# Simulation of Conjugate Heat Transfer in Thermal Processes with Open Source CFD

^{*}

## Abstract

**:**

## 1. Introduction

^{®}for fundamental problems. However, many researchers and users in the industry see a demand for constant validation and verification of these open-source CFD methods that are in constant development. Only for turbulent single phase flows without heat transfer several authors have published validation studies in recent years. In several publications, turbulence models in OpenFOAM

^{®}were validated for the simulation of flows over bluff bodies [10,11,12].

^{®}version 6-dev for conjugate heat transfer problems. The test cases had a growing complexity starting from a simple steady state problem over unsteady heat transfer to more realistic engineering applications. The applications were a fin effectiveness study, external convection at pipes, internal pipe heat transfer, and as a final example a simplified shell-and-tube heat exchanger. The validity of the techniques was shown for each test case by comparing the simulation results with experimental and analytical data available in the literature.

## 2. Physical Modeling

^{®}(Open Source Field Operation and Manipulation). OpenFOAM

^{®}is an object-oriented software library programmed in C++ and designed for the numerical solution of differential equations from continuum mechanics, as demonstrated by Jasak and Weller [14]. OpenFOAM

^{®}is distributed with a variety of predesigned solvers. Usually, the finite volume method (FVM) is applied. Here, the edition OF6-dev was chosen with the solvers chtMultiRegionFoam and buoyantPimpleFoam. For the fluid regions, the solution algorithm in both solvers was identical. In the following, the governing equations are briefly described.

## 3. Results

#### 3.1. Investigation of Fin Effectiveness

^{®}solver chtMultiRegionFoam was applied to simulate fin effectiveness.

#### 3.1.1. Numerical Set-Up of the Fin Test Case

#### 3.1.2. Results of the Fin Test Case

#### 3.2. External Heat Transfer at Pipes with RANS Approach

#### 3.2.1. Numerical Set-Up of External Pipe Test Case

#### 3.2.2. Results of the External Pipe Test Case

#### 3.3. Turbulent Heat Transfer of Internal Pipe Flow Using LES

^{®}were validated for steady state and transient heat transfer problems. However, in both cases, the heat transfer limitation was at the low Prandtl number flow around a certain geometry. This could be calculated with standard RANS models relatively easily. More difficult was the prediction of heat transfer of internal flows in process equipment with moderate or high Prandtl numbers. This section shows that the turbulence modeling techniques in OpenFOAM

^{®}can be applied for such problem with equal success. As a reference case, a simple turbulent pipe flow with heat transfer was chosen.

#### 3.3.1. Numerical Set-Up of the Internal Pipe Flow Test Case

#### 3.3.2. Results of the Internal Pipe Flow Test Case

#### Mean Velocity Profiles and Root Mean Square Fluctuations

#### Mean Temperature Profiles

#### Heat Transfer Analysis

#### 3.4. Shell-And-Tube Heat Exchanger Test Case

^{®}. Automated scripts are provided for the whole meshing, pre-processing and simulation steps. The example is shown here to demonstrate that the techniques described above can be applied to real process equipment and can be successfully used in the industry. The shell-and-tube heat exchanger was operated in counter-flow configuration. For reasons of simplicity, water was considered for both fluids. The mass flow for both fluids was the same and the thermodynamic properties were assumed constant. The material properties of the heat exchanger itself corresponded to aluminum. The parameters of the heat exchanger and the flow data are given in Table 6.

