TransientCharacteristicsofWater-JetPropulsionwithaScrew...

Research ArticleTransient Characteristics of Water-Jet Propulsion with a ScrewMixed Pump during the Startup Process

Wei Han12 Teng Zhang 1 You Liang Su1 Ran Chen1 Yan Qiang1 and Yang Han1

1Lanzhou University of Technology College of Energy and Power Engineering Lanzhou 730050 China2Key Laboratory of Fluid Machinery and Systems Lanzhou 730050 China

Correspondence should be addressed to Teng Zhang 18297669175163com

Received 16 March 2020 Accepted 15 April 2020 Published 4 May 2020

Academic Editor Julien Bruchon

Copyright copy 2020 Wei Han et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In order to investigate the transient hydrodynamic characteristics of water-jet propulsion with a screw mixed pump during thestartup period and to overcome the difficulties in measuring the transient process parameters over a very short period of time amethod based on a flume experiment combined with computational fluid dynamics (CFD) is proposed -e thrust and torque ofthe pump-jet propulsion according to mooring status at different rotational speeds were measured by the test which provided agroup of data for the boundary and initial conditions of the numerical calculation of the user-defined function (UDF) Con-secutive changes in the parameters of the water-jet propulsion dynamics can be captured from the numerical simulation of thestartup process with the UDF -us the transient hydrodynamic characteristics of water-jet propulsion according to time orrotation speed were obtained -e results show that the relationship between the thrust or torque of the water-jet propeller andpump rotational speed is close to the quadratic functions -e energy characteristic parameters of screw mixed water-jet pumpsuch as the flow rate head shaft power and efficiency rapidly increase and decrease and then remain relatively stable

1 Introduction

As an advanced propulsion mode thrust is generated bywater-jet propulsion with a screwmixed pump relying mostlyon the difference in momentum between the inlet and outletwater flows [1 2] -is method has many advantages overtraditional propeller propulsion such as higher efficiencylower noise more stable operation and better resistance tocavitation and it has been widely used in high-performancewarships and new submarines-e thrust and power of water-jet propulsion with a screwmixed pump are usually altered byadjusting the rotational speed and are scarcely affected by thesailing speed -e rotational speed of the impeller rapidlyreaches the designated value during the startup period andthe flow pattern changes from laminar to complex turbulentflow causing a rapid fluctuation in pressure a high-water flowimpact and a transient high load on the blade which all affectthe stability and longevity of the pump-erefore it is of greatsignificance to investigate the transient characteristics of thistype of water-jet propulsion during the startup period

Zhang et al [3] found that the quasi-steady calculationscould not be used to accurately predict the transient be-havior especially in the initial stage of startup Tsukamotoet al [4 5] found that the dimensionless head and flow ratebegan to decrease from initially large values reachingsteady-state values after a certain time below the steady-statecurve during the centrifugal pumprsquos startup processesChalghoum et al [6] analyzed the effects of the impellergeometric parameters and different openings of the dis-charge valve on external characteristics during the centrif-ugal pump startup period Li et al [7] established a closedcirculatory system with the centrifugal pump to study thetransient characteristics during the startup period whichavoided the calculation error caused by the uncertaintyregarding the boundary conditions of the inlet and outletTanaka and Tsukamoto [8ndash10] studied cavitation in cen-trifugal pumps during the startup period by flow field vi-sualization and found that the rapidly changing pressure andflow rate were related to the cavitation behavior of the pumpBased on the momentum moment theorem Ping et al [11]

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 5691632 9 pageshttpsdoiorg10115520205691632

deduced the basic equation of steady speed and the startingprocess of a centrifugal pump respectively and described theinfluence of impeller rotating acceleration and fluid accel-eration on the startup performance with a mathematicalequation Zhang et al [12] qualitatively analyzed the transientbehaviors in detail using the transient Euler equation ofturbomachinery during all kinds of operation periods andquantitatively calculated the instantaneous additional theoryheads and additional theory power Wang et al [13 14] set upa model to analyze the startup process of the mixed-flowpump based on the internal characteristics of the pump andthe one-dimensional unsteady motion equations of thepipeline Li et al [15] analyzed the starting characteristics ofthe mixed-flow pump based on a quasi-steady-state as-sumption which provides a new idea for revealing thetransient internal characteristics of the startup process of themixed-flow pump -e transient behavior of the pump wasanalyzed using pump characteristic curves [16] Li et al [17]found that in the startup process of the mixed-flow pump theflow stabilized in the impeller the scale of vortex decreasedgradually as the rotating speed approached the rated speedand the transient effect disappeared

-e above-described investigation of water-jet propulsionpumps mainly focused on the characteristics and optimaldesign of the pump [18ndash20] -ere is little research on thetransient response characteristics of propulsion performanceduring the startup process for water-jet propulsion with ascrew mixed pump Fu et al [21] found there are severeunsteady vortex flows in the vaneless space near the condi-tions under which the hydraulic torque on the runner equalsto zero Nouha et al [22] found that the pump dynamicbehavior with the impeller geometry during the startingperiods Tao et al [23] found that the increase in the volutecasing flow area is helpful to improve the operation stability ofthe pump Wang et al [24] found that the valve head changeduring the startup process had a significant transient effect Inthis paper the control of impeller speed realized by the user-defined function (UDF) in a numerical simulation and atechnique for controlling the frequency in an experiment toreveal the transient hydrodynamic coefficients during thestartup period of the water-jet pump are described

2 Experiment for Pump-Jet PropulsionAccording to Mooring Status

21 Experimental Equipment and Procedure -e experi-mental equipment mainly included digital torque and ro-tational speed measurers a high-precision electronic forcesensor a model of a submarine pump and a rotational speedgovernor as shown in Figure 1 -e components of the self-circulating high-precision flume mainly included the flumebody the water supply equipment the automatic flowmeasurement system the tail door control system and theADV flow velocity measurement system -e length widthand depth of the flume were 13 06 and 06m respectively-e flow rate of the flume was regulated by a closed-loopcontrol mode which has the characteristics of high accuracyand stable control and can meet the test requirements ofsteady and unsteady flows

