Nozzle Geometry Research Articles

Experimental Analysis of Cavitation Erosion: Parameter Sensitivity and Testing Protocols

The scientific goal of this study was to investigate the effects of various parameters on cavitation-induced erosion, with the aim to enhance the understanding and assessment of cavitation resistance in hydraulic systems. Cavitation erosion poses significant challenges to the durability and efficiency of hydraulic components, such as those found in hydropower plants and pumping stations. Prompted by the need to improve the reliability of cavitation testing and material assessment, this research conducted a comprehensive sensitivity analysis of a cavitation jet apparatus (CJA). This study employed an experimental platform that consisted of a vertical cylindrical test tank, a submerged nozzle, and an aluminum sample. By examining a range of orifice diameters, this research identified that smaller diameters led to increased erosion intensity, with the most pronounced effects observed at a diameter of 2 mm. Furthermore, various standoff distances (SoDs) were tested, which revealed that shorter distances resulted in greater erosion, with the highest impact noted at an SoD of 5 cm. This study also evaluated different nozzle geometries, where it was found that a 132° conical sharped edges nozzle, combined with an orifice diameter of 2 mm and an SoD of 5 cm, produced the most severe erosion. Conversely, chamfered edges nozzles and a commercial nozzle (MEG2510) with an SoD of 10 cm or greater showed reduced erosion. These results highlight that by standardizing the testing duration to 1200 s, the CJA could reliably assess the cavitation resistance of materials. This study established a clear relationship between increased pressure and higher impact forces, which led to more severe erosion. The findings underscore the effectiveness of the CJA in evaluating material resistance under various cavitation conditions, thus addressing a critical need for reliable cavitation testing tools.

Shock Wave and Aeroelastic Coupling in Overexpanded Nozzle

The growing demand for increasing the engine power of a liquid rocket is driving the development of high-power De-Laval nozzles, which is primarily achieved by increasing the expansion ratio. A high-expansion-ratio for De-Laval nozzles can cause flow separation, resulting in unsteady, asymmetric forces that can limit nozzle life. To enhance nozzle performance, various separation control methods have been proposed, but no methods have been fully implemented thus far due to the uncertainties associated with simulating flow phenomena. A numerical study of a high-area-ratio rocket engine is performed to analyze the aeroelastic performance of its structure under flow separation conditions. Based on numerical methodology, the flow inside a rocket nozzle (the VOLVO S1) is analyzed, and different separation patterns are comprehensively discussed, including both free shock separation (FSS) and restricted shock separation (RSS). Since the location of the flow separation point strongly depends on the turbulence model, both the single transport equation and two-transport-equation turbulence models are simulated, and the findings are compared with the experimental results. Therefore, the Spalart–Allmaras (SA) turbulence model is the ideal choice for this rocket nozzle geometry. A wavelet is used to analyze the amplitude frequencies from 0 to 100 Hz under various pressure fluctuation conditions. Based on a clear understanding of the flow field, an aeroelastic coupling method is carried out with loosely coupled computational fluid dynamics (CFD)/computational structural dynamics (CSD). Some insights into the aeroelasticity of the nozzle under separated flow conditions are obtained. The simulation results show the significant impact of the structural response on the inherent pressure pulsation characteristics resulting from flow separation.

Spray characteristics of steam-assisted oil atomization in Y-jet nozzles

Twin-fluid atomizers, valued for handling viscous fluids and high operating loads, are extensively used in combustion processes and oil refineries. In the latter scenario, internal mixing nozzles are employed in fluid catalytic cracking units for oil dispersion using steam as the dispersing medium. While steam-assisted atomization studies often focus on flue gas analysis, the associated steam/oil internal mixing process and the spray droplet dynamics lack proper investigation. Accordingly, this work explores the Y-jet nozzle performance for oil atomization using steam, aiming to determine favorable conditions for obtaining a stable spray with fine droplet distribution. This analysis is accomplished by characterizing the mixing chamber pressure, investigating the spray boundary instabilities using high-speed images, and exploring the spray droplet size using the shadowgraphy technique. Work relevance relies on performing experiments at industrially representative conditions, characterized by the similarity of important dimensionless numbers. Additionally, the nozzle design is optimized by varying key geometric parameters. The nozzle geometry and the operating condition impact on the steam-assisted atomization performance and spray behavior constitutes the main findings of this work. The outcomes highlight the relevance of the fluid dynamics investigation for optimized nozzle performance, involving a balance between spray stability and fine droplet distribution generation.

