Investigation into Using CFD for Estimation of Ship Specific Parameters for the SPICE Model for Prediction of Sea Spray Icing: Part 1—The Proposal

Abstract

A machine learning model for prediction of icing on vessels and offshore structures, Spice, was recently developed by Deshpande 2023. Some variables required for the prediction of icing rates in most prediction models, including Spice, such as the spray flux, cannot be easily measured. Existing models estimate these using empirical formulations that have been heavily criticized. Most existing models are also incapable of providing the distribution of icing on the structure. The current study demonstrates a method to estimate the local wind speeds, along with spray duration, spray period, and spray flux at different locations on the surface of a moving vessel. These, along with other easily measurable values of air temperature, water temperature, and salinity, are used to predict the icing rates. The result is a model, dubbed Spice2—an upgrade of the existing Spice model—that is able to provide the icing rates and the distribution of icing on the surface of vessels and other offshore structures. The model was demonstrated with a case study of a totally enclosed lifeboat where icing rates were predicted at different locations on its surface. Successful implementation of a two-phase simulation with a coupled wind–wave domain and a moving vessel was demonstrated. Research into simplification of the currently computationally expensive method is suggested. Validation of the proposed Spice2 model against a full-scale measurement is covered in part 2 of the study.

1. Introduction

Icing due to freezing sea spray has accounted for 90% of all offshore icing incidents [1]. Impact generated sea spray is attributed as the most important source of water in dangerous icing events [2,3,4,5,6,7]. Predicted icing rates from different existing models show considerable amounts of variation, and the limited number of comparisons with experimental or full-scale measurements makes it difficult to point out the most accurate model [7,8]. Retrieving full-scale measurements of icing data is complex, time consuming, and expensive [1,9]. The handful of full-scale measurements that do exist in the literature are difficult to use for the purpose of validation of prediction models [7]. In the complete absence of full-scale data for validation, and due to the impracticality of obtaining full-scale data for an individual vessel for tens of variations of metocean conditions, the best alternative is using data from controlled laboratory experiments. Deshpande, 2023, presented a machine learning model, dubbed Spice, for the prediction of sea spray icing based on data from a set of 30 controlled experiments [7]. The model uses seven variables as inputs. Variables like air temperature, water temperature, salinity, and wind speed are easy to measure as inputs for the model. The local wind speed at different points on the ship’s surface, which was found to have a big impact on the icing rates [7], could, however, vary with the motion of the ship over the waves and is dependent on the flow of wind around the ship’s structure. Additionally, another important factor contributing to the icing rates, the amount of water impinging on the surface—the spray flux, along with the spray duration and spray period—is not readily available. Thus, a feature calculator was added to Spice to estimate the unknown variables, like flux, from existing formulations [7]. It is to be noted that the SPICE model handles the spray flux as an independent variable. So, it does not matter where the value of the flux is derived from, making the model independent of ‘lab to full-scale’ scaling issues. The problem with estimation of spray flux with existing formulations was pointed out by several researchers [7,10,11]. In short, existing spray flux formulations which are derived from measurements on specific locations on individual vessels in a given set of metocean conditions, often as a function of the liquid water content (LWC), are difficult to put to general use [7]. Kulyakhtin, 2014, pointed out that these flux formulations are the ‘weakest link’ for any marine icing prediction model [1]. Ryerson, 1995, in a study that presented detailed spray measurements, themselves concluded that attempts to form empirical relationships from their data resulted in complex and insignificant relationships [11]. Researchers have, however, continued using these formulations, either arbitrarily choosing one of the few existing formulations [10], or presenting a comparison and using the ones that best suit their case [6]. Deshpande, 2023, argues that using empirical flux formulations for predicting icing rates and distribution of icing over the vessel or structure surface would limit the predictions to the type of ship (the literature provides measurements for medium-sized fishing vessels, MFVs, and a United States Coast Guard Cutter [12]), the location on the ship where the flux measurements were made, and the prevailing metocean conditions in when the flux measurements were made [7]. This is also pointed out in ISO 35106, where it is mentioned that none of the existing models predict sea spray icing on a wide range of vessels or structures [8]. Some researchers have suggested investigations into the use of computational fluid dynamics (CFD) for the measurement of flux and distribution [7,13], whereas other researchers have been critical of using CFD in this field of study, at least pertaining to heat transfer [6]. Kulyakhtin 2012 pioneered the use of CFD to estimate the distribution of spray impingement on a vessel, but the Zakrzewski formulation [4] was used for inputting a predefined spray, and the ship was considered as a stationary object [5].

