Element Heat Addition

Several Flow Simulator elements use the heat addition options described in this section. These elements include:

Orifices and Generic Losses
Discrete Loss
Heater-Cooler
FI CdComp
Fixed Flow Element
Orifice Plates
Valves
Expansions and Contractions

The table below contains the complete list of the heat addition options and numbers that are present in the *.flo file. However, not all elements include all options.

UI Name (*.flo Label)	Description
Heat Mode (HEAT_MODE)	Mode of heat transfer to/from the fluid in the element. 0: Adiabatic 1: Heat Addition (Btu/s) 2: Heat Addition per Mass Flow (Btu/lbm) 3: Fixed Fluid Delta Total (degF) 4: Fixed Fluid Total at exit (degF) 5: Heat load as NTU 6: Heat load as constant hA 7: Adiabatic with Joule-Thomson effect 8: Fixed Fluid Quality at Exit 9: Heat from Compression
Heat Input (QIN)	The value entered for QIN depends on the HEAT_MODE selected. HEAT_MODE: QIN value 0: QIN not used 1: Heat Input (Btu/s)* 2: Heat Input per Mass Flow (Btu/lbm) 3: Element Delta Total (degF) 4: Element Exit Total (degF) 5: NTU (unitless) 6: hA (BTU/hr/F) 7: Joule-Thomson Coefficient (degF/psi) 8: Element Exit Fluid Quality (0-1) 9: Compression efficiency (%) *In cases where multiple flow streams are modeled by a single element (for example, NED and NLU not equal to 1), set the value of QIN to model the heat flow from only one of the restrictions.
Fraction of QIN applied before restriction (QIN_RATIO)	Fraction of the total heat to be added before the restriction. (0 = None, 1 = All)

Heat Addition Details

The element heat addition equations for each mode are detailed in this section. The equations used also depend on the energy equations method. The energy equations can be solved using temperature*Cp or enthalpy.

Note: The enthalpy-based equations only work when Coolprop is used for the fluid properties.

0. Adiabatic: $∆ T_{t} = 0 o r ∆ H_{t} = 0$; The total temperature change for an adiabatic element may not be 0 when enthalpy is used for the energy equations. The Joule-Thomson (J-T) effect causes the total temperature to change due the pressure change across the element. The J-T effect is ignored when temperature is used in the energy equations unless a J-T coefficient is provided and HEAT_MODE=7.
1. Heat Addition: $∆ T_{t} = \frac{Q_{i n}}{\dot{m} {C p}_{a v g}} o r ∆ H_{t} = \frac{Q_{i n}}{\dot{m}}$; $Q_{i n}$ = Heat addition (user defined).
2. Heat Addition per mass flow: $∆ T_{t} = \frac{Q_{i n}}{{C p}_{a v g}} o r ∆ H_{t} = Q_{i n}$; $Q_{i n}$ = Heat addition per mass flow (user defined).
3. Element Delta T: $∆ T_{t} = Q_{i n}$ ( $Q_{i n}$ refers to the input variable name).; $Q_{i n}$ = Temperature change (user defined).; The element exit total enthalpy is obtained by sending Coolprop the element exit total temperature and static pressure.
4. Element Exit Total Temperature: $T_{t, e x i t} = Q_{i n}$ ( $Q_{i n}$ refers to the input variable name).; $Q_{i n}$ = Element exit total temperature (user-defined).; The element exit total enthalpy is obtained by sending Coolprop the element exit total temperature and static pressure.
5. NTU: $∆ T_{t} = (T_{s i n k} - T_{t, i n l e t}) (1 - e x p (Q_{i n}))$ ( $Q_{i n}$ refers to the input variable name).; $Q_{i n} = N T U = - \frac{h A}{\dot{m} {C p}_{a v g}}$ = Number of transfer units
6. HTC*Area: $∆ T_{t} = (T_{s i n k} - T_{t, i n l e t}) (1 - e x p (\frac{Q_{i n}}{\dot{m} {C p}_{a v g}}))$ ( $Q_{i n}$ refers to the input variable name).; $Q_{i n} = h A$ = HTC*Area
7. Adiabatic with Joule-Thomson Effect: If temperature used in energy equations and J-T coefficient are user-supplied:; $∆ T_{t} = Q_{i n} * (P_{s, e x i t} - P_{s, i n l e t})$ ( $Q_{i n}$ refers to the input variable name).; $Q_{i n}$ = Joule-Thomson coefficient (degF/psi).; If Enthalpy is used in the energy equation:; $∆ H_{t} = 0$ and retrieve $T_{t, e x i t}$ from Coolprop using $H_{t, e x i t}$ and $P_{s, e x i t}$ .
8. Fixed Fluid Quality at Exit: This option only works if enthalpy is used for the energy equations and Coolprop is used for the fluid properties. The $T_{t, e x i t}$ and $H_{t, e x i t}$ is retrieved from Coolprop using ${Q u a l i t y}_{e x i t}$ and $P_{s, e x i t}$ .; $Q_{i n}$ = the quality at the element exit.
9. Heat from Compression: This option is only valid for the elements that can have a pressure rise, like a fixed flow element or a Flow versus Source Pressure element. You must verify that the pressures on both sides of the element are accurate. If a fixed flow element is attached to a boundary, the boundary's pressure does not have to be accurate unless this HEAT_MODE is used.; If Temperature is used in energy equations and the fluid is a gas:
$∆ T_{t} = \frac{T_{t, i n l e t}}{η_{a d i a b}} * [{(\frac{P_{t, e x i t}}{P_{t, i n l e t}})}^{\frac{γ - 1}{γ}} - 1]$; If Temperature is used in energy equations and the fluid is a liquid:; $∆ T_{t} = \frac{P_{H y d r a u l i c}}{\dot{m} {C p}_{a v g}} (\frac{1}{η_{a d i a b}} - 1)$; $P_{H y d r a u l i c} = (P_{t, e x i t} - P_{t, i n l e t}) * \frac{\dot{m}}{ρ}$; If Enthalpy is used in the energy equation and there is any fluid phase:; $∆ H_{t} = \frac{(H_{t, i s e n t r o p i c, e x i t} - H_{t, i n l e t})}{η_{a d i a b}}$; Nomenclature:; $∆ T_{t} = T_{t, e x i t} - T_{t, i n l e t}$ = the total temperature change.; $∆ H_{t} = H_{t, e x i t} - H_{t, i n l e t}$ = the total enthalpy change.; $\dot{m}$ = mass flow rate.; ${C p}_{a v g}$ = specific heat using an average temperature.; $η_{a d i a b} = Q_{i n} / 100 =$ = compressor adiabatic efficiency.; $ρ$ = density

The QIN_Ratio

The heat can be applied before and/or after the restriction. If QIN_RATIO=0, all heat is added after the restriction and the “upstream” temperature used in the flow rate calculations is the temperature of the upstream chamber. The flow rate is only adjusted if the fluid is not an incompressible liquid.

The equation used to adjust the flow rate is derived using the flow function (ff) and does not change with a different temperature entering the restriction.

f f = f f_{a d j T}

\frac{\dot{m} \sqrt{T_{t, i n l e t}}}{P_{t, i n l e t} A r e a} = \frac{{\dot{m}}_{a d j T} \sqrt{T_{t, i n l e t, a d j T}}}{P_{t, i n l e t} A r e a}

{\dot{m}}_{a d j T} = \dot{m} \sqrt{\frac{T_{t, i n l e t}}{T_{t, i n l e t, a d j T}}}

T_{t, i n l e t, a d j T} = T_{t, i n l e t} + Q I N_{R A T I O} * ∆ T_{t}