Numerical Prediction of Accumulated Ice Loads on the Fishing Vessel F.V. Destination Lost in the Bering Sea S.R. Dehghani, Y.S. Muzychka, B. Colbourne Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John’s Abstract This study uses the current knowledge of marine icing to estimate the amount of spray ice load accumulated on the fishing vessel F.V. Destination that sank in the Bering Sea in February 2017. The analysis includes wave-impact sea spray and brine-spongy ice models. The input data including sea conditions, vessel information and weather information are provided by the US NTSB. The main assumptions in the analysis concern the frequency of spray generation, icing surfaces and sufficient water delivery for icing. The results of the icing model are strongly dependent on the input data provided by the NTSB. Results show that the highest rate of ice accumulation is about 2.7 ton/15min which occurred around 1700 AKST on February 10. The overall amount of ice accumulated on the vessel, which is calculated using the upper limits of the assumptions, is about 154 ton. Using the lower limits of the assumptions, this reduces to 92 ton. An analysis was conducted to estimate the effect of the predicted ice accumulation on the vessel stability with the result that the upper ranges of the predicted icing create a high probability of capsizing due to loss of stability Keywords: Marine icing; FV Destination; Ice accumulation; Numerical model; Capsizing Nomenclature ca cb ce ci cs es Hs h i ka kb ki ks L LHb Specific heat capacity of air (J/kg. K) Specific heat capacity of brine (J/kg. K) Equivalent specific heat capacity of brine-spongy ice (J/kg. K) Specific heat capacity of ice (J/kg. K) Specific heat capacity of brine-spongy ice (J/kg. K) Standard vapor pressure over the brine surface (Pa) Significant wave height (m) Convection heat transfer coefficient (W/m2 . K) Node number (---) Thermal conductivity of air (W/m. K) Thermal conductivity of brine (W/m. K) Thermal conductivity of ice (W/m. K) Thermal conductivity of brine-spongy ice (W/m. K) Length scale (m) Latent heat of fusion of brine (J/kg) 1 LHv m Nu n P P𝑎 Pr Qe Qh Qr Re RH S Sb Sc T Ta Tb Tb1 Tb2 Tf Ti Ts1 Ts2 t t0 Ur VFb V𝑎 Vs X Xe αcb αci αkb αki αLHb αsb αρb Latent heat of vaporization of brine (J/kg) Number of the node of solid phase closest to the phase interface (---) Nusselt number (---) Number of the discretized grids (---) Wave period (s) Atmospheric pressure (Pa) Prandtl number (---) Evaporation heat flux (J/s) Convection heat flux (J/s) Radiant heat flux (J/s) Reynolds number (---) Relative humidity (%) Overall salinity (‰) Salinity of brine pockets (‰) Schmidt number (---) Temperature (oC) Ambient temperature (oC) Temperature of brine layer (oC) First interpolated temperature of liquid phase (oC) Second interpolated temperature of liquid phase (oC) Freezing temperature of brine (oC) Initial temperature (oC) First interpolated temperature of solid phase (oC) Second interpolated temperature of solid phase (oC) Time (s) Initial time (s) Relative velocity (m/s) Volume fraction of brine (---) Wind speed (m/s) Vessel speed (m/s) Phase interface position (m) The extent of the spray cloud (m) Coefficient of the equation of specific heat capacity of brine (---) Coefficient of the equation of specific heat capacity of ice (---) Coefficient of the equation of thermal conductivity of brine (---) Coefficient of the equation of thermal conductivity of ice (---) Coefficient of the equation of latent heat of fusion of brine (---) Coefficient of the equation of salinity of brine (---) Coefficient of the equation of density of brine (---) 2 αρi ε εa εb μa ρa ρb ρe ρi ρs δ σ Coefficient of the equation of density of ice (---) Ratio of molecular weight of water and dry air (---) Emissivity of air flow (---) Emissivity of brine surface (---) Viscosity of air (kg/m. s) Density of air (kg/m3 ) Density of brine (kg/m3 ) Equivalent density of brine-spongy ice (kg/m3 ) Density of ice (kg/m3 ) Density of brine-spongy ice (kg/m3 ) Freezing fraction of solidification (---) Stefan-Boltzmann constant (W/m2 . K 4 ) 1. Introduction Marine icing poses