Spot Ignition Research Articles

Spotting ignition of plastic foam by a fast-moving hot metal particle

Spotting ignition involves dynamic interaction between fuel bed and hot particles, but the scientific understanding of the ignition by a fast-moving hot particle is still limited. Herein, a hot steel particle with various horizontal velocities, temperatures, and sizes is shot to ignite vertically oriented low-density expandable polystyrene foam. A high-speed particle can directly get embedded into the foam to achieve flash-point, fire-point, or no ignition, while a low-speed particle bounces away from the foam without ignition. Results show that for a particle of 1150 °C, its minimum velocity for embedding is 12.00 m/s. Such a critical velocity for hot-particle embedded or ignition slightly decreases as particle temperature increases. Minimum ignition temperature of these high-speed particles is 200 °C higher than that of near-static or with a low free-fall velocity, due to the shorter residence time and insufficient to produce a flammable mixture. Moreover, when the particle is neither too slow to bounce away nor too fast to get embedded, it will be partially embedded on the sample surface to burnout the fuel, posing the biggest fire hazard. It deepens our knowledge of the complex interaction between hot moving particles and insulation foam to reduce spotting fire risk for building façade.

Smoldering ignition and transition to flaming in wooden mulch beds exposed to firebrands under wind

Spotting ignition by firebrands is a significant fire spread pathway at the wildland-urban interface (WUI), where mulch products are commonly used as landscaping materials. Mulch is typically organic in nature, thus it may be easily ignited into a smoldering mode by firebrands and subsequently transition to flaming, leading to direct flame contact and radiant heat exposure to siding materials of adjacent structures. This work quantified the thresholds of smoldering ignition of four common types of commercially available mulch (black mulch (BM), forest floor (FF), redwood (RW), and fir bark (FB)) exposed to heating by smoldering firebrand piles, and their propensity for smoldering-to-flaming transition under external winds (up to 1.4 m/s). We found that there was a minimum mass of firebrand pile to achieve smoldering ignition of mulch (e.g., ∼0.1 g for FF). Beyond this minimum mass, the required wind speed to trigger smoldering ignition generally decreased as the mass of the firebrand pile increased, agreeing well with theoretical analysis. After smoldering ignition, smoldering-to-flaming transition could be observed when the wind speed exceeded a critical value (e.g., ∼1 m/s for FF), which was not affected by the initial spotting process. To achieve smoldering-to-flaming transition, the glowing mulch had to reach a critical temperature of around 850 °C. Mulch samples with larger particle sizes were more likely to smolder and transition to flaming, due to increased oxygen supply through larger inter-particle pores and channels and better firebrand accumulation due to a more crevice-like geometry on the fuel surface. This work advances the fundamental understanding of the ignition and burning behavior of landscaping mulches, and thus contributes to the prevention of extreme WUI fire events.

Spot ignition of a wildland fire and its transition to propagation

Spot ignition of a wildland fire and its transition to propagation

Computational study on the glowing combustion of a wooden ember landing on a non-reacting substrate

Despite the increasing frequency in spot ignition by embers in wildfires, research on the multiple physicochemical processes intrinsic to ember combustion is limited. In this study, a two-dimensional computational model was proposed to study the glowing combustion of a wooden ember. A global char oxidation reaction was used to represent the glowing combustion of the ember. A parametric study showed that the porosity, heat of reaction, and oxygen concentration were the most influential parameters on the ember combustion. Then, the model was compared to a series of bench-scale experiments in terms of glowing time and thermal response of a non-reacting substrate when exposed to a hot ember. The simulation results showed that ember combustion was mostly diffusion-controlled rather than kinetic-controlled. Thus, given the ember diversities in spotting fire, modelers should pay more attention to the difference in the physical properties instead of the kinetics between ember species.

