# Receiver Accumulator (2P)

Tank with liquid and vapor volumes of variable proportion

**Libraries:**

Simscape /
Fluids /
Two-Phase Fluid /
Tanks & Accumulators

## Description

The Receiver-Accumulator (2P) block represents a tank
with fluid that can undergo phase change. The liquid and vapor phases, referred to as
*zones*, are modeled as distinct volumes that can change in size
during simulation, but do not mix. The relative amount of space a zone occupies in the
system is called a *zone fraction*, which ranges from
`0`

to `1`

. The vapor-liquid mixture phase is not
modeled.

In an HVAC system, when this tank is placed between a condenser and an expansion
valve, it acts as a receiver. Liquid connections to the block are made at ports
**AL** and **BL**. When the tank is placed between
an evaporator and a compressor, it acts as an accumulator. Vapor connections to the
block are made at ports **AV** and **BV**. A fluid of
either phase can be connected to either port, however the fluid exiting from a V port is
in the vapor zone and an L port is in the liquid zone. There is no mass flow through
unconnected ports.

The temperature of the tank walls are set at port **H**.

The liquid level of the tank is reported as a zone fraction at port
**L**. If the liquid level reports `0`

, the tank
is fully filled with vapor. The tank is never empty.

### Heat Transfer

The total heat transfer, *Q _{H}*, is the sum
of the heat transfer in the liquid and vapor phases:

$${Q}_{\text{H}}={Q}_{\text{L}}+{Q}_{\text{V}}.$$

The portion of the heat transfer that goes to the liquid volume,
*Q _{L}*, accounts for the heat transfer
between the liquid and the wall and between the liquid and the vapor,

$${Q}_{\text{L}}=\left({S}_{c}+{z}_{L}{S}_{s}\right){\alpha}_{L}\left({T}_{H}-{T}_{L}\right)+{S}_{c}{\alpha}_{LV}\left({T}_{V}-{T}_{L}\right)$$

where:

*z*_{L}is the liquid volume fraction of the tank.*S*_{c}is the**Tank cross sectional area**parameter.*S*_{s}is surface area of the tank side, which the block calculates from the volume and tank cross-sectional area, assuming that the tank is cylindrical.*α*_{L}is the**Liquid heat transfer coefficient**parameter.*T*is the temperature of the tank wall._{H}*T*is the temperature of the liquid._{L}

The block calculates the heat transfer coefficient between the liquid and the vapor as

$${\alpha}_{LV}=\frac{1}{\frac{1}{{\alpha}_{L}}+\frac{1}{{\alpha}_{V}}}.$$

The portion of the heat transfer that goes to the vapor volume,
*Q _{V}*, accounts for the heat transfer
between the vapor and the wall and between the liquid and the vapor,

$${Q}_{V}=\left({S}_{c}+\left(1-{z}_{L}\right){S}_{s}\right){\alpha}_{V}\left({T}_{H}-{T}_{V}\right)+{S}_{c}{\alpha}_{LV}\left({T}_{L}-{T}_{V}\right),$$

where:

*α*_{V}is the**Vapor heat transfer coefficient**.*T*is the temperature of the vapor._{V}

The liquid volume fraction is determined from the liquid mass fraction:

$${z}_{\text{L}}=\frac{{f}_{\text{M,L}}{\nu}_{\text{L}}}{{f}_{\text{M,L}}{\nu}_{\text{L}}+\left(1-{f}_{\text{M,L}}\right){\nu}_{\text{V}}},$$

where:

*f*is the mass fraction of the liquid._{M,L}*ν*is the specific volume of the liquid._{L}*ν*is the specific volume of the vapor._{V}

### Energy Flow Rates Due To Phase Change

When the liquid specific enthalpy is greater than or equal to the saturated liquid specific enthalpy, the mass flow rate of the vaporizing fluid is:

$${\dot{m}}_{\text{Vap}}=\frac{{M}_{L}\left({h}_{L}-{h}_{L,Sat}\right)/\left({h}_{V}-{h}_{L,Sat}\right)}{\tau}.$$

where:

*M*is the total liquid mass._{L}*τ*is the**Vaporization and condensation time constant**parameter.*h*is the specific enthalpy of the liquid at the internal node._{L}*h*is the saturated liquid specific enthalpy at the internal node._{L,Sat}*h*is the specific enthalpy of the vapor._{V}*h*is the saturated vapor specific enthalpy._{V,Sat}

The energy flow associated with vaporization is:

$${\varphi}_{\text{Vap}}={\dot{m}}_{\text{Vap}}{h}_{V,Sat},$$

When the liquid specific enthalpy is lower than the saturated liquid specific
enthalpy, no vaporization occurs, and *ṁ _{Vap} =
0*.

Similarly, when the vapor specific enthalpy is less than or equal to the saturated vapor specific enthalpy, the mass flow rate of the condensing fluid is:

$${\dot{m}}_{\text{Con}}=\frac{{M}_{V}\left({h}_{V}-{h}_{V,Sat}\right)/\left({h}_{V}-{h}_{L,Sat}\right)}{\tau}.$$

where *M _{V}* is the total
vapor mass.

The energy flow associated with condensation is:

$${\varphi}_{\text{Con}}={\dot{m}}_{\text{Con}}{h}_{L,Sat},$$

When the vapor specific enthalpy is higher than the saturated vapor specific
enthalpy, no condensation occurs, and *ṁ _{Con} =
0*.

