A method for producing model ice and model ice obtainable by the method

Abstract

The present disclosure relates to a method for producing model ice onto surface (104b) of water (104) in a tank (101) positioned in a temperature-controlled environment (102) comprising ambient air using an internal-mix-assisted nozzle (103) comprising a nozzle tip (103c), wherein the nozzle tip is directed towards the surface of the water, the method comprising a) a spraying phase comprising: applying compressed air and pressurized water towards the nozzle tip (103c) of the internal-mix-assisted nozzle (103) thereby forming a spraying mixture; allowing the spraying mixture to flow through the nozzle tip to the ambient air thereby atomizing the pressurized water and forming a spray (105) directed towards the surface of the water and / or towards formed ice on the surface of the water; and allowing the spray to accumulate on the surface of the water and / or on the formed ice on the surface of the water, thereby producing model ice, and b) a freezing phase comprising allowing the model ice to consolidate in the ambient air.

Description

[0001] A METHOD FOR PRODUCING MODEL ICE AND MODEL ICE OBTAINABLE BY THE METHOD

[0002] FIELD

[0003] The present disclosure generally relates to a method for producing a model ice suitable for reduced-scale testing of interactions of ice with engineering structures. The disclosure also relates to a model ice obtainable by the method and use of the model ice.

[0004] BACKGROUND

[0005] Reduced-scale experiments are commonly used in modelling icebreakers, offshore platforms, wind turbines, and similar structures. These model-scale experiments allow engineers and researchers to study these structures in ice without expensive full-scale prototypes. When conducting model tests for ice structure interaction, it is important to scale the properties and characteristics of the ice using appropriate scaling laws. In practice, the scaling requires a weaker type of ice to be used to represent natural sea, lake or river ice in the tests. This weaker model ice is produced in test facilities using different techniques. Its strength and stiffness should be lower than those of natural ice by a factor of 5-30, but its density and frictional properties should remain close to those of natural ice.

[0006] Model ice production methods can be divided into seeding methods and spraying methods. Seeding methods involve spraying cold water into freezing air, the resulting mist settling on water surface and providing ice nuclei for subsequent columnar ice grains, which grow downward in a columnar structure. This technique has undergone several advancements. Saline model ice, initially developed by the Arctic and Antarctic Research Institute in the 1950s, uses salinity solutions of 1-3% to reduce strength. Later advancements, such as tempering, improved mechanical property scaling, particularly the strain modulus of elasticity-to-flexural strength (E / of) ratio. However, compressive-to-flexural strength ratios (cc / cf) remain low (<2), and the ice often exhibits ductile failure modes (Lau et al., 2007; Schwarz, 1975; Timco, 1980).

[0007] Urea-water model ice was developed as a less corrosive alternative of saline model ice, offering higher E / of ratios (>2000) and reduced plasticity. Challenges include anisotropy, non-homogeneous mechanical properties, and incorrect compressive strength scaling (Hirayama, 1983a, 1983b; Timco, 1980).Improved saline model ice techniques include the introduction of air bubbles in saline model ice for enhancing brittleness and for allowing better control of mechanical properties. However, issues like uneven strength distribution across ice layers and challenges in replicating crushing behaviour persist (Evers & Jochmann, 1993; Jochmann et al., 2021; von Bock Und Polach et al., 2020; Ziemer et al., 2022).

[0008] EG / AD / S model ice, developed in the 1980s, incorporates a solution of ethylene glycol (EG), aliphatic detergent (AD), and sugar (S) to achieve enhanced mechanical properties. EG reduces the ice's strength by creating impurity pockets, AD lowers surface tension, and sugar inhibits lateral crystal growth. Production of the EG / AD / S Model Ice involves pre-cooling, wet-seeding, and tempering, resulting in a homogeneous single-layered ice sheet. While EG / AD / S ice achieves E / of ratios of 1500-2500, it suffers from increased complexity in production and susceptibility to biological growth due to sugar additives (Timco, 1986). A spraying method involves fine misting of water, leading to granular ice formation in an upward direction.

[0009] FG (Fine Grain) model ice, developed at Wärtsilä Arctic Research Centre, uses saline water to produce fine-grained ice. Despite its advantages, it exhibits uneven strength distribution, with the upper layers being significantly stronger than the lower layers. Additionally, E / of ratios remain low (<2000) (Enkvist & Mäkinen, 1984).

[0010] GE (Granular ethanol -water) model ice, developed at Aalto University, is aiming to improve uniformity and consistency of the model ice. However, it exhibits poor scaling for compressive strength (oc / of < 1.5) and limited applicability in crushing-dominant tests (Jalonen & Ilves, 1990; R. von Bock und Polach et al., 2013; von Bock und Polach et al., 2019).

[0011] An advanced variant of FG ice, FGX (Fine Grain Enhanced) model ice adjusts salinity during spraying to enhance mechanical properties. While this reduces production time, challenges such as low oc / of ratios and brittleness at low flexural strengths remain (Nortala-Hoikkanen, 1990).

