1992 Vol. 7, No. 4

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DERIVATION OF THE UNIVERSAL PHYSICAL EQUATION OF TURBULENCE AND ITS CANONICAL FORM
Gao Ge
1992, 7(4): 295-304,391.
Abstract PDF(1091KB) icon2434 icon559
Abstract:
The fully- detailed derivation of the universal physical equation ofturbulence has been given. Instead of the conventional Reynolds average, a new method, named off-center ensemble average, is used to obtain the equation. Through some mathematical approximations and without introducing any empirical coefficients, the equation may provide a secondary order of accuracy, which satisfies the needs of engineering study of turbulence. In one-dimensional case, the momentum equation of turbulence is simplified as the mixed Burgers-Korteveg de Vries equation-the canonical equation of turbulence. The analysis of the Burgers-Kerteweg-de Vries equation gives the criterion of transition. The physical meaning of the equations is briefly discussed. It shows that dissipation and dispersion coexist as two basic physical principles of turbulence. The development of dissipation is monotonic, describing the conversion of the kinetic turbulence energy into heat due to viscosity. Dispersion can be either positive or negative. It represents the energy transformation between the mean flow and the large and micro-eddies before the energy is finally dissipated into molecular heat. Positive dispersion corresponds to cascading down process and negative dispersion means collection of energy. The mechanison of intermittency and anisotropy, and the effects of noise and developing history on turbulence are also discussed.
OPTIMIZATION OF A COMBINED-CYCLE PROPULSION SYSTEMFOR SPACE VEHICLE
Lian Xiaochun, Wu Jiansheng, Chen Fuqun, Wang Naixing
1992, 7(4): 305-308,392-393.
Abstract PDF(624KB) icon1571 icon411
Abstract:
This paper presents some results of optimization of operating modestransfer in a Supercharged Ejector Ramjet (SERJ) specified for first stage of a two-stage-to-orbit space vehicle. The SERJ consists of four subsystem:Fan, Ejector, Ramjet and Air liquefaction subsystem used as a heat exchanger. Three factors are considered for estimating propulsion system installed thrust; Internal and external performances of the inlet and the nozzle; power and air extractions from the engine. An objective of minimization is the minimum of the fuel consumption, which is attained by varying the transition conditions of different engine operation modes. Then the optimum transition corditions can be obtained between SERJ and fan ramjet modes, fan ramjet and ramjet modes, ramjet and ejctor ramjet modes, ejector ramjet and rocket modes.
VISCOUS FLOW FIELD PREDICTION IN AXISYMMETRIC PASSAGES
Zhang Guoqing, Hua Yaonan
1992, 7(4): 309-311,393.
Abstract PDF(343KB) icon1429 icon383
Abstract:
The viscous flow fields in the inflow axisymmetric passages of centrifugalcompressors are predicted with vorticity- stream function (ω-ψ) method. The expressions of q-ω turbulence model equations in orthogonal curvilinear coordinate system are derived here, and they are used to predict the turbulent flow fields. The q-τ turbulence model has an advantage in capability of treating the boundary conditions. The unsteady terms are introduced in the τ-equation and q, τ equations, and the time-marching method is applied to solution of these equations. In the case of turbulent flow prediction the wall function is used in the near-wall region. Several numerical examples of laminar and turbulent flows in a 2D channel and axisymmetric passages with complex boundaries show that their solutions obtained with the present method is in good agreeement with their exact solution or their experimental data.
DIGITAL SIMULATION OF TRANSONIC FLOW FIELDS IN A PLANAR NOZZLE
Zheng xiaoqing, Zen Jun
1992, 7(4): 312-314,393.
Abstract PDF(329KB) icon1837 icon391
Abstract:
This paper presents a method for simulation of transonic flow fields in a planar nozzle. For this purpose, the Jumeson-type Runge-Kutta finite volume method is applied to solving Euler equation with the aid of local time stepping and impicit residuals averaging techniques. In such a manner the convergence rate is sped up in planar nozzle flow solution, so that the steady state can be obtained in less than a hundred iterations. An adaptive dissipation term is added to the equations to eliminate the fluctuation of the flow parameters and the vibrations in front of and behind the shock. The results of the calculations are in good agreement with the test data and the results of calculations with other numerical methods.
