0 A_\\text{ref} \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

var element = document.getElementById("moose-equation-862f3cfe-b59e-4b9d-8ee9-9b477fe44962");katex.render("\\ddt{\\rho E V} = \\pr{\\dot{m} H}_\\text{in} - \\pr{\\dot{m} H}_\\text{out} + \\dot{W} \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where

$var element = document.getElementById("moose-equation-7b505b44-16ed-449e-a6da-eee2ab3449c1");katex.render("\\Delta p_0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the change in stagnation pressure,
$var element = document.getElementById("moose-equation-548d2be3-95f7-447d-946b-9bdc045268c9");katex.render("A_{\\text{ref}}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the reference cross-sectional area, and
$var element = document.getElementById("moose-equation-da6a907b-43c5-4df4-89ba-735177ef4bf3");katex.render("\\dot{W}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the work rate.

The pressure ratio $var element = document.getElementById("moose-equation-187e0b9d-ac12-43d9-8aed-4e701bdcb94f");katex.render("r_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , which is given by user-defined performance data (see Compressor performance data), is defined as the ratio of the outlet stagnation pressure to the inlet stagnation pressure:

(2)var element = document.getElementById("moose-equation-3ace3e08-6058-48fe-b639-94aaf653d07a");katex.render("r_p \\equiv \\frac{p_{\\text{0, out}}} {p_{\\text{0, in}}} \\eqp", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

The stagnation pressure change can then be computed as

(3)var element = document.getElementById("moose-equation-261dca77-2f75-4ce0-9ea1-e4d2c68dc50a");katex.render("\\Delta p_0 = p_{\\text{0, in}} (r_p - 1) \\eqp", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

The isentropic efficiency $var element = document.getElementById("moose-equation-13ed776f-3adf-4889-aa16-f1c2a7136b4c");katex.render("\\eta", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , which is given by user-defined performance data (see Compressor performance data), is defined as the ratio of the isentropic work rate $var element = document.getElementById("moose-equation-9fdf1342-9206-4361-88fc-ed6e8f59d95d");katex.render("\\dot{W}_s", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ to the actual work rate $var element = document.getElementById("moose-equation-8ae0b650-020c-48c7-89ca-74065e6bf95a");katex.render("\\dot{W}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ :

(4)var element = document.getElementById("moose-equation-8110b501-595c-4bba-94df-352536115132");katex.render("\\eta \\equiv \\frac{\\dot{W}_s}{\\dot{W}} \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

var element = document.getElementById("moose-equation-f38e8b07-5490-453d-b51b-3c712b41ccd3");katex.render("\\dot{W}_s = \\dot{m} (H_{\\text{out},s} - H_\\text{in}) \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

var element = document.getElementById("moose-equation-16ed8ae2-49b2-45d5-aec2-012cc3edf36b");katex.render("\\dot{W} = \\dot{m} (H_\\text{out} - H_\\text{in}) = \\frac{\\dot{W}_s}{\\eta} \\eqp", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

The connected Shaft receives a corresponding torque $var element = document.getElementById("moose-equation-f12a4ae7-6ac8-4b79-b32a-8d14a4e78d1c");katex.render("\\tau_\\text{compressor}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , computed using the work rate and shaft speed $var element = document.getElementById("moose-equation-1ebc40c1-b3a8-4227-bc96-c950c81f1355");katex.render("\\omega", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and also a friction torque $var element = document.getElementById("moose-equation-5b11f4ef-ea32-446b-b5fb-13327e760de7");katex.render("\\tau_\\text{friction}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ (discussed in Friction torque):

var element = document.getElementById("moose-equation-e7ec5294-9b87-42df-95f5-82f586bce1f5");katex.render("\\tau_\\text{shaft,compressor} = \\tau_\\text{compressor} + \\tau_\\text{friction} \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

var element = document.getElementById("moose-equation-12ccff80-92b2-42f7-9228-7414475cbd79");katex.render("\\tau_\\text{compressor} = -\\frac{\\dot{W}}{\\omega} \\eqp", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

Compressor performance data

Users specify performance curves that give the pressure ratio $var element = document.getElementById("moose-equation-56063d68-f4f7-4d4f-910b-f71170ccaf1a");katex.render("r_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and isentropic efficiency $var element = document.getElementById("moose-equation-0b85112d-3a79-4508-9a53-76793c405f2b");katex.render("\\eta", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ as functions of the mass flow rate and shaft speed. Specifically, the mass flow rate used is a quantity normalized by rated conditions, often referred to as the "relative corrected mass flow rate", given the symbol $var element = document.getElementById("moose-equation-9bfd81b1-c4fd-469c-8c56-86324ea2802e");katex.render("\\nu", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ :

(5)var element = document.getElementById("moose-equation-c4caa5b2-6eb9-4e41-80d4-372486af89a5");katex.render("\\nu \\equiv \\frac{ (\\frac{\\dot{m}}{\\rho_{\\text{0, in}} c_{\\text{0, in}}}) } { (\\frac{\\dot{m}}{\\rho_{\\text{0, in}} c_{\\text{0, in}}})_{\\text{rated}} } \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-c7bce49e-cb14-4e4a-9f7e-551e2991e97c");katex.render("\\rho_0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-5169cf27-c3fa-47e4-bee0-d5d5c2594840");katex.render("c_0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are stagnation density and sound speed, respectively. Similarly, the shaft speed used is also normalized by rated conditions, often referred to as the "relative corrected shaft speed", given the symbol $var element = document.getElementById("moose-equation-2ac94f67-b73e-4499-bf91-a89e63375885");katex.render("\\alpha", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ :

(6)var element = document.getElementById("moose-equation-63c6d157-141e-4372-b379-b3d3fe1e6e36");katex.render("\\alpha \\equiv \\frac{ (\\frac{\\omega}{c_{\\text{0, in}}}) } { (\\frac{\\omega}{c_{\\text{0, in}}})_{\\text{rated}} } \\eqp", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

The user provides an ordered list of relative corrected shaft speeds, which correspond to ordered lists of pressure ratio and isentropic efficiency functions:

var element = document.getElementById("moose-equation-f68e05ff-fe50-4ea9-a05b-e538d4333aaf");katex.render("\\left\\{\\alpha_1, \\alpha_2, \\ldots, \\alpha_n\\right\\} \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

var element = document.getElementById("moose-equation-d77f3ae4-8bdc-4f65-9a3d-e3a6e426b934");katex.render("\\left\\{r_{p,1}(\\nu), r_{p,2}(\\nu), \\ldots, r_{p,n}(\\nu)\\right\\} \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

var element = document.getElementById("moose-equation-f7a00f73-4522-4c3e-ae26-00b25f2240f9");katex.render("\\left\\{\\eta_1(\\nu), \\eta_2(\\nu), \\ldots, \\eta_n(\\nu)\\right\\} \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

Linear interpolation and extrapolation is used to get the dependence on $var element = document.getElementById("moose-equation-a7a379c9-b7b0-492a-a4a7-05c3fcb634f4");katex.render("\\alpha", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ between and outside of the provided $var element = document.getElementById("moose-equation-a2fc1b9b-7df0-4246-9d01-d36109e7b907");katex.render("\\alpha_i", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ values:

var element = document.getElementById("moose-equation-5698c631-eb77-408f-a655-b0fc4ea79506");katex.render("r_p(\\nu, \\alpha) = r_{p,i}(\\nu) + \\frac{r_{p,i+1}(\\nu) - r_{p,i}(\\nu)}{\\alpha_{i+1} - \\alpha_i}(\\alpha - \\alpha_i) \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

var element = document.getElementById("moose-equation-38542bca-6c50-4c11-9677-82a577043c40");katex.render("\\eta(\\nu, \\alpha) = \\eta_i(\\nu) + \\frac{\\eta_{i+1}(\\nu) - \\eta_i(\\nu)}{\\alpha_{i+1} - \\alpha_i}(\\alpha - \\alpha_i) \\eqp", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

Lastly, bounds are applied to the pressure ratio, since extrapolation outside of limited performance data may yield unphysical values.

var element = document.getElementById("moose-equation-b35e3be8-c7a0-419e-8b80-df521061d38d");katex.render("r_p^- \\leq r_p \\leq r_p^+ \\eqp", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

Friction torque

Friction torque always resists the direction of motion, so the sign of the compressor friction torque depends on the sign of the connected shaft speed. Positive shaft speed results in negative friction torque while negative shaft speed results in positive friction torque.

