Available online at www.sciencedirect.com
ScienceDirect
Procedia Engineering 00 (2014) 000–000
www.elsevier.com/locate/procedia
“APISAT2014”, 2014 Asia-Pacific International Symposium on Aerospace Technology,
APISAT2014
Numerical Simulation of Direct Action Liquid Rocket Engines
Hydro mechanical Flow Controllers
Iana Bakhmet, Zhang Lihui*
School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China
Abstract
Direct Action Flow Controllers include two main elements: a throttle that provides the required flow changes during the engine
operation, and a spool, stabilizing the pressure drop across the throttle. A mathematical model is required to determine the static
and dynamic characteristics for a specified design’s parameters. Basis on the mathematical models, were performed numerical
factor experiments with constructions of regression models. According to presented mathematical models were performed
numerical factor experiments. Presented liquid flow and pressure drop characteristics that depend from the regulator structural
factors, when statism coefficient equal to null. The results of mathematical experiments allowed to build regression models that
characterizing the degree of the influence of external factors on the design process and the onset of negative droop. Results show
what influence has diameter of the spool, the distance between the throttle and the spool, offset of cone throttle, the diameter of
the spool, the angle of cone throttle, length of the cone throttle on the flow regulator. The results can be used as guidelines for
another flow regulators design.
© 2014 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA).
Keywords: flow controller, flow regulator, liquid rocket engines, dynamic characteristic, static characteristic
1. Introductioni
Liquid Rocket Engine (LRE) hydromechanical flow regulators are one of the most important design elements of
the system [1-3]. Flow controllers used for boosters and provide their stable operation and allow vary their thrust by
the desired algorithm. The establishment of such controllers usually associated with experimental testing of engines.
* Corresponding author. Tel.:+ 86 -18810319445;.
E-mail address: bakhmet_yana@mail.ru
1877-7058 © 2014 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA).
2
Iana Bakhmet / Procedia Engineering 00 (2014) 000–000
The increase of the power, traction and armed rocket engine systems leads to increasing of the cost of experimental
research and design of flow regulators [4-7]. In this case, the most urgent problem of flow regulator researching
become a replacing experimental testing to the numerical experiment. Not a lot of scientific works describe flow
regulators construction, but among them we should select works [8-1]. In these papers examined general data of
direct action regulators, represented their static and dynamic characteristics and basic equations of the dynamics and
static. But materials about the influence of the basic structure parameters on the static and dynamic characteristics
are not available. In previous works authors presented impact set of structural parameters through by building
graphs. Charts quantity was large enough, charts quantity is large enough, what making difficult to descriptiveness
results. To optimize of work had been used regression dependence, which simplifies researching of structural
elements influence to the flow controller.
2. Numerical simulation of the flow regulator ii
Construction of flow controller are basis on the model that was proposed in the work [2], Figure 1.
As a stabilizer used spool, the hydraulic force which is compensated by the piston and the compression spring.
The combination of the throttle slide valve parts and provides proportional flow throttle flow area at constant
pressure drop [1]. As a basis for design is modeled proposed in [2], Figure 1.
Fig. 1. Elements of design.
Since the flow regulator is designed to establish the nominal mode of operation of the engine, it has to use
stationary mathematical model of the flow regulator, which is characterized by static or load characteristic.
The reaction of flow controller to external perturbations is characterized by dynamic properties that display
response rate of flow controller to external perturbations.
In the above work has been considered the problem of constructing static characteristic flow regulator LRE
presented in [2] with the possibility to study the influence of design parameters on its view of the characteristics and
analyze the dynamic model of the flow controller.
2.1. Static mode
Equations of statics are made for internal elements flow regulator shown in Fig. 1 The basis was chosen model
described in [3]. It includes three main equations of continuity and motion.
Equation allowed by analogy with [3], to build a static characteristic of a parametric function depending on the
flow rate (1) and pressure drop on the displacement of the spool (2).
m h 
FП
(1)
 ДР
PПР  K ПР h
2F ДР  2
 PГД 
З
2NFз h 2
Iana Bakhmet / Procedia Engineering 00 (2014) 000–000

3
 2
m
 2  F  





2

NF
h
з
ДР
(2)


 - flow through the flow
where: FП - working area of the piston; P - pressure difference across the throttle; m
control valve; PГД - hydrodynamic force generated by flow around the edge of the spool; PПР - initial mouthfuls
Ph   
 ДР
2

