Internal Heat Transfer Coefficient Distribution Research Articles

Boundary element method for contactless estimation of spatially varying internal heat transfer coefficient in circular pipes

In the present study it is proposed a solution approach of the Inverse Heat Conduction Problem (IHCP) intended at assessing the local heat transfer coefficient on the inner wall of a tube, under a forced convection problem. The estimation method is established on the Boundary Element Method (BEM) combined with the Truncated Singular Value Decomposition (TSVD) methodology, employed to manage the ill-conditioned nature of the problem. The numerical results of the direct problem, built by the BEM, are firstly validated, and consequently adopted as synthetic data inputs to resolve the IHCP and corroborate the whole assessment procedure. This approach is also tested with experimental data about forced convection problem in coiled pipes. In these geometries, the convective heat transfer coefficient changes considerably along the wall periphery and for this reason, it constitutes a perfect example to test the ability of the presented method to infer a spatially varying internal heat transfer coefficient distribution.

Cooling Optimization Theory—Part I: Optimum Wall Temperature, Coolant Exit Temperature, and the Effect of Wall/Film Properties on Performance

Gas turbine cooling system design is constrained by a maximum allowable wall temperature (dictated by the material and the life requirements of the component), minimum coolant mass flow rate (the requirement to minimize cycle-efficiency cost), and uniform wall temperature (to reduce thermal stresses). These three design requirements form the basis of an iterative design process. The relationship between the requirements has received little discussion in the literature, despite being of interest from both a theoretical and a practical viewpoint. In this paper, we consider the optimum cooling system for parts with both internal and film cooling. We show analytically that the coolant mass flow rate is minimized when the wall temperature is uniform and equal to the maximum allowable wall temperature. Thus, we show that achieving uniform wall temperature achieves minimum coolant flow rate, and vice versa. The purpose is to clarify the interplay between two design requirements that are often discussed separately in the literature. The penalty (in terms of coolant mass flow) associated with cooling nonisothermal components is quantified. We show that a typical high pressure nozzle guide vane (HPNGV) operating isothermally at the maximum allowable wall temperature requires two-thirds the coolant of a typical nonisothermal vane. The optimum coolant exit temperature is also considered. It is shown analytically that the optimum coolant exit temperature depends on the balance between the mean adiabatic film cooling effectiveness, the nondimensional mass flow rate, and the Biot number of the thermal barrier coating (TBC). For the large majority of gas turbine cooling systems (e.g., a typical HPNGV) it is shown that the optimum coolant exit temperature is equal to the local wall temperature at the point of injection. For a small minority of systems (e.g., long effusion cooling systems operating at low mass flow rates), it is shown that the coolant exit temperature should be minimized. An approximation relating the wall/film properties, the nondimensional mass flow, and the overall cooling effectiveness is derived. It is used to estimate the effect of Biot number (TBC and metal), heat transfer coefficient (HTC) ratio, and film properties on the performance of a typical HPNGV and effusion cooling system. In Part II, we show that designs which achieve uniform wall temperature have a particular corresponding internal HTC distribution.

Experimental assessment of the fluid bulk temperature profile in a mini channel through inversion of external surface temperature measurements

In previous works, a semi-analytical model allowing the simulation of heat transfer in a mini-channel has been presented. This model does not rely on the local internal heat transfer coefficient distribution. The focus of this study concerns the experimental characterization of the conjugate heat transfer in a vertical flat mini-channel of 1mm thickness. The objective here is to validate experimentally the previous approach on an experimental bench by using infrared thermography measurements on the external faces of the channel. The temperature observations are used then within an inverse approach in order to recover the external heat transfer coefficient (air) over the external faces (parameter estimation problem) as well as the internal boundary conditions (function estimation inverse problem). The interest of such an inverse approach, coupling a model and measurements, is to avoid introducing an intrusive instrumentation at this scale. It allows to validate a semi-analytical heat transfer model that takes into account conduction and advection in the fluid as well as conduction in the solid (conjugate heat transfer) without the use of any internal heat transfer coefficient.

Fluid temperature distribution inside a flat mini-channel: Semi-analytical wall transfer functions and estimation from temperatures of external faces

Modelling fluid flow and heat transfer inside a mini- or micro-channel constitutes a challenge because it requires taking into account many effects that do not occur in traditional macrostructured systems. A semi-analytical heat transfer model that takes into account conduction and advection in the fluid as well as conduction in the solid walls (conjugate heat transfer) of a flat mini-channel is first derived and verified. It is based on Fourier transforms of the temperature and normal flux in the direction of the Poiseuille flow. It allows to relate its bulk temperature Tb(x) to external surface sources by two transfer functions without the use of any internal heat transfer coefficient distribution, whatever the location of these sources. The second part of the paper is devoted to the use of this model in an inverse way, that is to retrieve the Tb(x) distribution starting from the additional observation of the noised synthetic temperature profiles over the external faces of both walls of the channel. Estimations of the average velocity and of the external heat transfer coefficient are first implemented. The temperature and flux distributions over the internal faces of the walls are estimated by an inverse method then, before a reconstruction of the internal bulk temperature profile.

The Measurement of Full-Surface Internal Heat Transfer Coefficients for Turbine Airfoils Using a Nondestructive Thermal Inertia Technique

A new method has been developed and demonstrated for the non-destructive, quantitative assessment of internal heat transfer coefficient distributions of cooled metallic turbine airfoils. The technique employs the acquisition of full-surface external surface temperature data in response to a thermal transient induced by internal heating/cooling, in conjunction with knowledge of the part wall thickness and geometry, material properties, and internal fluid temperatures. An imaging Infrared camera system is used to record the complete time history of the external surface temperature response during a transient initiated by the introduction of a convecting fluid through the cooling circuit of the part. The transient data obtained is combined with the cooling fluid network model to provide the boundary conditions for a finite element model representing the complete part geometry. A simple 1-D lumped thermal capacitance model for each local wall position is used to provide a first estimate of the internal surface heat transfer coefficient distribution. A 3-D inverse transient conduction model of the part is then executed with updated internal heat transfer coefficients until convergence is reached with the experimentally measured external wall temperatures as a function of time. This new technique makes possible the accurate quantification of full-surface internal heat transfer coefficient distributions for prototype and production metallic airfoils in a totally nondestructive and non-intrusive manner. The technique is equally applicable to other material types and other cooled/heated components.