Helmholtz Oscillator Research Articles

Effects of vent layout and vent area on dynamic characteristics of premixed methane-air explosion in a tube with two side-vented ducts

To further elucidate the influence mechanism of side vents on the dynamic characteristics of gas explosions in tubes is helpful to design more reasonable vent layouts. In this paper, 9.5% methane-air explosion experiments were conducted in a tube with two side-vented ducts, and the effects of vent layouts and vent areas on the dynamic characteristics of explosion overpressure and flame propagation speed were investigated. The results demonstrate that under the same condition with a single vent area of 100 mm × 100 mm, when only the end vent is open, the maximum explosion overpressure and the maximum flame propagation speed are the highest among the five vent layouts. When the side vents 1 and 2 and the end vent are open, the maximum explosion overpressure is the lowest, and an unusual discovery is that the flame front changes into a hemispherical shape, finger shape, quasi-plane shape, tulip shape and wrinkled structure. When only side vent 1 is open, a unique Helmholtz oscillation occurs, and a new discovery is that there is a consistent oscillation relationship among the overpressure, flame propagation speed and flame structure. Helmholtz oscillation occurs only when a single vent area is 100 mm × 100 mm–60 mm × 60 mm, and the oscillation degree decreases with decreasing vent area. During the vent failure stage, the maximum explosion overpressure is generated, the flame front begins to appear irregular shape, and the flame propagation speed shows a prominent characteristic peak. After the vent failure stage, the driving effect of the end vent on the flame is higher than that of the side vent on the flame. Furthermore, the correlation equations of the mathematical relationships among the maximum explosion overpressure Pred, the static activation pressure Pstat and the vent coefficient Kv under four vent layouts are established, respectively.

On the Krýlov–Bogoliúbov-Mitropólsky and Multiple Scales Methods for Analyzing a Time Delay Duffing–Helmholtz Oscillator

This study is divided into two important axes; for the first one, a new symmetric analytical (approximate) solution to the Duffing–Helmholtz oscillatory equation in terms of elementary functions is derived. The obtained solution is compared with the numerical solution using 4th Range–Kutta (RK4) approach and with the exact analytical solution that is obtained using elliptic functions. As for the second axis, we consider the time-delayed version for the same oscillator taking the impact of both forcing and damping terms into consideration. Some analytical approximations for the time delayed Duffing–Helmholtz oscillator are derived using two different perturbation techniques, known as Krylov–Bogoliubov–Mitropolsky method (KBMM) and the multiple scales method (MSM). Moreover, these perturbed approximations are analyzed numerically and compared with the RK4 approximations.

Experimental study on suppressing heat transfer deterioration of supercritical CO2 in vertical tubes based on Helmholtz oscillator

Heat transfer deterioration of supercritical CO2 (S-CO2) heated in gas heaters influences the efficiency and safe operation of the trans-critical CO2 system due to local high temperatures. To suppress the heat transfer deterioration of S-CO2, three Helmholtz oscillators with different nozzle diameters are designed and applied to the inlet of the heated vertical tube. The heat transfer characteristics of S-CO2 heated in the smooth tube and the smooth tube with Helmholtz oscillators are investigated at the mass fluxes from 144 to 750 kg/(m2·s), the heat fluxes from 23.0 to 128.1 kW/m2, the inlet temperatures of 15.0 and 25.0 °C, and the fixed pressure of 8.0 MPa. The results show that the heat transfer deterioration observed in the smooth tube is significantly inhibited by the Helmholtz oscillator. At G ≥ 400 kg/(m2·s), the ratio of local heat transfer coefficient and the thermal performance evaluation factor can be up to 9.86 and 3.09, respectively. The pulsating flow generated by the Helmholtz oscillator strengthens the mutual disturbance between near-wall fluid and the core fluid, resulting in more uniform thermophysical properties of S-CO2 in the radial direction and a much weaker buoyancy effect. In addition, the influence of the downstream nozzle diameter on the heat transfer characteristics of S-CO2 is more significant than that of the upstream nozzle diameter in the present study. Finally, a new empirical heat transfer correlation of S-CO2 in the smooth tube with Helmholtz oscillator is proposed, which takes into account the effect of the thermophysical properties of CO2 and the structure parameters of the Helmholtz oscillators with an accuracy of ±20 %.