CALCULATION OF PRESSURE RATIO AT NOZZLE EXIT WITH SHOCK
Zen Jun, Zhao Jingyun
1992, 7(4): 315-316,394.
Abstract PDF(341KB) icon1728 icon408
Abstract:
A mathematical model of a axisymmetric convergent-divengent nozzle isset up by multivariant linear regression analysis method. The relationships of pressure ratio at nozzle exit with shock to four geometric parameters, i. e. area ratio, half-convergent angle, half-divergent angle and radius ratio of throat curvature to throat, are considered. The pressure ratio only depends on the area ratio. Other parameters have little effect on it. The results provide the basis for testing and transonic calculation of the axsiymmetric convergent-divergent nozzle.
ELIMINATION OF OVERTEMPERATURE IN TURBOJET
Shang Yi, Zhang Baoan, Chen Xiaoxing
1992, 7(4): 317-318,394.
Abstract PDF(331KB) icon1452 icon390
Abstract:
This paper analyzes the reasons of the overtemperature in a turbojet andprovides the available measures to eliminate it, such as the strict requirements for the engine overhaul at the repair factory and the reasonable engine adjustment in the field maintenance. It is essential for the field maintenance to adjust properly the relationship between the turbine pressure ratio and the exhaust nozzle area, so that the turbine gas temperature comes down without afterburning temperature drop. In this way, the influence of the above problem on the operational performance of the engine can be minimized on condition that the engine reliability is guaranteed.
A SIMPLE SPANWISE MIXING MODELFOR TURBULENT DIFFUSION AND SECONDARY FLOWSIN MULTISTAGE AXIAL-FLOW COMPRESSORS
Li Shiming, Chen Maozhang
1992, 7(4): 319-324,391-392.
Abstract PDF(972KB) icon1692 icon466
Abstract:
Three kinds of coefficients are defined and introduced into the basicequations for meridional throughflow fields in multistage axial- flow compressors deduced by the authors which describe different kinds of spanwise mixing mechanism in a unified form. Then, a novel much simpler equation system is obtained without any unknown correlation terms included. It has been shown that these coefficients involve the full information of all the kinds of mixing mechanism. This novel equation system not only unifies the two analytical models for meridional throughflow with mixing which were presented by Adkins and Smith (1981) and Gallimore and Cumpsty (1986) respectively, but also makes the computations for multistage machines much easier. The calculations of the flow through multistage machines have been made by incorporating the new model into a streamline curvature throughflow calculation method. The agreement of the calculation results with experimental data has been improved. It is believed that this simpler equation system can be applied to the flows not only in subsonic compressors, but also in transonic and supersonic compressors, provided that a more appropriate model is proposed for the coefficients.
A METHOD FOR OPTIMIZING THE MERIDIONAL PASSAGE IN A CENTRIFUGAL COMPRESSOR
Rao Jiang, Li Jingping
1992, 7(4): 325-328,392.
Abstract PDF(423KB) icon1498 icon406
Abstract:
A method for optimizing the meridional passage of the rotor in acentrifugal compressor has been developed according to the theory of S1 and S2 stream filaments. Two optimization principles are introduced. First, the gradient of static pressure in stream line directon should be minimized as it is mainly responsible for the boundary layer separation at the hub and shroud. Second, the gradient of static pressure from hub to shroud should be lessened as possible for it is generally considered as the major reason for triggering the second flow in the passage. According to these two principles, a reasonable criterion has been set up. In order to optimize meridional passage automatically through computer programming, two practical approaches have been provided . In one approach, the passage is modified again and again by using formulas derived from the continuity equation and thermodynamic relations. In the other, a series of quadratic curves are introduced to form a series of meridional passages. In both these approaches, it is neccessary to predict the flow field by using "S2 inverse problem" computer code many times. Then, according to the above-mentioned criterion, the optimized meridional passage can be distinguished. Two numerical examples are given in this paper. Their results are obtained from the two approaches respectively. The comparison of the static pressure distributions at hub and shroud between the original and optimized passages indicates that this method obtains access to the expected results.
DYNAMIC CHARACTERISTICS OF TWO NEW VIBRATION MODES OF THE DISK-SHELL SHAPED GEAR
Yan Litang, Qiu Shijung, Gao Xiangqung
1992, 7(4): 329-334,394.