Near-infrared laser induced direct ignition of 4,4′,5,5′-tetranitro-1H,1′H-[2,2′-biimidazole]-1,1′-diamine by constructing diverse crystal structures

Although laser ignition is considered to be one of the most promising ways to detonate energetic materials due to its high safety and reliability, it is still a challenge to achieve direct ignition of energetic materials by a laser with low-power and near-infrared (NIR) band. In this paper, a molecular self-assembly strategy based on recrystallization was utilized to prepare 4,4′,5,5′-tetranitro-1H,1′H-[2,2′-biimidazole]-1,1′-diamine (DATNBI) crystals with various micro-nano structures. The characterization results suggest that DATNBI crystals with different degrees of roughness and defects by the induction of solvents and surfactants. The crystal defects can not only bring about the enhancement of light absorption of DATNBI in NIR band, but also advance its thermal decomposition, providing reliable support for direct laser ignition of DATNBI profit from the hot spot ignition theory. Combined with density functional theory, it is speculated that electrons of defect states achieve electron-hole recombination by laser radiation, thereby enhancing photothermal conversion. Compared with raw DATNBI, DATNBI crystals with rough surface and abundant defects can be directly ignited by a NIR laser and exhibits self-sustainable combustion. In summary, a direct NIR laser-ignitable energetic material has been prepared via appropriate crystal structure design.

Ignition Delay and Reaction Time Measurements of Hydrogen–Air Mixtures at High Temperatures

Induction and reaction times of hydrogen–air mixtures (ϕ = 0.5–2) have been measured behind reflected shock waves at temperatures of 1000–1600 K, pressures of 0.1, 0.3, 0.6 MPa in the domain of the extended second explosion limit. The measurements were performed in the shock tube with a completely transparent test section of 0.5 m long, which provides pressure, ion current, OH and high-speed chemiluminescence observations. The experimental induction time plots demonstrate a clear increasing of the global activation energy from high- to low temperature post-shock conditions. This trend is strongly pronounced at higher post-shock pressures. For a high-temperature range of T > 1200 K, induction time measurements show an activation energy for the global reaction rate of hydrogen oxidation of 64–83 kJ/mole. Detected reaction times exhibit a big scatter and a weak temperature dependence. The minimum reaction time value was nearly 2 µs. Obtained induction time data were compared with calculations carried out in accordance with the known kinetic mechanisms. For current and former shock-tube experiments within a pressure range of 0.1–2 MPa, critical temperatures required for strong (1000–1100 K), transient and weak auto-ignition modes behind reflected shock waves were identified by means of the pressure and ion-probe measurements in stoichiometric hydrogen-air mixture. The transfer from the strong volumetric self-ignition near the reflecting wall to the hot spot ignition (transient) was established and visualized below <1200 K with a post-shock temperature decreasing.

Crankcase Explosions in Marine Diesel Engines: A Computational Study of Unvented and Vented Explosions of Lubricating Oil Mist

Accidental crankcase explosions in marine diesel engines are presumably caused by the inflammation of lubricating oil in air followed by flame propagation and pressure buildup. This manuscript deals with the numerical simulation of internal unvented and vented crankcase explosions of lubricating oil mist using the 3D CFD approach for two-phase turbulent reactive flow with finite-rate turbulent/molecular mixing and chemistry. The lubricating oil mist was treated as either monodispersed with a droplet size of 60 μm or polydispersed with a trimodal droplet size distribution (10 μm (10 wt%), 250 μm (10 wt%), and 500 μm (80 wt%)). The mist was partly pre-evaporated with pre-evaporation degrees of 60%, 70%, and 80%. As an example, a typical low-speed two-stroke six-cylinder marine diesel engine was considered. Four possible accidental ignition sites were considered in different linked segments of the crankcase, namely the leakage of hot blow-by gases through the faulty stuffing box, a hot spot on the crankpin bearing, electrostatic discharge in the open space at the A-frame, and a hot spot on the main bearing. Calculations show that the most important parameter affecting the dynamics of crankcase explosion is the pre-evaporation degree of the oil mist, whereas the oil droplet size distribution plays a minor role. The most severe unvented explosion was caused by the hot spot ignition of the oil mist on the main bearing and flame breaking through the windows connecting the crankcase segments. The predicted maximum rate of pressure rise in the crankcase attained 0.6–0.7 bar/s, whereas the apparent turbulent burning velocity attained 7–8 m/s. The rate of heat release attained a value of 13 MW. Explosion venting caused the rate of pressure rise to decrease and become negative. However, vent opening does not lead to an immediate pressure drop in the crankcase: the pressure keeps growing for a certain time and attains a maximum value that can be a factor of 2 higher than the vent opening pressure.

