Irrig Sci (2017) 35:383–395
Optimization of a direct‑acting pressure regulator for irrigation
systems based on CFD simulation and response surface
· Guangyong Li
Received: 6 March 2016 / Accepted: 27 April 2017 / Published online: 24 June 2017
© Springer-Verlag Berlin Heidelberg 2017
A micro-irrigation system with variable topography or
large submain unit can lead to great variation in lateral
or sprinklers inlet pressure along the submain because of
hydraulic loss and terrain slope. Direct-acting pressure
regulators (PRs) perform a critical function in ensuring the
lateral or sprinklers inlet pressure required for high applica-
tion uniformity (Zhu et al. 2002; Lamaddalena and Pereira
2007; Ella et al. 2013).
Preset pressure and initial regulation pressure are two
important performance indexes of the PR. The geometri-
cal and spring parameters are the most important variables
affecting the performance of direct-acting PRs, and several
groups have studied them by experimental investigation
(Korven and Wilcox 1966; Von Bernuth and Baird 1990;
Kincaid and Romspert 1996; Tian et al. 2005; Yan et al.
2010). For example, it has been reported that the desired
downstream pressure of a butterﬂy disk-type PR can be
easily changed by adjusting the spring tension; as the initial
spring tension is increased, the downstream preset pressure
level increases (Kincaid and Romspert 1996). A linear rela-
tionship exists between the preset pressure and four fac-
tors which are spring stiffness, spring length, upstream and
downstream areas of the regulating part, and space between
the regulating part and the block cap (Tian et al. 2005).
Both the initial and maximum spring forces are in a posi-
tive linear relationship with the preset outlet pressure (Yan
et al. 2010).
Numerical simulations of the ﬂow in pressures regulat-
ing devices (including pressure regulators, pressure relief
valves, and safety valves, etc.) have been widely carried out
in recent years. Steady-state calculations at several ﬁxed
openings are performed to obtain detailed ﬂow information
by visualization and an analysis of the inside ﬂow ﬁeld of
Abstract A dynamic model of direct-acting pressure regu-
lator was developed using the layering dynamic mesh tech-
nique to numerically determine the performance indexes.
The validation test of the dynamic model was conducted.
The central composite design of the response surface meth-
odology was used to arrange the numerical experiments.
Two quadratic polynomial regression equations were ﬁt-
ted for the computational preset pressure (P
) and slope
of the performance line of the unregulated segment (η)
data in terms of ﬁve variables. The optimization model was
established and solved using genetic algorithm in combina-
tion with superimposed contour plot approach, which con-
sidered maximum achievable η under a certain P
object function. Results showed that numerical and meas-
and η agreed within −19.7 and 9.4%, respectively.
Effects of geometrical and spring parameters and their
interactions on P
and η were successfully revealed. In a
comparison between the optimization solution and simu-
lation conﬁrmation results, the relative deviations of P
and η lie within 4.8 and −7.1%. The optimized η for P
of 0.05, 0.07, and 0.1 MPa was improved by 16.5, 8.5, and
13.8%, respectively. The proposed optimization model can
be practically applied to design of pressure regulator.
Communicated by G. Merkley.
* Guangyong Li
College of Water Resources and Civil Engineering, China
Agricultural University, Beijing, China