On Large Eddy Simulation Based Conjugate Heat Transfer Procedure for Transient Natural Convection

Abstract

Natural convection is an important heat transfer mode for flexible operations of gas turbines and steam turbines. Its prediction presents considerable challenges. The strong interdependence between fluid and solid parts points to the need for coupled fluid–solid conjugate heat transfer (CHT) methods. The fundamental fluid–solid time scale disparity is further compounded by the long-time scales of practical turbine flexible operations. In addition, if a high-fidelity flow model (e.g., large eddy simulation (LES)) is adopted to resolve turbulence fluctuations, extra mesh dependency on solid domain mesh may arise. In this work, understanding of the extra solid mesh dependency in a directly coupled LES based CHT procedure is gained by an interface response analysis, leading to a simple and clear characterization of erroneously predicted unsteady interface temperatures and heat fluxes. A loosely coupled unsteady CHT procedure based on a multiscale methodology for solving problems with large time scale disparity is subsequently developed. A particular emphasis of this work is on efficient and accurate transient CHT solutions in conjunction with the turbulence eddy resolved modeling (LES) for natural convection. A two-scale flow decomposition associated with a corresponding time-step split is adopted. The resultant triple-timing formation of the flow equations can be solved efficiently for the fluid–solid coupled system with disparate time scales. The problem statement, analysis, and the solution methods will be presented with case studies to underline the issues of interest and to demonstrate the validity and effectiveness of the proposed methodology and implemented procedure.

LES-CHT for a Rotating Cavity With Axial Throughflow

“…Depending on the mesh spacing and material properties, this artificial amplification could reach over an order of magnitude. This has been observed in LES of natural convection by Fadl and He [13] and in combustors by Shahi et al [14].…”

“…Fadl and He [13] investigated the effect of under-resolving the thermal penetration depth in the solid domain (i.e. having a wall-normal mesh spacing larger than δ P ).…”

“…This is particularly an issue for getting past the initial transient in the solid times. The second reason is that under-resolving the thermal-penetration depth in the solid domain can risk over predicting the amplitude of the temperature fluctuations on the interface by one or two orders of magnitude [13]. This means that even though a certain frequency of fluctuation may not be dynamically relevant to the physics, if its penetration depth is under-resolved it could corrupt the entire flow field.…”

Full conjugate heat transfer modelling for steam turbines in transient operations

“…It has also been widely used for URANS applications for unsteady turbomachinery flows with much larger physical time steps than that dictated by the CFL restricted numerical stability requirement (e.g. Arnone et al [21], He [23]). It is noted that the dual timing procedure may require the physical time step to be larger than that limited by CFL.…”

“…The numerical stability requirement tends to restrict the time step size to a very small value (typically subseconds), e.g. [17], [18], [19], [20], [21], [22], [23] and [26]. When a transient CHT solution for natural convection is pursued, this time step limit can be particularly restrictive, given the time scale disparity between the fluid and solid domain.…”