Modularization modeling and simulation of turbine test rig main test system

Applied Mathematical Modelling 35 (2011) 5382–5399

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Applied Mathematical Modelling

journal homepage: www.elsevier .com/locate /apm

Modularization modeling and simulation of turbine test rig maintest system

Yang Chen a,⇑, Guobiao Cai a, Zhe Wu b

a School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100191, PR Chinab Beijing Aerospace Measurement & Control Corp., Beijing 100041, PR China

a r t i c l e i n f o a b s t r a c t

Article history:Received 6 April 2010Received in revised form 22 April 2011Accepted 26 April 2011Available online 1 May 2011

Keywords:Turbine test rig main test systemModularization modelingFinite volume methodRig regulating testNumerical simulation

0307-904X/$ - see front matter � 2011 Elsevier Incdoi:10.1016/j.apm.2011.04.041

⇑ Corresponding author.E-mail address: [email protected] (Y. Chen

Comprehensive applications of modularization modeling method have proven its effective-ness and versatility in system simulation field. This paper establishes the modularizationnumerical model of a turbine test rig main test system by using a finite volume numericalsystem developed. The simulation study based on an experiment is conducted. The com-parison with available experimental data indicates that the general trends of simulationcurves are in agreement with test curves and that there is obvious thermal stratificationphenomenon at different positions along combustion gas flow direction. Accordingly, itcan be concluded that the analysis of experimental data is reasonable and the establishednumerical system is effective. It is also found that the modeling of valve spool throttlingand the modeling of components-wall heat transfer are two key factors of affecting simu-lation accuracy.

� 2011 Elsevier Inc. All rights reserved.

1. Introduction

Conventional modeling method is aiming at a system of a specific type in the research field of liquid propulsion systemtransient and steady characteristics. In the method, the program codes are correlated with system structure, which inducesthat the codes must be modified if the system configuration changes [1]. This would inevitably increase research period andcost. Modular method can solve the problem effectively. The idea of modularization [2] is gradually formed to meet the de-mand of versatile system modeling. Its basic idea is firstly viewing the system as a assembly of some typical componentswhich are called modules, secondly establishing numerical model of every module and encapsulating it as a independentfunction module, finally establishing numerical model of the whole system by combination of relevant modules which needsto comply with some special rules. As all components of the same type are described by one module, the modeling and sim-ulation problem of all kinds of systems with different structures can be solved easily by computer.

Since the late 1980s, relevant researches have been evolving toward maturity and put into application in the form of sim-ulation software. Consider the following two examples: The rocket engine transient simulator (ROCETS) [3–5] developed byPratt and Whitney for NASA-MSFC and the versatile engine design software [6] developed by Rocketdyne which comprisesthe steady-state on-design and optimization (SSODO) code, the steady-state off-design (SSOD) code, the transient (TRANS)code. Functions of the two softwares can be approximately understood by their own name. The former is mainly applied todynamic simulation and the latter is mainly applied to preliminary design. In the 1990s, the DLR at German Aerospace Re-search Establishment developed a versatile modular method [7] for steady analysis of liquid rocket engine (LRE) cycles. Sub-sequent applications in SSME, RD-120 and a tripropellant engine prove the versatility and effectiveness of the method.

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http://dx.doi.org/10.1016/j.apm.2011.04.041

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Nomenclature

A cross-sectional area of pipeAv0 flow section area in time of valve full openingC, Cs perimeter of pipe cross section and pipe-wall deformation regionCd flow coefficientCp specific heat capacityD interior diameter of pipeE total energy per unit volumee internal energy per unit massfk dimensionless friction loss coefficient (also called Darcy friction factor)Gsg relative densityg gravity accelerationnh turbine rotate speedp, pt fluid pressure and total pressureQ thermal increment per unit volume resulted from radiation or chemical energy releaseQm, Qv mass flow rate and volume flow rate_q; q;qrho heat flux density per unit area from fluid to pipe wallR gas constantRe Reynolds numbersr radial direction of pipers radial coordinates of wall corresponding to the barycentre of control volumeS, Ss interior surface area of pipe wall in control-volume region and deformation regionS2 internal surface area of outer tube wallT, Tt temperature and total temperatureTf1; Tf2

in-tube fluid temperature and out-tube fluid temperature (ambient temperature)Twall; Tw2 internal temperature of inner tube wall and temperature of outer tube wall in case of vacuum sandwich struc-

turet timeu fluid velocity in x directionus expansion rate in pipe-wall exterior normal direction resulted from elastic deformation of pipe wallV volumex axial direction of pipe (one-dimensional flow direction)a coefficient of convective heat transfer from fluid to pipe wallc specific heat ratio of gase1, e2 blackness of inner and outer tube walles system blacknessh rotation degree from one-dimensional flow direction to gravity acceleration directionk thermal conductivityq densityr0 blackbody radiation constants valve relative opening

Subscriptsektexine external surface of inner tube walli, j, k serial number of state element, velocity element in flow field, and wall radial-direction grid, respectivelyf fluidn, nw total number of flow-field grids and wall temperature-field gridsw wall

Y. Chen et al. / Applied Mathematical Modelling 35 (2011) 5382–5399 5383

Majumdar et al. [8–14] developed the generalized fluid system simulation program (GFSSP) which was firstly published in1994 and original objective was to develop a program to calculate the pressure and flowrate distribution in Pratt & Whitney’sturbopump secondary flow circuit. Since then it is gradually developed to be a versatile software for steady and transientsimulation of one dimensional compressible flow network. The basic idea of GFSSP modeling is to divide the flow systeminto nodes and branches, the conservation equations are discretized in every finite control volume. GFSSP is capable of mod-eling common flow phenomena including rotation, heat transfer, phase change, mixing and has the function of computingthermophysical properties for many fluids. In recent ten years GFSSP has been developing by adding new-type modules andimproving algorithm [11–14]. Tarafder and Sarangi [15] at India Institute of Technology developed the cryogenic engineeringsimulation programs-liquid propulsion (CRESP-LP) which provides a steady and dynamic characteristics simulator to anal-ysis every component and subsystem in a virtual environment before the hardware is fabricated. The basic idea of CRESP-LP