[0012] ICMI model ice, disclosed by Hamburgische Schiffbau-Versuchsanstalt, HSVA, enhances crushing behaviour by incorporating larger, quasi-random crystal orientations. While the ice improves oc / of ratios (>2), it requires precise environmental controls and is limited to higher flexural strengths (Ziemer et al., 2022).As disclosed above, the required mechanical properties are difficult to achieve with existing model ice types. First, model ice may not be brittle enough compared to natural ice and fails in too plastic, ductile manner. Second, the ratio between compressive strength and flexural strength may not be correct: the strength values are roughly equal, whereas in natural ice the compressive strength is 3-5 times larger than the flexural strength. The low ratio of compressive strength to flexural strength (around 3 or less) is particularly limiting in crushing-dominated test such as offshore wind turbine piles.

[0013] Current model ice types are time- and energy-consuming to produce. All existing methods require extended freezing periods spanning from 2 to 15 hours, leading to significant energy consumption by cooling equipment. Moreover, the use of additives such as ethanol, urea, and sodium chloride to weaken the ice adds to the expense of these methods. Some methods also lead to heightened corrosion and maintenance demands.

[0014] Accordingly, there is still need for further methods for producing model ice.

[0015] SUMMARY

[0016] The following presents a simplified summary to provide a basic understanding of some aspects of different invention embodiments. The summary is not an extensive overview of the invention. It is neither intended to identify key or critical elements of the invention nor to delineate the scope of the invention. The following summary merely presents some concepts of the invention in a simplified form as a prelude to a more detailed description of exemplifying and non-limiting embodiments of the invention.

[0017] Accordingly, it is a first aspect of the present disclosure to provide a method for producing model ice onto surface of water in a tank positioned in a temperature-controlled environment comprising ambient air using an intemal-mix-assisted nozzle comprising a nozzle tip, wherein the nozzle tip is directed towards the surface of the water, the method comprising a) a spraying phase comprising:

[0018] applying compressed air and pressurized water towards the nozzle tip of the intemal-mix-assisted nozzle thereby forming a spraying mixture;

[0019] allowing the spraying mixture to flow through the nozzle tip to the ambient air thereby atomizing the pressurized water and forming a spray directed towards the surface of the water and / or towards formed ice on the surface of the water; and allowing the spray to accumulate on the surface of the water and / or on the formed ice on the surface of the water, thereby producing model ice, whereinpressure of the compressed air is from 2 bar to 100 bar, preferably from 3 bar to 7 bar, such as 4 bar,

[0020] temperature of the pressurized water is from -0.2 °C to +5 °C, such as 0 °C, pressure of the pressurized water is from 1 bar to 5 bar, such as 3 bar, and temperature of the ambient air is from -15 °C to -5 °C, such as -10 °C; and b) a freezing phase comprising allowing the model ice to consolidate in the ambient air, wherein temperature of the ambient air is from -15 °C to -5 °C, such as -10 °C. It is a second aspect of the present disclosure to provide a model ice obtainable by the method of the first aspect.

[0021] It is a third aspect of the present disclosure to provide use of the model ice of the second aspect for reduced-scale testing of interactions of ice with engineering structures.

[0022] Exemplifying and non-limiting embodiments of the invention are described in accompanied dependent claims.

[0023] Exemplifying and non-limiting embodiments of the invention both as to constructions and to methods of operation, together with additional objects and advantages thereof, are best understood from the following description of specific exemplifying embodiments when read in conjunction with the accompanying figures.

[0024] The verbs “to comprise” and “to include” are used in this document as open limitations that neither exclude nor require the existence of un-recited features. The features recited in dependent claims are mutually freely combinable unless otherwise explicitly stated. Furthermore, it is to be understood that the use of “a” or “an”, i.e., a singular form, throughout this document does not exclude a plurality.

[0025] BRIEF DESCRIPTION OF THE FIGURES

[0026] Exemplifying and non-limiting embodiments of the invention and their advantages are explained in greater detail below with reference to the accompanying figures, in which: Figure 1 shows an exemplary schematic system for producing model ice of the present disclosure.

[0027] Figure 2 shows a schematic presentation of an exemplary internal-mix-assisted nozzle suitable for using in the method of the present disclosure.

[0028] Figure 3 shows (a, b) ice surface and (c) grain structure (scale bar 1 mm) of an exemplary model ice prepared according to the method of the present disclosure.Figure 4 shows comparison of grain size distributions between a model ice of the present disclosure (VFG) and a state of art fine-grained ethanol doped (GE) model ice. The curves show the fitted lognormal distributions.

[0029] Figure 5 shows (a) a typical bending force time history from cantilever beam bending test (1. loading; 2. load due to the buoyancy force of failed beam; 3. unloading) and (b) a typical compression force time history from edge crushing test (1. loading; 2. failure) of an exemplary model ice of the present disclosure.

[0030] Figure 6 summarizes experimental results for a model ice of the present disclosure (a): ice thickness (hi); (b) ice density (p(); (c) compressive strength (GC); and (d) flexural strength (<jf) for different experimental conditions. The error bars reflect the standard deviation. Figure 7 shows comparison of Non-Linearity of Model Ice (NLMI) index values obtained for a model ice of the present disclosure with those reported in the literature for various model ice types, a) GE (Jalonen and Ilves 1990); b) GE (Li and Riska 1996); c) GE (von Bock und Polach et al. 2015); d) saline ice (von Bock und Polach et al. 2021); e) MIVET (von Bock und Polach et al. 2021; f) VFG of the present disclosure; g) Sea ice (Wang et al.

