Numerical Simulation of Freezing Progress of Plasma

YＡＮＧ+Yu-tao　WANG+Chao

【Abstract】In this paper， we use gambit and fluent to study the time needed and the temperature distribution of the plasma in the three frozen methods of air-cooled， plate-contact and alcohol-immersion quick freezing， this numerical simulation was used to solve the limitation of the equipment in the actual experiment， so as to guide the experimental work.

【Key words】Component； Plasma freezing； Cooling rate； Freezing methods； Temperature distribution

Plasma quality is affected by the rate of rapid freezing of plasma[1-3].Plasma made from whole bold donations， in spite of being diluted with anticoagulants at the rate of 9：1， centrifuged filtered and frozen to -30℃ and store at -30℃，usually contains levels of proteins and coagulation factors within the normal ranges seen in freshly drawn plasma from healthy individuals[4]. Rapid freezing is considered to be important in assuring plasma quality， although clear data on an optimum freezing rate is stilling lacking.， rapid freezing is also logistically important for blood banks. According to the way of freezing， the plasma quick freezing[5]machine mainly includes air-cooled， plate-contact and liquid-immersion with using different quick-freezing methods， the cost of the equipment is different， the time required for freezing and the quality of the frozen plasma are different[6-7].

In this paper， the mathematical model of plasma was established for analyzing the heat transfer process of three plasma quick-freezing methods. By using ANSYS-FLUENT， the air-cooled， plate-contact and alcohol-immersion quick freezing progress were studied. The simulation results were recorded， analyzed and compared.

The plasma model of plasma was simplified as a rectangular model， and the temperature field of three different types of freezer was simulated. The characteristics of the change and distribution were analyzed and discussed， which provided the theoretical basis for the rapid freezing progress of plasma

The mathematical model of plasma was established by analyzing the rapid freezing of plasma. The temperature distribution and variation of three different freezing methods were simulated

1 Numerical Simulation of Plasma Freezing

Using Gambit to structure physical packed plasma model before the numerical simulation， and mesh model， the model will be imported into the Fluent to solve the model， and set parameter， set regional， set three methods boundary conditions （air-cooled， plate-contact， alcohol-immersion）， set temperature monitoring points， then carry out iterative calculation and analysis the final result.endprint

1.1 1Solution method

The freezing progress for quick-frozen plasma is numerically investigated by using a finite volume solver， ANSYS-FLUENT. In the mathematical model， the following assumptions are considered：

The model is assumed to be ideal cuboid due to the blood bank commonly use 200ml packed plasma.

Flow is turbulence.

The thermo-physical properties of the fluid are constant.

The main mode to transfer heat from freezing medium （air or alcohol） to plasma is convection heat transfer.

The initial plasma temperature of the freezing process is 277.15K， the freezing point temperature of the plasma is 265.15K and when the central temperature is 243.15K， the simulation is ended.

The initial temperature of air， plate and alcohol is 228.15K

Plasma consists of 90% of water and 9% of protein， so the plasma density was 1.025-1.030， and the plasma viscosity was 0.0000142 （Pa·s）. The specific heat capacity of plasma is 3000J/ （kg· K）.

Consequently the complicated heat transfer problem is changed to an unsteady three-dimensional， thermal property-variable conductive heat transfer problem with the first and third boundary conditions.

According the Fouriers law， the heat can be expressed as：

ΔQ■=-λ■ΔSΔτ（1）

The heat got through the unit of volume in times was：

Q1=-■（？蒽？鄣Vλ■ds）dτ（2）

According the Gauss law：

Q1=--■（？蒽？鄣Vλ？犖2Tdxdydz）dτ（3）

The released heat by the element of volume duringτ1toτ2：

■cρ[T（x，y，zτ1-T（x，y，z，τ2））]dxdydz=-■■（cρ■■）dxdydz（4）

According to the energy conservation law：

Q1=Q2（5）

So the governing equation can be written as：

ρc■=？荦·（λ？荦T）（6）

ρc■=■λ■+■+■λ■（7）

The initial condition is：

T=T0 τ=0

The boundary condition is：

-λ（■）=h（T-Tf），x=x1

-λ（■）=h（T-Tf），y=y1（8）

-λ（■）=h（T-Tf），z=z1

In the mobile phase-change interface， must satisfy：

Ts[x（t），y（t），z（t），τ]=T1[x（t），y（t），z（t），τ]=Tp（9）

λs■+■+■-λ1■+■+■=ρsL■+■+■（10）

The thermal conductivity before freezing：

λ1=ωλw+（1-ω）λp（11）

The thermal conductivity after freezing：

λ2=λ1+ωm（λi-λw）（12）

Where T and refer to the temperature and time， respectively， while the subscripts f represent the freezing medium；， c and stand for the density， specific heat and heat conductivity， respectively， while the subscripts w， p and i represent the water， protein and ice， respectively； s， l， p and L， stand for the solid phase， liquid phase， phase-change and latent heat.endprint

Because of the change of plasma thermal conductivity， UDF is used to set the thermal conductivity of plasma. The program is as follows：

#include “udf.h”

DEFINE_PROPERTY（user_ thermal， cell， thread）

{

float temp，th；

temp =C_T（cell， thread）；

{

If （temp<273.）

th= 5.5806-0.0122*temp；

else

th= 0.5592；

}

return th；

}

2 Results and discussion

Different forms of plasma freezer are used in the medical field， the comparison factor between them is the time required to complete the rapid freezing， that is， when the temperature of the central point of the plasma reaches -30 ℃. And the D-value between the surface temperature and the center temperature is also an important factor.

