A conceptual model for turbulent ignition in high-pressure spray flames is presented. The model is motivated by first-principles simulations and optical diagnostics applied to the Sandia n-dodecane experiment. The combined analysis established a conceptual model for turbulent ignition in high-pressure spray flames which is based on a set of identified characteristic time scales. The suddenly forming steep gradients from successful high-temperature ignition initiate the propagation of a turbulent flame. It rapidly ignites the entire spray head on time scales which are generally significantly smaller than the corresponding cool flame wave time scales.
This work explores the mechanisms by which a post injection can reduce unburned hydrocarbon (UHC) emissions in heavy-duty diesel engines operating at low-temperature combustion conditions. Post injections, small, close-coupled injections of fuel after the main injection, have been shown to reduce UHC in the authors' previous work. In this work, we analyze optical data from laser-induced fluorescence of both CH2O and OH and use chemical reactor modeling to better understand the mechanism by which post injections reduce UHC emissions. The results indicate that post-injection efficacy, or the extent to which a post injection reduces UHC emissions, is a strong function of the cylinder pressure variation during the post injection. However, the data and analysis indicate that the pressure and temperature rise from the post injection combustion cannot solely explain the UHC reduction measured by both engine-out and optical diagnostics. The fluid-mechanic, thermal, and chemical interaction of the post injection with the main-injection mixture is a key part of UHC reduction; the starting action of the post jet and the subsequent entrainment of surrounding gases are likely both important processes in reducing UHC with a post injection.
An n-dodecane spray flame (Spray A from Engine Combustion Network) was simulated using a δ function combustion model along with a dynamic structure large eddy simulation (LES) model to evaluate its performance at engine-relevant conditions and to understand the transient behavior of this turbulent flame. The liquid spray was treated with a traditional Lagrangian method and the gas-phase reaction was modeled using a δ function combustion model. A 103-species skeletal mechanism was used for the n-dodecane chemical kinetic model. Significantly different flame structures and ignition processes are observed for the LES compared to those of Reynolds-averaged Navier-Stokes (RANS) predictions. The LES data suggests that the first ignition initiates in a lean mixture and propagates to a rich mixture, and the main ignition happens in the rich mixture, preferably less than 0.14 in mixture fraction space. LES was observed to have multiple ignition spots in the mixing layer simultaneously while the main ignition initiates in a clearly asymmetric fashion. The temporal flame development also indicates the flame stabilization mechanism is auto-ignition controlled. Soot predictions by LES present much better agreement with experiments compared to RANS, both qualitatively and quantitatively. Multiple realizations for LES were performed to understand the realization to realization variation and to establish best practices for ensemble-averaging diesel spray flames. The relevance index analysis suggests that an average of 5 and 6 realizations can reach 99% of similarity to the target average of 16 realizations on the mixture fraction and temperature fields, respectively. However, more realizations are necessary for the hydroxide (OH) and soot mass fractions due to their high fluctuations.
In this LDRD project, we developed a capability for quantitative high - speed imaging measurements of high - pressure fuel injection dynamics to advance understanding of turbulent mixing in transcritical flows, ignition, and flame stabilization mechanisms, and to provide e ssential validation data for developing predictive tools for engine combustion simulations. Advanced, fuel - efficient engine technologies rely on fuel injection into a high - pressure, high - temperature environment for mixture preparation and com bustion. Howe ver, the dynamics of fuel injection are not well understood and pose significant experimental and modeling challenges. To address the need for quantitative high - speed measurements, we developed a Nd:YAG laser that provides a 5ms burst of pulses at 100 kHz o n a robust mobile platform . Using this laser, we demonstrated s patially and temporally resolved Rayleigh scattering imaging and particle image velocimetry measurements of turbulent mixing in high - pressure gas - phase flows and vaporizing sprays . Quantitativ e interpretation of high - pressure measurements was advanced by reducing and correcting interferences and imaging artifacts.