[0031] 2022).

[0032] Figure 8 shows compressive versus flexural strength for model ice of the present disclosure compared to literature data. ■ = seeding EG / AD / S (Timco 1986); •= seeding urea (Timco 1980); A= seeding 0.6 % sodium (Timco 1980); o = spraying GE (0.3% (v / v) ethanol; produced in Aalto Ice and Wave Tank); ▼= spraying VFG of the present disclosure; a) = seeding-CD-EG / AD / S (2.5 times flex), best estimated (Spencer and Timco 1990); b) spraying GE-average value (Jalonen and Ilves 1990); c) spraying-FGX (1.5 times flex) (Nortala and Hoikkanen 1990).

[0033] DESCRIPTION

[0034] The specific examples provided in the description below should not be construed as limiting the scope and / or the applicability of the accompanied claims. Lists and groups of examples provided in the description below are not exhaustive unless otherwise explicitly stated. In one aspect the present disclosure concerns a method for producing model ice. An exemplary schematic presentation of the method of the present disclosure is shown in Figure 1. The method utilises a system comprising a tank 101, preferably an insulated tank positioned in a temperature-controlled environment 102, such as a refrigerated hallcomprising ambient air, and an internal -mix-assisted nozzle 103. In an internal -mix-assisted nozzle, air and liquid meet inside the nozzle and mix before the mixture leaves the nozzle. Internal-mix-assisted nozzles are well-known in the art. An exemplary internal-mix-assisted nozzle 103 is shown in figure 2. The internal-mix-assisted nozzle comprises an air inlet 103a, and liquid inlet 103b, and a nozzle tip 103c. In the method, the nozzle tip is positioned towards the surface of the water.

[0035] The model ice is produced onto surface 104a of water 104 positioned in the tank 101.

[0036] In the method more than one nozzle can be used to speed up the production of desired amount of model ice. Also, the nozzle(s) can be moved in x, y, and / or z-direction of the coordinate system 199 until desired amount of model ice is formed.

[0037] The method comprises

[0038] a) a spraying phase comprising:

[0039] applying compressed air and pressurized water towards the nozzle tip 103c of the internal-mix-assisted nozzle 103 thereby forming a spraying mixture;

[0040] allowing the spraying mixture to flow through the nozzle tip to the ambient air thereby atomizing the pressurized water and forming a spray 105 directed towards the surface of the water and / or towards formed ice on the surface of the water; and allowing the spray to accumulate on the surface of the water and / or on the formed ice on the surface of the water, thereby producing model ice, wherein

[0041] pressure of the compressed air is from 2 bar to 100 bar, preferably from 3 bar to 7 bar, such as 4 bar,

[0042] temperature of the pressurized water is from -0.2 °C to +5 °C, such as 0 °C, pressure of the pressurized water is from 1 bar to 5 bar, such as 3 bar, and temperature of the ambient air is from -15 °C to -5 °C, such as -10 °C;

[0043] b) a freezing phase comprising allowing the model ice to consolidate in the ambient air, wherein temperature of the ambient air is from -15 °C to -5 °C, such as -10 °C; and optionally

[0044] c) a tempering phase comprising increasing the ambient air to 0 °C - +2 °C.

[0045] In contrast to the state of art methods, water used for producing the model ice of the present disclosure does not need to include any additives to modify the freezing point or other aspects of the phase diagram or crystal growth. Exemplary additives typically used in the art are urea, sodium chloride, ethanol, sugar, ethylene glycol, and detergents.Preferably, the water for producing the model ice of the present disclosure does not include any additives such as urea, sodium chloride, ethanol, sugar, ethylene glycol, and / or detergents.

[0046] As defined herein, an insulated tank is a tank comprising thermal insulation material such as mineral wool, fibreglass, or polyurethane foam to maintain temperature of stored liquids. An exemplary insulated tank suitable for the method of the present disclosure comprise walls and bottom comprising thermal insulation material, and an open top configured to be in contact with the ambient air.

[0047] As defined herein, a spraying phase refers to the operational state in the production when spraying is active, i.e., the pressurized water is atomized and the spray is directed towards the water surface.

[0048] Duration of the spraying phase determines the thickness of the model ice. In an embodiment the duration of the spraying phase is from 1 h to 10 h.

[0049] In another embodiment, duration of the spraying phase is from 2 h to 4 h.

[0050] In still another embodiment, the spraying phase is 1 h, 2 h, 3 h, 4 h, 5h, 6h, 7h, 8h, 9h, or 10h.

[0051] In an embodiment the method comprises moving the nozzle(s) during the directing. The moving is in x, y and / or z direction of the coordinate system 199.

[0052] In an embodiment, distance of the nozzle tip from the surface of the water and / or from the surface of the formed ice on the surface of the water positioned in the tank in y-direction of the coordinate system 199 is from 5 to 150 cm, preferably from 20 cm to 100 cm, such as 50 cm.