considerable safety issues such as risks to the stability of marine vessels and to the safety of the crew during harsh weather conditions. There are many reports on fishing vessel sinkings due to marine icing. Hay (1956) reported the loss of the trawlers “Lorella” and “Roderigo” as a result of sea spray icing in the fishing grounds north of Iceland in January 1955. Blackmore and Lozowski (1994) reported that this accident was actually the beginning of research on the ship icing problems. Shekhtman (1971) reported that 10 Soviet ships in the Bering Sea were lost due to instability by the formation of ice in January 1965. Zakrzewski and Lozowski (1988) reported that many vessel losses have occurred due to icing. In the 1980s, Jørgensen (1982) reported the risks of superstructure icing due to seawater spray and atmospheric icing because of precipitation on offshore platforms. Ryerson (2011) covered the hazards of icing, which include: instability and loss of integrity of ships and offshore structures, malfunction of the operational equipment and communication antennas, slippery handrails, ladders or decks, unusable lifeboats and fire equipment, and the blocking of air vents. The icing phenomenon on marine vessels in the Arctic and other cold regions: atmospheric icing and marine or sea spray icing (Aksyutin, 1979; Shekhtman, 1971). Sea spray icing, or marine icing, occurs for two distinct reasons: wave-generated spray and wind-generated spray. Wave spray arises from the impingement of waves on marine vessels and structures. Wave-generated spray is generally a significant source that is a short and approximately periodic water flux created near the bow of vessels and the base of offshore structures. Wind-generated spray is a smaller source, but is a constant water flux that is created in the airflow during windy conditions. According to previous studies (Zakrzewski, 1986), sea spray is the main reason for icing in cold regions. Some parameters have considerable impacts on the icing phenomenon and ice accretion during a sea spray event. These include: (1) environmental factors such as wind velocity, air temperature, droplets temperature, the freezing temperature of seawater, salinity, the size and distribution of droplets, relative humidity, characteristics of swell waves (height, period, 3 propagation direction), sea or ocean conditions, and (2) the characteristics of marine vessels, including size and design of the vessels, vessel speed, and the angle between the vessel heading and wind/wave direction (Bodaghkhani et al., 2016; Dehghani-Sanij et al., 2017; Dehghani et al., 2016a, 2016b). Ice accretion models for marine icing phenomena require the rate of droplets traveling over a marine vessel and hitting freezing surfaces. Velocities and sizes determine the rate of heat transfer, vaporization and temperature changes of droplets. Droplet temperatures at the moment of impingement on the freezing surface add internal energy to the energy balance for the brine layer. In the case of frozen droplets, they add latent heat of fusion to the energy balance equation. The rate of mass flux of water to the freezing surface is determined based on droplet sizes and velocities (Dehghani et al., 2018; Dehghani et al., 2016b). The freezing of a thin layer of salt water and estimating the rate of ice accretion on cold substrates are challenging phenomena. Intermittent ice accretion due to wave-impact sea spray is a dominant mechanism of ice accretion that depends on heat transfer through the spongy substrate. The brine layer starts freezing by releasing and dissipating the latent heat of fusion through the substrate. The resultant ice is a two-phase medium including pure ice and trapped brine pockets. This type of freezing involves a two-phase substrate called spongy ice and a thin layer of a solution of water and salt called the brine layer. Trapped brine pockets, existing between pure ice dendrites, fill the porosity of the ice medium and create spongy ice (Dehghani et al., 2018; Schiesser and Griffiths, 2009). Accumulation of the first layer of spongy ice on a substrate of spongy ice affects the rate