5384 Y. Chen et al. / Applied Mathematical Modelling 35 (2011) 5382–5399

differs a little from GFSSP’s though both belong to modular approach. As the principle of system modularization disassemblyis according to actual physical equipment, the CRESP-LP has a higher integration level. The original version has 15 equipmentmodules including connecting pipe, control valve, pressurant bottle, gas turbine, centrifugal pump, combustion chamber andso on. As the flow conditions should cover a temperature range from triple point to several thousand Kelvin and a pressurerange from subatmospheric to several hundred bars, the CRESP-LP also packages of calculating fluid thermodynamic andtransport properties. Liu [1,16,17] at National University of Defense Technology in China developed the modularization mod-eling and simulation software for the transients of liquid propellant rocket engines (LRETMMSS) which establishes a finiteelement state-variable model system by employing two kinds of finite volume grids staggered in discrete space. LRETMMSSalso develops a set of simple and practical coding rules based on configuration matrix, which solves the problem of systemcomponents coding and link relationships describing. Peukert and Simon [18] at Astrium GmbH in Germany developed theATV propulsion system simulation software (ATVSim) aiming at the automated transfer vehicle (ATV) for the internationalspace station (ISS). ATVSim has a friendly graphical user interface. The computer aided process simulator (CAPSIM), which isthe core of ATVSIM, has modular structure, whereas the initially intended concept of full modularity was abandoned to favora mixed approach during the secondary development aiming at the ATV. The Kakuda Space Propulsion Center of the JapanAerospace Exploration Agency developed the rocket engine dynamic simulator (REDS) [19] to simulate the start and shut-down transient processes of LE-7A engine. The grids based on the volume-junction method is similar to the finite volumegrids staggered in discrete space. REDS has been modified for many times since 2001 and achieved successful applicationin LE-7A engine transient analysis. Currently it is being modified for application to other type engine systems. The advancedmodeling environment for performing simulations of engineering systems (AMESim) [19–21], which is developed by IMAG-INE S.A. in France, has manifold modeling modes suitable for users of every level, such as AMESet which is a standard andgraphical secondary development platform. AMESim is also equipped with many interfaces with other softwares includingMatlab/Simulink, Adams, iSIGHT and so on. There are 30 optional special libraries including hydraulic, pneumatic, thermal,mechanical, two-phase flow, signal control, electro mechanical, etc. and more than 3000 submodels, which enable AMESimto realize multi-domain modeling and simulation. AMESim’s solver can automatically and adaptively select the optimumintegration algorithm from more than ten numerical algorithms. Currently AMESim has been widely used in simulationand design of aeronautic and astronautic systems. There are some other softwares used in liquid propulsion system transientsimulation, which include: the CARINS [22,23] jointly developed by CNES and ONERA in France, the visual integrated sim-ulator for rocket engine cycle (VIRSEC) [19] developed by Mitsubishi Heavy Industries in Japan, the Flowmaster developed byFlowmaster International Ltd. (FMI) in the UK [24,25]. Meanwhile, the increasingly powerful function of the commercial soft-ware, Matlab, brings another typical approach for liquid propulsion system versatile simulation [26,27]. However, Matlab/Simulink is restricted to the system simulation field by modeling efficiency and operation speed.

In foregoing softwares, some [3,6,10,19] adopt FORTRAN language and programming method based on modular subrou-tine calling, some [1,15,22] adopt Microsoft Visual C++ or Java language and object oriented programming method, but all ofthem have the characteristics of good versatility and applicability. Many of them have visual user interface which enableusers to establish the simulation model of engine full system or subsystem easily so that they can simulate and analysisall kinds of steady or dynamic processes. Specially, the software of Rocketdyne integrates the design and optimization of en-gine with the numerical simulation and verification, which enable users to obtain the engine scheme which can meetrequirements just by computer. The versatility and effectiveness of many softwares such as ROCETS, GFSSP, LRETMMSS, CAR-INS, etc. have been confirmed by comparison with actual test data or earlier simulation data [11–14,16,17,23,26–28]. Futureimproving direction will focus on more detailed and accurate modular modeling of typical component, and integration ofsimulation and optimization function for optimization application [4,29].

The softwares represented by Refs. [3,6,10,15] have attained a comparatively high level in liquid propulsion system stea-dy and transient modeling and simulation. Their disadvantages mainly lie in two aspects: firstly, most of module numericalalgorithms belong to lumped parameter method although the distributed parameter describing of component can be real-ized by a sectional lumped parameter approach; secondly, the function of simulating heat transfer between fluid and solidwall is comparatively weaker than the function of simulating flow field.

As for the first disadvantage, an important improvement of Ref. [1] is to update the module algorithm of the general-pur-pose software from lumped parameter method to distributed parameter method which provides a novel and unified modelalgorithm named as the finite element state-variable model. Furthermore, as the integration level of every module is en-hanced in LRETMMSS, users can use it with much less time and vigor accordingly. There are two representative modesamong above softwares in algorithm structure, namely, node-branch structure and pipe-volume structure. The former re-solves the typical system components such as pipe, valve, turbo, pump, tank, etc. into flow network composed of some nodesand branches, then solving the mass, energy and specie conservation equations in the nodes while solving the momentumconservation equations in the branches. The latter increases the integration level compared with the former and forms twokinds of staggered finite control volumes, which finally forms the pipe-volume modularization-disassembly method. Thenode-branch structure can also realize distributed parameter describing for typical components such as nozzle [9], whichis equivalent to the staggered grids of pipe-volume structure. But the integration level of the latter is so high that the inde-pendence of every module is very strong, which decreases the requirement for special background of users.

As for the second disadvantage, there are mainly two development directions: (1) To develop the heat transfer (flow) partin the framework of flow (heat transfer) simulation software system and finally expand to be a unified flow/hear transfersimulation system [30]; (2) To enlist the combination between existing mature flow simulation software and heat transfer


software [31]. The former is supposed to take more responsibility. It may be difficult for expansion because the original flowmodeling method is not suitable to establishing the heat transfer model. However, once such software is expanded success-fully, a good syncretization will be obtained between flow field and temperature field simulation, and a powerful and unifiednumerical simulation system of flow/hear transfer network will be finally established. The later is in charge of less respon-sibility, but the difficulty is how to combine two mature software systems with different structures and functions into a uni-fied system. If it only depends on exterior data interface to link the two softwares instead of taking interior inosculation intoaccount, there will inevitably be difficulties in expanding transient simulation function, and the performance of eventuallyobtained system including calculation efficiency, stability and expansibility will be inferior to the former because of theunmatching in interior structure and numerical algorithm. Many special libraries such as thermal, thermal hydraulic, ther-mal-pneumatic of AMESim [20] are developed for the coupling simulation of flow and heat transfer.

This paper employs modular method to establish the numerical mode of a turbo test rig main test system based on thefinite volume model system [32] developed by us which attributes to the improvement and evolution of the finite elementstate-variable model system [1,16]. The simulation results are analyzed and evaluated by comparison with experimentaldata.

2. Physical model of the system

Fig. 1 shows the schematic diagram of the turbine test rig system which can be approximately divided into three parts:main test system, fuel–oil supply and ignition system, turbine and load system. The function of main test system is to pro-vide driving gas for rotation of the test turbine. The function of fuel–oil supply and ignition system is to provide fuel, whichwill be mixed with air to generate high-temperature and high-pressure gas after combusting in the BK-1 type heater as thedriving source of turbine rotation, for main test system. The turbine and load system is the test object of the test rig.

During the experimental process, air flow rate is adjusted mainly by three regulator valves including F1, F3, F4. As theflow branch where F1 locates has met the test requirement, the F2 regulator valve does not work. Fuel flow rate is adjustedby fuel regulator valve. The exhaust bypass is controlled by F5 regulator valve. The combustion gas flow rate at turbine inletis adjusted by F6 regulator valve and the backpressure at turbine outlet is adjusted by F7 regulator valve. The ultimate designis to adjust and control the combustion gas total temperature Tt7 by F1, F4, F3, the fuel regulator valve and total pressure pt7

by F5, F6, F1 at turbine inlet, consequently to provide stratified combustion gas actuating medium for the test of turbine andload. During the process from starting to more than 10,000 rpm (r/min) rotation speed, the rotation speed of turbine needs tobe adjusted by stages so that the values of some parameters such as combustion temperature, turbine rotation speed and allkinds of vibration will not exceed the safety range of experiment, otherwise a emergency shut-down must be implementedto interrupt the test for preventing test devices from damage.

