The present invention relates to a method for producing a model ice having a thickness hM on a body of a liquid in a tank, for simulating an interaction between objects having a length LF and natural ice having a thickness h _F , by means of a model object with a length LM interacting with said model ice in said tank, the method comprising: a) maintaining a temperature of the liquid in the proximity of a freezing point temperature of the liquid; b) exposing a surface of the liquid to an environment; c) maintaining a temperature of the environment below the freezing point temperature of the liquid; d) supplying a seed liquid to the environment, e) stopping the supplying of the seed liquid; f) raising the temperature of the environment above the temperature of step c).

Objects and model objects in the scope of the present disclosure may comprise vessels having a length LF, waves having a wavelength LF, and/or any other natural or manmade objects.

Likewise, the present invention relates to a model ice. The present invention also relates to a use of a model ice of thickness hufor simulating an interaction between vessels having a length LF and natural ice having a thickness hF, by means of a model vessel with a length LM..

A pertinent method for producing a model ice is known from US 4532772. The document discloses an improved method for producing an model ice suitable for ship model ice tests on a water surface by means of a spraying process. According to US 4532772 a 30 mm thick model ice is produced by a continuous spraying process within three hours. The spraying process is continued until at least the entire desired model ice thickness is achieved.

The disadvantage of this method is that the production process lasts a long time, requires a high amount of energy and the ice characteristics obtained do not correspond to the characteristics of natural ice.

The disadvantage of produced model ice is that not all properties are in the correct scale of natural ice. Notably, the stiffness in many kinds of prior art model ice will not correspond in scale to that of natural ice. The disadvantage of prior art use of the prior art model ice is that the interactions between vessels and model ice may not always be realistically modelled and sometimes might be overvalued.

Against this background it is an object of the invention to provide a method referred to above to produce, in avoidance of the disadvantages of the prior art, a model ice in less time, requiring a smaller amount of energy and yielding ice having characteristics which better correspond to the

characteristics of natural ice.

Furthermore, it is an object of the present invention to provide a model ice having realistically scaled properties of natural ice in simulation tests. Finally, it is an underlying problem of the invention to provide a use of the model ice to better simulate the behavior of natural ice in tests with model ships, scaled waves, and other objects.

According to the invention this problem is solved with a method according to claim 1 wherein step f) is carried out when the thickness hiu has attained a value of wherein a < 1. That way a model ice with a lower than

conventional model ice thickness is produced. At the same time, the model ice thus produced has increased flexural strength and stiffness compared to conventionally produced model ice. Thereby the characteristics, particularly regarding the failure force and/or concerning the stiffness, of the model ice are in a correct scale of the ice properties of natural ice e.g. sea ice or lake ice. Because of the lower model ice thickness, which leads to an increased flexural strength s _M , elasticity and stiffness E compared to prior art model ice, the ice-vessel interactions scale effect due to vertical motions are avoided and the performance prediction for the engine of actual vessels is increased. This allows a more exact modelling of the required real characteristics. In essence, the present invention teaches to deliberately violate the law of Froude and Cauchy which demands that the ratio between the thickness of the model ice and the thickness of the natural ice equal the ratio between the length of the model ship and the length of the real ship, according to a=1. Conveniently and surprisingly, producing the model ice in accordance with the method of the invention in many cases yields model ice having the mechanical properties, including in particular the flexural strength, which, according to scale, correspond to the natural ice. Ideally, within the scope of the invention, this is achieved while reducing the tempering time or while even fully dispensing of any further tempering.

Thus, the invention saves time and energy.

In an advantageous embodiment of the method according to the invention the interaction is simulated in a step contiguous to step f). That way a tempering process as in the prior art can be dispensed with which leads to a decreased process time for production and the simulating is possible earlier. Furthermore, this allows a reduction of production costs and production time.

In an advantageous embodiment of the method according to the invention step d) is performed discontinuously. That way the flexural strength and the stiffness increase while a reduction of the thickness of model ice which leads amongst others to less plastic deformation of ice before breaking which is advantageous to the correct scale of ice properties. The model ice which is produced when step d) is performed discontinuously is a finegrained ice. In an advantageous embodiment of the method according to the invention step d) is performed continuously. That way a reduced thickness associated with less variation of the flexural strength s _M through the thickness of model ice is attained. The model ice which is produced when step d) is performed continuously is columnar ice. In an advantageous embodiment of the method according to the invention step d) is carried out at a location above the surface of the liquid. That way model ice according to the invention is produced reaching a high flexural strength in the correct scale of natural ice properties and a reduced thickness of model ice. The increasing of the flexural strength s _M is directly proportional to the stiffness E.

In an advantageous embodiment of the invention, after step f) the

temperature is maintained above the temperature of step c) over a period of time. That way the flexural strength s _M can be decreased to a defined target, if necessary. That way the characteristics regarding in particular the flexural strength s _M and the stiffness E of model ice allow better scalability of testing results with the model ice according to the present invention.