Firstly the automatic flow measurement system and taildoor control system were used to keep the water level of theflume at a fixed height Secondly the rotational speed of thewater-jet pump was adjusted to a stable value by using therotational speed governor -e rotational speed and cor-responding torque were recorded using the digital torqueand rotational speed measurers -e corresponding thrustvalue at the stable speed was recorded by the high-precisionelectronic force sensor and used -e arithmetic averagevalue of the corresponding thrust was calculated by takingthree measurements at the same rotational speed to reducethe error in the data

22 -rust and Torque at the Different Rotational Speeds-e experimental results show that the thrust and torque atdifferent rotational speeds followed the quadratic functiondistribution and the curves for thrust and torque at differentrotational speeds are shown in Figure 2 and the mathe-matical relationship between thrust and torque is shown inequations (1) and (2)

T minus 021859 minus 843874 times 10minus 4n + 450341 times 10minus 6

n2 (1)

M 000926 minus 424441 times 10minus 5n + 157305 times 10minus 7

n2 (2)

3 Numerical Simulation

31 Geometric Model -e 3D geometric models and pa-rameters of water-jet propulsion with a screw mixed pumpare shown in Figure 3 which shows a 3-D model containingan impeller a guide vane and a nozzle Table 1 lists theprincipal specifications of the water-jet pump

32 Mesh Generation Fully tetrahedral meshes wereadapted to discretize the computational domains as shownin Figure 4 -e number of grids affects the accuracy ofnumerical calculations In theory the more the meshes thereare the higher the accuracy Having too many meshes in-creases the calculation time and reduces the speed of con-vergence -erefore to eliminate the influence of thenumber of grids on the calculation of the results it is nec-essary to check independence from the grid number Sixgroups of time steps are selected for numerical calculation asshown in Figure 5(a) as the time step increases the head h

1

2

3

54

6

7

Figure 1 -e experimental system of water-jet propulsion (1) Ul-trasonic velocimeter (2) thrust collector (3) speed torque indicator (4)submersible model (5) water-jet propulsion pump (6) high-precisionelectronic force gauge and (7) self-circulating experimental flume

2 Mathematical Problems in Engineering

gradually increases the efficiency η slowly increases with timeand when the mesh quantity is increased to 1728 million thehead and efficiency of the water-jet pump remain stable

33 Verification of Independence from the Grid Number andTime Step To ensure the accuracy and precision of thenumerical results an appropriate time step is needed InFigure 5(b) T1 T2 T3 and T4 are the numerical simulationresults for thrust with time steps of 00008 00001 00002and 00004 s respectively and T5 is the experimental valuewhen the system operation is stable It can be seen from the

figure that the errors for 000008 and 00004 s are 1459 and15125 respectively while the errors for 00001 and00002 s are smaller To ensure the precision of the numericalcalculations 00001 s is selected as the time step

34 Numerical Model and Boundary Condition

341 Governing Equations and Turbulence Model In areference-rotating frame related to the impeller passage thebasic equations of continuity and momentum are the following

zρzt

+ nabla ρv0( 1113857 0 (3)

ddt

ρv0( 1113857 + 2ρω times v0 + ρω times ω times r ρF minus nablap + μ + μt( 1113857nabla2v0

(4)

where ρ v0ω r F μ μt andnabla are the density of the fluid thevelocity vector the rotating angular velocity the spacevector the mass force the coefficient of kinetic viscosity thecoefficient of turbulent kinetic viscosity and the Hamilto-nian vector respectively

-e RNG k-ε model was chosen as the turbulent modelfor numerical study To realize the pressure speed couplingsolution two-order upwind schemes were adopted in thenumerical calculation and the finite volumemethod was alsoused as were the central difference schemes for the diffusionterms-e no-slip wall condition was applied for the walls ofthe hub and blade surface and for the other solid walls

342 UDF and Boundary Conditions -e thrust and torquevalue at the stable speed following its change are obtained-e law of the changes in thrust and torque with the changein rotational speed is analyzed and the determined rota-tional speed control law is provided for in the numericalsimulation -e speed of the impeller was controlled in theprocess of numerical simulation After the law of the integral

500 1000 1500 2000 2500 30000n(rmin)

0

5

10

15

20

25

30

35

40

45T

(N)

(a)

00

02

04

06

08

10

12

14

16

M(

nmiddotm

)

500 1000 1500 2000 2500 30000n(rmin)

(b)

Figure 2 -e variation of thrust and torque at the different rotational speeds (a) thrust and (b) torque

1 2 3

Figure 3 A 3-D model of water-jet propulsion with a screw mixedpump (1) Impeller (2) guide vane and (3) nozzle

Table 1 -e design parameters of the water-jet pump model

Geometric parameter ValueFlow rate 138m3hHead 13mRotational speed 1500 rpm-rust (TN) 10774Specific speed 278

Mathematical Problems in Engineering 3

acceleration of the impeller was made discrete a UDFprogram to control the change in speed was written -eprogram was loaded onto the impeller slip grid speedcontroller and the steady-state result was taken as the initialcondition of the unsteady calculation In each iteration stepof the unsteady calculation process the impeller speed wasupdated According to experimental statistics and relatedreferences [25] the variation of the rotational speed n of theimpeller can be described by equation (5) the change of nwith time t is shown in Figure 6 To accurately capture thetransient characteristics of the water-jet pump startupprocess the computational time interval was set to 00001 s-e maximum number of iterations for each time step wasset to 20 and 7000 steps was calculated to ensure the stabilityof the internal flow

n 15000t tle 01 s

1500 tgt 01 s1113896 (5)

For the startup simulation the contact surfaces betweentwo adjacent components were connected through an interfaceboundary-e acceleration of the impeller was simulated usinga sliding mesh method with rotational speeds assigned by aprescribed curve In this study the rotational speed increaseslinearly from zero to its rated speed of 1500 rmin in 01seconds (marked as t0) After 01 s the speed of the impellerwas constant -is was since the inlet and outlet boundaryconditions for an individual three-dimensional pump modelwere unsteady during the startup process and because it isdifficult to accurately specify the unsteady boundary condi-tions To eliminate the errors of the inlet and outlet unsteady

