Helmholtz Oscillator Research Articles

Experimental study of NH3/H2/Air premixed flame in a variable cross-section pipe with bluff body

Ammonia's distinctive chemical makeup, coupled with its ability to combust fully without carbon emissions, position it as a promising carbon-free fuel but requires careful management to mitigate NOx emissions. In practice, supplementing ammonia with hydrogen addresses its slow combustion rate and high ignition energy requirements. Meanwhile, the introduction of a bluff body (BB) within the pipe can alter the way of flame propagation. This study examines the combustion dynamics of the premixed ammonia/hydrogen/air flame in a pipe with a variable cross-section. The experimental findings demonstrate that increasing both equivalence ratio (Φ) and hydrogen volume fraction (αH2) significantly alters the flame front velocity (FFV) and maximum overpressure (Pmax), while also enhancing the symmetry of the flame across variable cross-section. The addition of BB creates a vortex in the flame, the formation of which intensifies the combustion of the flame behind the BB, which can promote the generation of Helmholtz oscillations, elevate the amplitude of the pressure, improve FFV, and shorten the flame propagation time in the pipe. With the increase of Φ and αH2, the time is shortened less. When Φ = 0.8, αH2 = 40%, the flame propagation time was shortened by 709 ms. When Φ = 1.2, αH2 = 60%, the flame propagation time was shortened by 5.67 ms only. In addition, Pmax and maximum flame front velocity (FFVmax) are more sensitive to αH2 than Φ. After the addition of BB, the increase amplitude of Pmax and FFVmax is increased. However, when Φ = 1.0 and Φ = 1.2, the amplitude of FFVmax increase decreases with the increase of αH2. This study can provide some suggestions for the application of NH3/H2 fuels in variable cross-sections as well as under obstacles.

Self-excited oscillation characteristics and mechanisms of supercritical CO2 flowing in a Helmholtz oscillator for enhancing heat transfer

The drastic variations in thermal properties of supercritical CO2 near its pseudo-critical point induce the formation of complex boundary layer structures within pipelines, rendering it susceptible to heat transfer deterioration under the influence of buoyancy forces. The Helmholtz self-excited cavity can generate self-excited pulsating jets, enhancing the intermixing between fluids inside the heat exchanger tubes, disrupting the thermal boundary layer, and suppressing heat transfer deterioration. In this study, the characteristics and mechanisms of self-excited oscillations of supercritical CO2 flowing vertically upward in the Helmholtz self-excited cavity were investigated using the large eddy simulation (LES) method. A detailed analysis of cavitation and vortex evolution within the cavity was conducted, along with an exploration of the influence of inlet pressure and structural parameters on the frequency characteristics of pulsations. The results indicate a close relationship between cavitation and vortex interactions and the pulsation frequency. An increase in inlet pressure leads to a significant cavitation phenomenon near the jet shear layer and an increase in vortex frequency. Dimensionless cavity length (Lc/d1) enlargement results in an increase in outlet pulsation frequency but a decrease in pulsation amplitude. The critical dimensionless ratio of cavity diameter (Dc/d1) plays a crucial role in maintaining the desired pulsation frequency and amplitude. Within the working range outlined in this paper, practical insights for system design and operation are provided by the optimal parameters of Lc/d1 = 3 and Dc/d1 = 10.

