A computer code DBS (Dynamic Boiler Simulation) was developed at the Department of Thermodynamics and Thermal Engineering at the Institute for Thermodynamic and Energy Conversion (ITE) at the TU Wien which can be used for the simulation of the transient behaviour of the fluid in heated tube networks under gravitation e. g. steam generators under start-up or load change operation conditions.

## Flow in the pipes

For the computation of the fluid flow in the tubes of the network a finite-volume-method was used on the basis of the primitive variables pressure and velocity. In this case the mass and momentum balance must be fulfilled at the same time. These conservative equations are classified as a system of parabolic-elliptic equations. For the calculation of a consistent pressure- and velocity field of the flow inside the tubes the two pressure-correction algorithms SIMPLER [1] and PISO [2] are used. Based on the convergence rate of DBS the program switches between both algorithms automatically. This results in a faster overall convergence of DBS. The mathematical model for the working medium in the tubes, which is modelled one-dimensionally in axial direction, uses the homogeneous equilibrium model for the two phase flow and applies a correction factor for the two phase pressure loss according to Friedel [3]. The collectors and distributors respectively are assumed to be single control volumes. The number of tubes which are connected to a header and also the number of pressure stages for the working medium is not restricted by the model.

## Flue gas side

The structure of the flue gas side is - corresponding to the working medium - also very general. The idea was to build up the flue gas pass as a network. It includes mixing and distribution points, inlets and outlets as well as recirculation paths. An individual flue gas pass can be subdivided into a number of parallel passes. These parallel passes are used for the simulation of flue gas passes with different flue gas streams. There is no energy and mass exchange between the flue gas fluxes of the individual passes. For the description of the flue gas the one-dimensional partial differential equation of the conservation law for the energy is used. The momentum balance for the flue gas is neglected. The flue gas mass flows are calculated quasi-stationary, while the energy balance is calculated unsteady. The discretization of the energy balance is done corresponding to the finite volume method.
The forced convective heat transfer coefficient between the flue gas and the tubes can be calculated under the use of a different number of correlations for plain or finned inline or staggered tube banks.
The heat exchange between the fluid and the wall is governed by Newton's law and the heat transfer through the wall is assumed to be in radial direction only.
The concept of the DBS was chosen in such a way that a modular structure of the code exist. This results in a very flexible implementation of new subroutines. For handling the data inside the code, the graph theory was used. With this concept the program allows the user a problem-oriented combination of the single plant components.

## Properties of water

A special attention at the development of DBS was given at the implementation of the properties for water and steam. The computation of the properties for water and steam in DBS is based on the analytical equations for the steam table of Haar et al. [4]. The allocation of the properties for water and steam is done by linear interpolating between binary stored grid points of the steam table. The boundaries of the stored steam table are 0.1 kJ/kg <= h <= 5000 kJ/kg and 0.1 bar <= p <=  450 bar. This wide range of boundary allows the solution algorithm a wide area for the iteration.

For more details to modelling DBS see [5].

## Literature

[1] S. V., Patankar: Numerical Heat Transfer and Fluid Flow, Series in Computational Methods in Mechanics and Thermal Sciences. Hemisphere Publ. Corp. Washington, New York, London 1980
[2] R. I. Issa, A. D. Gosman und A. P Watkins: The Computation of Compressible and Incompressible Recirculating Flows by a Non-Iterative Implicit Scheme, Journal of Computational Physics, Vol. 62, pp. 66-82 (1986)
[3] L. Friedl, Improved Friction Pressure Drop Correlation for Horizontal and Vertical Two-Phase Pipe Flow. In: European Two-Phase Group Meeting, Ispra, Italy, June 5-8, Paper E 2:1-25, 1979
[4] L. Haar, J. S. Gallagher und G. S .Kell: NBS/NRC Wasserdampftafeln, Hrsg.: U. Grigull, Springer-Verlag,  Berlin, 1988
[5] H. Walter: Modellbildung und numerische Simulation von Naturumlaufdampferzeugern, Fortschr.-Bericht VDI, Reihe 6, Nr.: 457, VDI Verlag, Düsseldorf, 2001