Visualization of the external flow field during a vented explosion for hydrogen-air mixtures: Effects of hydrogen concentrations and vent areas

To study the effects of hydrogen concentrations and vent areas on the vented hydrogen-air explosion, series of experiments were performed in a cylindrical tube under the conditions of 1 atm and 10 ℃. The pressure oscillation frequency is proportional to the hydrogen concentration, while the Helmholtz oscillation disappeared gradually with the increase of Kv. The position inside the container which was farther away from the vent cover would experience the higher dynamic loading. The volume concentration of the hydrogen at the external field (cExt) was always lower than the initial hydrogen concentration, that increased with the increase of the initial concentration, while it was zero at some concentrations with the increase of Kv. The external flame velocity of rich fuel was always larger than that of lean fuel. The deflagration to detonation (DDT) in the outer field was easier to achieve for the concentration near to 50 vol% and for lower Kv. The secondary explosion wave (PExt) increased firstly and then decreased with the increase of hydrogen concentration, which decreased with the increase of Kv in general. The maximum surface temperature rose with the increase of concentration and dropped with the increase of Kv in general. The high-temperature field was closer to the vent for lower concentration and higher Kv.

Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)

Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)

Research on the effect of the vent area on the external deflagration process during the explosion vent

Explosion-vent area is an important parameter for pressure vessel explosion vent design, which is of great significance to the safe operation of pressure vessels. The phenomenon of external explosion occurs outside the vent when the pressure vessel vents. The impact of explosion vent area on the external explosion was researched by numerical simulation in this paper. The results show that the impact of the explosion vent area on the external explosion is relatively significant. The large vent area has a larger area of high pressure, higher pressure and higher fluid turbulence intensity outside the vessel, which leads to more powerful explosion intensity. The smaller vent area leads to weaker external explosion intensity, but leads to higher pressure values inside the vessel. Additionally, the pressure-relief process of vessel with smaller vent area tends to form a “jet fire” and the pressure-relief efficiency is low, in which process, the external flame’s shapes show a long strip. The pressure-relief form of vessel with larger vent area tends to “external explosion” and the process of pressure relief is quicker, in which process, the shape of the external flame showing a “spherical”. Gas from the vent, the under-expansion flow in high-pressure develops into sub-atmospheric in process of moving forward, which can be compressed by surrounding air to intensify the thermochemical reaction, thus prompting the occurrence of external explosions. The larger the venting area is, the quicker the dissipation of the high-pressure area appears. As a result of the external explosion, the Helmholtz oscillation appears inside vessels. Larger vent area leads to larger amplitude and higher frequency of Helmholtz oscillations, in which process, the duration of Helmholtz oscillations is longer.

Experimental Studies on the Explosion Behaviors of Premixed Hydrogen-Air Mixtures in a Narrow Channel.

Premixed hydrogen–air explosion experiments were carried out in a 1000 mm × 50 mm × 10 mm half-open narrow channel, concerning with the influences of equivalence ratio and ignition position on explosion behaviors. Experimental phenomena were different from explosion in large space. The results indicated that when ignited at the closed end of the channel, three overpressure peaks appeared, caused by the rupture of the film, Helmholtz Oscillation, and the flame-acoustic interaction, respectively. As the equivalence ratio of the hydrogen–air mixtures varied from 0.6 to 1.6, the peak overpressure first increased and then decreased. The maximum peak overpressure occurred at ϕ = 1.2. The hydrogen flame would develop into the plane tulip structure without the influence of the end wall. With the ignition position moved to the open end, overpressure wave and flame oscillated significantly. Compared with other ignition positions, the minimum value of Pmax was obtained at IP950. Based on the explosion behaviors in the narrow channel, it was concluded that the closer the ignition was to the open end, the easier the oscillation was to be formed, the smaller the explosion hazard was.