Effect of vent size on vented H2/N2/air deflagration

In this work, the coupling of explosion venting (vent size) and inerting (N2) on H2/air deflagration was investigated. Experiments were carried out in a vertical rectangular duct with an upper opening at an initial temperature and pressure of 280 K and 101 kPa, and a vent coefficient Kv was employed to replace the vent size to elucidate its effect on pressure buildup and flame propagation during H2/N2/air deflagration. In the present study, the internal pressure profile is monitored by three pressure sensors, PS1-3, which are installed at the bottom, center, and top of the duct, respectively, and the external pressure profile is obtained by PS4. The results show that the maximum internal overpressure (pmax) recorded by PS1-3 all increase with increasing Kv, but pmax obtained from PS2 and PS3 tend to increase linearly. For a given Kv, the maximum and minimum amplitudes of pmax are measured by PS1 and PS3, respectively. Specifically, the greater the distance between the pressure sensor and the upper opening, the greater the amplitude of pmax. The relationship between the maximum reduced explosion pressure (pred) and Kv is investigated, where pred is defined as the highest pmax for a specific Kv. As Kv increases from 2.2 to 11.9, pred increases from 26.25 kPa to 88 kPa. The maximum external flame velocity (Vext) increases from 83 m/s to 454 m/s with increasing Kv from 2.2 to 11.9. The amplitude of the maximum external overpressure (pext) first increases and decreases with an increase in Kv from 2.2 to 11.9. The formation time (Δt) of pext decreases and then increases and finally decreases with increasing Kv from 2.2 to 11.9. When Kv is increased from 2.2 to 4.1, all external fireballs are presented as mushroom shapes, but the external fireballs are gradually transformed into jet shapes for Kv ≥7.8. Two pressure oscillations, including Helmholtz oscillations and acoustic oscillations, are found. Acoustic oscillations are found in all tests, but Helmholtz oscillations are only observed for Kv ≤ 4.1.

A comparison of Helmholtz oscillators with differently shaped petal nozzles

A comparison of Helmholtz oscillators with differently shaped petal nozzles

Experimental and theoretical investigations into overpressure during confined space explosions of methane-hydrogen mixture

This study aimed to deeply explore combustion and explosion behaviors within confined spaces fueled by methane-hydrogen blends. By experimenting in a 55 m³ chamber, it examined how different hydrogen mixing ratios (5%, 10%, 15%, and 30%) affect flame spread and overpressure buildup at an equivalence ratio of 1.1. Results showed that two main flame patterns emerge during venting: mushroom clouds and jet flames. Higher hydrogen percentages cause mushroom clouds to form earlier and grow larger; notably, a 30% blend produces a cloud 12% quicker than a 10% blend, reaching a maximum radius of about 2.7 m. Three types of overpressure were identified: Popen (venting structure opening), Pext (external explosion), and Phel (Helmholtz oscillations). Both Pext and Phel rise with increasing hydrogen content. At each blend level, Pext peaks at 1.87–6.42 kPa, while Phel ranges from 5.86 to 20.65 kPa. Pext plays a crucial role in peak overpressure during venting, particularly relevant for ventilation design considerations. To predict Pext, the study tested three engineering models and found that Taylor's spherical piston theory provided the closest match to experimental data, with a maximum error under 30% compared to other models. In summary, this research offers essential theoretical knowledge and practical evidence for designing safer ventilation and explosion relief systems for facilities handling methane-hydrogen mixtures in the process industry.

Phase control of escapes in the fractional damped Helmholtz oscillator

We analyze the nonlinear Helmholtz oscillator in the presence of fractional damping, a characteristic feature in several physical situations. In our specific scenario, as well as in the non-fractional case, for large enough excitation amplitudes, all initial conditions are escaping from the potential well. To address this, we incorporate the phase control technique into a parametric term, a feature commonly encountered in real-world situations. In the non-fractional case it has been shown that, a phase difference of ϕOPT≈π, is the optimal value to avoid the escapes of the particles from the potential well. Here, our investigation focuses on understanding when particles escape, considering both the phase difference ϕ and the fractional parameter α as control parameters. Our findings unveil the robustness of phase control, as evidenced by the consistent oscillation of the optimal ϕ value around its non-fractional counterpart when varying the fractional parameter. Additionally, our results underscore the pivotal role of the fractional parameter in governing the proportion of bounded particles, even when utilizing the optimal phase.