of ice accretion for the next layers. Estimating the thickness of spongy ice accumulated on marine structures has been an important subject of research for many years. The method of the control volume, which considers the average of the properties in target systems and is not an accurate method for fast phenomena with high gradients of properties, has been the main method of approach. A cold substrate of spongy ice is capable of absorbing the released latent heat of fusion that can control the rate of ice accretion. A substrate of spongy ice acts as a thermal capacitor in the process of ice accretion. In the cooling process, spongy ice becomes colder and the trapped brine pockets start to freeze and join the pure ice. The amount of freezing of the brine pockets depends on the corresponding cooling process and the final temperature of the spongy ice (Dehghani et al., 2017; Dehghani et al., 2018). The ice accumulated on the subject fishing vessel is calculated numerically using environmental and vessel data provided by NTSB. The numerical scheme uses the current published knowledge of marine icing phenomena and a numerical code which is recently developed by the authors. The results are strongly dependent on the input data and despite having considerable information related to this case, there are some unknown parameters that can cause uncertainties. 4 2. Wave-spray ice accretion The impact of a wave on a vessel bow creates a thin and unstable sheet of water on the bow surface (Dehghani et al., 2016a). The sheet of water splits into several strips. As the strips become unstable, they are divided into many droplets. The result is a cloud of spray which is called a wave-impact sea spray (Dehghani et al., 2016a). Wave-impact sea spray includes droplets of various sizes and velocities. The droplets travel over the marine vessel or the offshore structure to impinge on a surface or pass over the platform and return to the sea (Lozowski et al., 2000; Zakrzewski, 1987). The spray duration is a short period in the intervals of the wave impact. The wave-impact sea spray is an intermittent phenomenon and strongly dependent on time (Kulyakhtin and Tsarau, 2014; Ryerson, 1995). Fig. 1 illustrates wave-impact sea spray on a vessel bow. Fig. 1. Wave-impact sea spray on a vessel bow (Dehghani et al., 2016a). The incoming water on the front edge of marine vessels and offshore structures can be estimated based on the Liquid Water Content (LWC) and water flux (Forest et al., 2005; Zakrzewski, 1987). The spray cloud starts moving over the platform of vessels or offshore structures to reach the cold surfaces. The amount of impinging water droplets on the cold surfaces can be predicted by the droplet trajectory method. The duration of the spray cloud is normally shorter than the interval between the spray events. This means marine vessels and offshore structures are repeatedly subjected to a spray cloud for a short period. Ryerson (1995) reported that the average duration of a spray cloud is about 2.7 s. Other studies indicate that the spray duration is typically about 2 s (Borisenkov et al., 1975). The interval between the spray events can be estimated by assuming spray generation during every fourth wave encounter on a vessel bow (Lozowski et al., 2000). In typical sea conditions 5 (Zakrzewski, 1987), the average interval between spray events can be estimated as about 60 s. This means that usually in every minute, a spray event of about 2.5 s will occur. For wave-impact sea spray, the spray duration is much shorter than the interval periods. The average time ratio of spray duration and spray intervals is typically about 1/30 (Zakrzewski, 1987). Intermittent spray clouds move over the superstructures of marine vessels and offshore structures to reach the cold surfaces and substrates (Dehghani et al., 2016a; Lozowski et al., 2000; Zakrzewski, 1987). The water starts freezing after impinging on the cold surfaces. The freezing process is dependent on the atmospheric conditions and the characteristics of the vessels or offshore structures. The variables of wave-spray ice accretion are dependent on time. The