Effects of nozzle geometry and fiber orientation on the tensile strength of 3D printed continuous fiber reinforced composites

In material extrusion (MEX) based 3D printing, inter-filament voids are intrinsic to printing process. The void orientation, volume and shape are affected by multiple factors including the nozzle shape, stacking sequence and printing direction. In this study, the adverse effects of the inter-filament voids on tensile properties and damage modes were investigated numerically on 3D printed acrylonitrile butadiene styrene-carbon fiber (ABS/CF) continuous fiber-reinforced composites (CFRCs). Uniaxial tensile simulations were performed considering various nozzle geometries (circular, square), fiber orientations (θ=0o,30o,45o,60o,90o) relative to loading direction, and a regular stacking sequence of extrudates. The extrudate cross-section was modeled either using elliptical or superelliptical extrudates deposited from a circular or square nozzle, respectively. Excellent agreement was seen when the simulated results were benchmarked against several published experimental and numerical work. Simulated results showed that changing the nozzle shape from circular to square improved the mechanical properties across all fiber angles by lowering the void content by 7−8% and increasing the ultimate tensile strength (σT) by 11−18%, tensile stiffness (ET) by 6−8%, and the tensile failure strains (ϵT,fail) by 1−11%. For superelliptical extrudates the number of observed damage modes also reduced, and this is due to a 37.2% and 58.2% improvement in the inter-filament and inter-layer bond lengths, respectively. Also, when fiber angle became increasingly off-axis to tensile load direction, the strengths, moduli, and failure strains reduced for both circular and square nozzles. The significance of using microstructure geometries and explicitly modeling inter-filament voids for simulating MEX printed CFRCs was highlighted by comparing these results with both analytical calculations and simulated results of homogeneous solid CFRC blocks without voids.

The formation and post-formation processes of vortex rings discharged from laminar starting jets

Motivated by biological systems, vortex rings can enhance the propulsive efficiency in industrial systems. To study the vortex properties during the formation and post-formation stages, impulsively starting jets are investigated by simulations. The effects of the stroke ratio and nozzle geometry are studied at a fixed jet Reynolds number of 2500. The stroke ratio at the formation number is found to be not enough to produce a vortex ring with maximum circulation. The stroke ratio is suggested to be about twice as large as the formation number. An alternative criterion based on the circulation ratio is proposed to describe the onset of pinch-off. This criterion states that the pinch-off would start when the vortex ring attains about 80% of the total jet circulation. During the formation stage, the scaling laws for vortex trajectories and circulation are proposed for continuous formation. By combining the suggested scaling relations and Saffman's velocity formula, the evolution of non-dimensional energy can be predicted. During the post-formation stage, the scaling laws for vortex properties (e.g., the vortex ring diameter, translational velocity, and circulation) are found to be independent of both the nozzle configuration and the vortex Reynolds number. On the grounds of the invariance of impulse in vortex decay, the scaling laws of vortex motion are derived for the non-dimensional energy, circulation, and diffusivity scale of the vortex core. In consequence, the normalized energy and circulation found in experiments can be successfully derived from the similarity model for both nozzle configurations.

