Technical Assessment of Dry Ice Limits on Aircraft (2013)

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21 Review of Existing Information on Heat Transfer to Cold Cargo Insulated Cardboard Cartons Containing Dry Ice The manufacturers of insulated packages do not provide any detailed heat transfer performance characteristics of their packages. When this was discussed with the package manu- facturers’ sales representatives, they said it was the shipper’s responsibility to ensure that the proper quantity of dry ice was added to the package. Several package manufacturers stated that they had a testing laboratory and that if the ship- per requested, they could do a performance testing experi- ment, for a fee, which consisted of loading a given quantity of dry ice in a package and measuring the internal temper- ature as a function of time. Some would vary the ambient temperature for a few hours to simulate a higher ambient temperature, perhaps for the time between when the pack- age leaves the air-conditioned cargo handling facility and when the package is loaded on the aircraft and the venti- lation system is turned on. These simple experiments were done in lieu of any heat transfer modeling. There is an ASTM standard for such tests,33 though it is not clear how widely it is used. Some organizations, such as universities whose staff may frequently need to ship packages containing dry ice, have developed their own internally produced guidelines.34, 35, 36 The origin and basis for the guidelines in the publications are generally obscure and probably based on rules of thumb gained through experience. Insulated ULDs Containing Dry Ice Discussions with two manufacturers of insulated ULDs indicated that they had done heat transfer analyses but considered the results of those analyses to be proprietary. This chapter considers carbon dioxide production and focuses on the effect of heat transfer on carbon dioxide pro- duction; Chapter 9 considers ventilation and the removal of carbon dioxide through ventilation. Rationale for Basing Dry Ice Limits on Heat Transfer Analysis Cargo and packages that contain dry ice are sources of carbon dioxide gas. The carbon dioxide gas is given off when the dry ice sublimes. The sublimation rate* is determined by the rate of heat gain. Once heat reaches the dry ice, it sublimes and the gaseous car- bon dioxide leaves quickly through a bulk flow of gas. Thus, the dry ice sublimation rate is determined solely by the transfer of heat to the dry ice and is not limited by the transfer of carbon dioxide away from the surface. Therefore, understanding the dry ice sublimation rate requires an understanding of the rate of heat transfer. The rate of heat transfer is in turn determined by the pack- aging or container specifications and design, as well as by the ambient conditions. In this section we examine calculated heat transfer rates. The objective of the heat transfer calcula- tions is to provide an estimate of the amount of heat energy transferred per unit of time.† The rate of heat transfer and the resulting dry ice sublima- tion rate are related through the heat of sublimation, which for dry ice is 573 kJ/kg. If we know the rate of heat transfer, we can do a simple calculation to convert to an equivalent dry ice sublimation rate, also called the dry ice loss rate. For example, a heat transfer rate of 100 watts is equivalent to a dry ice loss rate of 630 g/hr, and a dry ice loss rate of 1 kg/hr is equivalent to a heat transfer rate of 160 watts (J/s). C h a p t e r 7 Heat Transfer and Carbon Dioxide Production *By sublimation rate is meant the mass of dry ice per unit of time that changes from a solid to a gas. In terms of SI units, this would be grams or kilograms of dry ice per hour. †In common SI units, this would be joules per second, or watts.

