# Multiphase Conjugate Heat Transfer Analyses on the Assembly Situation of Rotary Shaft Seals

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Governing Equations

**U**, the time t and the fluid density $\rho $ describe the conservation of mass. This equation ensures that the mass entering a system is equal to the mass leaving the system and the accumulation of mass within the system. The first part, the time derivative, describes the loss of mass in the system and the second part, the divergence term, describes the difference between the mass entering and the mass leaving the system. Since the air is assumed to be incompressible, the density is constant and the continuity equation can be simplified to [21]:

^{2}is the gravitational acceleration [23].

#### 2.2. Modeling

#### 2.2.1. Computational Domain

#### 2.2.2. Material Data

#### 2.2.3. Boundary and Initial Conditions

#### 2.2.4. Solver Settings

#### 2.3. Case Studies

#### 2.3.1. Variants with Additional Elements

- The oil fill level ${h}_{oil}$ in the domain oil chamber bearing;
- The frictional torque between the bearing and the shaft.

#### 2.3.2. Variants of the Shaft Design

#### 2.4. Experiments

## 3. Results

#### 3.1. Phase Interaction

#### 3.2. Temperature Contour Plot

## 4. Discussion

- ϑ
_{Max}at RSS-shaft: These were the maximum values of the temperature in the contact area between the sealing ring and the rotating shaft; see Figure 16a. - ϑ
_{Max}at RSS-environment: These were the maximum values of the temperature on one of the interfaces between the sealing ring and the environment; see Figure 16a.

#### 4.1. Variants with Additional Elements

#### 4.2. Shaft Design

#### 4.3. Accuracy of All Variants

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Symbol | Description | Unit |

$c$ | specific heat capacity | J/(kg·K) |

${C}_{m}$ | transport variable, volume-of-fluid (VOF) method | - |

${C}_{air}$ | transport variable for the air phase, VOF | - |

${C}_{oil}$ | transport variable for the oil phase, VOF | - |

$d$ | shaft diameter | mm |

$f$ | heat partition factor | - |

g | gravitational acceleration | m/s^{2} |

$h$ | enthalpy | J/kg |

${h}_{in}$ | incoming enthalpy | J/kg |

${h}_{out}$ | outgoing enthalpy | J/kg |

${h}_{tot}$ | total enthalpy | J/kg |

${h}_{oil}$ | oil fill level in the domain oil chamber bearing | mm |

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

$M$ | molar mass | kg/mol |

${M}_{fric}$ | frictional torque | N·m |

$n$ | rotational shaft speed | rev/min |

$p$ | pressure | Pa |

${p}_{air}$ | current air pressure | Pa |

$\dot{q}$ | heat flux density | kg/s^{3} |

$\dot{Q}$ | heat flux | W |

${\dot{Q}}_{fric}$ | frictional heat flux | W |

${\dot{Q}}_{fricseal}$ | frictional heat flux applied to the seal | W |

${\dot{Q}}_{fricshaft}$ | frictional heat flux applied to the shaft | W |

$R$ | universal gas constant | J/(mol·K) |

${\mathit{S}}_{M}$ | optional source term in the momentum equations | kg/(s^{2}·m^{3}) |

${\mathit{S}}_{buoy}$ | source term for buoyancy | kg/(s^{2}·m^{3}) |

${\mathit{S}}_{heat}$ | volumetric heat source | kg/(s^{3}·m^{2}) |

$t$ | time | s |

${T}_{air}$ | current air temperature | K |

$\vartheta $ | temperature | °C |

${\vartheta}_{air}$ | air temperature | °C |

${\vartheta}_{oil}$ | current oil temperature | °C |

${\vartheta}_{init}$ | initial temperature | °C |

${\vartheta}_{fluid}$ | fluid temperature | °C |

${\vartheta}_{wall}$ | wall temperature | °C |

$\mathbf{U}$ | flow velocity vector field | m/s |

${v}_{U}$ | circumferential velocity | m/s |

${V}_{A}$ | material parameter in the Vogel equation | Pa·s |

${V}_{B}$ | material parameter in the Vogel equation | K |

${V}_{C}$ | Vogel temperature | K |

$\dot{W}$ | working current | W |

$\alpha $ | heat transfer coefficient | W·K/m^{2} |

${\mathsf{\eta}}_{air}$ | dynamic viscosity of the air | Pa·s |

${\mathsf{\eta}}_{oil}$ | dynamic viscosity of the oil | Pa·s |

$\lambda $ | thermal conductivity | W/(m·K) |

${\lambda}_{air}$ | thermal conductivity of the air | W/(m·K) |

${\lambda}_{seal}$ | thermal conductivity of the sealing ring material | W/(m·K) |

