Advancement of a Cascade Refrigeration System for Enhanced Blood Plasma Preservation

2.1 Materials selection

Blood's liquid component is called blood plasma. Plasma, serving as the conveyance system, delivers essential nutrients to the cells of the body's organs and transports waste generated by cellular metabolism to be eliminated by the kidneys, liver, and lungs. The image is a yellowish liquid as shown in Figure 2. Table 1 characterised the physiochemical properties of blood plasma ranging appearance, heat capacity, boiling and melting points, freezing and storage temperatures among others.

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Figure 2. The human fresh frozen plasma

2.2 Design parameters

The following parameters were considered for the design of a two-stage cascade refrigeration system.

For the Low Temperature Cycle (process 1-2-3-4).

The Refrigerant is R410A, Evaporator temperature, T_EL=-35℃, Evaporator pressure, P_EL=0.2196MPa, Condenser temperature, T_CL=18℃ and Condenser pressure, P_CL=1.3613MPa.

For the High Temperature Cycle (process 5-6-7-8).

The Refrigerant is R404A, Evaporator temperature, T_EH=12℃, Evaporator pressure, P_EH=0.8772MPa, Condenser temperature, T_CH=40℃, Condenser pressure, P_CH=1.8148MPa, Ambient temperature, T_AP=35℃, Refrigeration capacity, Q_R=1kW and Temperature overlap, T_O=T_CL-T_EH=18℃-12℃=6℃.

Table 1. Summary of physiochemical properties of blood plasma

2.2.1 Refrigeration selection

The selection of R410A and R404A refrigerants in this study is purposely targeted rapid freezing and storing blood plasma proteins for shelf-life increase based on the refrigerants thermophysical properties of low-temperature values as shown in Table 2. The following factors were considered among others such as better mass flow rate, high refrigerating effect, high discharge pressure, short time for low-temp. attainment, better C.O.P, affordability (cheap) and availability and existing refrigeration components favour R410A and R404A [2, 3, 12, 13].

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Figure 3. CAD overview of the cascade system and blood plasma assembly

In many industries and medical sectors, the time to achieve the desired temperature is paramount utmost. Refrigerants R410A and R404A were chosen for rapid homogeneous freezing and storing fresh blood plasma in terms of refrigerating Effect and Discharge Pressure, R410A is slightly better than that of R22, achieving low-temperature in short time, R404A is recommended domestic refrigeration purpose, R410A is preferred over R22, mass flow rate, R404A is better when compared with R410A and R22, and thermodynamic properties for all refrigerants [14-17]. The CAD overview of the dev eloped system is presented in Figure 3.

Table 2. Refrigerants’ main properties of R404A and R410A [12, 13]

2.2.2 Heat load determination

In this study, the heat load is segmented into five specific categories: Heat conducted through the walls of the cooling area, thermal load from the products, heat influx from infiltration, heat absorbed from packaging, and operational thermal loads.

Heat transfer via evaporator walls. Wall heat gain, or wall leakage load, refers to the rate at which heat is transferred through the walls of the refrigerated space from outside to inside via conduction. This heat transfer through the evaporator walls depends largely on the temperature difference between the interior and exterior of the chamber, as well as factors such as the walls' thermal resistance, thickness, and surface area. Therefore, these factors are carefully considered in the design.

The external dimensions are 1.03 meters in length, 0.65 meters in width, and 0.50 meters in depth.

The internal dimensions are 0.62 meters in length, 0.49 meters in width, and 0.42 meters in depth.

Ambient product temperature, T_AP=35℃=08 K

Temperature of frozen plasma, T_FP=-35℃=238 K

Change in temperature, $\Delta T$=T_AP–T_FP=(308-238) K=70 K

The plate material is stainless steel sheet (0.001 m thick)

The insulating material is Styrofoam (0.1m thick)

The surface area covered by the insulator, A_ins is:

$\begin{gathered}\mathrm{A}_{\mathrm{ins}}=\{[(1.03 \times 0.65)+(1.03 \times 0.50)+(0.65 \times 0.50)] \times 2\}  \mathrm{m}^2 \\ \mathrm{~A}_{\text {ins}}=3.02 \mathrm{~m}^2\end{gathered}$             (1)

Hence, the speed at which heat conducts through the refrigerated walls space, $\dot{Q}_{\text {cond}}$ is defined as contained in [16].

$\dot{Q}=\mathrm{UA} \Delta T$            (2)

$\begin{gathered}\dot{Q}_{\text {cond}}=(0.314 \times 3.02 \times 70) \mathrm{W} \\ \dot{Q}_{\text {cond}}=0.0664 \mathrm{~kW}\end{gathered}$            (3)

The amount of heat transferred, denoted as $Q_c$, through the evaporator walls during three hours of continuous operation is approximated in the following manner:

$Q_{\text {cond}}=\dot{Q}_{\text {cond }} t$              (4)

$Q_{\text {cond}}=717.12 \mathrm{~kJ}$                (5)

The product heat load. The thermal discharge from the items intended for storage holds significant importance, particularly in cold storage facilities. In this context, the product load refers to the collective mass of the blood plasma (250 ml) and its bag each.  