The friction torque magnitude, $var element = document.getElementById("moose-equation-3d50c912-d467-42d3-85bf-c63e05f602ae");katex.render("\\tau_{\\text{friction}}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , is a function of shaft speed, $var element = document.getElementById("moose-equation-cfed9a0f-ace1-48c0-9392-eddb7b388ddf");katex.render("\\omega", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and four input parameters. If the ratio of shaft speed to "omega_rated", $var element = document.getElementById("moose-equation-dc84ea9b-3147-49d7-a0c1-e70006584fac");katex.render("\\alpha", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , is less than "speed_cr_fr", friction torque magnitude equals "tau_fr_const",

var element = document.getElementById("moose-equation-14edc2fc-e323-4d3f-a38b-1a260c76bb14");katex.render("\\tau_{\\text{friction}} = \\tau_{\\text{fr,const}},", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

otherwise, $var element = document.getElementById("moose-equation-0d28f3d2-4a5b-4778-bc45-42d4ab8984d0");katex.render("\\tau_{\\text{friction}}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a function of shaft speed and friction torque coefficients, "tau_fr_coeff",

var element = document.getElementById("moose-equation-7f293943-8d27-4beb-a8bd-dfca03503651");katex.render("\\tau_{\\text{friction}} = \\tau_{\\text{fr,coeff}}[0] + \\tau_{\\text{fr,coeff}}[1] \\mid \\alpha \\mid + \\tau_{\\text{fr,coeff}}[2] \\mid\\alpha \\mid^{2} + \\tau_{\\text{fr,coeff}}[3] \\mid \\alpha \\mid^{3}.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

Moment of inertia

The compressor moment of inertia, $var element = document.getElementById("moose-equation-9a55ae89-2803-441b-9135-fc23d0466006");katex.render("I_{\\text{compressor}}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , is a function of shaft speed, $var element = document.getElementById("moose-equation-9d6a3f41-7dff-41ea-b3cd-5755c7c5db88");katex.render("\\omega", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and four input parameters. If the ratio of shaft speed to "omega_rated", $var element = document.getElementById("moose-equation-f6010f80-716a-4d09-a225-e06d27bcb207");katex.render("\\alpha", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , is less than "speed_cr_I", compressor inertia equals "inertia_const",

var element = document.getElementById("moose-equation-31b40faf-daa5-48f5-a35b-e29b8c60d31c");katex.render("I_{\\text{compressor}} = I_{\\text{const}},", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

otherwise, $var element = document.getElementById("moose-equation-50775735-07f9-4c4e-a5d9-9597e4c9324e");katex.render("I_{\\text{compressor}}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a function of shaft speed and inertia coefficients, "inertia_coeff",

var element = document.getElementById("moose-equation-594d9b24-29c5-428e-b82a-cf62bd3677d4");katex.render("I_{\\text{compressor}} = I_{\\text{coeff}}[0] + I_{\\text{coeff}}[1] \\mid \\alpha \\mid + I_{\\text{coeff}}[2] \\mid\\alpha \\mid^{2} + I_{\\text{coeff}}[3] \\mid \\alpha \\mid^{3}.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

Form Loss

Complex multidimensional interactions inside the junction cannot be practically modeled mechanistically but are instead approximated using a form loss factor $var element = document.getElementById("moose-equation-b1baeec8-2d67-45f8-8706-73aa7716d35b");katex.render("K", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , which gives rise to source terms on the momentum and energy equations:

(7)var element = document.getElementById("moose-equation-9d0567f6-0c2c-4734-bd49-82defffb004d");katex.render("\\mathbf{S}^{\\text{momentum}} = - K (p_{0,1} - p_1) A_\\text{ref} \\frac{\\mathbf{u}_1}{\\|\\mathbf{u}_1\\|} \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

(8)var element = document.getElementById("moose-equation-a63b4d6c-0726-4c98-91e3-d2615e408429");katex.render("S^{\\text{energy}} = - K (p_{0,1} - p_1) A_\\text{ref} \\|\\mathbf{u}_1\\| \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where

$var element = document.getElementById("moose-equation-99f311d4-626f-4bfa-a9c1-869b76dab67c");katex.render("p_{0,1}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the stagnation pressure of the first flow channel (see Usage),
$var element = document.getElementById("moose-equation-58756488-f46f-4e78-a305-33d8c3886e31");katex.render("p_1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the static pressure of the first flow channel,
$var element = document.getElementById("moose-equation-364a7a82-5bd3-4b91-928c-fbf629634c34");katex.render("A_\\text{ref}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the reference cross-sectional area, and
$var element = document.getElementById("moose-equation-53cc218c-1b73-4384-a97e-b1022a840c8a");katex.render("\\mathbf{u}_1", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the velocity in the first connected flow channel.

References

INL. The RELAP5-3D Code Development Team, RELAP5-3D Code Manual Volume I: Code Structure, System Models and Solution Methods. pages 470–477, 2018. doi:INL/MIS-15-36723.

@article{CompressorR5,
    author = "INL",
    title = "The {RELAP5-3D} {C}ode {D}evelopment {T}eam, {RELAP5-3D} {C}ode {M}anual {V}olume {I}: {C}ode {S}tructure, {S}ystem {M}odels and {S}olution {M}ethods",
    journal = "",
    pages = "470-477",
    year = "2018",
    publisher = "Idaho National Laboratory",
    doi = "INL/MIS-15-36723"
}

(modules/thermal_hydraulics/test/tests/problems/brayton_cycle/closed_brayton_cycle.i)

# This input file is used to demonstrate a simple closed, air Brayton cycle using
# a compressor, turbine, shaft, motor, and generator.
# The flow length is divided into 6 segments as illustrated below, where
#   - "(C)" denotes the compressor
#   - "(T)" denotes the turbine
#   - "*" denotes a fictitious junction
#
#                Heated section               Cooled section
# *-----(C)-----*--------------*-----(T)-----*--------------*
#    1       2         3          4       5         6
#
# Initially the fluid is at rest at ambient conditions, the shaft speed is zero,
# and no heat transfer occurs with the system.
# The transient is controlled as follows:
#   * 0   - 100 s: motor ramps up torque linearly from zero
#   * 100 - 200 s: motor ramps down torque linearly to zero, HTC ramps up linearly from zero.
#   * 200 - 300 s: (no changes; should approach steady condition)

I_motor = 1.0
motor_torque_max = 400.0

I_generator = 1.0
generator_torque_per_shaft_speed = -0.00025

motor_ramp_up_duration = 100.0
motor_ramp_down_duration = 100.0
post_motor_time = 100.0
t1 = ${motor_ramp_up_duration}
t2 = ${fparse t1 + motor_ramp_down_duration}
t3 = ${fparse t2 + post_motor_time}

D1 = 0.15
D2 = ${D1}
D3 = ${D1}
D4 = ${D1}
D5 = ${D1}
D6 = ${D1}

A1 = ${fparse 0.25 * pi * D1^2}
A2 = ${fparse 0.25 * pi * D2^2}
A3 = ${fparse 0.25 * pi * D3^2}
A4 = ${fparse 0.25 * pi * D4^2}
A5 = ${fparse 0.25 * pi * D5^2}
A6 = ${fparse 0.25 * pi * D6^2}