The current study presents a hybrid (computational fluid dynamics–machine learning) model, CFD-ML, for predicting the icing rates and the distribution of ice on a vessel. It is an upgrade of the machine learning model ‘Spice’ presented by Deshpande, 2023 [7], and thereby dubbed Spice2.

The current study investigates the use of CFD for computing four of the seven variables required by SPICE for making icing rate predictions, namely, local wind speed, spray duration, spray period, and spray flux. The proposed method is to be seen as an upgrade to the existing Spice model, and the resulting model (CFD + Spice) is thereby dubbed ‘Spice2’. Computing these variables from CFD simulations makes Spice2 capable of determining icing distribution, and doing so independent of any existing empirical formulations used in the ‘feature calculator’ (see Deshpande, 2023) and makes the icing predictions vessel or structure specific—a step towards achieving a model for general (or universal) use as called for by ISO35106. Considering the availability of the 3D model and permission to use it for this study, a totally enclosed lifeboat (Viking Norsafe Miriam-8.5 with an overall length of 8.5 m, a total height of 3.55 m, and a beam length of 3.25 m) is used for the case study. The study investigates the use of CFD to estimate variables that are not available by direct measurement, such as the local wind speed, spray period, spray duration, and spray flux. For the purpose of demonstrating the method, these measurements are tracked with several probes on the vessel surface. The values of these variables, along with the air temperature, are fed as input to the existing ML mode, Spice. The output thereby is the icing rates at different locations on the lifeboat, for the same metocean conditions. The variables computed from CFD are compared to their values using existing formulations. The icing rates are compared to predictions by five existing models. The advantages and limitations of the method used in this study are discussed, and suggestions for further research and scope for improvement are presented.

2. Methodology

This study used Flow-3D^® for the CFD simulation, and post-processing of the simulation results was carried out with code in python. The following sub-sections describe the simulation setup and the post-processing calculation procedures.

2.1. The Case

A 3D model (.stl file) for the lifeboat was provided by Viking Norsafe AS for the purpose of this study. To simulate a real sea state, prevailing metocean conditions were taken from an arbitrary location on a random winter day in the Norwegian Sea from a weather forecasting website, where wind speeds (u10) were 10 m/s, with a wave height of 2 m, which also confirms with the Beaufort Scale [14], and a wave period of 6.2 s, which gives an approximate wavelength of 60 m using the deep water equation (Equation (1)) in linear wave theory. The air and water temperatures are taken as −9 °C and 2 °C, respectively. The wind and wave propagation directions are assumed to be the same, and a case where the lifeboat is heading straight into the wind and waves is presented. The salinity if unknown, and defaults to 32.89 ppt in Spice [7], and this is used in the current study, giving the density of 1026 kg/m³ Ref: [15].

$$\lambda ={\displaystyle \frac{g{T}_s^2}{2\pi }}$$

(1)

2.2. CFD Simulation Setup

Flow3D^®, a commercially available CFD software based on the Reynolds-averaged Navier–Stokes equations [16] was used for this study. Flow3D^® uses a cartesian fixed-mesh method Fractional Area/Volume Obstacle Representation (FAVOR) [17] for modeling complex geometry. The FAVOR method enables the modeling of moving object dynamics without a deforming mesh, making simulation setup comparatively user friendly and reducing simulation times [16].

A total of 13 probes are set up on the surface of the lifeboat as shown in Figure 1. Probe 2 is located at the front hatch. Probes 3 and 6 are located on the ‘deck’. Probe 4 is located near the top hatch. Probes 5, 7, 9, and 11 are located at the port, with probes 7 and 9 near the doors. Probe 8 is located on the pilot window, probe 10 on the topmost part of the superstructure. Probes 12 and 13 are at the aft, while probe 12 lies on the aft hatch. Probe 1 is a control probe placed under the waterline at the bow to check the functioning of the codes. The current study assumes symmetrical distribution of icing, and thus probes are not placed at the starboard. The General Moving Objects (GMO) model, which enables rigid body motions dynamically coupled with the fluid, as well as prescribed motions [18], is activated, and the probes are rigidly attached to the lifeboat.