The cooling chamber is designed to take in 16 pieces of blood plasma bags at a time.

$m_{t p}=0.256 \times 16=4.1 \mathrm{~kg}$           （6）

Therefore, the capacity of the evaporator (cooling chamber load on isolation) is 4.1 kg of blood plasma bags.

In other to determine the product load ($Q_{p r o d}$) of the cascade system, the load to be considered in the cold storages are divided into three groups via.

a. Chilling Load above Freezing, $Q_c$

This refers to the heat required to cool blood plasma from 30℃ to -0.59℃, the temperature at which the plasma begins to freeze. The chilling load above the freezing point is influenced by factors such as the mass of the product, its average specific heat above freezing, the initial temperature of the product, the target final temperature, and the duration of the chilling process.

$\mathrm{Q}_{\mathrm{c}}=\mathrm{m}_{\mathrm{tp}} \mathrm{c}_{\mathrm{p}} \Delta \mathrm{T}_1$         (7)

$\mathrm{Q}_{\mathrm{c}}=573.46 \mathrm{~kJ}$        (8)

b. Cooling load below freezing, $Q_{b f}$

This represents the heat acquired during additional cooling, transitioning from -0.59℃ to -35℃. The cooling requirement below freezing is contingent upon factors such as the product's mass, average specific heat of the items below freezing, current storage temperature, desired freezing temperature (the temperature within the refrigerated space), and the duration of cooling.

$\mathrm{Q}_{\mathrm{bf}}=\mathrm{m}_{\mathrm{fp} \times} \mathrm{C}_{\mathrm{fp} x} \Delta \mathrm{~T}_2$          (9)

$\mathrm{Qbf}_{\mathrm{bf}}=282.16 \mathrm{~kJ}$        （10）

c. Freezing load, $Q_f$

This refers to the heat absorbed during the transition of blood plasma from -0.59℃ to frozen plasma (latent heat of freezing). The freezing requirement is influenced by factors including the product's mass, its latent heat of freezing, and the duration of freezing.

$\mathrm{Qf}_{\mathrm{f}}=\mathrm{m}_{\mathrm{fp}} \mathrm{L}_{\mathrm{fp}}$        (11)

$\mathrm{Q}_{\mathrm{f}}=1258.70 \mathrm{~kJ}$         (12)

Therefore, the product heat load of the cascade system, $Q_{\text {prod }}$ is calculated as follows:

$\mathrm{Q}_{\text {prod}}=\mathrm{Q}_{\mathrm{c}}+\mathrm{Q}_{\mathrm{f}}+\mathrm{Q}_{\mathrm{bf}}$       (13)

$\mathrm{Q}_{\text {prod }}=195.77 \mathrm{~W}$        （14）

Heat increase due to infiltration. During the regular operation of a refrigerated facility, doors are occasionally opened to facilitate the movement of goods. Infiltration load stands as a significant factor within refrigeration systems. Infiltration air denotes the air that infiltrates a refrigerated enclosure through gaps and door openings, driven by the temperature contrast between the internal and external air, along with the dimensions of the refrigeration unit.

$Q_{i n f}=m_{\inf } C_{\mathrm{a}}\left(T_o-T_i\right)=1.55 \mathrm{~W}$           (15)

Heat increase from packaging. A considerable proportion of refrigerated products are often packaged, comprising potentially over 10% of the product's total weight. Packaging materials vary and may include plastic, steel, wood, glass, or any other material with low specific heat capacity. For instance, in this scenario, 250 grams of liquid plasma are each enclosed in plastic bags and suspended using hangers.

$Q_{p k}=m_{p k} C_{p k}\left(T_o-T_i\right) \times 10^3$           （16）

$Q_{p k}=4.25 \mathrm{~W}$       (17)

Operational load. The heat introduced into the system through activities such as lighting, door openings, and similar processes constitutes the service load. This operational load is addressed as a collective entity and presumed to represent 1% of the heat generated from the other two sources. Therefore, the service load, denoted as $Q$_serv, is calculated according to Eq. (18):

$Q_{\text {serv}}=\left(Q_{\text {cond }}+Q_{\text {prod}}+Q_{\text {inf }}+Q_{p k}\right) \times 1 \%$          （18）

$Q_{\text {serv}}=9.19$         (19)

2.2.3 Total heat load

This is the summation of all the heat loads, $Q_T$ as given by:

$\mathrm{Q}_{\mathrm{T}}=Q_{\text {cond }}+Q_{\text {prod }}+Q_{\text {inf }}+Q_{p k}+Q_{\text {serv }}$     （20）

$\mathrm{Q}_{\mathrm{T}}=927.88 \mathrm{~W}$          (21)

For the factor of safety, we take 40%:

$\begin{gathered}\mathrm{Q}_{\mathrm{TCL}}=\mathrm{Q}_{\mathrm{T}}+\mathrm{Q}_{\mathrm{T}} \times \mathrm{SF} =1.299 \mathrm{~kW}\end{gathered}$           （22）

However, twhe refrigeration system's performance is measured based on the quantity of heat it can extract within a specific duration. Assuming it takes 3 hours to absorb the mentioned heat load, the refrigeration capacity, represented as Q_Ref for the system is calculated accordingly. 