(a) (b) (c)

(d)

(e)

Figure 4 Computational domain meshes (a) Impeller (b) guide vane (c) nozzle (d) computing domain (e) locally encryption mesh


boundary conditions a hypothesis was formulated whichassumed that the flow was stationary and that the pressuredifference between the inlet and outlet was zero at the be-ginning of the startup Based on the above assumption theboundary conditions of the inlet and outlet were all set as totalpressure stable and the reference pressure was set as 0 atm

35 Comparison of Results from the Experiment and Nu-merical Simulation Figure 7 shows the 3-D model of thesubmarine pump the computational domain size is2000times 400times 400mm Given the complexity of the subma-rine geometry an unstructured tetrahedral mesh was used-e inlet of the computational domain extends by threetimes the impeller outer diameter forward of the bow theoutlet extends by four times the impeller outer diameter tothe rear of the submarine -e height and width of thecomputational domain are the same as those of the flumeFor the numerical simulation of the whole fluid

computational domain according to mooring status theinlet was set as velocity and the outlet was set as the outflow

-e numerical simulation results for thrust and torquecorrespond to the average values of five cycles at each speed andtheir relationships with pump speed are close to the quadraticfunctions -e comparison between the numerical simulationand experimental values of thrust and torque at variable rota-tional speeds is shown in Figure 8 As can be seen fromFigure 8(a) the numerical simulation thrust values for water-jetpropulsion with a screw mixed pump at different rotationalspeeds were larger than the corresponding experimental values-e total trendwas consistent and the error was limited to 32-is was mainly due to the existence of friction-based resistancefrom the experiment stand the inability of water in the flume toremain absolutely stationary when measuring the thrust of thewater-jet pump and the fact that a part of the thrust was used tobalance the drag of submarine -e torque of numerical sim-ulation and the experimental values of the water-jet pump atvarious rotational speeds were compared in Figure 8(b) -emaximum error between the numerical and experimental valuesof torque was 55 and the average error was 49 -e nu-merical simulation was in good agreement with the data fromthe experiment thus verifying the reliability of the numericalmethod

4 Results and Analysis

41 Transient External Characteristic of the Water-Jet Pro-pulsionPump During the startup stage the inlet pressure P1

0

20

40

60

80

100

Hη

06

08

10

12

14

16

18

20

Hea

d (m

)

00 10 times 106 15 times 106 20 times 106 25 times 106 30 times 10650 times 105

Grid number

(a)

5T

T1

T2

T3

T4

T5

2T 3T 4TTPeriod (s)

97

98

99

100

101

102

103

104

105

Effici

ency

()

T(N

)

(b)

Figure 5 (a) Grid independence check (b) time step independence check

Startup time = 01s

0200400600800

10001200140016001800

n (r

pm)

01 02 03 04 05 06 0700Time (s)

Figure 6 Impeller speed change curve of water-jet pump

Figure 7 -e 3-D model of the pump-jet submarine


of the pump initially decreases and then rises to its peakbefore gradually stabilizing -e outlet pressure P2 risesrapidly to its peak value and then drops to a steady value asshown in Figure 9(a) -e flow rate of the pump graduallyrises and tends to be stable as shown in Figure 9(b) Com-pared with the change of head there is no peak value of flowin the process of rising during the startup -e head of thewater-jet propulsion pump is mainly determined by the inletand outlet pressures When the pump rotation is acceleratedto the rated speed at 01 s the flow rate of the water-jetpropulsion pump is 781 of the stable value -e changes inshaft power and efficiency are shown in Figure 9(c) Com-pared with the change of efficiency the maximum value ofshaft power occurs before the pump rotation speed reachesthe rated speed -e change in thrust is more similar to theoutput characteristics of the step signal while the injection-velocity ratio is already close to the steady-state value at thebeginning as shown in Figure 9(d)

42 Dimensionless Parameter Analysis of theWater-Jet Pumpduring Startup In order to eliminate the influence of therotational speed on the external characteristics of the pumpthe dimensionless head ѱ and flow rate ϕ were investigatedto describe the transient responses as shown in equation (4)

ψ 2gH

u22

ϕ Q

πd2b2u2

(6)

whereQ is the instantaneous flow of the water-jet propulsionpump (m3s) d2 is the outer diameter of the impeller (m) b2is the impeller outlet width (m) H is the instantaneous head

of the water-jet propulsion pump (m) and u2 is the circularvelocity of the impeller outlet (ms)

-e dimensionless head initially decreases and then risesto its peak value in the startup stage as shown in Figure 10As the rotational speed increases the dimensionless headfluctuates within a large range Compared with the di-mensionless head the dimensionless flow rate does notinitially decrease during the startup phase

43 Transient Response of the Propulsion Dynamic Charac-teristics of the Pump during Startup In order to analyze thepropulsion dynamic characteristics of the water-jet pro-pulsion pump during startup the changes in the charac-teristic coefficients of water-jet propulsion with time wereused to describe the startup performance -e coefficientsare the inlet velocity coefficient J thrust coefficient Ktmoment coefficient Kq and open-water efficiency η0 re-spectively as shown in the following equation

J v1

nDd

Kt T

ρn2D4d

Kq M

ρn2D5d

η0 J

2πKt

Kq

(7)

where v1 n Dd ρ T and M are the inlet velocity rotationspeed external diameter fluid density thrust and torque ofthe pump respectively

To obtain the transient response curve of the coefficientsof the water-jet propulsion dynamic characteristics the

Numerical valuesExperimental values

0

5

10

15

20

25

30

35

40

45

T(N

)

500 1000 1500 2000 2500 30000n(rmin)

(a)


00

02

04

06

08

10

12

14

16

M(

nmiddotm

)

500 1000 1500 2000 2500 30000n(rmin)

(b)

Figure 8 -e comparison between the numerical and experimental values (a) -e n-T contrast curve of a submarine pump (b) the n-M contrastcurve of a submarine pump


Dimensionless headDimensionless flow rate

01 02 03 04 05 06 0700Time (s)