process is almost cyclic and repeats several times. Fig. 2 shows the cycle stages of wave-spray ice accretion. This type of ice accretion is different from wind spray ice accretion and atmospheric ice accretion which are almost continuous and steady ice accretion processes. Fig. 2. Main stages of a periodic process of ice accretion. Incoming spray clouds start the cyclic process by carrying droplets towards cold substrates. Droplets impinge on cold substrates and the freezing process starts. A thin layer of brine is formed on the cold substrates, freezing starts at the phase interface and the latent heat of fusion is released. Heat transfer mechanisms dissipate the released latent heat to the ambient air and substrate. Convection, radiation and evaporation heat transfers cause heat flow towards the ambient air and heat conduction causes transferring the heat towards the cold substrate. After a short time, the brine layer freezes and the new layer of solid ice will be directly in contact with the ambient air. Convection, radiation and evaporation heat transfers start cooling down the substrate. The substrate will be cold enough to be ready for the start of a new cycle. Wave-spray characteristics affect transient ice accretion processes and will be explained in the following sections. 6 The intermittent ice accretion phenomenon can be divided into two individual processes: cooling and freezing. Because of the short period of spray events, it can be concluded that for a long period, the front surface of the substrate will be dry and the surface will become colder due to heat transfer to the environment and sublayers of ice. In this paper, this stage is called the cooling stage. In the freezing stage, the outer surface of ice is wet with a thin layer of unfrozen brine. A new ice layer, which is confined by the old substrate and the brine layer, exists at this stage. Fig. 3 illustrates the freezing and cooling stages. Fig. 3. Illustration of the freezing and cooling stages. Latent heat released from the phase interface is dissipated during the ice accretion (Shakeel, 1987; Weeks, 2010; Weeks and Ackley, 1986). During the freezing process, heat conduction, convection, radiation, heat transfer due to evaporation and heat released due to solidification are relevant heat transfer processes (Kulyakhtin and Tsarau, 2014; Lozowski et al., 2000). The control volume around the phase interface includes a thin layer of brine (Horjen, 2015; Kulyakhtin and Tsarau, 2014; Lozowski et al., 2000; Shipilova et al., 2012). In the freezing stage, the heat balance is affected by heat conduction through the substrate of ice, heat convection to the ambient air, radiation to the surroundings, heat transfer due to evaporation of the brine layer, heat transfer due to the incoming supercool droplets and heat released due to the solidification of the brine. It is assumed that the temperature of the brine layer is constant and equal to the freezing point (Horjen, 2015; Kulyakhtin and Tsarau, 2014; Lozowski et al., 2000). Previous studies neglected heat conduction through the substrate of ice. They considered the other heat flows to be the main contributors in the heat balance (Horjen, 2015; Kulyakhtin and Tsarau, 2014; Lozowski et al., 2000; Shipilova et al., 2012). Fig. 4 illustrates the important factors of the heat transfer in the freezing stage. 7 Fig. 4. Heat transfer factors in the freezing stage. In the process of the cooling the outer surface of the substrate of ice, heat transfer factors are heat conduction through the substrate, convection and evaporation to the ambient air and radiation to the surroundings. Heat flow through the brine-spongy substrate affects the brine pockets and the confined pure ice. Cooling will solidify a portion of brine pockets to pure ice and heat flow will also melt a portion of pure ice and join it to the brine pockets (Weeks and Ackley, 1986). This implies that the cooling and heating cause an exchange of sensible heat and latent heat energy in the brine-spongy ice. Fig. 5 shows the heat flows in the cooling stage. Fig. 5. Heat transfer factors in the cooling stage. 