L1 = 10.0
L2 = ${L1}
L3 = ${L1}
L4 = ${L1}
L5 = ${L1}
L6 = ${L1}

x1 = 0.0
x2 = ${fparse x1 + L1}
x3 = ${fparse x2 + L2}
x4 = ${fparse x3 + L3}
x5 = ${fparse x4 + L4}
x6 = ${fparse x5 + L5}

x2_minus = ${fparse x2 - 0.001}
x2_plus = ${fparse x2 + 0.001}
x5_minus = ${fparse x5 - 0.001}
x5_plus = ${fparse x5 + 0.001}

n_elems1 = 10
n_elems2 = ${n_elems1}
n_elems3 = ${n_elems1}
n_elems4 = ${n_elems1}
n_elems5 = ${n_elems1}
n_elems6 = ${n_elems1}

A_ref_comp = ${fparse 0.5 * (A1 + A2)}
V_comp = ${fparse A_ref_comp * 1.0}
I_comp = 1.0

A_ref_turb = ${fparse 0.5 * (A4 + A5)}
V_turb = ${fparse A_ref_turb * 1.0}
I_turb = 1.0

c0_rated_comp = 351.6925137
rho0_rated_comp = 1.146881112

rated_mfr = 0.25

speed_rated_rpm = 96000
speed_rated = ${fparse speed_rated_rpm * 2 * pi / 60.0}

speed_initial = 0

eff_comp = 0.79
eff_turb = 0.843

T_hot = 1000
T_cold = 300
T_ambient = 300
p_ambient = 1e5

[GlobalParams]
  orientation = '1 0 0'
  gravity_vector = '0 0 0'

  initial_p = ${p_ambient}
  initial_T = ${T_ambient}
  initial_vel = 0
  initial_vel_x = 0
  initial_vel_y = 0
  initial_vel_z = 0

  fp = fp_air
  closures = closures
  f = 0

  scaling_factor_1phase = '1 1 1e-5'
  scaling_factor_rhoV = 1
  scaling_factor_rhouV = 1
  scaling_factor_rhovV = 1
  scaling_factor_rhowV = 1
  scaling_factor_rhoEV = 1e-5

  rdg_slope_reconstruction = none
[]

[Functions]
  [motor_torque_fn]
    type = PiecewiseLinear
    x = '0 ${t1} ${t2}'
    y = '0 ${motor_torque_max} 0'
  []
  [motor_power_fn]
    type = ParsedFunction
    value = 'torque * speed'
    vars = 'torque speed'
    vals = 'motor_torque shaft:omega'
  []
  [generator_torque_fn]
    type = ParsedFunction
    value = 'slope * t'
    vars = 'slope'
    vals = '${generator_torque_per_shaft_speed}'
  []
  [generator_power_fn]
    type = ParsedFunction
    value = 'torque * speed'
    vars = 'torque speed'
    vals = 'generator_torque shaft:omega'
  []
  [htc_wall_fn]
    type = PiecewiseLinear
    x = '0 ${t1} ${t2}'
    y = '0 0 1e3'
  []
[]

[Modules/FluidProperties]
  [fp_air]
    type = IdealGasFluidProperties
    emit_on_nan = none
  []
[]

[Closures]
  [closures]
    type = Closures1PhaseSimple
  []
[]

[Components]
  [shaft]
    type = Shaft
    connected_components = 'motor compressor turbine generator'
    initial_speed = ${speed_initial}
  []
  [motor]
    type = ShaftConnectedMotor
    inertia = ${I_motor}
    torque = 0 # controlled
  []
  [generator]
    type = ShaftConnectedMotor
    inertia = ${I_generator}
    torque = generator_torque_fn
  []

  [pipe1]
    type = FlowChannel1Phase
    position = '${x1} 0 0'
    length = ${L1}
    n_elems = ${n_elems1}
    A = ${A1}
  []
  [compressor]
    type = ShaftConnectedCompressor1Phase
    position = '${x2} 0 0'
    inlet = 'pipe1:out'
    outlet = 'pipe2:in'
    A_ref = ${A_ref_comp}
    volume = ${V_comp}

    omega_rated = ${speed_rated}
    mdot_rated = ${rated_mfr}
    c0_rated = ${c0_rated_comp}
    rho0_rated = ${rho0_rated_comp}

    speeds = '0.5208 0.6250 0.7292 0.8333 0.9375'
    Rp_functions = 'rp_comp1 rp_comp2 rp_comp3 rp_comp4 rp_comp5'
    eff_functions = 'eff_comp1 eff_comp2 eff_comp3 eff_comp4 eff_comp5'

    min_pressure_ratio = 1.0

    speed_cr_I = 0
    inertia_const = ${I_comp}
    inertia_coeff = '${I_comp} 0 0 0'

    # assume no shaft friction
    speed_cr_fr = 0
    tau_fr_const = 0
    tau_fr_coeff = '0 0 0 0'
  []
  [pipe2]
    type = FlowChannel1Phase
    position = '${x2} 0 0'
    length = ${L2}
    n_elems = ${n_elems2}
    A = ${A2}
  []
  [junction2_3]
    type = JunctionOneToOne1Phase
    connections = 'pipe2:out pipe3:in'
  []
  [pipe3]
    type = FlowChannel1Phase
    position = '${x3} 0 0'
    length = ${L3}
    n_elems = ${n_elems3}
    A = ${A3}
  []
  [junction3_4]
    type = JunctionOneToOne1Phase
    connections = 'pipe3:out pipe4:in'
  []
  [pipe4]
    type = FlowChannel1Phase
    position = '${x4} 0 0'
    length = ${L4}
    n_elems = ${n_elems4}
    A = ${A4}
  []
  [turbine]
    type = ShaftConnectedCompressor1Phase
    position = '${x5} 0 0'
    inlet = 'pipe4:out'
    outlet = 'pipe5:in'
    A_ref = ${A_ref_turb}
    volume = ${V_turb}

    treat_as_turbine = true

    omega_rated = ${speed_rated}
    mdot_rated = ${rated_mfr}
    c0_rated = ${c0_rated_comp}
    rho0_rated = ${rho0_rated_comp}

    speeds = '0 0.5208 0.6250 0.7292 0.8333 0.9375'
    Rp_functions = 'rp_turb0 rp_turb1 rp_turb2 rp_turb3 rp_turb4 rp_turb5'
    eff_functions = 'eff_turb1 eff_turb1 eff_turb2 eff_turb3 eff_turb4 eff_turb5'

    min_pressure_ratio = 1.0

    speed_cr_I = 0
    inertia_const = ${I_turb}
    inertia_coeff = '${I_turb} 0 0 0'

    # assume no shaft friction
    speed_cr_fr = 0
    tau_fr_const = 0
    tau_fr_coeff = '0 0 0 0'
  []
  [pipe5]
    type = FlowChannel1Phase
    position = '${x5} 0 0'
    length = ${L5}
    n_elems = ${n_elems5}
    A = ${A5}
  []
  [junction5_6]
    type = JunctionOneToOne1Phase
    connections = 'pipe5:out pipe6:in'
  []
  [pipe6]
    type = FlowChannel1Phase
    position = '${x6} 0 0'
    length = ${L6}
    n_elems = ${n_elems6}
    A = ${A6}
  []
  [junction6_1]
    type = JunctionOneToOne1Phase
    connections = 'pipe6:out pipe1:in'
  []

  [heating]
    type = HeatTransferFromSpecifiedTemperature1Phase
    flow_channel = pipe3
    T_wall = ${T_hot}
    Hw = htc_wall_fn
  []
  [cooling]
    type = HeatTransferFromSpecifiedTemperature1Phase
    flow_channel = pipe6
    T_wall = ${T_cold}
    Hw = htc_wall_fn
  []
[]

[ControlLogic]
  [motor_ctrl]
    type = TimeFunctionComponentControl
    component = motor
    parameter = torque
    function = motor_torque_fn
  []
[]

[Postprocessors]
  [heating_rate]
    type = ADHeatRateConvection1Phase
    block = 'pipe3'
    T = T
    T_wall = T_wall
    Hw = Hw
    P_hf = P_hf
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [cooling_rate]
    type = ADHeatRateConvection1Phase
    block = 'pipe6'
    T = T
    T_wall = T_wall
    Hw = Hw
    P_hf = P_hf
    execute_on = 'INITIAL TIMESTEP_END'
  []