Exact periodic solution of the undamped Helmholtz oscillator subject to a constant force and arbitrary initial conditions

The Helmholtz oscillator is a nonlinear mixed‐parity oscillator that models the asymmetric vibrations of many engineering and scientific systems. This paper investigated a general and completely integrable form of the Helmholtz oscillator and derived its exact periodic solution from the first integral of the governing differential equation. The considered Helmholtz oscillator has general linear and nonlinear stiffness constants, is subject to a constant force, and has arbitrary initial conditions. Its exact time period was derived in terms of the complete elliptic integral of the first kind, while the exact displacement was derived in terms of the Jacobi elliptic sine function. The validity of the exact solutions was verified for various combinations of the system parameters and initial conditions by comparing with numerical solutions. The exact solutions and numerical solutions were found to match perfectly. Furthermore, the exact solution was applied to analyze the vibration response of real‐world systems that could be modeled as Helmholtz oscillators. The present exact solutions provide benchmark solutions that could be used to determine the accuracy of new and existing approximate solutions for the Helmholtz oscillator.

Thermal radiation hazards of the external flow field for vented hydrogen–air explosion: Effect of nitrogen fraction

An experimental investigation is conducted to examine the impact of nitrogen fraction on vented explosions of hydrogen–air–nitrogen mixtures in a 1-m-long cylindrical duct at 1 bar and 281 K. The study employs high-speed shadowgraph imaging, a pressure testing system, and infrared thermal imaging to record the venting process. The results showed that as the nitrogen fraction increases, the rupture time of the vent cover gradually increases. However, the internal peak overpressure exhibits an opposite trend, with P2 (caused by the ignition of unburned gas outside the tube by the escaping flame) near the vent consistently dominating. The frequency of Helmholtz oscillations initially decreases and then increases with increasing nitrogen fraction. Higher nitrogen fractions are associated with a greater likelihood of lower external peak overpressure but a decreasing trend in maximum external impulse. The maximum temperature shows an initial decrease followed by an increase with the addition of nitrogen fraction. This trend is also observed for flame length, flame width, high-temperature duration (>500 °C), and heat energy. Furthermore, the study determined safety zones that are free from thermal radiation damage.

Effect of vent area on vented ammonia-hydrogen-air deflagrations in a 1-m-long duct

Although ammonia-hydrogen blended fuel has become a research hotspot, it is essential to recognize that adding hydrogen to ammonia increases the potential explosion hazard before considering the development of ammonia-hydrogen fuel. In this study, the effect of vent area on vented deflagrations of ammonia-hydrogen-air mixtures is investigated in a 1-m-long horizontal rectangular duct with a right end opening at an initial temperature of 293 K and an initial pressure of 101 kPa. A dimensionless vent coefficient Kv is used to define the vent area in this work to clarify the evolution of flame structures and overpressure inside and outside the duct. For a specific Kv, the amplitude of the maximum internal explosion overpressure (Pmax) monitored at the left end of the duct (LE) has a greater difference compared with other pressure monitoring points. The maximum amplitude of Pmax is always reached at the LE for Kv ≤ 3.2, while the difference in the maximum amplitude of Pmax between different monitoring points decreased significantly for Kv > 3.2. With the increasing of Kv from 2.2 to 20.1, Pmax obtained at the right end of the duct (RE) and the center of the duct increases monotonously, but Pmax monitored at the LE shows a non-monotonic increasing trend. A spike structure of penetrating flame bubbles resulting from negative pressure balance is only observed inside the duct for Kv ≤ 5.6. Two types of oscillations (Helmholtz and Acoustic oscillations) can be distinguished in some tests, and only acoustic oscillations of overpressure can be clearly found in tests with Kv > 7.8. With the increasing of Kv from 2.2 to 20.1, the shape of the external fireball will change significantly. As Kv increases from 2.2 to 5.6, the external fireball shapes are always mushroom-shaped. However, the shapes of the fireball become elongated for Kv > 7.8, and even the external fireball presents a jet shape for Kv = 20.1. With the increasing of Kv from 2.2 to 20.1, The maximum external overpressure increases first, thereafter decreases, and finally increases.

