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Estimation of local heat flux with CFD and enhanced conjugate gradient method for laminar and turbulent flow in a helical coil tube heat exchanger

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Abstract

The heat transfer analysis in a helical coil tube heat exchanger is challenging due to the complex flow field developed by the tube curvature. In this paper, estimation of uneven local heat flux is carried out at the fluid–solid interface in a helical coil tube heat exchanger for laminar and turbulent flow in two different ways. First, the governing continuity, momentum, and energy equations of working fluid for laminar and turbulent flow are solved to determine the heat flux at the fluid–solid interface with commercial CFD software Ansys Fluent. This heat flux is then used as a boundary condition to solve the governing equation of heat conduction in tube thickness by finite volume discretization method to obtain temperature field at the outer tube surface. The heat flux is now considered unknown and estimated with the newly developed enhanced conjugate gradient method (ECGM). ECGM has been designed to enhance the performance of traditional CGM by coupling with the stochastic Jaya algorithm. Ethylene glycol and water has been selected as a working fluid for laminar and turbulent flow, respectively. The average percentage error with ECGM in the estimation of heat flux profile obtained by CFD software in laminar flow and turbulent flow is 0.32 and 0.18 respectively. Even after adding random errors in the simulated temperature field, the ECGM algorithm produces a reasonable and stable solution.

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Abbreviations

APE:

Average percentage error

De :

Dean number

dG :

Direction of descent

E:

Total specific mechanical energy

\(\overrightarrow{{\mathrm{f}}_{\mathrm{c}}}\) :

Centrifugal force per unit mass (N/kg)

\(\overrightarrow{\mathrm{g}}\) :

Gravitational force per unit mass(N/kg)

H :

Coil pitch (m)

h :

Overall heat transfer coefficient (W/m2K)

k:

Thermal conductivity (W/mK)

J:

Objective function

M :

Number of sensors

Nu :

Nusselt number

p :

Fluid pressure (N/m2)

Pr:

Prandlt number

q :

Heat flux (W/m2)

R :

Coil radius (m)

\(\overrightarrow{\mathrm{R}}\) :

Position vector

r :

Radial coordinate (m)

Re :

Reynolds number

T :

Temperature (K)

U :

Fluid velocity (m/s)

\(\overrightarrow{V}\) :

Velocity vector

x:

Axial coordinate

a:

Actual

cal:

Calculated

e:

Estimated

eff:

Effective

env:

Environment

ext:

External

int:

Internal

m :

Measured

s :

Solid

t :

Tube

w:

Wall

G:

Number of iteration

‘:

New value

\({\alpha }\) :

Helix angle(rad)

β:

Search step size

\(\updelta\) :

Curvature ratio

δ(.):

Dirac delta function

\(\Delta\) :

Small number

γ:

Conjugation coefficient

λ:

Lagrange multiplier

\(\upmu\) :

Fluid viscosity (Ns/m2)

\(\nabla\) :

Gradient

ω:

Angular velocity (rad/s)

\(\uprho\) :

Fluid density (kg/m3)

\(\upsigma\) :

Standard deviation

\(\overline{\overline{t} }\) :

Stress tensor

\(\uptheta\) :

Angular coordinate (rad

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Acknowledgements

The author acknowledges the grant (EMR/2016/007821/CME) of Science and Engineering Research Board, Department of Science and Technology, Government of India and greatly appreciate the financial contribution towards this research.

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  1. Department of Mechanical and Aero-space Engineering, Institute of Infrastructure Technology Research and Management, Ahmedabad-380026, India

    Sanil Shah & Ajit Kumar Parwani

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  1. Sanil Shah
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Correspondence to Ajit Kumar Parwani.

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Shah, S., Parwani, A.K. Estimation of local heat flux with CFD and enhanced conjugate gradient method for laminar and turbulent flow in a helical coil tube heat exchanger. Heat Mass Transfer 58, 917–931 (2022). https://doi.org/10.1007/s00231-021-03138-2

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