Laser Sheet Research Articles

The Laboratory Characterization of Fugitive Aerosol Emissions From a Standard Jet Nebulizer With and Without a Filtered Mouthpiece.

Background and objective The risk of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission from patients with coronavirus disease 2019 (COVID-19) during nebulization is unclear. In this study, we aimed to address this issue. Methods Fugitive emissions of aerosolized saline during nebulization were observed using a standard jet nebulizer fitted with unfiltered and filtered mouthpieces connected via a mannequin to a breathing simulator. Fugitive emissions were observed by using a laser sheet and captured on high-definition video, and they were measured by using optical particle counters positioned where a potential caregiver may be administering nebulization and three other locations in the sagittal plane at various distances downstream of the mannequin. Results The use of a standard unfiltered mouthpiece resulted in significant emission of fugitive aerosols ahead of and above the mannequin (spread over 2 m in front). A mouthpiece with a filter-adaptor effectively suppressed the emissions, with only minor leakage from the nebulizer cup. Particle count measurements supported the visual observations, providing total particle count levels and aerosol concentration levels at the measurement locations. The levels decayed slowly with downstream distance. Conclusions The visualization described above captured the dispersion of emitted aerosols in the plane of the laser sheet, aligned with the sagittal plane. The particle count measurements provided temporal and spatial distributions of the aerosol concentration levels over the time and locations considered. However, the exhaled air and aerosolized droplets spread three-dimensionally in front of and above the mannequin.The results visually highlight the effectiveness of using a filtered mouthpiece in suppressing the fugitive aerosols and identify an approach for limiting the occupational exposure of healthcare workers to these emissions while administering nebulized therapies.

Multi-line OH-LIF for gas-phase temperature and concentration imaging in the SpraySyn burner

Gas-phase temperature and OH concentration images are measured in the SpraySyn nanoparticle-synthesis standard burner using multi-line OH laser-induced fluorescence (LIF) thermometry. In this burner, a spray flame fed by a combustible nanoparticle precursor solution is stabilized by a surrounding axisymmetric lean premixed laminar methane/oxygen pilot flame. For measuring OH rotational temperature, the laser is scanned across the 282.05–282.17 nm range and LIF excitation spectra are fitted for each image pixel by simulated spectra. Temperature maps are determined for the pilot flame and the ethanol spray flame with variable dispersion gas flow rates of oxygen used in the two-fluid nozzle. The addition of 2-EHA (2-ethylhexanoic acid) to the solution was found to increase the flame temperature. Laser attenuation across the flame was measured using simultaneous recordings of the fluorescence of uranine/water solution from two dye cuvettes illuminated with the laser sheet before and after the flame and the effect of attenuation was quantified. Absolute OH concentration distributions are determined by combining the LIF images, laser attenuation measurements, and derived temperature distributions. The temporal stability of the flame is investigated for various operating conditions by statistical evaluation of recorded instantaneous OH-LIF images.

Laboratory investigation of nominally two-dimensional anabatic flow on symmetric double slopes

We investigated the dynamics of highly turbulent thermally driven anabatic (upslope) flow on a physical model inside a large water tank using particle image velocimetry (PIV) and a thermocouple grid. The results showed that the flow exhibited pronounced variations in velocity and temperature and, importantly, could not be accurately modeled as a two-dimensional quasi-steady flow. Five significant findings are presented to underscore the three-dimensional nature of the flow, namely, the B-shaped mean velocity profiles, B-shaped turbulent flux profiles, synthetic streaks that revealed particles flowing perpendicular to the laser sheet, average vorticity maps revealing helical structure splitting, and identified vortices shooting away from the boundary toward the apex plume. Collectively, these findings offer novel insights into the flow behavior patterns of thermally driven complex terrain flows, which influence local weather and microclimates and are responsible for scalar transport, e.g., pollution.