#### 3.4.1. Numerical Set-Up of the Shell-and-Tube Heat Exchanger Test Case

#### 3.4.2. Results of the Shell-and-Tube Heat Exchanger Test Case

## 4. Conclusions

^{®}framework. First, the fin effectiveness of a regular straight fin was investigated using steady state simulations and the global heat transfer was analyzed. Then, external pipe flow was simulated in an unsteady fashion and local heat transfer phenomena were calculated. Thus, it was shown that it is not only possible to predict global heat transfer for steady state cases, but local phenomena at unsteady cases can also be simulated with a reasonable accuracy that is sufficient for many engineering purposes. After that, a turbulent internal pipe flow was simulated for different Reynolds and Prandtl numbers to demonstrate that highly accurate heat transfer simulations are feasible with these techniques. In the end, an example of a simplified heat exchanger was simulated and the application of the above demonstrated methods to plant scale engineering problems was demonstrated.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CHT | conjugate heat transfer |

LES | large-eddy simulation |

OpenFOAM | Open Source Field Operation and Manipulation |

Navier- RANS | Reynolds-Averaged Navier–Stokes |

STL | stereo-lithography |

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**Figure 2.**(

**left**) Numerical grid in fluid and solid block; and (

**right**) temperature contours along solid and fluid patches as well in a cross section for Simulation Case (b) L = 0.04 m.

**Figure 3.**Temperature profiles along the fin for different simulation cases compared to theory; solid lines and symbols: theory; dashed lines: simulation data.

**Figure 4.**Computational grid of the water, copper and air region: (

**left**) whole computational domain; and (

**right**) mesh in the vicinity of the pipe.

**Figure 5.**Temperature contours in a cross section: (

**left**) free convection; and (

**right**) forced convection.

**Figure 7.**Schematic representation of the computational domain. The coordinate system is given as $r,x,\omega $.

**Figure 8.**Contours of the flow and temperature field at an instantaneous time step, $Re=8000$, $Pr=7$: (

**top**) temperature; and (

**bottom**) magnitude of velocity.

**Figure 13.**Computational grid of the shell-and-tube heat exchanger that was generated with snappyHexMesh: (

**left**) cut through all regions (shell, tube, solid) at middle section; and (

**right**) cuts in axial direction for each region at a different axial position.

**Figure 14.**Temperature profiles along the fin for different simulation cases compared to theory; solid lines and symbols: theory; dashed lines: simulation data.

Parameter | Variable | Unit | Value |
---|---|---|---|

fin length | L | m | (a) $0.02$; (b) $0.04$; (c) $0.06$; (d) $0.08$ |

fin thickness | B | m | $0.002$ |

fin height | H | m | $0.05$ |

fin temperature at base | ${T}_{base}$ | K | 363 |

density of steel | ${\varrho}_{s}$ | kg/m${}^{3}$ | 7850 |

heat capacity of steel | ${c}_{s}$ | J/(kgK) | 645 |

thermodynamic conductivity of steel | ${k}_{s}$ | W/(mK) | 40 |

size of computational domain | $X,Y,Z$ | m | $0.3,0.1,0.1$ |

air temperature at inlet | ${T}_{a}$ | K | 300 |

air pressure at outlet | ${p}_{a}$ | bar | 1 |

air Prandtl number | $Pr$ | - | $0.7$ |

air turbulent Prandtl number | $P{r}_{t}$ | - | $0.9$ |

air inlet velocity | ${u}_{a}$ | m/s | 10 |

air Reynolds number | $R{e}_{a}=\frac{{\varrho}_{a}{u}_{a}H}{{\eta}_{a}}$ | - | 32,262 |

