Flow fields in low-pressure (LP) steam turbines, starting expansion well above the saturation line, show four pronounced non-equilibrium processes (called relaxation processes). The first one above the saturation line is centred around heterogeneous nucleation/ condensation, the second one around subcooling and the subsequent homogeneous nucleation/ condensation ('Wilson point'), and the third and the fourth ones are characterized by thermodynamic and mechanical effects in the established droplet-loaded part of the flow field.All these relaxation processes are interacting downwards in the progressive expansion in the turbine. In a multistage LP turbine, the most important ones are the second -because it is mainly responsible for the number of droplets (sizes) -and the third -because it creates most of the dissipation. In addition, the first and the fourth ones can damage the flow guiding geometry by corrosion and erosion, respectively.More than 40 years ago, Gyarmathy formulated the first strictly physical basis for these processes. Subsequently, many researchers have contributed to increase the physical understanding using both experimental and numerical methods. The intuition that the one-dimensional treatment of the flow field in multistage turbines cannot explain the measured droplet sizes behind the blading has been particularly relevant. It became clear that especially the temperature fluctuation within the blading has to be included in homogeneous nucleation/condensation considerations. Also of some importance has been the improved understanding of the first relaxation process, which was initially underestimated.This article highlights the current situation seen by a turbomachinery company that has been contributing to and supporting this discipline for many decades. A wide literature survey and a critical appraisal of published Baumann factors are included. High quality experimental tools and procedures are introduced on the basis of two generations of split-shaft model LP turbines and Damköhler numbers. Further, an overview of the in-house numerical tools and processes developed for wet steam applications is given.More recent experimental results on the influence of impurities and conditioning agents in the relaxation processes and newer numerical results on the influence of phase transition in the flow field around a blade row are presented.

During the expansion of steam in the low pressure (LP) stages of steam turbines, the originating two-phase wet-steam mixture causes considerable thermodynamic losses as well as aerodynamic losses. The reduction of these loss mechanisms is the subject of research project at the Institute of Steam and Gas Turbines, Aachen University. A three-dimensional nucleating wet steam ow with homogeneous/heterogeneous nucleation in the three front stages of an industrial LP-steam turbine is investigated numerically. The steady, viscous, and compressible metastable steam ow calculations are performed with a Navier-Stokes ow solver incorporating the IAPWS-IF97 steam tables. A union numerical approach for both the homo-and heterogeneous nucleation occurring on soluble nuclei is employed to capture the effects related to the nucleation phenomenon. The model links the interfacial surface tension, the size of nuclei, the chemical characteristics of the substances forming the droplets, and the expansion rate with the nucleation rate. In order to take into account the additional viscous effects due to shrouded bladings, the open shroud cavities are modeled in detail. Droplet density spectra, radial droplet number, droplet diameter, and wetness fraction distributions at the exit of the third stage are calculated. It is shown that impurities can cause nucleation to appear at lower supersaturations with higher nucleation rates compared to homogeneous nucleation of pure steam. In this way, thermodynamic and kinematic relaxation losses are reduced. Owing to the dissipative viscous effects near the endwalls, the nucleation fronts exhibit convex shapes. They are locally bound within the region of high expansion rates in the second stage's nozzle guide vane. For both heterogeneous and homogenous nucleating ows the wetness is highly dispersed with narrow droplet density spectra behind the three front stages.

Flowfields within turbines are generally three-dimensional and unsteady. Typically, the flow-fields in the interaction zone between the last stage and the diffuser are strongly inhomogeneous. This non-uniformity strongly limits the downstream diffusion process, so that significant improvement can be achieved by making the total pressure field in this zone more uniform. One way to achieve this is by using kinks in the endwall contours and, if necessary, one or two splitters. The use of balance-based space averaging and modelling procedures can help to characterize these flows, and to develop an optimum interaction zone and diffuser geometry. In the study described here, as an example the interaction zone of high-pressure/intermediate-pressure (HP/IP) and low-pressure (LP) diffusers of steam turbines were numerically and partly experimentally optimized for a fixed blading and exhaust. The operating conditions were also kept constant except that for low pressures the flowfield was studied for a range of back pressures (i.e. exhaust velocities). The optimization process starts with an initial flowfield in the interaction zone generated numerically or experimentally. Using these data a design procedure is applied that creates both a much more uniform total pressure field at the last stage exit and a diffuser geometry possibly with one or two splitters and proven for an earlier LP design experimentally. It was demonstrated that, depending on the inhomogeneity of the flow from the upstream stage, a performance improvement of several percentage points could be achieved.

Advanced experimental and numerical methods in the eld of uid dynamics and turbomachinery are increasingly successful in describing real ow elds, i.e. elds that are generally three-dimensional and unsteady. For many purposes, e.g. ow characterization, it is necessary to reduce these ow elds step by step to three-, two-or one-dimensional large-scale unsteady ow elds. This procedure permits a lower-level simulation of the ow elds. However, many averaging approaches are arbitrary or succeed in balancing the ow elds in only a few physical aspects. The rst author has already shown the steps of a balance-based procedure that avoids this limitation. Small-scale time averaging of (probabilistically) turbulent inhomogeneities by means of irreversible and reversible small-scale time averaging processes on a threefold in nitesimal control volume element has already been demonstrated. The present paper demonstrates the balance-based procedure of space averaging. It is carried out by averaging generally three-dimensional small-scale time-averaged (deterministic) inhomogeneities using irreversible and reversible space averaging processes on onefold in nitesimal and nite control surfaces. The procedure is, similarly to small-scale time averaging, based on conservative and independent non-conservative small-scale time-averaged integral balance equations. The general concept is to represent all the relevant uxes through the control surface by appropriate average quantities or numbers. The full use of the vector equations for the linear and angular momentum is important. One of the consequences in space averaging is the introduction of a wrench (parallel linear and angular momentum vectors), which is generally used only in mechanics for the reduction of force systems in space. The ow eld inhomogeneity is described on all dimensional levels via the diffusion intensity of the irreversible averaging process, and, only for space averaging, via the distance vector and the parameter of the wrench. A numerical example on different dimensional levels is presented in detail. The procedure also illustrates the basis of a new and more complete twoand one-dimensional large-scale unsteady theory generally in uid dynamics and especially in turbomachinery.

The computations done at present for turbulent flow fields use either time-averaged (Reynolds) or time-and-mass-averaged (Favre) quantities, together with time-averaged fluctuating terms (FTs). Large numbers of these FTs, which are derived from the time-averaged balance equations, occur whenever all relevant time-averaged balance equations are being used and all quantities, including the transport quantities, must be considered as turbulent. The FTs require a great deal of experimental and theoretical work — for example, for closing time-averaged balance equations using familiar heuristic methods. For general simplification, then, a new averaging procedure is presented here which employs no arbitrary breakdown of the turbulent quantities, thus completely avoiding the FTs. This method is based on hypothetical reversible and irreversible equilibration processes on three control surfaces perpendicular to the major axes and in the control volume of a fluid element. The time-averaged balance equations take on the same manageable form as the instantaneous balance equations. In addition, the effort required for closing the time-averaged balance equations is reduced to a minimum.