Peak risk of SARS-CoV-2 infection within 5 s of face-to-face encounters: an observational/retrospective study

The link between aerosol dynamics and viral exposure risk is not fully understood, particularly during movement and face-to-face interactions. To investigate this, we employed Particle Trace Velocimetry with a laser sheet and a high-speed camera to measure microparticles from a human mannequin’s mouth. The average peak time in the non-ventilated condition (expiratory volume, 30 L; passing speed, 5 km/h) was 1.33 s (standard deviation = 0.32 s), while that in the ventilated condition was 1.38 s (standard deviation = 0.35 s). Our results showed that the peak of viral exposure risk was within 5 s during face-to-face encounters under both ventilated and non-ventilated conditions. Moreover, the risk of viral exposure greatly decreased in ventilated conditions compared to non-ventilated conditions. Based on these findings, considering a risk mitigation strategy for the duration of 5 s during face-to-face encounters is expected to significantly reduce the risk of virus exposure in airborne transmission.

A TDLAS-based photofragmentation method for spatially resolved measurement of KOH and KCl as well as its application in biomass combustion processes

The release of gas-phase potassium species, mainly KOH, KCl, and K atoms, from burning biomass fuels can introduce severe problems to boilers, such as fouling, slagging, and corrosion. In the present work, an optical technique combining laser-induced photofragmentation and tunable diode laser absorption spectroscopy is developed for simultaneously measuring the concentration of KOH, KCl and K atoms with a high temporal and spatial resolution. Two laser sheets with a thickness of about 1 mm at wavelengths of 266 and 355 nm, respectively, were adopted to photodissociate KOH and KCl molecules into K atoms. A continuous wave laser at 766 nm generated by a tunable diode laser passed perpendicularly through the laser sheet to detect the K atom. The measured fragmentation-induced K-atom absorbance was correlated to KOH and KCl concertation through a calibration process in a homogenous combustion environment where the concentrations of KOH and KCl were monitored by UV absorption spectroscopy. The calibration curves were verified to be independent of temperature. A typical spatial resolution of 1 mm3 was realized where the value depended on the overlap volume of the UV laser sheet and the 766 nm laser beam. Finally, this technique was applied to measure the release behavior of KOH, KCl and K atoms from burning wood and straw pellets.

Effect of atomizer and cross-flows on liquid and gelled Jet A-1 fuel injection

The current study aims to experimentally investigate the effect of atomizer and cross-flow velocities on liquid and gelled Jet A-1 fuels. For gelled Jet A-1, Jet A-1 liquid, Thixatrol® ST and rectified xylene are the base fuel, gellant and solvent, respectively. Gelled Jet A-1 is prepared by adding 85% by weight of base fuel along with 7.5% by weight of gellant and solvent, each at optimum processing conditions. Atomization using a simple-plain-orifice atomizer is investigated to understand its effect on Jet A-1 gel fuel break-up without air cross-flow. Based on the investigation from qualitative flow visualization and quantitative analysis of Jet A-1 gel fuel break-up, a modified simple-plain-orifice atomizer called an internally impinging air-blast atomizer is made. Primary atomization using this new atomizer is studied to understand the break-up of liquid and gelled Jet A-1 gel fuels without any air cross-flow. Secondary atomization of liquid and gel fuel is investigated by transversely injecting fuel into different low-speed subsonic air cross-flow environments. Laser sheet Imaging (LSI) technique is used to capture spray images of both fuels. Break-up mechanisms of both liquid and gel fuels were observed, and the results were compared. Information on the cross-flow air mass flow rate effect on the liquid and gel spray is extracted by developing an algorithm in MATLAB using an image processing tool. Relative droplet size distribution of liquid and gel spray revealed their dependence on cross-flow air mass flow rate. Total droplet count of both liquid and gel fuel decreases significantly as the cross-flow Reynolds’ number increases. At higher cross-flow Reynolds’ number, gel droplets in the flow are observed to be more as compared to liquid fuel.

It’s About Time: Jet Interactions in an Asymmetrical Plenum

Hybrid Reynolds-Averaged Navier-Stokes–Large Eddy Simulation was used to reveal detailed flow information and timescales in an isothermal reactor cavity cooling system plenum four-jet configuration. Plenum asymmetry and nonuniformity work together to cause premature jet merging. Bulk stirring in the plenum causes lateral jet vortex shedding, strong jet-jet interactions, swirl, and premature confluence. Two dominant transient modes exist: a jet flow timescale and then a plenum circulation timescale that is nearly three orders of magnitude larger. A primary consequence is that frequencies far less than the presumed 10 Hz threshold for thermal striping are pervasive. A second result is that scale-resolved computational fluid dynamics (CFD) models (as well as experimental rigs) need hundreds of seconds of statistically stationary flow time (tens of thousands of jet timescales) to produce stationary time averages. Fluid typically arrives at positions on the laser sheet in less time than it spends at those positions fluctuating in the streamwise and lateral directions. Also, a previously undocumented, but experimentally confirmed, vortex trap was identified via CFD. Finally, two-point velocity correlation analyses demonstrated a few dozen strong correlations across positions on the laser sheet. Expected close-proximity correlations emerged, but others across larger spaces also were connected. Most of these correlated at timescales close to that of the jet.

