2005 Vol. 20, No. 1

  Previous Issue | Next Issue 
Display Method:
Grid-Optimized Dispersion-Relation-Preserving Schemes for Non-uniform Cartesian Grids
HU Rui, LI Xiao-dong
2005, 20(1): 1-7.
Abstract PDF(437KB) icon2419 icon417
Abstract:
When the classic Dispersion-Relation-Preserving (DRP) scheme is applied to practical problems using non-uniform grids,spurious numerical oscillations and instabilities will be excited due to the inherent lacking of numerical dissipation.A Grid-Optimized Dispersion-Relation-Preserving (GODRP) scheme for non-uniform grids was proposed by Cheong & Lee to remedy this problem.In this paper,the derivation and formulation of the GODRP scheme were improved for non-uniform Cartesian grids in a more general form.To show the characteristics of the improved GODRP scheme,a 2-D initial pulse problem was solved on an extremely non-uniform Cartesian mesh using both the GODRP scheme and the DRP scheme.Numerical results indicate that because of the inherent numerical dissipation,the GODRP scheme is more feasible to be applied to the aeroacoustic problems using the non-uniform Cartesian grids,and the enhancement of computation accuracy can be expected.
Numerical Simulation of Mixing Layer Effect on Sound Waves
XING Chao, LUO Ji-sheng
2005, 20(1): 8-12.
Abstract PDF(326KB) icon1858 icon405
Abstract:
Based on the integrated compressible fluid mechanics equations,using eigen value analysis,the new method of non-reflecting boundary condition was proposed for aeroacoustics simulation of disturbance in shear flows.With the new boundary conditions,the disturbance were simulated in static fluid,uniform flows and uniform shear flows,and the results show that the new boundary conditions given in this paper are appropriate.The evolvement of disturbance in compressible mixing layer was also simulated,and the transmitted characteristic of disturbance in compressible mixing layer was presented.
Real-Time Performance Simulation of a Mixed-Flow Two-Spool Augmented Turbofan Engine
CHEN Min, TANG Hai-long, ZHANG Jing
2005, 20(1): 13-17.
Abstract PDF(349KB) icon2437 icon454
Abstract:
Study of real-time performance simulation of a mixed-flow two-spool augmented turbofan engine used in a flight simulator was carried out.Based on the engine control law,component matching relationships and experimental data,taking into account features of flight simulator,the application of curve fitting,interpolation method,orthogonal design etc.,to engine real time model was investigated.A real-time simulation model of a mixed-flow two-spool augmented turbofan engine was established with C~(++)language.The results show that the error of steady state performance is less than 2% and that of the transient performance is less than 5%,and every 4 ms or less the model can complete a performance calculation.
Theoretical Model of the Large-Scale Eddy Structures in the Near Wake Region Behind an Airfoil
LONG Kai, LU Li-peng
2005, 20(1): 18-21.
Abstract PDF(318KB) icon1840 icon409
Abstract:
Based on the theory of flow instability and coherent structure,a new theoretical 2-D wave model of the large eddy structures in the near wake region behind an airfoil was proposed.By calculation,we obtained the streamlines and the vorticity contours.They were in good agreement with those of experimental observations.Also the theoretical results of Reynolds Stress variation show good agreement with experimental results.It can be concluded that this model can depict the physical mechanism of the large-scale eddy structures in the near wake region.
Aerodynamic Modeling and Analysis of Flapping-Wing MAV
LIU Lan, FANG Zong-de, HOU Yu, FU Wei-ping, WU Li-yan
2005, 20(1): 22-28.
Abstract PDF(437KB) icon1759 icon508
Abstract:
The unsteady aerodynamics associated with flapping flight of flapping-wing Micro Air Vehicles (MAVs) was studied using computational fluid dynamics.A three-dimensional flapping wing model was established for the MAV,which mimicked biological locomotion,such as insect flight.The Arbitrary Lagrangian Eulerian (ALE) finite element method with ANSYS/CFD was used to solve the Navier-Stokes equations numerically.The solution proves that the leading-edge vortices could generate enough lift to support a typical flapping MAV.Based on the bionics aerodynamic model,the variations of different parameters such as flapping amplitude,pitching amplitude and flapping frequency of the MAV were studied.Finally,exploratory flapping wing wind-tunnel test and flight test prove,in certain degree,the feasibility of the method presented.The modeling method,as well as the conclusions is suitable for the design and analysis of flapping-wing MAVs.
