Isogeometric analysis was applied very successfully to many problem classes like linear elasticity, heat transfer and incompressible flow problems but its application to compressible flows is very rare. However, its ability to accurately represent complex geometries used in industrial applications makes IGA a suitable tool for the analysis of compressible flow problems that require the accurate resolution of boundary layers. The convection-diffusion solver presented in this chapter, is an indispensable step on the way to developing a compressible solver for complex viscous industrial flows. It is well known that the standard Galerkin finite element method and its isogeometric counterpart suffer from spurious oscillatory behaviour in the presence of shocks and steep solution gradients. As a remedy, the algebraic flux correction paradigm is generalized to B-Spline basis functions to suppress the creation of oscillations and occurrence of non-physical values in the solution. This work provides early results for scalar conservation laws and lays the foundation for extending this approach to the compressible Euler equations in [1].

Unstable flow structures cause inevitable energy losses in all power energy systems, including turbomachines. In this study, a set of analyses was conducted with the use of spectral maps on the pressure signals obtained from an industrial centrifugal compressor. The spectral maps provide one a detailed visualization of the flow conditions present in the machine along the performance curve and to distinguish the flow phenomena present prior to the surge. The method accuracy is especially useful in detecting the inlet recirculation. The study was conducted at four impeller rotational speeds with varying loads imposed by a valve at the outlet. At each speed, the machine experienced different stages of unstable flow conditions prior to the surge. Five main frequency peaks that appeared in all cases were identified and discussed. The surge was observed at all impeller speeds. At lower ones, however, it appeared at higher valve closures. At higher speeds, the surge was much more intense. The study has also shown that the inlet recirculation appears also for the closed-type industrial impeller. The phenomenon was present in all conditions. The higher impeller speed, the faster onset of the inlet recirculation was. This structure has a strong potential for an early instability warning because it appears in various types of impellers, has a very particular spectral structure and its positioning is very predictable. This study gives another example of the inlet recirculation universality and potential for efficient anti-surge protection.

This paper presents tests of an anti-surge system based on pressure derivatives. The control algorithm was proven to work on different machines and with different unstable flow phenomena. Compressors are known to be affected by unstable flow conditions appearing at low mass flow rate conditions. The best known and most dangerous phenomenon is surge, which is a global instability affecting the entire impeller and regions upstream and downstream from it. A list of identified local phenomena includes among others: impeller rotating stall, diffuser rotating stall and inlet recirculation. All have a specific pressure signature that is used for early identification. The method presented in this paper is based on a control parameter named the Rate of Derivative Fluctuation (RDF). This approach involves a simple measure of flow instability that is universal and reacts to flow disturbances. RDF has been already confirmed to identify inlet recirculation and surge. The aim of this study is to conduct real-time tests of an anti-surge system implementing the RDF algorithm triggering the safety valve opening. The study confirmed the optimal position of the monitoring point. The results showed that the RDF is indeed sensitive to different types of flow instabilities appearing in different impellers, and that it provides efficient flow stability monitoring.

The paper focusses on the numerical and experimental investigation of the operation of a centrifugal compressor connected to a large plenum volume. The experimental study consisted of measurements of time-averaged and transient pressure values in a system based on the DP1.12 blower. The numerical analysis was based on the Greitzer model. The model parameters were determined so as to achieve best fit with the experimental signal. It was observed that out of two optimal solutions, one resolved the first harmonic of oscillations significantly better than the other. The obtained values of the B parameter varied with the operation point, which is contrary to the formal definition of this quantity. The values of angular Helmholtz frequency ωh were not sensitive to the change of operation point. This paper improves our understanding of the meaning of model parameters, which is a crucial step towards a more accurate prediction and prevention of surge.

This paper presents tests of an anti-surge system based on pressure derivatives. The control algorithm was proven to work on different machines and with different unstable flow phenomena. Compressors are known to be affected by unstable flow conditions appearing at low mass flow rate conditions. The best known and most dangerous phenomenon is surge, which is a global instability affecting the entire impeller and regions upstream and downstream from it. A list of identified local phenomena includes among others: impeller rotating stall, diffuser rotating stall and inlet recirculation. All have a specific pressure signature that is used for early identification. The method presented in this paper is based on a control parameter named the Rate of Derivative Fluctuation (RDF). This approach involves a simple measure of flow instability that is universal and reacts to flow disturbances. RDF has been already confirmed to identify inlet recirculation and surge. The aim of this study is to conduct real-time tests of an anti-surge system implementing the RDF algorithm triggering the safety valve opening. The study confirmed the optimal position of the monitoring point. The results showed that the RDF is indeed sensitive to different types of flow instabilities appearing in different impellers, and that it provides efficient flow stability monitoring.

The article describes an assessment of possible changes in constant fatigue life of a medium flow-coefficient centrifugal compressor impeller subject to operation at close-to-surge point. Some aspects of duct acoustics are additionally analyzed. The experimental measurements at partial load are presented and are primarily used for validation of unidirectionally coupled fluid-structural numerical model. The model is based on unsteady finite-volume fluid-flow simulations and on finite-element transient structural analysis. The validation is followed by the model implementation to replicate the industry-scale loads with reasonably higher rotational speed and suction pressure. The approach demonstrates satisfactory accuracy in prediction of stage performance and unsteady flow field in vaneless diffuser. The latter is deduced from signal analysis relying on continuous wavelet transformations. On the other hand, it is found that the aerodynamic incidence losses at close-to-surge point are underpredicted. The structural simulation generates considerable amounts of numerical noise, which has to be separated prior to evaluation of fluid-induced dynamic strain. The main source of disturbance is defined as a stationary region of static pressure drop caused by flow contraction at volute tongue and leading to first engine-order excitation in rotating frame of reference. Eventually, it is concluded that the amplitude of excitation is too low to lead to any additional fatigue.

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This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle of IGA, the parameterization and the governing state equation are treated using the same numerical technique. This leads to a scheme that is comparatively easy to differentiate, allowing for a fully symbolic derivation of the gradient and subsequent gradient-based optimization. To improve the efficiency and robustness of the scheme, the basis is re-selected during each optimization iteration and adjusted to the current needs. The scheme is validated in two test cases.