Effects of vocal fold oscillation characteristics on the aerosol droplet production

Although a large number of aerosol droplets are known to be produced from the human larynx during vocalizations, it remains unclear how vocal fold oscillations are involved in the droplet production. In this study, we synthesized vocalizations using two types of silicone vocal fold models and investigated the effects of these model configurations on the droplet production mechanisms by measuring the particle concentrations when artificial mucus was injected into the artificial larynx. One model, which oscillates with complete glottal closure, produced louder sounds with droplets, whose diameter ranged primarily from 0.3 to 2μm. In contrast, the other model, which oscillates without vocal fold collision, produced smaller sounds with droplets having larger diameters. Additional observations using the laser sheets and high-speed imaging demonstrated that the liquid films were formed just above the vocal folds when a constant jet flow was generated in the model which does not exhibit complete glottal closure. These results describe how different oscillation characteristics of the vocal folds may cause differences in droplet concentration.

An Inexpensive, Portable Shield to Improve Healthcare Worker Safety During Intubation Procedures.

Healthcare workers (HCW) are exposed to risk of infection during intubation procedures, in particular, in the prehospital setting. Here, we demonstrate a novel shield that can be used during intubation to block aerosols and droplets from reaching the HCW. The device is mounted on the patient's head and provides a barrier between patient and HCW. It incorporates a self-sealing port through which an endotracheal tube can be inserted. The port "floats" in the plane of the shield to facilitate maneuvering of the endotracheal tube. The shield is fabricated from transparent materials to enable the HCW to visualize the procedure. Using two complementary imaging methods, background oriented Schlieren imaging and laser sheet droplet imaging, we show that the device prevents detectable transmission of gas flow and droplets through the shield both before and after endotracheal tube insertion.Clinical Relevance- This device has the potential to protect HCWs from infections during intubation procedures, especially in the prehospital setting.

Comparison of Aerosol Emissions during Specific Speech Tasks

Recent investigations into the behavior of aerosolized emissions from the oral cavity have shown that particulate emissions do indeed occur during speech. To date, there is little information about the relative contribution of different speech sounds in producing particle emissions in a free field. This study compares airborne aerosol generation in participants producing isolated speech sounds: fricative consonants, plosive consonants, and vowel sounds. Prospective, reversal experimental design, where each participant served as their own control and all participants were exposed to all stimuli. While participants produced isolated speech tasks, a planar beam of laser light, a high-speed camera, and image software calculated the number of particulates detected over time. This study compared airborne aerosols emitted by human participants at a distance of 2.54cm between the laser sheet and the mouth. Statistically significant increases in particulate count over ambient dust distribution for all speech sounds. When collapsed across loudness levels, emitted particles in vowel sounds were statistically greater than consonants, suggesting that mouth opening, as opposed to the place of vocal tract constriction or manner of sound production, might also be influential in the degree to which particulates become aerosolized during speech. The results of this research will inform boundary conditions for computational models of aerosolized particulates during speech.

Quantifying the dynamical information content of pulsed, planar laser-induced fluorescence measurements.

We have analyzed the effects of the spreads in experimental parameters on the reliability of speeds and angular distributions extracted from a generic surface-scattering experiment based on planar laser-induced fluorescence detection. The numerical model assumes a pulsed beam of projectile molecules is directed at a surface. The spatial distribution of the scattered products is detected by imaging the laser-induced fluorescence excited by a thin, pulsed sheet of laser light. Monte Carlo sampling is used to select from realistic distributions of the experimental parameters. The key parameter is found to be the molecular-beam diameter, expressed as a ratio to the measurement distance from the point of impact. Measured angular distributions are negligibly distorted when this ratio is <∼10%. Measured most-probable speeds are more tolerant, being undistorted when it is <∼20%. In contrast, the spread of speeds or of corresponding arrival times in the incident molecular beam has only very minor systematic effects. The thickness of the laser sheet is also unimportant within realistic practical limits. These conclusions are broadly applicable to experiments of this general type. In addition, we have analyzed the specific set of parameters designed to match the experiments on OH scattering from a liquid perfluoropolyether (PFPE) surface in the Paper I [Roman et al., J. Chem. Phys. 158, 244704 (2023)]. This reveals that the detailed form of the molecular-beam profile is important, particularly on apparent angular distributions, for geometric reasons that we explain. Empirical factors have been derived to correct for these effects.