  [motor_torque]
    type = RealComponentParameterValuePostprocessor
    component = motor
    parameter = torque
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [motor_power]
    type = FunctionValuePostprocessor
    function = motor_power_fn
    execute_on = 'INITIAL TIMESTEP_END'
  []

  [generator_torque]
    type = ShaftConnectedComponentPostprocessor
    quantity = torque
    shaft_connected_component_uo = generator:shaftconnected_uo
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [generator_power]
    type = FunctionValuePostprocessor
    function = generator_power_fn
    execute_on = 'INITIAL TIMESTEP_END'
  []

  [shaft_speed]
    type = ScalarVariable
    variable = 'shaft:omega'
    execute_on = 'INITIAL TIMESTEP_END'
  []

  [p_in_comp]
    type = PointValue
    variable = p
    point = '${x2_minus} 0 0'
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [p_out_comp]
    type = PointValue
    variable = p
    point = '${x2_plus} 0 0'
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [p_ratio_comp]
    type = ParsedPostprocessor
    pp_names = 'p_in_comp p_out_comp'
    function = 'p_out_comp / p_in_comp'
    execute_on = 'INITIAL TIMESTEP_END'
  []

  [p_in_turb]
    type = PointValue
    variable = p
    point = '${x5_minus} 0 0'
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [p_out_turb]
    type = PointValue
    variable = p
    point = '${x5_plus} 0 0'
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [p_ratio_turb]
    type = ParsedPostprocessor
    pp_names = 'p_in_turb p_out_turb'
    function = 'p_in_turb / p_out_turb'
    execute_on = 'INITIAL TIMESTEP_END'
  []

  [mfr_comp]
    type = ADFlowJunctionFlux1Phase
    boundary = pipe1:out
    connection_index = 0
    equation = mass
    junction = compressor
  []
  [mfr_turb]
    type = ADFlowJunctionFlux1Phase
    boundary = pipe4:out
    connection_index = 0
    equation = mass
    junction = turbine
  []
[]

[Preconditioning]
  [pc]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  scheme = 'bdf2'

  end_time = ${t3}
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.01
    optimal_iterations = 5
    iteration_window = 1
    growth_factor = 1.1
    cutback_factor = 0.9
  []
  dtmin = 1e-5

  steady_state_detection = true
  steady_state_start_time = ${t2}

  solve_type = NEWTON
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8
  nl_max_its = 15

  l_tol = 1e-4
  l_max_its = 10
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'closed_brayton_cycle'
    execute_vector_postprocessors_on = 'INITIAL'
  []
  [console]
    type = Console
    show = 'shaft_speed p_ratio_comp p_ratio_turb compressor:pressure_ratio turbine:pressure_ratio'
  []
[]

[Functions]
  # compressor pressure ratio
  [rp_comp1]
    type = PiecewiseLinear
    data_file = 'rp_comp1.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_comp2]
    type = PiecewiseLinear
    data_file = 'rp_comp2.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_comp3]
    type = PiecewiseLinear
    data_file = 'rp_comp3.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_comp4]
    type = PiecewiseLinear
    data_file = 'rp_comp4.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_comp5]
    type = PiecewiseLinear
    data_file = 'rp_comp5.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []

  # compressor efficiency
  [eff_comp1]
    type = ConstantFunction
    value = ${eff_comp}
  []
  [eff_comp2]
    type = ConstantFunction
    value = ${eff_comp}
  []
  [eff_comp3]
    type = ConstantFunction
    value = ${eff_comp}
  []
  [eff_comp4]
    type = ConstantFunction
    value = ${eff_comp}
  []
  [eff_comp5]
    type = ConstantFunction
    value = ${eff_comp}
  []

  # turbine pressure ratio
  [rp_turb0]
    type = ConstantFunction
    value = 1
  []
  [rp_turb1]
    type = PiecewiseLinear
    data_file = 'rp_turb1.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_turb2]
    type = PiecewiseLinear
    data_file = 'rp_turb2.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_turb3]
    type = PiecewiseLinear
    data_file = 'rp_turb3.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_turb4]
    type = PiecewiseLinear
    data_file = 'rp_turb4.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_turb5]
    type = PiecewiseLinear
    data_file = 'rp_turb5.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []

  # turbine efficiency
  [eff_turb1]
    type = ConstantFunction
    value = ${eff_turb}
  []
  [eff_turb2]
    type = ConstantFunction
    value = ${eff_turb}
  []
  [eff_turb3]
    type = ConstantFunction
    value = ${eff_turb}
  []
  [eff_turb4]
    type = ConstantFunction
    value = ${eff_turb}
  []
  [eff_turb5]
    type = ConstantFunction
    value = ${eff_turb}
  []
[]

(modules/thermal_hydraulics/test/tests/components/shaft_connected_compressor_1phase/jac.test.i)

[GlobalParams]
  initial_p = 1e5
  initial_T = 300
  initial_vel = 0
  initial_vel_x = 0
  initial_vel_y = 0
  initial_vel_z = 0

  length = 1
  n_elems = 1
  A = 0.1
  A_ref = 0.1

  closures = simple_closures
  fp = fp
  f = 0

  scaling_factor_1phase = '1e-2 1e-2 1e-5'
  scaling_factor_rhoEV = 1e-5
[]

[Modules/FluidProperties]
  [fp]
    type = StiffenedGasFluidProperties
    gamma = 1.4
    cv = 725
    p_inf = 0
    q = 0
    q_prime = 0
  []
[]

[Closures]
  [simple_closures]
    type = Closures1PhaseSimple
  []
[]

[Components]
  [sw1]
    type = SolidWall1Phase
    input = fch1:in
  []

  [fch1]
    type = FlowChannel1Phase
    position = '0 0 0'
    orientation = '1 0 0'
  []

  [compressor]
    type = ShaftConnectedCompressor1Phase
    inlet = 'fch1:out'
    outlet = 'fch2:in'
    position = '1 0 0'
    volume = 0.3
    inertia_coeff = '1 1 1 1'
    inertia_const = 1.61397
    speed_cr_I = 1e12
    speed_cr_fr = 0
    tau_fr_coeff = '0 0 9.084 0'
    tau_fr_const = 0
    omega_rated = 1476.6
    mdot_rated = 2
    rho0_rated = 1.3
    c0_rated = 350
    speeds = '-1.0 0.0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.5'
    Rp_functions = 'Rp00 Rp00 Rp04 Rp05 Rp06 Rp07 Rp08 Rp09 Rp10 Rp11 Rp11'
    eff_functions = 'eff00 eff00 eff04 eff05 eff06 eff07 eff08 eff09 eff10 eff11 eff11'
  []

  [fch2]
    type = FlowChannel1Phase
    position = '1 0 0'
    orientation = '1 0 0'
  []

  [sw2]
    type = SolidWall1Phase
    input = fch2:out
  []

  [shaft]
    type = Shaft
    connected_components = 'compressor'
    initial_speed = 1476.6
  []

[]

[Functions]
  [Rp00]
    type = PiecewiseLinear
    x = '0 0.3736 0.4216'
    y = '1 0.9701 0.9619'
  []
  [eff00]
    type = PiecewiseLinear
    x = '0 0.3736 0.4216'
    y = '0.001 0.8941 0.6641'
  []

  [Rp04]
    type = PiecewiseLinear
    x = '0.3736 0.3745 0.3753 0.3762 0.3770 0.3919 0.4067 0.4216 0.4826'
    y = '1.0789 1.0779 1.0771 1.0759 1.0749 1.0570 1.0388 1.0204 0.9450'
  []
  [eff04]
    type = PiecewiseLinear
    x = '0.3736 0.3745 0.3753 0.3762 0.3770 0.3919 0.4067 0.4216 0.4826'
    y = '0.8941 0.8929 0.8925 0.8915 0.8901 0.8601 0.7986 0.6641 0.1115'
  []

