Makkonen´s model

In Makkonen’s model icing rate can be modeled with an equation

Makkonen´s equation

where 𝛼1 is collision efficiency,

𝛼2 sticking efficiency

and 𝛼3 represent ice accretion efficiency

𝛼1, 𝛼2 and 𝛼3 are correction factors, and their value is between 0 and 1. Empirical data is used to determine the correction factors and they are very dependent on the icing conditions.

A is area and

v is the velocity of the particles

and ω is the mass concentration of particles.

Collision efficiency 𝛼1 is the ratio at which water droplets hit the icing surface, as some droplets, especially the smaller ones, can be directed by airflow to miss the icing object.

Sticking efficiency 𝛼2 is the measure of how much of the water droplets, or snow, that hit the surface, stick to the ice layer. Supercooled water droplets do not bounce but freeze immediately. Adversely, snow can bounce off. Snow increases the complexity of icing and therefore many icing models have a hard time modelling icing events with snowflakes.

Ice accretion 𝛼3 efficiency is a measure of how many of the particles contacting the material surface form ice on it. Some droplets do not freeze to from ice, leading to wet ice growth. The heat balance of the object surface affects the number of droplets that freeze. The surface heat balance follows equation:

where 𝑄𝑓 is latent heat of freezing,

𝑄𝑣 is frictional heating of air,

𝑄𝑐 is loss of sensible heat to air,

𝑄𝑒 is heat loss due to evaporation,

𝑄𝑙 is heat loss because of warming of supercooled water to freezing point,

and 𝑄𝑠 is heat loss due to radiation.

The ice accretion efficiency is strongly affected by how well the latent heat of freezing can leave the surface.