Effect of the Density Ratio on Emulsions and Their Segregation: A Direct Numerical Simulation Study
Using direct numerical simulation (DNS) in combination with the volume of fluid method (VoF), we investigate the influence of the density ratio between the carrier and dispersed phase on emulsions, where the baseline simulation approximately corresponds to the ratio of water-in-gasoline emulsions. F...
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MDPI AG
2023-03-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/16/7/3160 |
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| author | Oscar Krzeczek Theresa Trummler Elias Trautner Markus Klein |
| author_facet | Oscar Krzeczek Theresa Trummler Elias Trautner Markus Klein |
| author_sort | Oscar Krzeczek |
| collection | DOAJ |
| description | Using direct numerical simulation (DNS) in combination with the volume of fluid method (VoF), we investigate the influence of the density ratio between the carrier and dispersed phase on emulsions, where the baseline simulation approximately corresponds to the ratio of water-in-gasoline emulsions. For this purpose, homogeneous isotropic turbulence (HIT) is generated using a linear forcing method, enhanced by a proportional–integral–derivative (PID) controller, ensuring a constant turbulent kinetic energy (TKE) for two-phase flows, where the TKE balance equation contains an additional term due to surface tension. Then, the forcing is stopped, and gravitational acceleration is activated. The proposed computational setup represents a unique and well-controlled configuration to study emulsification and segregation. We consider four different density ratios, which are applied in industrial processes, to investigate the influence of the density ratio on the statistically steady state of the emulsions, and their segregation under decaying turbulence and constant gravitational acceleration. At the statistically steady state, we hold the turbulence constant and study the effects of the density ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ρ</mi><mi>d</mi></msub><mo>/</mo><msub><mi>ρ</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula>, on the interface area, the Sauter mean diameter (SMD), and the statistical droplet size distribution. We find that all are affected by the density ratio, and we observe a relation between the SMD and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ρ</mi><mi>d</mi></msub><mo>/</mo><msub><mi>ρ</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula>. Furthermore, we assume a dependence of the critical Weber number on the density ratio. In the second part of our work, we study the segregation process. To this end, we consider the change in the center of mass of the disperse phase and the energy release, to analyze the dependence of segregation on the density difference <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>ρ</mi><mo>/</mo><msub><mi>ρ</mi><mi>d</mi></msub></mrow></semantics></math></inline-formula>. We show that segregation scales with the density difference and the droplet size, and a segregation time scale has been suggested that collapses the height of the center of mass for different density ratios. |
| first_indexed | 2024-03-11T05:38:07Z |
| format | Article |
| id | doaj.art-c5e2b89fdf3c4819a16b6d95c2e5f5f4 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-11T05:38:07Z |
| publishDate | 2023-03-01 |
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| series | Energies |
| spelling | doaj.art-c5e2b89fdf3c4819a16b6d95c2e5f5f42023-11-17T16:38:15ZengMDPI AGEnergies1996-10732023-03-01167316010.3390/en16073160Effect of the Density Ratio on Emulsions and Their Segregation: A Direct Numerical Simulation StudyOscar Krzeczek0Theresa Trummler1Elias Trautner2Markus Klein3Institute of Applied Mathematics and Scientific Computing, University of the Bundeswehr Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, GermanyInstitute of Applied Mathematics and Scientific Computing, University of the Bundeswehr Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, GermanyInstitute of Applied Mathematics and Scientific Computing, University of the Bundeswehr Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, GermanyInstitute of Applied Mathematics and Scientific Computing, University of the Bundeswehr Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, GermanyUsing direct numerical simulation (DNS) in combination with the volume of fluid method (VoF), we investigate the influence of the density ratio between the carrier and dispersed phase on emulsions, where the baseline simulation approximately corresponds to the ratio of water-in-gasoline emulsions. For this purpose, homogeneous isotropic turbulence (HIT) is generated using a linear forcing method, enhanced by a proportional–integral–derivative (PID) controller, ensuring a constant turbulent kinetic energy (TKE) for two-phase flows, where the TKE balance equation contains an additional term due to surface tension. Then, the forcing is stopped, and gravitational acceleration is activated. The proposed computational setup represents a unique and well-controlled configuration to study emulsification and segregation. We consider four different density ratios, which are applied in industrial processes, to investigate the influence of the density ratio on the statistically steady state of the emulsions, and their segregation under decaying turbulence and constant gravitational acceleration. At the statistically steady state, we hold the turbulence constant and study the effects of the density ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ρ</mi><mi>d</mi></msub><mo>/</mo><msub><mi>ρ</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula>, on the interface area, the Sauter mean diameter (SMD), and the statistical droplet size distribution. We find that all are affected by the density ratio, and we observe a relation between the SMD and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ρ</mi><mi>d</mi></msub><mo>/</mo><msub><mi>ρ</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula>. Furthermore, we assume a dependence of the critical Weber number on the density ratio. In the second part of our work, we study the segregation process. To this end, we consider the change in the center of mass of the disperse phase and the energy release, to analyze the dependence of segregation on the density difference <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>ρ</mi><mo>/</mo><msub><mi>ρ</mi><mi>d</mi></msub></mrow></semantics></math></inline-formula>. We show that segregation scales with the density difference and the droplet size, and a segregation time scale has been suggested that collapses the height of the center of mass for different density ratios.https://www.mdpi.com/1996-1073/16/7/3160direct numerical simulationsemulsionssegregationdensity effectcomputational fluid dynamics |
| spellingShingle | Oscar Krzeczek Theresa Trummler Elias Trautner Markus Klein Effect of the Density Ratio on Emulsions and Their Segregation: A Direct Numerical Simulation Study Energies direct numerical simulations emulsions segregation density effect computational fluid dynamics |
| title | Effect of the Density Ratio on Emulsions and Their Segregation: A Direct Numerical Simulation Study |
| title_full | Effect of the Density Ratio on Emulsions and Their Segregation: A Direct Numerical Simulation Study |
| title_fullStr | Effect of the Density Ratio on Emulsions and Their Segregation: A Direct Numerical Simulation Study |
| title_full_unstemmed | Effect of the Density Ratio on Emulsions and Their Segregation: A Direct Numerical Simulation Study |
| title_short | Effect of the Density Ratio on Emulsions and Their Segregation: A Direct Numerical Simulation Study |
| title_sort | effect of the density ratio on emulsions and their segregation a direct numerical simulation study |
| topic | direct numerical simulations emulsions segregation density effect computational fluid dynamics |
| url | https://www.mdpi.com/1996-1073/16/7/3160 |
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