${\lambda}_{shaft}$ | thermal conductivity of the shaft material | W/(m·K) |

$\rho $ | density | kg/m^{3} |

${\rho}_{air}$ | air density | kg/m^{3} |

${\rho}_{oil}$ | oil density | kg/m^{3} |

$\mathsf{\tau}$ | shear-stress tensor | Pa |

## References

- Bauer, F. Federvorgespannte-Elastomer-Radial-Wellendichtungen; Springer Fachmedien Wiesbaden: Wiesbaden, Germany, 2021; ISBN 978-3-658-32921-1. [Google Scholar]
- ISO 6194-1; Rotary Shaft Lip-Type Seals Incorporating Elastomeric Sealing Elements—Part 1: Nominal Dimensions and Tolerances. International Organization for Standardization, Beuth Verlag GmbH: Berlin, Germany, 2007.
- DIN 3760; Rotary Shaft Lip Type Seals. Norelem: Markgröningen, Germany, 1996.
- Kammüller, M. Zur Abdichtwirkung von Radial-Wellendichtringen; Berichte aus dem Institut für Maschinenelemente und Gestaltungslehre; Inst. für Maschinenelemente und Gestaltungslehre: Stuttgart, Germany, 1986; ISBN 978-3-921920-19-0. [Google Scholar]
- Kawahara, Y.; Abe, M.; Hirabayashi, H. An Analysis of Sealing Characteristics of Oil Seals. A S L E Trans.
**1980**, 23, 93–102. [Google Scholar] [CrossRef] - Leeuwen, H.J.; Wolfert, M.A. The Sealing and Lubrication Principles of Plain Radial Lip Seals: An Experimental Study of Local Tangential Deformations and Film Thickness. Tribol. Ser.
**1997**, 32, 219–232. [Google Scholar] - Feldmeth, S.; Bauer, F.; Haas, W. Abschätzverfahren Für Die Kontakttemperatur Bei Radial-Wellendichtungen. In Sealing Technology—Indispensable; Fachverband Fluidtechnik, Universität Stuttgart, Eds.; Fachverband Fluidtechnik im VDMA e.V: Frankfurt am Main, Germany, 2016; ISBN 978-3-8163-0684-9. [Google Scholar]
- Feldmeth, S.; Bauer, F.; Haas, W. Simulation of the Temperature Field in Radial Lip Seals Using a Multiscale Approach. In Seminar: Best Practices for Thermal Analyses and Heat Transfer; NAFEMS Deutschland, Österreich, Schweiz GmbH, Eds.; NAFEMS Deutschland, Österreich, Schweiz GmbH: Bernau am Chiemsee, Germany, 2014. [Google Scholar]
- Feldmeth, S.; Braeurer, P.; Franke, J.; Bauer, F. Temperature Measurement in the Sealing Contact—Sealing Systems Are Getting Smarter. In XXII Dichtungskolloquium; Riedl, A., Ed.; Vulkan Verlag GmbH: Münster, Germany, 2021. [Google Scholar]
- Brink, R.V. The Heat Load of an Oil Seal. In Proceedings of the 6th International Conference on Fluid Sealing, München, Germany, 27 February–2 March 1973. Paper C1. [Google Scholar]
- Upper, G. Dichtlippentemperatur von Radial-Wellendichtringen. In Theoretische Und Experimentelle Untersuchung; University of Karlsruhe: Karlsruhe, Germany, 1968. [Google Scholar]
- Universität Stuttgart InsECT Calculationtool. Version Beta-18.10.08. Available online: https://insect.ima.uni-stuttgart.de (accessed on 20 July 2023).