22 Other Cold Cargo There is a limited amount of technical literature on heat transfer modeling of cold packages in transit.37 For example, Kumar and Panigrahi modeled frozen fish placed in polyform- insulated cardboard cartons.38 Heat Transfer Calculations Heat Transfer to Packages As long as the thickness of the insulating material is much less than the dimensions of the sides of the package, the steady-state heat transfer rate can be modeled using the following equation: Q UA T= ∆ where Q = rate of heat transfer, W, U = overall heat transfer coefficient, W/m2 K, A = package area, m2, and DT = temperature difference between dry ice sublimation temperature and cargo bay temperature, K. The overall heat transfer coefficient U can be broken into components by considering the reciprocal of the coefficient to be a resistance that is made up of several resistances to heat transfer: one at the outside wall, another through the insula- tion, a third at the inside wall, and if necessary, the resistance at the surface of the dry ice. These individual resistances are normally expressed as shown by the following equation: 1 1 1 1 1 U h x k h x k h ho c c g f f i s = + + + + + In the equation, the subscripts o, g, i, and s indicate the heat transfer coefficients for the outside surface, the gap between the foam and the cardboard box, the inside surface of the foam, and the dry ice surface, respectively. There are two thermal resistance layers—the cardboard box and the foam—indicated by the subscripts c for the cardboard and f for the foam. The resistance of the cardboard and foam is expressed at a thickness x divided by its thermal conductivity k. The equation assumes that the heat transfer through the air gap between the cardboard and the foam is entirely by conduction. If convection within the air gap were occurring, the gap heat transfer coefficient, hg, would be specified by h′c in the following equation for vertical enclosed spaces, as found in McAdams:39 ′ =           h x k C L x x g t c k c f f f p 1 9 3 2  ρ β µ µ∆  =   [ ] n nC L x x tY 1 9 3 ∆ However, according to McAdams, for Grashof numbers (based on clearance gap thickness) below 2,000, natural con- vection is suppressed and the amount of heat transfer is con- trolled by conduction. For this situation, the Grashof number is defined as: GrNum: L g Tgap3 air2 air 2 = • • • •ρ β µ ∆ Estimating that the DT across the air gap is 10 K*, the Grashof number is calculated to be less than 20, which is far less than 2,000. Thus, we are justified in considering there to be simple conduction in the air gap; if only conduction is occurring, the equation would be: 1 ′ = h x kc g g where xg is the thickness of the gap and kg is the thermal conductivity of air. The heat transfer coefficient on the outer wall, ho, would either be heat transfer to an adjacent package or heat transfer to air in the cargo hold. If the package containing the dry ice was in a ULD, the entire ULD could be filled with dry ice packages. In this case, there would be no heat transfer from the package to the adjacent packages, which would be equally cold. If a package containing the dry ice was loaded into a ULD with other mixed packages, since the adjacent packages are likely to be contained in cardboard cartons and packed with a lot of poorly conducting padding, even here there would be little heat transfer to three or more of the sides of the cold package. The limiting condition occurs when the cold package is located such that there is convective heat transfer from the cold package on several of the surfaces, say all four sides and from the top. Because the desire in this modeling is to try to identify a heat transfer coefficient that would be bounding, convective heat transfer to air was chosen for further study. While the external heat transfer could be controlled by natu- ral or forced convection, only the natural convection case will be shown in what follows. Heat Transfer with Free Convection As a first assumption, the heat transfer to the top will be neglected. From McAdams,40 the following equation can be used to estimate the heat transfer coefficient from a vertical surface. *Subsequent experimental measurements with packages showed the DT to be more like 5 K.

23 h L k L g T c k o a a p =            0 52 3 2 0 . ρ β µ µ∆ . . . 25 3 0 250 52= [ ]L T Y∆ Where L is the length of the surface and DT is the difference between the ambient air temperature and the temperature of the surface of the package. The first term within the brackets is the Grashof number and the second the Prandtl number. Because the temperature difference is unknown, what must be done is to estimate the heat transfer rate across the insula- tion, then using that heat transfer rate, guess at a DT and iter- ate until the heat transfer rate across the gap is the same as it is for the insulation. The heat transfer on the inside surface of the package is somewhat problematic in that initially the package might be full of dry ice, and later in the journey the dry ice might only half fill the package. Inside there are two parallel heat paths, one from the surface to the void space filled with carbon dioxide and then to the dry ice itself and the other from the surface to the dry ice. In the experiments performed to look at the sublimation rate of dry ice from some typical packages, it was observed that toward the end of the effective cooling period the dry ice pellets were covered with a frost composed of ice crys- tals. In fact, if the package was filled with dry ice pellets on a