4.2 Details of the CFD simulation set-up
4.2.2 ANSYS CFX solver settings
The simulations conducted within ANSYS CFX were based on finite-volume discretiza-tion. The solution of the RANS equations was based on a coupled solver. The advection
64 4 CFD calculation models
flux was treated with a high resolution scheme. Also turbulence models, the volume frac-tion and energy equafrac-tions were calculated using high resolufrac-tion methodology. Steady and unsteady calculations were conducted with ANSYS CFX. For unsteady calculation, fixed time-stepping was used. Figure 4.11 displays the solver algorithm of ANSYS CFX for both steady and unsteady simulations. The algorithm starts with an initial simula-tion set-up. Step by step it solves hydrodynamic equasimula-tions, phase volume fracsimula-tions, the energy balance, flow turbulence and mass fractions. For steady calculations, the solver runs are repeated according to the predefined maximum iterations until a converged so-lution is achieved. In the case of transient simulations, the CFD code solves the flow governing equations according to specified time steps size. At every time step, a number of iterations are performed before achieving convergence. Once the calculated solution satisfies the determined convergence criteria then solver advances to the succeeding time step. This process continues up to the final time step. For ANSYS CFX simulations, the convergence criteria were met and the normalised RMS residuals were achieved to the order of10−5or lower.
In this work, the simulations of CD nozzles and 2D steam turbine stator cascade have been performed with ANSYS FLUENT. However, ANSYS CFX is comparatively faster, has good convergence and scaling, and is robust, particularly in 3D turbomachinery flow anal-ysis than ANSYS FLUENT. Due to these advantages, ANSYS CFX was the most suitable option compared to ANSYS FLUENT for 3D stator-rotor stage calculations. Therefore, all the 3D stator-rotor stage simulations have been done by using ANSYS CFX code.
4.2 Details of the CFD simulation set-up 65
Figure 4.11: The flow chart of the solver algorithm of ANSYS CFX.
66 4 CFD calculation models
67
5 Results and discussions
5.1 Influence of real gas modelling on condensing steam flows
To predict flow expansion accurately, the correct calculation of superheated steam proper-ties is required. Moreover, the nucleation and droplet growth processes are very sensitive to the thermodynamical properties, namely temperature and pressure. Near and below the saturation line, there is a rapid change in the relative concentration of the molecular clus-ter within steam, which leads to changes in the thermodynamics properties of the steam (Bakhtar and Piran, 1979). Further, the flow in the meta-stable region cannot be modelled accurately using the ideal-gas assumption. Therefore, the accurate prediction of steam expansion close to the saturation line requires a real gas model.
In this work, the influence of real gas modelling on condensing steam flows is studied using ANSYS FLUENT. For this purpose, the author’s local EOS (AEOS) for real gas and other steam properties was generated. However, the AEOS is applicable to a limited range of pressure and temperature. The performance of the AEOS has been compared with the EOS of Young (1988) (YEOS). The YEOS is the default selection in the wet-steam model of ANSYS FLUENT. The AEOS was implemented to ANSYS FLUENT with user defined subroutines. The formulations of both EOSs for real gas models are presented in section 3.4.
Firstly, the grid sensitivity analysis are presented in this section. Then, the influence of real gas modelling on non-equilibrium condensing flows in a nozzle is discussed. For this purpose, nozzle A of Moore et al. (1973) is used. At the inlet boundary,P01= 25kPa andT01=354.6K were applied. The grid density/resolution in the computational domain should have a significant effect on the results of the numerical simulation up to a cer-tain range. Thus, a grid independence study was conducted. The details about grids are discussed in section 4.1.1.1.
The pressure distribution predicted by various grids is shown in Figure 5.1. It can be observed that some information is missing in Grid A after the nozzle throat. Grid B and Grid C estimated relatively similar distributions of pressure. Further, Figure 5.2 presents the nucleation rate along the nozzle centreline computed with different grids. It can be seen that Grid A estimated a lower peak of the nucleation rate profile than Grid B and Grid C. Therefore, it can be inferred that Grid A is insufficient to capture the small details of the flow. Furthermore, the pressure and wetness fractions along the nozzle centreline obtained by three different grids are discussed in Publication I. The results show that the grid density influenced the pressure distribution. However, the wetness fraction is less sensitive to the grid size in the selected nozzle case. The results depict that the differences of the flow pattern between Grid B and Grid C are negligible. Therefore, Grid B was the optimum selection for further study.
The performance of AEOS for real gas has been assessed with the dry steam flow condi-tion. In Publication I, the calculated pressure distribution and Mach number of dry steam
68 5 Results and discussions
Static pressure [Pa]
4.100E+03 1.175E+04 1.950E+04
(a)
(b)
(c)
Figure 5.1: Contours of the pressure distribution predicted with (a) Grid A, (b) Grid B, and (c) Grid C.