From above-mentioned physical model and working characteristics, it can be found that there are a great number of flowpipes and regulating devices in the test rig, the gas temperature at turbine inlet is adjusted by controlling the mixing of hotcombustion gas and normal air, the inlet and outlet pressure of turbine are adjusted by regulating the opening of severalvalves. On the one hand, as the requirements for air flow rate, fuel flow rate, turbine pressure ratio and output power aredifferent in different test conditions, consequently the regulating schemes of valve opening exist great difference, addition-ally the combination of many valves increases greatly the complexity of regulating time sequence design. On the other hand,as there are only three tests (the first test failed) after the test rig was established, and each valve is regulated by manualcontrol and has no detailed record of the regulating time sequence, there is little adjusting experience to be accumulated.The combination of the two aspects makes present adjusting and testing of the test rig to become a arduous task for testing

Fig. 1. Schematic diagram of the turbine test rig system.


personnel. If we can simulate the testing process on condition that the hardware of test rig would not be started by numer-ical simulation method based on computer, then study the influence of each regulator valve operating on system dynamiccharacteristics, finally obtain appropriate adjusting scheme aiming at certain test condition, this will provide a low-cost andconvenient virtual test platform for engineering testing personnel. Specially, when the numerical models are verified andmodified for several times and are proven to be capable of describing actual working process accurately, we can employnumerical method to solve a part of experimental problems, which would consequently shorten debugging period, decreaseexperimental cost, and provide directive advice for test. Even if the accuracy of models is limited, it still can provide directionfor actual adjusting and testing by the qualitative conclusions from numerical research so long as the models meet therequirement of qualitative research. The research of this paper is conducted on above consideration.

3. Modeling approach

3.1. Conservation equations of quasi one-dimensional compressible transient pipe flow

Based on integral conservative equations in Eulerian type of specification suitable for control volume of continuous fluidmedia [33,34], integral and differential conservative equations of quasi one-dimensional (just consider the flow in axialdirection of pipe and the expanding or compressing of control volume in exterior normal direction of pipe wall resulted fromelastic deformation of pipe wall) compressible transient flow in pipe with variable section are derived by simplifying modelrationally on condition that Q = 0, which are given by:

@@t

R x2x1

qAdx ¼ ðquAÞx¼x1� ðquAÞx¼x2

;

@@t

R x2x1

quAdx ¼ qu2Aþ pA� �

x¼x1� qu2Aþ pA� �

x¼x2þR x2

x1p @A@x dxþ

R x2x1

qfxAdx�R x2

x1fRqAdx;

@@t

R x2x1

EAdx ¼ EuAþ puA� kA @T@x

� �x¼x1� EuAþ puA� kA @T

@x

� �x¼x2� ðpusSsÞr¼rs

þR x2x1

qfxuAdx� _qS;

8>>>>>>>><>>>>>>>>:

ð1Þ

@ðqAÞ@t þ

@ðquAÞ@x ¼ 0;

@ðquAÞ@t þ

@ðqu2AþpAÞ@x ¼ p @A

@x þ qAfx � qAfR;

@ðEAÞ@t þ

@ EuAþpuA�kA@T@xð Þ

@x ¼ �pusCs þ qfxuA� _qC;

8>>><>>>:

f x ¼ g cos h; f R ¼fkujuj

2D: ð2Þ

The vector matrix form of differential conservative equations can be written as:

@ U*

@tþ @ F

*

@x¼ H

*

; U*

¼qA

quA

EA

264

375; F

*

¼quA

ðqu2 þ pÞAEuþ pu� k @T

@x

� �A

264

375; H

*

¼0p @A@x þ qAðfx � fRÞ�pusCs þ qfxuA� _qC

264

375:

The total energy per unit volume is defined as follows:

E ¼ q eþ 12

u2� �

:

The heat flux density per unit area from control volume to pipe wall can commonly be considered as convective heattransfer, given by:

_q ¼ aðT � TwÞ:

Define C as the perimeter of pipe cross section and Cs as the perimeter of pipe-wall deformation region, so that:

S ¼Z x2

x1

C dx; Ss ¼Z x2

x1

Cs dx:

Finally give the state equations of fluid as follows:

p ¼ pðq; TÞ; e ¼ eðp;qÞ;

where Q is the thermal increment per unit volume in the control volume resulted from radiation or chemical energy release,e is the internal energy per unit mass, q, p, T and u are fluid density, pressure, temperature and velocity in x direction, respec-tively; x is the axial direction of pipe (one-dimensional flow direction), x1 and x2 are the axial coordinates of inlet and outletof arbitrary finite control volume in pipe flow, rs is the radial coordinates of wall corresponding to the barycentre of controlvolume; g is the gravity acceleration, h is the rotation degree from one-dimensional flow direction to gravity accelerationdirection, fk is a dimensionless friction loss coefficient (also called Darcy friction factor); D and A are the interior diameterand cross-sectional area of pipe; us is the expansion rate in pipe-wall exterior normal direction resulted from elastic


deformation of pipe wall, Ss is the interior surface area of deformation region; k is the coefficient of thermal conductivity, a isthe coefficient of convective heat transfer from fluid to pipe wall, Tw is the temperature of interior wall, S is the interior sur-face area of pipe wall in the region of control volume.

Above equations can be used to analyze quasi one-dimensional compressible transient flow in pipe with variable sectionon condition of considering the effects including pipe-wall elastic deformation, gravitational field, friction, axial heat conduc-tion, heat transfer between fluid and pipe wall. When the volume of the control volume is alterable (for example, the fluidcavity which segmental wall is a mobile piston), the physical meaning of the elastic deformation term in energy equation isthe expansion work exported by fluid.

By discretizing the integral conservative equations in two kinds of finite volume grids which are staggered in discretespace (shown in Fig. 2), a finite volume model [32] in the form of ordinary differential equations can be established to de-scribe quasi one-dimensional compressible transient pipe flow field.

3.2. Equations of temperature field in pipe wall

As a natural extension of flow field modeling method, the heat transfer part is developed in the framework of flow sim-ulation system. A finite volume model suitable for simulating pipe-wall transient heat transfer is obtained by employingtwo-dimensional finite control volume grids in axisymmetric cylindrical coordinates (shown in Fig. 3), which considers com-prehensively the interact between temperature field of pipe wall and flow field and considers the influence of environmenton system.

Although the two-dimensional heat transfer model of pipe wall is more accurate and comprehensive, the coupled itera-tive calculation of temperature filed and flow field would inevitably decelerate seriously the distributed parameter systemdynamic simulation. Thereby, the one-dimensional heat transfer model along radial direction can be employed on conditionthat the temperature gradient of fluid along pipe axial direction is relatively small, the zero-dimensional heat transfer modelor adiabatic model of pipe wall can also be employed on condition that the temperature difference among fluid, pipe walland environment is relatively small or the insulation measures are very good. The basic equations of two-dimensional heattransfer model are given as follows.

The main assumptions include:

(1) The inner tube of pipeline is cylinder pipe and the layer number of its wall is no more than two. The heat conduction inwall is axisymmetric;

(2) If the pipeline structure is vacuum sandwich structure, there is only radiation heat exchange between inner tube walland outer tube wall, and the temperature of outer tube wall is constant and equal to ambient temperature (that isTw2 ¼ Tf2 Þ;

(3) The atmosphere temperature outside pipe is the local environmental temperature and there is only convective heatexchange between atmosphere and outmost layer of pipe wall.

