Phase-Change Materials (PCMs) are materials having a high heat of fusion which, by melting and solidifying at a certain temperature, are capable of storing and releasing large amounts of energy. Heat is absorbed or released when the material changes phase from solid to liquid or liquid to solid.
A PCM employed for drying a moist, porous medium facilitates fabrication and construction of paper-based product such as packaging materials. Drying of moist, porous materials is common for various articles where water is employed to hydrate a substance prior to drying for generating a finished medium. Configurations herein employ PCM (Phase Change Materials) in the drying process of moist, porous materials. A layered PCM-based process as disclosed herein substantially reduces drying time associated with production of such substrates. For example, paper based packaging materials are often arranged from a liquid or moist layer form, and dried as a planar sheet to form a finished medium having strength and resiliency. Such a planar based process lends itself well to the methods herein.
A method for drying a planar substrate such as paper sheet goods for packing materials includes layering a temperature sensitive material such as a phase change material (PCM) on a substrate, in which the substrate has a moisture content and is adapted for moisture removal to form a planar medium. A drying process disposes the substrate adjacent to a plurality of heat transfer elements, and heat the layered substrate to a predetermined temperature based on a specific heat of the temperature sensitive material. The heat transfer elements, such as rollers, advance the layered substrate in serial communication through pocket ventilation regions between the heat transfer elements, such that the pocket ventilation regions permit drying of the substrate enhanced by the specific heat of the temperature sensitive material. Upon drying, the layered substrate forms the planar medium suitable for use as a packing medium or other suitable application. The pocket ventilation regions are defined by a travel distance between the rollers for allowing temperature ranges corresponding to the PCM to facilitate drying and eradication of moisture from the paper planar substrate.
Conventional approaches have not investigated the effect of phase change material (PCM) on drying of moist porous medium. The current numerical approach investigates the transport characteristics associated with the drying process of a paper sheet in the presence of a layer of PCM. Configurations herein demonstrate the effect of adding a PCM layer within the paper sheet on the moisture removal and thus, on the drying process. The disclosed approach permits drying by utilizing the latent-heat of fusion associated with the PCM to improve the energy efficiency of paper drying process. To avoid any unnecessary complications, a very simple conventional paper drying process is considered where there is no felt, impinging air jets, or infrared emitters present. Besides the innovative concept of paper drying with layered PCM, this approach also provides a fundamental understanding for drying of a smart packaging paper which contains PCM to better control the temperature of the content inside the package.
The drying process involves the evaporation of liquid moisture inside the paper sheet due to its exposure to the heated drums as well as the hot air. The paper sheet is heated due to its contact to the heated cylinders from one side while it is exposed to ambient air on the other end in the process known as “pocket air ventilation” which is defined as the space in the dryer section between two adjacent cylinders, in case of single-tier system, or between three cylinders, in case of a two-tier system.
The foregoing and other objects, features and advantages of the invention will be apparent from the following description of particular embodiments of the invention, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.
In an example configuration depicted further below, the temperature sensitive material is a Phase Change Material (PCM) having a specific heat for releasing thermal energy for drying the hydrated substance. The specific heat of the PCM layer is based on the substrate material such as to release latent heat at an optimal time in the drying process of the substrate.
In an alternate arrangement, such production forms a second layer of the hydrated substance with the temperate sensitive material disposed between the layers, thereby forming a “sandwich” of substrate material around the PCM layer. The resulting substrate forms a planar material that is sufficiently rigid for forming a packaging material, or other purposes as discussed below.
Drying of a planar substrate comprising hydrated or moist porous materials occurs by passing the sheet defining the substrate along a series of heated rollers, alternating sides so that the heat of the rollers applies to both sides of the substrate.
The energy for the drying process comes from saturated steam injected under pressure into the cylinders. The steam pressures in conventional dryers range from 0-1000 kPa (0-145 psi). As the steam condenses inside of the dryer drum, the latent heat of evaporation is released. The heat is transferred through the condensate layer and dryer shell to the paper on the outside surface. During the pocket ventilation, the majority of evaporation occurs from the substrate. For the efficient drying of paper, it is preferable to remove the water vapor from around the web to increase the driving force for evaporation. Therefore, not only the surface temperature is important in the water removal from the paper sheet, the drying performance is dependent on the rate of water removal to the hot and dry air. For instance, if the movement of air in the pockets is too low or close to stagnation, higher temperatures in the pockets does not help in improving drying rate. There should be sufficient airflow in the pockets for efficient drying.
