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中文核心期刊

1957 Vol. 1, No. 1

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1957, 1(1): 1-2. doi: 10.6052/0459-1879-1957-1-1957-008
THE VORTICITY STRUCTURE OF HOMOGENEOUS ISOTROPIC TURBULENCE IN IT5 FINAL PERIOD OF DECAY
CHOU PEI-YUAN, TSAI SHU-TANG
It has been known for sometime that turbulence is due to the ahaatic motion ofa large number of small eddies. By neglecting the non-lineax terms in the Navier-Stokes equations, the authors obtained recently a class of solutions which representthe velocity distxibutians of spherical vortices moving in an incompressible viscousfluid. It is obvious that, after the linearization of the Navier-Stokes equations of mn-Lion, velocitp distributions obtained. by differentiating the spherical vortex solutionpartially with respect to the coordinates along any direction in space for any numberof times also satisfp the equations of motion.We investigate the homagenEaus isotropic turlulerit motion of a liquid in its finalperiod of decay, when the non-linear terms in the Navier-Stokes equations can beneglected-The type ofvortices which are assumed to give rise to turbulence, is deterrnined by the following twoccanditians:In the first place, the vorticity distributionof the eddy should be concentrated in the vicinity of the geometrical center of thevortex instead of being spread over a largre volume; secondly, the total angular mamentom of the vertex should he constant instead of decreasing ar increasing with time. The first cnnditian requires that only the spherical vortex solution with theparameter k =5/4 and its partial dexivatives shomld be chosen. only in this specialcase, amongall the spherical voxtices, has its voxticity concentrated inthe regionaround its center. Solutions derived by partially differentiating its velocity distribition with respect to the ooaxdinates also have this property when compared with thesolutions obtained from those of the spherical vortices with other values of theparameter k by similar process.The second condition determines that partial cliff erentiation of the solution of the spherical vortex k=5/4 with respect to the coordinates only once is sufflclent. Partial differentiation with reRpect to the coordinate along the axis of symmetry of the velocity distribution yields the varticity η, the stream function ψ and the oharacteristio velocity U given. in the paper [(2.4) and (2.5)]. In the stream function ψ, we have introduced aftez the gaztial differentiation the part due to a uniform flow along the axia of symmetry. Without this part, the solution represents the motion of a standing axially symmetrical vortex. Partial differentiation with respent to the coordinates along any other dizeation in space, leads to the solution of asymmetrical vortices in general[(2.12) and (2.13)]. According to Synge and Lin, the double velocity correlation between two points in the fluid is the product of the velocity components u#em/em#u#em/em#″ averaged ovex all the directions of orientation of the axis of symmetry of the axially symmetrical eddy, and over all the positions of the vortex in the whole fluid (3.2). If the varteg Gcera asymmetriaal, another average over all the independent directions of differenti.a- dons should be added (3.3). Tn the actual computation, for the sake of convenience however, the double scalar vortiaitp anrrelation zs obtained first, and the double velocity correlation is found by solving the differential relations between them. Based upon either the axially symmetrical or aspmmetxiaal vortex as the element of turbulence, the calculatien leads to the same Millionshikov solution (4.4) of the Karman-Howarth equation, in vPhiah the ternus involving the triple velocity corre- Lations are neglected. Tt is well-known that both the velocity correlation and the law of turbulent energy decay of this solution agree with. Batahalor and Townsend's experiments. The present paper paints out finallp that the structure of turbulence, as revesled by the double velocity cnrrel.ation function, depends upon the vortiaity struofurs of its component eddies. h'urthermare, since their velocity distribution of a furbulent fluid in its final. period of decay ie now known, triple and higher order velocity correlations or correlation functions of oilier kinds can tie oalaulaLed. These theoretical predictions can be subjected to the direct experimental. verification.
1957, 1(1): 3-14. doi: 10.6052/0459-1879-1957-1-1957-009
THE AERODYNAMIC PROBLEM OF RADIALLY LONG BLADES IN TURBOMIACHINES
WU CHUNG-HUA
Fundamental. equations in the form most suitable for use in turhomachines derived from, basic principles of aero-thermodynamics are given first and a general discussion of thezr applications to the aero-thermodynamic design of turboma,ohines is made. In order to investigate the detailed variation of the flow of gas in tha channel formed by two neighboring blades, a relative stream surface in the middle of the channel is considered. After a discussion of commonlp used as well as possible design specifications, two forms of equations in terms of a stream function are given, applicable to most of the desibns discussed. The preceding results are used to investigate tha detailed flow in a single-stage axial-flow gas turhine, a single-stage and a seven-stage axial-flnw compressor and a mixed-flow inipelier. in the case of the gas tuxhins having cylindrical. hub and casing walls, designed fox a free-vortex type of tangential velocity distribution it is found: (1) the flow paths of teases deviate from cylindrical. surfaces beoause of the radial blade fort。and aonpressilJility of the gases,(2) the radial slow is sensitive to the location of the radial element of the blades,and (3) a large negative gradient of axial velocity in front of the rotor is observed. In the case of the single-stage axial compressor having cylindrical csasing and hub walls and the hub xadius, both designed far symmetrical veloaitp diagrams seven-stage axial compressor having a constant casing radius and an increasing at all radii, the analysis shows: (1) the radialiy increasing angular momentum of the air partials and the curved hub contour have the predominating iufluenve on the flow pattern; (2) the oompressibility of the air does not ohanoe the shapes of the stream Lines greatly but has a Large effect on the magnitude of the agiaL velocity; (3) the effect of the radial twist of the blade of this type of design on the flow pattern is small; (4) the air moving radially inward in passing through the inlet guide vanes, coutinues inward in the first rotor and moves radially outward in the following stator; (5) the radially inward and outward motion repeats in the succeeding stages of a multi-tage compressor; (6) the effect of this oscillatory radial flow is largest in the inlet stage a multi-tage compressor. In the case of the mixea-flow lmpeller designed for all radial blade elements; the trend in the variation of static pressure a long the caring obtain e 1 in the analysis, agrees well with the experimental data and the analpais also egpiains the reason of a local pressure drop along the oaring abservad in the experiments. In the last section, a vomparison is made between the radial variation of flow velocities in the gap between stator and rotor obtained in the preceding analyses of axial turbamaahines and those obtained in the simplified-radial-equilibrium calculation and in an approximate method based an sinusoidal radial-flow paths. The comparison shows that the first approximate methol gives considerable errors whereas tha second approximate method gives very accurate results.
1957, 1(1): 15-48. doi: 10.6052/0459-1879-1957-1-1957-010