02

03

04

05

06

07

08

09

ψ

000

003

006

009

012

015

Figure 10 -e dimensionless parameter variation curve of the water-jet propulsion pump

P1P2

01 02 03 04 05 06 0700Time (s)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500Pr

essu

re (P

a)

0

3000

6000

9000

12000

15000

18000

Pres

sure

(Pa)

(a)

TK

0

1

2

3

4

5

6

Flow

rate

Q(

kgs

)

000204060810121416

Hea

d H

(m

)

01 02 03 04 05 06 0700Time (s)

(b)

Pkη

01 02 03 04 05 06 0700Time (s)

0102030405060708090

Effici

ency

η (

)

0

10

20

30

40

50

60

70

Sha

pow

er P

k(W

)

(c)

TK

0

2

4

6

8

10

12

ru

st T

(N)

01 02 03 04 05 06 0700Time (s)

000510152025303540

Inje

ctio

n-ve

loci

ty ra

tio K

(d)

Figure 9 -e transient external characteristic curve of the water-jet pump during the startup process (a) P curve (b) Q-H curve (c) Pk-ηcurve and (d) T-K curve


variations of the inlet velocity thrust and torque with timecan be fitted as shown in Figures 6 and 9 -e expression ofthe transient propulsion characteristic parameters can bedescribed as follows

v1(t) 19

1 + e32minus 45tminus 001

T(t) 105


M(t) 033

12 + e3minus 45t+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)

-e expressions of the transient propulsion character-istic parameters with impeller rotation speed can be deducedfrom equations (8) coupling with equation (5) as follows

v1(n) 19

1 + e32minus (31000)nminus 001

T(n) 105


M(n) 033

12 + e3minus (31000)n+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)

By substituting equations (8) into equation (7) thetransient response of the water-jet propulsion dynamiccharacteristics during startup can be obtained as shown inFigure 11

As the motor reaches its stable speed the inlet velocitycoefficient and the thrust coefficient decrease rapidly fromthe maximum value and then increase slowly shown inFigure 10 After the impeller speed stabilizes they begin todecrease-e water-jet propulsion with a screwmixed pump

enters its stable operation stage Compared with the rota-tional speed the inlet velocity and thrust coefficients lagbehind in the startup phase After the impeller rotationspeed has stabilized the response curve of the momentcoefficient gradually decreases and has no oscillation pro-cess However the open-water efficiency plunges to itsminimum value at the initial time and then gradually in-creases to a stable value

5 Conclusions

-e transient characteristics of the screw mixed-flow water-jet propulsion pump during its startup were revealed in thispaper by a method coupling experiments and numericalsimulation -e main conclusions are as follows

(1) A propulsion dynamicmodel andmodelingmethodsfor the transient response of water-jet propulsionwith a screw mixed pump during the startup periodwere proposed based on the parameterstransformation

(2) During the startup process the transient externalcharacteristics of the water-jet pump including theflow rate head and shaft power are analogous to thestep inputs for the transient response characterized bytime which have obvious transient characteristicsincluding a rise time a peak time a delay time andoscillation times

(3) -e slope and step responses of the thrust and torqueto changes in the rotational speed can be describedby a set of exponential functions

(4) Before the motor speed is stable the values of thewater-jet propulsion dynamic parameters drop rap-idly and then gradually stabilize -e inlet speed andthrust coefficients reach their peak values after the

01 02 03 04 05 06 0700Time (s)

000

005

010

015

020

025

030

035

040

J

0000

0001

0002

0003

0004

0005

K t

0000

0002

0004

0006

0008

0010

K q

0

20

40

60

80

100

Ope

n w

ater

effici

ency

(η0)

0

200

400

600

800

1000

1200

1400

1600

n (r

min

)

JKtKq

η0n

Figure 11 Transient response curves of the coefficients of the dynamic characteristics of water-jet propulsion with a screw mixed pumpduring the startup period


motor speed stabilizes Otherwise the moment co-efficient and open-water efficiency have no oscillationprocess after the motor reaches a stable speed

Data Availability

-e data used to support the findings of this study are in-cluded within the article Results of this paper can be verifiedaccording to the data and methods given in the paper

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Authorsrsquo Contributions

W H conceived and designed the research T Z and Y Hdrafted the article Y S completed the English check R Cprocessed the data and Y Q performed the literature search

Acknowledgments

-is study was supported by the National Natural ScienceFoundation of China (grant nos 51669012 and 51966010)and the National Key RampDProgram Projects of China (grantno 2018YFB0606100)

References

[1] Y Y Ni and W M Liu ldquoOverview on research of water-jetpropulsionrdquo Ship amp Ocean Engineering vol 42 pp 1ndash5 2013

[2] L L Cao B X Che and L J Hu ldquoDesign method of water jetpump towards high cavitation performancesrdquo IOP ConferenceSeries Materials Science and Engineering vol 129 Article ID012067 2016

[3] Y L Zhang Z C Zhu H S Dou et al ldquoNumerical inves-tigation of transient flow in a prototype centrifugal pumpduring startup periodrdquo International Journal of Turbo amp Jet-Engines vol 34 no 2 pp 167ndash176 2016

[4] H Tsukamoto and H Ohashi ldquoTransient characteristics of acentrifugal pump during starting periodrdquo Journal of FluidsEngineering vol 104 no 1 pp 6ndash13 1982

[5] H Tsukamoto S Matsunaga H Yoneda and S HataldquoTransient characteristics of a centrifugal pump duringstopping periodrdquo Journal of Fluids Engineering vol 108 no 4pp 392ndash399 1986

[6] I Chalghoum S Elaoud M Akrout and E H TaiebldquoTransient behavior of a centrifugal pump during startingperiodrdquo Applied Acoustics vol 109 pp 82ndash89 2016

[7] Z Li D Wu and L Wang ldquoNumerical simulation of thetransient flow in a centrifugal pump during starting periodrdquoJournal of Fluids Engineering vol 132 Article ID 0811022010