[0053] In an embodiment the method comprises moving the nozzle(s) during the directing. In an embodiment the moving is in x, y and / or z direction of the coordinate system 199.

[0054] As defined herein a freezing phase refers to the operational state that follows spraying, during which no additional spray is introduced and the model ice is allowed to consolidate under controlled conditions. For model-scale testing requirements, the model ice of the present disclosure is ready for use after a short freezing period.

[0055] In an embodiment duration of the freezing phase is at least 1 min, at least 5 min, at least 10 min, at least 25 min or at least 30 min. Typically, the duration of the freezing phase is 30-60min. If the freezing time is extended, the ice may become too hard and thus it is no longer suitable for model-scale testing.

[0056] An advantage of the present method is that the freezing phase is short. Accordingly, the method produces high-quality model ice faster than prior art methods.

[0057] If further adjustment is needed, a third stage can be introduced to soften the ice by a tempering phase. During tempering, the temperature of the ambient air is raised close to the melting point of the model ice, typically to 0 °C - +2 °C to soften the ice and to achieve the correct scaling ratios.

[0058] In an embodiment, temperature of water on the surface of the water i.e., temperature of the water on which the spray is directed, is from -0.25 °C to +0.25 °C, preferably from -0.1 °C to +0.1 °C, such as 0 °C.

[0059] In an embodiment temperature of the compressed air is from -11 °C to -8 °C.

[0060] In another aspect the present disclosure concerns a model ice obtainable by the method disclosed above. Preferably, the model ice comprises the following features:

[0061] modal grain size is from 50 pm to 500 pm, preferably 300 pm,

[0062] density is 915-925 kg / m3, and

[0063] compressive versus flexural strength ratio (oc / of) is more than 3, preferably from 4 to 8.

[0064] In an embodiment Non-Linearity of Model Ice (NLMI) index of the model ice is 10-15%, such as 12%.

[0065] In still another aspect the present disclosure concerns use of the model ice for reduced-scale testing of interactions of ice, such as sea ice, lake ice, and river ice with engineering structures. Exemplary engineering structures are icebreakers, ships, off-shore structures, and wind turbines.

[0066] As defined herein reduced-scale testing involves evaluating smaller-sized physical models to predict the performance, behavior, or failure modes of full-scale prototypes. It enables cost-effective, high-series testing of complex engineering, structural, and material systems, using similitude theory and scaling laws to accurately interpret results. An exemplary reduced-scale testing platform utilizing model ice is Aalto Ice and Wave Tank of Aalto University (https: / / www.aalto.fi / en / iwt).

[0067] EXPERIMENTALFlexural strength

[0068] The in-situ cantilever beam (CBB) test is commonly used to evaluate the flexural strength of an ice sheet. Since flexural strength is not a fundamental material property, it is generally regarded as an index property. In this method, a floating cantilever beam of length L and width W was cut directly from the ice sheet. The beam dimensions were chosen to ensure beam-like bending behaviour and to avoid plate-like deformation characteristics. The recommended dimensions for the cantilever beams are as follows:

[0069] L = (5 - 7) x H, W= (2 - 3) x H

[0070] where H is the ice thickness.

[0071] The beam tip was loaded at a constant displacement rate until failure.

[0072] The applied force is recorded using a load cell, and the flexural strength is calculated via an Equation (1)

[0073] 6FLb

[0074] °f =Fir-(1)based on Bernoulli-beam theory, where F is maximum force required to break the beam, Lb is the distance from crack location to loading point, W is the width of the beam and H is the ice thickness.

[0075] Compressive strength

[0076] The in-situ compression test involved cutting cantilever beams from the ice sheet and applying compressive force at the free end.

[0077] The compressive force was recorded by a load cell, and the compressive strength was calculated using Equation (2)

[0078] F

[0079]

[0080] A(2)

[0081] where F is the maximum failure force, and A is the cross-sectional area of the beam, given by A = W x H.

[0082] Density

[0083] Ice density was measured in-situ by cutting a sample of known dimensions and submerging it without removal from the tank. With the beam volume known, ice density was calculated using Equation (3)F

[0084] Pi —T

[0085]

[0086] (3)

[0087] where pwis the density of the tank water, F is the buoyancy force, g is the acceleration due to gravity, and Vdis is the volume of displaced water, which is equal to the sample volume, calculated as follows: Vdis = W H

[0088] Thin section preparation

[0089] Thin sections of model ice were prepared by first storing samples at -15 °C. The samples were then flattened using a heated surface and adhered to a glass sheet with water droplets along the edges. A CNC machine was used to mill the sample to a thickness of 0.3±0.5 mm. To improve the visibility of grain boundaries in model ice, samples were examined under cross-polarized light. Due to the small grain size typically observed in sprayed model ice, a digital microscope (Celestron Handheld Digital Microscope Pro) was employed to capture detailed images of thin sections. This method allows for effective visualization of the ice microstructure.

[0090] After capturing images of the model ice sections, ImageJ software was used to analyze the grain size distribution. Typically, more than 500 individual grains were identified. The area of each grain was measured, and the equivalent diameter was calculated using Equation (4):

[0091]

[0092] where A is the area of the grain.