- Feldmeth, S.; Bauer, F.; Haas, W. Abschätzung der Kontakttemperatur bei Radial-Wellendichtungen mit der selbstentwickelten Open-Source-Software InsECT. In Proceedings of the SMK 2016, Schweizer Maschinenelemente Kolloquium, Rapperswil, Switzerland, 22–23 November 2016; TUDpress: Dresden, Germany, 2016. [Google Scholar]
- Grün, J.; Gohs, M.; Bauer, F. Multiscale Structural Mechanics of Rotary Shaft Seals: Numerical Studies and Visual Experiments. Lubricants
**2023**, 11, 234. [Google Scholar] [CrossRef] - Grün, J.; Feldmeth, S.; Bauer, F. Computational Fluid Dynamics of the Lubricant Flow in the Sealing Gap of Rotary Shaft Seals. In Proceedings of the M2D2022—9th International Conference on Mechanics and Materials in Desig, Funchal, Portugal, 26–30 June 2022; Gomes, J.F.S., Meguid, S.A., Eds.; pp. 1035–1050. [Google Scholar]
- Stakenborg, M.J.L. On the Sealing Mechanism of Radial Lip Seals. Tribol. Int.
**1988**, 21, 335–340. [Google Scholar] [CrossRef] - Wenk, J.F.; Scott Stephens, L.; Lattime, S.B.; Weatherly, D. A Multi-Scale Finite Element Contact Model Using Measured Surface Roughness for a Radial Lip Seal. Tribol. Int.
**2016**, 97, 288–301. [Google Scholar] [CrossRef] - Grün, J.; Feldmeth, S.; Bauer, F. The Sealing Mechanism of Radial Lip Seals: A Numerical Study of the Tangential Distortion of the Sealing Edge. Tribol. Mater.
**2022**, 1, 165–166. [Google Scholar] [CrossRef] - Salant, R.F. Soft Elastohydrodynamic Analysis of Rotary Lip Seals, Proceedings of the Institution of Mechanical Engineers. Part C J. Mech. Eng. Sci.
**2010**, 224, 2637–2647. [Google Scholar] [CrossRef] - Feldmeth, S.; Bauer, F.; Haas, W. Untersuchung Des Einflusses Verschiedener Versuchskonfigurationen Auf Die Dichtspalttemperatur Bei Radial-Wellendichtungen Mittels CHT-Simulation. In NAFEMS Magazin, Ausgabe 29; NAFEMS Deutschland, Österreich, Schweiz GmbH: Bernau am Chiemsee, Germany, 2014. [Google Scholar]
- Schwarze, R. CFD-Modellierung: Grundlagen und Anwendungen bei Strömungsprozessen; Springer Vieweg: Berlin/Heidelberg, Germany, 2013; ISBN 978-3-642-24377-6. [Google Scholar]
- Tu, J.; Yeoh, G.H.; Liu, C. Governing Equations for CFD—Fundamentals. In Computational Fluid Dynamics; Elsevier: Amsterdam, The Netherlands, 2008; pp. 65–125. ISBN 978-0-7506-8563-4. [Google Scholar]
- ANSYS CFX-Solver Theory Guide; ANSYS, Inc.: Canonsburg, PA, USA, 2009.
- VDI. VDI-Wärmeatlas, 11th ed.; Springer: Berlin/Heidelberg, Germany, 2013; ISBN 978-3-642-19980-6. [Google Scholar]
- Ungarish, M. Hydrodynamics of Suspensions: Fundamentals of Centrifugal and Gravity Separation; Springer: Berlin, Germany; New York, NY, USA, 1993; ISBN 978-3-540-54762-4. [Google Scholar]
- Gidaspow, D. Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions; Academic Press: Boston, MA, USA, 1994; ISBN 978-0-12-282470-8. [Google Scholar]
