We propose a generalization of proper orthogonal decomposition (POD) for optimal flow resolution of linearly related observables. This Galerkin expansion, termed 'observable inferred decomposition' (OID), addresses a need in aerodynamic and aeroacoustic applications by identifying the modes contributing most to these observables. Thus, OID constitutes a building block for physical understanding, leastbiased conditional sampling, state estimation and control design. From a continuum of OID versions, two variants are tailored for purposes of observer and control design, respectively. Firstly, the most probable flow state consistent with the observable is constructed by a 'least-residual' variant. This version constitutes a simple, easily generalizable reconstruction of the most probable hydrodynamic state to preprocess efficient observer design. Secondly, the 'least-energetic' variant identifies modes with the largest gain for the observable. This version is a building block for Lyapunov control design. The efficient dimension reduction of OID as compared to POD is demonstrated for several shear flows. In particular, three aerodynamic and aeroacoustic goal functionals are studied: (i) lift and drag fluctuation of a two-dimensional cylinder wake flow; (ii) aeroacoustic density fluctuations measured by a sensor array and emitted from a two-dimensional compressible mixing layer; † Email address for correspondence: michael.schlegel@tu-berlin.de
The material temperature field of a centrifugal compressor wheel is one important factor for the life time analysis of a compressor stage. Due to increasing thermal loads of advanced compressor stages, the thermal stresses and/or material temperature levels can exceed the allowed limits for a prescribed exchange interval and cooling techniques are needed to reduce the wheel temperature. One efficient cooling technique is the air impingement cooling. Unlike in gas turbines the impingement cooling is located in the back face region of the compressor wheel. From a computational point of view this means that the impingment jet is located in the stationary frame of reference and the cooled wall is located in the rotating frame of reference. In such a case the heat transfer problem becomes unsteady. The paper introduces a novel CHT-mixing plane interface for the frame change between stationary fluid domain and rotating solid domain to overcome the intrinsic unsteadiness caused by the jet impingement. Fluid mixing plane interfaces between rotor and stator are very common in industries to exploit periodic symmetries and to avoid time consuming unsteady compuations. However, the commercial solvers do not provide a mixing plane interface between fluid and solid domains. First, the new mixing plane approach is validated for a representative test case against a time resolved computation. In the second step, the new method is applied to a compressor stage. Two operating conditions, each with three different cooling mass flows have been computed. The comparison of the wheel temperature field corresponds very well to the computational results for all operating conditions. The temperature field analysis reveals valuable information on the heat transfer in highly loaded compressor stages which can be exploited in the design process of the compressor cooling.
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