[0093] To obtain the grain size distribution, a frequency analysis was performed on the calculated equivalent diameters. The diameter range was divided into a series of size intervals (bins), and the number of grains within each bin was counted. These counts were then normalized by the total number of grains to obtain the relative frequency for each size class. A plot of relative frequency versus equivalent grain diameter was generated, and a log-normal distribution was fitted to the data to facilitate visual comparison between samples.

[0094] Nozzle

[0095] Different types of spray nozzles, including an internal-mix-assisted nozzle, an external-mix-assisted nozzle, and hydraulic nozzles were tested. In the external mix configuration, air andwater are mixed outside the nozzle, while in the internal mix design, both water and air are mixed inside of the nozzle. A schematic presentation of an internal-mix-assisted nozzle suitable for the method of the present disclosure is shown in Figure 2.

[0096] Conditions used in tests with external (EM) and internal (IM) mix nozzles are shown in table 1.

[0097] Table 1

[0098] NXEES Tfi® Tsic ts ^F Test ID

[0099]

[0100] bar baraCaC h li EM_1 1.5 2 -9.14 - 0.08 0.09 3

[0101] EM_2 3 4 -8.99 - 0.08 0.09 3

[0102] EM_3 3 2 -9.06 - 0.06 0.05 3

[0103] EM_ 4 3 5 -8.91 - 0.08 0.09 2

[0104] EM_5 3 3 -9.55 - 0.08 0.10 2

[0105] EM_6 3 3 -9.59 - 0.09 0.15 2

[0106] EM_7 3 6 -9.81 - 0.11 0.06 2

[0107] EM_8 3 3 -15.2 - 0.04 0.03 2

[0108] EM_9 3 4 -14.53 - 0.00 -0.01 2

[0109] EM_10 3 4 -14.02 - 0.03 0.02 2

[0110] EM_11 3 4 -14.57 - 0.04 0.01 2

[0111] EM_12 3 4 -14.06 - 0.03 0.01 2

[0112] IM_13 3 4 -9.85 -9.85 -0.02 -0.05 3 2 IM_14 3 4 -9.98 -9.98 0.01 -0.06 6 3

[0113] IM-ig 3 4 -10.05 -10.0 -0.07 -0.06 3 1 IM_16 3 4 -10.03 -10.07 0.0 0.0 3 0.5 & 1 IM_17 3 4 -9.93 -10.0 0.0 -0.01 3 0.25 IM_18 3 4 -10.0 -10.04 0.0 0.0 3 0.5 & 1 IM_19 3 4 -10.01 -10.02 -0.08 -0.09 3

[0114] IM_2O 3 4 -9.68 -9.79 0.0 0.0 3 0.75 IM_21 3 4 -9.84 -9.83 0.02 0.0 3 0.5 & 1

[0115] The experimental matrix included 21 tests (EM I through IM 21), with varying air and water pressures, ambient air temperatures, and freezing durations. The parameters include pressure of the pressurized water (Pw) pressure of the compressed air Pa); ambient air temperature during the spray phase (Tas) temperature during the freezing phase (TaF); temperature of the pressurized water (Tsw); tank water temperature (Thw); spray phase duration (tS); freezing phase duration (tF). Tests focused on identifying optimal conditionsfor droplet freezing, minimizing slush formation, and achieving structural homogeneity and increased brittleness in the resulting ice.

[0116] Results and discussion

[0117] The external mix nozzle was tested under twelve different conditions (EM I to EM 12). Although this configuration allowed independent control of air and water flow, several operational challenges were identified. The first and most frequent issue was nozzle clogging: ice formation within the mixing zone often caused partial or complete blockage, disrupting spray uniformity. In addition, the resulting ice layers exhibited strong spatial variability, producing uneven thickness and heterogeneous structural characteristics across the test area. Finally, the ice generated under these conditions was mechanically weak, slushy, porous, and lacking the cohesion necessary to sustain mechanical loading.

[0118] Despite various attempts to improve the performance of the external mix (EM) nozzle, including adjustments to nozzle height, adjusting air pressure, and reductions in ambient air temperature, none of these modifications produced ice of satisfactory quality.

[0119] The internal mix nozzle, in turn, demonstrated stability and performance. Tests IM 13 to IM 21 were conducted under consistent water and air pressure conditions (3 bar and 4 bar, respectively), with ambient air temperature held at approximately -10 °C. Time histories for environmental parameters showed stability across tests.

[0120] An important practical advantage of the internal mix method is its efficiency in ice preparation. The model ice forms rapidly during the spraying, as the internally mixed air and water produce fine, frozen droplets that settle as a dry, pre-frozen layer. Consequently, the target ice thickness is reached much earlier than with conventional fine-grained (FG) ice. In FG spraying, the deposited layer remains soft for several hours and requires extended freezing to gain sufficient strength; furthermore, once the top surface becomes excessively hard, an additional tempering stage is typically needed to weaken the ice. In contrast, the model ice of the present disclosure reaches a usable mechanical state almost immediately after spraying, without the need for tempering. Overall, the total preparation time for the model ice of the present disclosure is roughly three to four times shorter than that of FG ice, representing a significant operational improvement for repeated or time-sensitive testing campaigns.