8 3. Formulation and Modelling 3.1 Heat transfer Models for calculating convective heat transfer for cylinders and planar components were presented previously (Horjen, 2015; Kulyakhtin and Tsarau, 2014; Lozowski et al., 2000; Shipilova et al., 2012). Important variables in these relations are the relative velocity of air and objects, air temperature and the length scales. Evaporative heat transfer, which is caused by evaporation of brine, represents another significant variable in the solidification. The factors of relative humidity and ambient pressure are needed to calculate the evaporative heat transfer. Convection heat flux is calculated using the relevant formula used by previous researchers (Kulyakhtin and Tsarau, 2014; Lozowski et al., 2000): Q h = h(Tb − Ta ) (1) The convection heat transfer coefficient is calculated using: h= Nuka (2) L Nusselt numbers for cylindrical and planar components are respectively equal to (Szilder and Lozowski, 2000): Nu = 3.0Re0.5 Nu = 0.036Pr 0.33 Re0.8 (3) (4) Reynolds number of the component is defined as follows: Re = ρa Ur L (5) μa Evaporation heat flux is calculated using the following equation (Kulyakhtin and Tsarau, 2014; Lozowski et al., 2000): Pr 0.63 εLHv Qe = h ( ) Sc P𝑎 ca (es (Tb ) − RHes (Ta )) (6) Radiant heat flux is calculated using (Lozowski et al., 2000): Q r = σ(εb Tb4 − εa Ta4 ) (7) The contribution of brine pockets in the conductive heat transfer through brine-spongy ice creates a phenomenon that acts like a thermal capacitor. In a transient condition, heat cannot flow 9 through brine-spongy ice without melting a portion of the ice. Brine-spongy ice cannot become colder without freezing a portion of the brine pockets (Shakeel, 1987; Weeks, 2010; Weeks and Ackley, 1986). Fig. 6 illustrates varying sizes of brine pockets at the end of the freezing and cooling stages. At the end of the freezing stage, the brine-spongy ice exists at the highest temperature. The brine pockets exist at the maximum volume, and consequently, the volume fraction of brine is at a maximum. This stage is a thermally discharged stage. The cooling stage is a stage of charging the brine spongy ice thermally. By cooling the brine-spongy ice, a portion of brine pockets starts to freeze, and at the end of the cooling stage, the brine pockets exist at the minimum volume. In this stage, the volume fraction of brine is minimal. Fig. 6. Illustration of the role of thermal capacitance in brine-spongy ice accretion. Cooled brine-spongy ice has a significant capacity to absorb heat. Due to the contribution of latent heat, this capacity is enhanced. The process of cooling brine-spongy ice increases its thermal capacity until all of the brine pockets are frozen. The temperature of completely frozen brine pockets is about -21 oC (Shakeel, 1987; Weeks, 2010; Weeks and Ackley, 1986). This means brinespongy ice can act as a thermal capacitor in a temperature range from the start of the freezing point to about -21 oC. At temperatures less than -21 oC, there are only ice and solid salt phases. At those temperatures, the latent heat mechanism cannot be active; therefore, the brine-spongy ice behaves like a solid material. 3.2 Brine-spongy ice The governing equation of heat transfer in brine-spongy ice, proposed by Dehghani et al. (2017), is obtained as: ρe ce ∂T ∂t ⃗ . (k s ∇ ⃗ T) =∇ ρe ce = (ρs cs − S ρi LHb T2 (8) 49.185 × 10−3 ) (9) 10 This partial differential equation is dependent on the overall salinity and thermal properties of brine pockets, ice and brine-spongy ice. Table 1 shows relations which describe the thermal properties of ice, brine and brine-spongy ice (Cox and Weeks, 1975; Weeks, 2010; Weeks and Ackley, 1986). Eq. (8), Eq. (9) and the equations of properties in Table 1 yield 13 equations and 13 unknowns leading to a set of linear and nonlinear equations. The unknowns are temperature, brine conductivity, brine heat capacity, brine salinity, brine density, brine heat of fusion, ice density, ice thermal conductivity, ice heat capacity, spongy ice conductivity, spongy ice density, spongy ice heat capacity and volume fraction of brine. Properties of spongy ice are considered as