The transient unsteady heat-conduction differential equations in axisymmetric cylindrical coordinates can be expressedas:

A

qcp@T@s¼ @

@xk@T@x

� �þ 1

r@

@rrk@T@r

� �¼ @

@xk@T@x

� �þ @

@rk@T@r

� �þ 1

rk@T@r: ð3Þ

The internal boundary conditions of convective heat transfer are calculated by:

_qi;0 ¼ �ki;0@T@r¼ a1 Tf1

� Twall� �

: ð4Þ

The external boundary conditions of convective heat transfer are calculated by:

_qi;nw ¼ �ki;nw

@T@r¼ a2 Tektexine � Tf2

� �: ð5Þ

(i+1)th

state elementxj-1xi-1

uj-1 uj

un-1 un

xi

i-1 Ei-1

(pi-1)0 E0

( p0)

a

pa

u0 u1

x0 x0 x1 xj-2xi-2

uj-2

i-2 Ei-2

(pi-2)n-1 En-1

(pn-1)

xn-1xn-1 xn

b

pb

i Ei

(pi)

( j+1)th

velocity element uj+1

xi+1

xj Aj

a Ab

A0 A0 A1 Ai-2 Aj-2 Ai-1 Aj-1 Ai Ai+1 An-1 An-1 An

Fig. 2. Finite control volume grids of one-dimensional compressible transient pipe flow.

Fig. 3. Finite control volume grids of two-dimensional axial symmetric pipe wall heat transfer.


The external boundary conditions of radiation heat transfer in case of vacuum sandwich structure are calculated by:

_qi;nw ¼ �ki;nw

@T@r¼ 1

1e1þ S1ektexine

S2

1e2� 1

� �r0 T4ektexine � T4

w2

� �¼ esr0 T4

ektexine � T4w2

� �; ð6Þ

where T, q, Cp and k stand for the temperature of pipe wall control volume, the density, the specific heat capacity and thethermal conductivity of control volume materials, respectively; Twall, Tektexine and Tw2 are the internal temperature andexternal temperature of inner tube wall, and the temperature of outer tube wall respectively (in case of vacuum sandwichstructure); Tf1 and Tf2 mean in-tube fluid temperature and out-tube fluid temperature, respectively; a1 and a2 spell theconvection heat transfer coefficients from the in-tube fluid/out-tube fluid to the tube wall; S1ektexine

; e1; S2 and e2 standfor the external surface area and the blackness of inner tube wall, the internal surface area and the blackness of outer tubewall, respectively; r0 means blackbody radiation constant and es is deemed the system blackness. _qi;0, in the internalboundary conditions of convective heat transfer, means heat flux density per unit area from in-tube flow field state ele-ment to pipe wall.

As indicated by Fig. 3, the unsteady state heat conduction differential equation, with any finite control volume in the pipe-wall temperature field, can work out the axisymmetric two-dimensional heat transfer model of the ordinary differentialequation through spatial discretization [32].

3.3. Valve spool and orifice throttling model

(1) Pressure ratio-based injector orifice modelThrottling occurs when the fluid flows through a valve spool or an orifice (a suddenly-narrowed cross section). As theswirl emerges and interacts, the physical section will definitely bring out mathematical discontinuity. Meanwhile, theopening degree of spool can range from complete shutdown (s = 0) to full opening (s = 1). Therefore, it would be arather difficult proposition to accurately describe the dynamic throttling effect of the spool with one-dimensional flowmodel. It can be even concluded that the proposition suffers from constitutional infirmity due to a big deviation of theactual flow phenomena. The conventional idea of modeling regards valve spool as a lumped parameter grid, so theone-dimensional momentum equation here is unable to represent the flow variation caused by the changes in theopening degree of the spool, especially, when the opening degree is zero, the momentum equation cannot deal withthe phenomenon of zero flow rate. Therefore, the conventional modeling method works because it replaces the one-dimensional momentum equation with the valve mass flow rate algebraic equation Qm = f(s,p1,q1,p2,q2). The model,in essence, is an injector model in case that the spool throttling area is much smaller than the pipeline flow area. Thespecific approach is to firstly consider the flow at spool as ideal gas isentropic flow and to secondly take into accountthe local pressure loss effect and the switching law of the valve through the flow coefficient Cd and the relative open-ing s respectively after the derivation of the mass flow rate equation. The flow coefficient here is not the conventionalratio of calculation flow rate to actual flow rate but a revise of the isentropic equation, that is, an empirical coefficient


used for taking the local pressure loss effect of the valve into account. To distinguish it from the injector component inthe front of the liquid engine combustion chamber, it is called injector orifice model herein.Spool throttling mass flow rate equation is given by:

Q m ¼sCdAv0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2cc�1 p1q1

p2p1

� �2c � p2

p1

� �cþ1c

sp2p1> 2

cþ1

� � cc�1;

sCdAv0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffip1q1c 2

cþ1

� �cþ1c�1

rp2p16

2cþ1

� � cc�1;

8>>>><>>>>:

p1 > p2 P 0: ð7Þ

In the case of reverse flow, that is, when the Eq. (7) meets 0 6 p1 < p2, p1 and p2 should exchange positions, and a minussign should be added in the front of the mass flow rate result.In the equation, p1, q1, p2 and q2 mean the spool upstream fluid pressure and density, the spool downstream pressureand density, respectively. s stands for the valve relative opening; Cd is flow coefficient, representing the throttlingcharacteristic of valve, and equivalent to functions of s. The Cd � s curves need to be worked out for different kindsof valves through testing and to be adjusted for different fluid media in line with viscosity and density; Av0 pointsout the flow section area in time of full opening (s = 1).

(2) Pressure difference-based injector orifice modelCurrently, there are about two categories of solutions to spool or orifice throttling [16,26,35–40]: in the first solution,both the flow coefficient and the flow section area are deemed functions of spool opening. The two variables, varyingwith the change of opening, both affect the flux of spool throttling. Hence, it is a solution which is closer to the realityas well as a way the pressure ratio-based injector orifice model adopts; the other solution is to integrate the two vari-ables into one variable, Generally, that is, Cd_latter = Cd_formerAv_former. The former need to make sure two relations,namely, the univariate function relationship between flow section area and opening, and the multivariable functionrelationship between flow coefficient and such factors as spool opening, fluid properties and spool shapes. The latter,integrating the effect of flow section area into the flow coefficient, only needs to confirm the function relationshipdefined between flow coefficient and those factors, which likely aims at facilitating the experiment on spool throttlingcharacteristics. However, the characteristic testing data of flow coefficient defined by the latter are inferior to those ofthe former in terms of universality due to the integration of two function relations. Meanwhile, the spool throttlingmass flow rate algebraic equation the latter adopts is usually a relational expression based on upstream and down-stream pressure difference, which is only applied to incompressible fluid (usually liquid) while the upstream anddownstream pressure ratio relationship is usually adopted for compressible fluid (usually gas). The key regulatorvalves used in the test rig system are made by Wuzhong Instrument Co. Ltd. The following is the spool throttlingmodel provided in the company’s valve information [40], in which the international unit is adopted.

Q m ¼q 1

3600 Cd � 287 1:02105

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðp1�p2Þðp1þp2Þ

GsgT

qp1 � p2 <

p12 ;

q 13600 Cd

2491:02105 p1ffiffiffiffiffiffiffiGsgTp p1 � p2 P p1

2 ;

8><>: p1 > p2 P 0; ð8Þ

where

Var ¼Var1þVar2

2 p1 � p2 <p12 ;

Var1 p1 � p2 P p12 ;

(p1 > p2 P 0; Var 2 fq; Tg;

the relative density is defined by Gsg = q/qAir, and the air density, qAir = 1.220 kg/m3.In the case of reverse flow, that is, when the Eq. (8) meets 0 6 p1 < p2, p1 and p2 should exchange positions, and a minussign should be added in the front of the mass flow rate result.