  [Rp05]
    type = PiecewiseLinear
    x = '0.3736 0.4026 0.4106 0.4186 0.4266 0.4346 0.4426 0.4506 0.4586 0.4666 0.4746 0.4826 0.5941'
    y = '1.2898 1.2442 1.2316 1.2189 1.2066 1.1930 1.1804 1.1677 1.1542 1.1413 1.1279 1.1150 0.9357'
  []
  [eff05]
    type = PiecewiseLinear
    x = '0.3736 0.4026 0.4106 0.4186 0.4266 0.4346 0.4426 0.4506 0.4586 0.4666 0.4746 0.4826 0.5941'
    y = '0.9281 0.9263 0.9258 0.9244 0.9226 0.9211 0.9195 0.9162 0.9116 0.9062 0.8995 0.8914 0.7793'
  []

  [Rp06]
    type = PiecewiseLinear
    x = '0.4026 0.4613 0.4723 0.4834 0.4945 0.5055 0.5166 0.5277 0.5387 0.5609 0.5719 0.583 0.5941 0.7124'
    y = '1.5533 1.4438 1.4232 1.4011 1.3793 1.3589 1.3354 1.3100 1.2867 1.2376 1.2131 1.1887 1.1636 0.896'
  []
  [eff06]
    type = PiecewiseLinear
    x = '0.4026 0.4613 0.4723 0.4834 0.4945 0.5055 0.5166 0.5277 0.5387 0.5609 0.5719 0.583 0.5941 0.7124'
    y = '0.9148 0.9255 0.9275 0.9277 0.9282 0.9295 0.9290 0.9269 0.9242 0.9146 0.9080 0.900 0.8920 0.8061'
  []

  [Rp07]
    type = PiecewiseLinear
    x = '0.4613 0.5447 0.5587 0.5726 0.5866 0.6006 0.6145 0.6285 0.6425 0.6565 0.6704 0.6844 0.6984 0.7124 0.8358'
    y = '1.8740 1.6857 1.6541 1.6168 1.5811 1.5430 1.5067 1.4684 1.4292 1.3891 1.3479 1.3061 1.2628 1.2208 0.8498'
  []
  [eff07]
    type = PiecewiseLinear
    x = '0.4613 0.5447 0.5587 0.5726 0.5866 0.6006 0.6145 0.6285 0.6425 0.6565 0.6704 0.6844 0.6984 0.7124 0.8358'
    y = '0.9004 0.9232 0.9270 0.9294 0.9298 0.9312 0.9310 0.9290 0.9264 0.9225 0.9191 0.9128 0.9030 0.8904 0.7789'
  []

  [Rp08]
    type = PiecewiseLinear
    x = '0.5447 0.6638 0.6810 0.6982 0.7154 0.7326 0.7498 0.7670 0.7842 0.8014 0.8186 0.8358 0.9702'
    y = '2.3005 1.9270 1.8732 1.8195 1.7600 1.7010 1.6357 1.5697 1.5019 1.4327 1.3638 1.2925 0.7347'
  []
  [eff08]
    type = PiecewiseLinear
    x = '0.5447 0.6638 0.6810 0.6982 0.7154 0.7326 0.7498 0.7670 0.7842 0.8014 0.8186 0.8358 0.9702'
    y = '0.9102 0.9276 0.9301 0.9313 0.9319 0.9318 0.9293 0.9256 0.9231 0.9153 0.9040 0.8933 0.8098'
  []

  [Rp09]
    type = PiecewiseLinear
    x = '0.6638 0.7762 0.7938 0.8115 0.8291 0.8467 0.8644 0.8820 0.8997 0.9173 0.9349 0.9526 0.9702 1.1107 1.25120'
    y = '2.6895 2.2892 2.2263 2.1611 2.0887 2.0061 1.9211 1.8302 1.7409 1.6482 1.5593 1.4612 1.3586 0.5422 -0.2742'
  []
  [eff09]
    type = PiecewiseLinear
    x = '0.6638 0.7762 0.7938 0.8115 0.8291 0.8467 0.8644 0.8820 0.8997 0.9173 0.9349 0.9526 0.9702 1.1107 1.2512'
    y = '0.8961 0.9243 0.9288 0.9323 0.9330 0.9325 0.9319 0.9284 0.9254 0.9215 0.9134 0.9051 0.8864 0.7380 0.5896'
  []

  [Rp10]
    type = PiecewiseLinear
    x = '0.7762 0.9255 0.9284 0.9461 0.9546 0.9816 0.9968 1.0170 1.039 1.0525 1.0812 1.0880 1.1056 1.1107 1.2511'
    y = '3.3162 2.6391 2.6261 2.5425 2.5000 2.3469 2.2521 2.1211 1.974 1.8806 1.6701 1.6169 1.4710 1.4257 0.1817'
  []
  [eff10]
    type = PiecewiseLinear
    x = '0.7762 0.9255 0.9284 0.9461 0.9546 0.9816 0.9968 1.0170 1.0390 1.0525 1.0812 1.0880 1.1056 1.1107 1.2511'
    y = '0.8991 0.9276 0.9281 0.9308 0.9317 0.9329 0.9318 0.9291 0.9252 0.9223 0.9116 0.9072 0.8913 0.8844 0.6937'
  []

  [Rp11]
    type = PiecewiseLinear
    x = '0.9255 1.0749 1.134 1.2511'
    y = '3.9586 2.9889 2.605 1.4928'
  []
  [eff11]
    type = PiecewiseLinear
    x = '0.9255 1.0749 1.1340 1.2511'
    y = '0.9257 0.9308 0.9328 0.8823'
  []
[]

[Preconditioning]
  [SMP_PJFNK]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  scheme = 'bdf2'

  start_time = 0
  dt = 0.001
  num_steps = 1
  abort_on_solve_fail = true

  solve_type = 'newton'
  line_search = 'basic'
  petsc_options_iname = '-snes_test_err'
  petsc_options_value = '1e-10'

  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-6
  nl_max_its = 15

  l_tol = 1e-4
  l_max_its = 10
[]

(modules/thermal_hydraulics/test/tests/problems/brayton_cycle/open_brayton_cycle.i)

# This input file is used to demonstrate a simple open-air Brayton cycle using
# a compressor, turbine, shaft, motor, and generator.
# The flow length is divided into 5 segments as illustrated below, where
#   - "(I)" denotes the inlet
#   - "(C)" denotes the compressor
#   - "(T)" denotes the turbine
#   - "(O)" denotes the outlet
#   - "*" denotes a fictitious junction
#
#                  Heated section
# (I)-----(C)-----*--------------*-----(T)-----(O)
#      1       2         3          4       5
#
# Initially the fluid is at rest at ambient conditions, the shaft speed is zero,
# and no heat transfer occurs with the system.
# The transient is controlled as follows:
#   * 0   - 100 s: motor ramps up torque linearly from zero
#   * 100 - 200 s: motor ramps down torque linearly to zero, HTC ramps up linearly from zero.
#   * 200 - 300 s: (no changes; should approach steady condition)

I_motor = 1.0
motor_torque_max = 400.0

I_generator = 1.0
generator_torque_per_shaft_speed = -0.00025

motor_ramp_up_duration = 100.0
motor_ramp_down_duration = 100.0
post_motor_time = 100.0
t1 = ${motor_ramp_up_duration}
t2 = ${fparse t1 + motor_ramp_down_duration}
t3 = ${fparse t2 + post_motor_time}

D1 = 0.15
D2 = ${D1}
D3 = ${D1}
D4 = ${D1}
D5 = ${D1}

A1 = ${fparse 0.25 * pi * D1^2}
A2 = ${fparse 0.25 * pi * D2^2}
A3 = ${fparse 0.25 * pi * D3^2}
A4 = ${fparse 0.25 * pi * D4^2}
A5 = ${fparse 0.25 * pi * D5^2}