We investigate the mixing, penetration, and ignition characteristics of high-pressure n-dodecane sprays having a split injection schedule (0.5/0.5 dwell/0.5 ms) in a pre-burn combustion vessel at ambient temperatures of 750 K, 800 K and 900 K. High-speed imaging techniques provide a time-resolved measure of vapor penetration and the timing and progression of the first- and second-stage ignition events. Simultaneous single-shot planar laser-induced fluorescence (PLIF) imaging identifies the timing and location where formaldehyde (CH2O) is produced from first-stage ignition and consumed following second-stage ignition. At the 900-K condition, the second injection penetrates into high-temperature combustion products remaining in the near-nozzle region from the first injection. Consequently, the ignition delay for the second injection is shorter than that of the first injection (by a factor of two) and the second injection ignites at a more upstream location near the liquid length. At the 750 K and 800 K conditions, high-temperature ignition does not occur in the near-nozzle region after the end of the first injection, though formaldehyde remains from first-stage reactions. Under these conditions, the second injection penetrates into cool-flame products that are slightly elevated in temperature (∼100 K) relative to the ambient. This modest temperature increase and the availability of reactive cool-flame products reduces the first- and second-stage ignition delay of the second injection by a factor of approximately two relative to the first injection. At the 750-K ambient condition, high-temperature ignition of the first injection does not occur until the second injection enriches the very fuel-lean downstream regions.
The ignition and flame stabilization characteristics of two synthetic fuels, having significantly different cetane numbers, are investigated in a constant volume combustion vessel over a range of ambient conditions representative of a compression ignition engine operating at variable loads. The synthetic fuel with a cetane number of 63 (S-1) is characterized by ignition delays that are only moderately longer than n-dodecane (cetane number of 87) over a range of ambient conditions. By comparison, the synthetic fuel with a cetane number of 17 (S-2) requires temperatures approximately 300 K higher to achieve the same ignition delays. The much different ignition characteristics and operating temperature range present a scenario where the lift-off stabilization may be substantially different. At temperatures below 1000 K, the S-2 fuel undergoes a long transient stabilization phase during which the lift-off location moves as much as 15 mm upstream (i.e., toward the injector orifice) after the ignition of the first flame kernel. This behavior is much different than S-1, n-dodecane, or with conventional diesel, in which past research shows that the lift-off location stabilizes very close to the ignition location shortly after the premixed burn. The longer ignition delays for S-2 frequently result in fuel-lean mixtures at the ignition location where the spray becomes over-mixed (i.e., too fuel-lean) and the high-temperature ignition event is noticeably less robust (i.e., smaller and less intense ignition kernels) as observed by high-speed chemiluminescence imaging. High-speed chemiluminescence imaging and pressure measurements show strong evidence of cool-flame (i.e., first-stage or low-temperature) reactions prior to high-temperature ignition for S-1 while they are less evident for S-2.
Knox, Benjamin W.; Genzale, Caroline L.; Pickett, Lyle M.; Garcia-Oliver, Jose M.; Vera-Tudela, Walter
This work contributes to the understanding of physical mechanisms that control flashback, or more appropriately combustion recession, in diesel sprays. A large dataset, comprising many fuels, injection pressures, ambient temperatures, ambient oxygen concentrations, ambient densities, and nozzle diameters is used to explore experimental trends for the behavior of combustion recession. Then, a reduced-order model, capable of modeling non-reacting and reacting conditions, is used to help interpret the experimental trends. Finally, the reduced-order model is used to predict how a controlled ramp-down rate-of-injection can enhance the likelihood of combustion recession for conditions that would not normally exhibit combustion recession. In general, fuel, ambient conditions, and the end-of-injection transient determine the success or failure of combustion recession. The likelihood of combustion recession increases for higher ambient temperatures and oxygen concentrations, as well as for higher reactivity fuels. The likelihood of combustion recession was further linked to the characteristics of end-of-injection entrainment. A simple equation, linking equivalence ratio at the lift-off length, ϕ(LOL), with a dimensionless parameter related to the end-of-injection entrainment wave, was found to well predict the propensity for combustion recession of dodecane sprays over a wide range of experimental data and 1-D model predictions. Our results suggest that this relationship is ϕ(LOL) ∼ Deff/(αUeff)0.474, where Deff is the effective orifice diameter, αα is the end-of-injection ramp-down duration, and Ueff is the effective injection velocity.