Acoustic flow resonances in installed rectangular jets

Zonal Large Eddy Simulations (LES) of complex installed rectangular jet flows are performed for subsonic jet conditions of the Central Institute for Aviation Motors (CIAM) experiment, where a strong tone was reported. For far-field noise modelling, the zonal LES solutions are coupled with the permeable formulation of the Ffowcs Williams and Hawkings (FW-H) method. The obtained noise spectra predictions are compared with the acoustic measurements in the CIAM facility. To reduce statistical noise of the relatively short LES time series, contributions due to several dominant low frequency tones and the remaining broadband signal are computed separately, using a tailored Fourier transform technique for each signal type. For cross-validation, noise spectra measurements of an equivalent isolated round jet in the CIAM facility are compared with the empirical sJet model calibrated on the NASA Small Hot Jet Acoustic Rig (SHJAR) jet noise database. While the two datasets agree reasonably well for mid to high frequencies, larger discrepancies are observed for low frequencies, which are attributed to acoustic reflections in the non-anechoic CIAM facility. The differences in noise levels between the CIAM dataset and the sJet model representing the NASA jet noise data are used to determine the experimental uncertainty of the CIAM noise measurements for each frequency and observer angle. For the installed rectangular jet, it is shown that far-field noise spectra predictions of the zonal LES-FW-H method for both the fundamental tone, its sixth harmonic corresponding to the jet Strouhal number of around 1, and the broadband component are broadly within the experimental error bar for most observer angles. Some discrepancies between predictions of the zonal LES method and the CIAM measurements for the main low frequency tone for the 30o and 90o, where the experimental uncertainty at low frequencies is largest are also noted. After validating the acoustic solutions, spectral and conditional averaging analysis methods are applied to elucidate mechanisms of the acoustic-flow resonance in the installed rectangular jet flow. The numerical dispersion relation is obtained to analyse phase velocities of the upstream and downstream travelling pressure waves in the stream-wise direction. The conditional analysis of pressure fluctuations inside the jet reveals the emergence of internal reflection points corresponding to a rapid change of the acoustic wave phase as well as the saddle points interpreted as localised zones of vorticity shed from the side-wall edges. To independently investigate the effect of trailing edges and corner points of the jet embodiment geometry on closing the acoustic-flow resonance cycle, several modifications of the baseline rectangular nozzle are considered, such as introducing chevron-like lobes and cuts on the trailing edges of the side walls as well as smoothing the sharp corner points of the wall edges. Following the series of additional zonal LES runs with the modified installed nozzle geometries, an optimized tone-less modification of the original installed nozzle was obtained, in broad agreement with the conditional analysis results. The obtained tone-less modification of the installed rectangular jet is further analyzed to provide insights into its similarity and differences from the aeroacoustics of the reference isolated round jet in the same CIAM facility.

Effect of Nozzle Geometry on the Injection Characteristics of Liquid CO2 as a Volatile Lubricant and Coolant for Aluminum Hot Stamping

Effect of Nozzle Geometry on the Injection Characteristics of Liquid CO2 as a Volatile Lubricant and Coolant for Aluminum Hot Stamping

The application of the state-of-the-art turbulence models in the OpenFOAM CFD codes and the validation for different flow control cases in the continuous casting process

Computational fluid dynamics (CFD) is an established approach to study flow behaviour. Despite advances in mathematical numerical modelling in recent decades, accurately predicting the turbulent flow behaviour of steel using CFD remains a challenge. In the continuous casting process, two main flow control systems are employed to transfer liquid steel from the tundish to the mould, namely stopper control and slide gate control. In additional to these two main flow control systems, the casting nozzle geometries, casting rate, and casting mould dimensions vary considerably, and this complexity makes it difficult to precisely simulate turbulent flow in the casting channel. In this paper, examples are presented showing how different turbulence models influence the simulation results, using the latest version of the open source CFD simulation software OpenFOAM. Prior to the CFD modelling, RHI Magnesita's water modelling facilities in Leoben (Austria) were used to validate the state-of-the-art turbulence models selected for a particular casting nozzle geometry and flow control system.

3D-printing bauxite residue/fly ash-containing geopolymers as promising metal sorbents for water treatment

Herein, we demonstrate for the first time the feasibility of employing significant amounts (up to 80 wt%) of unexplored industrial wastes (red mud and biomass fly ash) in the production of highly porous 3D-printed geopolymer lattices envisioned for wastewater treatment applications. This without compromising the mechanical performance of the geopolymers relative to those obtained using commercial precursors. The impact of the fly ash incorporation content in the fresh-state (calorimetric and reological characterization) and hardened-state (porosity and mechanical strength) properties of the produced structures was evaluated. Moreover, the influence of key printing parameters, including nozzle diameter and geometry alignment, on the resulting properties of the lattices was also evaluated. The most promising compositions were then evaluated as lead sorbents under continuous flow. The waste-based 3D-printed lattices showed remarkable adsorption ability reaching >95 % removal efficiency after 2 h. This sustainable strategy is in line with the United Nations sustainable development goals and the transition to a circular economy, reducing the consumption of natural resources and simultaneously contributing to reducing water pollution.