Acoustic stimulation of oil production by a downhole emitter based on a jet-driven Helmholtz oscillator

Development of oil fields by the most common waterflooding method leads to an increase in the water cut of the recoverable oil and a low oil recovery factor (for Russia, about 30–40%). The solution to this actual problem seems to be in the combination of the applied waterflooding method with the elastic wave action. This paper presents the results of the use of acoustic stimulation as an unconventional but promising approach to enhanced oil recovery. This study developed a borehole emitter and acoustic action technology to stimulate oil production. In this borehole hydrodynamic emitter, based on the jet-driven Helmholtz oscillator, the generation of intense acoustic pressure oscillations occurs due to the energy of the fluid flow injected into the formation. Bench tests made it possible to determine the operating parameters and frequency characteristics of the device. Field tests were carried out in Russia at an oil field that is in a late stage of development. An increase in oil production has been achieved; the water cut of the produced oil has been reduced; the injectivity of the injection well has been increased due to the restoration of the filtration properties of the bottom-hole zone. Thus, the developed technical devices, operating at kilohertz frequencies, and the production technology can be used as a promising method for stimulating oil flow and enhancing oil recovery. The advantages of the proposed acoustic treatment are their relatively low cost, simplicity of device design, high efficiency, and environmental friendliness, as well as the possibility of combining this technology with almost all traditional methods of enhanced oil recovery.

Effect of different vent covers on the overpressure and flame propagation characteristics of hydrocarbon fuel-air mixture venting explosion

A series of hydrocarbon-air fuel venting explosion experiments were carried out in a 20-L small-scale vent tank, and the effect of four different vent covers with an inherent rupture pressure of 10 kPa on the overpressures and flame propagation characteristics was studied. The results of the experiments showed that all the internal and external overpressure-time profiles have five typical overpressure peaks, induced by burst of the vent cover (△p1), inertia effect (△pneg), burned gas releasing (△p2), external explosion (△p3) and Helmholtz oscillation (△phel), respectively. The dynamic process of the flame was basically tally with the rule of ‘smooth and hemispherical flame-twisted and stretched flame-mushroom cloud-like/ellipsoidal flame-extinguishing flame’, but some differences were still existed due to the specific damage mode of each vent cover. When the vent opening was sealed by different vent covers, the values of internal and external overpressure peaks, maximum rate of overpressure rises, flame front location along different directions, and flame front speed along different directions showed various trends. Specifically, the enhancement effect of the metal cover plate and PE vent cover was significantly weaker than that of the paper vent cover and Al vent cover for the overpressure and vertical flame parameters, while, the enhancement effect of the metal cover plate was found to be greater than the other three for the horizontal flame parameters. Consequently, PE cover had the optimum performance for the explosion venting under the same inherent rupture pressures. These results improve our understanding on gas explosion dynamics in a semi-confined space with a vent cover, and provides the overpressure and flame characteristics of gas venting explosion under different vent boundary conditions from the qualitative and quantitative view.

Effect of hydrogen concentration on the vented explosion of hydrogen–air mixtures in a 5-m-long duct

A series of vented hydrogen-air explosion experiments were carried out in an end-vented rectangular tube, and the effect of hydrogen concentrations varying from 10% to 50% on the flame evolution and the maximum overpressure inside and outside the duct were investigated. Experimental results reveal that the flame behavior was strongly affected by hydrogen concentration: the flame speed at the vent exit first increased and then decreased as hydrogen concentration was increased; a tulip flame and two bright fireballs were respectively observed within and outside the duct in some tests. Two dominant pressure peaks and two types of oscillations could be distinguished in the internal pressure curves, corresponding to the rupture of the membrane, venting of the burned gas, Helmholtz, and acoustic oscillations, respectively. Under the current experimental conditions, the pressure peak with a low amplitude owing to the rupture of membrane dominated the external pressure–time histories for hydrogen concentrations less than 25%. However, when the hydrogen concentration ranged from 30% to 50%, the pressure peak caused by the second external explosion become dominant. Besides, the influence of the external explosions on the internal pressure peak structures was discussed. As hydrogen concentration was increased, the maximum internal overpressure first increased and then decreased, whereas the maximum external overpressure increased monotonically. In this study, the maximum reduced overpressures calculated by Molkov’s best-fit model agreed well with the experimental data for near-stoichiometric and rich hydrogen-air mixtures.

