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Laminar Flow and Heat Transfer in U-Bend CFD Simulation

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This simulation is validated according to the results of the article “Laminar flow and heat transfer in U-bends: The effect of secondary flows in ducts with partial and full curvature”.

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Paper Description

The present problem simulates the fluid flow inside a tube with a U-shaped bend. The simulation was performed and validated according to the information and results of the reference article “Laminar flow and heat transfer in U-bends: The effect of secondary flows in ducts with partial and full curvature“. The fluid defined inside the tube was therminol; Its properties include density equal to 793.9 kg.m-3, specific heat capacity equal to 2315, thermal conductivity equal to 0.116 Wm-1.K-1 and viscosity equal to 0.00173 kg.m-1.s-1.

The simulation has been done in different Reynolds numbers according to the paper. The present simulation has been done in Reynolds number of 1000, which according to the formula related to Reynolds number in the paper, the inlet velocity in the pipe is equal to 0.21791 m.s-1. In this model, the thermal boundary condition on the pipe wall is used; So that a constant heat flux of 1156 W.m-2.K-1 is defined on the pipe wall. The purpose of the present problem is to investigate the behavior of the flowing fluid in the pipe and its heat transfer in the passage through the pipe bend.

U-Bend Pipe Geometry & Mesh

The present 3-D model is drawn using Design Modeler software. This model consists of a tube consisting of a bend. This bend is in the form of two knees connected to each other. The diameter of the pipe is 0.01m and the radius of curvature of each elbow is 0.015m. The following figure shows a view of the geometry.

laminar flow

The meshing of the model has been done using ANSYS Meshing software and the mesh type is structured. The element number is 2268000. The following figure shows the mesh.

laminar flow

Laminar Flow CFD Simulation

To simulate the present model, several assumptions are considered:

  • We perform a pressure-based solver.
  • The simulation is steady.
  • The gravity effect on the fluid is ignored.

A summary of the defining steps of the problem and its solution is given in the following table:

Viscous model Laminar
Energy on
Boundary conditions
Inlet Velocity inlet
velocity magnitude 0.21791 m.s-1
temperature 408 K
Outlet Pressure outlet
gauge pressure 0 Pascal
Walls Wall
wall motion stationary wall
heat flux 1156 W.m-2.K-1
Solution Methods
Pressure-velocity coupling   SIMPLE
Spatial discretization pressure second order
momentum second order upwind
energy second order upwind
Initialization method   Hybrid

Paper Validation

At the end of the solution process, the results are compared and validated with the results of the reference article. First, the results related to the amount of fluid temperature on the inner wall of the pipe and its bending are validated. This validation is performed according to the diagram in Figure 14-b of the article. For this purpose, a graph of temperature changes in terms of position for the inner wall of the pipe is drawn. Temperature and position are both dimensionless, and the related formulas is presented in the article. The following figure shows a graph of dimensionless temperature changes in terms of dimensionless position.

laminar flow

Then the Nusselt number is investigated in different sections of pipe bending. For this purpose, the value of Nusselt number according to the formula in the article, in five different sections (P1, P2, P3, P4, and P5) has been obtained and its ratio to the value of Nusselt number in section P1 has been calculated. These resulting numbers are validated with the values of the dimensionless Nusselt number in the mentioned sections according to the diagram of Figure 19-b. The following table shows the values of the Nusselt number ratio at different sections of the pipe bend.

  Present work Reference work
[email protected] / [email protected] 1 1
[email protected] / [email protected] 5.826 5.247
[email protected] / [email protected] 7.669 8.028
[email protected]4 / [email protected] 6.197 6.737
[email protected] / [email protected] 7.649 8.884


At the end of the simulation, two-dimensional and three-dimensional contours related to pressure, velocity, and temperature, as well as two-dimensional and three-dimensional velocity vectors are obtained. The desired two-dimensional section is considered in the Y-Z section.

All files, including Geometry, Mesh, Case & Data, are available in Simulation File. By the way, Training File presents how to solve the problem and extract all desired results.


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