According to the invention the problem relating to the aforementioned model ice is solved with a model ice obtainable by a method according to one of claims 1 to 6. That way model ice has properties in the correct scale of natural ice e.g. sea ice or lake ice. That way the ratio of stiffness E of model ice to the flexural strength s _M is greater than 2000. Furthermore, model ice according to the invention has the correct scale and is obtainable in a reduced production time. Ideally, in an improved variant of model ice according to the invention, the correlation of the loading force F to a displacement of the model ice is linear or approximately linear and directly proportional or approximately proportional. This can be reached, within the scope of the invention, by appropriately adjusting the chemical composition of the liquid in the tank. Sometimes, according to a preferred embodiment, the addition of suitable chemicals will serve to attain a linear relationship between the loading force F and a displacement of the model ice.

In an advantageous embodiment of the model ice according to the invention it is formed as a fine-grained ice. That way model ice according to the invention is produced reaching a high flexural strength in the correct scale of natural ice properties and a reduced thickness of model ice.

In an advantageous embodiment of the model ice according to the invention it is formed as columnar ice. That way model ice according to the invention is produced reaching a high flexural strength in the correct scale of natural ice properties and a reduced thickness of model ice.

According to the invention the problem related to a use is solved by the use of a model ice of thickness , with a < 1 , for simulating an

interaction between vessels having a length LF and natural ice having a thickness hp, by means of a model vessel with a length LM. The present disclosure will hereinafter be described in connection with an embodiment shown in the drawings., Further aspects and embodiments will become apparent by reference to the drawings and by studying of the following description.

Brief description of the drawings: Figure 1 : Schematic representation of temperature control of the

production process of columnar model ice until now represented as a continuous graph and the model ice according to the invention represented as a dashed graph.

Figure 2: Schematic representation of temperature control of the

production process of fine-grained model ice until now represented as a continuous graph and the model ice according to the invention represented as a dashed graph.

Figure 3: Tank filled with the liquid with an model ice at the surface

exposed to the environment having at least one nozzle

Figure 1 shows the temperature control of the production process of columnar ice as it is managed in the state of the art as a first graph represented as a continuous graph.

The illustration is schematic and temperature may vary in practice and the tempering temperature might be below the freezing point temperature 1 of the liquid in the tank. For the production process a tank 12 with an opening filled with a liquid 13 having a temperature in the proximity of the freezing point temperature of the liquid 1 is provided. The tank 12 is exposed to an environment 17 temperature below the freezing point temperature 1 of the liquid.

The first step is the supplying of a seed liquid 2 sprayed as a dense for or mist through nozzles into the environment above the opening of the tank 19. Due to the low environment temperature and the relatively small size of the droplets, most of the droplets freeze in the environment or at the surface of the liquid in the tank and form an ice nuclei. Due to the high density of droplets the ice crystals cannot grow much laterally, but only downward and in this way a small crystal diameter is maintained.

After stopping the supplying of the seed liquid 2 the growth of the ice crystals 3 starts with continuous cooling downwards into the liquid. The crystals do not yet grow predominantly vertically. Prior to this, the growth of crystals 3 undergoes a process called“geometrical selection ". This growth of the ice crystals 3 creates a layer of a significantly different (not columnar) crystal structure than the rest of the ice sheet which is columnar. This layer is holding most of the strength, due to its particular crystal structure and the fact that it is exposed to the low environment temperature and not the warmer temperature of the liquid in the tank 14.

The consolidation 4 continues from the time to and the environment temperature is continuously very low so that the model ice can grow to its target thickness. Additionally, the strength of the model ice is this phase is very high.

After the time of achieving the target thickness of columnar ice 5 from the time t2 follows the step of raising the temperature 6 of the environment to which the tank with liquid is exposed to above the freezing point

temperature of the liquid 1. During the tempering process 7 the model ice is “warmed up” to stop the growth of the ice crystals 3 and to diminish the high strength to a scalable target strength.

The second graph in the diagram of Figure 1 shows the temperature control of the production process of the model ice according to the invention produced with the seeding method as a dashed graph.

At the beginning the productions steps are the same as for production of the model ice until now. As Figure 1 shows the time of achieving the target thickness of model ice according to the invention 8 is shorter than the time of achieving the thickness of columnar ice 5. That is why the raising of the temperature 6 at the time ti above the freezing point temperature of the liquid 1 starts earlier compared to the time fc starting the raising of the temperature 6 of the environment for the production of columnar ice. The target thickness of model ice according to the invention is violating the geometrical scaling law with respect to the ice thickness.