Ignition limit of EPS foam by a hot particle under cross wind

The ignition of the building insulation materials by a hot particle is a typical spot fire phenomenon, but the scientific understanding is still limited. In this work, a hot steel spherical particle (6-16 mm and 800-1200 °C) was dropped onto the low-density expandable polystyrene (EPS) foam with an external airflow velocity of 0-4 m/s to obtain the ignition limit at the flash point and fire point. Airflow provides an alternative shortcut transition of unstable flash flame to a strong fire point and fuel burnout, because airflow increases the oxygen supply and flame heating rather than cooling the particle. As the airflow velocity increases, both flash and fire points first become easier to reach because airflow facilitates the mixing of pyrolysates and oxygen in the Smothering Regime. When the airflow velocity increases to the Thermal Regime, the delay time remains stable. Further increasing the airflow velocity to the Chemical Regime, the ignition delay time slightly increases until the airflow blows off the flash flame by cooling the particle or blowing away the flammable mixture from the hot surface. Such a competitive effect of airflow on hot particle ignition is also qualitatively verified by theoretical analysis. Flame retardants inside EPS foam do not change the flash ignition but inhibit the transition to fire point and burnout, even under the assistance of airflow. This work enhances the comprehension of the complex interactions between flash points and fire points in the spotting or hot-particle ignition of the building facades.

A visualization investigation on the characteristic and mechanism of spontaneous ignition condition of high-pressure hydrogen during its sudden release into a tube

Hydrogen is regarded as one of the promising fuels in the next decades. However, the spontaneous ignition of high-pressure hydrogen blocks its safe utilization. In this investigation, a visualization investigation is carried out to study on the characteristic and mechanism of spontaneous ignition condition of high-pressure hydrogen during its sudden release into a tube. A rectangular tube with transparent observation window is employed. The high-speed images of spontaneous ignition conditions and light signals emitted from ignition are obtained. Four spontaneous ignition conditions are observed: (1) no ignition; (2) failed ignition with one ignition spot; (3) failed ignition with two ignition spots and (4) successful ignition. The critical burst pressure for four ignition condition is determined. The jet fire (successful ignition) could be generated in the cases with a shorter distance from ignition spot to leading shock wave and contact surface due to the stronger shock wave affection and sufficient flammable mixture maintaining the chemical reaction and flame propagation. The second ignition is the precondition forming the successful ignition. The scaled ignition delay time and distance could be predicted by using the derived dimensionless shock pressure.

On the role of transverse detonation waves in the re-establishment of attenuated detonations in methane–oxygen

This investigation concerns the problem of detonation attenuation in stoichiometric methane-oxygen and its re-establishment following its interaction with obstacles, using high resolution numerical simulation. The main focus was on the role of the transverse detonation on the re-establishment of the detonation wave, and the importance of applying a numerical combustion model that responds appropriately to the thermodynamic state behind the complex shock wave dynamics. We applied an efficient thermochemically derived four-step global combustion model using an Euler simulation framework to investigate the critical regimes present. While past attempts at using one- or two- step models have failed to capture transverse detonations, for this scenario, our simulations have demonstrated that the four-step combustion model is able to capture this feature. We thus suggest that to correctly model detonation re-initiation in characteristically unstable mixtures, an applied combustion model should contain at least an adequate description to permit the correct ignition and state variable response when changes in temperature and pressure occur, i.e., behind shocks. Our simulations reveal that (1) there is a relationship between the critical outcomes possible and the mixture cell size, and (2) while pockets of unburned gas may exist when a detonation re-initiates, it is not the direct rapid consumption of these pockets that gives rise to transverse detonations. Instead, the transverse detonations are initiated through pressure amplification of reaction zones at burned/unburned gas interfaces whose combustion rates have been enhanced through Richtmyer–Meshkov instabilities associated with the passing of transverse shock waves, or by spontaneous ignition of hot spots, which can form into detonations through the Zeldovich gradient mechanism. In both situations, non-uniform ignition delay times are found to play a role. Finally, we found that the transverse detonations are in fact Chapman–Jouguet detonations, but whose presence contributes to overdriving the re-initiated detonation along the Mach stem.

