AN EFFICIENT METHOD FOR SOLVING THE MIXED DIRECT-INVERSE PROBLEM OF THE TRANSONIC ROTATIONAL FLOW IN PLANE CASCADES

The method in [1] has been extended to the case of rotational flow in this paper. A new method for dealing with the shock wave is presented. This method has the advantages of both the shock-fitting and the shock capturing methods. The direct problem and the mixed direct-inverse prob- lem of the rotational flow in a transonic plane cascade at both design and off design conditions are solved, and the results show that the present method has rapid convergence rate and high accuracy even for the flow with moderately strong shocks. The calculations have been carried out on the DPS-8 computer, and for the direct problem, only 50-80 iterations are needed, and 50-80 seconds of CPU time are required.

Vertical rotation effect on turbulence characteristics in an open channel flow

This paper solves the three-dimensional Navier-Stokes equation by a fractional-step method with the Reynolds number Reτ=194 and the rotation number Nτ=0-0.12. When Nτ is less than 0.06, the turbulence statistics relevant to the spanwise velocity fluctuation are enhanced, but other statistics are suppressed. When Nτ is larger than 0.06, all the turbulence statistics decrease significantly. Reynolds stress budgets elucidate that turbulence kinetic energy in the vertical direction is transferred into the streamwise and spanwise directions. The flow structures exhibit that the bursting processes near the bottom wall are ejected toward the free surface. Evident change of near-surface streak structures of the velocity fluctuations are revealed.

Some Effects of Rotation Rate on Planetary-Scale Wave Flows

A series of experiments were performed in a rotating annulus of fluid to study effects of rotation rate on pianeta ry-scale baroclinic wave flows. The experiments reveal that change in rotation rate of fluid container causes variation in Rossby number and Taylor number in flows and leads to change in flow patterns and in phase and amplitude of quasi-stationary waves. For instance, with increasing rotation rate, amplitude of quasi-stationary waves increases and phase shifts upstream. On the contrary, with decreasing rotation rate, amplitude of quasi-stationary waves de creases and phase shifts downstream. In the case of the earth's atmosphere, although magnitude of variation in earth's rotation rate is very small, yet it causes a very big change in zonal velocity component of wind in the atmosphere and of currents in the ocean, and therefore causes a remarkable change in Rossby number and Taylor number determining regimes in planetary-scale geophysical flows. 1 he observation reveals that intensity and geographic location of subtropic anticyclones in both of the Northern and Southern Hemispheres change consistently with the variation in earth's rotation rate. The results of fluid experiments are consistent, qualitatively, with observed phenomena in the atmospheric circulation.

Stability Criteria to the Incompressible Inviscid Linear Fluid between Two Rotation Coaxial Cylinders

The stability and instability phenomenon coupled with the rotation effect and the thermal convection between two concentric cylinders was studied. By means of the Normal-Modes method, the stability or instability criteria for the linearized system in terms of the oscillation frequency, the axial wavelength and the background thermal gradient are proved. Besides, some numerical simulation for the axisymmetric perturbations is presented.

HIGH SPEED FLOW DESIGN USING THE THEORY OF OSCULATING CONES AND AXISYMMETRIC FLOWS

An inverse method of characteristics was introduced into the design concept of using osculating cones (OC) in the supersonic flow, which can extend the domain of options for generating the aerospace vehicle configurations with supersonic leading edge as well as inlet diffusers. Some more practical waverider shapes with higher volumetric efficiency can be obtained through using the concept of osculating axisymmetric (OA) flows with rotationality in the post shock flow field by inputting curved shocks.