An intermediate water gravity wavelength and wave height measurement inside a large wave flume tank

This paper discusses an intermediate water gravity wavelength and wave height measurement method. Three methods were used to obtain wave height, wavelength, and period. Firstly, conventional methods used two Honeywell pressure sensors mounted at the bottom of the wave tank at two different locations. Secondly, using the transfer function of the flap wavemaker (the relationship between wave height and the wave paddle stroke). Thirdly, the Laser Sheet technique (PIV image processing technique). The significant wave height and period from pressure reading sensors of regular gravity waves were obtained from the Raleigh distribution and Zero up crossing technique. Wavelength was obtained indirectly by using a dispersion relationship that was solved by using the Newton Raphson numerical method from both the pressure sensors and the transfer function of the flap wavemaker. This experiment was focused on getting the direct value of wave measurements by developing an image processing technique in a clear large wave flume tank to replace the conventional methods and eliminate the error that may produce by using the numerical methods. The PIV setup with the CCD camera was used to capture wave images. The image processing technique based on Canny edge detection with constant threshold value was used to detect the edge of the waves. The experimental result showed a good agreement between the results obtained from these three methods, with the percent of error up to 8.683%.

Influence of air swirl orientation on the spray characteristics of a micro-channel-based rotary (MCR) atomizer

In this work, we investigate the atomization and spray characteristics of a novel rotary atomizer with micro-channel grooves, using optical diagnostics. Micro-jets emanate from the grooves provided in the rotating injector. The spiraling liquid jets interact with the surrounding high-speed swirling air flow, resulting in the creation of a well-dispersed fine spray. Attention is focused on the effects of air swirler orientation with respect to that of injector rotation. Accordingly, the co- and counter-swirl cases are investigated. The primary jet breakup process is visualized using back-lit illumination technique, which also provides the measurement of jet breakup length. The jet break-up modes are identified for different air swirl strength and orientation and injector rotational speed. The size, number density and velocity components of the spray droplets are measured using PDPA technique at different axial and radial locations. Air velocity is also measured (in the absence of liquid injection) using the LDV technique. In addition, Laser Sheet Imaging (LSI) is employed to investigate the overall spray structure. Results show that the droplet size significantly reduces when air swirl strength or injector rotational speed is increased. Though not much difference is observed in the characteristic droplet size between the co- and counter-swirl cases, the droplet size distribution is narrower and droplet dispersion is improved for the latter. The current findings demonstrate the potential of the rotary injector to dynamically control the spray characteristics as per requirement.

BIO22: Effects of Leakage Flows around TAVI models on Thrombus Formation by Optical Visualization Method with Various Geometries in Vitro

Background: There is a possibility of leakage (PVL; Paravalvular leak) flow around TAVI (Transcatheter Aortic Valve Implantation) and a high risk of thrombus formation. To find out the mechanism of thrombus formation by this leakage flow is important issue. In our previous studies, effects of the high shear rate on the thrombus formation rate at wall on orifice flow were examined by observation of thrombus formation using laser sheet, and it was found that the thrombus formation rates increase with the high shear rates. In this study, observation of thrombus formation around TAVI models including leakage flows by laser sheet in vitro with various geometries. Method: Experimental objects are orifice pipe flow and the leakage models with (Fig.1) for observation of thrombus formation. Each leakage size h is 0mm, 0.5mm, 1mm respectively with 20 mm diameter with stenosis to simulate valve part. The target flow filed with fresh blood plasma of pigs is observed with high speed CCD camera by laser sheet. Once the thrombus formation starts, the scattering wave can be detected by this system. The movies for three kinds of geometries and two flow rates (3 and 5l/min). Results & Conclusions: As for visualization results, typical distribution of thrombus formation area at h= 0, 0.5, 1 mm is shown in Fig.2. Due to the increasing of leakage size, the thrombus formation area at the outer wall decreases. In case of leakage size h=0.5 and 1 mm, these areas correspond to wake size at the back side of the stenosis. Figure 3 shows the thrombus formation rate by evaluation of the thrombus area with changing the leakage size and geometries. It was found that the thrombus formation rate increases with the leakage size, and there are differences between the two geometries. These findings related thrombus formation area were also evaluated from the leakage flow rates in the CFD (Computational Fluid Dynamics) results. And it was also found that this formation rates increase with leakage flow rate obtained by CFD. In conclusion, there is a high possibility to generate thrombus formation with larger leakage flow for TAVI. In future, the effects of valve motion should be investigated.