2.1 Air-cooled frozen

From Fig.1， we can draw the conclusions：

when the plasma center temperature down to -30℃， freezing time is 4143s， that is 69min， when the plasma temperature monitoring vertex down to -30℃， freezing time is 1380s， that is 23min， when the plasma monitoring middle point temperature drop to -30℃， freezing time is 3985s， it is 66min.

The rapid freezing of plasma from the plasma surface to the interior， the surface temperature is low， where the temperature at the apex and at the edge is lowest， because the disturbance of cold air is strengthened at the apex and at the edges， while the boundary layer is destroyed and the heat transfer is enhanced here.

From the angle of the cross section nephogram， the temperature distribution from the center to the circumference is annular， the center temperature is the highest， the temperature near the edge is parallel to the edge of the layer.

The temperature change of plasma center is divided into three sections， precooling， crystallization and cryogenic section， it is obvious that the constant temperature of crystallization phase is 265.15K， and accounts for the time in the whole frozen plasma in 3/4， cryogenic section of the plasma is larger than pre cooling section，

2.2 Plate-contact frozen

From Fig.2， we can draw the conclusions that，when the plasma center temperature down to -30℃， freezing time is 1461s， that is 24.4min； when the plasma temperature monitoring vertex down to -30℃， freezing time is 1415s， that is 23.6min， when the plasma monitoring middle point temperature drop to -30℃， freezing time is1450s， it is 24.2min.

The freezing of plasma begins with the contact surface of plasma and flat plate， and the temperature of the contact surface between plasma and plate is the lowest.endprint

From the angle of the cross section nephogram， at the beginning of freezing， the plasma temperature distribution is approximately parallel with the contact surface， and the center temperature is the highest. With the quick freezing， the temperature distribution develops gradually from the center to the periphery.

The temperature change of plasma center is divided into three sections， precooling， crystallization and cryogenic section， it is obvious that the constant temperature of crystallization phase is 265.15K， and in the whole frozen plasma in time is about the whole process of 4/7.

The temperature drop rate of the precooling section is larger than that in the cryogenic stage， which does not seem to accord with the law of the heat conductivity of the plasma in the cryogenic section than that in the precooling section. This is because， for contact heat conduction， the temperature D-value driving force plays a major factor， and the temperature D-value between the slab and the plasma in the precooling section is larger， so the temperature drop rate is greater.

2.3 Alcohol-immersion frozen

From Fig.3， we can draw the conclusions：

when the plasma center temperature down to -30℃， freezing time is 1235s， that is 20.6min， when the plasma monitoring middle point temperature drop to -30℃， freezing time is 1114s， it is18，6min.

The rapid freezing of plasma takes place from the plasma surface to the interior， and the surface temperature of the plasma block is lowest due to the contact of alcohol at -45℃， which is close to the temperature of the alcohol solution.

From the angle of the cross section nephogram， with the rapid freezing time， the temperature distribution is gradually stratified， and the center temperature is the highest.

The temperature change of plasma center is divided into three sections， precooling， crystallization and cryogenic section， it is obvious that the constant temperature of crystallization phase is 265.15K， and accounts for the time in the whole frozen plasma in 3/4.

3 Conclusions

In the three forms， the fastest freezing is alcohol immersion freezing， 20.6min. Followed by plate contact plasma fast freezing， 24.4min； time for the air-cooled plasma is the longest， 69min. The air cooled plasma quick freezing machine is the first generation of plasma quick freezing machine.

The plasma freezing process can be divided into 3 stages， the precooling section， the crystallization section and the deep freeze section. The plasma freezing time in the crystallization section is more than half of the whole frozen process， and the time is the longest.endprint

The air-cooled plasma freezing method is carried out from the plasma surface to the interior； the plate-contact and alcohol-immersion freezing is carried out by contacting to the center.

The plasma temperature distribution in plate-contact plasma freezing method is more uniform； however， the D-value of the surface temperature and internal temperature of air cooled plasma rapid freezing and alcohol immersion plasma freezing are larger.

The temperature profiles of air cooled plasma rapid freezing and alcohol immersion plasma freezing are similar， and both of them are annular from the periphery to the center， the temperature in the center is the highest. The frozen plasma by the plate-contact freezing is distributed like a rugby which the up and down temperatures of plasma， the interface are the lowest while the center temperature is the highest. The temperature in the center is the highest， and it gradually develops into a layered distribution when it is close to the contact surface between the plate and the plasma.

【References】

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Fig.1 AIR-COOLED

Fig.2 PLATE-CONTACT

Fig.3 ALCOHOL-IMMERSIONendprint