[0121] Figure 3 presents visual observations of the model ice of the present disclosure. The surface of the ice appears smooth (figure 3a). The structure is granular and lacks visible layering, asevident from the ice texture (figure 3b). The thin section image (figure 3c) confirms the finegrained nature of the ice.

[0122] Figure 4 shows a clear distinction between the grain size distributions of the model ice of the present disclosure (VFG) and fine-grained ethanol-doped (GE) model ice. The grain size distributions, shown in the figure are derived from the image analysis procedure described above. The model ice of the present disclosure displays a narrow log-normal distribution with a sharp peak near 300 pm, reflecting a uniform and finely structured microstructure. In contrast, the GE ice exhibits a much broader distribution extending up to 4000 pm. The lognormal fitting further confirms that the average grain size in the model ice of the present disclosure is roughly one-fifth that of the GE ice, demonstrating the effectiveness of the finegrained production process in achieving smaller and more uniform ice grains.

[0123] Figure 5a, b presents the samples time histories of bending and compressive forces for ice produced using the internal mix nozzle in test IM 20. The ice was produced through a spraying process lasting 3 hours at -10 °C, followed by an additional 45 minutes freezing. The thickness of the ice was 25 mm.

[0124] An illustration of the time history of bending force is presented in Figure 5a. This bending force indicates a flexural strength of 33.6 kPa. The force is increasing linearly and at the failure point there is an abrupt decrease which means the beam is broken all the way through thickness. It is evident from the figure that the failure is brittle, even at this relatively low flexural strength.

[0125] Similarly, the compressive force plot (Figure 5b) shows a steady increase in load until an abrupt failure. As can be seen in the figure, the force is increasing almost linearly up to the peak and then it fails, and a sudden decrease is visible in time history. The oscillations following the failure arise from the dynamic response of the loading device. This peak force corresponds to a compressive strength of 230.9 kPa. The range of ratio of compressive to flexural strength has increased to 6-15 on average. A notable improvement on other methods, where this ratio is typically 3 or less.

[0126] The results for the model ice of the present disclosure are summarized in figure 6a-d, which presents physical and mechanical properties obtained under varying test conditions.

[0127] As shown in Figure 6a, the ice thickness (hi) remains consistent across all experiments, varying between 25 and 27 mm. Similarly, the ice density (p() exhibits minimal variation, remaining within the range of 915–925 kg / m3(Figure 6b).Figures 6c and 6d show that both the compressive strength (GC) and flexural strength (of) increase rapidly with freezing time. The corresponding rise in the compressive- to-flexural strength ratio indicates a shift in mechanical behaviour toward greater brittleness, a conclusion also supported by Figure 5.

[0128] These results highlight the efficiency of the present method, which enables the formation of structurally consistent and mechanically stable model ice within a short freezing time. This rapid production capability offers a practical advantage for large-scale ice tank operations, where reducing the freezing duration not only increases the number of achievable tests but also improves overall energy efficiency.

[0129] Table 2 includes the density (pi) of the model ice of the present disclosure (VGF) and those of various model ice types reported in the literature. A typical density range of first-year sea ice and the theoretical density of pure freshwater ice is also provided for reference.

[0130] Table 2

[0131] ice type density (kg / m3) reference

[0132] VFG 915-925 present disclosure

[0133] GE 926-934 Lemstom et al 2022

[0134] FGX 880-910 Nortala and Hoikkanen 1990 Saline (HSVA) 750-930 Evers and Jochmann 1993 Urea 890-990 Timco 1980

[0135] EG / AD / S 945-980 Spencer and Timco 1990 first-year sea ice 840-940 Timco and Frederking 1996 pure fresh water ice 917.6 theoretical

[0136]

[0137] VFG, the model ice of the present disclosure, exhibits a density between 915 and 925 kg / m3, lying close to the theoretical value for freshwater ice and well within the sea-ice density range. The slightly higher measured values (up to 925 kg / m3) are attributed to experimental uncertainties. Compared with other model ice formulations, such as saline, urea-doped, or ethanol-doped (GE) model ices, the model ice of the present disclosure shows minimal variation and the highest uniformity.

[0138] The non-linearity of the mechanical response was evaluated using the Non-Linearity of Model Ice (NLMI) index.Figure 7 shows the comparison of the Non-Linearity of Model Ice (NLMI) values of the VFG model ice of the present disclosure with those reported in the literature for chemically doped model ices, including GE and saline-based formulations. The VFG ice demonstrates a remarkably low NLMI value of approximately 12%, indicating a near-brittle failure behaviour. In contrast, most conventional model ices exhibit NLMI values ranging from 35% to over 90%, reflecting more ductile or plastic deformation modes. The NLMI of the VFG ice approaches that of natural sea ice, which is reported to be approximately 10% based on data taken from Wang et al. 2022. This suggests that the VFG ice exhibits limited plastic deformation prior to failure, closely resembling the brittle behaviour observed in natural sea ice.

