A steady state approach to calculation of valve pressure rise rate ...

Konference ANSYS 2011
A steady state approach to calculation
of valve pressure rise rate characteristics
Ján Oravec
Technical centre, Sauer-Danfoss a.s., Považská Bystrica
joravec@sauer-danfoss.com
Abstract: Pressure relief valves are widely used in hydrostatic circuits. The pressure rise rate characteristics are
one of the most important descriptions of the valves performance. This article proposes design of the basic
pressure rise rate characteristic of valve using only a few CFD calculations. These calculations are performed
for several poppet strokes and flow values. The method is shown for charge pressure relief valve but can be used
similarly for any poppet type valve.
Keywords: pressure relief valve, hydrostatics, pressure rise rate characteristic, CFD
1. Introduction
Pressure relief valves are essential components in hydrostatic systems. They protect the systems against
excessive pressures or maintain pressures at desired levels. The performances of such valves are represented by
their pressure rise rate characteristics. A simplified one is shown in Fig. 1. Note, the valve remains closed while
pressure is lower than the cracking pressure. If the pressure exceeds the cracking pressure, p cr , the valve opens to
allow escaping of working fluid (hydraulic oil) to a reservoir. A small slope of the characteristic is desired in
standard working range of the valve. If the poppet reaches its maximal stroke limit, the valve behaves like a
constant orifice for higher flow rates.
Because each the point of the characteristic represents different poppet stroke (also flow, pressure…), the
standard calculation (as well as real measurement) leads to transient task including remeshing and solution of
equation of motion.
pressure (drop)
cracking pressure (p cr)
poppet at maximal
stroke
flow rate
Fig. 1. Simplified pressure rise rate characteristic

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If we take into account some simplifications:
dynamic effects are avoided,
valve at fixed poppet stroke behaves like an orifice which has quadratic function behavior for wide
range of flow rates,
we can design the valve characteristic from several CFD steady state calculations. This approach is shown for
charge pressure relief valve.
spring pretension
mechanism
nut with guide
R guide
pump end cap
outlet channel
connected to pump
case
case pressure marked
by blue (p case )
R seat
springs
balance chamber
poppet
gallery (channel)
charge pressure
marked by red (p charge )
inlet branch of the
gallery for measurement
as well as CFD purposes
these branches are
closed for measurement
as well as CFD purposes
Fig. 2. Design of charge pressure relief valve

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2. Charge pressure relief valve (CPRV)
The function of CPRV is to maintain charge pressure of the closed hydrostatic system at a designated level
above case pressure (Sauer-Danfoss, 2011). The CPRV is a direct acting poppet valve (Fig. 2). It opens and
discharges fluid to the pump case when pressure exceeds the designated level, p charge , at a channel called gallery.
The valve poppet has a cone which acts against a seat created in the pump end cap (Fig. 2). The poppet guiding
is provided by a guide designed in the nut. The 2 springs provide force which acts in direction to close the valve.
Pretension of one spring can be adjusted by a bolt to reach desired level of the cracking pressure. The pretension
force can be calculated from equation:
( ) , (1)
where and radii are evident from Fig. 2.
As the poppet moves, the spring force corresponds to equation:
where is spring rate and is poppet stroke.
, (2)
3. CFD model
As mentioned above, the steady state approach is used here. The CFD models (Fig. 3) are prepared for 3 poppet
strokes (0.5 mm, 1.5 mm and 3 mm). There is used combination of hexahedral, tetrahedral and wedge mesh
types created using ANSYS ICEM CFD.
The CFD analysis is performed in ANSYS Fluent.
Material properties of hydraulic oil Shell Tellus 46 are used. The fluid is assumed as incompressible. Based on
previous investigation, experience and comparison with testing, laminar model is chosen in this specific case.
Pressure outlet boundary condition is applied to the pump housing passage. The pressure
constant for all the calculated cases.
Velocity inlet boundary condition is experienced as suitable and stable for this task. Inlet velocity and flow rate
are related to each other by simple relation:
, (3)
where is inlet flow rate, is inlet velocity magnitude and is inlet area. The velocity magnitude (flow
rate respectively) is ramped to several values for each the stroke model. At least, 3 discrete velocity magnitudes
are needed for each the stroke to be able approximate results by quadratic function.
As a result from each the CFD calculation is:
pressure at inlet ( ),
flow force induced by oil to the poppet ( ).
is
For reference, pressure contours and streamlines in region of control passage are shown in Fig. 4 for 1 mm
poppet stroke and 70 lmin -1 flow rate case.