L1 = 10.0
L2 = ${L1}
L3 = ${L1}
L4 = ${L1}
L5 = ${L1}

x1 = 0.0
x2 = ${fparse x1 + L1}
x3 = ${fparse x2 + L2}
x4 = ${fparse x3 + L3}
x5 = ${fparse x4 + L4}

x2_minus = ${fparse x2 - 0.001}
x2_plus = ${fparse x2 + 0.001}
x5_minus = ${fparse x5 - 0.001}
x5_plus = ${fparse x5 + 0.001}

n_elems1 = 10
n_elems2 = ${n_elems1}
n_elems3 = ${n_elems1}
n_elems4 = ${n_elems1}
n_elems5 = ${n_elems1}

A_ref_comp = ${fparse 0.5 * (A1 + A2)}
V_comp = ${fparse A_ref_comp * 1.0}
I_comp = 1.0

A_ref_turb = ${fparse 0.5 * (A4 + A5)}
V_turb = ${fparse A_ref_turb * 1.0}
I_turb = 1.0

c0_rated_comp = 351.6925137
rho0_rated_comp = 1.146881112

rated_mfr = 0.25

speed_rated_rpm = 96000
speed_rated = ${fparse speed_rated_rpm * 2 * pi / 60.0}

speed_initial = 0

eff_comp = 0.79
eff_turb = 0.843

T_hot = 1000
T_ambient = 300
p_ambient = 1e5

[GlobalParams]
  orientation = '1 0 0'
  gravity_vector = '0 0 0'

  initial_p = ${p_ambient}
  initial_T = ${T_ambient}
  initial_vel = 0
  initial_vel_x = 0
  initial_vel_y = 0
  initial_vel_z = 0

  fp = fp_air
  closures = closures
  f = 0

  scaling_factor_1phase = '1 1 1e-5'
  scaling_factor_rhoV = 1
  scaling_factor_rhouV = 1
  scaling_factor_rhovV = 1
  scaling_factor_rhowV = 1
  scaling_factor_rhoEV = 1e-5

  rdg_slope_reconstruction = none
[]

[Functions]
  [motor_torque_fn]
    type = PiecewiseLinear
    x = '0 ${t1} ${t2}'
    y = '0 ${motor_torque_max} 0'
  []
  [motor_power_fn]
    type = ParsedFunction
    value = 'torque * speed'
    vars = 'torque speed'
    vals = 'motor_torque shaft:omega'
  []
  [generator_torque_fn]
    type = ParsedFunction
    value = 'slope * t'
    vars = 'slope'
    vals = '${generator_torque_per_shaft_speed}'
  []
  [generator_power_fn]
    type = ParsedFunction
    value = 'torque * speed'
    vars = 'torque speed'
    vals = 'generator_torque shaft:omega'
  []
  [htc_wall_fn]
    type = PiecewiseLinear
    x = '0 ${t1} ${t2}'
    y = '0 0 1e3'
  []
[]

[Modules/FluidProperties]
  [fp_air]
    type = IdealGasFluidProperties
    emit_on_nan = none
  []
[]

[Closures]
  [closures]
    type = Closures1PhaseSimple
  []
[]

[Components]
  [shaft]
    type = Shaft
    connected_components = 'motor compressor turbine generator'
    initial_speed = ${speed_initial}
  []
  [motor]
    type = ShaftConnectedMotor
    inertia = ${I_motor}
    torque = 0 # controlled
  []
  [generator]
    type = ShaftConnectedMotor
    inertia = ${I_generator}
    torque = generator_torque_fn
  []

  [inlet]
    type = InletStagnationPressureTemperature1Phase
    input = 'pipe1:in'
    p0 = ${p_ambient}
    T0 = ${T_ambient}
  []
  [pipe1]
    type = FlowChannel1Phase
    position = '${x1} 0 0'
    length = ${L1}
    n_elems = ${n_elems1}
    A = ${A1}
  []
  [compressor]
    type = ShaftConnectedCompressor1Phase
    position = '${x2} 0 0'
    inlet = 'pipe1:out'
    outlet = 'pipe2:in'
    A_ref = ${A_ref_comp}
    volume = ${V_comp}

    omega_rated = ${speed_rated}
    mdot_rated = ${rated_mfr}
    c0_rated = ${c0_rated_comp}
    rho0_rated = ${rho0_rated_comp}

    speeds = '0.5208 0.6250 0.7292 0.8333 0.9375'
    Rp_functions = 'rp_comp1 rp_comp2 rp_comp3 rp_comp4 rp_comp5'
    eff_functions = 'eff_comp1 eff_comp2 eff_comp3 eff_comp4 eff_comp5'

    min_pressure_ratio = 1.0

    speed_cr_I = 0
    inertia_const = ${I_comp}
    inertia_coeff = '${I_comp} 0 0 0'

    # assume no shaft friction
    speed_cr_fr = 0
    tau_fr_const = 0
    tau_fr_coeff = '0 0 0 0'
  []
  [pipe2]
    type = FlowChannel1Phase
    position = '${x2} 0 0'
    length = ${L2}
    n_elems = ${n_elems2}
    A = ${A2}
  []
  [junction2_3]
    type = JunctionOneToOne1Phase
    connections = 'pipe2:out pipe3:in'
  []
  [pipe3]
    type = FlowChannel1Phase
    position = '${x3} 0 0'
    length = ${L3}
    n_elems = ${n_elems3}
    A = ${A3}
  []
  [junction3_4]
    type = JunctionOneToOne1Phase
    connections = 'pipe3:out pipe4:in'
  []
  [pipe4]
    type = FlowChannel1Phase
    position = '${x4} 0 0'
    length = ${L4}
    n_elems = ${n_elems4}
    A = ${A4}
  []
  [turbine]
    type = ShaftConnectedCompressor1Phase
    position = '${x5} 0 0'
    inlet = 'pipe4:out'
    outlet = 'pipe5:in'
    A_ref = ${A_ref_turb}
    volume = ${V_turb}

    treat_as_turbine = true

    omega_rated = ${speed_rated}
    mdot_rated = ${rated_mfr}
    c0_rated = ${c0_rated_comp}
    rho0_rated = ${rho0_rated_comp}

    speeds = '0 0.5208 0.6250 0.7292 0.8333 0.9375'
    Rp_functions = 'rp_turb0 rp_turb1 rp_turb2 rp_turb3 rp_turb4 rp_turb5'
    eff_functions = 'eff_turb1 eff_turb1 eff_turb2 eff_turb3 eff_turb4 eff_turb5'

    min_pressure_ratio = 1.0

    speed_cr_I = 0
    inertia_const = ${I_turb}
    inertia_coeff = '${I_turb} 0 0 0'

    # assume no shaft friction
    speed_cr_fr = 0
    tau_fr_const = 0
    tau_fr_coeff = '0 0 0 0'
  []
  [pipe5]
    type = FlowChannel1Phase
    position = '${x5} 0 0'
    length = ${L5}
    n_elems = ${n_elems5}
    A = ${A5}
  []
  [outlet]
    type = Outlet1Phase
    input = 'pipe5:out'
    p = ${p_ambient}
  []

  [heating]
    type = HeatTransferFromSpecifiedTemperature1Phase
    flow_channel = pipe3
    T_wall = ${T_hot}
    Hw = htc_wall_fn
  []
[]

[ControlLogic]
  [motor_ctrl]
    type = TimeFunctionComponentControl
    component = motor
    parameter = torque
    function = motor_torque_fn
  []
[]

[Postprocessors]
  [heating_rate]
    type = ADHeatRateConvection1Phase
    block = 'pipe3'
    T = T
    T_wall = T_wall
    Hw = Hw
    P_hf = P_hf
    execute_on = 'INITIAL TIMESTEP_END'
  []

  [motor_torque]
    type = RealComponentParameterValuePostprocessor
    component = motor
    parameter = torque
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [motor_power]
    type = FunctionValuePostprocessor
    function = motor_power_fn
    execute_on = 'INITIAL TIMESTEP_END'
  []