[0139] Figure 8 presents the relationship between compressive strength (cc) and flexural strength (or) for the very fine-grained (VFG) model ice of the present disclosure in comparison with various model ice types reported in the literature. The VFG data points (marked with symbol ▼ ) align above the trend lines established for seeded and ethanol-doped (GE) model ices. This positioning indicates that the VFG ice attains a higher compressive-to-flexural strength ratio than conventional formulations. Such behaviour signifies enhanced mechanical stiffness and a tendency toward more brittle failure, consistent with the observed increase in equivalent elastic modulus and the low non-linearity index (NLMI). The combination of a high Sc / of ratio, higher stiffness, and reduced ductility confirms that the VFG model ice exhibits good mechanical performance and a more realistic brittle behaviour compared to traditional model ice types.

[0140] The results demonstrate that the use of internal-mix air-assisted nozzles under well-controlled thermal and pressure conditions enables the consistent production of very finegrained (VFG) model ice with enhanced mechanical properties. In contrast to external-mix nozzles, which exhibited operational challenges such as clogging, non-uniform coverage, and weak ice formation, the internal-mix configuration yielded ice that was structurally homogeneous, mechanically stiffer, and reproducible.

[0141] Image-based microstructural analysis confirmed a narrowly distributed fine-grained texture with a modal grain size of 300 pm, accompanied by a pronounced suppression of coarse crystals. Ice thickness remained consistent (25±27 mm), and density values fell within the typical density range of sea ice, evidencing stable and repeatable production conditions. The VFG ice exhibited rapid and steady strengthening with increasing freezing time.Both the compressive (GC) and flexural (of) strengths increased, accompanied by a corresponding rise in the equivalent elastic modulus (Eeq), indicating higher stiffness. The normalized bending response closely followed the ideal linear trend, suggesting predominantly elastic deformation up to failure. Simultaneously, the Non-Linearity Index (NLMI) decreased from above 60% at tr = 20 min to approximately 12% at tr = 60 min, signifying a transition from ductile to brittle behaviour. In the GC± Of plot, the VFG data consistently lie above those of seeded and ethanol-doped (GE) model ices, indicating higher Gc / or ratios and a mechanical response more closely resembling that of natural sea ice. In practical terms, the method of the present disclosure enables the formation of structurally uniform and mechanically stable ice within relatively short freezing durations. Such rapid cycle times enhance experimental throughput and improve the overall energy efficiency of large-scale ice tanks.

[0142] Water droplets typically supercool and remain liquid for some time also in freezing temperatures (Puolakka, 2024). Supercooling is undesirable in spray icemaking because it lowers the heat transfer from flying droplets into the ambient air. In the present method, droplets are nucleated and start to freeze immediately upon exiting the nozzle avoiding supercooling. This allows for larger temperature difference and greater heat transfer from the droplets during their flight. Compared to supercooled droplets, the nucleated droplets contain less heat and are easier to freeze to the target solid fraction after impact with the ice surface. The nucleated droplets are also producing much finer grains.

[0143] Nucleation is achieved in the present method through the Joule-Thomson effect by simultaneous ejection of water and compressed air from a nozzle. The compressed air atomizes the water into extremely fine droplets and nucleates the droplets as it rapidly cools during expansion. The water and air pressure and nozzle must be controlled to achieve the best result. The current method produces model ice with improved mechanical properties compared to existing methods. The method may also offer time and cooling energy savings in model ice production through higher temperatures and refrigeration plant efficiencies. Importantly, it eliminates the requirement for any chemical additives. Additionally, this technique allows ice production at higher temperatures compared to traditional spraying methods, where ice is typically produced at temperatures below -10 °C.

[0144] In summary, the method of the present disclosure provides a robust approach for producing model ice characterized by:

[0145] fine and uniform grain structure,increased stiffness and elastic modulus,

[0146] high Gc / of ratios, and

[0147] low NLMI values indicative of brittle behaviour.

[0148] REFERENCES

[0149] Enkvist, E. and Makinen, S. (1984). A fine-grain model ice. Proc, of the 7th Int. Symp. on Ice (IAHR), Hamburg, Germany, 217-227.

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[0151] Hirayama, K. (1983b). Properties of urea-doped ice in the CRREL test basin. COLD REGIONS RESEARCH AND ENGINEERING LAB HANOVER NH.

[0152] Jalonen, R. and Ilves, L. (1990). Experience with a chemically-doped fine- grained model ice. Proc, of the 10th IAHR International Symposium on Ice, Espoo, Finland, 2, 639-651. Jochmann, P., Ziemer, G., Myland, D., Reimer, N., and Hisette, Q. (2021). Status and needs for ice tank testing in a changing climate. IOP Conference Series: Materials Science and Engineering, 1201(1), 012060. https: / / doi. Org / 10.1088 / 1757-899X / 1201 / l / 012060 Lau, M., Wang, J., and Lee, C. (2007). Review of ice modeling methodology. Proceedings of the 19th International Conference on Port and Ocean Engineering Under Arctic Conditions, 13.

[0153] Lemstrom, I., A. Polojarvi, and J. Tuhkuri (2022). Model-scale tests on ice-structure interaction in shallow water: Global ice loads and the ice loading process. Marine Structures 81, p. 103106.

[0154] Li, Z. and Riska K. Model test of ice interactions with inclined and vertical structures in shallow water, IAHR Ice Symposium 1996, Beijing.