- Freudenberg FST GmbH Produktdatenblatt Radialwellendichtungen BAUM 75 FKM 585 Bauform. In eCatalog Simmerringe Und Rotationsdichtungen. 2020. Available online: https://Api.Fst.Com/Assets/Productdatasheet_de_baum.Pdf (accessed on 8 July 2023).
- IBC Wälzlager GmbH. Deutschland IBC Hochpräzisions-Wälzlager, High Precision Bearings; Katalog der IBC Wälzlager GmbH: Solms, Germany, 2010; p. 186. [Google Scholar]
- DIN German Institute for Standardization DIN EN ISO 3838: Determination of Density or Relative Density; Beuth Verlag GmbH: Berlin, Germany, 2004.
- Feldmeth, S.; Olbrich, C.; Bauer, F. Influence of Lubricants on the Thermal Behaviour of Rotary Shaft Seals. In Sealing Technology—Old School and Cutting Edge; Fachverband Fluidtechnik, Universität Stuttgart, Eds.; Fachverband Fluidtechnik im VDMA e.V: Frankfurt am Main, Germany, 2022. [Google Scholar]
- Laukotka, E. FVA-Heft 660. In Referenzöle—Datensammlung; Forschungsvereinigung Antriebstechnik: Frankfurt, Germany, 2007. [Google Scholar]
- DIN 53017; Viscometry: Determination of the Temperature Coefficient of Viscosity. Beuth Verlag GmbH: Berlin, Germany, 1993.
- Fulcher, G.S. Analysis of recent measurements of the viscosity of glasses. J. Am. Ceram. Soc.
**1925**, 8, 339–355. [Google Scholar] [CrossRef] - Menter, F.R. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications. AIAA J.
**1993**, 32, 1598–1605. [Google Scholar] [CrossRef] - Blazek, J. Computational Fluid Dynamics: Principles and Applications, 2nd ed.; Elsevier: Amsterdam, The Netherlands; San Diego, CA, USA, 2005; ISBN 978-0-08-044506-9. [Google Scholar]
- Katopodes, N.D. Turbulent Flow. In Free-Surface Flow; Elsevier: Amsterdam, The Netherlands; San Diego, CA, USA, 2019; pp. 566–650. ISBN 978-0-12-815489-2. [Google Scholar]
- Ansys CFX-Solver Modeling Guide; Release 2021 R2 2021; ANSYS, Inc.: Canonsburg, PA, USA, 2021.
- Kunstfeld, T.; Haas, W. Dichtungsumfeld: Einfluss Des Bespritzungs- Und Luftseitigen Umfeldes Auf Die Dichtwirkung von Radial-Wellendichtungen: Abschlussbericht FKM Vorhaben Nr. 236; Forschungshefte, Forschungskuratorium Maschinenbau e.V. (FKM); Forschungskuratorium Maschinenbau e.V.: Frankfurt am Main, Germany, 2001; Heft 261. [Google Scholar]
- Schaeffler Technologies AG & Co. KG. Wälzlagerpraxis: Handbuch zur Gestaltung und Berechnung von Wälzlagerungen, 4th ed.; Antriebstechnik; Vereinigte Fachverl: Mainz, Germany, 2015; p. 455. ISBN 978-3-7830-0401-4. [Google Scholar]
- Jung, S.; Daubner, A.; Haas, W. Measurement and Simulation of Two-Phase Flow in Sealing Application. In Sealing Technology—Indispensable; Fachverband Fluidtechnik, Universität Stuttgart, Eds.; Fachverband Fluidtechnik im VDMA e.V: Frankfurt am Main, Germany, 2016. [Google Scholar]