(3) Calculation scheme of flow coefficientWuzhong Instrument Co. Ltd., gives the flow characteristic curves of flow coefficient and the percentage of spoolstroke (that is relative opening) for various regulator valves it makes. In accordance with these curves, three kindsof characteristic formulas can be obtained by fitting on flow coefficient Cd and spool relative opening s. It is notewor-thy that the pressure difference-based injector orifice model scheme should be adopted when these characteristiccurves are used.

3.4. Thermodynamic calculation model

The mixture of air (as mixture of N2, O2 and Ar, the equivalent molecular formula of alternative air is N1.5624O0.4192Ar0.0092)and kerosene (RP-3 aviation kerosene, the equivalent molecular formula of No. 3 jet fuel alternative is C9.49H19.54) containsfive elements-H, C, N, O and Ar. As inert gas, Ar is supposed not to take part in reaction. Considering that combustion prod-


ucts include 12 elements, H, N, O, Ar, H2, N2, O2, CO2, CO, H2O, OH and NO in the H, C, N, O and Ar system, the correspondingthermodynamic calculation model is set up by the method of chemical equilibrium constant.

3.5. Modularization modeling approach

Table 1 shows the module information of eight typical components generated from modularization disassembly of theturbine test rig main test system. Among them, fluid source, gas pipe, gas volume, gas valve and gas generator pipe are fivebasic modules, on the basis of which other modules are born through combination and development.

Fig. 4 displays the finite control volume grids of gas generator pipe in which there is an inlet of oxidant gas injector and aninlet of fuel fluid source of mass flow rate type. At the inlet boundary, the boundary grid of connected component is con-nected with the combustion zone of the module. The flow zone of the module is equivalent to a combustion gas pipe.The outlet boundary is similar to the gas pipe module and can link volume-type or valve-type components.

Assumptions:

(1) The process from propellant spraying into the combustion zone to converting into combustion gas is instantaneousafter a time lag and the combustion time delay is a constant;

(2) The mixture ratio of the combustion zone is solely decided by the mass flow rate ratio of oxidizer to fuel injection,without considering the participation of residual gas into the afterburning;

(3) The combustion process is adiabatic, and the combustion reaction heat is entirely absorbed by generated gas;(4) The generated gas and the residual gas in the combustion zone can instantaneously and homogenously mix, meeting

temperature and element balance;(5) The combustion products are perfect gases, with ignorance of the effect caused by changes and differences of specific

heat ratios;(6) The volume of the liquid propellant at the combustion zone is ignored;(7) The combustion gas turns into completely frozen flow with elements and thermophysical properties unchanged after

entering the flow zone;(8) The flow is one-dimensional perfect gas flow, with ignorance of the effect caused by the gravity field;(9) The wall is a rigid wall, with ignorance of the elastic deformation of the wall, and the wall friction at the flow zone is

calculated in case of quasi-steady state.

Fig. 5 exhibits a flowchart of modularization modeling and simulation through using developed software. Maxer-ror < Error, in the calculation end conditions, is used for steady-state simulation while Time < Total_Simulation_Time isapplied to dynamic working process simulation.

4. Numerical model of the system

The turbine test rig is a complex system, where there are numerous physical and chemical phenomena such as atomiza-tion, ignition, combustion, mixing, rotation, flow and heat transfer, as well as flows of various media like fuel oil, water,normal-temperature air, high-temperature combustion gas, and mixed gas. Furthermore, each flow is controlled by corre-sponding variety and amount of regulator valves. Considering the high difficulty in the whole system modeling, this stagehas conducted numerical modeling and research on the main test system. The fuel–oil supply system, with experimentalmeasuring data (time-parameters) of fuel volume flow rate Qvf (converted to mass flow rate Qmf when used) and oil-sourcetemperature Tf as the inlet boundary conditions of the main test system, can be simplified into a fluid source of flow rate andtemperature inlet. The ignition system can be simplified into an event-triggered variable by a real-time control variable ofignition time established in corresponding module of the BK-1 type heater. As the test-bed testing object is not confined to aspecific turbine or a specific load, the turbine and load system can be simplified into a total pressure outlet fluid sourcethrough regarding experimental measuring data of turbine inlet total pressure pt7 and total temperature Tt7 as the outletboundary conditions of the main test system. In addition, The exhaust bypass (the branch where F5 is situated) regards

Table 1Modularization disassembly of turbine test rig main test system.

Module type name Type code Identifier Module attribute

Fluid source 00 FS BasisGas pipe 02 GP BasisGas volume 12 GVol BasisGas mixing apparatus 17 GMA CombinationGas steady apparatus 20 GSA CombinationGas valve 22 GV BasisGas injector 32 GI CombinationGas generator pipe 35 GGP Basis and combination

(i+1)th

state element

xj-2xi-2

uj-2

uj

un

un+1

xi

i-2 Ei-2

(pi-2)1 E1

(p1)

c pc

(RT)c Vc

u1 u2

x0x2 xj-3xi-3

uj-3

i-3 Ei-3

(pi-3)n En

(pn)

xn

xn

xn+1

b

pb

( j+1)th

velocity element

xi+1xj

Ab

A0

A0 A2 Ai-3 Aj-3 Ai-2

Aj-2

Ai Ai+1

AnAn

An+1

x1

A1

x1

A1

u0

i Ei

(pi)

xj-1xi-1

Ai-1Aj-1

i-1 Ei-1

(pi-1) Aj

uj-1

Combustion zone Flow zone

xj+1

Aj+1

i+1 Ei+1

(pi+1)

uj+1

uj+2

xi+2

Ai+2

un-1

xn-1

xn-1

An-1An-1

n-1 En-1

(pn-1)0 p0

(RT)0 V0

p

Oxidant gas injector inlet

Qmf

Fuel mass flow rate fluid source

inletAa

x0

Av1 uv1

Av0

Fig. 4. Finite control volume grids of gas generator pipe.

Fig. 5. Flowchart of modularization modeling and simulation.


experimental measuring data of pressure p5 and total temperature Tt5 at the bypass measurement nozzle as the outletboundary conditions of the main test system, which is a pressure outlet fluid source. F1–6 six regulator valves are consideredas gas valve module components, and the spool throttling model and flow coefficient calculation scheme can be decided inaccordance with the valve type by the data and curves from Wuzhong Instrument Co. Ltd.

Fig. 6 shows the numerical simulation model of the turbine test rig main test system. During modularization modeling,the system is divided into 3 fluid sources (FS1–3), 18 gas pipes (GP1–18), 5 gas volumes (GVol1–5), 1 gas mixing apparatus(GMA1), 1 gas steady apparatus (GSA1), 8 gas valves (GV1–8), 1 gas injector (GI1) and 1 gas generator pipe (GGP1), by whicha 38-component numerical system is established.

The following demonstrates that the numerical system is applied to simulating the first 260 s rig regulating processing ofa test. The length (unit: m), outer diameter and thickness (unit: mm) of every pipe are as shown in Fig. 6. The flow field gridsof pipe-type components are divided by 100 mm/grid. The length along flow direction of the lumped parameter components(such as gas valve, gas volume, etc.) should be two standard grid units, i.e. 200 mm. The total volume of the gas source (com-posed of a number of high-pressure air bottles) is designated to be 2000 m3. The regulating time sequence design of F1–6 sixregulator valves is shown in Table 2. When the simulation starts, a close distribution of initial flow field and wall temper-ature field is given, and the ignition is made after 10 s cold flow simulation. The emphasis should be placed on comparing the20–260 s results of simulation and experiment. In this way, the initial field is not necessarily designed to be the same as thatin experiment. The experimental measuring data, namely, the test data in the form of time-parameters point list of Qmf, p5

and pt7, should be applied to the boundary conditions of three fluid sources FS1–3.

