# Thermo

Source: https://help.sim-flow.com/documentation/panels/thermo
Last updated: 2026-10-14

## Introduction

![image](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f19f15005.png)

In the **Thermo** panel, you can define thermophysical properties of your material. In contrast to the [Transport Properties](https://help.sim-flow.com/documentation/panels/transport-properties) panel, here you define material properties for compressible flow solvers.

## Material Models

![img 5959f2577a221](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f2577a221.png)

To fully describe material properties for compressible simulations, you need to define three material models:

- **Equation of State**
- **Thermodynamics**
- **Transport**

Available material models will depend on the selected solver. Additionally, not all combinations of these models are available, which means that when you change the **Equation of State** , the list of **Thermodynamics** and **Transport** models will change.

![img 5959f260b9e27](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f260b9e27.png)

Besides the models, you need to specify the molar mass of your material under the **Specie** input group.

### Equations of State

![img 5959f30c1da78](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f30c1da78.png)

The **Equation of State** model defines the relationship between parameters of state: density, pressure, and temperature. Available equations of state depend on the currently selected solver and, in the case of the multi-region solvers, on whether the mesh region is solid or fluid.

**Available Equations of State:**

- **Perfect Gas**
- **Incompressible Perfect Gas**
- **Constant Density**
- **Perfect Fluid**
- **Adiabatic Perfect Fluid**
- **Peng-Robinson**
- **Polynomial**

#### Perfect Gas

![perfect gas](https://help.sim-flow.com/documentation/panels/images/thermo/perfect-gas.png)

The **Perfect Gas** equation of state describes the behavior of a hypothetical [perfect gas](https://en.wikipedia.org/wiki/Ideal_gas) , which is a good approximation for real gases under moderate pressures. It can be expressed as:

\(\rho=\frac{p}{R \cdot T}\)

where:

- **\(\rho\)** - density
- **\(p\)** - pressure
- **\(R\)** - specific [gas constant](https://en.wikipedia.org/wiki/Gas_constant)
- **\(T\)** - temperature

The only constant in this equation is \(R\), which can be calculated from the universal gas constant and molar mass. Therefore, the **Perfect Gas** equation of state does not require additional inputs.

#### Incompressible Perfect Gas

![incompressible perfect gas](https://help.sim-flow.com/documentation/panels/images/thermo/incompressible-perfect-gas.png)

The **Incompressible Perfect Gas** equation of state uses a constant reference pressure in the perfect gas equation of state rather than the local pressure, so that the density only varies with temperature and composition. It can be expressed as:

\(\rho=\frac {p_{ref}}{R \cdot T}\)

where:

- **\(\rho\)** - density
- **\(p_{ref}\)** - reference pressure
- **\(R\)** - specific [gas constant](https://en.wikipedia.org/wiki/Gas_constant)
- **\(T\)** - temperature

![img 5959f336be93f](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f336be93f.png)

**Inputs:**

- **\(p_{ref} [Pa]\)** - reference pressure

#### Constant Density

![constant density](https://help.sim-flow.com/documentation/panels/images/thermo/constant-density.png)

The **Constant Density** equation of state assumes that density is constant:

\(\rho = const\)

where:

- **\(\rho\)** - density

![img 5959f3b3b3e71](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f3b3b3e71.png)

**Inputs:**

- **\(\rho [{kg}/m^3]\)** - density

#### Perfect Fluid

![perfect fluid](https://help.sim-flow.com/documentation/panels/images/thermo/perfect-fluid.png)

The **Perfect Fluid** equation of state calculates density using the following expression:

\(\rho=\rho_0 +\frac{p}{R \cdot T}\)

where:

- **\(\rho\)** - density
- **\(\rho_0\)** - reference density
- **\(p\)** - pressure
- **\(R\)** - specific [gas constant](https://en.wikipedia.org/wiki/Gas_constant)
- **\(T\)** - temperature

![img 5959f35c7f721](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f35c7f721.png)

**Inputs:**

- **\(R [J/{kg} K]\)** - "specific gas constant"
- **\(\rho_0 [{kg}/m^3]\)** - reference density

Note: The "specific gas constant" needs to be explicitly specified since it cannot be computed from molar mass using perfect gas laws.

