scholarly journals Estimation of local heat flux for turbulent flow in a helical coil tube by conjugate gradient method

2021 ◽  
Vol 2116 (1) ◽  
pp. 012108
Author(s):  
S Shah ◽  
A K Parwani
Keyword(s):  
Heat Flux ◽  
Turbulent Flow ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Local Heat ◽  
Helical Coil ◽  
Tube Heat Exchanger ◽  
Solid Interface ◽  
Local Heat Flux

Abstract Estimation of local heat flux is challenging in a helical coil tube heat exchanger due to the complex flow field developed by tube curvature. The heat flux has uneven distribution in the angular direction of the tube cross-section. The current research aims to estimate the local heat flux at the fluid-solid interface for the turbulent flow of water in a helical coil tube by solving the inverse heat conduction problem (IHCP). Conjugate gradient method (CGM) with an adjoint problem is used as an inverse algorithm. First, the commercial CFD software ANSYS FLUENT is used for solving the governing equations of continuity, momentum, and energy for turbulent flow to obtain the heat flux at the fluid-solid interface. This heat flux is used to determine the temperature distribution at the outer surface of the tube. The heat flux is then considered unknown and it is estimated by CGM algorithm with the developed in-house code in MATLAB. The result shows that the estimation of heat flux by CGM is very accurate.

Thermal Load Determination in Dry Machining Through a Fixed Identifiability Conjugate Gradient Method

2017 ◽  
Author(s):  
Patric Figueiredo ◽  
Marc Deppermann ◽  
Reinhold Kneer
Keyword(s):  
Heat Flux ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Work Piece ◽  
Unknown Boundary ◽  
Dry Machining ◽  
Machining Processes ◽  
Step Size ◽  
The Difference

To estimate the heat flowing into the workpiece in machining processes, an inverse algorithm based on the Conjugate Gradient Method (CGM) is proposed to estimate the unknown boundary heat flux. Outgoing from infrared temperature measurements the heat flowing into the work-piece for an orthogonal cut can be estimated. To increase convergence of the estimated solution, a sensitivity analysis of the direct problem is performed to determine the identifiability of the boundary heat flux on the measurement site. The proposed Fixed Identifiability Conjugate Gradient Method (FIX-CGM) computes a step size function considering the identifiability of the unknown boundary condition to minimize the objective function. In contrast, the CGM computes a scalar step size by integrating the difference between measured and calculated temperature over time. Results show that applying the FIX-CGM for a benchmark case with a step heat flux faster convergence, better accuracy and less sensitivity to noise are achieved.

Estimation of Unknown Boundary Heat Flux in Laminar Circular Pipe Flow Using Functional Optimization Approach: Effects of Reynolds Number

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Peng Ding ◽  
Wen-Quan Tao
Keyword(s):  
Heat Flux ◽  
Reynolds Number ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Outer Boundary ◽  
Circular Pipe ◽  
Unknown Boundary ◽  
Optimization Approach ◽  
Inverse Algorithm

An inverse forced convection problem was studied in this paper. The unknown space-dependent heat flux at the outer boundary of a circular pipe was identified from the temperature measurements within the flow using the algorithm based on an improved conjugate gradient method, which is a combination of the modified inverse algorithm proposed by Ozisik et al. (Huang and Ozisik, 1992, “Inverse Problem of Determining Unknown Wall Heat Flux in Laminar Flow Through a Parallel Plate Duct,” Numer. Heat Transfer, Part A 21, pp. 2615–2618) and the general inverse algorithm based on the conjugate gradient method. The effects of the convection intensity, the number of thermocouples, the location of the thermocouples, and the measurement error on the performance of the modified inverse algorithm method and the improved inverse algorithm were studied thoroughly through three examples. It is shown that the improved inverse algorithm can greatly improve the solution accuracy in the entire computation domain. The accuracy and stability of both the modified inverse algorithm method and the improved inverse algorithm are strongly influenced by the Reynolds number and the shape of the unknown heat flux. Those functions, which contain more high-frequency components of Fourier series, are more sensitive to the increase in the Reynolds number.

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