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This study made it possible to determine by the application of thermodynamics in finished time, the points of instruction necessary to the development of a regulation system for the rationalization of the power consumption in a cold store. These points were obtained by determining the optimal variations of temperature as well to the condenser and the evaporator corresponding to the minimum capacity absorptive by the compressor for a maximum COP.

Response to the demands imposed by the market, of the directives related to the rational use of energy and the safeguarding of the environment, the design of the current cold stores requires to a certain extent, taking into account of various constraints, in particular: thermodynamic constraints (minimization of the irreversibilities); technological constraints (pressure losses, losses of fluid cooling) and economic constraints (value for money) [

These optimal values will make it possible for the system of regulation to adapt the operation of the installation to the temperature variations for a COP maximum (refrigerating COP = production/consumption). The COP in addition expresses the viability of a refrigerating cycle. Optimization will consist in determining the optimal variation of temperature

・ Material

The cold store

Technical data of the installation:

・ Method for Calculation

The operation of the cold stores with mechanical compression of the vapors has for cycle of reference, the ideal cycle of reversed Carnot. In accordance with the second principle of thermodynamics: heat cannot pass from the cold source of T_{f} temperature to the hot spring of temperature T_{a} without consuming work of the external medium.

The ideal cycle of reversed Carnot is reversible as well internal as (Equation (1)) external in other words the processes of compression and of relaxation are with constant entropy and the transfer of heat between the fluid and the source is carried out with infinitesimal differences in temperature. A multi-field analysis of the refrigerating cycle of Carnot highlights the increase in the surface of transfer of heat necessary to the process of vaporization and condensation as the differences in temperature are reduced, is:

with: Exchanged total Q = heat; k = heat exchange coefficient; ∆T = difference in temperature; A = thermal heat-transferring surface.

When the transfer of heat takes place in extreme cases reversible of way, we have

On the other hand, for an installation producing a real heat flow Q_{0} to the evaporator, the transfer of heat supposes the existence of a finished difference ∆T in temperature, the cycle of Carnot is irreversible external and the time of contact of the fluid with the sources of heat of surface A limited also has a finished value. The irreversible optimization of cycle will consist in maximizing its performance by the maximization of its coefficient of performance.

The energy assessment of the installation is given by expression (2):

And the coefficient of performance of the installation, by Equation (3):

It is observed that for a mass throughput of the refrigerating agent, the energy assessment can be also written in the form of Equation (4):

If one poses

The entropic assessment as for him is written by Equation (6):

The equations of heat transfer to the evaporator and the condenser are given by expressions (7) and (8):

with

with

From two Equations (7) and (8), it results the entropic expression (9):

The dimensional notations are declined as it follows:

The parameters to be taken into account for the optimization of the installation are the following ones:

The variables to be taken into account for the optimization of the installation are the following ones: Independent variables:

・ A dimensional refrigerating power (Equation (12)):

・ A dimensional calorific power of the condenser (Equation (13)):

・ A dimensional mechanical work is:

・ The coefficient of performance becomes:

That is to say:

By replacing the notations previously established in the entropic equations, we obtain:

However

One has:

By simplifying the room temperature of Equation (20), then by dividing the equation by the coefficient of heat exchange total K, one has:

However,

In addition, it is known that

In other words Equation (23), can be still written in the form:

It results from it that:

Consequently after substitution

where

After some simplifying transformations of the denominator

We obtain a final expression

Let us pose

The value which cancels this derivative makes it possible us to obtain the maximum value and consequently the coefficient of performance

And

By replacing

We can express according to in the form:

What enables us to obtain:

・ minimal a dimensional calorific power (Equation (34)):

・ minimal a dimensional mechanical work (Equation (35)):

The coefficient of maximum irreversible performance of the installation (Equations (36) or (37)):

If

Carnot.

・ and the output of the installation is the report of the performance coefficient of the ideal cycle of Carnot (Equation (38)):

out in an isothermal way, [

So that the installation produces a real heat flow

performance

tion W to obtain is very high, the coefficient of performance is also null. To maximize the coefficient of performance in our case means a minimal consumption of energy W_{min} (Equation (35)). Optimization will consist in determining the optimal variation of

evaporator temperature corresponding to a consumption minimal of energy for obtaining flow. In substituent the dimensional optimal temperature

It goes without saying we always seek to obtain a better coefficient of refrigerating performance of the installation while keeping in mind that it should not exceed its theoretical maximum with knowing the coefficient of performance of Carnot. It should be noted that in practice, it was noted that when the cold stores function out of their optimal operating range, they see their refrigerating power decreased because of internal and external irreversibilities. Those can even reduce the coefficient of performance to zero, thus the cold store is then likely to function without producing refrigerating power (exactly like a disconnected car). The optimal operating ranges obtained in our study (

- Refrigerating power: 497.6 kw; - Power of the condenser: 666 kW; - Coefficient of performance COP: 2.95; | - Total thermal conductance: 118,657 W/k; - Temperature of the refrigerant: 280 K; - Room temperature: 308 K. |
---|

performance 5.88. This coefficient of performance is largely higher than that is presented by the manufacturer 2.95, for the simple reason that in our study we do not take account of the losses caused by the internal irreversibilities. Lastly, to guarantee an optimal operation of the installation, the system of regulation of this one will have to be programmed according to the points of instruction of the optimal operating ranges.

Ebale, L.O., Mabiala, B. and Tomodiatounga, D.N. (2016) Optimization by Thermodynamics in Time Finished of a Cold Store with Mechanical Compression of the Vapor. Journal of Electronics Cooling and Thermal Control, 6, 139-152. http://dx.doi.org/10.4236/jectc.2016.64013

A: Heat-transferring surface

A_{c}: Surface of the condenser

A_{0}: Surface of the evaporator

BEAC: Bank of the States of Central Africa

BP: Low pressure

COP: Coefficient of performance

h: Enthalpy

HR: Relative humidity

K: Coefficient of total heat exchange by convection

m: Mass throughput

P: Pressure

PMB: Dead bottom centre

PMH: Not high dead

T: Temperature

t: Time of contact of the fluid with the exchangers (evaporator and condenser)

v: Specific volume

W: Consumed mechanical energy

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