On the St. Venant Flexure Problem for Cross Sections of a Series of Symmetrical Airfoils


LIN TONG-JI

This paper deals with the problem of flexure cantilever beam with a symmetrical airfoil cross.The loading is applide at the free end ai right angles to the plane of symmetrical as shown in fig.1.The material is assumed to be homegeneus and isotropic,and the body forces are assumed to be negligble.In general,such a beam will twist as bend.

1957, 1(1): 49-62. doi: 10.6052/0459-1879-1957-1-1957-011
ON THE RECIPROCAL THEOREMS IN THE DYNAMICS OF ELASTIC BODIES AND SOME APPLICATIONS
HU HAI-CHANG
In this paper the reciprocal theorems in the dynamics of olastio are overtematically explained and extend to the case of anisotropic and nonhomoeneous elastic bodles with linear internal and external damping.Applicationsare made to problmes of strustural dynamics,theory of elaslicity and vibration prevention.
1957, 1(1): 63-76. doi: 10.6052/0459-1879-1957-1-1957-012
EFFECT OF STRESS-STRAIN CURVE OF MATERIAL ON SOLUTION OF PLANE-STRESS PROBLEMS WITH LARGE PLSTIC DEFORMATION
LEE MING-HUA

A brief review of author's previous work on the plastie plane stress problems with axial symmetry is first made. Results obtained for two of such problems, which show that the effeets of τ(γ) of the material and of loading on the distributions of the proportionate strains and of the ratios of principal stresses are very samll, are summmarized. An analysis of the equations is then made and the preceding ersults are explained. Equations of equilibrium in terms of the principal stresses and of the principal strains are derived for the two-dimensional plane stress problems without body force but considering finite strains. An analysis of these equations leads to the surmise that the effects of τ(γ) of the material on the distributions of the proportionate strains and of the ratios of the principal stresses are samll, provided that the proportionate strains and the ratios of the principal stresses at the boundary remain the same at different loads. On the other hand, the effects of τ(γ) of the material and of the load on the distributions of proportionate stresses are large. A simple approximate method of solution is obtained by using these results. The results obtained in this paper are compared with Ilyushin's theory of small elastic-plastic deformation.

1957, 1(1): 77-94. doi: 10.6052/0459-1879-1957-1-1957-013
PLASTIC FLOW IN THE EXTRUSION OF RIBS ON FLAT PLATES
WANG JEN
We consider the extrusion of ribs on thin flat plates as a problem in the theory of plane strain for perfectly plastic-ringid materials. These assamptions imply that ι≥2(w+d), (Fig. 1), and that the effect of work hardening being distributed over the deformed regions.The problem is one of coining. The anthor is unaware of other solutions treated in the prosent manner, except a similar initial motion problem given in Ref. 15. However, if the thickness h of the plastic material is large compared to the width of the extruded bar d, the flow region will be concentrated around the die and this is the familiar problem of inverted extrusion (Ref. 16) has recently given an approximate solution to the present problem. His results are discussed in section 4.
1957, 1(1): 95-108. doi: 10.6052/0459-1879-1957-1-1957-014
МАтЕМАТИЧЕСКИЙ АНАЛИЗ МАРКСИсТСКОЙ ТЕОРИИ О ВОСЛРОИЗВОДСТВЕ(Ⅰ)
Хо Пзо-сю, Л Динъ-по
Зто Лервая из статой в которой Лрименяюот математику в изуч марк-систской теории воснродства.
1957, 1(1): 109-130. doi: 10.6052/0459-1879-1957-1-1957-015
ABOUT AN INTGRAL OF SURFACE WAVES
PAN LIANG-JU
1957, 1(1): 131-137. doi: 10.6052/0459-1879-1957-1-1957-016
A NOTE ON THE REACTIONS OF A RECTANGULAR PLATE SIMPLY SUPPORTED AT FOUR CORNERS
HU HAI-CHANG
Consider an isotropio rectangular plate simply supported at four corners and loaded arbitrarily. Take a rectangular coordinate axes x, y along tha edges of the plate. It is proved that the reaction Rc at the corner x-a, y=b equals
Rc=(1/ab)∫∫xyq(x,y)dxdy.
1957, 1(1): 138-139. doi: 10.6052/0459-1879-1957-1-1957-017