Eutectic Cooling System Design

Describing a eutectic solution

The formal definition of a eutectic solution would be, a homogeneous mixture of substances that melts or solidifies at a single temperature that is lower than the melting point of any of the constituents.

To break this definition down into simpler terms, we will need to understand that the melting temperature of any pure material (a one-component system) at constant pressure is a single unique temperature [Represented in the graph].

This unique temperature for water, at atmospheric conditions happens to be 0°C. The addition of NaCl [salt] at different concentrations, tends to depress the point of freezing to different levels. A eutectic solution [with respect to water & salt in this case] is hence one where a certain quantity of salt has been added to water, such that its freezing point is depressed to its lowest possible point [shown below]

Eutectic refrigeration exploits the latent heat absorption capabilities of ice that is formed at this eutectic point.

Eutectic solutions are filled inside containers & pre-frozen. These containers are then placed inside the chamber that needs to be cooled. As the pre-frozen eutectic solution [now solid blocks of ice] begins to thaw, it absorbs its latent heat from the chamber [to be refrigerated] and hence keeps it cool. The container which holds the eutectic solution is called a eutectic pad.

Eutectic pads are of many variants, but broadly 2 types:

1)    Those that contain only the eutectic solution & must be frozen in a separate refrigerated environment before being placed inside the chamber that needs cooling

2)    Those that contain the eutectic solution & also a network of evaporator tubes running inside it, through which a cold refrigerant is passed that freezes the eutectic solution. These kind of pads need not be refrigerated separately & are permanently fixed inside the chamber that requires cooling.

The picture on the right shows how pads of the kind stated in point 2 are permanently fixed inside the container of a truck. These have an evaporator network in them that are fed with refrigerant with an aim to freeze the eutectic solution contained inside, to the required freezing point.

This article attempts to explains the system design for eutectic pads mentioned in point 2. The steps involved in the system design are:

1. Determining the heat that needs to be removed from the chamber requiring cooling. This is done by carrying out a heat load estimation exercise.
2. Selecting the eutectic pads for the job
3. Determining the rate at which the heat needs to be removed to freeze the solution in the eutectic pads

Heat Load Estimation

This article assumes a pre-calculated heat load value already exist and so, does not describe the estimation in detail. The major sources of heat entry into a chamber maintained at a refrigerated temperature would be -

• Transmission – accounts for the ingress of heat through the walls of the refrigerated chamber. Calculated using the relation Q = U . A . dT [U-Overall Heat Transfer Coefficient ; A - Area of heat exchange ; dT - Difference in temperature between the refrigerated space & the surrounding]
• Product load – attributed to the energy required to lower the temperature of the product from the ambient temperature[at which the product was loaded into the chamber] to the desired storage temperature. The load is classified into 3 categories

1. Sensible pull down above freezing
2. Latent pull down
3. Sensible pull down below freezing [neglected in this case]

Note: Most refrigeration systems that solely employ eutectic cooling, do not perform a “pull down” of product temperatures from their ambient conditions, instead only maintain the temperatures at which they were loaded in.

• Infiltration - is the load on the system due to the ambient air entering the refrigerated space through door openings.
• Miscellaneous – such as those from electrical components & infiltration through door gaskets.

The total heat load is evaluated with an appropriate factor of safety, and is represented as Qh

Eutectic Pad Selection

Eutectic pads are often times equated to thermal batteries. This is evident by the way manufacturers specify the capacity of a eutectic pad in terms of Wh [Watt-Hrs]. This can be interpreted as the watts consumed in specified duration of 1 hour. An example of a specification sheet for eutectic pads is shown below. Courtesy FIC Italy

For example, a eutectic pad of 1080 Wh capacity would signify that the selected pad would absorb 1080 Watts of energy for 1 hour as the solution changes phase from solid to liquid i.e. as it melts. Suppose the heat load of the room is 540 W, then this eutectic pad would support cooling for 2 hours. Calculated as 1080/540 [Wh/W] = 2 hrs at the stated melting point. Therefore, 1080 Wh is the latent heat energy that the pad can absorb as it changes phase from solid to liquid.