The mixing field of sprays injected into high temperature and pressure environments has been observed to be tightly connected to spreading angle, therefore linking vaporization and combustion processes to the angular dispersion of the spray. Visualization of the Engine Combustion Network three-hole, Spray B diesel injector shows substantial variation in near-field spreading angle with respect to time compared to past measurements of the single-hole, Spray A injector. The source of these variations originating inside the nozzle, and the implications on mixing, evaporation, and combustion of the diesel plume, need to be understood. In this study, we characterize the ECN-target plume for a Spray B injector (Serial # 211201), which already benefits from extensive and detailed internal measurements of nozzle geometry and needle movement, while comparing to the single-hole Spray A with the same type of detailed geometry and understanding. We measure the spreading angle, liquid penetration, and vapor penetration with respect to time of the spray of interest using standardized diagnostics in a high-temperature, high-pressure capable optically accessible combustion chamber. High-speed Mie scattering and diffused back-illumination imaging (DBI) are applied for liquid penetration, and schlieren imaging, for vapor penetration. The measurements show that the near-field spreading angle is wide for the first 300 μs after the start of injection before dropping rapidly during a quasi-steady period and then increasing well before the end of injection. Changes in spreading angle are not coincident with needle motion throttling, suggesting more complicated internal flow transients. With DBI long-distance microscopy, a partially transparent region indicates that an intact liquid core at the nozzle exit occurs frequently in quasi-steady period, which is coincident with a narrow spreading angle. The liquid penetration measured by DBI is comparable to that of Mie-scattering using criteria and standardization already established by the ECN community for Spray A. The Spray B liquid and vapor penetration rates are slower than that of Spray A, showing responses connected to the transient spreading angle.
We applied simultaneous schlieren and formaldehyde (CH2O) planar laser-induced fluorescence (PLIF) imaging to investigate the low- and high-temperature auto-ignition events in a high-pressure (60 bar) spray of n-dodecane. High-speed (150 kHz) schlieren imaging allowed visualization of the temporal progression of the fuel vapor penetration as well as the low- and high-temperature ignition events, while formaldehyde fluorescence was induced by a pulsed (7-ns), 355-nm planar laser sheet at a select time during the same injection. Fluorescence from polycyclic aromatic hydrocarbons (PAH) was also observed and was distinguished from formaldehyde PLIF both temporally and spatially. A characteristic feature previously recorded in schlieren images of similar flames, in which refractive index gradients significantly diminish, has been confirmed to be coincident with large formaldehyde fluorescence signal during low-temperature ignition. Low-temperature reactions initiate near the radial periphery of the spray on the injector side of the spray head. Formaldehyde persists on the injector side of the lift-off length and forms rapidly near the injector following the end of injection. The consumption of formaldehyde coincides with the position and timing of high-temperature ignition and low-density zones that are clearly evident in the schlieren imaging. After the end of injection, the formaldehyde that formed on the injector side of the lift-off length is consumed as a high-temperature ignition front propagates back toward the injector tip.
The development of accurate predictive engine simulations requires experimental data to both inform and validate the models, but very limited information is presently available about the chemical structure of high pressure spray flames under engine- relevant conditions. Probing such flames for chemical information using non- intrusive optical methods or intrusive sampling techniques, however, is challenging because of the physical and optical harshness of the environment. This work details two new diagnostics that have been developed and deployed to obtain quantitative species concentrations and soot volume fractions from a high-pressure combusting spray. A high-speed, high-pressure sampling system was developed to extract gaseous species (including soot precursor species) from within the flame for offline analysis by time-of-flight mass spectrometry. A high-speed multi-wavelength optical extinction diagnostic was also developed to quantify transient and quasi-steady soot processes. High-pressure sampling and offline characterization of gas-phase species formed following the pre-burn event was accomplished as well as characterization of gas-phase species present in the lift-off region of a high-pressure n-dodecane spray flame. For the initial samples discussed in this work several species were identified, including polycyclic aromatic hydrocarbons (PAH); however, quantitative mole fractions were not determined. Nevertheless, the diagnostic developed here does have this capability. Quantitative, time-resolved measurements of soot extinction were also accomplished and the novel use of multiple incident wavelengths proved valuable toward characterizing changes in soot optical properties within different regions of the spray flame.
