Accumulators
Performance
The accumulator is initially charged to a pressure P0 that is set at a level lower than the minimum
operating pressure P1. The pressure of the gas will vary with changes in the volume, but the
relationship between these parameters will depend on the amount of heat transferred to the
surroundings. It is usual to assume a polytropic expansion index for the gas the value of which
depends on the operating times and the duty cycle.
Gas
P,V
Separator
Accumulator pressure
Referring to Figure 2, the gas states are defined as:
Pre-charge:
Minimum operating:
Maximum operating:
pressure P0 and volume V0.
pressure P1 and volume V1.
pressure P2 and volume V2.
For a gas having a mass 'm', an absolute temperature 'T' and a polytropic index 'n', the universal
gas laws for a perfect gas give:
PV n  cons tan t
(1)
PV  mRT
(2)
R = Universal gas constant
The accumulator is connected to an appropriate point in the hydraulic system such that when the
pressure falls the gas will expand and deliver a volume of fluid V into the hydraulic system thus
maintaining its pressure. The maximum volume is given by:
V  V1  V2
(3)
Using a polytropic index, n1, for compression from V0 to V2, for the period when the fluid pressure
increases to its maximum value, equation (1) gives:
P0V0n1  P2V2n1
Thus
P
V2   0
 P2



1
n1
V0
(4)
Also, for the gas expansion from V2 to V1 with a polytropic index of n2:
P
V1   2
 P1



1
n2
V2
(5)
Equations 4 and 5 with equation 3 give:
P
V  V0  0
 P2



1
n1

 P2

 P1



1
n2


 1

(6)
The values of the polytropic indices cannot be accurately predicted and it is usual to take the value
of n1 as 1 (isothermal) and n2 as  for the gas, where this value is obtained for the expected
operating temperature and pressure.
Thus equation 6 produces:
V0 
 P2

P
 0

 P2

 P1



1







 1

V
(7)
This equation gives a conservative value for most applications. In certain cases, e.g. high or low
temperatures, it may be necessary to apply a correction factor and, in those situations, information
should be obtained from the manufacturer.
The value for  can be obtained from Figure 3 that applies to real gases and should be used in
accumulator sizing calculations.
-430C
Adiabatic Index
00C
470C
1070C
0
50
100
150
200
Pressure bar
250
300
350
Variation in adiabatic index with pressure and temperature for nitrogen
Contamination control
Filters
Differential
pressure device
Mounting
face
Sampling
port
Seal
Bypass
valve
Element
support
Removable
bowl
Filter
element
High-pressure filter (Pall)
The main features of a replaceable element high-pressure filter are shown in Figure 6. As the fluid
passes radially inward through the element contaminant is trapped in the material. With time the
pressure drop across the filter will increase at a rate that is dependent on the fluid condition and
eventually this will cause the bypass valve to open thus passing contaminated fluid directly into the
system. However, the pressure drop can be monitored either mechanically or by electronic
methods and this aspect is an important feature in a properly maintained system.
The performance of a filter is based on its ability to trap particles which is defined by its beta ratio,
 , that is obtained from appropriate test methods.
The beta ratio is defined as:
x 
No . of particles  particle size' x' upstream
No . of particles  particle size' x' downstream
The beta ratio is defined for particle sizes above the given level because the number of trapped
particles varies with the size, which is referred to as a distribution.
Filters are selected on the basis of achieving the desired contamination levels and having sufficient
contaminant holding capacity to maintain the required contamination levels under the worst
envisaged circumstances.
Various selection methods are available from different filter
manufacturers, the majority of which are based on an absolute filter rating at a given  ratio. Figure
7 contains an example showing the performance of different elements with a x = 200 rating where
x is the minimum particle size for a beta ratio of 200.
Contaminant
ingression R
Q,ND
System
Q,NU
NU
ND
Generally it is not feasible to analyse systems in respect of the generation of contaminant
particles and ingression from the environment. However a simple model such as that in Figure 8
can be used to show that:
R 
and
Q  1
R

Q(   1 )
NU 
ND
For beta ratios in the region of 10 and above, ND reduces as the inverse proportion of the beta
ratio, which is represented by the chart.
ISO 4406 standard code for contamination levels.
Coolers
Thermodynamic aspects
C P T
as
dm
 QP
dt
P
dm
 Q , then T 
dt
C P
Where
dm
= Mass flow rate
dt
kg s-1
Cp = Specific heat
T = Temperature
2.1 kJ kg-1 K-1 (typical value)
K
 = Density
P = Pressure loss
870 kg m-3 (typical value)
N m-2
m3s-1
Q = Flow
Therefore, for a system with a 100 bar pressure loss, the temperature rise will be:
T 
The input power, W0  QP
P
C p
 5.5 C
 T 
Wo
C pQ
where Wo is the power input given in Watts.
Cooler characteristics
Heat dissipation (kW)
4.3
Oil flow (L/min)
Cooler Performance Characteristics
The cooling characteristics are usually presented in the form shown in Figure 11, which will apply
for a particular value of inlet temperature difference. For different values a correction factor is
applied to suit the application.
Reservoirs
If possible, the reservoir design should be such that any entrained air is released before the fluid is
passed to the system inlet. A baffle can be used to increase the flow circulation and hence improve
the air release. It also reduces the fluid movement due to motion of the reservoir itself.
Passing the return flow through a diffuser in the reservoir reduces the fluid velocity and, by directing
the fluid away from the bottom of the reservoir, reduces the re-entrainment of solid contaminant and
water from the bottom of the reservoir. Transient changes in the fluid level and the release of air
require the fitment of a breather. This must contain a filter that is sized to the minimum
requirements of the system. It is preferable that the fluid is filtered during topping-up or replenishing.