# Why receivers and accumulators in refrigeration cycles?

Receivers or accumulators are often used in refrigeration cycles. They are basically very simple components, but their function in the overall system is quite complex. We want to take a closer look at them and understand the effects on the overall refrigeration system.

Manuel Gräber

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September 4, 2020

djsrki / 123rf.com

## Everything depends on everything

In this article we assume that the reader is already familiar with the basics of refrigeration and is familiar with a simple refrigeration cycle. Otherwise, it is better to start first with the basics of refrigeration cycles. As shown in the figure below, a simple refrigeration cycle consists of the components compressor, condenser, expansion valve and evaporator.

In lectures for engineers thermodynamic cycles such as a standard refrigeration cycle are presented and calculated. In the calculations, some variables are taken as given. These are, for example, the two pressure levels, the compressor outlet temperature, superheating and subcooling. With these specifications the cycle can be calculated explicitly, as shown in the following log-ph-diagram, starting at point 1.

In reality, however, this explicit connection does not exist. Rather, everything depends on everything. There is no clear causal relationship between pressures, mass flow and superheating or subcooling. These variables all influence each other. This makes an explicit calculation for practical problems impossible, iterative numerical solution methods must be used.

For the physical understanding of a refrigeration cycle it is helpful to divide the individual physical quantities into degrees of freedom and unknowns, and not to think in predefined causal relationships. To have an determined overall system, the number of degrees of freedom and unknowns must be equal.

## Degrees of freedom and unknowns

First we look at a simple refrigeration cycle without receiver or accumulator, as in the figure above. The size of the evaporator and condenser and the efficiency of the compressor are variable. We neglect pressure losses in the heat exchangers. The inlet temperatures and mass flows of the secondary heat transfer fluids are given. This results in the following degrees of freedom for the design of the system:

• Compressor speed
• Compressor efficiency
• Expansion valve opening
• Size of the evaporator
• Condenser size

On the other hand there are the following unknowns:

• Evaporation pressure
• Condensation pressure
• Superheat before compressor
• Temperature after compressor
• Subcooling after condenser
• Mass flow rate of the refrigerant

The first 5 unknowns define the cycle in a ph diagram. And together with the 6th unknown (mass flow rate) the heat flows and powers are given.

In thermodynamics lectures it is common practice to define a refrigeration cycle with specifications for these unknowns. If you, as a finished engineer, want to select the components for a refrigeration circuit in practice, you are faced with a problem: The 6 unknowns have only 5 degrees of freedom. That means with these 5 degrees of freedom I cannot set all 6 unknown quantities independently of each other. One of these unknown variables would always dependent on the other variables.

The solution of the riddle is a missing degree of freedom, the refrigerant charge. What every refrigeration technician knows from practical experience, many engineers with basic knowledge of thermodynamics are not yet aware of. Refrigerant charge is an important parameter in the operation of refrigeration cycles. It has a great influence on the position of cycles in a ph diagram.

## More refrigerant leads to higher pressures

A refrigeration cycle is a closed system with constant total fluid mass, apart from unwanted leakages. Like any closed thermodynamic system, the mass of the fluid stored in it has a direct influence on its state, described by state variables such as pressure and temperature. Just like a bicycle tire, the pressure increases when more mass is added.

A special feature of the refrigeration cycle is that fluid is not only present as gas, as in a bicycle tire. Instead, there are both liquid and gaseous phases at different points in the cycle. This makes it a bit more complicated, you can even construct cases where the pressure initially drops even though you add refrigerant mass. But as a general rule of thumb, more mass means higher pressures. It should be mentioned again that resulting pressure levels depend not only on the refrigerant charge, but also on all other degrees of freedom listed above.

The two pressure levels (evaporation and condensing) have a significant influence on the efficiency of a refrigeration cycle. This leads to the fact that for given boundary conditions (especially secondary inlet temperatures) there is an optimal refrigerant charge at which energy efficiency is at its maximum. Unfortunately, this optimal refrigerant charge also changes when boundary conditions change. This means that a refrigerant cycle that is optimally filled at 20°C outside temperature is anything but optimally filled at 30°C. In this case, the energy efficiency is unnecessarily low.