Abstract PDF(609KB) icon1802 icon437
Abstract:
Two new vibration modes of the disk-shell shaped big medium gears placedon the three separate medium shafts of a turboprop engine have been found. They have the same nodal diameters as the conventional ones but their frequencies are higher. The tooth ring vibrates both radially and axially and has greater deflection than the gear hub. The resonance of these two new nodal diameter modes is much more dangerous than that of the conventional nodal diameter modes. Moreover they occur just nearly at the upper and lower bounds of the gear operating speed range. A special detuning method is developed for removing the resonance of these two new modes out of the upper and lower bounds respectively and the effectiveness of the damping rings in this case has been researched. The vibration responses measured on the reductor casing have been then reduced to a quite low level after the damping rings were applied to the three big medium gears.
CALCULATION OF FLASH TEMPERATURE ON TOOTH SURFACE OF INTERNAL HELICAL GEARS
Fang Zongde, Chen Guoding, Shen Yunwen
1992, 7(4): 335-338,394-395.
Abstract PDF(506KB) icon2192 icon427
Abstract:
An accurate calculating approach for flash temperature of internal helicalgears is presented. Firstly, the load distribution on tooth surface is obtained by using 3-D finite element method and loaded tooth contact analysis technique. Then, the relative velocities and curvature radii of every node on the tooth surfaces for a pair of internal helical gears are determined. Under these conditions, the flash temperature on tooth is calculated by using Block's basic equation. Further, the thermal elastohydrodynamic analysis of line contact is applied to determination of the temperature distribution in oil film. This analysis is more accurate, though more tedious. The calculated results reveal the relationship between the gear parameters and flash temperature, which will help engineers in designing internal helical gears with high scuffing load capacity.
TRACTION CHARACTERISTICS OF SYNTHETIC LUBRICANTS AT HIGH SLIDING SPEED CONTACTS
Chen Guoding, Wang Buyin, Wu Liyan, Li Jianhua
1992, 7(4): 339-342,395.
Abstract PDF(394KB) icon1757 icon455
Abstract:
The traction characteristics of synthetic lubricants at high sliding speedcontacts are studied according to the thermal partial elastohydrodynamic lubrication theory for consideration of surface roughness effect and the Ree-Eyring theological model for mirroring the non-Nowtonian behavior of the lubricant. The analysis program developed incorporates a computational algorithm which can efficiently and accurately find out the pressure and temperature distributions and determine the traction coefficient of synthetic lubricants. The variations of the traction coefficient of synthetic lubricants with the load, rolling and sliding speed, lubricant viscosity and ambiance temperature are obtained and the comparison between the calculated results presented in current work and the experimental results of ref. [2] is also shown. The method adopted in present investigation is instructive for dynamic study of aviation high-speed rolling bearings.
THERMAL ANALYSIS OF AEROENGINE MAIN SHAFT BALL BEARING
Han Mingzheng, Rao Shouqi
1992, 7(4): 343-347,395.
Abstract PDF(516KB) icon1417 icon494
Abstract:
An analysis of the heat generation in a high speed ball bearing system of anaeroengine is considered in detail on the basis of dynamical analysis. First, the heat generation rate is calculated according to the elastohydrodynamic lubrication theory. Then, considering complex relationship of heat transfer, the temperature contribution in the ball bearing system is calculated by using the combination of the finite element method, finite difference method, system heat equilibrium method and empirical formulas. Contribution of inner heat sources and treatment of boundary conditions in the calculation are analyzed thoroughly. Finally, thermal analysis of the ball bearing for a specified Aeroengine is made. Calculation results are shown in a good agreement with the experimental data offered by Shenyang Aeroengine Research Institute.
3-D FINITE ELEMENT CYCLIC SYMMETRICAND CONTACT STRESS ANALYSISFOR A COMPLETE GEAR TRAIN
Yin Zeyong, Xu Youliang, Gao Xiangqun, Wei Gang
1992, 7(4): 348-350,396.