DL
2 FL3

З
2
springs; K ПР - spring stiffness;  - density of the fluid; h - displacement of the piston from its initial position;;
D - inside diameter of the body; L - the distance between the outlet and the throttle valve opening; FL - crosssectional area of fluid flow in the controller; N - the number of spool bores.
Model was investigated for three kinds of holes spool: rectangular, triangular, circular.
Figure 2 shows the static characteristics of the flow controller with different forms of spool holes.
For calculation was used presented in work [2, 3], flow control parameters. Static characteristics are presented in
Figure 3 and Figure 4.
Were analyzed impacts of the flow controller charactertics on the compression spring, Figure 4, Figure 5. (1 435 N, 2 - 835 N, 3- 1235 N)
Calculations showed that the flow controller for the specified design parameters characterized by negative
derivative, which characterized by decreasing part of the curve characteristics of the flow, i.e. presence of negative
droop. Having negative droop due to the fact that the hydrodynamic forces vary more than the elastic force of the
spring, when the movable part of the regulator is moving [1].
Figure 3 and Figure 4 shows that the throttle opening increases fuel consumption, increases the pressure drop
across the beginning of the negative droop (moves statism to the right).
Fig. 2. Load characteristics of the different types of spool hole
Fig. 3. Characteristics of flow controller for different angles of the
throttle regulator (α= 10, 30, 50 degree).
Figure 5 shows tightening of the spring leads to an increase in flow, pressure drop start negative droop increases
(moves statism to the right).
4
Iana Bakhmet / Procedia Engineering 00 (2014) 000–000
Fig. 5. Dependence derivative of the static characteristic on the
pressure drop for different mouthfuls spring.
Fig. 4. Dependence of the static characteristics for different mouthfuls
spring
The model allows to make a numerical simulation with selected design parameters with minimal statism of static
characteristics.
2.2. Influence of structural parameters on the Flow Controller design
Since the flow control valve is a lot of parametric objects, study the effect of various design factors is
conveniently carried out by the regression model, the numerical coefficients which characterize the effect of factors
on the parameters of the controller. Basic design factors selected to determine their impact on the work flow
regulator shown in Figure 1.
In a preliminary experiment it was determined that L hasn’t significantly affect to the flow regulator.
Because in the model [5] the distance L , determines pressure losses of liquid friction to the flow controller
body.
Table 1. Levels of factors variation.
Factor
xd
, mm
Ds ,mm
 ,degree
Ld ,mm
k , N/m
Tspr , N
Definition
x1
x2
x3
x4
x5
x6
Main Level
1,25
52,5
27,5
35
150
60
In the second phase of the study were selected only 6 parameters without the factor L . Changing of each
parameters was 30% from baseline, Table 1. During the work has been built up the plan of full factorial experiment
26, which contained of 64 different experiences. Calculated responses were processed by the conventional method of
treatment factorial experiment [4]. For all experiments, as a response data were determined:
 , kg/s − fluid flow through the flow controller when droop factor equivalent null PG . Definition - ym .
1. m
For fuel consumption in coded values factors, with accounting the influence of confounding factors, derived model
has the form (3):
ym  0,388  0,227 x1  0,052 x2  0,003586 x3  0,0003797 x4  0,027 x5  0,08x6  0,03x1 x2 
 0,002211x1 x3  0,0006141x1 x4  0,012 x1 x5  0,05x1 x6
(3)
Iana Bakhmet / Procedia Engineering 00 (2014) 000–000
5
2. P , Pa − pressure drop when statism coefficient equivalent to zero. Definition - y P .
For the pressure drop in the coded values factors, model has the form (4):
y P  4,629  1,577 x1  0,344 x2  0,16 x3  0,238x4  1,972 x5  0,526 x6  0,056 x1 x2  0,207 x1 x3 
 0,111x1 x4  0,731x1 x5  0,025x1 x6 .
(4)
As a result of the models construction has been determined:
1. Linear model of calculation without the influence of joint factors characterized by 7% relative error.
Accounting of mixed factors improves the accuracy to 1.9% relative error.
2. The linear model of differential pressure, excluding the effect of joint factors characterized by a relative 11.7%
error. Accounting for confounding factors improves the accuracy to 9.8% relative error. It is possible that this
accuracy is not satisfactory for the model and its need to be count like pressure drop model of the second-order.
Obtained results:
1. The largest influence on the output values aside increases have offset cone throttle.
2. The spring stiffness has larger influence on the pressure drop than in the fuel consumption.
3. Cone throttle has little effect on the pressure drop (0.53%) and on the fuel consumption (0.65%).
4. The largest influence on the output values in the decreasing length of the cone throttle.
The least impact on the pressure drop has  with combined effect of: xd - Tspr , xd - Ds , xd - Ld .
2.3. Dynamics characteristic of the flow regulator
The model took into account the reduced mass in the flow controller (mass of the spool and fluid
displacement):
2
2
 F2  the reduced friction:
 F2 