The computational domain consists of a box of length 40 m along the length of the lifeboat with the bow placed at 20 m. The width is 10 m, with the lifeboat placed in the center. The height of the domain is 20 m, with the mean water level at the center of the domain. In the absence of details for the ship’s center of mass and moments of inertia, a constant mass density of 250 kg/m³ was assumed. This resulted in a draft of 1 m, which is roughly equivalent to the draft without passengers. The lifeboat was allowed to heave and pitch freely, and other motions were constrained. The continuity and momentum equations for the case of incompressible fluids including volume of fluid (VOF) and FAVOR variables are given as follows [16]:

$${\displaystyle \frac{\partial }{\partial x_i}}\left(u_i{A}_i\right)=S\left(x_i\right)$$

(2)

$${\displaystyle \frac{\partial u_i}{\partial t}}+{\displaystyle \frac{1}{V_F}}\left(u_j{A}_j{\displaystyle \frac{\partial u_i}{\partial x_j}}\right)=-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial p}{\partial x_i}}+g_i+{\displaystyle \frac{1}{V_F}}{\displaystyle \frac{\partial }{\partial x_j}}{A}_j\left(\nu {\displaystyle \frac{\partial u_i}{\partial x_j}}-\overline{u_i^{\prime }{u}_j^{\prime }}\right)$$

(3)

where:

$u_i$—average fluid velocity

$u_i^{\prime }$—velocity fluctuation

$x_i$—represents coordinate directions (i = 1, 2, 3 for x, y, z directions, respectively)

$\rho$—average fluid density

p—mean fluid pressure

$\nu$—kinematic viscosity

$g_i$—gravitational acceleration

$S\left(x_i\right)$—source term to account for the effect of moving objects to displace fluid

$V_F$—fractional volume open to flow

$A_i$—fractional area open to flow in respective directions.

$-\overline{u_i^{\prime }{u}_j^{\prime }}$—Reynolds stress term (modeled by the RNG κ-ε turbulence model [19])

A wave boundary condition was applied at the inlet with a wave height of 2 m, wavelength of 60 m, and a mean fluid depth of 2000 m. For reducing the computational domain, instead of the ship speed (u_s) being applied to the lifeboat, a current of 3.09 m/s was introduced in the water. The waves and current in the simulation are defined with the Stokes and Cnoidal wave model (Fourier series method) in Flow-3D^® where the mean fluid depth is the undisturbed fluid depth for an infinite reservoir with a flat bottom [16].

For introducing wind into the domain, a custom boundary condition given by Equation (4) was coded in Flow-3D in Fortran. Equation (4) represents the wind power law over the surface of the sea with a friction coefficient (z₀) of 1.87 × 10⁻⁴ m [20], and a corresponding friction velocity (u*) of 0.337 m/s to give a wind speed at 10 m (u₁₀) of 10 m/s. The additional parameter of ship speed (3.09 m/s) is added for a similar reason as the current to simulate the ship surge.

$$u_z=u_s+{\displaystyle \frac{u^{*}}{\kappa }}\ln \left({\displaystyle \frac{z-z_{waterSurface}}{z_0}}\right)$$

(4)

The renormalization group (RNG) k − ε model is activated for modeling the turbulence. The RNG model uses similar equations to the standard k − ε turbulence model, but the equation constants are derived explicitly. The RNG model is more accurate at modeling strong shear regions [16]. Additionally, the densities of water and air were set to 1026 kg/m³ and 1.225 kg/m³, respectively.

Flow-3D implements ‘free gridding’ using the Fractional Area Volume Obstacle Representation (FAVOR) method. This makes meshing considerably more straightforward, using simple rectangular or cubical construction of grids. Numerical accuracy is not sacrificed when selecting FAVOR over a body-fitted meshing method [16]. The cell size (ω) was set to 0.2 m, which gave a satisfactory render of the lifeboat, considering the computational time of over a day required to run the simulation. The initial conditions include the water surface elevation and the current. The total simulation was set to 20 s, a short time owing to technical difficulties with batch post-processing of results in the software, wherein text outputs for each timestep had to be manually handled. This, however, was enough to simulate 5 impacts of the lifeboat with the incoming waves and is assumed to be a satisfactory representation of the case.