Laminar Flow in the Gap between Two Rotating Parallel Frictional Plates in Hydro-viscous Drive

The velocity, pressure and temperature distributions of the flow in the gap between hydro-viscous drive friction disks are the key parameters in the design of hydro-viscous drive and angular velocity controller. In the previous works dealing with the flow in the gap between disks in hydro-viscous drive, few authors considered the effect of Coriolis force on the flow. The object of this work is to investigate the flow with consideration of the effects of centrifugal force, Coriolis force and variable viscosity. A simplified mathematical model based on steady and laminar flow is presented. An approximate solution to the simplified mathematical model is obtained by using the iteration method assuming that the fluid viscosity remains constant. Then the model considering the effect of variable viscosity is solved by means of computational fluid dynamics code FLUENT. Numerical results of the flow are obtained. It is found that radial velocity profile diverges from the ideal parabolic curve due to inertial forces and tangential velocity profile is nonlinear due to Coriolis force, and pressure has two possible solution branches. In addition, it is found that variable viscosity plays an important role on pressure profiles which are significantly different from those of fluid with constant viscosity. The experimental device designed for this work consists of two disks, and one of them is fixed. Experimental pressure and temperature of the flow within test rig are obtained. It is shown that the trend of numerical results is in agreement with that of experimental ones. The research provides a theoretical foundation for hydro-viscous drive design.

COMPUTATIONALINTELLECTUAL ANALYTICAL THEORYOF COMPUTATIONAL ANALYTICAL APPROACH TOROTATING FLOW OF NON_NEWTONIAN FLUID

A combination of the computational symbolic calculation, mathematical approach and physico-mechanical model lends to a computational intellectual analytical approach developed by the author. There is a principal difference between the computer proof and the computer derivation completed by the computer, also difference between the numerical and symbolic calculations. In this investigation the computational analytical approach is extended, and an unsteady flow of non-Newtonian fluid in the gap between two rotating coaxial cylinders is studied. The Oldroyd fluid B model is used by which the Weissenberg effects are explained in a good comparison with the experiments. The governing equations are reduced to a partial differential equation of 3 rd order for the dimensionless velocity. Using the computer software Macsyma and an improved variational approach the problem with the initial and boundary conditions is then reduced to a problem of an ordinary differential equation for different approximations. The analytical solutions are given for the 1 st, 2 nd and 3 rd approximations. The present investigation shows the ability of the computational symbolic manipulation in solving the problems of non-Newtonian fluid flows. There is a possibility of that to solve the problems in mathematics and mechanics. An important conclusion can be drawn from the results that the transition from a steady state to another steady state is non-unique.

Numerical Investigation of Submarine Hydrodynamics and Flow Field in Steady Turn

This paper presents numerical simulations of viscous flow past a submarine model in steady turn by solving the Reynolds-Averaged Navier-Stokes Equations（RANSE） for incompressible, steady flows. The rotating coordinate system was adopted to deal with the rotation problem. The Coriolis force and centrifugal force due to the computation in a bodyfixed rotating frame of reference were treated explicitly and added to momentum equations as source terms. Furthermore, velocities of entrances were coded to give the correct magnitude and direction needed. Two turbulence closure models（TCMs）, the RNG k-ε model with wall functions and curvature correction and the Shear Stress Transport（SST） k-ω model without the use of wall functions, but with curvature correction and low-Re correction were introduced, respectively. Take DARPA SUBOFF model as the test case, a series of drift angle varying between 0° and 16° at a Reynolds number of 6.53×10^6 undergoing rotating arm test simulations were conducted. The computed forces and moment as a function of drift angle during the steady turn are mostly in close agreement with available experimental data. Though the difference between the pressure coefficients around the hull form was observed, they always show the same trend. It was demonstrated that using sufficiently fine grids and advanced turbulence models will lead to accurate prediction of the flow field as well as the forces and moments on the hull.

Numerical study on three-dimensional flow field of continuously rotating detonation in a toroidal chamber

Gaseous detonation propagating in a toroidal chamber was numerically studied for hydrogen/oxygen/nitrogen mixtures. The numerical method used is based on the three-dimensional Euler equations with detailed finiterate chemistry. The results show that the calculated streak picture is in qualitative agreement with the picture recorded by a high speed streak camera from published literature. The three-dimensional flow field induced by a continuously rotating detonation was visualized and distinctive features of the rotating detonations were clearly depicted. Owing to the unconfined character of detonation wavelet, a deficit of detonation parameters was observed. Due to the effects of wall geometries, the strength of the outside detonation front is stronger than that of the inside portion. The detonation thus propagates with a constant circular velocity. Numerical simulation also shows three-dimensional rotating detonation structures, which display specific feature of the detonation- shock combined wave. Discrete burning gas pockets are formed due to instability of the discontinuity. It is believed that the present study could give an insight into the interest- ing properties of the continuously rotating detonation, and is thus beneficial to the design of continuous detonation propulsion systems.

