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.

Research on Damping Vibration Reduction Design Method of Aeroengine Supporting Structure System

Typical turbofan engine-support-structure systems having a high thrust-to-weight ratio are light, and the structure primarily comprises a plate and shells. The local vibration response of the support structure is excessively large when different frequency loads are applied. A structural vibration response control method based on dry friction damping is proposed to control the excessive vibration response. A dry friction damper with dynamic suction was designed to enhance the damping characteristics of the rotor supporting structure system in the wide frequency domain, without sacrificing the dynamic stiffness of the structure. The system is designed to effectively control the vibration response of the supporting structure at the working-speed frequency. Through theoretical modeling and simulation analyses, the influence of friction contact and damper structure characteristics on the damping effect is described quantitatively. Furthermore, the design idea and the damping process of the supporting structure are described. The calculation results show that the contact friction of the dry friction damper can consume the vibration energy of the supporting frame. A reasonable design of the contact characteristics and geometric configuration parameters of the damper can further optimize the vibration-reduction effect, and thereby improve the vibration response control design of the supporting structure system of aeroengines.

Implementation of a Rig Test for Rotor/Stator Interaction of Low-Pressure Compressor Blades and Comparison of Experimental Results With Numerical Model

To investigate the contact phenomenon between the blade tip and the abradable coated casing, a rig test was designed and built. This rig test fills the following constraints: simplification of the low-pressure compressor environment but realistic mechanical conditions, ability to test several designs in short time, at low cost and repeatability. The rig test gives the opportunity to investigate the behavior of different blade designs regarding the sought phenomenon, to refine and mature the phenomenon comprehension and to get data for the numerical tool validation. The numerical tool considers a 3D finite elements model of low-pressure compressor blades with a surrounding rigid casing combined with a specialized model to take into account the effects of the wear of the abradable coating on the blade dynamics. Numerical results are in good agreement with tests in terms of: critical angular speed, blade dynamics and wear pattern on the abradable coated casing.

Hybrid Numerical-Experimental Model Update Based on Correlation Approach for Turbine Components

Bladed-disks in turbo-machines experience high cycle fatigue failures due to high vibration amplitudes. Therefore, it is important to accurately predict their dynamic characteristics including the mechanical joints at blade-disk (root joint) or blade-blade (shroud) interfaces. These joints help in dampening the vibration amplitudes. Before the experimental identification of these joints, it is of paramount importance to accurately measure the interface degrees-of-freedom (DoF). However, they are largely inaccessible for the measurements. For this reason, expansion techniques are used in order to update the single components before their coupling. But the expansion can be affected adversely if the measurements are not properly correlated with the updated model or if they have significant errors. Therefore, a frequency domain expansion method called System Equivalent Model Mixing (SEMM) is used to expand a limited set of measurements to a larger set of numerical DoF. Different measured models — termed the overlay models — are taken from an impact testing campaign of a blade and a disk and coupled to the numerical model according to the SEMM. The expanded models — termed the hybrid models — are then correlated with the validation channels in a round-robin way by means of Frequency Response Assurance Criteria (FRAC). The global correlations depict whether or not a measurement and the respective expansion is properly correlated. By this approach, the least correlated channels can be done away with from the measurements to have a better updated hybrid model. The method is tested on both the structures (the blade and the disk) and it is successfully shown that removing the uncorrelated channels does improve the quality of the hybrid models.

Identification of the Essential Features of the Transient Amplification of Mistuned Systems

The dynamic behavior of bladed disks in resonance crossing has been intensively investigated in the community of turbomachinery, addressing the attention to (1) the transienttype response that appear when the resonance is crossed with a finite sweep rate and (2) the localization of the vibration in the disk due to the blade mistuning. In real conditions, the two mentioned effects coexist and can interact in a complex manner. This paper investigates the problem by means of analytic solutions obtained through asymptotic expansions, as well as numerical simulations. The mechanical system is assumed as simple as possible: a 2-dof linear system defined through the three parameters: damping ratio ξ, frequency mistuning Δ, rotor acceleration Ω˙. The analytic solutions are calculated through the multiple-scale method.

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.