Application of Digital Twin Concept for Supercritical CO2 Off-Design Performance and Operation Analyses

To date variety of supercritical CO2 cycles were proposed by numerous authors. Multiple small-scale tests performed, and a lot of supercritical CO cycle aspects studied. Currently, 3-10 MW-scale test facilities are being built. However, there are still several pieces of SCO2 technology with the Technology Readiness Level (TRL) 3-5 and system modeling is one of them. The system modeling approach shall be sufficiently accurate and flexible, to be able to precisely predict the off-design and part-load operation of the cycle at both supercritical and condensing modes with diverse control strategies. System modeling itself implies the utilization of component models which are often idealized and may not provide a sufficient level of fidelity. Especially for prediction of off-design and part load supercritical CO2 cycle performance with near-critical compressor and transition to condensing modes with lower ambient temperatures, and other aspects of cycle operation under alternating grid demands and ambient conditions. In this study, the concept of a digital twin to predict off-design supercritical CO2 cycle performance is utilized. In particular, with the intent to have sufficient cycle simulation accuracy and flexibility the cycle simulation system with physics-based methods/modules were created for the bottoming 15.5 MW Power Generation Unit (PGU). The heat source for PGU is GE LM6000-PH DLE gas turbine. The PGU is a composite (merged) supercritical CO2 cycle with a high heat recovery rate, its design and the overall scheme are described in detail. The calculation methods utilized at cycle level and components’ level, including loss models with an indication of prediction accuracy, are described. The flowchart of the process of off-design performance estimation and data transfer between the modules as well. The comparison of the results obtained utilizing PGU digital twin with other simplified approaches is performed. The results of the developed digital twin utilization to optimize cycle control strategies and parameters to improve off-design cycle performance are discussed in detail.

Influence of Equation-of-States on Supercritical CO2 Combustion

Fossil fuel based direct-fired supercritical CO2 (sCO2) cycles are gaining the attention of industry, academia and government due to their remarkable efficiency and carbon capture at high-source temperatures. Modeling plays an important role in the development of sCO2 combustors because experiments are very expensive at the designed operating conditions of these direct-fired cycles. Inaccurate density estimates are detrimental to the simulation output. Hence, this work focuses on comprehensive evaluation of the influence and applicability various equation-of-states (EOS) which are being used in the supercritical combustion modeling literature. A state-of-the-art supercritical combustion modeling methodology is used to simulate counter-flow supercritical CO2 flames by using various equation-of-states. The results show that, using the corresponding state principle to evaluate compressibility factor is not accurate. Also, van der Waal type EOSs predictions can be as accurate as complex Benedict-Webb-Rubin EOSs; hence van der Waal EOSs are more suitable to simulate sCO2 combustor simulations. Non-ideal effects are significant under the operating conditions considered in this work. The choice of EOS significantly influences the flame structure and heat release rate. Also, assuming the binary interaction parameter as zero is reasonable in sCO2 combustion simulations.

Modeling Complex Contact Conditions and Their Effect on Blade Dynamics

Dry friction devices such as underplatform dampers are commonly included in turbine bladed disks designs to mitigate structural vibrations and avoid high cycle fatigue failures. The design of frictionally damped bladed disks requires adequate models to represent the friction contact. A widely used approach connects contact node pairs with normal and tangential springs and a Coulomb friction law. This simple model architecture is effective in capturing the softening behavior typically observed on frictionally damped structures subjected to increasing forcing levels. An unexpected hardening behavior was observed on the frequency response functions of two-blades-plus-damper system tested by the authors in a controlled laboratory environment. The reason behind this unexpected behavior will be carefully analyzed and linked to the damper kinematics and to the dependence of contact elasticity on the contact pressure. The inadequacy of contact models with constant spring values will be discussed and alternatives will be proposed. The importance of being able to represent complex contact conditions in order to effectively predict the system dynamics is shown here using a laboratory demonstrator, however its implications are relevant to any other case where large contact pressure variations are to be expected. The nonlinear steady state simulations of the blades-plus-damper system will be carried out using an in-house code exploiting the Multi-Harmonic Balance Method (MHBM) in combination with the Alternating Frequency Time (AFT) Method.

