On the Values for the Turbulent Schmidt Number in Environmental Flows
Abstract
:1. Introduction
- (a)
- Is it possible to determine similarities in the values of this number among water and air systems?
- (b)
- Is there any difference/similarity between dissolved and particulate matter?
- (c)
- Is it possible to infer some physical behavior from the analysis of the Schmidt number as a function of the concentration or the level of stratification?
- (d)
- How does the Schmidt number vary with flow characteristics?
2. The Turbulent Schmidt Number within the RANS Approach
3. Review of the Literature on the Parameterization of the Turbulent Schmidt Number
3.1. Water Systems
3.2. Atmosphere Systems
4. Case Studies
4.1. Contaminant Dispersion Due to Transverse Turbulent Mixing in a Shallow Water Flow
4.2. Tracer Transport in a Contact Tank
4.3. Sediment Transport in Suspension
5. Discussion
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Substance | Formula | Schmidt Number Sc for T = 25 °C | |
---|---|---|---|
Air | Water | ||
Methane | CH4 | 0.99 | 570 |
Oxygen | O2 | 0.84 | 441 |
Nitrogen | N2 | --- | 240 |
Carbon dioxide | CO2 | 1.14 | 410 |
Ammonia | NH3 | 0.57 | 360 |
Ethanol | C2H6O | 1.50 | 540 |
Methanol | CH3OH | 1.14 | 540 |
Cyclohexane | C6H12 | --- | 985 |
Reference | Environmental Flow | Comments |
---|---|---|
Arnold et al. [22] | Flow and tracer transport in open channels | Exp − Sct = 0.5–0.9 |
Djordjevic [23] | Flow and tracer transport in open channels | Exp/Num − Sct = 1 |
Lin and Shiono [24] | Flow and tracer transport in open channels | Exp/Num − Sct = 0.72 |
Simões and Wang [25] | Flow and tracer transport in open channels | Exp/Num − Sct = 0.5 (horizontal), 1 (vertical) |
Gualtieri [30] | Flow and tracer transport in a contact tank | Exp/Num − Sct = 1 |
Rauen et al. [33] | Flow and tracer transport in a contact tank | Exp/Num − Sct = 1 |
Kim et al. [31] | Flow and tracer transport in a contact tank | Exp/Num − Sct = 0.3 |
Zhang et al. [34,35,36] | Flow and tracer transport in a contact tank | Exp/Num − Sct = 0.7 |
Angeloudis et al. [26,27,28,29] | Flow and tracer transport in a contact tank | Exp/Num − Sct = 0.7 |
Martínez-Solano et al. [32] | Flow and tracer transport in a water tank | Exp/Num − Sct = 0.7 |
Oliver et al. [37] | Inclined negatively buoyant discharges | Exp/Num − Sct = 0.6 |
Graf and Cellino [41] | Sediment-laden open channel flows | Exp − Sct > 1 (no bedforms), Sct < 1 (bedforms) |
Hsu and Liu [42] | Sediment-laden open channel flows | Exp/Num − Sct = 0.7 |
Amoudry et al. [39] | Sediment-laden open channel flows | Exp/Num − Sct = 0.7 (bed), Sct = 0.52 (surface) |
Muste et al. [47,48] | Sediment-laden open channel flows | Exp − Sct = 1. 4–2.11 (sand), Sct = 0.22–0.52 (nylon) |
Toorman [52] | Sediment-laden open channel flows | Exp/Num − Sct = 0.5–0.8 |
Bombardelli and Jha [40] | Sediment-laden open channel flows | Exp/Num − Sct = 0.56–0.7 (dilute mixtures) |
Jha and Bombardelli [44,45,46] | Sediment-laden open channel flows | Exp/Num − Sct = 0.4–0.9 (k-ε model) |
Jha [43] | Sediment-laden open channel flows | Exp/Num − Sct = 0.2–1.3 |
Absi [38] | Sediment-laden open channel flows | Exp/Num − Sct = Sct (z) |
Huang et al. [49] | Density stratified turbulence | Exp/Num − Sct = 1.3 |
Huq and Stewart [50] | Density stratified turbulence | Exp − Sct = Sct (Ri, T*) |
Walker et al. [51] | T-junction mixing experiments | Exp/Num − Sct = 0.1–0.2 |
Reference | Environmental Flow | Comments |
---|---|---|
Koeltzsch [66] | Tracer transport in a boundary layer | Exp − Sct = 0.3–1, Sct = Sct (BL height) |