Research of Turbofan Engine Transient Process with Thrust Vectoring Nozzle
QU Yu-an, XIE Shou-sheng, SONG Zhi-ping
2005, 20(1): 29-32.
Abstract PDF(301KB) icon1722 icon378
Abstract:
The mathematical model of turbofan engine transient process with thrust vectoring nozzle was established.The effects of thrust vectoring angle and angular velocity of vectoring on turbofan engine operation were investigated.The results show that the gas temperature at turbine inlet has different peak value at different thrust vectoring angle.The peak value increases with the increase of thrust vectoring angle. No significant change of the engine response to fuel step was found.
Effects of Swept Angle on Supersonic Mixing
JIN Zhe-yan, WANG Qiang, Eriqitai
2005, 20(1): 33-37.
Abstract PDF(330KB) icon1644 icon373
Abstract:
Numerical simulations were conducted to study the fluid dynamic mechanisms of a scramjet combustor with H2 as the fuel.An implicit finite volume method was used to solve the 3-D,viscous,turbulent Navier-Stokes equations and chemical species continuity equations.The effects of ramp swept angle on supersonic mixing were analyzed.The results show that swept ramps give better mixing results and stronger stream vorticity than unswept ramp and that mixing is strengthened with the increase of swept angle,but a total pressure recovery coefficient drop is accompanied.
Technical Improvement Scheme Analysis of Thrust-Weight Ratio 10 Aeroengine
WU Xue-hui, CHENG Bang-qin, TAO Zeng-yuan
2005, 20(1): 38-43.
Abstract PDF(354KB) icon1744 icon435
Abstract:
On the basis of a large number of computation and estimation researches,the improvement schemes for increasing aeroengine thrust-weight ratio were studied.Analysis of sensitivity of the aeroengine performance to the design parameters and preliminary optimization calculation were carried out.Due to aerodynamic and thermodynamic progress along with the advancement of materials and technology,aeroengine thrust-weight ratio may reach 12.Then by means of weight decreasing design and the application of especially low weight composite,aeroengine thrust-weight ratio may further enhance to 15. Through the relative difficulty analysis,a viable and short-term realizable improvement scheme, which can enhance the thrust-weight ratio to 15,was presented.
Reynolds Number and Humidity Effect on the Small Deviation Model of Turbofan Engines
LV Jian-wei, LI Jun
2005, 20(1): 44-48.
Abstract PDF(534KB) icon1862 icon485
Abstract:
Effect of Reynolds number and humidity on the performance of turbofan engines was investigated,and a small deviation model was established which was used to analyze the performance of certain turbofan engines.The influence coefficient matrix was obtained.The result provides a numerical reference for the quantitative and qualitative analysis of the Reynolds number and humidity effects on turbofan engine performance.
Influence of α1 and α2 Modulation on the Engine Acceleration of a Turbofan Engine
LI Wei, LI Jun, LIU Zong-long
2005, 20(1): 49-53.
Abstract PDF(321KB) icon1519 icon387
Abstract:
Based on the acceleration model,the acceleration code for engine with variable geometry channels was developed using component matching technique.The delay or ahead of schedule of high pressure compressor variable guide vanes and low pressure compressor variable guide vanes modulation was studied.The results show that for the case of the channel modulation ahead of schedule,there will be a increase of thrust and high pressure compressor surge margin,and a decrease of low pressure compressor surge margin,and vice versa for the case of modulation delay of schedule.The influence brings about by high pressure compressor variable guide vanes is higher than that of low pressure compressor variable guide vanes.
Dynamic Model of Rotor System with Support Loosening and its Diagnosis Method
LIU Xian-dong, HE Tian, LI Qi-han
2005, 20(1): 54-59.
Abstract PDF(533KB) icon1825 icon445
Abstract:
Aiming at the specific features of the non-linear rolling bearing-rotor system with pedestal loosening at one support,the dynamics equations of rolling bearing-rotor system were derived using Hertz theory,non-linear dynamics and rotor dynamics,after taking into account the nonlinear condition of looseness.The dynamics equations were numerically integrated for cases with and without looseness,and the vibration signals were obtained for the two cases.The vibration signals were treated with the Fourier transformation and the wavelet transformation respectively.Comparing and analyzing the results,it can be seen that both methods can diagnose the support’s loosening fault of the rolling bearing-rotor system effectively,however,the wavelet transformation can diagnose the fault at lower rotating speed,i.e.earlier than the Fourier transformation.The result presented can provide some reference for diagnosing the pedestal loosening fault.
