Übertragungsverhalten des Wärmeübergangs am Zylinder bei pulsierender Queranströmung
Technische Thermodynamik
Zusammenfassung der Projektergebnisse
The aim of the project was to study the dynamic behavior of heat transfer and skin friction of a heated cylinder in pulsating cross flow over a range of Reynolds numbers. The unsteady response of the rate of heat transfer to fluctuations in flow velocity plays a vital role for the Rijke tube, which is a prototype of a thermoacoustic device that is often used to study thermoacoustic phenomena, in particular thermoacoustic instabilities. The latter occur e.g. in gas turbines or rocket engines and represent a significant challenge for the development of clean, reliable and flexible combustion technology. On the other hand, the thermoacoustic effect can be be exploited beneficially in thermoacoustic engines or refrigerators. In general, unsteady transfer of heat and momentum plays a role in many other applications in process and energy technology, such as the movement particles in fluids (Basset force). In this study the frequency responses of skin friction and heat transfer were determined by a combination of computational fluid dynamics (CFD) with system identification (SI) techniques. With this “CFD/SI” approach, CFD is used to simulated the response of the system to an imposed, unsteady, broad-band input signal. The time series of input and response – in the present case cross-flow velocity and heat or momentum transfer, respectively – generated in this way are then post-processed with SI to identify reduced-order models (ROM) that closely approximate the dynamics of the true system. Frequency responses and pertinent time scales of unsteady heat and momentum transfer and the corresponding governing time constants may be deduced from the ROMs. Accurate CFD simulations must be used to generate the time series data. Thus a comprehensive grid independence study was performed, considering the influence of domain size, cell size and time step size both for steady and unsteady cases. For the latter high frequency velocity perturbations were imposed, resulting in very thin acoustic boundary layers. The SI procedure applied previously to the analysis of unsteady heat transfer in pulsating flows was revisited and advanced identification schemes were investigated. it was found that an output error model is to be preferred over finite impulse response models due to its recursive nature, which allows to parametrize the dynamic behavior with only five to ten identified coefficients. Wavelet based excitation signals were used providing an optimal trade-off between the requirements of CFD simulation and SI. Regularization, a technique to enhance the identification of impulse responses was dropped since no significant improvement could be determined. Uncertainties arising in the identification process originating from noise in the data were quantified and assessed as variance of the identified parameters. The frequency response functions of heat transfer and skin friction were identified for several Reynolds numbers over a wide range of frequencies. The dynamic behavior was examined in detail, pertinent results from other studies were used for comparison. Limitations of the earlier studies were revealed. For the heat transfer at moderate mean flow Reynolds numbers a 1st order approximation was developed incorporating the dependence on mean flow Reynolds number. This meta-model brides the gap between existing models for low and high Reynolds numbers, respectively providing better predictions for the dynamic behavior than expressions reported in literature. High flexibility with Reynolds number as parameter and low complexity are additional advantages of the new model. The newly identified models shed light on the physics involved and may be used in further investigations, for example as ROMs of the heat source embedded in hybrid models of (thermo-) acoustical systems. Moreover, the accumulated experience in CFD simulation of pulsating flows and system identification in the scope of heat transfer and skin friction may be readily transferred to similar problems in thermofluiddynamics to develop ROMs and frequency response functions.
Projektbezogene Publikationen (Auswahl)
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(2017) Dynamics of unsteady heat transfer in pulsating flow across a cylinder. International Journal of Heat and Mass Transfer 109 1111–1131
Witte, Armin; Polifke, Wolfgang
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Heat transfer frequency response of a cylinder in pulsating laminar cross flow, presented at: 17. STAB-Workshop, Göttingen (2015)
A. Witte, W. Polifke
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Identification of the heat transfer frequency response in pulsating laminar and subcritical flow across a cylinder, Journal of Physics: Conference Series. 745 (2016) 32055
A. Witte, A. Cabrera, W. Polifke
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Modeling the Heat Transfer and Skin Friction Frequency Response of a Cylinder in Cross-Flow - a Unifying Perspective, in: Proceedings of 12th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, HEFAT, Malaga, Spain, (2016) ISBN 978-1-77592-124-0, pp. 1022–1027
A. Witte, W. Polifke