This report documents the results of a project funded by DoD's Strategic Environmental Research and Development Program (SERDP) on the science behind development of predictive models for soot emission from gas turbine engines. Measurements of soot formation were performed in laminar flat premixed flames and turbulent non-premixed jet flames at 1 atm pressure and in turbulent liquid spray flames under representative conditions for takeoff in a gas turbine engine. The laminar flames and open jet flames used both ethylene and a prevaporized JP-8 surrogate fuel composed of n-dodecane and m-xylene. The pressurized turbulent jet flame measurements used the JP-8 surrogate fuel and compared its combustion and sooting characteristics to a world-average JP-8 fuel sample. The pressurized jet flame measurements demonstrated that the surrogate was representative of JP-8, with a somewhat higher tendency to soot formation. The premixed flame measurements revealed that flame temperature has a strong impact on the rate of soot nucleation and particle coagulation, but little sensitivity in the overall trends was found with different fuels. An extensive array of non-intrusive optical and laser-based measurements was performed in turbulent non-premixed jet flames established on specially designed piloted burners. Soot concentration data was collected throughout the flames, together with instantaneous images showing the relationship between soot and the OH radical and soot and PAH. A detailed chemical kinetic mechanism for ethylene combustion, including fuel-rich chemistry and benzene formation steps, was compiled, validated, and reduced. The reduced ethylene mechanism was incorporated into a high-fidelity LES code, together with a moment-based soot model and models for thermal radiation, to evaluate the ability of the chemistry and soot models to predict soot formation in the jet diffusion flame. The LES results highlight the importance of including an optically-thick radiation model to accurately predict gas temperatures and thus soot formation rates. When including such a radiation model, the LES model predicts mean soot concentrations within 30% in the ethylene jet flame.
This paper presents experimental results for two fuel-related topics in a diesel engine: (1) how fuel volatility affects the premixed burn and heat release rate, and (2) how ignition quality influences the soot formation. Fast evaporation of fuel may lead to more intense heat release if a higher percentage of the fuel is mixed with air to form a combustible mixture. However, if the evaporation of fuel is driven by mixing with high-temperature gases from the ambient, a high-volatility fuel will require less oxygen entrainment and mixing for complete vaporization and, consequently, may not have potential for significant heat release simply because it has vaporized. Fuel cetane number changes also cause uncertainty regarding soot formation because variable ignition delay will change levels of fuel-air mixing prior to combustion. To address these questions, experiments are performed using a constant-volume combustion chamber simulating typical low-temperature-combustion (LTC) diesel conditions. We use fuels that have the same ignition delay (and therefore similar time for premixing with air), but different fuel volatility, to assess the heat-release rate and spatial location of combustion. Under this condition, where fuel volatility is decoupled from the ignition delay, results show almost the same heat release rate and spatial location of the premixed burn. The effect of ignition quality on soot formation has also been studied while maintaining similar levels of fuel-ambient mixing prior to combustion. To achieve the same ignition delay, the high-cetane-number fuel is injected into an ambient gas at a lower temperature and vice versa. The total soot mass within the spray is measured and compared for fuels with different cetane numbers but with the same premixing level (e.g. the same ignition delay and lift-off length). Experimental results show that the combination of high cetane number and low ambient gas temperature produces lower soot than the other combination, because the ambient temperature predominantly affects soot formation.
Shadowgraph/schlieren imaging techniques have often been used for flow visualization of reacting and non-reacting systems. In this paper we show that high-speed shadowgraph visualization in a high-pressure chamber can also be used to identify cool-flame and high-temperature combustion regions of diesel sprays, thereby providing insight into the time sequence of diesel ignition and combustion. When coupled to simultaneous high-speed Mie-scatter imaging, chemiluminescence imaging, pressure measurement, and spatially-integrated jet luminosity measurements by photodiode, the shadowgraph visualization provides further information about spray penetration after vaporization, spatial location of ignition and high-temperature combustion, and inactive combustion regions where problematic unburned hydrocarbons exist. Examples of the joint application of high-speed diagnostics include transient non-reacting and reacting injections, as well as multiple injections. Shadowgraph and schlieren image processing steps required to account for variations of refractive index within the high-temperature combustion vessel gases are also shown.