Applied Investigation of Chaboche’s Unified Visco-Plastic Constitutive Model of Coupled Creep Damage
SHI Duo-qi, YANG Xiao-guang, WANG Yan-rong
2005, 20(1): 60-65.
Abstract PDF(402KB) icon2076 icon486
Abstract:
In order to improve the capability of Chaboche’s unified visco-plastic model in describing the tertiary creep,with Kachanov’s equation of damage evolution based on Lemaitre’s effective stress being used,Chaboche’s visco-plastic potential function was utilized to obtain the inelastic flow rule and hardening rule coupling to damage.It is shown that the form of the evolutionary equations of internal variables remains the same, and that the damage variable is not explicit in the equations.The modified constitutive model with damage was applied to the description of the uni-axial and bi-axial creep behaviors of a Ni-based superalloy,Udimet 720 Li,by coding the user’s material subroutine,UMAT,in ABAQUS platform.The finite element analysis of cruciform specimens shows that the inconsistency between uni-axial and bi-axial creep modeling capability exists in Kachanov’s damage law,especially at the time of rupture.The calculated creep behaviors match well with the experimental ones when a multi-axial damage factor is introduced into the damage evolutionary equation.
Continuous Parameter Model and Vibration Modal of Splitter Vane Rotor
YE Xian-lei, WANG Jian-jun, ZHU Zi-gen, LI Qi-han
2005, 20(1): 66-72.
Abstract PDF(473KB) icon1612 icon499
Abstract:
The continuous parameter model which was used to investigate the splitter vane rotor was introduced.The blades of the model were Timoshinko beam and the disc was treated as thin plate.The boundary conditions and the continuity conditions were satisfied by means of artificial springs introduced between the disk and the blades,which greatly simplified the choice of admissible function in Ritz procedure.The model was solved by the Ritz method,and the orthogonal polynomials generated by the Gram-Schmidt process were employed as admissible function for both disk and blades.With this approach,the matrix derived from kinetic energies becomes diagonal and numerical manipulation can become easy and stable.At last,a splitter vane rotor structure wass investigated using the Combined Model of the present work.Some results were compared with those obtained by professional FEA software ANSYS.Very good agreement among the results is demonstrated.
Thermal-Mechanical Fatigue and Isothermal Low Cycle Fatigue Fracture Behavior of Powder Metallurgy Superalloy FGH95
ZHANG Guo-dong, LIU Shao-lun, HE Yu-huai, WANG Wu-xiang, ZHONG Bin
2005, 20(1): 73-77.
Abstract PDF(386KB) icon1769 icon418
Abstract:
High temperature low cycle fatigue behavior of Powder Metallurgy superalloy FGH95 was studied.A basic triangular cycle with a constant temperature of 600℃ and an inphase triangular cycle with maximum and minimum temperature of 350℃ and 600℃ respectively were used for thermal-mechanical fatigue testing.The strain ratio of minimum to maximum strain is -1.0.The influence of the above two loading cycle on cyclic stress response behavior,mechanism of fracture at high temperature and fatigue life was investigated.At same strain amplitude,it was found that the TMF life of in-phase loading form is shorter than that of isothermal low cycle fatigue loading form.High temperature low cycle fatigue behavior of PM superalloy FGH95 depends not only on loading form,but also on magnitude of stain.The microstructure damage behavior of high temperature low cycle fatigue is discussed.The results show that fatigue,creep and oxidation damage always develops simultaneously during low cycle fatigue at high temperature.Fracture is mainly intergranular and transgranular under inphase thermal-mechanical fatigue. The path of crack initiation and growth is transgranular under conditions of isothermal low cycle fatigue.
Effect of High Speed Dynamic Balance Technique on Turboshaft Engine Vibration Reduction
DENG Wang-qun, GAO De-ping, LIU Jin-nan, LEI Mo-zhi
2005, 20(1): 78-85.