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poppet modeled at 3 stroke
positions
detail of hexahedral mesh
in control passage area
pressure outlet (p case)
velocity inlet
Fig. 3. CFD model
limits are set manually
Fig. 4. Pressure contours and streamlines in control passage region
(1 mm stroke, 70 lmin -1 flow)

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4. Post-processing
The post-processing plays big role in this task. We have data from 9 CFD calculations (3 strokes × 3 flow rates
per each stroke = 9 calculations) in this specific example. Therefore further data processing in a spreadsheet or
other suitable tool is needed.
The input and output values can be collected into a table form for further processing. One table proposal is
following:
stroke flow rate pressure drop flow force
Tab. 1. Proposed table for collection of CFD inputs and outputs
The visualization of data points can be seen in Fig. 5. The triangle points in graph C represent dependency of the
pressure drop on flow rate. The different colors relate to different poppet strokes. Similarly, the square points in
graph B represent dependency of the flow force on flow rate.
The data points can be approximated by quadratic polynomial trendlines (continuous colored lines in graphs B
and C) for each the stroke value. The flow force at constant stroke can be then written in form:
where , , and
, (4)
are polynomial coefficients obtained from the spreadsheet trendline properties.
It is obvious the flow force has to be in balance with the spring force (2) at each the point of final pressure rise
rate characteristic. Therefore we can write:
Solution of this quadratic equation is:
( ) (5)
√ ( )
, (6)
where the sign plus or minus is chosen in way to obtain physically correct result. So, using (6) we get flow rate
at which there is balance between flow force and spring force at constant stroke (compare graphs A and B in Fig.
5 to see balance between spring force and flow force for each the stroke) .

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C
s 1=const.
p s1
p cr
q s1
A
B
s 1=const.
s 1
Fig. 5. Visualisation of the pressure rise rate characteristic design
Similarly to the flow forces approximation, we can also approximate the pressure drop data points using
quadratic polynomial trendlines in form:
, (7)
where the polynomial coefficients , , and are obtained again from the spreadsheet trendline properties. If we
use the calculated flow rate from (6), we obtain corresponding pressure drop:
, (8)
This procedure is repeated for all the 3 strokes so we obtain the flow rate and pressure drop pairs:
[ ] [ ] [ ] (9)
plus we have the additional point [
] The final pressure rise rate characteristic can be designed from
those points – see red line in graph C in Fig. 5.
5. Comparison with measurement
A simplified hydraulic scheme used for measurement of the CPRV is shown in Fig. 6a. An auxiliary pump H
provides oil to the testing device. The throttle valve TV is fully open so the pressure indicated by the gauge G1 is
small in comparison with the cracking pressure of the tested CPRV. As the TV restricts flow area, the load of

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CPRV increases and it starts to operate. Pressure before CPRV (G1) and behind it (G2) is recorded together with
flow rate (Q). Note the measurement process should be sufficiently slow to avoid dynamic effects of the system.
It is possible to perform measurement of the CPRV installed in a simple test block or installed in the pump end
cap. The measured valve performance with the one calculated by CFD are shown in Fig. 6b for comparison.
G1
G2
CPRV
TV
Q
H
a
b
Fig. 6. Measurement hydraulic scheme (a) and comparison CFD with measurement (b)
6. Conclusion
The design of pressure rise rate characteristic of charge pressure relief valve using steady state CFD simulation is
shown in the article. The model is prepared for 3 constant strokes. Minimally 3 different flow rate conditions
needs to be calculated for each the stroke due to possibility of data approximation by quadratic polynomial
functions. Both pressure drop and flow force functions are approximated in relation to flow rate. The final
pressure rise rate characteristic of the valve is found using condition of equilibrium of flow force and spring
force at each the specific stroke.
Because of computing only a few steady state cases, the proposed method saves computing time as well as effort
to set up the analysis in comparison to transient CFD computation.
Another advantage is the effect of the cracking pressure or spring rate change is re-calculated immediately in the
spreadsheet without any additional CFD calculation requirement.
7. Bibliography
1. “H1 Axial Piston Pumps Single and Tandem”, Basic Information, Sauer-Danfoss, 11062168-Rev BB-Apr
2011.
2. Imre M., Kriššák P., Rahmfeld R., Zavadinka P., “Porovnanie simulačných a meraných výsledkov
škrtiaceho ventila”, Hydraulika a pneumatika, 1-2/2010, ISSN 1335-5171.