Study on flexible/rigid protection mechanism of hydrogen/methane premixed gas explosion in urban underground space

Explosion accidents are one of the factors that impede urban underground space development and utilization, and it is imperative to study safety precautions in case of an explosion in an urban underground space. Given this problem, a polyurethane sponge and carbon fiber board with Blocking Rates (BR) of 0.2, 0.4 and 0.6 were used to explore the combustion and explosion characteristics of hydrogen/methane premixed gas in a confined space in the presence of a flexible and rigid obstacle. The results indicated that both the flame and pressure exhibit Helmholtz oscillation characteristics in case of a rigid obstacle. When the BR of both flexible and rigid obstacle were 0.4, the explosion intensity index was the highest. It first increased and then declined with the increase of flexible obstacle BR. In the presence of a flexible obstacle, the Helmholtz oscillation phenomenon was completely suppressed, and explosion intensity indices were minimized, as the flexible obstacle BR increased, it first increased and then declined. Under the rigid obstacle preset conditions, the explosion hazard significantly increased compared to the flexible constructions. The research results provide a theoretical basis for protective facilities to suppress combustion and explosion phenomena in underground spaces.

Combined inhibition effect of vacuum chamber and inert gas on LPG explosion

In order to investigate combined inhibition effect of vacuum chamber and inert gas on Liquefied petroleum gas (LPG) explosion, the explosion experiment was carried out on the self-built gas explosion experiment pipe (L/D = 47.5). The flame propagation and explosion pressure characteristics of LPG were investigated at different vacuum degrees and 10% CO2 volume fraction (VF). The results showed that it is feasible to use a photosensitive solenoid valve to open the vacuum chamber. The Photoreceptor Solenoid Valve can open the vacuum chamber in time; Compared to add only 10% CO2, after installing the vacuum chamber, the maximum pressure peaks were all delayed; The pressure drops rapidly and a short period of negative pressure appeared, and the negative pressure duration becomes shorter as the vacuum degree increases; At various vacuum degrees levels, the maximum pressure peak value occurs at 0.06 vacuum degrees, primarily due to the combined influence of residual fuel quantity, Helmholtz oscillation, and turbulence near the flame front. The Pmax in the pipe and the flame intensity at any position is lower than that when only adding 10% CO2; high vacuum is more conducive to extinguish the flame and increase the thickness of the flame; the pumping effect of the vacuum chamber inhibits the rise of explosion pressure and flame propagation velocity. The combined explosion suppression is more effective on LPG explosions compared to add only 10% CO2. When selecting vacuum degree, it is important to consider the impact of the opening time and different vacuum degree within the vacuum chamber on pressure formation and flame propagation.

Effects of transverse concentration gradients on the vented explosion of methane-air mixtures

Experiments were performed in a 90-L vessel with a side vent to investigate the effects of transverse concentration gradients on the vented explosion of non-uniform methane-air mixture. Controlled by a mass flow meter, methane was injected uniformly into the vessel through 18 nozzles that are evenly distributed at the top to configure a methane-air mixture with an average methane volume fraction of 10.9%. Various transverse concentration gradients were obtained by altering the free diffusion time of the methane in the vessel. The deflagration flame was recorded through a high-speed camera at a frequency of 1000 Hz, and the internal overpressure at different locations was captured through three piezoelectric sensors. Experimental results reveal that larger concentration gradient resulted in lower flame propagation rate, longer time for the burst of the vent cover, and stronger pressure oscillations. Concentration gradient affects the typical flame structure, especially the formation and development of the tulip flame. Under the present experimental conditions, Helmholtz oscillations occurred in all tests. Concentration gradient has a negative correlation with the frequency of Helmholtz oscillations but a positive correlation with the duration of oscillations. In conclusion, the variation of concentration gradient obviously affects flame propagation and pressure evolution during vented explosions, which deserves more attention in the design of explosion protection.