2.3. Post-Processing of CFD Results

Required variables are retrieved at each timestep from the simulations as text files and handled thereafter in python. The probes track some variables, such as the fluid and probe velocity, in the instantaneous cell location of individual probes. However, some variables, like the volume fraction of the object within each cell, cannot be tracked at the probe and therefor had to be retrieved from the 3D matrix at every timestep by mapping the instantaneous location of individual probes in the 3D matrix.

Equation (5) gives the relative wind speed at each probe and at each timestep. The relative wind speed at each probe is used for the icing predictions.

$$w{s}_{rel}=\sqrt{{\left(u_{probe}-u_{fluid}\right)}^2+{\left(v_{probe}-v_{fluid}\right)}^2+{\left(w_{probe}-w_{fluid}\right)}^2}$$

(5)

The fraction of fluid (fof) specifies the ratio of fluid inside a cell to the open volume of the cell at each timestep. If the cell is a surface cell, i.e., partially occupied with the lifeboat, the open volume can be retrieved from the fraction of lifeboat volume (v_f1) in the cell. The lifeboat volume fraction is not available from the probe data. For this to be retrieved, the location of the probe at every timestep is mapped to the 3D domain and the data from the node of the closest surface cell (0 < v_f1 < 1) using Euclidean distance with the math.dist() function in python. Using cubical cells, as a result of the previously described FAVOR method, simplifies the volume of fluid calculations. The total volume of fluid in the cell at each timestep is given by Equation (6).

$$v_f={\omega }^3\left(1-v_{f1}\right)·fof$$

(6)

The volume of fluid entering the cell per second can be calculated by Equation (7); here, the volume fluid exiting the cell is ignored as the thermodynamics module is replaced with the machine learning model which only considers the mass-flux of the spray entering the cell.

$$v_{fin}={{\displaystyle \sum }}_{t=0}^{t=t_{sim}}{\displaystyle \frac{\Delta v_{f at time t}}{t_{sim}}}, where \Delta v_f>0$$

(7)

The instantaneous fraction of fluid at the probes is also used to compute the spray duration and spray period. If the fraction of fluid is 0, there is no water present in the cell; if the fraction of fluid is 1, the cell is completely filled with water. Alternatively, any value for the fraction of fluid between 0 and 1 represents a cell partially filled with water. The signal processing module in python, scipy.signal, is first used to find ‘peaks’ in the spray. A prominence threshold of 0.05 was used to find peaks in the fof values. This value can be adjusted as necessary, looking at the plots (see Figure 2). Next, the start times of sprays were found with a reverse loop starting from the peak to the time when the fof becomes zero before the peak. Similarly, the end times were found with a forward loop when fof becomes zero after the peak. The presence of multiple peaks in the same spray event gives single spray start and end times. If the start or end times are not found in the entire loop, these are set to the start and the end times of the simulation, respectively. The number of spray events (N) are thus the number of spray starts or the number of spray ends. Unlike traditional spray period and spray duration formulations, it was seen that these values are dependent on the location on the lifeboat. This would be the case in reality, where various locations would receive impinging water for different amounts of time, and some wave impacts would result in no spray at a particular location. The spray period and spray duration are calculated with Equation (8) and Equation (9), respectively, using the means of individual events. Spray period and spray duration are traditionally used to calculate the spray; however, the Spice model uses these as independent variables which have a rather small effect on the icing rate [7]. In the case of a single spray event at a probe, the spray period is set to the maximum value for spray period at other probe locations.

$${\tau }_{per}={{\displaystyle \sum }}_{i=1}^{i=N}{\displaystyle \frac{{\left(t_{start}\right)}_i}{N}}$$

(8)

$${\tau }_{dur}={{\displaystyle \sum }}_{i=1}^{i=N}{\displaystyle \frac{{\left(t_{end}\right)}_i-{\left(t_{start}\right)}_i}{N}}$$

(9)