Modeling smoldering ignition by an irradiation spot

Irradiation spots, such as lasers, lightning strikes, and concentrated sunlight, are common ignition sources in building and wildland fires, where smoldering is generally first ignited and then transitions to flaming. In this work, a physics-based 2-D computational model that integrates heat-and-mass transfer and heterogeneous chemistry is built to investigate the smoldering ignition of typical solid fuels using irradiation spots. Simulation results predict that, given the size of the irradiation spot, the ignition time decreases as the radiant heat flux increases. However, as the diameter of the irradiation spot decreases, the modeled minimum heat flux of smoldering ignition increases significantly, agreeing well with experiments and theoretical analysis. When the irradiation spot is smaller than 20-50 mm, assumptions of constant ignition temperature and fuel-burning flux become invalid. The commonly-used physical dimensions of thermally thin/thick fuels are not applicable for smoldering spotting ignition due to the significant radial conductive heat loss in the lateral direction. Further analyses show that the minimum irradiation of smoldering ignition increases as the fuel thickness increases, but it is insensitive to the fuel moisture content. This is the first time that a sophisticated 2-D model has been used to predict the smoldering ignition using irradiation spots, which deepens the understanding of the ignition by a remote heating source and large irradiation.

Cooperative spot ignition by idealized firebrands: Impact of thermal interaction in the fuel

Firebrand spotting is a major cause for structure losses in wildland-urban interface (WUI) fires. When firebrands land nearby and accumulate into groups or piles, they can act as a more competent ignition source compared to single firebrands. While experimental studies have demonstrated this, and measured the enhanced ability to ignite fuels, it is not understood under what critical conditions the firebrands act as an accumulation rather than individual isolated firebrands. This work is an experimental and numerical study of how the fuel bed thermal interactions influence the subsequent flaming ignition propensity of wood in contact with two electric heaters acting as idealized firebrands. The experiments use electrical cartridge heaters of two sizes (7.5 and 15 mm in width) which produce an incident heat flux to the fuel (up to 60 kW/m2) to create controllable heating conditions comparable to those from firebrands. It is observed that decreasing the heater size requires higher heat fluxes to the fuel for ignition to occur. When a second heater is introduced within a certain critical distance it is found to hasten ignition or make ignition possible with a lower incident heat flux to the fuel. Numerical modelling is used to elucidate the importance of thermal interactions in the fuel on the propensity of flaming ignition. The numerical modelling is also used to examine a broader range of idealized firebrand sizes (5 − 50 mm) and the separation distance between idealized firebrands in finer resolution. The model 2D captures the qualitative ignition behaviour well and even shows quantitative agreement in most cases.

Laser-induced plasma-ignited hydrogen jet combustion in engine-relevant conditions

This work aims to investigate the mechanisms governing H2 jet flame evolution and stabilisation by precisely controlling the jet ignition location using a laser-induced plasma in compression-ignition engine-relevant conditions. The experiments examine the flame evolution with high-speed schlieren imaging and pressure trace measurements in an optically-accessible constant-volume combustion chamber over a range of ambient O2 concentration (10–21 vol%) and temperature (600–800 K) conditions. Optical results reveal that in most cases, a localised flame kernel forms at the time and location of the laser-induced plasma and grows in connected regions to engulf the entire upstream and downstream jet volume of the ignition spot. The images also reveal that the flame lift-off is sensitive to ambient O2 and temperature changes. The flame appears attached to the nozzle at 21 vol% O2, but becomes lifted at a lower ambient O2 concentration and a colder temperature. A simplified numerical analysis suggests that edge-flame deflagration into stratified premixed fuel-ambient reactant streams explains the lift-off response to ambient O2 and temperature changes. Furthermore, at the lowest tested O2 concentration, the flame stabilisation occurs in leaner mixtures at the jet peripheral where it is likely exposed to stronger turbulence-chemistry interactions.

Determination of Cooling Rate and Temperature Gradient during Formation of Cathode Spot Craters in a Vacuum Arc

Due to the extreme thermal conditions and short lifetimes, experimental exploration of cathode spots in vacuum arcs is very difficult. The intensive heat in the cathode spot is believed to be generated by ion bombardment and by Joule heating. However, thermal conditions occurring inside the re-melted material in craters created by cathode spots are not accurately known. During the exposure to cathodic arc plasmas, an Al-Cr cathode’s surface was locally melted by successive ignition and extinction of cathode spots. The melted layer, that quickly solidified, was characterized by the formation of several thin layers with a thickness of a few micrometers that were stacked on top of each other. The corresponding solidification patterns displayed cellular and dendritic microstructures. A phase field-based model was used to simulate and determine the thermal process conditions that led to the dendritic structures observed within the re-melted layer. Different combinations of cooling rates and temperature gradients were numerical explored to determine the most probable thermal conditions under which the cathode material re-solidifies. The results showed that the material in the vicinity of the cathode spot crater re-solidified under the condition of a cooling rate of about 3 × 105 K/s and a temperature gradient of about 6 × 107 K/m. These results constitute valuable data for the validation of numerical models dedicated to cathode spot formation.