#### Adiabatic Perfect Fluid

![adiabatic perfect fluid](https://help.sim-flow.com/documentation/panels/images/thermo/adiabatic-perfect-fluid.png)

The **Adiabatic Perfect Fluid** equation of state calculates density using the following expression:

\(\rho=\rho_0 \cdot (\frac{p+B}{p_0 +B})^{\frac{1}{\gamma}}\)

where:

- **\(\rho\)** - density
- **\(\rho_0\)** - reference density
- **\(p\)** - pressure
- **\(p_0\)** - reference pressure
- **\(B\)** - pressure offset
- **\(\gamma\)** - adiabatic expansion constant

![img 5959f372baefa](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f372baefa.png)

**Inputs:**

- **\(p_0 [Pa]\)** - reference pressure
- **\(\rho_0 [{kg}/m^3]\)** - reference density
- **\(\gamma [-]\)** - adiabatic expansion constant
- **\(B [Pa]\)** - pressure offset

#### Peng-Robinson

![peng robinson](https://help.sim-flow.com/documentation/panels/images/thermo/peng-robinson.png)

The **Peng-Robinson** equation of state is a better approximation of the behavior of real gases than the **Perfect Gas** . It is expressed using the following relations:

\(p=\frac{BT}{V_m-b}-\frac{a \alpha}{ V_m^2+2bV_m-b^2}\)

\(a \approx 0.45724 \cdot \frac{B^2 T_c ^2}{p_c}\)

\(b \approx 0.07780 \cdot \frac{B T_c }{p_c}\)

\(\alpha = (1+\kappa(1- T_r^{1/2}))^2\)

\(\kappa \approx 0.37464 + 1.54226 \omega - 0.26992 \omega^2\)

\(T_r=\frac{T}{T_c}\)

where:

- **\(p\)** - pressure
- **\(T\)** - temperature
- **\(V_m\)** - [molar volume](https://en.wikipedia.org/wiki/Molar_volume)
- **\(T_c\)** - temperature at the [critical point](https://en.wikipedia.org/wiki/Critical_point_%28thermodynamics%29)
- **\(p_c\)** - pressure at the [critical point](https://en.wikipedia.org/wiki/Critical_point_%28thermodynamics%29)
- **\(V_c\)** - molar volume at the [critical point](https://en.wikipedia.org/wiki/Critical_point_%28thermodynamics%29)
- **\(\omega\)** - [acentric factor](https://en.wikipedia.org/wiki/Acentric_factor)
- **\(B\)** - [universal gas constant](https://en.wikipedia.org/wiki/Gas_constant)

![img 5959f38b2a586](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f38b2a586.png)

**Inputs:**

- **\(T_c [K]\)** - temperature at the critical point
- **\(p_c [Pa]\)** - pressure at the critical point
- **\(V_c [m^3/{kmol}]\)** - molar volume at the critical point
- **\(\omega [-]\)** - acentric factor

#### Polynomial

![polynominal](https://help.sim-flow.com/documentation/panels/images/thermo/polynominal.png)

The **Polynomial** equation of state calculates density using a polynomial function:

\(\rho = \Sigma_{i = 0}^{n} a_1 \cdot T^i\)

where:

- **\(\rho\)** - density
- **\(T\)** - temperature
- **\(a_i\)** - polynomial coefficients

![img 5959f39db7c91](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f39db7c91.png)

**Inputs:**

- **\(a_i [ \frac{kg}{m^{3} \cdot T^{-i}}]\)** - polynomial coefficients

### Thermodynamics Models

![img 5959f4a4c622b](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f4a4c622b.png)

The **Thermodynamics** models define the relationship between basic parameters of state (pressure and temperature) and derived secondary parameters of state such as enthalpy, entropy and internal energy.