  [generator_torque]
    type = ShaftConnectedComponentPostprocessor
    quantity = torque
    shaft_connected_component_uo = generator:shaftconnected_uo
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [generator_power]
    type = FunctionValuePostprocessor
    function = generator_power_fn
    execute_on = 'INITIAL TIMESTEP_END'
  []

  [shaft_speed]
    type = ScalarVariable
    variable = 'shaft:omega'
    execute_on = 'INITIAL TIMESTEP_END'
  []

  [p_in_comp]
    type = PointValue
    variable = p
    point = '${x2_minus} 0 0'
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [p_out_comp]
    type = PointValue
    variable = p
    point = '${x2_plus} 0 0'
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [p_ratio_comp]
    type = ParsedPostprocessor
    pp_names = 'p_in_comp p_out_comp'
    function = 'p_out_comp / p_in_comp'
    execute_on = 'INITIAL TIMESTEP_END'
  []

  [p_in_turb]
    type = PointValue
    variable = p
    point = '${x5_minus} 0 0'
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [p_out_turb]
    type = PointValue
    variable = p
    point = '${x5_plus} 0 0'
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [p_ratio_turb]
    type = ParsedPostprocessor
    pp_names = 'p_in_turb p_out_turb'
    function = 'p_in_turb / p_out_turb'
    execute_on = 'INITIAL TIMESTEP_END'
  []

  [mfr_comp]
    type = ADFlowJunctionFlux1Phase
    boundary = pipe1:out
    connection_index = 0
    equation = mass
    junction = compressor
  []
  [mfr_turb]
    type = ADFlowJunctionFlux1Phase
    boundary = pipe4:out
    connection_index = 0
    equation = mass
    junction = turbine
  []
[]

[Preconditioning]
  [pc]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  scheme = 'bdf2'

  end_time = ${t3}
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.01
    optimal_iterations = 5
    iteration_window = 1
    growth_factor = 1.1
    cutback_factor = 0.9
  []
  dtmin = 1e-5

  steady_state_detection = true
  steady_state_start_time = ${t2}

  solve_type = NEWTON
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8
  nl_max_its = 15

  l_tol = 1e-4
  l_max_its = 10
[]

[Outputs]
  exodus = true
  [csv]
    type = CSV
    file_base = 'open_brayton_cycle'
    execute_vector_postprocessors_on = 'INITIAL'
  []
  [console]
    type = Console
    show = 'shaft_speed p_ratio_comp p_ratio_turb compressor:pressure_ratio turbine:pressure_ratio'
  []
[]

[Functions]
  # compressor pressure ratio
  [rp_comp1]
    type = PiecewiseLinear
    data_file = 'rp_comp1.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_comp2]
    type = PiecewiseLinear
    data_file = 'rp_comp2.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_comp3]
    type = PiecewiseLinear
    data_file = 'rp_comp3.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_comp4]
    type = PiecewiseLinear
    data_file = 'rp_comp4.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_comp5]
    type = PiecewiseLinear
    data_file = 'rp_comp5.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []

  # compressor efficiency
  [eff_comp1]
    type = ConstantFunction
    value = ${eff_comp}
  []
  [eff_comp2]
    type = ConstantFunction
    value = ${eff_comp}
  []
  [eff_comp3]
    type = ConstantFunction
    value = ${eff_comp}
  []
  [eff_comp4]
    type = ConstantFunction
    value = ${eff_comp}
  []
  [eff_comp5]
    type = ConstantFunction
    value = ${eff_comp}
  []

  # turbine pressure ratio
  [rp_turb0]
    type = ConstantFunction
    value = 1
  []
  [rp_turb1]
    type = PiecewiseLinear
    data_file = 'rp_turb1.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_turb2]
    type = PiecewiseLinear
    data_file = 'rp_turb2.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_turb3]
    type = PiecewiseLinear
    data_file = 'rp_turb3.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_turb4]
    type = PiecewiseLinear
    data_file = 'rp_turb4.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []
  [rp_turb5]
    type = PiecewiseLinear
    data_file = 'rp_turb5.csv'
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
    extrap = true
  []

  # turbine efficiency
  [eff_turb1]
    type = ConstantFunction
    value = ${eff_turb}
  []
  [eff_turb2]
    type = ConstantFunction
    value = ${eff_turb}
  []
  [eff_turb3]
    type = ConstantFunction
    value = ${eff_turb}
  []
  [eff_turb4]
    type = ConstantFunction
    value = ${eff_turb}
  []
  [eff_turb5]
    type = ConstantFunction
    value = ${eff_turb}
  []
[]

(modules/thermal_hydraulics/test/tests/components/shaft_connected_compressor_1phase/shaft_motor_compressor.i)

area = 0.2359
dt = 1.e-3

[GlobalParams]
  initial_p = 1e5
  initial_T = 288
  initial_vel = 60
  initial_vel_x = 60
  initial_vel_y = 0
  initial_vel_z = 0
  A = ${area}
  A_ref = ${area}
  f = 100
  scaling_factor_1phase = '0.04 0.04 0.04e-5'
  closures = simple_closures
  fp = fp
[]

[Modules/FluidProperties]
  [fp]
    type = IdealGasFluidProperties
  []
[]

[Closures]
  [simple_closures]
    type = Closures1PhaseSimple
  []
[]

[Components]
  [compressor]
    type = ShaftConnectedCompressor1Phase
    inlet = 'pipe:out'
    outlet = 'pipe:in'
    position = '0 0 0'
    scaling_factor_rhoEV = 1e-5
    volume = ${fparse area*0.45}
    inertia_coeff = '1 1 1 1'
    inertia_const = 1.61397
    speed_cr_I = 1e12
    speed_cr_fr = 0
    tau_fr_coeff = '0 0 0 0'
    tau_fr_const = 0
    omega_rated = 200
    mdot_rated = 21.74
    rho0_rated = 1.1812
    c0_rated = 340
    speeds = '0.0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 2'
    Rp_functions = 'Rp00 Rp04 Rp05 Rp06 Rp07 Rp08 Rp09 Rp10 Rp11 Rp11'
    eff_functions = 'eff00 eff04 eff05 eff06 eff07 eff08 eff09 eff10 eff11 eff11'
  []
  [pipe]
    type = FlowChannel1Phase
    position = '0.1 0 0'
    orientation = '1 0 0'
    length = 10
    n_elems = 20
  []

  [motor]
    type = ShaftConnectedMotor
    inertia = 1e2
    torque = 100
  []

  [shaft]
    type = Shaft
    connected_components = 'motor compressor'
    initial_speed = 100
  []
[]


[Functions]
  [Rp00]
    type = PiecewiseLinear
    x = '0 0.3736 0.4216'
    y = '1 0.9701 0.9619'
  []
  [eff00]
    type = PiecewiseLinear
    x = '0 0.3736 0.4216'
    y = '0.001 0.8941 0.6641'
  []

  [Rp04]
    type = PiecewiseLinear
    x = '0.3736 0.3745 0.3753 0.3762 0.3770 0.3919 0.4067 0.4216 0.4826'
    y = '1.0789 1.0779 1.0771 1.0759 1.0749 1.0570 1.0388 1.0204 0.9450'
  []
  [eff04]
    type = PiecewiseLinear
    x = '0.3736 0.3745 0.3753 0.3762 0.3770 0.3919 0.4067 0.4216 0.4826'
    y = '0.8941 0.8929 0.8925 0.8915 0.8901 0.8601 0.7986 0.6641 0.1115'
  []

  [Rp05]
    type = PiecewiseLinear
    x = '0.3736 0.4026 0.4106 0.4186 0.4266 0.4346 0.4426 0.4506 0.4586 0.4666 0.4746 0.4826 0.5941'
    y = '1.2898 1.2442 1.2316 1.2189 1.2066 1.1930 1.1804 1.1677 1.1542 1.1413 1.1279 1.1150 0.9357'
  []
  [eff05]
    type = PiecewiseLinear
    x = '0.3736 0.4026 0.4106 0.4186 0.4266 0.4346 0.4426 0.4506 0.4586 0.4666 0.4746 0.4826 0.5941'
    y = '0.9281 0.9263 0.9258 0.9244 0.9226 0.9211 0.9195 0.9162 0.9116 0.9062 0.8995 0.8914 0.7793'
  []