A Numerical Study on Conjugate Heat Transfer for Supercritical CO2 Turbine Blade With Cooling Channels

The first stage of turbine in a Brayton cycle faces the maximum temperature in the cycle. This maximum temperature may exceed creep temperature limit or even melting temperature of the blade material. Therefore, it becomes an absolute necessity to implement blade cooling to prevent them from structural damage. Turbine inlet temperatures for oxy-combustion supercritical CO2 (sCO2) are promised to reach blade material limit in near future foreseeing need of turbine blade cooling. Properties of sCO2 and the cycle parameters can make Reynolds number external to blade and external heat transfer coefficient to be significantly higher than those typically experience in regular gas turbines. This necessitates evaluation and rethinking of the internal cooling techniques to be adopted. The purpose of this paper is to investigate conjugate heat transfer effects within a first stage vane cascade of a sCO2 turbine. This study can help understand cooling requirements which include mass flow rate of leakage coolant sCO2 and geometry of cooling channels. Estimations can also be made if the cooling channels alone are enough for blade cooling or there is need for more cooling techniques such as film cooling, impingement cooling and trailing edge cooling. The conjugate heat transfer and aerodynamic analysis of a turbine cascade is carried out using STAR CCM+. The turbine inlet temperature of 1350K and 1775 K is considered for the study considering future potential needs. Thermo-physical properties of this mixture are given as input to the code in form of tables using REFPROP database. The blade material considered is Inconel 718.

Blade Root Joint Modelling and Analysis of Effects of Their Geometry Variability on the Nonlinear Forced Response of Tuned and Mistuned Bladed Disks

One of the major sources of the damping of the forced vibration for bladed disk structures is the micro-slip motion at the contact interfaces of blade-disk joints. In this paper, the modeling strategies of nonlinear contact interactions at blade roots are examined using high-fidelity modelling of bladed disk assemblies and the nonlinear contact interactions at blade-disk contact patches. The analysis is performed in the frequency domain using multiharmonic harmonic balance method and analytically formulated node-to-node contact elements modelling frictional and gap nonlinear interactions. The effect of the number, location and distribution of nonlinear contact elements are analyzed using cyclically symmetric bladed disks. The possibility of using the number of the contact elements noticeably smaller than the total number of nodes in the finite element mesh created at the contact interface for the high-fidelity bladed disk model is demonstrated. The parameters for the modeling of the root damping are analysed for tuned and mistuned bladed disks. The geometric shapes of blade roots and corresponding slots in disks cannot be manufactured perfectly and there is inevitable root joint geometry variability within the manufacturing tolerances. Based on these tolerances, the extreme cases of the geometry variation are defined and the assessment of the possible effects of the root geometry variation on the nonlinear forced response are performed based on a set of these extreme cases.

Non-Uniform Two-Phase Flow of Supercritical Carbon Dioxide Centrifugal Compressor

An asymmetric structure of volute in a supercritical carbon dioxide centrifugal compressor induces a non-uniform circumferential distribution of the upstream flow field, which inevitably affects the formation of a two-phase region of carbon dioxide in an impeller. In this work, unsteady simulations for centrifugal compressors were conducted. First, the influence of low static strip induced by low static pressure near volute tongue on the impeller flow field was presented. Then, the non-uniform flow field distribution in the impeller passages and flow characteristics of the passages at the impeller inlet were obtained. Finally, the two-phase regions in the impeller were presented. The results demonstrate that for a centrifugal compressor with volute, the two-phase region appears not only on the suction surface of the leading edge of the blade, but also in some impeller passages, on the pressure surface of the blade near the leading edge, and in the leading edge and mid-chord of tip clearance, under the design conditions. The low static pressure strip induced by the volute leads to a high-speed region in the impeller passages where the temperature and pressure of supercritical carbon dioxide fall below the critical point and carbon dioxide enters the two-phase region. Meanwhile, the static pressure on the blade surface is distorted under the influence of a high-speed region in the passages, resulting in the formation of a two-phase region at the tip clearance. The flow distortion of passages at the impeller inlet results in the appearance of two-phase regions on the both sides of leading edge of the blade. The dryness on the suction side of the blade leading edge and the leading edge of the tip clearance is lower, which indicated that the proportion of liquid-phase carbon dioxide is higher in these two-phase regions.