Fig. 6. Numerical simulation model of the turbine test rig main test system.


The pipe-wall radial-direction one-dimensional heat transfer model is used for module components of gas pipe, gas valve,gas steady apparatus and gas injector. The gas volume module components adopt the pipe-wall zero-dimensional heat trans-fer model. The combustion zone of the gas generator pipe module component is considered as wall heat insulation while theflow zone uses pipe-wall radial-direction one-dimensional heat transfer model. The wall heat insulation is applied to the gasmixing apparatus module component. The pipe-wall radial-direction grid sequence numbers of the components adoptingone-dimensional heat transfer model total 4.

GV2 (F2) and GV3 (F1) adopt equal percentage flow characteristic fitting formula scheme of HCB cage-type double-seathigh-capacity sleeve regulator valve. GV7 (F5) and GV8 (F6) adopt DN200 and DN250 flow characteristic fitting formulaschemes of VBS soft-seat butterfly valve, respectively. The four regulator valves correspondingly employ pressure differ-ence-based injector orifice model. GV6 (F4) remains fully closed during the rig regulating test. Therefore, it is not importantto choose which formula to be used and it would be workable if only the flow value, worked out through the formula underzero opening, is zero, where the same scheme is adopted as GV2 and GV3.

GV1 (F0), GV4 (safety valve), and GV5 (F3) remain fully open in the test, so there is no change in the opening degree. Con-sequently, the throttling conditions of these valves would not affect the variation trends of simulation curves. The pressureratio-based injector orifice model is employed here.

5. Results and discussion

Fig. 7 shows the experimental curves of pressures, total pressures, total temperatures, fuel mass flow rate and turbinerotate speed in the turbine test rig system which are measured by sensors in a rig regulating test. The data acquisition fre-quency stands at 1 Hz, i.e. a data point per second. The experimental curves of �2500 s have recorded the variations of stateparameters at various measuring points in the speed-up process of the turbine from starting rotation to rotate speed of27,500 r/min by stages after ignition and in the slowdown process from the highest speed by stages. This paper has con-ducted numerical simulation on the first 260 s in the rig regulating process. Locations of the measuring points are shownby the schematic diagram of the turbine test rig system in Fig. 1. Some measuring points are designed for measuring theparameters of the same location, but only typical measuring curves are picked up in charting. For example, Tt13 and Tt14

are total temperatures concluded at the third and the fourth Tt1 measuring points. It can be seen that the curves concludedby different sensor measuring points at the same location are not certainly identical.

Figs. 8a–l show comparison between the simulation results and the experimental measurements. The simulation dataoutput frequency is 10 Hz, namely, a data point per 0.1 s. The subheads of figures are named after the respective measuringpoints. The locations of the simulation data points are shown by the numerical simulation model of the turbine test rig maintest system in Fig. 6. In Fig. 8a–g, i and k, the parameter curves marked with symbols like triangle, circle, etc. and the turbinerotate speed nh curve are experimental data while the parameter curves without symbols or with the component name (suchas GP1, GGP1, etc.) as prefix are simulation data of respective component grids in Fig. 6 corresponding to the sensor-mea-suring points in Fig. 1. The parameter curves in Fig. 8h, j and l are simulation data. In names of simulation curves, 0, n/2 andn � 1 in flow direction stand for the entrance grid, middle grid and exit grid of pipe, respectively while 0 and nw in radialdirection stand for the internal pipe-wall grid and external pipe-wall grid, respectively.

As shown in Fig. 8a, there is no evident decline in the pressure experimental curves of the inflow measurement nozzleupstream and downstream during 0–260 s test. However, it is visible that the pressure simulation curve at GP1 exit grid goesdownhill. The total temperatures curves are both on the decline, but the drop of the simulation curve is more obvious thanthat of the experimental curves (Tt91, Tt92). In view of the �2500 s test curves in Fig. 7a and b, the general trends of thepressure p91 and total temperature Tt91 curves are both on the decline as air flows out in the experimental process, andthe temporary rise of the pressure curve at some stages may be caused by experimental measuring problems as well asby working problems of the gas source composed of air bottle groups. For instance, the upstream pressure of the inflowmeasurement nozzle measured in the experiment, p91, is unexpectedly lower than the downstream pressure, p101, inFig. 8a. In practice, there are four sensor measuring points in upstream and downstream of the inflow measurement nozzle,

Table 2Regulating time sequence design of six regulator valves in 0–260 s.

Simulation time Manually-recorded values (bold-faced and italic) andanalyzed assumptive values (normal) on relativeopenings of six regulator valves in numerical model

Sensor-measured values of fluid sources and turbine rotate speed (101,325 Pa of standard atmosphericpressure for gauge pressure conversion)

Test time

GV3 GV2 GV5 GV6 GV7 GV8 FS1 FS2 FS3 Turbine 10:16:00Startingpoint

DN100 DN200 DN150 DN200 DN200 DN250 830 kg/m3

Relative opening Fuel oil flow rate Pressure Totaltemperature

Totalpressure

Totaltemperature

Rotatespeed

F1 F2 F3 F4 F5 F6 Qmf kg/s p5/Pa Tt5/K pt7/Pa Tt7/K nh r/min Time/s

0s 0.184 0 1.0 0 0.25 0 0 s10 s Ignition 0.014447 106,746 431.615 100,536 326.112 14.0629 1060 0.03 0.013674 106,805 441.840 98,247 325.773 25.3133 6070 0.04 0.014156 104,957 442.124 103,248 326.499 570.955 7080 0.05 0.014243 103,645 442.105 108,672 336.453 2339.13 80120 0.07 0.014340 102,572 448.293 108,672 355.771 2329.76 120130 0.106 0.013680 103,943 447.747 118,194 363.834 4693.27 130150 0.190 0.01520 102,930 449.502 123,077 375.055 5042.97 150160 0.210 0.014981 102,870 446.559 124,102 378.814 5031.72 160170 0.220 0.014444 104,719 443.855 126,513 379.898 5040.15 170180 0.240 0.015208 105,196 441.285 130,914 382.964 5040.15 180190 0.250 0.015229 104,122 438.06 135,496 383.732 5038.28 190200 0.270 0.016866 103,645 435.015 139,897 384.098 5077.65 200210 0.280 0.01771 106,567 433.072 143,455 385.301 4991.40 210220 0.290 0.019250 105,851 430.858 153,949 385.978 5021.40 220230 0.300 0.020644 108,475 429.572 163,720 386.428 5042.03 230236 0.317 0.14 0.021588 107,342 430.893 168,305 389.006 4997.96 236246 0.159 0.024199 105,732 436.84 232,713 394.436 5038.28 246260 s Simulation end No manually-recorded values on valve opening

available at the following stage. . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . 10:57:34Test end

Y.Chenet

al./Applied

Mathem

aticalM

odelling35

(2011)5382–

53995393

t / s

p,p

t/MPa

Qmf/(kg/s)

n h/(r/min)

0 500 1000 1500 2000 25000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0

0.01

0.02

0.03

0

10000

20000

30000

p91p31p51pt7pt8Qmfnh

t / s

T,T

t/K

Qmf/(kg/s)

n h/(r/min)