**Figure 2.**Factors affecting the contact temperature, according to [7].

**Figure 5.**Simulated configurations with slinger disc and baffle plate. (

**a**) SD_small. (

**b**) SD_large. (

**c**) BP_small. (

**d**) BP_large.

**Figure 6.**Geometry of the bearing arrangements. (

**a**) X-arrangement. (

**b**) O-arrangement. (

**c**) ball bearing. (

**d**) cylindrical roller.

**Figure 8.**Simulated configurations, hollow shaft designs. (

**a**) air_filled. (

**b**) oil_filled_35. (

**c**) oil_filled_50. (

**d**) oil_filled_60.

**Figure 9.**Simulated configurations: shaft shoulder designs. (

**a**) shoulder_air_short. (

**b**) shoulder_air_long. (

**c**) shoulder_oil_short. (

**d**) shoulder_oil_long.

**Figure 11.**Oil distribution in the oil chamber for different rotational shaft speeds, reference variant. (

**a**) $n$ = 0 rev/min. (

**b**) $n$ = 2000 rev/min. (

**c**) $n$ = 8000 rev/min.

**Figure 12.**Streamlines of the oil in the domain oil chamber for $n$ = 2000 rev/min, reference variant. (

**a**) Streamlines of oil, with sectional view of the model. (

**b**) Streamlines of oil, top view. (

**c**) velocity scale.

**Figure 14.**Volume fraction of the oil in the domain oil chamber bearing; $n$ = 2000 rev/min. (

**a**) Bea_X. (

**b**) Bea_Ba and Bea_Cyl. (

**c**) Bea_O.

**Figure 15.**Contour plots for $n$ = 2000 rev/min, variants with bearings: (

**a**) X-arrangement; (

**b**) O-arrangement; (

**c**) ball-bearings; and (

**d**) cylindrical roller bearings.

**Figure 16.**Temperature measurement procedure: (

**a**) sealing ring with interfaces; (

**b**) location of performed measurements.

**Figure 17.**Variants with slinger disc or baffle plate: simulation results (full colored) compared to the measured temperatures (hatched).

**Figure 18.**Variants with bearings: simulation results (full colored) compared to the measured temperatures (hatched).

**Figure 19.**Temperature distribution along a circumferential line: (

**a**) contour plot with the line around the shaft sleeve; (

**b**) temperature plot for $n$ = 2000 rev/min.

**Figure 20.**Temperature distribution along the horizontal line: (

**a**) contour plot with the horizontal line; (

**b**) temperature plot for $n$ = 2000 rev/min.

**Figure 21.**Hollow shaft: measured temperatures (hatched) compared to the simulation results (fully colored).

**Figure 22.**Shaft with shoulder design: measured temperatures (hatched) compared to the simulation results (fully colored).

**Figure 23.**Difference between the measured temperature and the temperature obtained from the simulation for all simulated variants.

Material | Thermodynamic State | $\mathbf{Density}\mathit{\rho}$ [kg/m ^{3}] | Heat Capacity c [J/(kg·K)] | Thermal $\mathbf{Conductivity}\mathsf{\lambda}$ [W/(m·K)] |
---|---|---|---|---|

Elastomer | Solid | 1900 | 1650 | 0.215 |

Aluminum | Solid | 2800 | 860 | 145 |

Steel 100Cr6 | Solid | 7830 | 470 | 46 |

Air (Ideal Gas) | Gas | Equation (14) | 1004.4 | Equation (15) |

Oil | Liquid | 885 | 2200 | 0.13 |

Designation | Bearing | Slinger Disc: Inner Diameter | Baffle Plate: Outer Diameter |
---|---|---|---|

SD_small | - | 93 mm | - |

SD_large | - | 87 mm | - |

BP_small | - | (78.7 mm) | 93 mm |

BP_large | - | (78.7 mm) | 87 mm |

Bea_X | tapered roller bearing, X-arrangement | - | - |

Bea_O | tapered roller bearing, O-arrangement | - | - |

Bea_Ba | ball bearing | - | - |

Bea_Cyl | cylindrical roller | - | - |

Designation | Filling | Shaft Shoulder | Inner Shaft Diameter |
---|---|---|---|

air_filled | air | - | 60 mm |

oil_filled_35 | oil | - | 35 mm |

oil_filled_50 | oil | - | 50 mm |

oil_filled_60 | oil | - | 60 mm |

shoulder_air_short | solid | air-side, short | - |

shoulder_air_long | solid | air-side, long | - |

shoulder_oil_short | solid | oil-side, short | - |

shoulder_oil_long | solid | oil-side, long | - |

**Table 4.**Variants with bearings: input parameters oil fill level and frictional heat, and the resulting temperature; $n$ = 2000 rev/min.

