Large Eddy Simulation of Self-Excited Oscillation Pulsed Jet (SEOPJ) Induced by a Helmholtz Oscillator in Underground Mining
Abstract
:1. Introduction
2. Computational Details
2.1. Flow Configuration
2.2. Governing Equation
2.3. Computational Domain and Boundary Condition
3. Results and Discussion
3.1. Validation
3.2. Frequency Spectrums
3.3. Transient Flow Field
3.4. Mean Flow Field
3.5. Coherent Structure
4. Conclusions
- The frequency spectrum of SEOPJ has multiple peaks, while the maximum value is at the low frequency. With increasing operating pressure, the major frequency of pulsation leans in the direction of high frequency.
- After the upstream fluid enters the Helmholtz oscillator, a stable periodic velocity core is formed at the outlet due to the effect of the chamber and the collision wall. After entering the outflow field, the external flow field will be subjected to periodic impact and the ambient fluid was strongly entrained.
- For a SEOPJ Helmholtz oscillator with different cavity lengths, the length of the core segment decreases with the increase of the cavity length. The longer the cavity length, the greater the energy loss caused by the cavity and the faster the axial velocity attenuation at the jet outlet. Compared with the conical nozzle, the length of the core section of SEOPJ was shorter, but the jet had better bunching, smaller diffusion angle and better mixing performance.
- The nozzle with small cavity diameter is more disorderly near the nozzle outlet, and the vortex scale is larger, which is more obvious in the downstream section. As the cavity diameter is larger, the space for energy storage and modulation in the chamber increases, the instability of the flow field at the downstream outlet decreases, and the vortex at the outlet is more orderly. The effect of cavity diameter on the SEOPJ is mainly reflected in the feedback modulation of the jet in the cavity.
Author Contributions
Funding
Conflicts of Interest
Abbreviations
x | Radial direction |
y | Flow direction |
z | Lateral direction |
d1 | Upstream nozzle diameter |
d2 | Downstream nozzle diameter |
α | Impinge wall angle |
Lc | Cavity length |
Dc | Cavity diameter |
Ub | Bulk velocity |
Re | Reynolds number |
ρ | Medium density |
u | Medium velocity |
p | Medium pressure |
ui | Instantaneous velocity |
xi | Three-dimensional coordinate directions |
τij | Sub-grid-scale (SGS) tensor |
δij | Kronecker’s delta |
νt | Eddy viscosity |
Sij | Resolved scale strain rate tensor |
Δx | Cell length of x directions |
Δy | Cell length of y directions |
Δz | Cell length of z directions |
uτ | Shear velocity |
y1 | Mesh thickness of the first layer |
Pmax | Maximum pressure of nozzle outlet |
Pmin | Minimum pressure of nozzle outlet |
Di | Upstream inlet pipe diameter |
Pi | Inlet pressure |
fp | Peak frequency |
s | Flow distance |
u0 | Average velocity at the nozzle outlet |
Q | Q criterion |
Ω | Vorticity tensor |
S | Strain rate tensor |
Δt | Time interval |
t | Transient time |
t0 | Initial time |
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d1 [mm] | d2/d1 | L/d1 | D/d1 | α [°] | Re |
---|---|---|---|---|---|
2.6 | 1.2 | 1 | 8 | 120 | 1 × 105~2 × 105 |
2 | 8 | ||||
3 | 8 | ||||
4 | 8 | ||||
4 | 4 | ||||
4 | 6 | ||||
4 | 10 |
Mesh | Nodes | Pmax [MPa] | Pmin [MPa] |
---|---|---|---|
Case 1 (Coarse) | 6,350,000 | 2.551 | 0.943 |
Case 2 (Medium) | 10,260,000 | 2.749 | 1.094 |
Case 3 (Fine) | 15,420,000 | 2.698 | 1.116 |
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Fang, Z.; Wu, Q.; Zhang, M.; Liu, H.; Jiang, P.; Li, D. Large Eddy Simulation of Self-Excited Oscillation Pulsed Jet (SEOPJ) Induced by a Helmholtz Oscillator in Underground Mining. Energies 2019, 12, 2161. https://doi.org/10.3390/en12112161
Fang Z, Wu Q, Zhang M, Liu H, Jiang P, Li D. Large Eddy Simulation of Self-Excited Oscillation Pulsed Jet (SEOPJ) Induced by a Helmholtz Oscillator in Underground Mining. Energies. 2019; 12(11):2161. https://doi.org/10.3390/en12112161
Chicago/Turabian StyleFang, Zhenlong, Qiang Wu, Mengda Zhang, Haoyang Liu, Pan Jiang, and Deng Li. 2019. "Large Eddy Simulation of Self-Excited Oscillation Pulsed Jet (SEOPJ) Induced by a Helmholtz Oscillator in Underground Mining" Energies 12, no. 11: 2161. https://doi.org/10.3390/en12112161