humid day, the supply of dry ice pellets may have been frosted even prior to use. Such ice crystals could provide a signifi- cant thermal resistance. Because of this thermal resistance, the temperature of the gas inside the package can be some- what warmer than the sublimation temperature, and we did observe this during our package tests. However, again, in keeping with the need to provide a bounding estimate of the dry ice sublimation rate, calcula- tions were performed using an assumed carbon dioxide gas temperature of -78°C. This implies a temperature difference of about 100°C, assuming the ambient air is at 22°C. Given these simplifications, it is now possible to estimate the value of the overall heat transfer coefficient and to obtain from that estimate the rate of sublimation of the dry ice. The box that was modeled was 290 mm (0.94 ft) by 240 mm (0.79 ft) by 200 mm (0.66 ft) high. Thus, the total surface area of the box was 0.212 m2 (2.28 ft2). The thickness of the EPS foam* was 42.5 mm (0.139 ft). The thermal conductivity of the EPS was taken as 0.035 W/m K. The heat of sublimation of dry ice at atmospheric pressure is 573 J/g. The equation for the top of the package is of the same form as the equation for the vertical surfaces. The only difference is that the coefficient in front of the equation changes from 0.53 to 0.27, reflecting the less efficient transfer when cooling a horizontal surface facing upward. Because there is no convection from the bottom of the package and because of the probability that the package sits on another package, most likely with padding, the heat loss from the bottom is estimated to be zero. It may be seen that each of these assumptions could be investigated and clarified and the model made correspond- ingly more sophisticated. However, the goal here is to provide a reasonable estimate. The calculated heat gain for such a package is estimated to be 9.4 W, leading to a calculated area-normalized dry ice loss rate of 169 g/m2 ? hr. Heat Transfer to Insulated Unit Load Devices In addition to considering dry ice loss rates from cardboard cartons, we believe that it is important to look at insulated ULDs. The reasons are twofold: (1) Large-scale shipments often use insulated ULDs, and these ULDs use lots of dry ice, up to 200 kg each, so insulated ULDs are potentially big sources of carbon dioxide. (2) Regulations have been writ- ten and policies established that give ULDs special treatment, such as higher limits for the total number of kg of dry ice per aircraft* and a waiver from the per-package limit.† Thus, we believe it is crucial to understand how ULDs behave, how they may be different from EPS-insulated cartons, and whether this special treatment is justified. The heat transfer analysis for insulated ULDs is similar to that for packages. In the case of insulated ULDs, the walls are composites of structural and insulating materials. We do not have a blueprint for their design, and we do not know the wall thickness, the type of insulation used, and the configuration of the structural components. Thus, an a priori calculation of the expected heat transfer through the wall of an insu- lated ULD is not possible. However, we can calculate apparent overall U values based on available dry ice loss rate data and then use these U values in other calculations. Discussion of Heat Transfer Analysis Results Uncertainties in the Heat Transfer Analysis There are several uncertainties in this model. First of all, a one-dimensional steady-state heat transfer model was used. Clearly, with these small packages there are edge effects both within the EPS and also on the outside of the package. If a *Also known and sold under the trademark Styrofoam. *For example, consider ICAO variation No. CO-9 for Continental Air- lines whereby the dry ice limit for a Boeing 777 goes from 200 kg to 1,088 kg if ULDs are used. †See statement in 49 CFR 173, Section 217 that “The quantity limits per package . . . are not applicable to dry ice being used as a refrigerant . . . in a unit load device.”

24 two-dimensional model had been used, the temperature drop between the surface of the package and the ambient air would have been lower on the corners, lowering the rate of heat gain and therefore the calculated rate of sublimation. Another uncertainty is in the thermal conductivity of the EPS. Looking in the literature, it is possible to obtain a range of thermal conductivity values. This is not the result of exper- imental error but is due to differences in the density of the EPS and in the temperature at which the thermal conductiv- ity is measured. Less dense EPS tends to have a lower thermal conductivity. It would be possible to improve the agreement with the experimental results by adjusting the thermal con- ductivity, and the adjusted thermal conductivity would still be in the range of published thermal conductivities listed in the literature. The modeling could be made more conserva- tive by picking a higher EPS conductivity when setting these dry ice carriage limits. On the other hand, it is also possible that the heat trans- fer to the dry ice pellets is reduced because the pellets are coated with a layer of water ice crystals. Such frost may be observed visually if dry ice pellets are left to sublime in the open air. This behavior, which was observed when dry ice pellets were placed in a simple, uninsulated cardboard box and allowed to sublime, is complex and dependent on the amount of moisture available when the package is packed with dry ice. Under humid