In the following stage and while the paper sheet 110′ (
Another example provides felt based substances to the porous medium to enhance the drying process. Felts support the web structure typically formed by the porous medium and enhance the heat transfer for drying as well as strengthen and improve the finished product. In a particular configuration, the approach herein provides method for forming a planar material by forming a hydrated substance on a planar surface, and applying a temperature sensitive material on the hydrated substance forming a layer having parallel planar structure to the hydrated substance. The hydrated substance may be a liquid or pulp-like form, and is sufficiently viscous or structured to hold a planar shape alone or with a felt base. The method forms the substrate 110 by drying the hydrated substance via the application of heat from the temperature sensitive material 150, in which the substrate has a generally planar shape.
The following steps illustrate the concept of drying process in the presence of a layer of PCM.
The PCM layer absorbs heat at its contact interface with the paper sheet 110′ during the heating period and undergoes solid-to-liquid phase change. During the pocket ventilation process, the PCM releases the stored heat due to the exposure of the sheet to the lower temperature, enhancing the water evaporation from the paper sheet. The pocket ventilation regions are selected based on a travel time of the layered substrate 110 between the heating elements and on a temperature range experienced by the layered substrate during travel through the pocket ventilation region
While releasing heat to the paper sheet, the PCM 150 solidifies during the pocket ventilation process. In the example arrangement, the layered temperature sensitive material is a phase change material (PCM) having a specific heat greater than a specific heat of the substrate, and the heat transfer elements are heated rollers for advancing the layered substrate in succession along the heated rollers. Alternate substances may be layered for increasing the efficiency of the drying process. The example configuration includes selecting the phase change material based on a temperature at which the PCM transitions to a solid for extracting latent heat from the PCM
The previous three steps repeat as the sheet goes to the next cycle.
Note that the PCM properties must be tuned to the corresponding drying operating conditions. The latent heat of melting of PCM is represented by the temperature dependent specific heat presented in
The approach shown in
The governing equations for the mass and energy balance through the sheet thickness are as follows. The mass balance equation is stated as:
The transport of liquid water inside the paper sheet is modelled through Darcy's law which governs the capillary pressure distribution inside the porous moist sheet,
The capillary pressure, Pca, is obtained from an empirical correlation:
Pca=0.84×105s−0.63 (3)
where 0<s<1 is the liquid saturation inside the porous medium and can be related to the moisture content through the following equation,
s=f(MC) (4)
This correlation determines the capillary pressure in wood as a function of saturation. It was developed with consideration of both experimental data and a mechanistic model and includes an irreducible saturation level of approximately 0.1, below which liquid flow was no longer possible. An additional expression for capillary pressure in paper needs to be developed, since the porous structure of wood is not the same as the structure of paper. The transport of vapor phase inside the paper sheet is governed through Fick's law:
The molecular diffusivity, Dv, is related to the operating temperature through:
The energy transfer inside the paper sheet is governed by the following energy balance equation,
The thermal mass of the paper sheet, ρsh, cpsh, is calculated based on the temporal and spatial distribution of liquid and vapor content as well as the properties of the dry paper sheet and its porosity:
ρshcpsh=ρfcpf(1−ε)+ρwcpwSε (10)
keff=kf(1−ε)+kwSε+ka(1−ε)ε (11)
where ε is the sheet's porosity which is assumed to be constant.