Optical study of active narrow throat pre-chamber assisted internal combustion engine at lean limit

The pre-chamber assisted ignition offers several much-needed upgrades to gas engines, ranging from improved combustion efficiency and stability to extended lean limits. The concept has received intermittent attention from researchers over the past century, and the concept's fundamental understanding remains segmented. This study investigates pre-chamber assisted combustion (PCC) in a heavy-duty gas engine fueled by methane at the lean limits. The engine is operated at two lean limits at intake pressures of 1.2 and 1.4 bar. At lower intake pressure, global excess air ratio (λglobal) is 2.4, while at higher intake pressure λglobal is 2.6. The comparison of two lean limits through experimental data and GT-Power 1D model reveals the underlying ignition and combustion. Using a combination of acetone PLIF (N-PLIF) and OH* chemiluminescence imaging allows visualization of both the reacting and non-reacting part of the pre-chamber jet. The results suggest that pressure differential across the pre-chamber and main chamber controls the reacting jet growth speed. The combustion chamber boundaries affect the main combustion through the wall jet part of the impinging pre-chamber jets as higher OH* concentrations are observable at stagnation points of the jet. In addition, the study reports the appearance of post-combustion jets and dispersed OH* pockets as the combustion dwindles. The narrow throat pre-chamber shows a spectral pressure signature reminiscent of the Helmholtz oscillator, and circumferential resonant modes dominate the main chamber combustion. Although the PCC offers great ignitibility, the main chamber mixture cannot sustain prolonged combustion at a lean limit lambda value.

Excitation of Acoustic Modes by Tone Harmonics of a Hole in a Jet-Driven Helmholtz Oscillator

Excitation of Acoustic Modes by Tone Harmonics of a Hole in a Jet-Driven Helmholtz Oscillator

Nonlinear dynamics, coexistence of attractors and microcontroller implementation of a modified Helmholtz Jerk oscillator

In this work, we converted a two-dimensional modified Helmholtz oscillator into a three-dimensional modified Helmholtz jerk oscillator. The study of the stability of the fixed points is made and by using the theorem of Hopf, the condition of existence of the bifurcation of Hopf is sought. By numerical simulations relating to the diagrams of the basin of parameters, attraction, bifurcation, the Lyapunov exponents and the phase portrait, the global dynamics as well as the coexistence of the attractors of the system are analyzed. This study revealed that the considered modified Jerk Helmholtz oscillator can generate Hopf bifurcation, bistable limit cycles, coexistence of chaotic and periodic attractors for appropriate choices of system parameter values. The microcontroller based implementation of the modified Jerk Helmholtz oscillator is proposed to experimentally verify the obtained analytical and numerical results. Finally, to control the amplitude of the Lyapunov attractor and exponent, we added two new parameters in the modified Helmholtz jerk oscillator.

Global analysis of stochastic and parametric uncertainty in nonlinear dynamical systems: adaptative phase-space discretization strategy, with application to Helmholtz oscillator

Global analysis of stochastic and parametric uncertainty in nonlinear dynamical systems: adaptative phase-space discretization strategy, with application to Helmholtz oscillator

Excitation of Acoustic Modes by Tone Harmonics of a Hole in a Jet-Driven Helmholtz Oscillator

Periodic pressure fluctuations were studied experimentally in the model of a jet-driven Helmholtz oscillator with a cylindrical chamber with a round air jet impinging on the sharp edge of the outlet. The evolution of the amplitude–frequency spectrum of the hole tone from its appearance at a jet velocity of about 2 m/s to excitation of the first acoustic resonance mode at the Helmholtz frequency was studied. The hole tone was a family of harmonics that progressively became more complex as the length and velocity of the jet increased. The successive occurrence of a family of acoustic modes on the harmonics of the jet tone with a further increase in jet velocity is studied. Modes at the Helmholtz frequency arose alternately on the harmonics of the hole tone in the gain band of the oscillator, starting from the highest harmonic. The first mode occurred at the highest harmonic; the second mode, at the previous harmonic; and so on. The final mode arose at the fundamental harmonic of the hole tone and had the maximum amplitude. With a further increase in the Reynolds number, periodic pressure fluctuations became disordered turbulent fluctuations. With a sufficient chamber size and jet velocity, azimuthal and half-wave resonances appeared at the highest harmonic of the hole tone. The largest Reynolds number at which resonance at the Helmholtz frequency was observed was 105.