### Mass Balance

The total tank volume is constant. Due to phase change, the volume fraction and mass of the fluid changes. The mass balance in the liquid zone is:

$$\frac{\text{d}{M}_{\text{L}}}{\text{d}t}={\dot{m}}_{\text{L,In}}-{\dot{m}}_{\text{L,Out}}+{\dot{m}}_{\text{Con}}-{\dot{m}}_{\text{Vap}},$$

where:

$$\dot{m}$$

_{L,In}is the inlet liquid mass flow rate at all L and V ports.$$\dot{m}$$

_{L,Out}is the outlet liquid mass flow rate:$${\dot{m}}_{\text{L,Out}}=-\left({\dot{m}}_{\text{AL}}+{\dot{m}}_{\text{BL}}\right),$$

$$\dot{m}$$

_{Con}is the mass flow rate of the condensing fluid.$$\dot{m}$$

_{Vap}is the mass flow rate of the vaporizing fluid.

The mass balance in the vapor zone is:

$$\frac{\text{d}{M}_{\text{V}}}{\text{d}t}={\dot{m}}_{\text{V,In}}-{\dot{m}}_{\text{V,Out}}-{\dot{m}}_{\text{Con}}+{\dot{m}}_{\text{Vap}},$$

where:

*M*is the total vapor mass._{V}$$\dot{m}$$

_{V,In}is the inlet vapor mass flow rate at all L and V ports.$$\dot{m}$$

_{V,Out}is the outlet vapor mass flow rate:$${\dot{m}}_{\text{V,Out}}=-\left({\dot{m}}_{\text{AV}}+{\dot{m}}_{\text{BV}}\right).$$

If there is only one zone present in the tank, the outlet mass flow rate of the fluid is the sum of the flow rate through all of the ports:

$${\dot{m}}_{\text{phase,Out}}=-\left({\dot{m}}_{\text{AL}}+{\dot{m}}_{\text{BL}}+{\dot{m}}_{\text{AV}}+{\dot{m}}_{\text{BV}}\right).$$

where $$\dot{m}$$_{phase,Out} is $$\dot{m}$$_{L,Out} if the fluid is entirely liquid, and $$\dot{m}$$_{V,Out} if the fluid is entirely vapor.

### Energy Balance

The fluid can heat or cool depending on the heat transfer between the tank and
wall, which is set by the temperature at port **H**.

The energy balance in the liquid zone is:

$${M}_{\text{L}}\frac{\text{d}{u}_{\text{L}}}{\text{d}t}+\frac{\text{d}{M}_{\text{L}}}{\text{d}t}{u}_{\text{L}}={\varphi}_{\text{L,In}}-{\varphi}_{\text{L,Out}}+{\varphi}_{\text{Con}}-{\varphi}_{\text{Vap}}+{Q}_{\text{L}}.$$

where:

*u*is the specific internal energy of the liquid._{L}*ϕ*is the inlet liquid energy flow rate at all L and V ports._{L,In}*ϕ*is the outlet liquid energy flow rate:_{L,Out}$${\varphi}_{\text{L,Out}}=-\left({\varphi}_{\text{AL}}+{\varphi}_{\text{BL}}\right).$$

*ϕ*is the energy flow rate of the condensing vapor._{Con}*ϕ*is the energy flow rate of the vaporizing liquid._{Vap}*Q*is the heat transfer between the tank wall and the liquid._{L}

The energy balance in the vapor zone is:

$${M}_{\text{V}}\frac{\text{d}{u}_{\text{V}}}{\text{d}t}+\frac{\text{d}{M}_{\text{V}}}{\text{d}t}{u}_{\text{V}}={\varphi}_{\text{V,In}}-{\varphi}_{\text{V,Out}}-{\varphi}_{\text{Con}}+{\varphi}_{\text{Vap}}+{Q}_{\text{V}}.$$

*u*is the specific internal energy of the vapor._{V}*ϕ*is the inlet vapor energy flow rate at all L and V ports._{V,In}*ϕ*is the outlet vapor energy flow rate:_{V,Out}$${\varphi}_{\text{V,Out}}=-\left({\varphi}_{\text{AV}}+{\varphi}_{\text{BV}}\right).$$

*Q*is the heat transfer between the tank wall and the vapor._{V}

If there is only one zone present in the tank, the outlet energy flow rate is the sum of the flow rate through all of the ports:

$${\varphi}_{\text{phase,Out}}=-\left({\varphi}_{\text{AL}}+{\varphi}_{\text{BL}}+{\varphi}_{\text{AV}}+{\varphi}_{\text{BV}}\right).$$

where *ϕ _{phase,Out}* is

*ϕ*if the fluid is entirely liquid, and

_{L,Out}*ϕ*if the fluid is entirely vapor.

_{V,Out}### Momentum Balance

There are no pressure changes modeled in the tank, including hydrostatic pressure. The pressure at any port is equal to the internal tank pressure.

The Receiver Accumulator block models the vapor and liquid volumes separately. If you input vapor or liquid quickly, the block may compress the vapor volume and the pressure may rise faster than expected. The pressure rises because when there is a high vapor or liquid mass flow rate input, the temperature rise due to compression is faster than the heat transfer that cools the vapor. If you add the vapor slowly, the heat transfer between the vapor and the liquid brings the vapor temperature down, which allows it to condense into liquid, and the pressure will not spike. Additionally, if you wait until the block achieves equilibrium, adding vapor or liquid shifts the mass fraction and does not cause pressure spikes.

### Assumptions and Limitations

Pressure must remain below the critical pressure.

Hydrostatic pressure is not modeled.

The container wall is rigid, therefore the total volume of fluid is constant.

The thermal mass of the tank wall is not modeled.

Flow resistance through the outlets is not modeled. To model pressure losses associated with the outlets, connect a Local Restriction (2P) block or a Flow Resistance (2P) block to the ports of the Receiver-Accumulator (2P) block.

A liquid-vapor mixture is not modeled.

## Examples

## Ports

### Output

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2018b**