Helmholtz vibrations in bowed strings.

For almost 160 years, it has been known that Helmholtz oscillations, unique to vibrating strings in bowed instruments (violin, cello, etc.), have two distinct regimes: "slip" and "stick." During the slip regime, the force at the bow-string interaction is attributed to friction between the sliding bow hair and the vibrating string, with a friction coefficient that decreases with increasing relative velocity. Yet the hair-string interaction during the stick regime is less understood. We propose that the interaction force during the stick regime is proportional to the product of the longitudinal acoustic impedance of the bow hair to the relative bow-string velocity. We validate this hypothesis by solving the string's differential equation of motion, including an enhanced formulation to avoid parasitic high-frequency oscillations. This physical model enables us to analyze, in real time, the characteristics of the Helmholtz oscillations, including the string shape, excitation of harmonics, Schelleng ripples, and string energy, showing that the bowed string gains energy during the stick regime and loses energy during the slip regime.

Numerical Study on Flow-Induced Noise of Deflector Jet Servo Valve Based on LES/Lighthill Hybrid Method

The flow-induced noise occurring in the prestage of the deflector jet servo valve (DJV) significantly affects the performance of DJV, which is a critical issue for electrohydraulic servo valves. To capture the root causes of flow-induced noise, DJV is numerically studied using computational aeroacoustics (CAA) methods in this paper. The acoustic field is investigated with Lighthill’s acoustic analogy based on the pulsation data from a large eddy simulation (LES). The flow-induced noise generation mechanism in DJV is revealed by analyzing the sound pressure level and vorticity distribution at different moments. Moreover, a kind of oscillation cavity model based on the Helmholtz oscillator is built, which reveals that the flow-induced noise is caused by self-excited oscillation and vortex. In addition, the result shows that continuous broadband dipole noise with medium- and high-frequency components of 1100 Hz and 2501 Hz dominates the DJV flow field. In order to avoid unexpected resonance, the natural frequency of the prestage should not coincide with the frequency of the flow oscillation frequency. Thus, this work can benefit the design and optimization of the prestage structure.

The characteristics and mechanisms of self-excited oscillation pulsating flow on heat transfer deterioration of supercritical CO2 heated in vertical upward tube

Heat transfer deterioration (HTD) of supercritical CO2 heated in a tube influences the efficiency and safe operation of the system due to the occurrence of local high temperature. To suppress and delay the HTD, the characteristics and mechanisms of self-excited oscillation pulsating flow on HTD of supercritical CO2 are studied by experiment and simulation at pressure 8 MPa, mass fluxes from 350 to 800 kg/m2·s, heat fluxes from 30 to 200 kW/m2. The Helmholtz oscillator is introduced into the inlet of the vertical tube for generating a pulsating flow of supercritical CO2. The heat transfer performance is compared with that of without Helmholtz oscillator at the inlet of the tube. The results show that the self-excited oscillation pulsating flow improve the heat transfer performance significantly. The heat transfer parameters present oscillations with small amplitude along flow direction before pseudo-critical point (Tpc). The average heat transfer coefficient can be up to 3.4 times and the enhancement takes place mainly at the HTD region which is located at the entrance section of the heated tube. The effect of suppressing HTD is more significant at higher heat flux, and the peak of wall temperature can be reduced by 100 K at a heat flux of 200 kW/m2. Compared to the steady flow, the mechanism analysis of the self-excited oscillation pulsating flow based on radial distributions of velocity, turbulent kinetic energy (TKE), and density reveals that the velocity distribution of “M−shape” appears later and gentler. The production and diffusion of TKE are improved at log layer (30 < y+ < 0.2r). In addition, the period and the amplitude do not show monotonous trends on heat transfer performance. The effects of pulsating parameters on HTD are optimized that the heat transfer performance with the period of 0.016 s and the amplitude of 100 kg/m2·s is the best in calculated cases.