3D tracking of particles in a dusty plasma by laser sheet tomography

The collective behavior of levitated particles in a weakly ionized plasma (dusty plasma) has raised significant scientific interest. This is due to the complex array of forces acting on the particles and their potential to act as in situ diagnostics of the plasma environment. Ideally, the three-dimensional (3D) motion of many particles should be tracked for long periods of time. Typically, stereoscopic imaging using multiple cameras combined with particle image velocimetry is used to obtain a velocity field of many particles, yet this method is limited by its sample volume and short time scales. Here, we demonstrate a different, high-speed tomographic imaging method capable of tracking individual particles. We use a scanning laser sheet coupled to a single high-speed camera. We are able to identify and track tens of individual particles over centimeter length scales for several minutes, corresponding to more than 10 000 frames.

A fluorescent PIV technique for turbomachinery flows

This paper presents the development and applications of a fluorescent Particle Image Velocimetry (PIV) technique as a countermeasure for undesired light reflections on surfaces of channel walls or obstacles. The employment of the fluorescent dye-doped tracer particle with a wavelength-specific optical filter enables a separation of the stokes-shifted particle light emission from reflections on the surfaces. Aiming at applying the technique to engine-like turbomachinery flows, the fluorescent tracer particles were made out of pyrromethene 567 and Di-Ethyl-Hexyl-Sebacat considering multiple aspects of characteristics. The developed particles were firstly tested in a low-speed wind tunnel with a metal turbine blade placed in the flow path and a laser sheet oriented to impinge the blade surface. With the installation of an adequate optical filter, the undesired light reflections were successfully removed, and reasonable vector calculations were enabled in proximity to the reflective blade surfaces. Secondly, the fluorescent PIV was performed on a high-pressure turbine stage hosted in a high-speed short-duration rotating turbine rig to demonstrate the feasibility of the technique in engine-representative turbomachinery flows.

Study on predictions of spray target position of gasoline direct injection injectors with multi-hole using physical model and machine learning

A lot of effort is being invested in improving the performance of injectors, the core components of gasoline direct injection (GDI) engines, such as injection stability and accuracy. The purpose of this study is to establish models that can predict spray targeting according to the design parameters of GDI injector, to improve the injection accuracy and enhance the engine performance. First, this study used laser sheet beam visualization technology to measure the spray targeting images of injectors with different design parameters in different cross-sections and obtained the spray targeting coordinates through image post-processing. Then, using the experimental data, two different approaches (empirical formula and machine learning), were used to create models for predicting spray targeting, and their applicability was compared. The research results showed that both the physical model and the machine learning model had a prediction accuracy of >0.98 in terms of R2, but the physical model had a lower prediction error in terms of the root mean square error (RMSE). Further, the tendency of the target coordinate to change is proportional to 0.2 power of the injection pressure (Pinj0.2), −0.1 power of ratio of hole length to hole diameter ((L/D)−0.1), and − 1.5 power of the angle between axes of two holes (θij−1.5).

