“…(4) The first-principles loss model is accurate within 1-2 percentage points as compared to 3D RANS for all the selected test cases. In contrast, the semi-empirical Traupel loss model [27] significantly underestimates the stage efficiency, but it provides an accurate trend prediction with loading. The results obtained with 3D URANS are in accordance with those obtained by steady-state simulations and the physical loss model, except for the case niMM 1 , in which the trend of c Pv is not monotone along the expansion.…”
Section: Discussionmentioning
confidence: 90%
“…The time-averaged total-to-total efficiency obtained by steady and unsteady CFD for the test cases iCO 2 and iMM characterized by increasing loading coefficient is displayed in Fig. 14, along with the efficiency trend calculated with the turbine stage model coupled to the physical loss model as well as to the semi-empirical Traupel loss model [27]. The color bars in the charts are indicative of 61=2% efficiency deviation with respect to the time-averaged values computed by 3D URANS.…”
The impact of non-ideal compressible flows on the fluid-dynamic design of axial turbine stages is examined. First, the classical similarity equation is revised and extended to account for the effect of flow non-ideality. Then, the influence of the most relevant design parameters is investigated through the application of a dimensionless turbine stage model embedding a first-principles loss model. The results show that compressibility effects induced by the fluid molecular complexity and the stage volumetric flow ratio produce an offset in the efficiency trends and in the optimal stage layout. Furthermore, flow non-ideality can lead to either an increase or decrease of stage efficiency up to 3-4% relative to turbines designed to operate in dilute gas state. This effect can be predicted at preliminary design phase through the evaluation of the isentropic pressure-volume exponent. 3D RANS simulations of selected test cases corroborate the trends predicted with the reduced-order turbine stage model. URANS computations provide equivalent trends, except for case study niMM1, featuring a non-monotonic variation of the generalized isentropic exponent. For such turbine stage, the efficiency is predicted to be higher than the one computed with any steady-state model based on the control volume approach.
“…(4) The first-principles loss model is accurate within 1-2 percentage points as compared to 3D RANS for all the selected test cases. In contrast, the semi-empirical Traupel loss model [27] significantly underestimates the stage efficiency, but it provides an accurate trend prediction with loading. The results obtained with 3D URANS are in accordance with those obtained by steady-state simulations and the physical loss model, except for the case niMM 1 , in which the trend of c Pv is not monotone along the expansion.…”
Section: Discussionmentioning
confidence: 90%
“…The time-averaged total-to-total efficiency obtained by steady and unsteady CFD for the test cases iCO 2 and iMM characterized by increasing loading coefficient is displayed in Fig. 14, along with the efficiency trend calculated with the turbine stage model coupled to the physical loss model as well as to the semi-empirical Traupel loss model [27]. The color bars in the charts are indicative of 61=2% efficiency deviation with respect to the time-averaged values computed by 3D URANS.…”
The impact of non-ideal compressible flows on the fluid-dynamic design of axial turbine stages is examined. First, the classical similarity equation is revised and extended to account for the effect of flow non-ideality. Then, the influence of the most relevant design parameters is investigated through the application of a dimensionless turbine stage model embedding a first-principles loss model. The results show that compressibility effects induced by the fluid molecular complexity and the stage volumetric flow ratio produce an offset in the efficiency trends and in the optimal stage layout. Furthermore, flow non-ideality can lead to either an increase or decrease of stage efficiency up to 3-4% relative to turbines designed to operate in dilute gas state. This effect can be predicted at preliminary design phase through the evaluation of the isentropic pressure-volume exponent. 3D RANS simulations of selected test cases corroborate the trends predicted with the reduced-order turbine stage model. URANS computations provide equivalent trends, except for case study niMM1, featuring a non-monotonic variation of the generalized isentropic exponent. For such turbine stage, the efficiency is predicted to be higher than the one computed with any steady-state model based on the control volume approach.
“…In the literature, many articles can be found dealing with the design and calculation of the mechanical behavior of the coupled blade system. An overview of the fundamentals can be found in Traupel, 3 while Traupel, 4 Prohl 5 or Thomas 6 presented a more detailed work on the calculation of vibrational stress of packaged bladed systems. However, due to the limited calculation resources in the past, damping wire designs for blades were mainly based on empirical and analytical methods 7 as well as operation experience, often with trial and error.…”
Section: Damping Elements Developmentmentioning
confidence: 99%
“…The damping performance diagram is shown in Figure 8 where the vibration amplitudes are plotted in relation to the excitation force and µ as a parameter. The amplitudes are normalized to the measured value, obtained in the test rig, and the excitation force is normalized to the static steam loads on the blade airfoil at the corresponding thermodynamic load point from the measurements, thus it is equal to the stimulus (Traupel 3 ). Figure 8.Damping performance diagram.…”
Section: Numerical Investigation Of the Dynamic Behaviormentioning
Many industrial steam turbine applications require the capability for variable speed operation in combination with high mass flow rates and high back pressure levels. Especially the low-pressure blading has to be designed carefully with respect to the mechanical integrity. An effective way to reduce blade vibration is the introduction of a simple lacing wire to couple the moving blades. In this paper, the structural behavior of blades coupled by a wire is verified by means of linear and nonlinear finite element method. Different modeling techniques for the coupling effects are presented and discussed. Special focus is put on the nonlinear effects of the contact between blade and wire to investigate the frictional damping performance of the system. The obtained numerical results are validated by strain gauge measurements on a full-scale test turbine under real steam conditions in an industrial steam turbine test rig. The experimental data show low blade vibration amplitudes in the whole operational range indicating a high damping performance of the investigated wire design. The calculation results from the forced response analysis including the frictional effects are in good agreement with the experimental data.
“…The compressor off-design characteristics were derived by applying a stage-stacking analysis [34][35][36], while the calculations of the isentropic efficiency of each stage were based on the pressure drop assumptions presented in Templalexis et al [37], and the works of Lieblein [38] and Saravanamuttoo et al [39]. The gas turbine off-design characteristics were derived following the method described in Stodola [40] and in Traupel [41].…”
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