Experimental study on external explosion for vented hydrogen deflagration in a rectangular tube with different vent coefficients

Experiments on hydrogen-air vented deflagration in a smooth rectangular tube were conducted with various vent area for different hydrogen concentration. The high-speed schlieren camera was employed to visualize the external flow field. The internal and external overpressures were obtained from five pressure transducers. The effects of vent area for different hydrogen concentration were discussed on the build-up of internal/external overpressures and the evolution of external flow field. Two types of internal overpressure structure, affected by Helmholtz oscillation and external flow field, were observed for different vent coefficient and hydrogen concentration. The increase of hydrogen concentration promotes external mixture reactivity and the external overpressure. The increase of vent coefficient drives the increase of outlet speed of vented gas and flame and generally promotes external overpressure. The higher speed flame provides stronger ignition energy to external combustible gas cloud. For the high hydrogen concentration of 18 vol%, external overpressure increases linearly with vent coefficient. The rise of external overpressure can cause the increase of internal overpressure when it is large enough, particularly in the case of large vent coefficient, and the internal overpressure peak affected by external explosion can even dominate the maximum internal overpressure.

Effect of vent area on the vented methane-air deflagrations in a 1 m3 rectangular vessel with and without obstacles

The effects of vent area on pressure and flame evolution in a 1 m3 vessel with and without obstacles were investigated. Five pressure peaks of Popen, Pout, Pext, Phel, and Pvib, which correspond to vent activation, flame venting, external explosion, Helmholtz oscillation, and the coupling of acoustic waves and flames, respectively, were observed without obstacles when the vent coefficient Kv ≤ 6.25. However, the pressure peaks of Pext and Pout from the external explosion and flame venting disappeared when Kv > 6.25. Moreover, the pressure peaks of Popen and Pvib produced by vent activation and acoustically enhanced combustion become dominant when Kv ≥ 12.5. With the installation of obstacles, the pressure peak Pvib induced by acoustically enhanced combustion disappeared. The other four pressure peaks were observed when Kv < 6.25. The pressure peaks induced by the external explosion and the Helmholtz oscillation disappeared when Kv ≥ 12.5. Nevertheless, the pressure peak resulting from the obstacles was observed and became dominant at Kv ≥ 12.5. It takes less time for the external flame to propagate to the maximum displacement in the tests with obstacles than that without obstacles, and the maximum flame length for the former is smaller than the latter.

Ceiling-vented deflagrations of a hydrogen-air mixture in a 75 m3 container

A series of hydrogen explosions were conducted in a real scale container with and without vents. The effects of hydrogen concentration, ignition location, obstacles on the vented hydrogen-air explosions were investigated. Hydrogen explosions with concentration of 12% and 16% were conducted in constant volume container, and the maximum peak overpressure can reach 45 kPa and 175 kPa, respectively. During the vented hydrogen explosions, three overpressure peaks generated by the vent rupture, Helmholtz oscillation, and the thermo-acoustic-vibration coupling, respectively, were recorded. The maximum peak overpressure is about several kilopascal, the pressure reduction can reach 97.1% by comparison with peak overpressure developed in closed container. The obstacles change the way that the flame travel inside the container, and resultantly the flame propagates vertically and increases the flame area, which promotes the reaction and increases the peak overpressure, which also increases with the hydrogen concentration. Three engineering models used to depict the relationship between the vent area and the maximum reduced explosion pressure were assessed. Results show that the these models over-predict the maximum reduced explosion pressure for high-reactivity mixtures. However, for low reactivity, the Molkov’ models show a scatter while the NFPA68 gives a better prediction.