Diesel injection parameters effect on liquid-phase diesel spray penetration after the end-of-injection (EOI) is investigated in a constant-volume chamber over a range of ambient and injector conditions typical of a diesel engine. Our past work showed that the maximum liquid penetration length of a diesel spray may recede towards the injector after EOI at some conditions. Analysis employing a transient jet entrainment model showed that increased fuel-ambient mixing occurs during the fuel-injection-rate ramp-down as increased ambient-entrainment rates progress downstream (i.e. the entrainment wave), permitting complete fuel vaporization at distances closer to the injector than the quasi-steady liquid length. To clarify the liquid-length recession process, in this study we report Mie-scatter imaging results near EOI over a range of injection pressure, nozzle size, fuel type, and rate-of-injection shape. We then use a transient jet entrainment model for detailed analysis. Results show that an increased injection pressure correlates well with increasing liquid length recession due to an increased entrainment wave speed. Likewise, an increased nozzle size, with higher jet momentum and faster entrainment wave, enhances the liquid length recession. A low-density, high-volatility fuel does not decrease the strength of the entrainment wave; however, it decreases the steady liquid length causing the entrainment wave to reach the liquid spray tip earlier, which ultimately results in faster liquid length recession. A slow ramp down in injection rate causes a weaker entrainment wave so that the liquid length recession occurs even prior to injector close.
The United States produces only about 1/3 of the more than 20 million barrels of petroleum that it consumes daily. Oil imports into the country are roughly equivalent to the amount consumed in the transportation sector. Hence the nation in general, and the transportation sector in particular, is vulnerable to supply disruptions and price shocks. The situation is anticipated to worsen as the competition for limited global supplies increases and oil-rich nations become increasingly willing to manipulate the markets for this resource as a means to achieve political ends. The goal of this project was the development and improvement of technologies and the knowledge base necessary to produce and qualify a universal fuel from diverse feedstocks readily available in North America and elsewhere (e.g. petroleum, natural gas, coal, biomass) as a prudent and positive step towards mitigating this vulnerability. Three major focus areas, feedstock transformation, fuel formulation, and fuel characterization, were identified and each was addressed. The specific activities summarized herein were identified in consultation with industry to set the stage for collaboration. Two activities were undertaken in the area of feedstock transformation. The first activity focused on understanding the chemistry and operation of autothermal reforming, with an emphasis on understanding, and therefore preventing, soot formation. The second activity was focused on improving the economics of oxygen production, particularly for smaller operations, by integrating membrane separations with pressure swing adsorption. In the fuel formulation area, the chemistry of converting small molecules readily produced from syngas directly to fuels was examined. Consistent with the advice from industry, this activity avoided working on improving known approaches, giving it an exploratory flavor. Finally, the fuel characterization task focused on providing a direct and quantifiable comparison of diesel fuel and JP-8.
Experiments were conducted in an optically accessible constant-volume combustion vessel to investigate soot formation at diesel combustion conditions - in a high exhaust-gas recirculation (EGR) environment. The ambient oxygen concentration was decreased systematically from 21% to 8% to simulate a wide range of EGR conditions. Quantitative measurements of in-situ soot in quasi-steady n-heptane and No.2 diesel fuel jets were made by using laser extinction and planar laser-induced incandescence (PLII) measurements. Flame lift-off length measurements were also made in support of the soot measurements. At constant ambient temperature, results show that the equivalence ratio estimated at the lift-off length does not vary with the use of EGR, implying an equal amount of fuel-air mixing prior to combustion. Soot measurements show that the soot volume fraction decreases with increasing EGR. The regions of soot formation are effectively 'stretched out' to longer axial and radial distances from the injector with increasing EGR, according to the dilution in ambient oxygen. However, the axial soot distribution and location of maximum soot collapses if plotted in terms of a 'flame coordinate', where the relative fuel-oxygen mixture is equivalent. The total soot in the jet cross-section at the maximum axial soot location initially increases and then decreases to zero as the oxygen concentration decreases from 21% to 8%. The trend is caused by competition between soot formation rates and increasing residence time. Soot formation rates decrease with decreasing oxygen concentration because of the lower combustion temperatures. At the same time, the residence time for soot formation increases, allowing more time for accumulation of soot. Increasing the ambient temperature above nominal diesel engine conditions leads to a rapid increase in soot for high-EGR conditions when compared to conditions with no EGR. This result emphasizes the importance of EGR cooling and its beneficial effect on mitigating soot formation. The effect of EGR is consistent for different fuels but soot levels depend on the sooting propensity of the fuel. Specifically, No.2 diesel fuel produces soot levels more than ten times higher than those of n-heptane.