conditions, this heat transfer phenomena could be a significant resistance to heat transfer that was not modeled. Cargo compartments are generally supplied with ventila- tion air. Interior air flows are complex and we do not know the exact pattern of air flows and associated air velocities, which in any case would change with the configuration of each different load. The possibility of air currents over or against the package is one reason why onboard measure- ments are desirable. Steady-State Versus Transient Analysis In modeling the heat transfer, there is a steady-state phase and perhaps several transient phases. The first transient phase occurs when the dry ice is first loaded and the internals of the package cool down. The extent of this phase depends heavily on whether the load has been pre-cooled. A second transient phase occurs if the ambient air temperature changes, and a third occurs if the ambient pressure changes. Of those three transient phases, the cool-down phase has the potential for the greatest rate of carbon dioxide emission. For example, if the material being shipped has to be cooled down from 22°C to -78°C, a temperature difference of 100 K, and its mass of material is comparable to the mass of dry ice loaded in the package, 10% to 20% of the dry ice can be sub- limed just cooling down the material prior to being shipped. Since this loss occurs within the first 1 to 2 hours, and the quantity of dry ice reported on the shipping papers is usu- ally based on the weighing performed before this cool-down period, the quantity of dry ice present during shipment is often overstated. (This is another way that mass-based limits may benefit from an unintentional safety factor.) The other two transient phases, the change in ambient tem- perature and pressure, are smaller. The magnitude of the envi- ronmental temperature change may be estimated as follows: on a warm day, the exterior temperature might increase 10°C to 15°C when going from the cargo building to the cargo bay of an airplane, going from perhaps 25°C to 40°C. Based on a dry ice sublimation temperature of -78°C or 195 K, the difference between the dry ice temperature and the ambient temperature would increase from 103 K to 115 K. Because the rate of heat transfer is proportional to the difference in temperature, if the temperature change persisted for long enough, the 15°C exte- rior temperature change would result in a 15% increase in the emission rate of carbon dioxide. A change in ambient pressure will occur as the aircraft gains altitude. Although aircraft cabins and cargo compartments are pressurized, the pressure maintained in the cabin or com- partment is not sea-level pressure* but a lower pressure. This lower pressure is limited to the equivalent of ambient pres- sure at an altitude of 2,440 meters (8,000 ft), corresponding to a pressure of 75.26 kPa.41 The reduction in pressure from the pressure at sea level to the pressure at 2,440 meters results in the lowering of the sublimation temperature of dry ice by about 3.4 K, from about 195 K to 191 K. With this pressure change, there are really two transient phases in the dry ice sublimation rate: the first is the rapid carbon dioxide gas release from the cooling down of the con- tents of the package to the new equilibrium dry ice sublima- tion temperature, which is about 3.4 K lower, and the second is the 4% increase in temperature difference between the new dry ice temperature and cargo compartment temperature. While a 4% increase in the emission rate from one individ- ual package is relatively small, if the carbon dioxide concentra- tion is near the limit, the aggregate effect could be significant because all packages on the airplane would be experiencing the transition at the same time. It is recognized that the sublimation rate will be affected by changes in the ambient pressure and temperature. The largest changes in temperature are expected to occur on the ground when the packages are sitting out in the hot sun before loading. The changes in pressure occur as the plane ascends to its cruising altitude and then again when the plane starts its descent. These transient phases are expected *Sea-level pressure is 101.325 kPa.

25 Many details of heat transfer can be included in a model: heat transfer to the inside wall of the box, the thermal con- ductivity of the EPS foam insulation, the thermal conductiv- ity of the cardboard, free or forced convection on the outside of the box, contact resistances, radiation losses, and so forth. But looking at the heat transfer model carefully, nearly all of the resistance to heat transfer is determined by the thickness of the EPS foam; everything else is either negligible or small. The heat transfer process that leads to dry ice sublimation and consequent carbon dioxide gas production is well enough understood that the observed sublimation rate for packages and insulated ULDs can be modeled adequately with a fairly simple one-dimensional heat transfer model. to be relatively brief and result in changes in the sublima- tion rate of a few percent, and it is believed that there will be long periods of time where steady-state heat-transfer models will be applicable. Summary of Dimensional Analysis and Heat Transfer Model Results The dimensional analysis results showed that the sublima- tion rate depends on the surface area of the package or ULD, the temperature difference between the inside and the out- side, and the thermal conductivity of the package walls, and that the mass of dry ice does not matter.