Hierarchical Bayesian approach to developing probabilistic models for generation and transport of firebrands in large outdoor fires under limited data availability

Spot ignition by wind-dispersed firebrands is an important factor for large outdoor fires. However, the large probabilistic variability in the generation, transport, and ignition processes makes it difficult to quantify the risk. Data collection under a wide range of conditions is essential for quantifying uncertainty. Generally, this can be addressed only with relatively small-scale experiments conducted repeatedly under the desired conditions, simultaneously involving ambiguity in the consistency of the full-scale behavior. However, data collection in full-scale experiments is complex, particularly for behaviors such as large outdoor fires, which makes it difficult to acquire sufficient data for statistical analysis. To fill this gap, we employed a hierarchical Bayesian approach to alleviate the estimation variance of the probabilistically varying characteristics of the spot-ignition processes involved in full-scale behavior. In the present analysis, the results of two previous experiments were used: a full-scale experiment that burnt a three-story wooden building, and a wind tunnel experiment that burnt wood cribs in an open-top combustion apparatus. Pooled models, using mixed data from all experiments without considering the relationship between data sources, were less successful in developing probabilistic distributions in some instances. By contrast, hierarchical Bayesian models (HBMs) are relatively robust, compensating for the scarcity of full-scale data with small-scale data. The obtained HBMs were applied to estimate the probabilistic distributions for the size and transport distance of firebrands under the hypothesized fire conditions. A comparison between the HBMs and existing probabilistic models demonstrated a significantly short dispersal range of firebrands by the latter, which may lead to an underestimation of hazards in practical applications. This study presents a methodology for constructing a reasonable probabilistic model for the processes of spot ignition behavior, which often encounter the issue of data limitations for statistical analysis.

Applying Machine Learning for Firebrand Production Prediction

This article presents a machine learning (ML) based metamodeling framework for firebrand production prediction. This framework was implemented to predict the firebrand areal mass density (FAMD) and firebrand areal number density (FAND) of landing firebrands using a large set of data from full-scale laboratory firebrand production experiments. The independent variables used in our ML models to predict the dependent variables FAND and FAMD were landing (or travel) distance, wind speed, and fuel type (structural and vegetative fuels). It was demonstrated that the non-linear non-parametric ML model, K-nearest neighbors (KNN), works the best for this purpose. The KNN model predicted discrete FAND and FAMD values with an accuracy higher than 90%. The current ML model can be used to predict locations with high risk of spotting ignition potential. This research is a small step towards the bigger goal of creating a numerical firebrand production simulator.

Doping of Al/CuO with microwave absorbing Ti3C2 MXene for improved ignition and combustion performance

Nanothermites have a wide application in many civil and defense applications, including propulsion and detonations systems, micro-electromechanical (MEMs) and other systems that require fast energy release rate and low ignition temperature. Traditional ignition methods are commonly based on surface excitation (spot ignition), possessing a risk of undesired ignition. Safe and selective microwave (MW)-based igniting systems can interact with an ignitable material (typically a thermite) over its full volume at once. Unfortunately, thermites have low susceptibility to MW due to the presence of Al2O3 oxide shell on Al particles, which would commonly require a high ignition power of MW radiation and long ignition delay times. In this work, Ti3C2 MXene was introduced as a MW susceptor into Al/CuO energetic nanocomposites. The samples were ignited using a MW probe, showing that the introduction of MXene into Al/CuO/MXene could significantly reduce the power required for its MW ignition, as well as shorten the ignition delay time versus the parent Al/CuO nanothermite. Besides, presence of MXene could modulate and control a heat release, gas production and combustion performance of the Al/CuO/MXene composites, substantially extending safety, flexibility and adaptability of new nanothermites to various operational requirements.