0 500 1000 1500 2000 2500250

300

350

400

450

500

550

600

650

0

0.01

0.02

0.03

0

10000

20000

30000

QmfTt91Tt14Tt33Tt51Tt7Tt8nh

t / s

p,p

t/MPa

Qmf/(kg/s)

n h/(r/min)

0 20 40 60 80 100 120 140 160 180 200 220 240 2600

0.2

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1

1.2

1.4

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p91p31p51pt7pt8Qmfnh

t / s

T,T

t/K

Qmf/(kg/s)

n h/(r/min)

0 20 40 60 80 100 120 140 160 180 200 220 240 260250

300

350

400

450

500

550

600

650

0

0.01

0.02

0.03

0

2000

4000

6000

8000

10000QmfTt91Tt13Tt14Tt33Tt36Tt51Tt7Tt8nh

(a) Pressures and total pressures (b) Temperatures and total temperatures

(c) Pressures and total pressures in 0-260s (d) Temperatures and total temperatures in 0-260s

Fig. 7. Experimental measurements of the turbine test rig.


respectively, and the magnitudes and the amplitudes of the pressure curves measured by the eight measuring points are dif-ferent. For example, the pressures range from 1.55 MPa to 1.71 Mpa, which indicates that curves measured by different sen-sors at the same location are not in full accord. The obviousness of the decline of simulation curves against that ofexperimental curves attributes not only to underestimate of the simulation on the components-wall heat transfer fluxbut also to inconformity of GVol1 settings (such as volume) with the actual situation of the air bottle groups.

As indicated by Fig. 8b, the total temperature simulation curve at GGP1 middle grid is well (maximum error no more than6%) in line with the heater-downstream total temperature Tt14 experimental curve in 20–260 s dynamic variation process,although the oscillation of the simulation curve is a little more visible than that of the measurements, which is becausethe simulation data output frequency is 10 Hz while the experimental data output frequency is 1 Hz, as well as attributesto simulation stability.

According to Fig. 8c, the simulation and the experiment are the same in two aspects. Firstly, the variation trend of thetotal temperature simulation curve at GP16 exit grid is in accord with that of the experimental curves (Tt51, Tt52) at bypassmeasurement section. Secondly, judging from the testing curves in other figures and Fig. 8c, the experimental curves mea-sured at all total temperature measuring points (such as Tt13, Tt14, Tt51, Tt52, Tt33, Tt36 and Tt7) produce evident thermal strat-ification, that is, the temperature of combustion gas gradually declines along the flow direction, which can be also seen insimulation curves. Since there is no obvious thermal stratification among the total temperature curves under the compo-nents-wall adiabatic model, it can be concluded that the phenomenon is caused by the heat-transfer cooling effect of com-ponents wall on combustion gas. The difference between the simulation and the experiment mainly lies in the phenomenonthat the curve magnitude of the simulation is higher than that of the experiment. There are three reasons, that is, the incom-plete conformity of valve switching time sequence and magnitude with the experiment, the underestimate on the compo-nents-wall heat transfer flux, and some problems caused by experimental measurement which can be seen from theimperfect accordance of curves measured by different sensors at the same location.

Judging from Fig. 8d, the variation trends of the pressure simulation curves at GP17 grids fully agree with those of themain-line measurement nozzle upstream (p31) and downstream (p41) pressure experimental curves in the whole rig

t / s

p/MPa

T t/K

0 20 40 60 80 100 120 140 160 180 200 220 240 2601.58

1.6

1.62

1.64

268

270

272

274

276

278p91p101Tt91Tt92GP1-p(n-1)GP1-Tt(n-1)

t / s

T t/K

n h/(r/min)

0 20 40 60 80 100 120 140 160 180 200 220 240 260400

440

480

520

560

600

0

2000

4000

6000

8000

10000

Tt13Tt14nhGGP1-Tt(n/2)

measurement nozzle upstream and downstream

t / s

T t/K

n h/(r/min)

0 20 40 60 80 100 120 140 160 180 200 220 240 260400

420

440

460

480

500

0

2000

4000

6000

8000

10000

Tt51Tt52nhGP16-Tt(n-1)

t / s

p/MPa

n h/(r/min)

0 20 40 60 80 100 120 140 160 180 200 220 240 2600.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0

2000

4000

6000

8000

10000

p31p41nhGP17-p(n/2)GP17-p(n-1)

upstream and downstream

t / s

T t/K

n h/(r/min)

0 20 40 60 80 100 120 140 160 180 200 220 240 260300

330

360

390

420

450

480

510

540

0

2000

4000

6000

8000

10000

Tt33Tt36nhGP17-Tt(n/2)GP17-Tt(n-1)

t / s

p/MPa

T t/K

0 20 40 60 80 100 120 140 160 180 200 220 240 2600

0.05

0.1

0.15

0.2

0.25

0.3

300

320

340

360

380

400

420

440

460

480

500

pt7Tt7GP18-pt(n-1)GP18-Tt(n-1)

(a) Pressures and total temperatures of inflow (b) Heater-downstream total temperatures

(c) Total temperatures at bypass measurement section (d) Pressures of main-line measurement nozzle

(e) Total temperatures at main-line measurement section (f) Total pressure and total temperature of turbine inlet

Fig. 8. Comparison of simulation results with experimental measurements.


regulating process of 20–260 s, especially at the stage of regulator valves and fuel flow rate adjustment, which proves, on theone hand, the regulating time sequence of six regulator valves obtained by analysis in Table 2 is reasonable and shows, onthe other hand, the simulation algorithm has certain validity and precision. The difference in the variation magnitude

t / s

T w/K

T w/K

T w/K

T 0/K

0 20 40 60 80 100 120 140 160 180 200 220 240 260270.5

270.6

270.7

270.8

270.9

271

278

278.4

278.8

279.2

279.6

Tw10T0GP1-Tw(0.0)GP1-Tw(n/2.0)GP1-Tw(n-1.0)GP1-Tw(n-1.nw)

t / s

qrho/W

/m2

qrho/W

/m2

qrho/W

/m2

Re

0 20 40 60 80 100 120 140 160 180 200 220 240 260-250

-200

-150

-100

-50

0

50

100

0

300000

600000

900000

1.2E+06

1.5E+06

1.8E+06

GP1-Re(0)GP1-qrho(0)GP1-Re(n-1)GP1-qrho(n-1)

t / s0 20 40 60 80 100 120 140 160 180 200 220 240 260

310

320

330

3aa40

350

360

370

380

390

400

410

420 Tw6GP16-Tw(0.0)GP16-Tw(n/2.0)GP16-Tw(n-1.0)GP16-Tw(n-1.nw)

t / s

Re

0 20 40 60 80 100 120 140 160 180 200 220 240 2600

5000

10000

15000

20000

25000

0

100000

200000

300000

400000

500000

600000

700000


t / s0 20 40 60 80 100 120 140 160 180 200 220 240 260

320

330

340

350

360

370

380

390Tw4GP17-Tw(0.0)GP17-Tw(n/2.0)GP17-Tw(n-1.0)GP17-Tw(n-1.nw)

t / s

Re

0 20 40 60 80 100 120 140 160 180 200 220 240 2600

3000

6000

9000

12000

15000

0

100000

200000

300000

400000

500000

600000

700000


(g) Wall temperatures at inflow measurement section (h) Simulation results of Reynolds numbers and convective and ambient temperature heat flux densities at GP1 entrance and exit grids

(i) Wall temperatures at bypass measurement section (j) Simulation results of Reynolds numbers and convective heat flux densities at GP16 entrance and exit grids

(k) Wall temperatures at main-line measurement section (l) Simulation results of Reynolds numbers and convective heat flux densities at GP17 entrance and exit grids

Fig. 8 (continued)


between simulation and experiment attributes not only to the disparity between the opening-flux relationship calculated bythrottling model used in each regulator valve and the relationship in real rig regulating experiment but also to the incom-pletion of the manual recording time sequence of the experimental data with which the regulating time sequence is designedin accordance. As indicated by the figure, unlike the obvious stratification of total temperature curves, there is no evidentstratification in the main-line measurement nozzle upstream and downstream (totally eight measuring points, two shownin the figure) pressure experimental curves.