[8] T Tanaka and H Tsukamoto ldquoTransient behavior of a cav-itating centrifugal pump at rapid change in operating con-ditions-part 1 transient phenomena at openingclosure ofdischarge valverdquo Journal of Fluids Engineering vol 121 no 4pp 841ndash849 1999

[9] T Tanaka and H Tsukamoto ldquoTransient behavior of a cav-itating centrifugal pump at rapid change in operating con-ditions-part 2 transient phenomena at pump startupshutdownrdquo Journal of Fluids Engineering vol 121 no 4pp 850ndash856 1999

[10] T Tanaka and H Tsukamoto ldquoTransient behavior of a cav-itating centrifugal pump at rapid change in operating con-ditions-part 3 classifications of transient phenomenardquoJournal of Fluids Engineering vol 121 no 4 pp 857ndash8651999

[11] S L Ping D Z Wu and L Q Wu ldquoTransient effect analysisof centrifugal pump during rapid starting periodrdquo Journal ofZhejiang University vol 41 pp 814ndash817 2007

[12] Y L Zhang Z C Zhu and H C Lin ldquo-e calculation ofadditional theory head generated by centrifugal pump duringstartup periodrdquo Chinese Quarterly of Mechanics vol 33pp 456ndash460 2012

[13] L Q Wang D Z Wu S Y Zheng et al ldquoTest and numericalcalculation of transient performance of mixed-flow-pumpduring starting periodrdquo Journal of Zhejiang University vol 38pp 100ndash104 2004

[14] L Q Wang D Z Wu and S Y Zheng ldquoExperimental studyon transient performance of a mixed-flow-pumprdquo Journal ofFluid Mechanics vol 31 pp 1ndash3 2003

[15] W Li L L Ji andW D Shi ldquoStarting characteristic of mixed-flow pump based on quasi-steady state assumptionrdquo Trans-actions of the Chinese Society of Agricultural Engineeringvol 32 no 7 pp 86ndash92 2016

[16] K Farhadi ldquoTransient behaviour of a parallel pump in nuclearresearch reactorsrdquo Progress in Nuclear Energy vol 53 no 2pp 195ndash199 2011

[17] W Li Y Zhang W Shi L Ji Y Yang and Y Ping ldquoNu-merical simulation of transient flow field in a mixed-flowpump during starting periodrdquo International Journal of Nu-merical Methods for Heat and Fluid Flow vol 28 no 4 2018

[18] J A Han C Li and J J Zhong ldquoHydraulic design andperformance analysis of waterjet axial flow pumprdquo Journal ofEngineering -ermophysics vol 35 pp 2412ndash2416 2014

[19] D Huang Z Y Pan and XW Pan ldquoNumerical simulation ofcavitation flow in counter-rotating axial-flow pumprdquo Journalof Drainage and Irrigation Machinery Engineering vol 33no 4 pp 311ndash315 2015

[20] Y Wang P Y Cao and G Yin ldquoFlow feature and bladeloading of a water-jet pump under non-uniform suctionflowrdquo Journal of Propulsion Technology vol 38 pp 75ndash812017

[21] X Fu D Li H Wang G Zhang Z Li and X Wei ldquoAnalysisof transient flow in a pump-turbine during the load rejectionprocessrdquo Journal of Mechanical Science and Technologyvol 32 no 5 pp 2069ndash2078 2018

[22] K Nouha E Sami C Issa et al ldquoEffects of starting time andimpeller geometry on the hydraulic performance of a cen-trifugal pumprdquo in Proceedings of the International ConferenceDesign amp Modeling of Mechanical Systems Springer ChamSwitzerland 2018

[23] Y Tao S Yuan J Liu et al ldquoInfluence of cross-sectional flowarea of annular volute casing on transient characteristics ofceramic centrifugal pumprdquo Chinese Journal of MechanicalEngineering vol 32 no 1 2019

[24] Y Wang J Chen H Liu et al ldquoTransient characteristicanalysis of ultra-low specific-speed centrifugal pumps duringstartup period under shut-off conditionrdquo Transactions of theChinese Society of Agricultural Engineering vol 33 no 11pp 68ndash74 2017

[25] Z Li P Wu D Wu and L Wang ldquoExperimental and nu-merical study of transient flow in a centrifugal pump duringstartuprdquo Journal of Mechanical Science and Technologyvol 25 no 3 pp 749ndash757 2011


deduced the basic equation of steady speed and the startingprocess of a centrifugal pump respectively and described theinfluence of impeller rotating acceleration and fluid accel-eration on the startup performance with a mathematicalequation Zhang et al [12] qualitatively analyzed the transientbehaviors in detail using the transient Euler equation ofturbomachinery during all kinds of operation periods andquantitatively calculated the instantaneous additional theoryheads and additional theory power Wang et al [13 14] set upa model to analyze the startup process of the mixed-flowpump based on the internal characteristics of the pump andthe one-dimensional unsteady motion equations of thepipeline Li et al [15] analyzed the starting characteristics ofthe mixed-flow pump based on a quasi-steady-state as-sumption which provides a new idea for revealing thetransient internal characteristics of the startup process of themixed-flow pump -e transient behavior of the pump wasanalyzed using pump characteristic curves [16] Li et al [17]found that in the startup process of the mixed-flow pump theflow stabilized in the impeller the scale of vortex decreasedgradually as the rotating speed approached the rated speedand the transient effect disappeared

-e above-described investigation of water-jet propulsionpumps mainly focused on the characteristics and optimaldesign of the pump [18ndash20] -ere is little research on thetransient response characteristics of propulsion performanceduring the startup process for water-jet propulsion with ascrew mixed pump Fu et al [21] found there are severeunsteady vortex flows in the vaneless space near the condi-tions under which the hydraulic torque on the runner equalsto zero Nouha et al [22] found that the pump dynamicbehavior with the impeller geometry during the startingperiods Tao et al [23] found that the increase in the volutecasing flow area is helpful to improve the operation stability ofthe pump Wang et al [24] found that the valve head changeduring the startup process had a significant transient effect Inthis paper the control of impeller speed realized by the user-defined function (UDF) in a numerical simulation and atechnique for controlling the frequency in an experiment toreveal the transient hydrodynamic coefficients during thestartup period of the water-jet pump are described