Flesch et al. [63] | Contaminant emission from soil | Exp − Sct = 0.6 |
Wilson [69] | Concentration measurements above a wheat crop | Exp − Sct = 0.68 and 0.78 |
Tominaga and Stathopoulos [67] | Review paper | Exp/Num − Sct = 0.2–1.3 |
Riddle et al. [68] | Pollutant dispersion in the built environment | Exp/Num − Sct = 0.3 and 0.7 |
Di Sabatino and Buccolieri [61] | Pollutant dispersion in the built environment | Exp/Num − Sct = 0.4 and 0.7 |
Blocken et al. [58] | Pollutant dispersion in the built environment | Exp/Num − Sct = 0.3–1 |
Chavez et al. [59] | Pollutant dispersion in the built environment | Exp/Num − Sct = 0.1–0.7 |
Mokhtarzadeh-Dehghan et al. [54] | Pollutant dispersion in the built environment | Exp/Num − Sct = 0.4–2.5 as f(Ri*) |
Ebrahimi and Jahangirian [62] | Pollutant dispersion in the built environment | Exp/Num − Sct = 0.7 |
Chen et al. [60] | Pollutant dispersion in the built environment | Exp/Num − Sct = 1.0 and corrected from wind tunnel data |
Hassan et al. [65] | Supersonic crossflow | Exp/Num − Sct = 1.0 and adaptive Sct |
Galeazzo et al. [64] | Jet in crossflow | Exp/Num − Sct = 0.3–0.9 |
Goldberg et al. [70] | Different type of air flows | Exp/Num − Sct variable |
Ross [71] | Flow over forested hills | Exp/Num − Sct = Sct (z) |
Shi et al. [72] | Density stratified jets | Exp/Num − Sct = Sct (velocity and density gradient) |
Run | Sct | Dt-y (m2/s) | Reference |
---|---|---|---|
Exp. | --- | 1.41 × 10−4 | Lau and Krishnappan [74] |
1 | 0.8 | 2.10 × 10−4 | Present study |
2 | 0.9 | 1.95 × 10−4 | Present study |
3 | 1.0 | 1.88 × 10−4 | Gualtieri [73] |
4 | 1.2 | 1.51 × 10−4 | Present study |
5 | 1.3 | 1.42 × 10−4 | Present study |
Numerical Model Sct | Outlet Hydraulic Efficiency Indicators | |||||
---|---|---|---|---|---|---|
tp/T | t10/T | t90/T | tg/T | Μο | σ2 | |
0.2 | 0.904 | 0.702 | 1.345 | 0.991 | 1.933 | 0.074 |
0.4 | 0.843 | 0.700 | 1.356 | 0.994 | 1.938 | 0.077 |
0.6 | 0.834 | 0.695 | 1.374 | 0.998 | 1.976 | 0.082 |
0.8 | 0.825 | 0.690 | 1.391 | 1.001 | 2.015 | 0.088 |
1.0 | 0.817 | 0.685 | 1.407 | 1.004 | 2.052 | 0.093 |
1.2 | 0.809 | 0.681 | 1.421 | 1.006 | 2.087 | 0.099 |
1.4 | 0.802 | 0.677 | 1.435 | 1.009 | 2.120 | 0.104 |
1.6 | 0.794 | 0.674 | 1.448 | 1.011 | 2.150 | 0.108 |
1.8 | 0.788 | 0.671 | 1.460 | 1.013 | 2.177 | 0.113 |
Exp. | 0.833 | 0.695 | 1.418 | 1.005 | 2.113 | 0.097 |
Authors | Technique for Velocity Measurements | Variables Observed * |
---|---|---|
Lyn [92] | Laser-Doppler anemometry | Vmix, C |
Muste and Patel [47] | Discriminator laser-Doppler velocimetry | Vc, Vd, T |
Nezu and Azuma [93] | Particle tracking velocimetry | Vc, Vd, C, T |
Muste et al. [48] | Particle image velocimetry and particle tracking velocimetry | Vc, Vd, C, T |
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Gualtieri, C.; Angeloudis, A.; Bombardelli, F.; Jha, S.; Stoesser, T. On the Values for the Turbulent Schmidt Number in Environmental Flows. Fluids 2017, 2, 17. https://doi.org/10.3390/fluids2020017
Gualtieri C, Angeloudis A, Bombardelli F, Jha S, Stoesser T. On the Values for the Turbulent Schmidt Number in Environmental Flows. Fluids. 2017; 2(2):17. https://doi.org/10.3390/fluids2020017
Chicago/Turabian StyleGualtieri, Carlo, Athanasios Angeloudis, Fabian Bombardelli, Sanjeev Jha, and Thorsten Stoesser. 2017. "On the Values for the Turbulent Schmidt Number in Environmental Flows" Fluids 2, no. 2: 17. https://doi.org/10.3390/fluids2020017
APA StyleGualtieri, C., Angeloudis, A., Bombardelli, F., Jha, S., & Stoesser, T. (2017). On the Values for the Turbulent Schmidt Number in Environmental Flows. Fluids, 2(2), 17. https://doi.org/10.3390/fluids2020017