Abstract PDF(262KB) icon1420 icon502
Abstract:
A complete gear train of a reduction gearbox is the object of finite elementstress analysis. One of the basic segments of the complete gear train is taken as the computational model in the light of the cyclic symmetry of the gear train, meanwhile the contact transmission forces between the corresponding meshed teeth are considered in the analysis of the model. For simplicity the corresponding meshed lines are used instead of the actual contact surfaces. Both torque and centrifugal loads are involved in the analysis. The stresses in all the parts of a complete gear train can be determined by one analysis. The computed results show that the contact force on a meshed tooth is correlative not only to the length of the meshed line, but also to its position, and, moreover, the neglect of the stress resulted from centrifugal load is inappropriate to a high speed gear train.
OPTIMUM BALANCING OF FLEXIBLE ROTOR
Liu Qizhou, Tao Xie
1992, 7(4): 351-354,396.
Abstract PDF(401KB) icon1585 icon460
Abstract:
A new criterion for optimum balancing of a flexible rotor is introduced,which is the minimum rotor strain energy criterion with constrains. This criterion meets the requirements for integral design of structure strength and performance of a gas turbine aeroengine. In this criterion the balance correction masses (quantity and orientation) are the optimum design variable, the objective function of optimization is the total strain energy of the rotor and its supports. The response amplitudes at several cross-section along the rotor are taken as its constraints. The Powell's method and the net random-ray method are chosen as optimum methods. A program is written with FORTRAN 77 for the whole optimization procedure. The program has been testified by a numerical example in comparison with its experiments.
STUDY ON PERFORMANCE OF SQUEEZE FILM DAMPER WITH OIL-AIR TWO-PHASE FLUID
Shen Xinmin, Li Qihan, Du Lijie
1992, 7(4): 355-358,396-397.
Abstract PDF(500KB) icon1583 icon406
Abstract:
This paper presents an analytical method for lubrication film performanceof squeeze film damper with oil-air two-phase fluid on the basis of the testing results and numerical analysis of oil film cavitation. The calculational results for the pressure distribution of lubrication oil film are in good agreement with the experimental results. The damper performance data obtained from two-phase fluid analysis are also compared with the results calculated by pure oil film damper. It is proven that the data can be used for the engineering analyses. The analytical method can be extended for the other bearings with similar lubrication film of oil-air two-phase fluid.
A FEM OF THERMOELASTO-PLASTIC ANALYSIS WITH DUE REGARD FOR LOADING PATH
Zhang Dongxu, Song Limin
1992, 7(4): 359-362,397.
Abstract PDF(388KB) icon2005 icon389
Abstract:
Until now a lot of investigations have been done on the thermoelasto-plastic analysis. Its genaral approach is to add up all the external forces on the structure to form a so-called load vector and to divide the element states into elastic, plastic and elastplastic elements, but the variation of the element states during the loading procedure and the loading path are always ingnored. In fact these two factors do affect the reliability of the analytic results. In order to improve the accuracy of the thermoelasto-plastic analysis, two algorithms are proposed which imitate the loading path and take the shifting of the element states into account. The external forces are expressed as the functions of time respectivley. Thereby the analysis procedure corresponds to the loading procedure. The element states are classified into six kinds according to the different stress-strain states. Thus a program system is developed. Two examples are given to show the difference between the analysis results under different loading path.
A NEW MECHANICAL MODEL AND ALGORITHM FOR FINITE ELEMENT ANALYSIS OF CONTACT PROBLEMS
He Junyi
1992, 7(4): 363-367,397.
Abstract PDF(491KB) icon1957 icon394
Abstract:
A new mechanical model for FEM analysis of contact problems ispresented, in which a nodal point on the surface of contact body comes into contact with an arbitrary point on the surface of target body instead of the nodal point pair model. It is convenient to construct FE nets. The boundary conditions such as stick slid with friction and open contact were given in terms of this model. The contact boundary conditions as Lagrangian multipliers are substituted into the functional according to the principle of modified potential energy and therefrom the symmetrical nonlinear governing equations are deduced for the static and dynamic contact problems with material and/or geometric nonlinearities. Due to the symmetrization of equations, the general effective solution methods of nonlinear equations can also be used to the contact governing equations. In the paper the judgement criteria of contact conditions after each iteration are presented, which can decide whether and how the contact conditions of each contact nodal point to be modified.

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