Bea_X | Bea_O | Bea_Ba | Bea_Cyl | |
---|---|---|---|---|

Oil fill level ${h}_{oil}$ [mm] | −100 (empty) | +100 (full) | 0 (center shaft) | 0 (center shaft) |

Frictional Heat ${\dot{Q}}_{fric}$ [W] (bearing near the seal) | 263.7 | 274.0 | 59.6 | 20.8 |

Frictional Heat ${\dot{Q}}_{fric}$ [W] (bearing distant from the seal) | 263.7 | 274.0 | 59.6 | 59.6 |

Frictional Heat ${\dot{Q}}_{\mathrm{f}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{s}\mathrm{e}\mathrm{a}\mathrm{l}}$ [W] (sealing ring) | 0.2 | 0.2 | 0.2 | 0.2 |

Frictional Heat ${\dot{Q}}_{\mathrm{f}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{s}\mathrm{h}\mathrm{a}\mathrm{f}\mathrm{t}}$ [W] (shaft surface) | 38.0 | 38.0 | 38.0 | 38.0 |

Simulation result: ϑ_{Max} [°C] at RSS-environment | 116.1 | 97.5 | 98.0 | 97.3 |

**Table 5.**Simulation results and measurements of the reference variant, depending on the input parameter $n$.

Input Parameter | Simulation Results | Measurement | ||
---|---|---|---|---|

$\mathbf{Shaft}\mathbf{Speed}\mathit{n}$ [rev/min] | $\mathbf{Circumferential}\mathbf{Speed}{\mathit{v}}_{\mathit{U}}$ [m/s] | ϑ_{Max} [°C] atRSS-Shaft | ϑ_{Max} [°C] atRSS-Environment | ϑ_{Max} [°C] atRSS-Environment |

2000 | 8.38 | 98.1 | 95.9 | 95.3 |

4000 | 16.76 | 109.4 | 105.4 | 105.6 |

8000 | 33.51 | 145.2 | 138.9 | 124.8 |

**Table 6.**Minimum and maximum temperatures along the circumferential line in the sealing contact, $n$ = 2000 rev/min.

Bea_X | Bea_O | Bea_Ba | Bea_Cyl | |
---|---|---|---|---|

${\vartheta}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ along the circumferential line [°C] | 114.7 | 95.3 | 94.3 | 93.8 |

${\vartheta}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ along the circumferential line [°C] | 116.8 | 97.5 | 97.7 | 97.1 |

No. | Simplification | Still Accurate Results? |
---|---|---|

1 | The frictional heat generated in the contact area between the sealing ring and shaft was given into the simulation model as a boundary condition. | yes |

2 | For all simulated variants, the same parameters for determining the frictional torque and, thus, also the frictional heat generated in the contact area between the sealing ring and shaft were defined. | yes ^{1} |

3 | Only two differences between all the variants with bearings: frictional torque of the bearings and oil fill level in the volume between the bearings and the sealing ring. | yes |

4 | Neither the spring nor the metal insert of the sealing ring were considered; the whole sealing ring was assumed to be made of elastomer. | yes |

5 | For the variants with a baffle plate, an air-filled volume was formed, which was not considered in the simulations. | no |

6 | The same geometry model was used for the all variants with bearings. | yes ^{2} |

7 | The air in the air-filled hollow shaft was not considered in the simulation model. | yes |

^{1}with one exception: the variant with tapered roller bearings in the O-arrangement.

^{2}on one condition: the pumping effect and the frictional torque of the bearings had to be known.

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**MDPI and ACS Style**

Hannss, J.; Grün, J.; Olbrich, C.; Feldmeth, S.; Bauer, F.
Multiphase Conjugate Heat Transfer Analyses on the Assembly Situation of Rotary Shaft Seals. *Appl. Sci.* **2023**, *13*, 11026.
https://doi.org/10.3390/app131911026

**AMA Style**

Hannss J, Grün J, Olbrich C, Feldmeth S, Bauer F.
Multiphase Conjugate Heat Transfer Analyses on the Assembly Situation of Rotary Shaft Seals. *Applied Sciences*. 2023; 13(19):11026.
https://doi.org/10.3390/app131911026

**Chicago/Turabian Style**

Hannss, Jacqueline, Jeremias Grün, Christoph Olbrich, Simon Feldmeth, and Frank Bauer.
2023. "Multiphase Conjugate Heat Transfer Analyses on the Assembly Situation of Rotary Shaft Seals" *Applied Sciences* 13, no. 19: 11026.
https://doi.org/10.3390/app131911026