Abstract PDF(399KB) icon2430 icon448
Abstract:
The experiment of high speed dynamic balance was done after power turbine rotor balance is destroyed.The vibration of the whole engine on test rig was measured and analyzed before and after the high speed dynamic balance of the power turbine rotor was conducted.The results show that the whole engine vibration is significantly reduced.High speed dynamic balance technique of flexible rotor plays an important role in reducing vibration of the turboshaft engine.
Large-Eddy Simulation of Turbulent Combustion in A Model Combustor
YAN Ying-wen, ZHAO Jian-xing
2005, 20(1): 86-91.
Abstract PDF(665KB) icon1698 icon417
Abstract:
Two different subgrid-scale combustion models were used for the Large-Eddy Simulation (LES) of turbulent chemical reaction flows in a model combustor with V-gutter flame holder.The subgrid eddy viscosity was determined by using k-equation subgrid-scale (KSGS) model.To take into account the influence of heat radiation on wall temperature and gas temperature distributions,heat flux model was applied to predict heat flux distributions.The LES equations were solved with SIMPLE algorithm and hybrid scheme.Comparison of numerical results with experimental data shows that the two different subgrid-scale combustion models can all be used to simulate the combustion,but the G-equation flamelet model is better than the EBU subgrid combustion model.These results provide confidence that the LES may lead to a better understanding of the combustion process.
Experimental and Numerical Study of Ejection Characteristics of Circular Lobe Ejector with Bend Mixers
LIU You-hong, LIU Wei
2005, 20(1): 92-97.
Abstract PDF(445KB) icon1746 icon400
Abstract:
For the purpose of infrared stealth, the lobe and bend exhaust nozzle is required for the turbo shaft engine to eject surrounding cooling air and to change the direction of exhaust jets.The test model used was a set of circular twelve-lobe nozzles with bend mixers.The effects of the mixer bend angles β,the mixer to lobe cross sectional area ratio λ and the cross sectional area ratio σ of the secondary inlet to lobe on ejection ratio φ was studied.The experimental results show that for β=40°,the ejection ratio φ of the bend mixer is the same as that of the cylindrical mixer with the same diameter.For β>40°,the ejection ratioφ relative to the cylindrical mixer decreases significantly.With the increase of the mixer cross sectional area ratio λ,at first the ejection ratio φ increases and then decreases.The maximum ejection ratio φmaxis less than that of the cylindrical mixer,but the optimal cross sectional area ratio λmaxis about the same as that of the cylindrical mixer.The ejection ratio φ increases approximately linearly with the cross sectional area ratio σ.Because of the symmetrical feature of the lobe mixer,for simplicity,3D incompressible flow field of half of the mixer was numerically simulated.The calculated wall static pressure coefficients agree well with the measured ones.The numerical results show that the main reason for the significant decrease of the ejection ratio φ when the mixer bend angle is larger than 40° is due to the high static pressure along the bend part of the mixer,and the high static pressure chokes the effective flow passage area.
Finite Element Method for Heat Conduction Analysis in Porous Media with Consideration of Radiative Effects
ZHANG Hong-wu, FU Zhen-dong
2005, 20(1): 98-103.
Abstract PDF(522KB) icon1691 icon436
Abstract:
A finite element method for the computation of coupled heat transfer problems in the translucent porous medium was developed.Deducing control equations to the finite element computing forms was realized.Transient solutions of heat transfer through a translucent porous medium placed in a flow passage and submitted to incident radiation were obtained.The one-dimensional physical model took into account simultaneously the heat conduction,convection and radiation in the porous medium,which was assumed to be homogenous continuum,absorb,emit,and scatter thermal radiation.The coupled equations of conductive and convective heat transfer have to be solved simultaneously.Some techniques were used so that the coupled equations and the radiation heat transfer equation could be transformed into the computing forms.The initial temperature conditions were introduced in the iterative computation,and thus the transient solutions were obtained using time integration technique.The effects of some material parameters on transient temperatures were investigated by numerical computations.
Numerical Study of Internal and External Flow Mixing for Rectangular Nozzles with Large Aspect Ratio
ZHANG Bo, JI Hong-hu
2005, 20(1): 104-110.
Abstract PDF(619KB) icon1804 icon420
Abstract:
The mixing characteristics of external flow with jets from five rectangular nozzles with aspect ratio of 1,4,8,12,16 and from an axisymmetric nozzle were studied numerically.All nozzles studied had equal exit area.The results show that the rectangular nozzles lead to a relatively shorter jet core region and faster velocity and temperature decay rate than the axisymmetric one on centerline.This trend increases with the increase of aspect ratio.