**Available Thermodynamics Models:**

- **Constant**
- **Polynomial**
- **Janaf**

#### Constant

The **Constant** thermodynamics model defines specific heat to be constant:

\(C_p=const\)

where:

- **\(C_p\)** - specific heat under constant pressure

![img 5959f4b4133e3](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f4b4133e3.png)

**Inputs:**

- **\(C_p [J/{kg} K]\)** - specific heat under constant pressure
- **\(H_f [J/{kg}]\)** - [enthalpy of formation](https://en.wikipedia.org/wiki/Standard_enthalpy_of_formation)

#### Polynomial

![img 5959f4c829b99](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f4c829b99.png)

The **Polynomial** model calculates specific heat using a polynomial function:

\(C_p=\Sigma _{i = 0}^n a_1 \cdot T^i \)

where:

- **\(C_p\)** - specific heat under constant pressure
- **\(T\)** - temperature
- **\(a_i\)** - polynomial coefficients

**Inputs:**

- **\(H_f [J/{kg}]\)** - [enthalpy of formation](https://en.wikipedia.org/wiki/Standard_enthalpy_of_formation)
- **\(S_f [J/{kg} K]\)** - [standard entropy](https://en.wikipedia.org/wiki/Standard_molar_entropy)
- **\(a_i [ 1/{kg} T^{-1-i}]\)** - polynomial coefficients

#### Janaf

![img 5959f4d7858d7](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f4d7858d7.png)

The **Janaf** model calculates specific heat as a function of temperature using coefficients from JANAF tables of thermodynamics. Two sets of coefficients need to be specified, the first set for temperatures below a common temperature, the second for temperatures above the common temperature. The formula for calculating specific heat is:

\(C_p =R \cdot \Sigma_{i=0}^4 a_i \cdot T^i\)

where:

- **\(C_p\)** - specific heat under constant pressure
- **\(R\)** - gas constant
- **\(a_i\)** - JANAF coefficients

**Inputs:**

- **\(T_{low} [K]\)** - low temperature limit for model applicability
- **\(T_{high} [K]\)** - high temperature limit for model applicability
- **\(T_{common} [K]\)** - temperature delimiter for when to use low or high coefficients
- **\(a_i [K^-i]\)** (lowCpCoeffs/highCpCoeffs) \([K^{-1}]\) - JANAF coefficients

### Transport Models

![img 5959f5607e408](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f5607e408.png)

The **Transport** models define thermal conductivity and viscosity, which are later used in transport equations for momentum and energy.

**Available Transport Models:**

- **Constant**
- **Sutherland**
- **Polynomial**

#### Constant

![img 5959f5607e408](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f5607e408.png)

The **Constant** transport model assumes that transport properties are constant. In this model, thermal conductivity is calculated using the formula:

\(\kappa = \frac{C_p \cdot \mu}{P_r}\)

where:

- **\(\kappa\)** - thermal conductivity
- **\(C_p\)** - specific heat under constant pressure
- **\(\mu\)** - dynamic viscosity
- **\(P_r\)** - Prandtl number

![img 5959f56e03eff](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f56e03eff.png)

**Inputs:**

- **\(\mu [Pa \cdot s]\)** - dynamic viscosity
- **\(P_r [-]\)** - Prandtl number

#### Sutherland

![sutherland](https://help.sim-flow.com/documentation/panels/images/thermo/sutherland.png)

The **Sutherland** model calculates dynamic viscosity from the Sutherland formula:

\(\mu=\frac{A_s T^{0.5}}{1+\frac{T_s}{T}}\)

where:

- **\(\mu\)** - dynamic viscosity
- **\(T\)** - temperature
- **\(A_s\)** - Sutherland coefficients
- **\(T_s\)** - Sutherland temperature

![img 5959f58e13f02](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f58e13f02.png)

**Inputs:**

- **\(A_s [{kg}/m s K ^0.5 ]\)** - Sutherland coefficients
- **\(T_s [K]\)** - Sutherland temperature

#### Polynomial

![transport polynominal](https://help.sim-flow.com/documentation/panels/images/thermo/transport-polynominal.png)

The **Polynomial** transport model calculates dynamic viscosity and thermal conductivity from polynomial expressions:

\(\mu=\Sigma_{i=0}^n a_{\mu i} \cdot T^i\)

\(\kappa=\Sigma_{i=0}^n a_{\kappa i} \cdot T^i\)

where:

- **\(\mu\)** - dynamic viscosity
- **\(\kappa\)** - thermal conductivity
- **\(T\)** - temperature
- **\(a_{x i}\)** - polynomial coefficients

![img 5959f5a65f691](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f5a65f691.png)

**Inputs:**

- **\(a_{\mu i} [Pa s K ^-i ]\)** - dynamic viscosity polynomial coefficients
- **\(a_{x i} [W/m K ^{1+i} ]\)** - thermal conductivity polynomial coefficients

## Cavitation Properties

When you select a cavitation solver, a set of properties specific to this solver will be displayed.

