CFD Analyses of Density Gradients under Conditions of Supersonic Flow at Low Pressures
Abstract
:1. Introduction
2. Methodology
- Accurate capture of shock and contact discontinuities.
- Entropy-conserving solution capabilities.
- Suppression of the carbuncle phenomenon, a common numerical instability associated with low-dissipative shock-capturing schemes.
- Robust accuracy and convergence across a wide Mach number range.
3. Results
3.1. Comparison of Experiment and CFD Simulation
- The differential pressure between points A and B was measured to be 74,400 Pa using a DPS 300 sensor with a range of 100 kPa and an accuracy of ±1% FSO BFSL (over the entire range fitted with a linear curve).
- The differential pressure between points B and C was measured to be 8500 Pa using a DPS 300 sensor with a range of 25 kPa and an accuracy of ±1% FSO BFSL (over the entire range fitted with a linear curve).
- The differential pressure between points C and D was measured to be 4500 Pa using a DPS 300 sensor with a range of 4 kPa and an accuracy of ±1% FSO BFSL (over the entire range fitted with a linear curve).
3.2. CFD Analyses of the Influence of the Pressure Magnitude on the Shock Wave Location
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
References
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B | C | D | |
---|---|---|---|
CFD | 21,771 | 13,405 | 7752 |
Experiment | 21,000 | 12,800 | 7600 |
ε | 3.5 | 4.5 | 1.9 |
Aperture | ||||||
---|---|---|---|---|---|---|
Position | y [mm] | µ [10−5 Pa·s] | ρ [kg·m−3] | Vmax [m·s−1] | D [mm] | T [K] |
Aperture | 0.0022 | 1.56 | 0.73 | 297.7 | 2 | 254.5 |
Nozzle | 0.005 | 0.803 | 0.075 | 602.1 | 3.88 | 120.4 |
Point on Path [mm] | Char. Dimension [m] | Mean Velocity [m·s−1] | Density [kg·m−3] | Dyn. Viscosity [Pa·s] | Temperature [K] | Re Number [-] |
---|---|---|---|---|---|---|
0 | 0.002 | 148.85 | 0.73 | 1.56 × 10−5 | 254.5 | 13,930.83 |
2.5 | 0.0027 | 142.55 | 0.241 | 1.57 × 10−5 | 255.5 | 5908.11 |
5 | 0.0035 | 287.4 | 0.095 | 8.98 × 10−5 | 135.2 | 10,641.48 |
7.5 | 0.08 | 118.3 | 0.196 | 1.63 × 10−5 | 268.5 | 111,730.47 |
Variant (Further Marked) | p0 (Input Pressure) [Pa] | pv (Output Pressure) [Pa] |
---|---|---|
101,325 Pa | 1,013,250 | 101,325 |
50,000 Pa | 500,000 | 50,000 |
10,000 Pa | 100,000 | 10,000 |
5000 Pa | 50,000 | 5000 |
2000 Pa | 20,000 | 2000 |
Labeling | Unit | Theory | |
---|---|---|---|
Mach number | Mv | [-] | 2.16 |
Speed of sound in the chamber for T0 = 24 °C | a0 | [m·s−1] | 345.5 |
Outlet speed of sound | av | [m·s−1] | 248.5 |
Outlet velocity | vv | [m·s−1] | 536.8 |
Outlet temperature | Tv | [K] | 153.7 |
Outlet cross-section | Av | [mm2] | 1.39 |
Labeling | Unit | Theory | Point | Line | |
---|---|---|---|---|---|
Mach number | Mv | [-] | 2.16 | 2 | 2.1 |
Speed of sound in the chamber for T0 = 24 °C | a0 | [m·s−1] | 345.5 | - | - |
Outlet speed of sound | av | [m·s−1] | 248.5 | - | - |
Outlet velocity | vv | [m·s−1] | 536.8 | 530.9 | 530 |
Outlet temperature | Tv | [K] | 153.7 | 160 | 157 |
Outlet cross-section | Av | [mm2] | 1.39 | - | - |