2 Experiment for Pump-Jet PropulsionAccording to Mooring Status

21 Experimental Equipment and Procedure -e experi-mental equipment mainly included digital torque and ro-tational speed measurers a high-precision electronic forcesensor a model of a submarine pump and a rotational speedgovernor as shown in Figure 1 -e components of the self-circulating high-precision flume mainly included the flumebody the water supply equipment the automatic flowmeasurement system the tail door control system and theADV flow velocity measurement system -e length widthand depth of the flume were 13 06 and 06m respectively-e flow rate of the flume was regulated by a closed-loopcontrol mode which has the characteristics of high accuracyand stable control and can meet the test requirements ofsteady and unsteady flows

Firstly the automatic flow measurement system and taildoor control system were used to keep the water level of theflume at a fixed height Secondly the rotational speed of thewater-jet pump was adjusted to a stable value by using therotational speed governor -e rotational speed and cor-responding torque were recorded using the digital torqueand rotational speed measurers -e corresponding thrustvalue at the stable speed was recorded by the high-precisionelectronic force sensor and used -e arithmetic averagevalue of the corresponding thrust was calculated by takingthree measurements at the same rotational speed to reducethe error in the data

22 -rust and Torque at the Different Rotational Speeds-e experimental results show that the thrust and torque atdifferent rotational speeds followed the quadratic functiondistribution and the curves for thrust and torque at differentrotational speeds are shown in Figure 2 and the mathe-matical relationship between thrust and torque is shown inequations (1) and (2)

T minus 021859 minus 843874 times 10minus 4n + 450341 times 10minus 6

n2 (1)

M 000926 minus 424441 times 10minus 5n + 157305 times 10minus 7

n2 (2)

3 Numerical Simulation

31 Geometric Model -e 3D geometric models and pa-rameters of water-jet propulsion with a screw mixed pumpare shown in Figure 3 which shows a 3-D model containingan impeller a guide vane and a nozzle Table 1 lists theprincipal specifications of the water-jet pump

32 Mesh Generation Fully tetrahedral meshes wereadapted to discretize the computational domains as shownin Figure 4 -e number of grids affects the accuracy ofnumerical calculations In theory the more the meshes thereare the higher the accuracy Having too many meshes in-creases the calculation time and reduces the speed of con-vergence -erefore to eliminate the influence of thenumber of grids on the calculation of the results it is nec-essary to check independence from the grid number Sixgroups of time steps are selected for numerical calculation asshown in Figure 5(a) as the time step increases the head h

1

2

3

54

6

7

Figure 1 -e experimental system of water-jet propulsion (1) Ul-trasonic velocimeter (2) thrust collector (3) speed torque indicator (4)submersible model (5) water-jet propulsion pump (6) high-precisionelectronic force gauge and (7) self-circulating experimental flume







zρzt

+ nabla ρv0( 1113857 0 (3)

ddt


(4)




500 1000 1500 2000 2500 30000n(rmin)

0

5

10

15

20

25

30

35

40

45T

(N)

(a)

00

02

04

06

08

10

12

14

16

M(

nmiddotm

)

500 1000 1500 2000 2500 30000n(rmin)

(b)


1 2 3






n 15000t tle 01 s

1500 tgt 01 s1113896 (5)


(a) (b) (c)

(d)

(e)









0

20

40

60

80

100

Hη

06

08

10

12

14

16

18

20

Hea

d (m

)


Grid number

(a)

5T

T1

T2

T3

T4

T5

2T 3T 4TTPeriod (s)

97

98

99

100

101

102

103

104

105

Effici

ency

()

T(N

)

(b)


Startup time = 01s

0200400600800

10001200140016001800

n (r

pm)

01 02 03 04 05 06 0700Time (s)






ψ 2gH

u22

ϕ Q

πd2b2u2

(6)





J v1

nDd

Kt T

ρn2D4d

Kq M

ρn2D5d

η0 J

2πKt

Kq

(7)




0

5

10

15

20

25

30

35

40

45

T(N

)

500 1000 1500 2000 2500 30000n(rmin)

(a)


00

02

04

06

08

10

12

14

16

M(

nmiddotm

)

500 1000 1500 2000 2500 30000n(rmin)

(b)




01 02 03 04 05 06 0700Time (s)

02

03

04

05

06

07

08

09

ψ

000

003

006

009

012

015


P1P2

01 02 03 04 05 06 0700Time (s)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500Pr

essu

re (P

a)

0

3000

6000

9000

12000

15000

18000

Pres

sure

(Pa)

(a)

TK

0

1

2

3

4

5

6

Flow

rate

Q(

kgs

)

000204060810121416

Hea

d H

(m

)

01 02 03 04 05 06 0700Time (s)

(b)

Pkη

01 02 03 04 05 06 0700Time (s)

0102030405060708090

Effici

ency

η (

)

0

10

20

30

40

50

60

70

Sha

pow

er P

k(W

)

(c)

TK

0

2

4

6

8

10

12

ru

st T

(N)

01 02 03 04 05 06 0700Time (s)

000510152025303540

Inje

ctio

n-ve

loci

ty ra

tio K

(d)




v1(t) 19


T(t) 105


M(t) 033

12 + e3minus 45t+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)


v1(n) 19


T(n) 105


M(n) 033

12 + e3minus (31000)n+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)




5 Conclusions






01 02 03 04 05 06 0700Time (s)

000

005

010

015

020

025

030

035

040

J

0000

0001

0002

0003

0004

0005

K t

0000

0002

0004

0006

0008

0010

K q

0

20

40

60

80

100

Ope

n w

ater

effici

ency

(η0)

0

200

400

600

800

1000

1200

1400

1600

n (r

min

)

JKtKq

η0n




Data Availability






Acknowledgments


References
































zρzt

+ nabla ρv0( 1113857 0 (3)

ddt


(4)




500 1000 1500 2000 2500 30000n(rmin)

0

5

10

15

20

25

30

35

40

45T

(N)

(a)

00

02

04

06

08

10

12

14

16

M(

nmiddotm

)

