Evaluation of a rate form of the equation of state L.H. Fick, P.G. Rousseau, C.G. du Toit North-West University Energy Postgraduate Conference 2013

Introduction Integrated system simulation codes are applied in the analysis, design, optimization and integration of complex thermal-hydraulic systems. These include compressed air, water and gas reticulation networks, heat exchanger networks, mine ventilation and cooling systems, as well as nuclear and coal- and gas-fired power plants. Examples of such codes are RELAP, TRACE, Flowmaster and Flownex (which was originally developed at NWU in South Africa). These are not CFD codes solving the N-S equations for a complex flow field, but rather focus on the integrated system performance of components such as pipes, valves, pumps, compressors, turbines, heat exchangers etc.

Simulation methodology Conservation equations: –Mass conservation (solved for all nodes) –Energy conservation (solved for all nodes) –Momentum conservation (solved for all elements) Equation of state (rate form): –Pressure and temperature (solved for all nodes)

Rate form of the EOS Pressure: Temperature:

Approximation functions Functions developed to minimise deviation from reference steam tables: –Chosen pressure range divided in to several regions to maintain high accuracy. –Slopes or derivatives of the functions are required, therefore a continuous first derivative across the entire pressure range is required.

Approx. function derivatives Approximation functions for thermodynamic properties at saturation conditions are written as a function of pressure only. Derivatives required to solve the rate form of the EOS is therefore generated simply by differentiating AF with regards to pressure. Compared with A-EOS values via perturbation calculations.

Transient simulation model Transient simulation model of a pipe and reservoir network chosen platform for evaluation of the rate form of the equation of state: Network consists of four reservoirs (nodes) connected by five pipes (elements). Network formulated in EES (Engineering Equation Solver) and is able to simulate various component geometries and transient phenomena.

Transient network simulation Case study: Mass source of 1kg/s in node 2 for 0.2 seconds. Values for node pressures show high correlation between rate and algebraic form of the EOS. Maximum error is roughly 0.16%.

Time step dependence Accuracy of the rate form of the equation of state dependent on the time step length. Property values delivered by rate form of the equation of state approaches values delivered by algebraic form as time step length decreases.

Conclusions Approximation functions for saturated steam properties were evaluated. Maximum error < 0.4%. Gradient functions derived and evaluated. Average error small but with several significant outliers. Comparison between algebraic and rate forms of EOS for transient thermal equilibrium network simulation shows maximum error < 0.2%. This work is based upon research supported by the South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation. Thank you