REYNOLDS-STRESS MODELLING OF TURBULENT ROTATING FLOWS

The present analysis shows that the EVM can not reflect the turbulence physics in non-inertial frame. The effects of Coriolis force on turbulence is embodied naturally in the Reynolds-stress transport equation. It is observed that the existing second-moment closure model with appropriate near-wall treatment can adequately predict flows in rotating channel and in axially rotating pipe for moderate rotation rate.

Series Solution for Rotating Flow of an Upper Convected Maxwell Fluid over a Stretching Sheet

The equations for two-dimensional flow of an upper convected Maxwell （UCM） fluid in a rotating frame are modeled. The resulting equations are first simplified by a boundary layer approach and then solved by a homotopy analysis method （HAM）. Convergence of series solution is discussed through residual error curves. The results of the influence of viscoelastic and rotation parameters are plotted and discussed.

Lie Point Symmetry Algebras and Finite Transformation Groups of Baroclinic Mode for Rotating Stratified Flows

The transformation groups and symmetries of the baroclinic mode for rotating stratified flow can be obtained via the standard approach. Applying the symmetry group on some special solutions, the newly obtained results disprove a known conjecture.

Three-dimensional channel flow of second grade fluid in rotating frame

An analysis is performed for the hydromagnetic second grade fluid flow between two horizontal plates in a rotating system in the presence of a magnetic field. The lower sheet is considered to be a stretching sheet, and the upper sheet is a porous solid plate. By suitable transformations, the equations of conservation of mass and momentum are reduced to a system of coupled non-linear ordinary differential equations. A series of solutions to this coupled non-linear system are obtained by a powerful analytic technique, i.e., the homotopy analysis method （HAM）. The results are presented with graphs. The effects of non-dimensional parameters R, A, M2, a, and K2 on the velocity field are discussed in detail.

Flow of a Viscoplastic Fluid on a Rotating Disk

The equations describing the flow of a viscoplastic fluid on a rotating disk are de-rived and are solved by perturbation technique and nurmerical computation respectivelyfor 2 cases. This makes it possible to calculate the thickness distribution of film. Twokinds of distribution of thickness have been found. For the viscoplastic fluid for whichboth viscosity and yield stress are independent of radial coordinate r, the thickness hdecreases with increasing r. For a Bingham fluid for which both viscosity and yieldstress are function of time and r. the thickness h increases with increasing r.

Observation of Central Toroidal Rotation Induced by ICRF on EAST

Core plasma rotation of both L-mode and H-mode discharges with ion cyclotron range of frequency（ICRF） minority heating（MH） scheme was measured with a tangential X-ray imaging crystal spectrometer on EAST（Experimental Advanced Superconducting Tokamak）.Cocurrent central impurity toroidal rotation change was observed in ICRF-heated L-and H-mode plasmas.Rotation increment as high as 30 km/s was generated at ~1.7 MW ICRF power.Scaling results showed similar trend as the Rice scaling but with significant scattering,especially in L-mode plasmas.We varied the plasma current,toroidal field and magnetic configuration individually to study their effect on L-mode plasma rotation,while keeping the other major plasma parameters and heating unchanged during the scanning.It was found that larger plasma current could induce plasma rotation more efficiently.A scan of the toroidal magnetic field indicated that the largest rotation was obtained for on-axis ICRF heating.A comparison between lower-single-null（LSN）and double-null（DN） configurations showed that LSN discharges rendered a larger rotation change for the same power input and plasma parameters.