Effects of nitrogen addition on vented hydrogen–air deflagration in a vertical duct

In this paper, experiments were performed to investigate the coupling effects of venting and nitrogen addition ratio (χ) on flame behavior and pressure evolution during hydrogen–air deflagration within and outside a 1-m-high vertical duct with a vent on its top. Experimental results reveal that χ has significant effects on the pressure–time histories in the duct. Helmholtz oscillations of the internal overpressure were observed in all tests, and acoustic type oscillations appears in the tests only for χ = 25% and 30%. For a certain χ, the maximum overpressure (Pmax) increased with the distance to the vent, i.e., the highest overall explosion overpressure was attained near the duct bottom; however, the difference in Pmax between various measuring points decreases with an increase in χ. In all tests, a pressure peak in the duct was observed shortly after external explosion. The maximum internal and external overpressure decreased as χ was increased.

External explosions of vented hydrogen-air deflagrations in a cubic vessel

The effects of hydrogen concentration and ignition location on the external explosion were experimentally investigated during vented hydrogen-air deflagrations in a cubic vessel. Hydrogen concentration ranging from 14 vol% to 50 vol% and three ignition locations (front, center, and back ignitions) were focused with the ambient temperature and pressure of 283 K and 100.5 kPa, respectively. The pressure histories and flame behavior inside and outside the vessel were recorded. Experimental results show that Helmholtz oscillation was always found for front ignition. Three overpressure peaks of Popen, Phel and Pvib resulting from the vent rupture, Helmholtz oscillation and flame-acoustic-oscillation were recorded respectively. For center and back ignitions, an additional overpressure peak Pext, generated by the external explosion, was monitored. Popen was the maximum one for front ignition while Pext became the maximum one with increasing hydrogen concentration for center and back ignitions. However, the maximum overpressure for back ignition was significantly larger than those for front and center ignitions. Only one external overpressure peak was recorded for front ignition. However, as hydrogen concentration was larger than 18 vol%, two external overpressure peaks were recorded for center and back ignitions, and the one induced by the external explosion for back ignition was significantly larger than that for center ignition. Moreover, external explosion affected significantly affects the flame evolution outside the vessel.

Experimental study of the effects of vent area and ignition position on internal and external pressure characteristics of venting explosion

Explosion venting can cause not only internal damage but can cause external damage to buildings. Since little attention is paid to the damage caused by both explosions simultaneously, vented explosion tests were performed in a 4.5 m3 square chamber, to investigate the internal and external pressure characteristics and their correlation. The results show that ignition location has little effect on venting pressure (P1), but significantly affects the Helmholtz oscillations and high-frequency oscillation pressure (P4). Central and front ignitions lead to the maximum P4 and longest Helmholtz oscillation, respectively; during venting, two pressure peaks (defined as Pe1 and Pe2) were recorded due to the shock wave and combustion wave, respectively. Pe1 has an inverse proportional relationship with distance. Pe2 is proportional to P1. When the vent area exceeds 0.16 m2, Pe2 under rear ignition plays a more dominant role than that of other ignition points, however, the vent area is equal to 0.16 m2, Pe2 with central ignition becomes dominant. The external pressure peaks corresponding to the external flame development were captured. The longest length of the jet flame was observed at central ignition and rear ignition forms the largest external combustion area.

Gasoline Vapor Explosion Modes in Confined Space under Weak Constraint Conditions

The article focuses on the establishment of the experiment system in confined space with weak constraint surface. It also studies the overpressure variation of gasoline vapor explosion, the mechanism of flame shapes with time, and the coupling relationship between them under different weak constraint conditions. Meantime, the development modes of external flame after the damage of weak constraint are categorized. The results show that: 1. With the increasing area of weak constraint surface, the development modes of external flame can be categorized into: under-expansion jet combustion, jet combustion, external explosion. 2. When an external explosion occurs, the change of internal overpressure in confined space is more complicated, with multiple overpressure peaks as well as strong Helmholtz oscillations. 3. Lower initial gasoline vapor concentration and large area of weak constraint surface are more conducive to external explosion.