The reaction zone of a diesel fuel jet stabilizes at a location downstream of the fuel injector once the initial autoignition phase is over. This distance is referred to as flame lift-off length. Recent investigations have examined the effects of a wide range of parameters (injection pressure, orifice diameter, and ambient gas temperature, density and oxygen concentration) on lift-off length under quiescent diesel conditions. Many of the experimental trends in lift-off length were in agreement with scaling laws developed for turbulent, premixed flame propagation in gas-jet lifted flames at atmospheric conditions. However, several effects did not correlate with the gas-jet scaling laws, suggesting that other mechanisms could be important to lift-off stabilization at diesel conditions. This paper shows experimental evidence that ignition processes affect diesel lift-off stabilization. Experiments were performed in the same optically-accessible combustion vessel as the previous lift-off research. The experimental results show that the ignition quality of a fuel affects lift-off. Fuels with shorter ignition delays generally produce shorter lift-off lengths. In addition, a cool flame is found upstream of, or near the same axial location as, the quasi-steady lift-off length, indicating that first-stage ignition processes affect lift-off. High-speed chemiluminescence imaging also shows that high-temperature self-ignition occasionally occurs in kernels that are upstream of, and detached from, the high-temperature reaction zone downstream, suggesting that the lift-off stabilization is not by flame propagation into upstream reactants in this instance. Finally, analysis of the previous lift-off length database shows that the time-scale for jet mixing from injector-tip orifice to lift-off length collapses to an Arrhenius-type expression, a common method for describing ignition delay in diesel sprays. This Arrhenius-based lift-off length correlation shows comparable accuracy as a previous power-law fit of the No.2 diesel lift-off length database.
The effects of wall interaction on combustion and soot formation processes of a diesel fuel jet were investigated in an optically-accessible constant-volume combustion vessel at experimental conditions typical of a diesel engine. At identical ambient and injector conditions, soot processes were studied in free jets, plane wall jets, and 'confined' wall jets (a box-shaped geometry simulating secondary interaction with adjacent walls and jets in an engine). The investigation showed that soot levels are significantly lower in a plane wall jet compared to a free jet. At some operating conditions, sooting free jets become soot-free as plane wall jets. Possible mechanisms to explain the reduced or delayed soot formation upon wall interaction include an increased fuel-air mixing rate and a wall-jet-cooling effect. However, in a confined-jet configuration, there is an opposite trend in soot formation. Jet confinement causes combustion gases to be redirected towards the incoming jet, causing the lift-off length to shorten and soot to increase. This effect can be avoided by ending fuel injection prior to the time of significant interaction with redirected combustion gases. For a fixed confined-wall geometry, an increase in ambient gas density delays jet interaction, allowing longer injection durations with no increase in soot. Jet interaction with redirected combustion products may also be avoided using reduced ambient oxygen concentration because of an increased ignition delay. Although simplified geometries were employed, the identification of important mechanisms affecting soot formation after the time of wall interaction is expected to be useful for understanding these processes in more complex and realistic diesel engine geometries.
Laser-extinction diagnostics can provide spatially and temporally resolved measurements of attenuation from combustion-generated soot within the path of the beam. When laser-extinction techniques are utilized in high-pressure combustion environments, however, a number of complications may be encountered that are not present in low-pressure environments. Several of these experimental difficulties were investigated in diesel engine environments, and solutions that facilitated acquisition of reliable laser-extinction data were demonstrated. Beam steering due to refractive index gradients within the combusting gases was observed, and a full-angle beam divergence of over 100 mrad was measured. A spatial-filtering scheme was employed to reduce the collection of forward-scattered light and background combustion luminosity while ensuring full collection of the steered beam. To further reject combustion luminosity, a narrow-bandpass laser-line filter was employed, after diffusing the transmitted light sufficiently to avoid the effects of significant spatial non-uniformities of the filter. As the windows were subjected to thermal and mechanical stresses, dynamic etaloning effects due to the photoelastic properties of synthetic fused silica were observed. Dynamic changes in the polarization of the exit beam were also observed, as stress-induced birefringence in the windows caused dynamic phase retardation of the transmitted beam. Although these photoelastic effects could not be eliminated, they were mitigated by introducing curvature to the wavefronts in the laser-extinction beam and using polarization-insensitive elements in the detection optics. Soot deposits on window surfaces were removed ablatively using a coaxial, high-energy, pulsed Nd:YAG laser beam.