After raising the temperature 6 at the time ti above the freezing point temperature of the liquid 1 the dashed graph in Figure 1 shows the tempering process? for producing model ice according to the invention. During the tempering process 7 the model ice is“warmed up” to stop the growth of ice crystals 3 and to diminish the high strength to a scalable target strength. Ideally, the tempering process 7 might be very short or is not needed at all then just raising the temperature 6 at the time ti is as much as needed to stop the growth of the ice crystals 3.

Figure 2 shows the temperature control of the production process of finegrained ice as it is managed in the state of the art as a first graph

represented as a continuous graph.

The illustration is schematic and temperature may vary in practice and the tempering temperature might be below the freezing point of the liquid in the tank.

For the production process a tank 12 with an opening filled with a liquid 13 having a temperature in the proximity of the freezing point temperature 1 of the liquid is provided. The tank is exposed to an environment temperature below the freezing point temperature 1 of the liquid.

The first step is the supplying of the seed liquid 2 sprayed as a dense of fog into the environment above the opening of the tank 19. The small droplets impinge on the surface of liquid 14 in the cold tank 12 there they settle as ice crystals. In difference to the columnar ice, this process is repeated many times until enough layers of crystals are laid down to meet the target ice thickness. The ice crystals stay granular (small spheres of around one to three mm diameter, which depends on the spraying process). When achieving the target thickness of fine-grained ice 9 the supplying of the seed liquid 2 stops.

Following this, there is a decreasing of the temperature 10 of the

environment to which the tank 12 with liquid in the tank 13 is exposed to. At the end of the decreasing of the temperature 10 to a very low temperature there is the beginning of the period of the generation 11.

During the period of the generation 11 the temperature of the environment to which the tank 12 with liquid in the tank 13 is exposed to is very low to generate strong freeze-bonds between the small crystals. The process requires a significant amount of time, because the coldness has to penetrate the model ice down to the bottom layer. This however causes a significant change of properties through the thickness, because the top layer is exposed for a long time to low temperatures, while the bottom layer is surrounded by the liquid in the tank 13 which is warmer than the freezing temperature of the liquid 1. This also causes a very hard and strong top layer (von Bock und Polach, 2015).

At the time t4 there is the step of raising the temperature 6 of the

environment to which the tank 13 with liquid 14 is exposed to above the freezing point temperature of the liquid 1 following the period of the generation 11. During the tempering process 7 the model ice is“warmed up” to stop the growth of ice crystals 3 and to diminish the high strength to a scalable target strength.

The second graph in the diagram of Figure 2 shows the temperature control of the production process of the model ice according to the invention produced with the spraying method as a dashed graph.

At the beginning the production steps are the same as for production of the fine-grained ice until now. As Figure 2 shows the time of achieving the target thickness of model ice according to the invention 8 is shorter than the time of achieving the thickness of fine-grained ice 9. That is why the raising of the temperature 6 at the time t ₃ above the freezing point temperature of the liquid 1 starts earlier compared to the time t ₄ starting the raising of the temperature 6 of the environment for the production of fine-grained ice. The target thickness of model ice according to the invention violates the geometrical scaling law of Froude and C y which demand that

A=LF/LM=hF/hM. According to the invention, in contravention of said scaling law, the model ice thickness is deliberately reduced by a factor a < 1 to

Within the scope of the invention, the stiffness s _M of the model

ice according to the invention must then be scaled correspondingly, following the scaling law s _M = s _F L _M /(L _F * a ² ).

After raising the temperature 6 at the time t ₃ above the freezing point temperature of the liquid 1 the dashed graph in Figure 2 shows the tempering process 7 for producing model ice according to the invention. During the tempering process 7 the model ice is“warmed up” to stop the increase of ice thickness and to diminish the high strength to a scalable target strength. In the case of fine-grained ice, increase of thickness is effected by spraying additional layers of crystals onto the surface. In the case of columnar ice, on the other hand, the ice itself will grow thereby increasing the ice thickness. Ideally, the tempering process 7 might be very short or is not needed at all then just raising the temperature 6 at the time t ₃ is as much as needed to stop the growth of ice crystals 3.

Figure 3 shows the tank 12 which is filled with the liquid 13. Above the surface of the liquid 14 there is an model ice 15 with the thickness 16. The tank 12 which is filled with the liquid 13 is exposed to the environment 17 maintained at a specific temperature.

In the environment 17 there is at least one nozzle 18 through which the liquid is sprayed into the environment 17 above the opening of the tank 19. List of reference numerals

1 freezing point temperature of the liquid

2 supplying of the seed liquid

3 growth of ice crystals

4 consolidation

5 time of achieving the target thickness of columnar ice

6 raising of the temperature

7 tempering process

8 time of achieving the target thickness of of fine-grained model ice according to the invention

9 time of achieving the thickness of fine-grained ice in the prior art

10 the decreasing of the temperature

11 period of generation

12 tank

13 liquid in the tank

14 surface of the liquid

15 model ice

16 thickness

17 environment

18 nozzle

19 opening of the tank

20 seed liquid