[0155] Nortala-Hoikkanen, A. (1990). FGX model ice at the Masa-Yards arctic research centre. IAHR Ice Symposium, Espoo, 247-259.

[0156] Puolakka, O. (2024). Droplet supercooling in marine icing tests. Cold Regions Science and Technology,219, 104121. https: / / doi. Org / https: / / doi.org / 10.1016 / j.coldregions.2024.104121Schwarz, J. (1975). On the flexural strength and elasticity of saline ice. Proc. IAHR 3rd Int. Symp. on Ice Problems, Hanover, NH, USA, 373–386.

[0157] Spencer, D. and G. Timco (1990). CD model ice: a process to produce correct density (CD) model ice. Vol. 2, pp. 745-755.

[0158] Timco, G. W. (1980). The mechanical properties of saline-doped and carbamide (urea)- doped model ice. Cold Regions Science and Technology, 3(1), 45-56. https: / / doi.org / 10.1016 / 0165-232X(80)90006-3

[0159] Timco, G. W. (1986). EG / AD / S: A new type of model ice for refrigerated towing tanks. Cold Regions Science and Technology, 12(2), 175-195.

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[0163] von Bock und Polach, R. U. F. (2015) Numerical analysis of the bending strength of modelscale ice, Cold Regions Science and Technology 118, 91-104.

[0164] von Bock und Polach, R. U. F., Ettema, R., Gralher, S., Kellner, L., and Stender, M. (2019). The non-linear behaviour of aqueous model ice in downward flexure. Cold Regions Science and Technology, 165, 102775. https: / / doi. Org / https: / / doi.org / 10.1016 / j.coldregions.2019.05.001.

[0165] Von Bock und Polach, R. U. F., Ziemer, G., Klein, M., Hartmann, M. C. N., Toffoli, A., and Monty, J. (2020). Case Based Scaling: Recent Developments in Ice Model Testing Technology. Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE, 7. https: / / doi.org / 10.1115 / OMAE2020-18320.

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Claims

Claims1. A method for producing model ice onto surface (104b) of water (104) in a tank (101) positioned in a temperature-controlled environment (102) comprising ambient air using an intemal-mix-assisted nozzle (103) comprising a nozzle tip (103c), wherein the nozzle tip is directed towards the surface of the water, the method comprisinga) a spraying phase comprising:applying compressed air and pressurized water towards the nozzle tip (103 c) of the intemal-mix-assisted nozzle (103) thereby forming a spraying mixture; allowing the spraying mixture to flow through the nozzle tip to the ambient air thereby atomizing the pressurized water and forming a spray (105) directed towards the surface of the water and / or towards formed ice on the surface of the water; and allowing the spray to accumulate on the surface of the water and / or on the formed ice on the surface of the water, thereby producing model ice, wherein pressure of the compressed air is from 2 bar to 100 bar, preferably from 3 bar to 7 bar, such as 4 bar,temperature of the pressurized water is from -0.2 °C to +5 °C, such as 0 °C, pressure of the pressurized water is from 1 bar to 5 bar, such as 3 bar, and temperature of the ambient air is from -15 °C to -5 °C, such as -10 °C; and b) a freezing phase comprising allowing the model ice to consolidate in the ambient air, wherein temperature of the ambient air is from -15 °C to -5 °C, such as -10 °C.

2. The method according to claim 1 further comprisingc) a tempering phase comprising increasing the temperature of the ambient air to 0 °C - +2 °C.

3. The method according to claim 1 or 2, wherein the spraying phase comprises moving the intemal-mix-assisted nozzle.

4. The method according to any one of claims 1 to 3, wherein temperature of the water at surface of the water is from -0.25 °C to 0.25 °C, preferably from -0.1 °C to 0.1 °C, such as 0 °C.

5. The method according to any one of claims 1 to 4, wherein temperature of the compressed air is from -11 °C to -8 °C.

6. The method according to any one of claims 1 to 5, wherein distance of the nozzle tip from the surface of the water and / or from the surface of the formed ice is from 5 cm to 200 cm, such as 50 cm.

7. The method according to any one of claims 1 to 6, wherein duration of the spraying phase is from 1 h to 10 h,8. The method according to any one of claims 1 to 7, wherein duration of the spraying phase is from 2 h to 4 h.

9. The method according to any one of claims 1 to 8, wherein duration of the freezing phase is at least 1 min.

10. The method according to any one of claims 1 to 9, wherein duration of the freezing phase is from 30 min to 60 min.

11. A model ice obtainable by the method according to any one of claims 1-10.

12. The model ice according to claim 11 comprising the following features:modal grain size is from 50 pm to 500 pm, preferably 300 pm,density is 915-925 kg / m3, andcompressive versus flexural strength ratio (oc / of) is more than 3, preferably from 4 to 8.

13. The model ice according to claim 12 having Non-Linearity of Model Ice (NLMI) index 10-15 %, such as 12%.

14. Use of the model ice according to any one of claims 11 to 13 for reduced-scale testing of interactions of ice with engineering structures.

15. The use according to claim 14, wherein the engineering structures comprise icebreakers, ships, offshore platforms, and wind turbines.

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