Numerical Study of the Relationship between Pressure Exponent n and Combustor Exit Temperature
TIAN Xue-qing, HUANG Wei-guang
2005, 20(1): 111-115.
Abstract PDF(340KB) icon1322 icon417
Abstract:
By numerical simulation of two different gas turbine combustors,the selection of pressure exponent n in combustion efficiency simulation test was investigated.It is suggested that for hydrocarbon fuel,the pressure exponent n may be selected in the range of 1.6～2.0,when the combustion process is reaction-controlled. When the combustion process is diffusion-controlled,the range of 1.0～1.4 is suggested.The result is useful for the model test of gas turbine combustors.
Numerical Study of the Blowing Angle Effecton Effusi on Cooling Effectiveness
HU Ya-ping, JI Hong-hu
2005, 20(1): 116-119.
Abstract PDF(429KB) icon1646 icon403
Abstract:
The influences of the coolant flow blowing angle α on the effusion cooling effectiveness of a porous plate were investigated.Nine cases were studied,which cover three blowing angles of α=30°,60°,90° and for each angle three blowing ratios of M=0.5,1.0,2.0.The results show that with the increase of α the cooling effectiveness reduces for all the calculated cases.For cases of α=30° and 60° the distribution of cooling effectiveness η along the whole plate are very similar for any given blowing ratio.While for the cases of α=90°,the distributions of cooling effectiveness are quite different.Although the cooling effectiveness of the cases with α=90° for any given blowing ratio is the worst among the three angles stated,its absolute value is still quite high compared with the conventional film cooling.
Effect of Axial Spacing between Rotor and Stator on Axial Compressor Stability
ZHANG Huan, HU Jun, LI Chuan-peng, WANG Ying-feng
2005, 20(1): 120-124.
Abstract PDF(327KB) icon1860 icon435
Abstract:
The effect of stator on axial compressor aerodynamic stability was studied both theoretically and experimentally for a low speed compression system.The theoretical analysis shows that stator could suppress flow disturbances in compressors and enhance the compressor stability,in case of the stator does not stall first.The experimental results of a low speed single stage compressor show that stall flow coefficient decreases with the decrease of the axial spacing between rotor and stator because of the increasing influence of the stator.
Numeric Simulation of Inducer Shroud Bleeding Effect on Centrifugal Compressor Performance
DAI Si-min
2005, 20(1): 125-129.
Abstract PDF(518KB) icon2029 icon399
Abstract:
In order to investigate the applied techniques that can be used to enlarge the centrifugal compressor surge-margin and to solve the problem in certain engineering design,3D viscous Computation Fluid Dynamics (CFD) code was used to simulate the inducer shroud bleeding effect on centrifugal compressor performance.Numerical experiments have been carried out to test certain design parameters involved in the application of this technique.The results show that inducer shroud bleeding has a remarkable effect on the centrifugal compressor performance improvement.
Study of an Engine Electronic Controller’s Core Circuit Module Based on DSP and CAN
ZHANG Tian-hong, MOU Lu-yong, DING Yi, DENG Zhi-wei
2005, 20(1): 130-135.
Abstract PDF(253KB) icon1662 icon422
Abstract:
To meet the demands of complex control algorithm and distributed control,a design scenario of the electronic core circuit module,which was based on DSP (Digital Signal Processor) and CAN (Controller Area Network),was proposed and realized for DEEC (Digital Electronic Engine Control).Several key problems of hardware and software design were expounded,and the hardware-in-loop simulation validated the feasibility of the module.This module can also be applied in integrated flight-propulsion control and distributed aeroengine control,where the high capability of arithmetic calculation and real-time communication are required.
Fault Isolation of Aeroengine Speed Decreasing Signal Based on Parallel Multiple Robust Observers
QIAN Kun, XIE Shou-sheng, HU Jin-hai, YU Dong-jun
2005, 20(1): 136-141.
Abstract PDF(389KB) icon1743 icon446
Abstract:
Through researching of the mechanism causing engine speed decreasing signal,a method of fault isolation for certain turbofan aeroengine based on parallel multiple robust observers was proposed.Normal condition and four fault modes for the actual system were established.Then the method was applied to fault detection and isolation of the aeroengine sensors that cause the speed decreasing signal.Results of numerical simulation and error analysis show that this method is highly reliable and highly accurate in fault isolation.