Effect of Ramp Geometry on Single Expansion Ramp Nozzle Performance Characteristics

In high-speed flight regimes, the drag plays a significant role in determining the overall performance of the aerospace vehicle. One proposed solution is to integrate a single expansion ramp nozzle (SERN) at the aft of the vehicle to mitigate the drag effects. This work investigates the effects of nozzle geometry on flow and performance characteristics of SERN with a thrust-optimized parabolic and minimum-length nozzle ramp contours, which have not been explored with regard to these aspects. A computational study is carried out on these two ramp contours using compressible Reynolds Averaged Navier–Stokes equations over a range of nozzle pressure ratio (NPR). In the tested range of NPR, the restricted shock separation is found to be the chief mode of flow separation in SERN, along with the change in the size of recirculation zone and separation bubble. At NPR 3, the thrust-optimized parabolic ramp contour shows an increment of thrust coefficient by 29.2% over the minimum-length nozzle; whereas at NPR 3.5, the minimum-length nozzle demonstrates an increment of thrust coefficient by 56.3% over the thrust-optimized parabolic at 0-deg M cowl angle. Further, in the tested range of NPR, the minimum-length nozzle shows an improved lift coefficient at 5 deg cowl angle.

Jet mixing optimization using a flexible nozzle, distributed actuators, and machine learning

In this paper, we introduce the first jet nozzle allowing simultaneous shape variation and distributed active control, termed “Smart Nozzle” in the sequel. Our Smart Nozzle manipulates the jet with an adjustable flexible shape via 12 equidistant stepper motors and 12 equidistantly placed inward-pointing minijets. The mixing performance is evaluated with a 7 × 7 array of Pitot tubes at the end of the potential core. The experimental investigation is carried out in three steps. First, we perform an aerodynamic characterization of the unforced round jet flow. Second, we investigate the mixing performance under five representative nozzle geometries, including round, elliptical, triangular, squared, and hexagonal shapes. The greatest mixing area is achieved with the square shape. Third, the symmetric forcing parameters are optimized for each specified nozzle shape with a machine learning algorithm. The best mixing enhancement for a symmetric active control is obtained by the squared shape, which results in a 1.93-fold mixing area increase as compared to the unforced case. Symmetrically unconstrained forcing achieves a nearly 4.5-fold mixing area increase. The Smart Nozzle demonstrates the feasibility of novel flow control techniques that combine shape variation and active control, leveraging the capabilities of machine learning optimization algorithms.

Analyze the influence of nozzle shape and orientation on inline arrangement of multiple jets impingement on a concave surface

ABSTRACT The present study reports the thermal behavior of multiple jets on a hot concave surface with different nozzle geometries such as circular and elliptical and different orientation. Tests are performed with five different nozzles at different values of nondimensional nozzle to surface distance (z/d = 2–10) and Reynolds number (5000–28,000). Here, the parameter coefficient of variation (COV) is used to estimate the non-uniformity in the local Nu variation. For N-2, the value of CO V y , non − dim is found to be 50–60% higher compared to N-3 at z/d = 2; while at z/d ≥ 8, for N-3, the value of CO V y , non − dim is found to be 10–15% higher compared to N-2. The higher temperature uniformity ( CO V x , non − dim ) is noted in the fountain region compared to impingement region for the circular and elliptical nozzles. The thermal performance of elliptical jets is found to be sensitive toward the jet orientation at lower z/d values. The magnitude of temperature non-uniformity decreases with the increase in the z/d values. Among the tested nozzles, Nozzle N-2 consistently demonstrates superior performance across all nozzle-to-plate distances and with an increase in the z/d value improvement with nozzle N-2 reduces.

Numerical simulation of cavitating flow in liquid Nitrogen through a convergent nozzle