## Self-regulating buffer vessels

In order to optimize efficiency of refrigeration cycles under varying boundary conditions, buffer vessels are often installed to store not needed refrigerant and release it when needed.

The basic functional principle is separation of gaseous and liquid phase by gravity. The buffer vessel can either be installed on the high-pressure side after the condenser, where they are called receiver. Or on the low pressure side after the evaporator, where they are called accumulator. These components are designed to provide saturated liquid at receiver outlet and saturated vapor at accumulator outlet. Both cycle variants are shown here:

Depending on the state of incoming refrigerant, the level of liquid refrigerant in the buffer vessel increases or decreases. And since liquid density is much greater compared to that of gas, stored refrigerant mass changes with the filling level.

These buffer vessels are self-regulating in a closed refrigeration cycle, provided only one buffer vessel is installed.

## The stationary state

In order to understand the self-regulating behavior, some considerations about the stationary state of the entire system are helpful. Due to the separation behaviour of buffer vessels, there is always saturated liquid or saturated vapor at its outlet. If we assume a stationary state, total energy and mass of the buffer vessel must remain constant. That means the incoming mass flow rate is equal to the outgoing mass flow rate. And – neglecting pressure losses – refrigerant state must be the same at inlet and outlet. From this follows directly:

• At receiver inlet and condenser outlet must be saturated liquid in a stationary state (exactly 0 K subcooling).
• At separator inlet and evaporator outlet must be saturated vapor in a stationary state (exactly 0 K superheating).

The following conclusion can be drawn from these considerations: By installing a buffer vessel in a refrigeration cycle, one loses the degree of freedom “refrigerant charge” and at the same time fixes one of the unknowns superheating or subcooling to zero.

This shows, for example, that it makes little sense to use the expansion valve to control superheat if a suction-side accumulator is installed in a cycle.

## Influence on dynamics

The previous considerations refer exclusively to the stationary state of a refrigeration cycle. But a buffer vessel also has a decisive influence on the dynamics.

When changing from one stationary operating point to another, for example by changing the external recooling temperature at the condenser, a shift of mass in the refrigeration cycle takes place. Refrigerant is stored in or removed from the buffer vessel. This dynamic is strongly dependent on the operating point or, expressed mathematically, is strongly non-linear.

As an example we consider the case that mass has to be removed from a suction side accumulator. As always, we have saturated vapor at the outlet. The buffered refrigerant is present as a liquid. To get it out of the accumulator, it must evaporate. However, the required evaporation enthalpy must be supplied somehow. If no significant heat flow enters the component from the outside, the only possibility is to supply the required evaporation enthalpy via an increased enthalpy flow and thus superheated refrigerant at the inlet. However, the maximum possible superheating is limited by other boundary conditions (e.g. minimum suction pressure). Therefore, the needed internal mass transfer can only take place very slowly. It is often the slowest and thus for the control design most important dynamic in a refrigeration cycle.

## Refrigeration cycle simulation

A receiver or accumulator has a variety of effects on a refrigeration cycle – both on the stationary operating points that are set and on the dynamics. In order to take these effects fully into account when designing a cycle and controls, computer simulation is very helpful. With the model library TIL we at TLK offer a professional tool to perform such calculations. Please contact us if you want to learn more about it!

Dr.-Ing.

Manuel Gräber

Managing Director

TLK Energy

Dr.-Ing. Manuel Gräber works on modeling, optimization and controlling of thermal systems since 2008. He received his PhD at TU Braunschweig after finishing his thesis on “Energy-Optimal Control of Refrigeration Processes”. As research assistant at TU Braunschweig and employee of TLK-Thermo GmbH, Manuel Gräber carried out numerous research and development projects with various partners from industry. His focus is the combination of a broad theoretical knowledge base in different disciplines with practical experience of concrete engineering projects.