Wave washing is a phenomenon where an incoming spray mechanically removes any ice formed on the surface. Large amounts of water impinging on the surface could also lead to the possible melting of ice. Deshpande, 2024, mentions that the Spice model in its current form does not include wave washing, but owing to the fact that it is not a transient model, the mean over a large period covers the possible melting within the tested range of spray flux [7]. In some cases, the fluid fraction was observed to be relatively high for a spray. To tackle these cases, a threshold for the fraction of fluid is set, where, if the fraction of fluid exceeds the threshold during a spray event, wave washing is assumed and the water impinging on the lifeboat during this spray event is considered not to lead to icing. Additionally, since wave washing is assumed, any ice formed before the event of wave washing is also considered to be lost. This effectively would result in no ice in locations where the simulation ends with a wave washing event. This is implemented by setting the fraction of fluid to zero wherever the conditions are satisfied—giving the effective fraction of fluid (fof_eff). The wave washing threshold for the fraction of fluid was set to 0.62, which is the mean volume of fluid per cubic meter or the mean liquid water content (LWC) of the three largest sprays observed by Ryerson 1995 [11]. This changes Equation (6) and Equation (7) to Equation (10) and Equation (11), respectively.

$$v_{f\_eff}={\omega }^3\left(1-v_{f1}\right)·{fof}_{eff}$$

(10)

$$v_{fin\_eff}={{\displaystyle \sum }}_{t=0}^{t=t_{sim}}{\displaystyle \frac{\Delta v_{f\_eff at time t}}{t_{sim}}}, where \Delta v_f>0$$

(11)

The FAVOR method constructs the lifeboat at each timestep, and the shape marginally changes at each timestep; this is different to a body-fitted mesh where the shape of the object is accurately the same at each timestep. Owing to the motion of the lifeboat, the mean surface area of the lifeboat, neglecting surface roughness, within a cell is assumed to be equal to the surface area of the cell. Thus, the effective spray flux per hour leading to icing, considering the spray duration and spray period, is given by Equation (12), where N_hr is the number of sprays per hour, in accordance with the requirement of the Spice model.

$$\varnothing ={\displaystyle \frac{{\rho }_{w\times }{v}_{fin\_eff}{\tau }_{dur}{N}_{hr}}{{\omega }^2}}$$

(12)

at various locations on the lifeboat from the CFD simulation. This marks the end of the post-processing of the results from the CFD simulation. Four variables—relative wind speed (ws_rel), spray period (τ_per), spray duration (τ_dur) and the spray flux (φ)—were computed.

2.4. The SPICE Model

The values for each probe, along with the air temperature, water temperature, and salinity are given as input to the Spice model presented by Deshpande, 2024, to obtain the predicted icing rates. For the purpose of demonstration, the prediction range in the Spice model is ignored in the current study. The ML model Spice, in short, predicts the icing rates from 7 inputs. In the case of Spice2, air and water temperatures, and salinity, are input directly from the metocean data, whereas the CFD computed values of the other 4 variables, wind speed, spray duration, spray period, and spray flux, are used. Comprehensive details of the working of the Spice model can be found in Deshpande, 2024, and are not repeated here for conciseness.

3. Results

Figure 2 shows the variation of the fraction of fluid at each probe. The highlighted regions show the spray events in which the fraction of fluid reaches over the threshold for wave washing. As expected, the control probe which is under the waterline has a constant fraction of fluid equal to one. Probes 4, 5, and 7 end with sprays where the fraction of fluid is over the wave washing threshold, and thus the effective volume of fluid resulting in icing is zero. It can be seen that water never reaches probe 10. In the case of probe 6, there is a wave washing region, but another spray event having a fraction of fluid below the wave washing threshold is observed. The maximum fraction of fluid at other probes is always less than the wave washing threshold, and thereby all the fluid entering these cells counts towards the effective volume of fluid causing icing.

Zakrzewski, 1986, mentions that the spray is caused due to the ship–wave impact [20]. While this is true, slamming that occurs after the vessel passes the wave crest is observed to produce more spray [21,22]. In the case of smaller and lighter vessels in relatively mild conditions such as in this case study, the vessel is entirely lifted with the wave and no ‘impact’ occurs. However, the slamming that takes place after the passage of the wave crest could cause some amount of spray. This can be seen in Figure 3 and Figure 4, which show the fraction of fluid in the domain before and after passing a wave crest. When the lifeboat passes a wave crest, some fluid can be seen on and around the structure of the lifeboat.