This research has dealt with the simulation of liquid nitrogen cavitation inside a convergent nozzle. This is important in cryogenic industrial applications. So in this study, computational fluid dynamics methods have been used for simulating the cavitation phenomenon. The Two-phase model in this research has been a hybrid/mixed model. Also, k- ε turbulence model has been employed in realizable state. For meshing the nozzle geometry, Gambit software has been used, while for numerical simulation, Ansys Fluent software has been employed. For simulation of cavitation, Schnerr and Sauer cavitation model has been utilized. This research has also examined the effect of changing the nozzle outlet diameter and the impact of changing the pressure difference in the inlet and outlet of the nozzle on the cavitation. As a novelty and unlike what would have been expected based on the Bernoulli effect, the results obtained from the simulation showed that the increase/decrease in the nozzle's outlet diameter resulted in an enhanced/diminished extent of cavitation in the nozzle's outlet region. Also, the increase/decrease of the pressure difference in the input and output of the nozzle would lead to a higher/lower extent of cavitation. This research also found that the effect of altering the nozzle's outlet diameter on the extent of cavitation has been far higher than the effect of changing pressure difference in its inlet and outlet. The results also indicated that upon reduction of the nozzle's outlet diameter from the base state (1.02 mm) by 10, 20, 30, 40, and 50 %, the volume fraction of the vapor diminished by 22.23, 43.029, 60.66, 74.73, and 87.16 % respectively. Finally, with the increase in the nozzle's outlet diameter from the base state (1.02 mm) by 10, 20, 30, 40, and 50 %, the volume fraction of the vapor increased by 26.83, 55.27, 84.47, 117.12, and 149.31 % respectively.

Study on the spray characteristics of transverse jets with elliptical nozzles in supersonic crossflows using the volume of fluid–discrete phase model

The atomization characteristics of liquid jets injected transversely into a supersonic crossflow significantly affect the performance of scramjet engines. Existing research on this topic has mainly focused on circular nozzles, while the influence of nozzle geometry, particularly elliptical nozzles, has received relatively limited attention. Therefore, this study employs a numerical simulation method coupling the volume of fluid and discrete particle model to investigate the breakup and atomization characteristics of transverse liquid jets from elliptical nozzles with different aspect ratios under supersonic crossflow conditions, as well as the total pressure loss. The simulation model is validated against experimental data obtained from a pulse wind tunnel, including measurements of the liquid jet penetration depth and the Sauter mean diameter (SMD). The results indicate that for elliptical nozzles with an aspect ratio (AR) greater than 1, columnar breakup occurs earlier, and the columnar breakup length is shorter compared to circular nozzles. As the AR increases, the jet penetration depth decreases, while the spray expansion angle increases. Furthermore, the SMD of the atomized spray field from the circular nozzle is larger than that from the elliptical nozzles, and the SMD of the spray field is smallest for an elliptical nozzle with AR of 4. Finally, the elliptical nozzles exhibit a higher total pressure recovery coefficient, indicating reduced total pressure loss in the combustion chamber. This reduction in pressure loss is expected to improve the thrust performance of the scramjet engine.

Optimising Bioprinting Nozzles through Computational Modelling and Design of Experiments.

3D bioprinting is a promising technique for creating artificial tissues and organs. One of the main challenges of bioprinting is cell damage, due to high pressures and tensions. During the biofabrication process, extrusion bioprinting usually results in low cell viability, typically ranging from 40% to 80%, although better printing performance with higher cell viability can be achieved by optimising the experimental design and operating conditions, with nozzle geometry being a key factor. This article presents a review of studies that have used computational fluid dynamics (CFD) to optimise nozzle geometry. They show that the optimal ranges for diameter and length are 0.2 mm to 1 mm and 8 mm to 10 mm, respectively. In addition, it is recommended that the nozzle should have an internal angle of 20 to 30 degrees, an internal coating of ethylenediaminetetraacetic acid (EDTA), and a shear stress of less than 10 kPa. In addition, a design of experiments technique to obtain an optimal 3D bioprinting configuration for a bioink is also presented. This experimental design would identify bioprinting conditions that minimise cell damage and improve the viability of the printed cells.

CFD-DEM modelling of particle entrainment in wheel–rail interface: a parametric study on train characteristics

Rail-sanding is employed to improve the train’s wheel–rail traction loss in low adhesion conditions. This can significantly impede trains’ kinematics, operation, and performance by hindering the train’s acceleration and deceleration, resulting in delays and unreliability of transport system as well as causing safety risks and in the worst cases train collisions. Rail-sanding has its own merits in recovering the wheel–rail traction but can result in a sand wastage of more than 80% due to its low sand entrainment efficiency. In this research, computational fluid dynamics is coupled to discrete element modelling to study the behaviour of sand particles during rail-sanding. A parametric study based on the train characteristics, including train velocity, sand flow rate, and the geometry of the sander nozzle, is performed by comparing the entrainment efficiency of the sand particles. It is found that train velocities over 30 m/s result in the entrainment efficiency of almost zero. A moving air layer generated at the wheel–rail interface influences the lower bound of acceptable particle size range. The flow rate and nozzle geometry can be designed to enhance entrainment efficiency.