Cavitation Reactor for Pretreatment of Liquid Agricultural Waste

One of the most well-known methods of intensifying the process of anaerobic digestion is the pretreatment of raw materials. For the first time, the use of a jet-driven Helmholtz oscillator for biomass pretreatment is proposed. The design of the device is optimal for creating hydraulic cavitation; however, in this case, acoustic oscillations are generated in the system and resonance occurs. In this study, the optimal design of this device was determined for the subsequent design of a cavitation reactor. The diameter of the resonant chamber was varied in the range from 28.3 to 47.5 mm, and its length from 6 to 14 mm; in addition, the diameter of the outlet was changed from 6.1 to 6.3 mm. Based on the experimental data obtained, it was found that the optimal ratio of the length of the resonator chamber to the diameter of the inlet nozzle is 1.73, and the inner diameter of the resonator chamber to the diameter of the inlet nozzle corresponds to 5.5. Improving the technology of agricultural waste disposal will ensure their maximum involvement in economic circulation, reduce the consumption of traditional fuel and energy resources, and improve the technological and machine-building base, which makes it possible to produce competitive cavitation reactors.

Characteristics of nano-PMMA dust explosion through the vented tube

The explosion venting experiments of 150 nm polymethyl methacrylate (PMMA) dust with different lengths (L) and diameters (D) of the vent tube are conducted. The effect of tube size on overpressure and flame propagation behavior is explored. High-frequency and low-frequency Helmholtz oscillations are observed on the overpressure curves in the chamber. The (dP/dt)max in the chamber is increased with high-frequency oscillations, while the maximum flame width is also visible with low-frequency Helmholtz oscillations. As the L increases from 0 m to 2 m, the Pred,max increases by 29.2–145.1% and the (dP/dt)max increases by 38.4% − 127.7%. With the increase of the D, the Pred,max in the chamber and vent tube decreases, and the flame transforms from an under-expansion jet flame to a subsonic jet flame. Due to the interaction between the external flow field and the concentration of unburned particles, the maximum external overpressure increases alongside with the incease of the tube length and diameter. In addition, the maximum calculation error of EN14491 is 1100%, while NFPA68 seriously underestimates the explosion venting pressure. A modified prediction model is established to provide a design method for a safe vent through the vent tube of the nano-dust explosion.

Effects of H2 addition on the instability characteristics of CO/air and CH4/air in a horizontal narrow channel

ABSTRACT This paper investigates the instability characteristics of CO/H2/air and CH4/H2/air mixtures in a narrow channel under standard temperature and pressure conditions. The CO/H2 mixture exhibits a greater overpressure growth rate and maximum explosion overpressure as compared to the CH4/H2 mixture at the same hydrogen content. As the hydrogen content increases, the maximum explosion overpressure (P max) value increases, while the corresponding time (θ) value gradually decreases. The maximum explosion overpressure of CH4/H2 and CO/H2 mixtures is 28.27 kPa and 25.09 kPa, respectively. The flame wrinkles to form cells due to the Darius-Landau instability, and the interaction between the vortex tube and premixed flame affects the structure of turbulent premixed combustion. The oscillation frequency of the overpressure increases with increasing hydrogen content, and the oscillation belongs to the Helmholtz oscillation. The CO/H2 mixtures exhibit greater flame thickness than CH4/H2 mixtures, resulting in lower Peclet numbers and therefore greater relative importance of heat losses. As the hydrogen content increases, the sensitivity coefficient of R99 (OH + CO <=> H + CO2) in the CO/H2 mixture gradually decreases, while the sensitivity coefficients of R38 (H + O2 <=> O + OH) and R84 (OH + H2 <=> H + H2O) increase. The elementary reaction R38 plays a leading role in increasing the laminar burning velocity of the CH4/H2 mixture. The trend of R38 variation in the two mixtures is opposite with increasing hydrogen content.