  [Rp06]
    type = PiecewiseLinear
    x = '0.4026 0.4613 0.4723 0.4834 0.4945 0.5055 0.5166 0.5277 0.5387 0.5609 0.5719 0.583 0.5941 0.7124'
    y = '1.5533 1.4438 1.4232 1.4011 1.3793 1.3589 1.3354 1.3100 1.2867 1.2376 1.2131 1.1887 1.1636 0.896'
  []
  [eff06]
    type = PiecewiseLinear
    x = '0.4026 0.4613 0.4723 0.4834 0.4945 0.5055 0.5166 0.5277 0.5387 0.5609 0.5719 0.583 0.5941 0.7124'
    y = '0.9148 0.9255 0.9275 0.9277 0.9282 0.9295 0.9290 0.9269 0.9242 0.9146 0.9080 0.900 0.8920 0.8061'
  []

  [Rp07]
    type = PiecewiseLinear
    x = '0.4613 0.5447 0.5587 0.5726 0.5866 0.6006 0.6145 0.6285 0.6425 0.6565 0.6704 0.6844 0.6984 0.7124 0.8358'
    y = '1.8740 1.6857 1.6541 1.6168 1.5811 1.5430 1.5067 1.4684 1.4292 1.3891 1.3479 1.3061 1.2628 1.2208 0.8498'
  []
  [eff07]
    type = PiecewiseLinear
    x = '0.4613 0.5447 0.5587 0.5726 0.5866 0.6006 0.6145 0.6285 0.6425 0.6565 0.6704 0.6844 0.6984 0.7124 0.8358'
    y = '0.9004 0.9232 0.9270 0.9294 0.9298 0.9312 0.9310 0.9290 0.9264 0.9225 0.9191 0.9128 0.9030 0.8904 0.7789'
  []

  [Rp08]
    type = PiecewiseLinear
    x = '0.5447 0.6638 0.6810 0.6982 0.7154 0.7326 0.7498 0.7670 0.7842 0.8014 0.8186 0.8358 0.9702'
    y = '2.3005 1.9270 1.8732 1.8195 1.7600 1.7010 1.6357 1.5697 1.5019 1.4327 1.3638 1.2925 0.7347'
  []
  [eff08]
    type = PiecewiseLinear
    x = '0.5447 0.6638 0.6810 0.6982 0.7154 0.7326 0.7498 0.7670 0.7842 0.8014 0.8186 0.8358 0.9702'
    y = '0.9102 0.9276 0.9301 0.9313 0.9319 0.9318 0.9293 0.9256 0.9231 0.9153 0.9040 0.8933 0.8098'
  []

  [Rp09]
    type = PiecewiseLinear
    x = '0.6638 0.7762 0.7938 0.8115 0.8291 0.8467 0.8644 0.8820 0.8997 0.9173 0.9349 0.9526 0.9702 1.1107 1.25120'
    y = '2.6895 2.2892 2.2263 2.1611 2.0887 2.0061 1.9211 1.8302 1.7409 1.6482 1.5593 1.4612 1.3586 0.5422 -0.2742'
  []
  [eff09]
    type = PiecewiseLinear
    x = '0.6638 0.7762 0.7938 0.8115 0.8291 0.8467 0.8644 0.8820 0.8997 0.9173 0.9349 0.9526 0.9702 1.1107 1.2512'
    y = '0.8961 0.9243 0.9288 0.9323 0.9330 0.9325 0.9319 0.9284 0.9254 0.9215 0.9134 0.9051 0.8864 0.7380 0.5896'
  []

  [Rp10]
    type = PiecewiseLinear
    x = '0.7762 0.9255 0.9284 0.9461 0.9546 0.9816 0.9968 1.0170 1.039 1.0525 1.0812 1.0880 1.1056 1.1107 1.2511'
    y = '3.3162 2.6391 2.6261 2.5425 2.5000 2.3469 2.2521 2.1211 1.974 1.8806 1.6701 1.6169 1.4710 1.4257 0.1817'
  []
  [eff10]
    type = PiecewiseLinear
    x = '0.7762 0.9255 0.9284 0.9461 0.9546 0.9816 0.9968 1.0170 1.0390 1.0525 1.0812 1.0880 1.1056 1.1107 1.2511'
    y = '0.8991 0.9276 0.9281 0.9308 0.9317 0.9329 0.9318 0.9291 0.9252 0.9223 0.9116 0.9072 0.8913 0.8844 0.6937'
  []

  [Rp11]
    type = PiecewiseLinear
    x = '0.9255 1.0749 1.134 1.2511'
    y = '3.9586 2.9889 2.605 1.4928'
  []
  [eff11]
    type = PiecewiseLinear
    x = '0.9255 1.0749 1.1340 1.2511'
    y = '0.9257 0.9308 0.9328 0.8823'
  []

  [S_energy_fcn]
    type = ParsedFunction
    value = '-(tau_isen+tau_diss)*omega'
    vars = 'tau_isen tau_diss omega'
    vals = 'compressor:isentropic_torque compressor:dissipation_torque shaft:omega'
  []
  [energy_conservation_fcn]
    type = ParsedFunction
    value = '(E_change - S_energy * dt) / E_tot'
    vars = 'E_change S_energy dt E_tot'
    vals = 'E_change S_energy ${dt} E_tot'
  []
[]

[Postprocessors]
  # mass conservation
  [mass_pipes]
    type = ElementIntegralVariablePostprocessor
    variable = rhoA
    block = 'pipe'
    execute_on = 'initial timestep_end'
  []
  [mass_compressor]
    type = ScalarVariable
    variable = compressor:rhoV
    execute_on = 'initial timestep_end'
  []
  [mass_tot]
    type = SumPostprocessor
    values = 'mass_pipes mass_compressor'
    execute_on = 'initial timestep_end'
  []
  [mass_conservation]
    type = ChangeOverTimePostprocessor
    postprocessor = mass_tot
    change_with_respect_to_initial = true
    compute_relative_change = true
    execute_on = 'initial timestep_end'
  []

  # energy conservation
  [E_pipes]
    type = ElementIntegralVariablePostprocessor
    variable = rhoEA
    block = 'pipe'
    execute_on = 'initial timestep_end'
  []
  [E_compressor]
    type = ScalarVariable
    variable = compressor:rhoEV
    execute_on = 'initial timestep_end'
  []
  [E_tot]
    type = LinearCombinationPostprocessor
    pp_coefs = '1 1'
    pp_names = 'E_pipes E_compressor'
    execute_on = 'initial timestep_end'
  []
  [S_energy]
    type = FunctionValuePostprocessor
    function = S_energy_fcn
    execute_on = 'initial timestep_end'
  []
  [E_change]
    type = ChangeOverTimePostprocessor
    postprocessor = E_tot
    execute_on = 'initial timestep_end'
  []

  # This should also execute on initial. This value is
  # lagged by one timestep as a workaround to moose issue #13262.
  [energy_conservation]
    type = FunctionValuePostprocessor
    function = energy_conservation_fcn
    execute_on = 'timestep_end'
  []
[]

[Preconditioning]
  [SMP_PJFNK]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  scheme = 'implicit-euler'

  dt = ${dt}
  num_steps = 6

  solve_type = 'NEWTON'
  line_search = 'basic'
  petsc_options_iname = '-pc_type'
  petsc_options_value = ' lu'
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-6
  nl_max_its = 15

  l_tol = 1e-4
  l_max_its = 10

  [Quadrature]
    type = GAUSS
    order = SECOND
  []
[]

[Outputs]
  velocity_as_vector = false
[]

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