Enhanced aerosol-jet printing using annular acoustic field for high resolution and minimal overspray

Aerosol jet printing has the potential to fabricate fine features on various substrates due to its large stand-off distance. However, the presence of overspray and instability, particularly at high printing resolutions, has limited its widespread application. In this study, we introduce an efficient approach called annular acoustic focusing for aerosol jet printing. By determining the optimal focusing frequency (5.8 MHz) for silver nanoparticles using a particle ejection model, we achieve precise and stable printing. We also propose a modified print nozzle geometry, resulting in ultrafine traces (line width < 6 μm, overspray < 0.1 μm). Compared to printing without acoustic focusing, the line width of the traces decreases to 60 ± 5% while their conductivity increases to 180 ± 5%. Additionally, several 8 h experiments demonstrate excellent printing stability. This research opens up possibilities for the fabrication of conformal electronics with high precision and improved conductivity using aerosol jet printing.

Effect of the asymmetric flow behaviour of molten steel on solidified shell in slab continuous casting mould

The flow behaviour of molten steel in the mould has an important influence on the solidification quality of the slab. A three-dimensional transient mould model has been developed to describe the effect of the asymmetric flow behaviour of molten steel on solidified shells in the mould. The causes of the asymmetric behaviour of molten steel in the mould were discussed, and the interaction between deviation flow and solidified shell was analysed. The results show that the asymmetric distribution of the flow field is caused by the difference in flow rate at the outlets on both sides of the nozzle and the irregular interaction between the molten steel and the complex nozzle geometry. The level fluctuation is correlated with the deviation flow of the molten steel on the opposite side. The velocity variation trend of the two models is similar, but the fluctuation amplitude of the velocity on both sides of the nozzle in the non-solidification model is more drastic. The conversion period of the deviation flow in the solidification model is longer than that in the non-solidification model. Moreover, the velocity and angle of incident and return flow on both sides are different due to the deviation flow, which mainly affects the solidification of the shell at and below the impact point of the molten steel. The deviation flow will strengthen the impact of the main stream on the shell, resulting in a significant decrease in the thickness at the impact point, while the thickness of the shell below the impact point fluctuates greatly.

Modeling non-monotonic variation of plume angle with superheat index of flash boiling spray

There is an urgent need for modeling angles and widths of liquid jet with internal phase change, but existing semi-empirical models rely strongly on coefficient fitting and lack a thorough understanding of the additional phase-change physics. In the present work, we proposed a theoretical model to predict the non-monotonic variation of plume angle with the defined superheat index of flash boiling spray. Assuming that the plume angle is determined by the trajectories of tiny droplets in the perimeter of the spray, this model identifies the angle with the inverse tangent of the ratio of the streamwise and crosswise velocities of the tiny droplets. The streamwise velocity is determined by solving a one-dimensional two-phase flow within the channel, and the crosswise velocity is determined by modeling the burst of an equivalent bubble at the exit of the nozzle. Compared with the existing semi-empirical models, this model is free of fitting parameters, and it agrees well with the experimental data from a rectangular microchannel with discrepancies being sufficiently discussed. This model has the potential of being applied to modeling the plume angle of flash boiling sprays with different nozzle geometries in various atomization practices.

Investigating the effect of deicing parameters using high-pressure water jet

Maritime operations are impacted by ice accretion on decks, bulkheads, and offshore structures during the winter or in extremely frigid climates. In most cases, the traditional method of deicing maritime vessels is human labor, which requires enormous effort and lengthy hours for unsatisfactory results, particularly when the ice adhesion strength is high. This study experimentally examined combined effects of operational parameters, including operating pump pressure, nozzle geometry, water jet temperature, standoff distance, and time of cut, on the depth and width of a cut through an ice block. In comparison to other parameters, the influence of nozzle geometry on both the width and depth of cut was found to be more significant, with R-squared values of 85% and 62% respectively. Increasing the depth and width of the cut facilitated the delamination and disintegration of ice from an aluminum mold. This indicates that water jet deicing on maritime vessels could be effective, therefore achieving the objective of this study. The optimization of operational parameters is used to develop a cuttability chart for various thicknesses of accumulated ice on marine vessels.