Case | (a) | (b) | (c) | (d) |
---|---|---|---|---|

L | $0.02$ m | $0.04$ m | $0.06$ m | $0.08$ m |

${\eta}_{th}$ | 0.800 | 0.545 | 0.385 | 0.294 |

${\eta}_{sim}$ | 0.814 | 0.552 | 0.389 | 0.295 |

Parameter | Variable | Unit | Value |
---|---|---|---|

pipe inner diameter | ${d}_{i}$ | m | $0.0283$ |

pipe outer diameter | ${d}_{o}$ | m | $0.0442$ |

pipe length | ${L}_{p}$ | m | $0.0884$ |

size of air domain | $X,Y,Z$ | m | $0.8,1.4,0.0884$ |

natural convection reference case: | |||

water temperature | ${T}_{w}$ | K | 315 |

water velocity | ${u}_{w}$ | m/s | 5 |

air temperature | ${T}_{a}$ | K | 300 |

air Prandtl number | $P{r}_{a}$ | - | $0.7$ |

Raleigh number | $Ra$ | - | $0.86\times {10}^{5}$ |

forced convection reference case: | |||

water temperature | ${T}_{w}$ | K | 330 |

water velocity | ${u}_{w}$ | m/s | 5 |

air temperature | ${T}_{a}$ | K | 300 |

air Prandtl number | $P{r}_{a}$ | - | $0.7$ |

air velocity | ${u}_{a}$ | m/s | $0.0489$ |

Reynolds number | $R{e}_{D}$ | - | 130 |

$\mathit{Re}=({\mathit{U}}_{\mathit{m}}{\mathit{d}}_{\mathit{h}})/\mathit{\nu}$ | 8000 | 8000 | 8000 | 16,000 |

Pr | 5 | 7 | 9 | 7 |

${\mathit{y}}_{\mathbf{1}}^{+};\Delta {\mathit{r}}_{\mathit{min}}^{+}$ | 0.05 | 0.051 | 0.052 | 0.09 |

$\Delta {\mathit{\omega}}_{\mathit{max}}^{+}$ | 9.2 | 9.1 | 9.2 | 16.2 |

$\Delta {\mathit{x}}^{+}$ | 18.5 | 18.2 | 18.5 | 32.5 |

${\mathit{Re}}_{\mathit{\tau}}=({\mathit{U}}_{\mathit{\tau}}{\mathit{d}}_{\mathit{h}})/\mathit{\nu}$ | 520 | 509 | 514 | 909 |

$\mathit{Re}=({\mathit{U}}_{\mathit{m}}{\mathit{d}}_{\mathit{h}})/\mathit{\nu}$ | 8000 | 8000 | 8000 | 16,000 |

Pr | 5 | 7 | 9 | 7 |

${\mathit{Nu}}_{\mathit{simulation}}$ | 59.3 | 69.3 | 73.5 | 116.0 |

${\mathit{Nu}}_{\mathit{Gnielinski}}$ | 61.9 | 70.2 | 77.0 | 128.0 |

Parameter | Variable | Unit | Value |
---|---|---|---|

mass flow rate | $\dot{m}$ | kg/s | $0.05$ |

hot inlet temperature | ${\theta}_{1}^{\prime}$ | K | 600 |

cold inlet temperature | ${\theta}_{2}^{\prime}$ | K | 300 |

heat capacity | c | J/(kgK) | 4181 |

Prandtl number | $Pr$ | - | $6.62$ |

heat exchanger parameters | |||

number of pipes | n | - | 5 |

length of pipes | ${L}_{p}$ | m | $0.174$ |

inner diameter of pipes | ${D}_{p}$ | m | $0.012$ |

outer diameter of pipes | $P{r}_{a}$ | - | $0.02$ |

total heat transfer area | ${A}_{HTX}$ | m${}^{2}$ | $0.044$ |

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**MDPI and ACS Style**

Renze, P.; Akermann, K.
Simulation of Conjugate Heat Transfer in Thermal Processes with Open Source CFD. *ChemEngineering* **2019**, *3*, 59.
https://doi.org/10.3390/chemengineering3020059

**AMA Style**

Renze P, Akermann K.
Simulation of Conjugate Heat Transfer in Thermal Processes with Open Source CFD. *ChemEngineering*. 2019; 3(2):59.
https://doi.org/10.3390/chemengineering3020059

**Chicago/Turabian Style**

Renze, Peter, and Kevin Akermann.
2019. "Simulation of Conjugate Heat Transfer in Thermal Processes with Open Source CFD" *ChemEngineering* 3, no. 2: 59.
https://doi.org/10.3390/chemengineering3020059