Example Scenario

• A room has to be maintained at - 20 °C
• Customer requires this temperature to be maintained for 4 hours.
• Pre-estimated heat load into the system = 1500 W

From the table above, we will need to select combinations of pads that can help sustain cooling for the stipulated time of 4 hours, at a freezing point closest to -20°C

• Depending on the space available inside the refrigerated space, pads of appropriate sizes & cooling loads are selected.
• In this case, I selected EFR 850 & EFR 1250.
• Add the capacities of both pads = 1070 + 1730 = 2800 Wh
• The heat load into the system was estimated to be 1500 W
• Therefore, 2800/1500 = 1.86 hrs worth of cooling can be produced with these combinations of pads. This is lower than the 4 hours that the customer requires.We will need to increase the number of pads, based on the space available inside the chamber
• We will select 4 x EFR 850 pads & 1 x EFR 1250 pads
• This amounts to 6010 Wh of cooling
• Diving by the heat load = 6010/1500 = 4 hrs of cooling
• This is in line with the customers’ needs

Calculating Rate of Heat Exchange

Customers usually have a stipulated time within which the eutectic pads need to be frozen. Our next actions would be to size a compressor to pull down the eutectic solution at the rate specified by the customer.

We will need to consider the total quantity of eutectic solution inside each eutectic pad. Its sensible heat has to be removed as well as its latent heat at specified temperature.

• Weight of eutectic solution in the EFR 850 pad is = 26 kgs [this weight is provided by the supplier]
• Therefore, since we have 4 EFR 850 pads = 4 * 26 = 104 kgs
• We will need to remove the sensible heat from it before we reach the freezing temperatures
• Calculating sensible pull down for EFR 850 pads :
• Q[efr850] = m * Cp * dT
• Q sensible[efr850] = 104 * 2.16 * [32 – (-23)] = 12,355.2 kJ -----[1]
• Q latent[efr850] = 3210 W-h (from the specification table) -------[2]
• Assuming the pull down needs to happen within 10 hours
• Divide [1] & [2] by 10 hours & converting to Watts
• Q sensible[efr850] = 12,355.2/10 = 12,355.2 / (10*3600) = 343.2 W -----[3]
• Q latent[efr850] = 3210/10 = 321 W  ------[4]

Same exercise is repeated on the other pads

• Weight of eutectic solution in the EFR 1250 is = 40 kgs

Specific heat of the solution would be provided by the supplier

• Q sensible[efr1250] = m * Cp * dT
• Q sensible[efr1250] = 40 * 2.16 * [32 – (-23)] = 4,752 kJ ------[5]
• Q latent[efr1250] = 1730 Wh (from the specification table) ----[6]
• Assuming the pull down needs to happen within 10 hours
• Divide [5] & [6] by 10 hours & converting to Watts
• Q sensible[efr850] = 4752/(10*3600) = 132 W -----[7]
• Q latent[efr1250] = 1730/10 = 173 W ---[8]
• Adding all heat loads ---- [3] + [4] + [7] + [8]
• Q Total = 969.2 W [ -30°C SST & 45°C SDT assuming ambient of 32°C]
• The is the rate at which heat needs to be removed from the eutectic pads, to freeze the solution inside at -23°C in a span of 10 hours.

Design Nuances

Designing a eutectic cooling system requires a lot of variables to be considered and arriving at an optimized design is a matter of in depth research & development. This can be attributed to a number of factors

1. The factor of safety considered in the heat load calculation will need to be adjusted based on actual field data.
2. The efficiency of the insulated container that houses these pads has a direct impact on the system performance.
3. Heat losses through doors & gaskets can be quite harrowing to estimate numerically, and difficult to model without proper tests in the field.
4. As the eutectic pads are pulled down to its designed freezing point, high humidity conditions tend to create a layer of frost on the surface of the pads that inhibit efficient heat transfer between the said pads & the room. Picture above is quite self explanatory of this point.
5. As the frozen blocks of ice begin to thaw, some portions of the ice tend to covert to liquid quicker than others. This liquid tends to seep to the bottom of the pad through gravity, & form a fine layer that acts like an insulation to the rest of the ice. Eutectic pads placed on the ceiling of the container are more susceptible this kind of inefficiency.
6. As noted in the calculation, the eutectic solution is pulled down from an ambient of 32°C to its freezing point. In practice, this happens only on the first pull down, as the eutectic solution rarely reaches equilibrium with the ambient temperature due to the insulated box in which it is placed. Hence the rate of pull down required will not be as high as calculated for this scenario, but points 4 & 5 will need to be kept in mind during system sizing.

References

• University of Cambridge - (DoITPoMS) - Teaching & Learning packages [https://www.doitpoms.ac.uk/tlplib/phase-diagrams/cooling.php]
• FIC Italy - Technical Documentation [https://www.fic.com/en]