Seen from Fig. 8e, the same stratification phenomenon occurs in the total temperature simulation values at GP17 grids asthe experiment, and the general variation trend of the total temperature simulation curves is in accord with that of theexperiment. Particularly at the first 60 s stage when GV8 is closed, the total temperatures at middle and exit grids are a littlelower than the initial values due to heat transfer of flow field to pipe wall, which well tallies with the experimental curves(Tt33, Tt36). Like the situation in Fig. 8c, the shortcoming lies in the phenomenon that the magnitudes of the total temperaturesimulation curves after 60 s are higher than that of the measurements, and the total temperature simulation curves surgeinstantaneously after opening of GV8 while the experimental curves gradually climb over time.

The situation in Fig. 8f is similar to that in Fig. 8e. The 0–60 s total temperature simulation curve at GP18 exit grid nearlycoincides with the turbine inlet total temperature Tt7 experimental curve. With the opening of GV8 in 60–80 s, the total tem-perature simulation curve rapidly goes up while the experimental curve moves up slowly, and there is a big difference inmagnitude between simulation and measurement. As the turbine inlet total pressure test data are directly used as the outletboundary condition of FS3 for simulation, the total pressure simulation curve coincides with the experimental curve (pt7). Bythe same token, the pressure test (p51) and simulation results at FS2 are not shown in Fig. 8c.

Figs. 8g–1 show the heat transfer conditions between flow field and pipe wall at three pipe-wall-temperature measuringpoints as well as the comparison between pipe-wall-temperature simulation results and experimental measurements.

As shown in Fig. 8g and h, the convective heat exchange densities of various GP1 grids from flow field to pipe wall, differentfrom those pipes through which combustion gas flows, are negative during 20–260 s, which shows that in-pipe air keepsabsorbing heat from pipe wall. That is because the temperature of air bottles, contrary to the phenomenon that the temperatureof a gas bottle increases as air is filled, gradually drops as air flows out, which induces that the grid temperatures of pipelinebetween GVol1 and GGP1 through which normal-temperature air flows all decline with the fall of gas source temperature.The drop of air temperature accordingly results in the decrease of wall temperature, which is demonstrated by the phenomenonin Fig. 8g that the experimental measuring wall temperature Tw10 at inflow measurement section is�9 K lower than the ambi-ent temperature T0 and keeps declining. The wall temperature simulation curves slightly goes up at early stage, which is be-cause the initial values of GP1 flow field and wall grids are designed at 270.8 K and the temperature difference is zero. Inthis case, although air temperature is on the decline after 0 s and the temperature difference between GP1 flow field and wallis on the increase, the cooling effect of the convective heat transfer from flow field to wall is inferior to the heating effect of theconvective heat transfer from external environment to wall at the small-flow-rate phase of air without action of GV3, whichresults in the slight wall-temperature climb at the beginning. When the temperature difference between flow field and wallincreases to a certain point, the convective heat transfer of internal pipe wall makes stronger effect than that of external pipewall, thus the temperatures of various pipe-wall grids start falling. As the flow rate of air, with opening of GV3, gradually in-creases after 150 s, the decline of the pipe-wall temperature becomes increasingly evident. Since GP1 is a tapered pipe andthe inner diameter reduces from 305 mm at entrance section to 203 mm at exit section, Fig. 8h shows that the Reynolds numberat exit section is higher than that at entrance section. Therefore, the convective heat exchange at exit section is stronger and thewall temperature simulation curves at exit section decline more obviously at late stage. In addition, there is the temperature-declining air inside the pipe while the normal-temperature environment outside the pipe, so the temperature of internal pipe-wall grid is lower than that of the external pipe-wall grid.

As indicated by Fig. 8i and j, the temperature simulation curve at GP16 exit wall grid is close to the experimental curve ofwall temperature Tw6 at bypass measurement section. Due to the heat transfer from combustion gas, the pipe wall temper-ature is always on the rise during 20–260 s and climbs a little less slowly after �70 s than 20–60 s. The two characteristicsshown in the experimental curve are also proven in the simulation curves, which indicates that the simulation results havecertain precision.

Seen from Fig. 8k and l, the similarity of the temperature simulation curves at GP17 middle and exit wall grids with theexperimental curve of wall temperature Tw4 at main-line measurement section is inferior to that in Fig. 8i, but their generaltrends are comparatively consilient. The pipe-wall grids at GP17 middle and rear sections maintain initial temperature be-fore 60 s, and the pipe-wall temperature gradually ascends after �80 s owing to the heat transfer from combustion gas withopening of GV8 during 60–80 s. These two characteristics are reflected both by experimental curve and simulation curves.

6. Conclusions

Through the simulation study of turbine test rig main test system, the following conclusions can be obtained:

(1) Although there are many uncertainties, such as different opening-flux relationships for different throttling calculationschemes, and the complexity of transient simulation resulted from the coupling of various factors including structures(like reducing pipe, branch, convergence, etc.), flow, combustion, mixing and so on, during the simulation of 38-com-ponent numerical system, the general variation trends of various state parameters obtained through simulation areconsistent with the experimental curves, which shows that the analysis on test data is reasonable and the establishednumerical system has certain validity.

(2) There is no obvious thermal stratification among total temperatures at various measurement points calculated underthe components-wall adiabatic model. After considering the components-wall heat transfer, the simulation results ofvarious system components are more reasonable and closer to the experimental measurements. Meanwhile, the


regulating time sequence design of six regulator valves directly decides the trends of simulation curves. It can be con-cluded that the modeling of components-wall heat transfer and the modeling of valve spool throttling are two keyfactors of affecting simulation precision.

(3) The spool throttling model scheme and the flow characteristic curves given by Wuzhong Instrument Co. Ltd., for theregulating valves the company develops are based on liquid media (The flow coefficient is defined to aim at water), sothe formula of its spool throttling model adopts relational expression based on upstream and downstream pressuredifference, that is, pressure difference-based injector orifice model. However, the pressure difference relationalexpression can be only applied to density-basically-unchanged incompressible fluid (usually refer to liquid). For com-pressible fluid (usually refer to gas), the upstream and downstream pressure ratio relational expression is usuallyused. Therefore, there are applicability problems when the model system is used for describing gas media with a widevariation range of state parameters such as pressure and density. The more accurate simulation is supposed to adoptpressure ratio-based injector orifice model and make characteristic tests with air as medium on regulator valve com-ponents to obtain corresponding flow characteristic curves.

(4) The test curves measured by different sensors at the same location are not completely consistent, thus it is necessaryto evaluate the reliability of dynamic measurement of experimental data.

Acknowledgments

The authors thank Dr. Peng Xu from the research team for his guidance in software interface, Mr. Yulong Huang and Mr.Ning Gao from Beijing Aerospace Measurement & Control Corp. for their data support, Professor Haixing Wang from BUAAand the anonymous referees for their revision advice, Ms. Jihong Zhao for her language support.

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Modularization modeling and simulation of turbine test rig main test system

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