Impacts of defect distribution on the ignition of crystalline explosives: An insight from the overlapping effect

Many challenges remain in our understanding of the role that heterogeneities play in determining material responses, especially under extreme conditions. In this study, four defect distribution patterns were first built and shocked to quantitatively assess the effects of the spatial distribution of void defects on the hot spot formation and ignition of 1,3,5-trinitroperhydro-1,3,5-triazine crystals through reactive molecular dynamics simulations. A high correlation was found between void concentration and the hot-spot temperature, average temperature, and energy release rate of the defect distribution patterns, which is referred to as an overlapping effect. A higher dispersion degree of defects can result in a lower overlapping effect. A higher concentration of void defects leads to a higher shock-induced average system temperature, a higher increasing rate of temperature, and a higher energy release rate. Two hot spots could grow into a larger hot spot when they are closer (i.e., in a void pattern with a smaller dispersion degree), which is beneficial for the growth of chemical reactions and explosive ignition. Otherwise, they could be quenched due to their subsequent heat dissipation. For the shock-induced decomposition, a one-dimensional pattern of void defects exhibited the highest RDX decay rate and yielded reaction products the earliest compared with other patterns.

Hot spot ignition and growth from tandem micro-scale simulations and experiments on plastic-bonded explosives

Head-to-head comparisons of multiple experimental observations and numerical simulations on a deconstructed plastic-bonded explosive consisting of an octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine crystal embedded in a polymeric binder with a 4 ns duration 20 GPa input shock are presented. Hot spots observed in high-resolution direct numerical simulations are compared with micro-scale shock-induced reactions visualized using nanosecond microscope imaging and optical pyrometry. Despite the challenges and limitations of both the experimental and simulation techniques, an agreement is obtained on many of the observed features of hot spot evolution, e.g., (1) the magnitude and time variation of temperatures in the hot spots, (2) the time to fully consume the crystals (∼100 ns) of size (100–300 μm) employed in this study, and (3) the locations of hot spot initiation and growth. Three different mechanisms of hot spot formation are indicated by simulations: (1) high-temperature hot spots formed by pore collapse, (2) lower temperature hot spots initiated at the polymer–crystal interface near corners and asperities, and (3) high-temperature reaction waves leading to fast consumption of the energetic crystal. This first attempt at a head-to-head comparison between experiments and simulations not only provides new insight but also highlights efforts needed to bring models and experiments into closer alignment, in particular, highlighting the importance of distinctly three-dimensional and multiple mechanisms of the hot spot ignition and growth.

Experimental investigation and comparison of flame acceleration, hot spot ignition, and initiation of detonation in curved and straight channels

An experimental investigation of the deflagration to detonation transition (DDT) in four types of channels with rectangular cross sections and various boundary conditions is presented. The experimental channels included curved and straight channels with closed and open outlets. Experimental tests were performed using a stoichiometric mixture of ethylene and oxygen with initial pressures of 10–60 kPa. Flame shape was observed by a high-speed camera. Local velocity at high spatial resolution was calculated as the ratio of the distance between the flame fronts in sequential frames to the time interval between them. The amplification of a shock wave ahead of the flame and evolution of a series of shock waves after hot spot ignition were monitored using pressure transducers. In addition, a soot-foil technique was used to confirm the exact location of the onset of the overdriven detonation wave. The experiments showed that for a curved channel, three flame shapes (spherical, tulip, and tongue) were observed before hot spot ignition. Notably, the flame was tongue-shaped for about half the time required for the DDT. A funnel of unreacted gas formed between the tongue-shaped flame and the outer wall, at which hot spots were most frequently triggered. The locations of hot spots strongly depended on initial pressure in curved channels with closed outlets. When the pressure was relatively low (p0 < 22 kPa), hot spots always ignited at the intersection of the tongue-shaped flame and the outer wall (the root of the tongue-shaped flame), while relatively high initial pressure (p0 > 33 kPa) caused the hot spots to explode at the surface of the outer wall near the head of the tongue-shaped flame. At intermediate pressures, i.e., 22 ≤ p0 ≤ 33, hot spots ignited at both locations. The above results were very reproducible. Finally, the DDT for closed and open outlets in curved channels were compared with two types of straight channels, and it was found that the time required from ignition to onset of an overdriven detonation in the four types were, in order of magnitude, open curved, closed curved, open straight, and closed straight channels.