RПР  RЗОЛ  8      LОТВ  
 FОТВ 
 FОТВ 
Equations represent a system of differential equations of first order form (5-9):

dm ДР g  F ДР   
 ДР
P  P 

m 2ДР 
ВХ
1
2


dt
L ДР
2g F ДР  


M ПР  M З  FОТВ LОТВ 
(5)

 рр g  FЗ h 
dm
З
 2рр 

P1  PВЫХ 
m
2
dt
LЗ


  g  2  Fз h


(6)
dh
H
dt
dP1
dt
dH
dt


(7)

V
m ДР    F2  H  m pp
a2
g
 F2 


 FОТВ 
F1 PВХ
2
M З  FОТВ LОТВ 


(8)

 F2
 P1   PПР  RЗ  8      LОТВ  
F

 ОТВ





2

H 


(9)
 K ПР h  LКР h   del  P1  PВЫХ 
 ДР =0,6 kg/s, h = 0,4 cm, P1 = 200 kg/cm2, m З =0,6 kg/s, H =0.
Initial values has been taken: m
System of differential equations was solved by method of Runge-Kutta, through the procedure: rkfixed (y, x1, x2,
intvls, D) in Mathcad software. System solution allowed to determine the dynamics of the flow controller in the
beginning of work. The controller output to the stationary mode occurred on 0.02 s. Stationary mode determined by
the fact that the expenditures through the throttle and valve becomes equal, Figure 6, and the spool stops, Figure 7.
6
Iana Bakhmet / Procedia Engineering 00 (2014) 000–000
Fig. 6. Changing the flow rate through the throttle and valve, and at the
beginning of work.
Fig. 7. Changing of the spool hole opening at the beginning of work.
4. Conclusions
Results of the static and dynamic characteristics allow the design phase to obtain advice on the right choice of
parameters and structural elements of calculated flow regulator. Was determined that the static flow control
characteristics are weakly dependence on the regulator inlet pressure. The results demonstrated that the dynamic
characteristics are aperiodic. Examining the behaviour of the flow regulator for different geometries of the spool
hole is determined that the most successful form it is triangle, which move the negative droop to the right. The
behaviour of the flow controller for circular and rectangular holes do hasn’t significant differences.
References
[1] Glikman B.F., Automatic control of liquid propellant rocket engines/ M.: Mechanical Engineering, 1989. – 296 pp.
[2] Belyaev E. N., Chvanov V.K., Chervakov V.V., Mathematical modeling workflow liquid rocket engines /– M.: MAU, 1999.- 228 pp.
[3] Lebedinskii E.V., Zaitsev B.V., Sobolev A.A., Multi-level mathematical modeling of flow control LRE // GNC FGUP « Keldish Center ».
[4] Egorov A.E., Azarov G.N., Koval A.V., Investigation of devices and automation systems using experimental design / KHNU, 1986.- 240pp.
[5] Bakhmet I. G., Construction of the flow characteristics of the flow regulator LRE , AET. - 2013. - № 10 (107) – pp. 136-140.
[6] George P. Sutton , History of Liquid-Propellant Rocket Engines in Russia, Formerly the Soviet , Journal of Propulsion and power, Vol. 19,
No. 6, Noveber–December 2003 Union Los Angeles, California, 90049.
[7] Dieter K. Huzel and David H. Huang, Design of Liquid Propellant Rocket Engines Scientific and Technical Information Division, Office of
Technology Utilization 1967, National Aerospace Aeronautics and Space Administration, Washington, D.C.
[8] Sutton, George Paul, Rocket propulsion elements: an introduction to the engineering of rockets, by George P. Sutton, Oscar Biblarz.--7th ed.
p. cm. I SBN 0-471-32642-9.
[9] Liu Yongfeng, Pei Pucheng, Numerical simulation of direct injection gasoline engine model [A], Tsinghua University, Beijing, China.
[10] Holster Jesse L．Analytical Model for Liquid Rocket Propellant Feedline Dynamics［J］．Journal of Spacecraft，1973，11(3):180187pp.
[11] Huang Yuhui , Wang Zhenguo , ZhouJin, Nonlinear theory of combustion stability in liquid rocketengine based on chemistry dynamics,
National University of Defense Technology, Changsha, Vo l . 4 5 No.4, SCIENCE IN CHINA(Series B) August 2002..
[12] V. Ahuja, A. Hosangadi, and P.A. Cavallo, Combustion Research and Flow Technology, Analyses Of Transient Events In Complex Valve
and Feed Systems, 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit10 - 13 July 2005, Tucson, Arizona, AIAA 20054549.
[13] Francis H Harlow, Anthony A Amsden, , DOI: .1016/0021-9991(71)90002-7.
Iana Bakhmet / Procedia Engineering 00 (2014) 000–000
7