Improved Dissipation Rate Equation for Swirling and Rotating Pipe Flows

The nature of turbulent swirling and rotating flow in a straight pipe is investigated using a family of near-wall two-equation models. Specifically, the viability of three different near-wall two-equation models is assessed. These models are asymptotically consistent near the wall. The first two models, one with isotropic and another with anisotropic eddy viscosity invoked, solved a dissipation rate equation with no explicit correction made to account for swirl and flow rotation. The third model assumes an isotropic eddy viscosity but solves an improved dissipation rate equation that has explicit corrections made to account for swirl and flow rotation. Calculations of turbulent flows in the swirl number range 0.25 - 1.3 with and without a central recirculation region reveal that, with the exception of the third model, neither one of the other two models can replicate the mean field at the swirl numbers tested. Furthermore, taking stress anisotropy into account also fails to model swirl effect correctly. Significant improvements can be realized from the third model, which is based on an improved dissipation rate equation and the assumption of isotropic eddy viscosity. The predicted mean flow and turbulence statistics correlate well with measurements at low swirl. At high swirl, the two-equation model with an improved dissipation rate equation can still be used to model swirling and rotating pipe flows with a central recirculation region. However, its simulation of flows without a central recirculation region is not as satisfactory.

Three-dimensional mixed convection squeezing flow

The unsteady mixed convection squeezing flow of an incompressible Newtonian fluid between two vertical parallel planes is discussed. The fluid is electrically conducting. The governing equations are transformed into ordinary differential equations （ODEs） by appropriate transformations. The transformed equations are solved successfully by a modern and powerful technique. The effects of the emerging parameters on the flow and heat transfer characteristics are studied and examined. The values of the skin friction coefficient and the local Nusselt number are tabulated and analyzed.

SURFACE COMPOSITE GEAR AND PIPE MADE BY SEPARATED EUTECTIC TECHNOLOGY

It is found that the anomalous eutectics can be separated on macroscopic scale by flow caused by electromagnetic stirring, and the separated phase is the leading faceted phase with the solution entropy over 23 J/(mol&middotK). By using this technology, a new kind of composite pipe and gear with good abrasive properties were made without adding any reinforced particles. Emphases were paid on the researches about formation mechanism of separated eutectic and abrasive property of the composite pipe or gear. The result shows that the entropy of solution controlling the eutectic microstructure is also valid and useful as a criterion of separated eutectic, and the kind and its chemical scope of the off-eutectic used to make composite can be calculated according to this theory.

Effects of Thermal Gradients and Rotational Flows on Grain Growth in 22 t Steel Ingots

Heavy ingots are widely used in many industrial fields. The coarse grains formed during the process of in- got solidification influence the properties and fracture behaviors of the final products. The coarse grain growth was simulated under different thermal gradients. A 30Cr2Ni4MoV steel ingot was melted in a cubic crucible with dimen-sions of 15 cm×10 cm×23 cm, and the cooling conditions on each side of the crucible were controlled by different thermal curves. The influences of thermal gradients and rotational flows on grain growth in heavy steel ingots were then investigated both numerically and experimentally. The results showed that when the amplitude of the rotation angle was 60°, the metal was solidified under a reciprocating horizontal rotational condition when the angular velocity was 10 （°）/s or 20 （°）/s. As the thermal gradient increased, the lengths of the primary columnar grains in- creased, and the diameters of equiaxed grains decreased. When the direction of flow rotation was perpendicular to the direction of grain growth, the columnar grain zone was nearly eliminated, and the average diameter of equiaxed grains was 0.5 mm.

窄条控制件对旋转振荡板尾流的控制

两个小窄条对称地放于两侧,对宽厚比B/H=3的旋转振荡平板的尾流旋涡脱落进行抑制.板在平行于来流位置附近绕对称轴作旋转振荡,振幅为10°.窄条长边与板的旋转轴平行,窄条表面与来流方向垂直,窄条宽度与板的厚度之比b/H=1/3.控制参数为窄条位置.尾流流动显示图片和尾流脉动速度谱结果表明,当窄条位于有效区域内时,板两侧的涡脱落得到有效抑制.有效区尺度随着无量纲频率的增大而增大,随着雷诺数的增大而减小.