Figure 5 and Figure 6 show the distribution of the fraction of fluid on the lifeboat before and after passing a wave crest, respectively. Where there is almost no visible fluid above the waterline before passage of the wave crest, it can be observed that fluid is dispersed over parts of the structure after the passage of the wave crest.

Figure 7 and Figure 8 show the velocity field before and after passing a wave crest. Firstly, the current being equal to the ship speed and the wind profile given by Equation (4) can be observed to have been successfully implemented in the simulation. After the passage of the wave crest, when the lifeboat marginally slams into the water, a region with high velocity can be observed near the bow in Figure 8.

The spray period, spray duration, and spray flux data calculated from the fraction of fluid measurements from Figure 2 at each probe are shown in Figure 9, Figure 10, and Figure 11, respectively. Additionally, the mean wind speed measured at each probe is shown in Figure 12.

Figure 9 shows that the average spray period at each probe varies and is less than what is estimated with both existing spray period formulations. The Zakrzewski formulation considers every second wave impact to result in spray, and the Lozowski formulation considers every fourth wave impact to result in spray. They do not consider the location of measurement, which results from the CFD simulation show to affect the spray period. More details about these existing formulations, including their equations, and how they have been implemented or simplified in Spice for the purpose of comparison, along with their original references, can be found in Deshpande, 2024 [7].

Figure 10 shows that the average spray duration experienced at each probe also, like the spray period, varies for the same set of metocean conditions. Existing formulations for spray duration do not consider the location of measurement, each of which could experience varying spray durations. The mean spray duration at the different probes varies from marginally greater than as estimated with the Lozowski formulation to much less than all existing formulations. The Zakrzewski formulation greatly overestimates the spray duration for the current case. More details about the existing formulations can be found in Deshpande, 2024 [7].

Deshpande, 2024, gives details about how existing formulations of spray flux could give vastly different results. Spray flux was shown to be one of the most important variables for the prediction of sea spray icing [7]. Existing formulations for estimation of spray flux are a function of height above the mean sea level but would give the same value for all locations on the ship at the same height. This is clearly not true as, for example, the bow and the aft regions would experience vastly different amounts of spray. The flux experienced at different locations, before and after considering the previously described assumptions of wave washing, are shown in Figure 11. Figure 11 also compares the flux estimated from the CFD simulations to those of existing formulations made available in SPICE. More details about the existing formulations can be found in Deshpande, 2024 [7]. Results from the CFD simulations show the vast amount of difference in the flux at various locations on the ship, and how much variation exists between various existing formulations. Irrespective of the absolute values of the spray flux at each location, the enormous variation at different locations highlights the inefficiency of using existing empirical models for estimation of spray flux in sea spray icing models. Any model attempting to estimate distribution of ice using empirical formulations for spray flux without tools like CFD would result in major errors in prediction of icing rates.

The wind speeds measured at different probe locations are shown in Figure 12. The wind speeds would vary depending on the ship design, which affects the wind flow around the vessel. Very low wind speeds at, for example, probe 13, could be a direct result of a wake region at the aft of the vessel; however, a reason why the measured wind speeds in the CFD simulation are generally lower than the relative wind speed estimated at the given height could be the proximity of the probe centers to the vessel surface.

Figure 13 shows the results of the icing rates at different probes. The plot provides icing rates estimated with the other models for comparison as in Deshpande, 2024 (rm: Roebber&Mitten, ov: Overland, ku_mod: modified Marice, st_mod: modified Stallabrass, ri: Rigice04; see Deshpande, 2024, for more details regarding each of these models) at a height of 3 m, which is approximately the height above the mean sea level at which the deck is located when on top of a wave crest. Icing rates are represented in both, kg/m²/h as obtained from the Spice model, and in mm/h assuming an ice density of 900 kg/m³ [7]. Additionally, the plot provides icing rates estimated by the first Spice model using only the inputs given in

Table 1. Available information.