![img 5959f612e0247](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f612e0247.png)

### Compressibility Models

![img 5959f65db2946](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f65db2946.png)

Cavitation properties require you to define a **Compressibility Model** that describes the compressibility of the mixture.

**Available Compressibility Models:**

- **Linear**
- **Wallis**
- **Chung**

#### Linear Model

![img 5959f66c934ff](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f66c934ff.png)

The **Linear** model defines mixture compressibility as a linear combination of vapor and liquid compressibilities:

\(\psi=\gamma \cdot \psi_v +(1-\gamma)\cdot \psi_l\)

where:

- **\(\psi\)** - mixture compressibility
- **\(\psi_v\)** - vapor compressibility
- **\(\psi_l\)** - liquid compressibility
- **\(\gamma\)** - vapor phase fraction

**Inputs:**

- **\(\Psi_v [s^2/m^2]\)** - vapor compressibility
- **\(\Psi_l [s^2/m^2]\)** - liquid compressibility

#### Wallis Model

![img 5959f67bdf587](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f67bdf587.png)

The **Wallis** model computes mixture compressibility using the following equations:

\(\psi =(\gamma \rho_{v,sat} + (1-\gamma) \rho_{l,sat})(\gamma \frac{\psi_v}{ \rho_{v,sat}}+(1-\gamma)\frac{\psi_l}{ \rho_{l,sat}})\)

where:

- **\(\psi\)** - mixture compressibility
- **\(\psi_v\)** - vapor compressibility
- **\(\psi_l\)** - liquid compressibility
- **\(\rho_{v,sat}\)** - vapor saturation density
- **\(\rho_{l,sat}\)** - liquid saturation density
- **\(\gamma\)** - vapor phase fraction

**Inputs:**

- **\(\Psi_v [s^2/m^2]\)** - vapor compressibility
- **\(\Psi_l [s^2/m^2]\)** - liquid compressibility
- **\(\rho_{v,sat} [{kg}/m^3]\)** - vapor saturation density
- **\(\rho_{l,sat} [{kg}/m^3]\)** - liquid saturation density

### Chung Model

![img 5959f68d7b43e](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f68d7b43e.png)

The **Chung** model computes mixture compressibility using the following equations:

\(s_{fa} = \frac{\frac{\rho_{v,sat}}{\psi_v}}{(1-\gamma)\frac{\rho_{v,sat}}{\psi_v}+ \gamma \frac{\rho_{l,sat}}{ \psi_l}}\)

\(\psi=((\frac{1-\gamma}{ \sqrt{\psi_v}} + \frac{\gamma s_{fa}}{\sqrt{\psi_l}}) \frac{\sqrt{\psi_v \psi_l}}{s_{fa}})^2\)

where:

- **\(\psi\)** - mixture compressibility
- **\(\psi_v\)** - vapor compressibility
- **\(\psi_l\)** - liquid compressibility
- **\(\rho_{v,sat}\)** - vapor saturation density
- **\(\rho_{l,sat}\)** - liquid saturation density
- **\(\gamma\)** - vapor phase fraction

**Inputs:**

- **\(\Psi_v [s^2/m^2]\)** - vapor compressibility
- **\(\Psi_l [s^2/m^2]\)** - liquid compressibility
- **\(\rho_{v,sat} [{kg}/m^3]\)** - vapor saturation density
- **\(\rho_{l,sat} [{kg}/m^3]\)** - liquid saturation density

## Region Properties

![img 5959f81468995](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f81468995.png)

When you select a multi-region solver, a list of regions will be displayed. By clicking on a region name, you will be able to define properties for this region. The definition of material models for each region is the same as in single-region solvers.

## Phase Properties

![img 5959f8509d96c](https://help.sim-flow.com/documentation/panels/images/thermo/img_5959f8509d96c.png)

When you select a multiphase solver, a list of current phases will be displayed. When you select a phase in the list, transport properties for this phase will be displayed below.

In addition to individual phase properties, you need to define additional values:

- **\(\sigma [N/m]\)** - surface tension between the phases
- **\(p_{min} [Pa]\)** - lower limit for pressure

## Material Database

You can load material properties from the database in the way described for the **Transport Properties** panel.