Impact of spray dynamics on combustion instabilities investigated by changing the atomizer recess in a swirl combustor

The present article is aimed at identifying the impact of spray-wall interaction on combustion instabilities. This is achieved by systematically modifying the liquid fuel atomizer location with respect to the injector outlet in experiments carried out on a single-injector swirling combustor. The injector is characterized by a high swirl number and a relatively high pressure drop, and features a pressure atomizer that delivers liquid heptane fuel in the form of a fine spray. In the first set of experiments, longitudinal self-sustained oscillations (SSOs) are examined by varying the atomizer recess distance and using three combustion chamber lengths. Three distinct instability regions characterized by jumps in amplitude and frequency are observed as a function of the atomizer recess. At lower SSO frequencies (obtained for longer chambers), the pressure fluctuation amplitude in the chamber decreases as the atomizer recess distance is reduced, tending towards a stable operation. An opposite behavior is observed at comparatively higher SSO frequencies (obtained with a shorter chamber), where the system becomes less unstable at higher atomizer recess distances. The oscillation frequency is also found to change and increases as the recess distance is reduced. Three recess distances corresponding to each zone of operation are selected to further analyze the flow and flame structures and dynamics. It is found that the mean velocity profiles only reveal moderate differences in the air flow field, but there are significant changes in the fuel spray distribution in the neighborhood of the injector axis. Laser sheet images of the spray reveal two patterns—one where the spray predominantly interacts with the injector end piece when the atomizer is recessed, and the other where this interaction is minimal. In the latter case, corresponding to a small recess, the fuel spray is directly conveyed into the chamber. It is next found that the spray distribution affects the flame pattern defining two distinct configurations. Finally, the flame response to external disturbances is characterized by flame describing functions (FDFs) that allow carrying out a stability analysis. FDF results obtained with two independent methods indicate that the gain and phase at the three recess positions vary substantially and that this can be used in combination with a low-order model to interpret the instability behavior of the system. This study might serve to guide the modeling of combustion dynamics and help design injectors that are less sensitive to instabilities.

Experimental study on vertical temperature distribution of the two-layer smoke flow in tunnel during construction

For a tunnel fire during construction, the formation of two-layer smoke flow underneath the ceiling accelerates the smoke descent threatening the personnel evacuation. As an important indicator of smoke diffusion, the gas temperature distribution inside tunnel is worthy of analysis in depth. However, the vertical temperature profiles within this kind of two-layer smoke flow inside tunnel have not been experimentally studied. To fill the gap, this paper conducts a series of fire experiments in a 1/20 reduced-scale tunnel model. Multi-variables including fire heat release rate, fire position, lifting-up height of fire source, inclined shaft slope, are considered. The visible flame shape, O2 volume fraction and gas temperature are recorded and measured. The burning of the propane gas persists steadily for 20 mins without the occurrence of self-extinction. The structural evolutions of the smoke layer are predicted by FDS simulation and traced by the laser sheet. The smoke descent process in the main tunnel is divided into three stages. The effects of fire source position, inclined shaft slope, fire heat release rate and lifting-up height on the gas temperature distributions inside tunnel are analyzed. The measured temperature rise and the perpendicular distance from the ceiling are normalized by ΔTmax and LT, respectively. At various longitudinal positions (1.82 ≤ │X-dm│/Hef ≤ 10.68), the normalized temperature distributions follow the same curve, independent of the values of Qm, dm and hm. The self-similarity of the vertical temperature distribution within the two-layer smoke flow are sufficiently proved. It is found that ΔT/ΔTmax with z/LT shows a two-regional variation. Based on over 1,740 temperature data from 36 experimental cases, an experimental equation is proposed to describe the gas temperature rise in the region between the fire source and the closed end. The proposed model shows good agreement with the measured data, which can help the researchers to better assess the smoke layer height inside tunnel.

Experimental Study on the Smoke Temperature Decrease near Natural Vents Induced by Air Entrainment in a Tunnel Fire

Previous studies have shown that there is a large difference in the temperature of smoke in the upstream and downstream of a vertical shaft, but no quantitative study on the subject has been conducted. In this paper, a model experimental test was conducted to study the effect of a natural vertical shaft on the distribution of smoke temperature in tunnel fires. A laser sheet was used as an assisting tool to show the smoke flow field. A series of tests were conducted with shaft heights varying from 0.2 m to 1.2 m and a heat release rate (HRR) of 9 kW, 17 kW, 29 kW, and 65 kW. The entrainment phenomenon around the vertical shaft was analyzed, and the results showed that the amount of fresh air entrainment is the main reason for the temperature decrease in upstream and downstream smoke temperatures. Based on the experimental results, an empirical model for predicting the amount of fresh air entrainment and a prediction model of the downstream smoke temperature were proposed, and the predicted values are in good agreement with the experimental values.