Variable	Ship Speed	u10	Wave Height	Wave Length	Ship Heading	Air Temp.	Water Temp.	Salinity
Units	(knots)	(m/s)	(m)	(m)	(°)	(°C)	(°C)	ppt
Inputs	6 (3.09 m/s)	10	2	60	0 (straight into waves and wind)	−9	2	32.89

, and estimating the other variables using the ‘feature calculator’ [7]. Information is also provided regarding the flux and relative wind speed computed at each probe. The plot is sorted by ascending value for icing rates predicted by Spice2. The original Marice model uses CFD to estimate distribution of droplet impingement on the structure, and RIGICE04 provides vertical distribution of icing in steps of 1 m [5,23]. All other models, including that of Spice in its original form, and ku_mod, developed for representational purposes, estimate a general icing rate for a given case and are unable to provide the distribution of icing over the vessel or structure. Thus, the icing rate estimated with these models at any given probe is constant.

Probe 1, the control probe gives no icing as expected, where Figure 2 shows that the algorithm detects it as a wave washing region for the entirety of the simulation. As pointed out earlier, probes 4, 5, and 7 end with wave washing zones, and as expected result in no icing. Figure 2 shows that no water reached probe 10, and thus no icing is observed. The three biggest factors for icing rates in Spice are wind speed, flux, and air temperature [7]. As the current model does not consider any internal heat generated by the lifeboat, the air temperature at all nodes is constant as the set temperature of −9 °C. Thus, it is only the local relative wind speed and the local flux that dominate the difference in icing rates at the probes. The variation in icing rates at probes 11 and 13 is rather small given the difference in flux; however, it can be seen that the wind speed at probe 11 is almost 5 times that at probe 13, leading to a marginally higher icing rate. Probes 6 and 9 have similar flux and wind speeds, and thus similar icing rates. Probe 3, which is on the ‘deck’ at the bow, shows the highest effective flux, and relatively high local relative wind speeds, and thus the highest icing rate.

Addressing Safety Considerations and Environmental Impact

Assessing the locations prone to icing can help optimize design and address potential safety issues. A model that can predict not only the icing rate but also the distribution of icing over the vessel or structure is needed for addressing safety concerns while also considering design optimization. International standards like the ISO19906, DNV-OS-A201, and the Polar Code require equipment for personnel safety, including regarding doors, escapeways, fire systems, and ventilation systems, to be completely functional under icing conditions and ideally kept ice-free [8,12,24,25,26]. Icing at probe 8 indicates that the visibility of the pilot could be blocked in icing conditions. Icing at probe 9 indicates that there could be chances of the escape door jamming in the case of heavy icing. The inlet to the ventilation system is located near probe 11, and could be blocked in the case of heavy icing. Icing at probes 3 and 6 indicates that the deck, though rarely necessary to climb onto, in the case of similarly totally enclosed lifeboats, could be slippery in icing conditions. Icing at probes 2 and 12 could cause jamming of the hatches at the bow and aft.

Spice2 could be used by ship designers at the design stage to assess the stability and placement of critical equipment as well as during the retrofitting of equipment to address safety concerns. Heating provided in winterized class ships as anti-icing measures could be optimized to save energy if icing rates at different locations are known in given metocean conditions. Structural integrity is a primary concern, and icing loads prescribed by international standards are kept in mind at the design stage. If distribution of the ice loads can be accurately known, design optimization would lead to a positive environmental impact.

4. Conclusions and Discussion

A hybrid CFD-ML model for the prediction of icing rates and the distribution of icing on vessels and offshore structures, dubbed Spice 2, is demonstrated with a case study of a fully enclosed lifeboat. Spice2 is an extension of the existing Spice model using ML to predict icing rates, which uses CFD to compute some of the inputs required for predictions, making Spice2 capable of predicting the distribution of ice in addition to the icing rates. Existing models give a general single icing rate for a set of metocean conditions. Additionally, they use empirical formulations for spray duration, spray period, and flux [7]. These formulations are based on a limited number of studies on particular ships in a particular set of metocean conditions. Researchers have been critical of using these formulations for a general model for predicting icing, naming these as the weakest link in prediction models [1] and calling for newer methods independent of these limitations [7]. The current study demonstrates the estimation of spray period, spray duration, spray flux, and local relative wind speeds using seakeeping CFD simulations. These variables, obtained from the CFD simulations, along with measured values of air and water temperatures, and salinity, are run through a machine learning model, Spice, presented by Deshpande, 2024. Computation of the above-mentioned variables for individual cases makes the current Spice2 model a step in the direction of a truly universal model for the prediction of sea spray icing that could be applied to vessels and offshore structures of all sizes.