Nozzle Flow Computation of Classical Hybrid Rocket Motors
TIAN Hui, CAI Guo-biao, WANG Hui-yu, ZHANG Zhen-peng
2005, 20(1): 142-146.
Abstract PDF(535KB) icon1663 icon467
Abstract:
Numerical solutions of full Navier-Stokes equations with chemical reaction flow were established for the nozzle flow of the LOX/HTPB hybrid rocket motor.Lower-Upper decomposition scheme and MUSCL-type and VanLeer approach were used.A chemical reaction model with 8 components and 10 elementary reactions was presented.The nozzle entrance condition was obtained by thermodynamic calculation.The nozzle flows under several different oxidizer mass flow rates and grain length were calculated.The relationship between oxidizer mass flow rate and specific impulse was analyzed,which will be useful for the hybrid rocket motor design.
Numerical Simulation of Regenerative Cooling in Two Dimensional Plug Nozzles
LI Jun-wei, LIU Yu, QIN Li-zi
2005, 20(1): 147-153.
Abstract PDF(487KB) icon2109 icon403
Abstract:
In order to understand the heat transfer characteristics of regenerative cooling in two dimensional plug nozzle,a computational model was established and numerical simulation was carried out.The flowfield and the heat transfer characteristics of plug nozzle at different ambient pressures were investigated. Nozzle flow was assumed to be frozen, and convective and radiative heat transfer from gas to solid wall was considered. Discretization of the governing equations was performed with two order upstream scheme, and radiative heat transfer equation was solved with Discrete Ordinates (DO) method.Absorption coefficient of water vapor was calculated by Leckner formula.The results show that heat transfer condition internal the nozzle is the worst,and should pay more attention.The heat transfer characteristics on plug surface varies with operating conditions.At sea level condition,heating of the plug is the worst,and with the increase of pressure ratio,it is lessened and at last keeps unchanged with ambient pressure.An unreasonable plug contour design can cause a very high temperature peak on it.
Early Detection of Gear Crack Based on Cyclic Time Series
CHEN Zhong-sheng, YANG Yong-min, HU Zheng, SHEN Guo-ji
2005, 20(1): 154-158.
Abstract PDF(345KB) icon1926 icon437
Abstract:
On the basis of gear vibration signals analysis,one novel method of detecting faults based on linear periodical time-varying autoregressive (LPTV-AR) model according to its cyclostationarity was proposed.The algorithm of identifying model parameters using higher-order cyclic-cumulants was established,which possessed the ability to suppress additive stationary noise.The proposed method was used to detect and predict the incipient gear crack fault of a helicopter.The results show that the approach has good performance of prediction and can detect early gear crack fault using the kurtosis of residual signals.At the same time it provides an idea of detecting faults of rotating machinery using only normal samples.
Application of Genetic Algorithm to the Fuzzy Reliability Optimal Design of Profile Modified Helical Gear Under The Action of Friction
LI Xiu-lian, DONG Xiao-ying, CAO Qing-lin, LEI Liang-yu
2005, 20(1): 159-163.
Abstract PDF(325KB) icon1603 icon390
Abstract:
Considering the limitation and deficiencies in traditional gear strength theory, based on genetic algorithm,a new method of fuzzy reliability optimal design for the profile modified helical gear transmission in consideration of the action of sliding friction between teeth is presented.This method combines fuzzy reliability design theory with optimization technique and excellences of genetic algorithm.The calculated result shows that the proposed method is effective for the optimum design of profile modified helical gear transmission.
Spline Function Assessment of Prior Distribution for Complex System Bayesian Reliability Evaluation
LIU Qi, FENG Jing, ZHOU Jing-lun
2005, 20(1): 164-168.
Abstract PDF(465KB) icon1675 icon438
Abstract:
To acquire proper prior distribution is a key problem in complex system Bayesian reliability evaluation.Based on the empirical Bayes theory,a spline density fitting for the prior function of system’s mission reliability was studied.The reliability test data based on Weibull,exponential and binomial distribution model was analyzed, and reliability evaluation formula was presented.Finally an example was given to show this method is simple in calculation and usable for engineering application.

Copyright © 《Journal of Aerospace Power》 All Rights Reserved.

Supported by: Beijing Renhe Information Technology Co., Ltd.