The purpose of the ''International Wet Steam Modeling Project'' is to review the ability of computational methods to predict condensing steam flows. The results of numerous wet-steam methods are compared with each other and with experimental data for several nozzle test cases. The spread of computed results is quite noticeable and the present paper endeavours to explain some of the reasons for this. Generally, however, the results confirm that reasonable agreement with experiment is obtained by using classical homogeneous nucleation theory corrected for non-isothermal effects, combined with Young's droplet growth model. Some calibration of the latter is however required. The equation of state is also shown to have a significant impact on the location of the Wilson point, thus adding to the uncertainty surrounding the condensation theory. With respect to the validation of wet-steam models it is shown that some of the commonly used nozzle test cases have design deficiencies which are particularly apparent in the context of two-and three-dimensional computations. In particular, it is difficult to separate out condensation phenomena from boundary layer effects unless the nozzle geometry is carefully designed to provide near-one-dimensional flow.
Within steam turbine flows, condensation phenomena give rise to complex droplet spectra that can span more than two orders of magnitude in size. To predict the behavior of the two-phase flow and the resulting losses, the interactions between the vapor phase and droplets of all sizes must be accurately calculated. The estimation of thermodynamic losses and droplet deposition rates, in particular, depends on the size range and shape of the droplet spectrum. These calculations become computationally burdensome when a large number of droplet groups are present, and it is therefore advantageous to capture the complete droplet spectrum in a compressed form. This paper compares several methods for reducing the complexity of the droplet spectrum: a single representative droplet size (equivalent monodispersion), the moment method (including various growth rate approximations), the quadrature method of moments (QMOM), and spectrum pruning. In spectrum pruning, droplet groups are individually nucleated, but their number is subsequently reduced by combining groups together in a manner that preserves droplet number, wetness fraction, and the shape of the initial spectrum. The various techniques are compared within a Lagrangian framework by tracking the two-phase behavior along predefined pressure–time trajectories. Primary and secondary nucleation, droplet evaporation, and a representative turbomachinery case are modeled. The calculations are compared in terms of speed, accuracy, and robustness. It is shown that both the moment methods and spectrum pruning provide an appreciable improvement in accuracy over the use of an “equivalent” monodispersion without compromising calculation speed. Although all the examined methods are adequate for primary nucleation and droplet growth calculations, spectrum pruning and the QMOM are most accurate over the range of conditions considered.
Condensing nozzle flows have been used extensively to validate wet steam models. Many test cases are available in the literature, and in the past, a range of numerical studies have dealt with this challenging task. It is usually assumed that the nozzles provide a one- or two-dimensional flow with a fully turbulent boundary layer (BL). The present paper reviews these assumptions and investigates numerically the influence of boundary layers on dry and wet steam nozzle expansions. For the narrow nozzle of Moses and Stein, it is shown that the pressure distribution is significantly affected by the additional blockage due to the side wall boundary layer. Comparison of laminar and turbulent flow predictions for this nozzles suggests that laminar–turbulent transition only occurs after the throat. Other examples are the Binnie and Green nozzle and the Moore et al. nozzles for which it is known that sudden changes in wall curvature produce expansion and compression waves that interact with the boundary layers. The differences between two- and three-dimensional calculations for these cases and the influence of laminar and turbulent boundary layers are discussed. The present results reveal that boundary layer effects can have a considerable impact on the mean nozzle flow and thus on the validation process of condensation models. In order to verify the accuracy of turbulence modeling, a test case that is not widely known internationally is included within the present study. This experimental work is remarkable because it includes boundary layer data as well as the usual pressure measurements along the nozzle centerline. Predicted and measured boundary layer profiles are compared, and the effect of different turbulence models is discussed. Most of the numerical results are obtained with the in-house wet steam Reynolds-averaged Navier–Stokes (RANS) solver, Steamblock, but for the purpose of comparison, the commercial program ansys cfx is also used, providing a wider range of standard RANS-based turbulence models.
Condensing nozzle flows have been used extensively to validate wet steam models. Many test cases are available in the literature and in the past a range of numerical studies have dealt with this challenging task. It is usually assumed that the nozzles provide a one- or two-dimensional flow with a fully turbulent boundary layer. The present paper reviews these assumptions and investigates numerically the influence of boundary layers on dry and wet steam nozzle expansions. For the narrow nozzle of Moses and Stein it is shown that the pressure distribution is significantly affected by the additional blockage due to the side wall boundary layer. Comparison of laminar and turbulent flow predictions for this nozzles suggests that laminar-turbulent transition only occurs after the throat. Other examples are the Binnie nozzle and the Moore nozzles for which it is known that sudden changes in wall curvature produce expansion and compression waves that interact with the boundary layers. The differences between two- and three-dimensional calculations for these cases and the influence of laminar and turbulent boundary layers are discussed. The present results reveal that boundary layer effects can have a considerable impact on the mean nozzle flow and thus on the validation process of condensation models. In order to verify the accuracy of turbulence modelling a test case that is not widely known internationally is included within the present study. This experimental work is remarkable because it includes boundary layer data as well as the usual pressure measurements along the nozzle centreline. Predicted and measured boundary layer profiles are compared and the effect of different turbulence models is discussed. Most of the numerical results are obtained with the in-house wet steam RANS-solver, Steamblock, but for the purpose of comparison the commercial program ANSYS CFX is also used, providing a wider range of standard RANS-based turbulence models.
While wetness formation in steady flows such as nozzles and cascades is well understood, predicting the polydispersed droplet spectra observed in turbines remains challenging. The characteristics of wetness formation are affected by the expansion rate at the Wilson point. Because the expansion rate varies substantially both axially and circumferentially within steam turbines, the location of the Wilson point within a blade row is a primary factor determining the droplet spectrum and phase change losses. This effect is first investigated using a single streamline with a varying expansion rate, and it is shown that the phase change losses during spontaneous condensation are highest when a large region of high subcooling precedes the Wilson point. The conditions resulting in the highest wetness loss in the nucleation zone do not correspond to those that produce the largest downstream droplets. The effect of nucleation location is then assessed using a non-equilibrium RANS calculation of a realistic low pressure (LP) steam turbine geometry. A quasi-three dimensional (Q3D) flow domain is used to simplify the analysis, which is performed both steadily and unsteadily to isolate the effects of wake-chopping. The inlet temperature is varied to investigate the impact of the Wilson point location on the steady and unsteady wetness loss and droplet spectra. The trends observed in the 1D analysis are repeated in the steady RANS results. The unsteady results show that the Wilson zone is most sensitive to wake-chopping when located near a blade trailing edge and the following inter-row gap. The predicted wetness losses are compared to those predicted by the Baumann rule.
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