# Numerical solution of 2D wet steam flow with non-equilibrium condensation and real thermodynamics

## Abstract

An approach to modeling of wet steam flow with non-equilibrium condensation phenomenon is presented. The first part of our flow model is homogeneous Euler system of transport equations for mass, momentum and total energy of wet steam (mixture). The additional second part describes liquid phase via non-homogeneous system of transport equations for moments of droplets number distribution function and relies on corrected classical nucleation theory. Moment equations are closed by linearization of droplet growth rate model. All necessary relations for thermodynamic properties of steam are provided by IAPWS set of equations. However, properties of condensate are simply modeled by liquid saturation data. Two real equations of state are implemented. Recently developed CFD formulation for entropy (does not require iteration process) and so-called IAPWS special gas equation for Helmholtz energy (one iteration loop is necessary). Flow model is validated on converging-diverging supersonic nozzle with Barschdorff geometry. Simulations were performed by in-house CFD code based on finite volume method and stiff character of equations was solved by symmetrical time operator splitting. Achieved results satisfactorily agreed with experimental data.

- Authors:

- Department of Technical Mathematics, FME CTU Prague, Karl. nám. 13, CZ-12135 Prague 2 (Czech Republic)
- Institute of Thermomechanics, AS CR, Dolejškova 5, CZ-18200, Prague 8 (Czech Republic)

- Publication Date:

- OSTI Identifier:
- 22391043

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1648; Journal Issue: 1; Conference: ICNAAM-2014: International Conference on Numerical Analysis and Applied Mathematics 2014, Rhodes (Greece), 22-28 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; DISTRIBUTION FUNCTIONS; DROPLETS; ENTROPY; EQUATIONS OF STATE; EQUILIBRIUM; FLOW MODELS; FLUID MECHANICS; LIQUIDS; MIXTURES; NUCLEATION; NUMERICAL SOLUTION; STEAM; THERMODYNAMICS; TRANSPORT THEORY

### Citation Formats

```
Hric, V., and Halama, J.
```*Numerical solution of 2D wet steam flow with non-equilibrium condensation and real thermodynamics*. United States: N. p., 2015.
Web. doi:10.1063/1.4912347.

```
Hric, V., & Halama, J.
```*Numerical solution of 2D wet steam flow with non-equilibrium condensation and real thermodynamics*. United States. doi:10.1063/1.4912347.

```
Hric, V., and Halama, J. Tue .
"Numerical solution of 2D wet steam flow with non-equilibrium condensation and real thermodynamics". United States.
doi:10.1063/1.4912347.
```

```
@article{osti_22391043,
```

title = {Numerical solution of 2D wet steam flow with non-equilibrium condensation and real thermodynamics},

author = {Hric, V. and Halama, J.},

abstractNote = {An approach to modeling of wet steam flow with non-equilibrium condensation phenomenon is presented. The first part of our flow model is homogeneous Euler system of transport equations for mass, momentum and total energy of wet steam (mixture). The additional second part describes liquid phase via non-homogeneous system of transport equations for moments of droplets number distribution function and relies on corrected classical nucleation theory. Moment equations are closed by linearization of droplet growth rate model. All necessary relations for thermodynamic properties of steam are provided by IAPWS set of equations. However, properties of condensate are simply modeled by liquid saturation data. Two real equations of state are implemented. Recently developed CFD formulation for entropy (does not require iteration process) and so-called IAPWS special gas equation for Helmholtz energy (one iteration loop is necessary). Flow model is validated on converging-diverging supersonic nozzle with Barschdorff geometry. Simulations were performed by in-house CFD code based on finite volume method and stiff character of equations was solved by symmetrical time operator splitting. Achieved results satisfactorily agreed with experimental data.},

doi = {10.1063/1.4912347},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1648,

place = {United States},

year = {Tue Mar 10 00:00:00 EDT 2015},

month = {Tue Mar 10 00:00:00 EDT 2015}

}