Variant 101,325 Pa | |||||
Outlet static pressure | pv | [Pa] | 101,325 | 250,906 | 102,324 |
Outlet density | ρv | [kg·m−3] | 2.29 | 2.9 | 2.2 |
Variant 50,000 Pa | |||||
Outlet static pressure | pv | [Pa] | 50,000 | 130,398 | 50,906 |
Outlet density | ρv | [kg·m−3] | 1.13 | 1.48 | 1.1 |
Variant 10,000 Pa | |||||
Outlet static pressure | pv | [Pa] | 10,000 | 13,924 | 10,569 |
Outlet density | ρv | [kg·m−3] | 0.226 | 0.29 | 0.227 |
Variant 5000 Pa | |||||
Outlet static pressure | pv | [Pa] | 5000 | 6580 | 5495 |
Outlet density | ρv | [kg·m−3] | 0.113 | 0.126 | 0.116 |
Variant 2000 Pa | |||||
Outlet static pressure | pv | [Pa] | 2000 | 2506 | 2288 |
Outlet density | ρv | [kg·m−3] | 0.045 | 0.051 | 0.049 |
Shock Wave Position | |||
---|---|---|---|
Variant | 1 [mm] | 2 [mm] | 3 [mm] |
101,325 Pa | 1.06 | 3.06 | 3.68 |
50,000 Pa | 1.04 | 3.1 | 3.7 |
10,000 Pa | 0.92 | 3.2 | 3.62 |
5000 Pa | - | - | 3.62 |
2000 Pa | - | - | 3.5 |
Variant | Point | Char. Dimension [m] | Mean Velocity [m·s−1] | Density [kg·m−3] | Dyn. Viscosity [Pa·s] | Temperature [K] | Re Number [-] |
---|---|---|---|---|---|---|---|
101,325 Pa | 1 | 0.00113 | 258.5 | 2.74 | 1.09 × 10−5 | 167 | 73,428.23 |
2 | 0.00127 | 186 | 2.91 | 1.43 × 10−5 | 229 | 41,935.86 | |
3 | 0.08 | 246 | 1.73 | 1.16 × 10−5 | 178 | 2,935,034.48 | |
50,000 Pa | 1 | 0.00113 | 259 | 1.35 | 1.09 × 10−5 | 167 | 36,248.12 |
2 | 0.00127 | 182.5 | 1.36 | 1.45 × 10−5 | 232 | 21,738.9 | |
3 | 0.08 | 241 | 0.84 | 1.18 × 10−5 | 181.6 | 1,372,474.58 | |
10,000 Pa | 1 | 0.00113 | 259 | 0.27 | 1.1 × 10−5 | 168 | 7203.36 |
2 | 0.00127 | 239.5 | 0.323 | 1.2 × 10−5 | 186 | 8180.29 | |
3 | 0.08 | 272.5 | 0.208 | 1.01 × 10−5 | 154 | 448,950.5 | |
5000 Pa | 1 | 0.00113 | 258.5 | 0.137 | 1.1 × 10−5 | 169 | 3624.85 |
2 | 0.00127 | 245 | 0.165 | 1.18 × 10−5 | 182 | 4350.83 | |
3 | 0.08 | 273 | 0.109 | 1.01 × 10−5 | 154 | 234,769.23 | |
2000 Pa | 1 | 0.00113 | 242 | 0.0685 | 1.196 × 10−5 | 184 | 1574.12 |
2 | 0.00127 | 243.5 | 0.067 | 1.18 × 10−5 | 183 | 1755.88 | |
3 | 0.08 | 269.5 | 0.046 | 1.03 × 10−5 | 157 | 96,287.38 |
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Bayer, R.; Bača, P.; Maxa, J.; Šabacká, P.; Binar, T.; Vyroubal, P. CFD Analyses of Density Gradients under Conditions of Supersonic Flow at Low Pressures. Sensors 2024, 24, 5968. https://doi.org/10.3390/s24185968
Bayer R, Bača P, Maxa J, Šabacká P, Binar T, Vyroubal P. CFD Analyses of Density Gradients under Conditions of Supersonic Flow at Low Pressures. Sensors. 2024; 24(18):5968. https://doi.org/10.3390/s24185968
Chicago/Turabian StyleBayer, Robert, Petr Bača, Jiří Maxa, Pavla Šabacká, Tomáš Binar, and Petr Vyroubal. 2024. "CFD Analyses of Density Gradients under Conditions of Supersonic Flow at Low Pressures" Sensors 24, no. 18: 5968. https://doi.org/10.3390/s24185968
APA StyleBayer, R., Bača, P., Maxa, J., Šabacká, P., Binar, T., & Vyroubal, P. (2024). CFD Analyses of Density Gradients under Conditions of Supersonic Flow at Low Pressures. Sensors, 24(18), 5968. https://doi.org/10.3390/s24185968