The current study shows that estimation of spray flux from CFD simulations is possible, something that, to the best of the authors’ knowledge, has not yet been attempted in this field of study and marks a paradigm shift into how models approach the prediction problem. This study is a modest first attempt to demonstrate the concept of using CFD for estimating the ship-related parameters required for the prediction of sea spray icing. The outputs of basic variables from the CFD simulations are further post-processed to estimate the vessel-dependent parameters for the prediction of sea spray icing. The concept is demonstrated with a particular lifeboat, and the simulation, in the case of vessels or structures of different sizes or shapes, would indeed have to be tweaked as per requirements; but obtaining values for the variables in question, like the fraction of fluid and the volume fraction at probe locations is not a problem for users well versed with CFD. Spice2 comes into play when these variables are already available from CFD simulations and need to be post-processed. Thus, it could be safely claimed that the method is independent of the size and shape of the vessel or structure. Two clear advantages of Spice2 are that it is independent of any empirical formulations for coarse estimation of important variables affecting icing rates; and that in addition to icing rates, it provides the distribution of icing over the structure, albeit while increasing the prediction time significantly. There is, however, considerable scope for improvement before implementing it in practice. A coupled two-phase simulation with both wind and waves and a free-surface and a moving object is computationally expensive. There are multiple physical phenomena taking place simultaneously at very different scales. The wind–wave interaction and the generation of spray droplets due to slamming can be studied closely at millimeter-levels, whereas forces acting on the vessel and its movements can be resolved at a much larger scale. Dynamics of splashing are computable with CFD at extremely small scales [27]. Researchers mention that numerical tools are better than analytical solutions for studying the slamming of ships, but also point to the heavy computational efforts required to obtain accurate results, and recommend approximations for simplification [28]. The grid size in the current study was chosen keeping in mind the balance of computational time required and demonstration of the method. It was found to be satisfactory for resolving the lifeboat structure, and demonstrating the possibility of the calculation of the spray parameters, but full-scale testing is required to validate the model. Further studies could also investigate whether the CFD simulation can differentiate flux values due to green water or sea spray. A small note regarding this is available in Part 2 of this study. A grid independence and time-step independence study were not performed, keeping in mind the time and resources available. The CFD method presented in this study is a modest first attempt to study the possibility of using CFD for obtaining the vessel-dependent parameters for use in the Spice algorithm. Further research into validating and improving this method or simplifying the simulation is recommended. Full-scale measurements of spray data available in the literature, for example in Ryerson 1995, were made on a completely different class of vessel, and cannot be used for the purpose of validation. In general, the accuracy of numerical models increase with finer mesh sizes, up to a point where the results tended to become less dependent of the mesh size. Considering the nature of spray dynamics, where droplets as small as a few micrometers are observed, it can be said that the accuracy of the results of the current study would only increase if a finer mesh were used.

A limitation of using a coupled wind–wave domain in CFD simulations is that the directions of wind and wave propagation need to be the same. A case where wind is at an angle to the waves is difficult to simulate. The model makes some approximations for wave washing with previous spray measurement. The Spice model was not trained on ablation, melting, or wave washing [7]. Additionally, minor traces of water left after a relatively large spray, or a part of the spray after a majority of the water had impinged on the surface could indeed result in icing. Thus, even though probes 4, 5, and 7 show no icing by the current assumption of the wave washing threshold, some icing could be possible in those regions. Future studies should be directed towards the simplification of the CFD method used in this study, such that a much finer mesh could be used without requiring days for the simulation to run. Specifically for models similar to or successors to Spice2, future research could be aimed at experimenting with melting, and wave washing of accreted ice. Calculation at every cell instead of a limited number of probe locations would make ice load calculations more accurate and easier for visualization of ice accretion.

The exact value of the wave washing threshold remains a pure assumption. This threshold might also be dependent on the quantity of ice already present. On the other hand, the prediction values from the simulation are intended to be used from the time there is no ice, and thus, it might be sufficient to assume a single constant value for the threshold. Future research could study wave washing and determine the correct value of the threshold to be used.

Full-scale data available in the literature is scarce, and not detailed enough for the validation of models [7]. Part 2 of this study presents a new set of full-scale measurements and the verification of the Spice2 model against this full-scale test.