In the presence of PCM layer (see
and at the two interfaces of the paper and PCM layer, the following condition is valid: Tpaper=TPCM. It should be noted that the thermal contact resistance between the paper and PCM layer is neglected. While the thermal conductivity of both the paper and the PCM are assumed to be constant with temperature, the specific heat of the PCM is defined as a function of temperature illustrated in
The moisture evaporation is represented through the following boundary condition at the two ending nodes of the paper sheet 110′ (
where the mass transfer coefficient, km, is determined from the Chilton-Colburn form of the Reynold's analogy. The last term in Eq. (13) is an arbitrary factor included to represent reductions in moisture available for evaporation at the free surface during drying, since evaporation relationships available in the literature are based on the presence of a fully wetted surface. Use of an adjusted evaporation rate to reflect reductions in evaporation from the paper web during drying is similar to previous studies which forcibly decreased the sheet evaporation rate at pre-determined critical moisture content in order to simulate the falling rate period of drying. The vapor pressure, Pv is calculated using an exponential curve fit:
The heat exchange on the heated cylinder is estimated through the thermal contact conductance equation:
where the following empirical expression is used for the thermal conductance, hi
where 0.68<P<328.81 kPa, 0.084<BW<0.313 kg/m2, 4.8%<ω<60%, Tavg=85° C. The contact conductance increases with increasing pressure, increasing moisture levels, and decreasing sheet basis weight. It is assumed that the temperature of the heated cylinder, Tcyl, remains constant due to its continuous exposure to the superheat steam. On the opposite side of the paper sheet where it is exposed to convective air flow, the following convection boundary condition is applied:
q″conv=ha(T−Ta) (17)
The convection heat transfer coefficient is estimated through turbulent flow over cylinders 130 and flat plate, respectively, for the portion pertinent to the paper sheet on the heated drums and traveling in between. The boundary conditions presented so far must change in time to represent the motion of the paper sheet along the heated cylinders and within the pocket-drying region. The following two equations describe the temporal variation of the evaporation mass flux at the boundaries at the two ends of the paper sheet,
where th and tconv are times for the paper sheet being on the cylinder and traveling in between (pocket-drying region). This equation implies that the vapor can be transported to the ambient air only on the side exposed to it while the other end remains adiabatic. Note that the boundary condition is switched between the two ends to represent the travel of the paper sheet over and under subsequent cylinders. The temporal variation of the thermal boundary condition is analogous to Eq (18). with the sole difference of adiabatic boundary condition on the side contacting the cylinder being replaced by the thermal conductance equation, Eq. (16) to account for the heat exchange between the cylinders and the paper sheet.
As described earlier, in the conventional arrangement of paper-drying, the paper sheet undergoes a continuous series of heating cylinders 130 and ventilation processes between the rollers. In this setting, every heated cylinder 130 is followed by a duration of ventilation with the corresponding times obtained from the operating velocity and the length of each phase.
The pocket ventilation regions 160 occupy a distance based on a temperature fluctuation for permitting release of latent heat defined by the specific heat of the phase change medium 150. In a particular configuration, the pocket ventilation region is defined by a distance corresponding to seven rollers. Alternate arrangements may dispose a carrier layer 150′ (
The configuration with the PCM layer 150 shows a modest increase in the moisture content generated by the condensation due to the slightly slower temperature rise during the first heating cycle. As illustrated in
In the disclosed approach, the transport characteristics associated with the drying process of a paper sheet in the presence and absence of a layer of phase change material (PCM) was investigated. The numerical solution of the mathematical model provides the moisture and temperature profiles within the paper sheet in the presence and absence of PCM. Two different arrangement of the heated cylinders and air ventilation pockets have been introduced. The results demonstrate that drying can be enhanced by introducing the PCM layer 150 to improve moisture removal from the porous paper sheet.
While the system and methods defined herein have been particularly shown and described with references to embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.
This patent application claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Patent App. No. 62/005,447, filed May 30, 2014, entitled “DRYING USING PHASE CHANGE MATERIAL (PCM),” incorporated by reference in entirety.
This invention was made with government support under grant No. NSF CBET 1133353, awarded by the National Science Foundation. The government has certain rights in the invention.
Number | Name | Date | Kind |
---|---|---|---|
4202113 | Kankaanpaa | May 1980 | A |
20150114592 | Ide | Apr 2015 | A1 |
Number | Date | Country |
---|---|---|
102005041223 | Mar 2007 | DE |
0668396 | Aug 1995 | EP |
668393 | Jun 2002 | EP |
344058 | Jul 1972 | SU |
Entry |
---|
DE102005041223A1; retrieved Jun. 22, 2017. |
EP0668396A1; retrieved Jun. 22, 2017. |
Translation of DE102005041223A1; retrieved Jun. 22, 2017. |
Translation of EP0668396A1; retrieved Jun. 22, 2017. |
International Search Report for PCT/US2015/033482; dated Sep. 17, 2015; 2 pages. |
Number | Date | Country | |
---|---|---|---|
20150345861 A1 | Dec 2015 | US |
Number | Date | Country | |
---|---|---|---|
62005447 | May 2014 | US |