Modal Analysis of Turbine Blades by Means of Distributed Optical Fiber Sensors

This paper investigates the possibility of identifying and monitoring the modal shapes of a turbine blade by means of continuous optical fiber sensors based on Optical Backscatter Reflectometry (OBR). The advantage of this approach would be the possibility of embedding the sensors in future carbon fiber blades, in order to make this modal analysis approach available also for the blade operating conditions, since no modifications in the blade fluid-structure interaction occur. The paper describes the proposed method and provides some experimental results obtained on a 3D printed model of an existing steam turbine blade.

Implications of Phase Change on the Aerodynamics of Centrifugal Compressors for Supercritical Carbon Dioxide Applications

Closed Joule-Bryton cycles operating with carbon dioxide in supercritical conditions (sCO2) are nowadays collecting a significant scientific interest, due to their high potential efficiency, the compactness of their components, and the flexibility that makes them suitable to exploit diverse energy sources. However, the technical implementation of sCO2 power systems introduces new challenges related to the design and operation of the components. The compressor, in particular, operates in a thermodynamic condition close to the critical point, whereby the fluid exhibits significant non-ideal gas effects and is prone to phase change in the intake region of the machine. These new challenges require novel design concepts and strategies, as well as proper tools to achieve reliable predictions. In the present study, we consider an exemplary sCO2 power cycle with main compressor operating in proximity to the critical point, with an intake entropy level of the fluid lower than the critical value. In this condition, the phase change occurs as evaporation/flashing, thus resembling cavitation phenomena observed in liquid pumps, even though with specific issues associated to compressibility effects occurring in both the phases. The flow configuration is therefore highly nonconventional and demands the development of proper tools for fluid and flow modeling, which are instrumental for the compressor design. The paper discusses the modeling issues from the thermodynamic perspective and then highlighting the implications on the compressor aerodynamics. We propose tailored models to account for the effect of the phase change in 0D mean-line design tools as well as in fully 3D computational fluid-dynamic (CFD) simulations. In this way, a design strategy is build-up as a combination of mean-line tools, industrial design experience, and CFD for detailed flow analysis. The application of the design strategy reveals that the potential onset of the phase change might alter significantly the performance and operation of the compressor, both in design and in off-design conditions.

Sparse Reconstruction Method of Non-Uniform Sampling and its Application in Blade Tip Timing System

Based on the blade vibration theory of turbomachinery and the basic principle of blade timing systems, a sparse reconstruction model is derived for the tip timing signal under an arbitrary sensor circumferential placement distribution. The proposed approach uses the sparsity of the tip timing signal in the frequency domain. The application of compressive sensing in reconstructing the blade tip timing signal and monitoring multi-mode blade vibrations is explored. To improve the reconstruction effect, a number of numerical experiments are conducted to examine the effects of various factors on synchronous and non-synchronous signals. This enables the specific steps involved in the compressive sensing reconstruction of tip timing signals to be determined. The proposed method is then applied to the tip timing data of a 27-blade rotor. The results show that the method accurately identifies the multi-mode blade vibrations at different rotation speeds. The proposed method has the advantages of low dependence on prior information, insensitivity to environmental noise, and simultaneous identification of synchronous and non-synchronous signals. The experimental results validate the effectiveness of the proposed approach in engineering applications.

Interaction Between Coriolis Forces and Mistuning on a Cyclic Symmetric Structure With Geometrical Nonlinearity

An investigation of the interaction between Coriolis forces and mistuning on a cyclic symmetric structure is presented in this paper. The sensitivity of the eigenvalues and eigenvectors to mistuning is first studied with the perturbation method. A lumped parameter model is used to perform a modal analysis using a numerical approach after which geometrical nonlinearity is added to compare behavior with the linear case. Two different modes are thoroughly investigated for different rotational speeds, the first with an eigenvalue isolated from the others and the second presenting a frequency veering zone. The evolution from a standing wave domination at low speeds to a travelling wave domination at high speeds is observed for the isolated mode, whereas a standing wave domination remains around the veering zone for the second mode studied. It is also shown that the geometrical nonlinearity reinforces the mistuning effect versus the Coriolis forces.