Accumulator Components

Accumulator Component General Description

Anaccumulator is a pressure storage reservoir in which the fluid is held under pressure that is applied by an external source. The external source can be an engine, a spring, a raised weight, or a compressed gas. An accumulator enables a hydraulic system to cope with extremes of demand using a less powerful pump, to respond more quickly to a temporary demand, and to smooth out pulsations.

Quick Guide for Creation in the GUI

There are two accumulator subtypes under “Compressible Gas Elements” section and five accumulator subtypes under “Incompressible Liquid Elements” section available in Flow Simulator.

Accumulator Component Inputs

Table of the inputs for the Accumulator component.

Accumulator Component Theory Manual

This section contains a governing equation of how mass, momentum & Energy conservation for all accumulator subtypes. Implicit Time Stepping solution is used to solve conservation equation as explained below.

Nomenclature:
	V: volume
A: cross section area	gc: Gravitational Constant
P: pressure	R: gas constant
	T: Temperature
V: volume	t: time
Cp: Specific Heat
Subscripts:
t: total	liq: liquid
s: static	g: gas
Superscripts:
n: iteration

Generic Fixed Volume and Gas Chamber

Mass Conservation

Compressible Flow

Mass accumulated inside the control volume is

Assuming first order backward time-stepping

Then, we define the residual equation similar to steady solver except for transient terms

We need to calculate:

For 2^nd order central time stepping

Incompressible Flow

Mass accumulated inside the control volume is

Assuming first order backward time stepping

Then, we define the residual equation similar to steady solver except for transient terms

Since density is a strong function of temperature and weak function of pressure, we assume temperature is independent of pressure

For 2^nd order central time stepping

Momentum conservation

Energy conservation

Air Vessel, Vented Air Vessel, Bladder Fixed Geometry and Bladder Variable Geometry

The following derivations hold for all the following sub-types: Air Vessel, Vented Air Vessel, Bladder Fixed Geometry and Bladder Variable Geometry.

Mass Conservation

The continuity equation with the classical mass flux convention is given as

Using a first order backward Euler time stepping, we get

Then the Jacobian matrix becomes:

Pressure at the exit of the accumulator will be given as

For each time step and inner iteration, we should calculate mass. Since we have a single equation for 2 unknowns, we will assume the previous iteration’s flow rate while calculating the remaining mass

Then, we have to solve for a non-linear equation for

G is the residual equation which needs to converge to a very small number.

Finding the mass inside the volume:

Now that we have defined the main residual equation, we will look at the calculation of remaining mass inside the volume. Since it will be mainly a function of h, or fluid height, the resulting equation will be in terms of h:

Case 1: Emptying

Case 2: Filling

Correcting the Continuity Equation

First order implicit Finite Difference:

Case 1: Emptying:

Only contribution to Jacobian matrix will be on the off-diagonal term

Case 2: Filling:

Only contribution to Jacobian matrix will be on the off-diagonal term

Second order implicit Finite Difference:

Case 1: Emptying:

Only contribution to Jacobian matrix will be on the off-diagonal term

Case 2: Filling:

Only contribution to Jacobian matrix will be on the off-diagonal term

Momentum and Energy Conservation

Case 1: Emptying Volume

In the above equation + if filling, and – if emptying

Taking derivative

Case 2: Filling Volume

In the above equation + if filling, and – if emptying

Taking derivative

Special Case: Ventilation Option for the Vented Air Vessel

If the ventilation is on, we need to calculate the mass of the trapped gas

If , we will have in flow

If , we will have out flow

Accumulator Component Outputs

The following listing provides details about Accumulator Component output variables.