500 1000 1500 2000 2500 30000n(rmin)

(b)


1 2 3






n 15000t tle 01 s

1500 tgt 01 s1113896 (5)


(a) (b) (c)

(d)

(e)









0

20

40

60

80

100

Hη

06

08

10

12

14

16

18

20

Hea

d (m

)


Grid number

(a)

5T

T1

T2

T3

T4

T5

2T 3T 4TTPeriod (s)

97

98

99

100

101

102

103

104

105

Effici

ency

()

T(N

)

(b)


Startup time = 01s

0200400600800

10001200140016001800

n (r

pm)

01 02 03 04 05 06 0700Time (s)






ψ 2gH

u22

ϕ Q

πd2b2u2

(6)





J v1

nDd

Kt T

ρn2D4d

Kq M

ρn2D5d

η0 J

2πKt

Kq

(7)




0

5

10

15

20

25

30

35

40

45

T(N

)

500 1000 1500 2000 2500 30000n(rmin)

(a)


00

02

04

06

08

10

12

14

16

M(

nmiddotm

)

500 1000 1500 2000 2500 30000n(rmin)

(b)




01 02 03 04 05 06 0700Time (s)

02

03

04

05

06

07

08

09

ψ

000

003

006

009

012

015


P1P2

01 02 03 04 05 06 0700Time (s)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500Pr

essu

re (P

a)

0

3000

6000

9000

12000

15000

18000

Pres

sure

(Pa)

(a)

TK

0

1

2

3

4

5

6

Flow

rate

Q(

kgs

)

000204060810121416

Hea

d H

(m

)

01 02 03 04 05 06 0700Time (s)

(b)

Pkη

01 02 03 04 05 06 0700Time (s)

0102030405060708090

Effici

ency

η (

)

0

10

20

30

40

50

60

70

Sha

pow

er P

k(W

)

(c)

TK

0

2

4

6

8

10

12

ru

st T

(N)

01 02 03 04 05 06 0700Time (s)

000510152025303540

Inje

ctio

n-ve

loci

ty ra

tio K

(d)




v1(t) 19


T(t) 105


M(t) 033

12 + e3minus 45t+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)


v1(n) 19


T(n) 105


M(n) 033

12 + e3minus (31000)n+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)




5 Conclusions






01 02 03 04 05 06 0700Time (s)

000

005

010

015

020

025

030

035

040

J

0000

0001

0002

0003

0004

0005

K t

0000

0002

0004

0006

0008

0010

K q

0

20

40

60

80

100

Ope

n w

ater

effici

ency

(η0)

0

200

400

600

800

1000

1200

1400

1600

n (r

min

)

JKtKq

η0n




Data Availability






Acknowledgments


References




























n 15000t tle 01 s

1500 tgt 01 s1113896 (5)


(a) (b) (c)

(d)

(e)









0

20

40

60

80

100

Hη

06

08

10

12

14

16

18

20

Hea

d (m

)


Grid number

(a)

5T

T1

T2

T3

T4

T5

2T 3T 4TTPeriod (s)

97

98

99

100

101

102

103

104

105

Effici

ency

()

T(N

)

(b)


Startup time = 01s

0200400600800

10001200140016001800

n (r

pm)

01 02 03 04 05 06 0700Time (s)






ψ 2gH

u22

ϕ Q

πd2b2u2

(6)





J v1

nDd

Kt T

ρn2D4d

Kq M

ρn2D5d

η0 J

2πKt

Kq

(7)




0

5

10

15

20

25

30

35

40

45

T(N

)

500 1000 1500 2000 2500 30000n(rmin)

(a)


00

02

04

06

08

10

12

14

16

M(

nmiddotm

)

500 1000 1500 2000 2500 30000n(rmin)

(b)




01 02 03 04 05 06 0700Time (s)

02

03

04

05

06

07

08

09

ψ

000

003

006

009

012

015


P1P2

01 02 03 04 05 06 0700Time (s)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500Pr

essu

re (P

a)

0

3000

6000

9000

12000

15000

18000

Pres

sure

(Pa)

(a)

TK

0

1

2

3

4

5

6

Flow

rate

Q(

kgs

)

000204060810121416

Hea

d H

(m

)

01 02 03 04 05 06 0700Time (s)

(b)

Pkη

01 02 03 04 05 06 0700Time (s)

0102030405060708090

Effici

ency

η (

)

0

10

20

30

40

50

60

70

Sha

pow

er P

k(W

)

(c)

TK

0

2

4

6

8

10

12

ru

st T

(N)

01 02 03 04 05 06 0700Time (s)

000510152025303540

Inje

ctio

n-ve

loci

ty ra

tio K

(d)




v1(t) 19


T(t) 105


M(t) 033

12 + e3minus 45t+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)


v1(n) 19


T(n) 105


M(n) 033

12 + e3minus (31000)n+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)




5 Conclusions






01 02 03 04 05 06 0700Time (s)

000

005

010

015

020

025

030

035

040

J

0000

0001

0002

0003

0004

0005

K t

0000

0002

0004

0006

0008

0010

K q

0

20

40

60

80

100

Ope

n w

ater

effici

ency

(η0)

0

200

400

600

800

1000

1200

1400

1600

n (r

min

)

JKtKq

η0n




Data Availability






Acknowledgments


References

































0

20

40

60

80

100

Hη

06

08

10

12

14

16

18

20

Hea

d (m

)


Grid number

(a)

5T

T1

T2

T3

T4

T5

2T 3T 4TTPeriod (s)

97

98

99

100

101

102

103

104

105

Effici

ency

()

T(N

)

(b)


Startup time = 01s

0200400600800

10001200140016001800

n (r

pm)

01 02 03 04 05 06 0700Time (s)






ψ 2gH

u22

ϕ Q

πd2b2u2

(6)





J v1

nDd

Kt T

ρn2D4d

Kq M

ρn2D5d

η0 J

2πKt

Kq

(7)




0

5

10

15

20

25

30

35

40

45

T(N

)

500 1000 1500 2000 2500 30000n(rmin)

(a)


00

02

04

06

08

10

12

14

16

M(

nmiddotm

)