weighted properties of ice and brine. The properties in Table 1 are empirical relations found by previous investigators (Cox and Weeks, 1975; Weeks, 2010; Weeks and Ackley, 1986). These are dependent on the coefficients which are obtained experimentally. Table 2 includes the coefficients in the equations of Table 1. With initial conditions, which are the initial distribution of temperature in the brine-spongy ice, the boundary conditions, and also the overall salinity of brine-spongy ice, this set of 13 equations and 13 unknowns can be solved. The results predict the thermal response of brine-spongy ice at each moment of time. Table 1. Properties of pure ice, brine, and brine-spongy ice. Properties Equations cb αcb0 + αcb1 T + αcb2 T 2 + αcb3 T 3 ci αci0 + αci1 T ρb ρb cs cb VFb + ci (1 − V ) ρs ρs Fb kb αkb0 + αkb1 T + αkb2 T 2 ki αki0 + αki1 T k b VFb + k i (1 − VFb ) ks LHb αLHb0 + αLHb1 T + αLHb2 T 2 Sb αsb1 T + αsb2 T 2 + αsb3 T 3 αρb0 + αρb1 Sb ρb αρi0 + αρi1 T ρi ρb VFb + ρi (1 − VFb ) ρs 11 Table 2. Coefficients for the equations of the properties in Table 1. Values Coefficients (0) (1) (2) (3) 4211.249 111.437 5.125 αcb( ) 93.545× 10−3 2118.5199 7.8000 0 0 αci( ) 0.5664 αkb( ) 3.0822× 10−3 1.8388× 10−5 0 2.2399 0 αki( ) -10.7517× 10−3 0 -333400.326 -4958.217 -29.894 0 αLHb( ) 0 -17.5730 -0.381246 αsb( ) −3.28366 × 10−3 1000 0.8 0 0 αρb( ) 917 -0.1403 0 0 αρi( ) 3.3 Wave-impact sea spray The movement and frequency of spray clouds determine the rate of water delivery to the cold surfaces of the vessel. The extent of the spray is calculated using the formula suggested by Lozowski et al. (2000). In this formula, the maximum travel distance of the spray cloud is calculated by: Xe = 2Hs + 0.04(1.56P + Vs )2 − 10 (10) Where Xe is the extent of the spray cloud, Hs is the significant wave height, P is the period of the sea wave and V𝑠 is the vessel speed. It is assume that one wave among 3 to 5 waves that strike the vessel can successfully generate a spray cloud. 4. Case Definition and Assumptions Three categories of information are required to define the case completely for numerical simulations. The first category is related to the sea information including significant wave heights, sea surface temperature, wave period, wave direction and seawater salinity. The second category is the weather condition including wind speed, wind direction, air temperature, relative humidity of air and precipitation. The third category of information is the vessel information including vessel geometry, vessel speed and vessel direction. The data mentioned above are provided by the US National Transportation Safety Board (NTSB). The model is defined considering two individual conditions, full load and low load conditions. Figs. 7 and 8 show the full and low load conditions. In the full load condition, the vessel is occupied by crab cages. For the low load condition, it is assumed that the necessary equipment is on the deck and there are no cages on the deck. The geometry of the vessel extracted from Figs. 8 and 9. The path of the vessel is shown in Fig. 10. 12 Fig. 6. A picture of the full load condition Fig. 7. A picture of the low load condition Fig. 8. Side view of the vessel Fig. 9. Top view of the vessel 13 Fig. 10. The path of the vessel The significant wave heights and wave period from February 09 to February 11 are shown in Fig. 11. The information of the vessel speed and wind speed can be found in Fig. 12. The air temperature is plotted in Fig. 13. Fig. 11. The significant wave height and wave period during the vessel’s travel 14 15 Fig. 13. Air temperature Time (AKST. Feb. 09 to Feb. ll) >85. 8; >85. 2 >83. cu; >85. >83. :2 >83. >85. :3 9 9: >85. .63 >83 >85. 2: >83. 7: >85. >83. .3 >8m4 >85. >85. .3. >83. 2.352. 3322 3: >83. .5. >83. 2 .u >85. cu; cu; >83. C..- >qu cu. >85. 3. 9 >83Fig. 12. Vessel speed and Wind speed Time (AKST, Feb. 09 to Feb. II) .23 .8: .4 >874. c. .m >85. an; >8w4 3. >83 >85. cu; >83. 8. >83. >85. 8; >85. 3. >83. 5; :m 53 >85. 3; >85. >85. 3; >83. >822. :3 >83. .2 >83. >83. HEM >89. u. 3 >83. mm; >83. >83. 33m >85. c. .u >85. Ou.u>83. 2! >83. 2; >85. cu. >83. 8. >83. 0