$Q_{\text {Ref}}=1.299 \mathrm{~kW}$          （23）

2.2.4 Compressor analysis

The designed compressor size is 1.74 hp taking one horsepower as 0.746 hp. The required compressor size to produce the refrigerating capacity of 1.299 kW for three hours daily is approximately 2 hp (1 hp compressor each). The Evaporator and Condenser were selected and bought based on this compressor capacity [15].

2.2.5 Design of evaporator

The refrigeration capacity is calculated by using Eq. (24) taking u = 0.04345 kW/m²K  

 $Q_{\text {Ref }}=\mathrm{UA} \Delta \mathrm{T}=1.299 \mathrm{~kW}$            （24）         

Therefore, the coil length in the evaporator becomes;

$L=16.99 \mathrm{~m}$         (25)

Length of coil in one turn:

$\mathrm{L}_{\text {te }}=(0.07)+(0.145 \times 2)$           （26）

$\mathrm{L}_{\mathrm{te}}=0.36 \mathrm{~m}$              （27）

The quantity of coil revolutions around the inner section of the evaporator, denoted as $\mathrm{N}_{\mathrm{te}}$, is determined by:

$\mathrm{N}_{\mathrm{te}}=\frac{\text { Length of coil }}{\text { Length of coil in one turn }}$               (28)

$\mathrm{N}_{\mathrm{te}}=47$ turns               (29)

The internal depth of the loading area within the evaporator measures 0.42 meters. The spacing between consecutive coil loops, denoted as $G_{\text {coil}}$, is specified as follows:

$G_{\text {coil }}=\frac{D_e}{N_{t e}}$              （30）

$G_{\text {coil }}=0.0089 \mathrm{~m}$            (31)

2.2.6 Development of low temperature cycle condenser

The heat discharged by the LTC condenser, denoted as QCL, is characterized by:

$\mathrm{Q}_{\mathrm{CL}}=\dot{m}_L\left(\mathrm{h}_2-\mathrm{h}_3\right)$              （32）

$\mathrm{QcL}=1.726 \mathrm{~kW}$               (33)

The rate at which liquid refrigerant flows, denoted as $V$, is defined by the following formula:

$V=6.55 \times 10^{-6} \mathrm{~m}^3 / \mathrm{s}$           (34)

Subsequently, the area of the condenser tube's cross-section, A, is determined by Eq. (35):

$A=\frac{v}{V}$           (35)

$\mathrm{A}=12.89 \times 10^{-6} \mathrm{~m}^2$             (36)

The internal diameter of the condenser tube is computed as follows: 

$A=\frac{\pi d_i^2}{4}$      (37)

$\mathrm{d}_{\mathrm{i}}=4.05 \mathrm{~mm}$        (38)

The internal diameter of the tube was so small because of the small load of the cascade system. But the internal diameter that will be considered for the fabrication will be a tube with inner diameter of 6 mm.

2.3 Development of HTC condenser

The heat discharged by the HTC condenser, denoted by $\mathrm{Q}_{\mathrm{CH}}$, is characterized by.

2.3.1 Design of HTC condenser 

The heat rejected by HTC condenser, $\mathrm{Q}_{\mathrm{CH}}$ is defined by Eq. (36):

$\mathrm{Q}_{C H}=\dot{m}_H\left(\mathrm{~h}_6-\mathrm{h}_7\right)$             (39)

$\mathrm{Q}_{C H}=1.954 \mathrm{~kW}$           (40)

Volumetric flow rate of liquid refrigerant:

$\mathrm{V}=1.617 \times 10^{-5} \mathrm{~m}^3 / \mathrm{s}$            (41)

The cross-section area of the condenser tube is given by:

$A=\frac{V}{v}$          (42)

$\mathrm{A}=3.183 \times 10^{-5} \mathrm{~m}^2$         (43)

Inner Diameter of the condenser tube is calculated thus:

$A=\frac{\pi d^2}{4}$            (44)

$\mathrm{d}=3.18 \mathrm{~mm}$               (45)

The internal diameter of the tube was so small because of the small load of the cascade system. But the internal was considered for the fabrication will be a tube with inner diameter of 6 mm.

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Figure 4. The developed cascade system

The machine's parts, including a compressor for HTC and LTC each, a condenser, two expansion valves, and an electrical fan motor, were acquired and linked to the copper pipes using bolts, nuts, rivets, welding, soldering, and riveting as needed for a unitary mechanism. The machine was filled with the appropriate working fluid (R410A and R404A, respectively, for HTC and LTC's respective refrigerants), and it was then linked to an electrical supply for a test run. While testing the system to determine its coefficient of performance, pressure and temperature detectors (gauges and digital thermocouples) were mounted at each compressor's intake and output, condenser, and evaporator for quantification of the corresponding pressure and temperature for computation. The fabricated cascade system is presented in Figure 4.