500 1000 1500 2000 2500 30000n(rmin)

(b)




01 02 03 04 05 06 0700Time (s)

02

03

04

05

06

07

08

09

ψ

000

003

006

009

012

015


P1P2

01 02 03 04 05 06 0700Time (s)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500Pr

essu

re (P

a)

0

3000

6000

9000

12000

15000

18000

Pres

sure

(Pa)

(a)

TK

0

1

2

3

4

5

6

Flow

rate

Q(

kgs

)

000204060810121416

Hea

d H

(m

)

01 02 03 04 05 06 0700Time (s)

(b)

Pkη

01 02 03 04 05 06 0700Time (s)

0102030405060708090

Effici

ency

η (

)

0

10

20

30

40

50

60

70

Sha

pow

er P

k(W

)

(c)

TK

0

2

4

6

8

10

12

ru

st T

(N)

01 02 03 04 05 06 0700Time (s)

000510152025303540

Inje

ctio

n-ve

loci

ty ra

tio K

(d)




v1(t) 19


T(t) 105


M(t) 033

12 + e3minus 45t+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)


v1(n) 19


T(n) 105


M(n) 033

12 + e3minus (31000)n+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)




5 Conclusions






01 02 03 04 05 06 0700Time (s)

000

005

010

015

020

025

030

035

040

J

0000

0001

0002

0003

0004

0005

K t

0000

0002

0004

0006

0008

0010

K q

0

20

40

60

80

100

Ope

n w

ater

effici

ency

(η0)

0

200

400

600

800

1000

1200

1400

1600

n (r

min

)

JKtKq

η0n




Data Availability






Acknowledgments


References





























ψ 2gH

u22

ϕ Q

πd2b2u2

(6)





J v1

nDd

Kt T

ρn2D4d

Kq M

ρn2D5d

η0 J

2πKt

Kq

(7)




0

5

10

15

20

25

30

35

40

45

T(N

)

500 1000 1500 2000 2500 30000n(rmin)

(a)


00

02

04

06

08

10

12

14

16

M(

nmiddotm

)

500 1000 1500 2000 2500 30000n(rmin)

(b)




01 02 03 04 05 06 0700Time (s)

02

03

04

05

06

07

08

09

ψ

000

003

006

009

012

015


P1P2

01 02 03 04 05 06 0700Time (s)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500Pr

essu

re (P

a)

0

3000

6000

9000

12000

15000

18000

Pres

sure

(Pa)

(a)

TK

0

1

2

3

4

5

6

Flow

rate

Q(

kgs

)

000204060810121416

Hea

d H

(m

)

01 02 03 04 05 06 0700Time (s)

(b)

Pkη

01 02 03 04 05 06 0700Time (s)

0102030405060708090

Effici

ency

η (

)

0

10

20

30

40

50

60

70

Sha

pow

er P

k(W

)

(c)

TK

0

2

4

6

8

10

12

ru

st T

(N)

01 02 03 04 05 06 0700Time (s)

000510152025303540

Inje

ctio

n-ve

loci

ty ra

tio K

(d)




v1(t) 19


T(t) 105


M(t) 033

12 + e3minus 45t+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)


v1(n) 19


T(n) 105


M(n) 033

12 + e3minus (31000)n+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)




5 Conclusions






01 02 03 04 05 06 0700Time (s)

000

005

010

015

020

025

030

035

040

J

0000

0001

0002

0003

0004

0005

K t

0000

0002

0004

0006

0008

0010

K q

0

20

40

60

80

100

Ope

n w

ater

effici

ency

(η0)

0

200

400

600

800

1000

1200

1400

1600

n (r

min

)

JKtKq

η0n




Data Availability






Acknowledgments


References




























01 02 03 04 05 06 0700Time (s)

02

03

04

05

06

07

08

09

ψ

000

003

006

009

012

015


P1P2

01 02 03 04 05 06 0700Time (s)

ndash2000

ndash1500

ndash1000

ndash500

0

500

1000

1500Pr

essu

re (P

a)

0

3000

6000

9000

12000

15000

18000

Pres

sure

(Pa)

(a)

TK

0

1

2

3

4

5

6

Flow

rate

Q(

kgs

)

000204060810121416

Hea

d H

(m

)

01 02 03 04 05 06 0700Time (s)

(b)

Pkη

01 02 03 04 05 06 0700Time (s)

0102030405060708090

Effici

ency

η (

)

0

10

20

30

40

50

60

70

Sha

pow

er P

k(W

)

(c)

TK

0

2

4

6

8

10

12

ru

st T

(N)

01 02 03 04 05 06 0700Time (s)

000510152025303540

Inje

ctio

n-ve

loci

ty ra

tio K

(d)




v1(t) 19


T(t) 105


M(t) 033

12 + e3minus 45t+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)


v1(n) 19


T(n) 105


M(n) 033

12 + e3minus (31000)n+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)




5 Conclusions






01 02 03 04 05 06 0700Time (s)

000

005

010

015

020

025

030

035

040

J

0000

0001

0002

0003

0004

0005

K t

0000

0002

0004

0006

0008

0010

K q

0

20

40

60

80

100

Ope

n w

ater

effici

ency

(η0)

0

200

400

600

800

1000

1200

1400

1600

n (r

min

)

JKtKq

η0n




Data Availability






Acknowledgments


References




























v1(t) 19


T(t) 105


M(t) 033

12 + e3minus 45t+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(8)


v1(n) 19


T(n) 105


M(n) 033

12 + e3minus (31000)n+ 006

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(9)




5 Conclusions






01 02 03 04 05 06 0700Time (s)

000

005

010

015

020

025

030

035

040

J

0000

0001

0002

0003

0004

0005

K t

0000

0002

0004

0006

0008

0010

K q

0

20

40

60

80

100

Ope

n w

ater

effici

ency

(η0)

0

200

400

600

800

1000

1200

1400

1600

n (r

min

)

JKtKq

η0n




Data Availability






Acknowledgments


References




























Data Availability






Acknowledgments


References



























TransientCharacteristicsofWater-JetPropulsionwithaScrew...

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