Low-Dimensional Models for Turbulent Heat Transfer in Flexible Cylinder Arrays

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ABSTRACT Proposal Number: CTS 9901732Principal Investigator: G. Karniadakis This award, in conjunction with award 9903346, is to support an investigation into the flow around and the heat transfer from tube banks. Turbulent heat transfer from tube banks depends strongly on the specific geometric configuration employed, and is influenced substantially by the flow-induced vibrations that the tubes may be subject to. In particular, the recent use of high strength materials has produced more slender structures, which are more susceptible to vibration. Existing models for predicting heat transfer and flow-induced vibrations are semi-empirical and even the most sophisticated ones depend critically on time-dependent coefficients, which are difficult to measure. In this work a model is proposed that exhibit some of the complexity of turbulent heat transfer in flexible cylinder arrays but in a simplified setting. Evidence from experimental and direct numerical simulation studies has shown that despite their complexity this type of coupled systems exhibit low-dimensionality and can be modeled effectively using dynamical systems techniques motivated by the theory of approximate inertial manifolds using nonlinear Galerkin models based on hierarchical modes extracted from numerical and experimental data bases using the ``method of snapshots". These models, in addition to the overall force coefficients and Nusselt number, provide detailed spatio-temporal description of the velocity and temperature fields. The experimental and numerical data bases will be obtained at one representative value of Peclet number using DPIV/T measurements and dynamic spectral simulations developed in a previous NSF grant. More specifically, the objective of this renewal grant is two-fold: First, to develop new experimental and simulation tools that will enable high temporal and spatial resolution of general flow/heat-structure interaction problems. Second, to construct reduced dynamical models that retain the spatio-temporal complexity of the full systems and predict accurately the mean and fluctuating quantities of interest.