−1 −0.5 0 0.5 1 1.5 2
0 10E+05 10E+10 10E+15 10E+20 10E+25
x/L Nucleation rate [m−3s−1]
Grid A Grid C Grid B
Figure 5.2: Nucleation rate along the nozzle centreline calculated with different grid res-olutions.
along the nozzle centreline with the AEOS are compared with the YEOS results. Some variation has been observed in both cases. Subsequently, the AEOS is applied to the con-densing steam flow simulations. Concon-densing steam flow is dry initially. After reaching the Wilson point, liquid droplets are created and a two-phase flow is established. The gen-erated liquid droplet starts to grow rapidly by transferring latent heat in the surrounding
5.1 Influence of real gas modelling on condensing steam flows 69
subcooled vapour phase. Consequently, the heat addition to the vapour phase from the liquid phase increases the flow temperature and pressure. The increment/rise in pressure is known as the condensation disturbance.
Figure 5.3 displays the contours of pressure distribution estimated by both real gas mod-els. YEOS yields a higher pressure drop than AEOS because of the higher expansion rate. After the throat of the nozzle, the pressure was raised due to a latent heat release from liquid droplets to the vapour phase. The Mach number contours are presented in Figure 5.4. YEOS estimated a shock wave with higher intensity after the throat of the nozzle than AEOS, which is likely due to the higher pressure drop, as can be seen in Fig-ure 5.3. The local speed of sound is increased due to the temperatFig-ure increment via the latent heat exchange from growing droplets. As a result, the Mach number is decreased in the condensation zone. The Mach number is increased in the divergent part of the nozzle due to the increment in the flow velocity.
Static pressure [Pa]
4.100E+03 1.2075E+04 2.005E+04
(a)
(b)
Figure 5.3: Contours of the pressure distribution predicted by (a) YEOS and (b) AEOS.
Mach number [-]
1.094E+00
4.600E-01 1.730E+00
(a)
(b)
Figure 5.4: Contours of the Mach number predicted by (a) YEOS and (b) AEOS.
70 5 Results and discussions
Further, Figure 5.5 presents a comparison between the predicted results for both real gas models. The precise modelling of non-equilibrium condensing flow is eventually dependent on the accuracy of the nucleation and the droplet growth estimations. As shown in Eq. (3.11), the nucleation rate is expressed as a function of thermodynamic properties and the surface tension.
Figure 5.5: Predicted results of the (a) droplet surface tension, (b) subcooling level, (c) nucleation rate, (d) droplet number, and (e) wetness fraction along the nozzle centreline.
5.1 Influence of real gas modelling on condensing steam flows 71
The surface tension plays an important role in the nucleation rate. A higher surface tension produces a wider nucleation zone, and as a result it delays the onset of condensation.
YEOS yielded a higher value for surface tension compared to AEOS (Figure 5.5(a)).
During the expansion of steam, the flow remains dry in a meta-stable equilibrium state before the subcooling becomes high enough to start nucleation. At the Wilson point, the subcooling exceeds its maximum and the highest peak of the nucleation rate appears, and finally, nucleation terminates. It can be noticed that YEOS yielded a higher value for the subcooling level and nucleation rate due to the higher expansion rate. Further, in the case of YEOS, the subcooling and nucleation rate expanded in the downstream of the nozzle compared to the AEOS case (Figure 5.5(b) and (c)). Figure 5.5(d) indicates that YEOS estimated a higher droplet number than AEOS. The increment in the droplet number could be described by the higher nucleation rate. The flow expansion influenced the Wilson point of the flow field, which affected the nucleation rate. Additionally, the wetness fraction in the flow starts to increase after the nucleation reaches the highest peak.
Figure 5.5(e) demonstrates that the wetness generation shifts downstream of the nozzle in the case of YEOS because of the wider nucleation region.
The predicted pressure distribution and mean droplet radius along the nozzle centreline for both cases are compared with the experiments of Moore et al. (1973) in Figure 5.6.
As discussed before, the flow temperature and pressure increases due to the latent heat
−2 0 2 4 6
Figure 5.6: Predicted results of (a) the pressure ratio, and (b) the mean droplet radius along the nozzle centreline compared with the nozzle A experiments of Moore et al. (1973).
releases from the rapidly growing droplets. If the droplet number is higher, it releases more latent heat, which increases the peak of condensation disturbance. Accordingly, in the case of YEOS, the calculated peak of condensation disturbance is higher. The pressure distribution in AEOS was in better agreement with the experiments than that of YEOS.
A higher nucleation rate is associated with a lower growth rate, i.e. whenever a large number of tiny liquid droplets nucleate, there will be less growth. In contrast, when lower nucleation happens, the growth rate is predominant and therefore larger liquid droplets are present. Therefore, in the case of YEOS, the average droplet radius is lower compared
72 5 Results and discussions
to the AEOS due to a large number of droplets. Based on the presented results, it can be seen that the estimation of real gas properties plays a vital role in condensing steam flow modelling.