THREE-DIMENSIONAL TURBULENCE NUMERICAL SIMULATION OF A STEPPED SPILLWAY OVERFLOW

In this paper, the k ε turbulence model is used to simulate the three dimensional turbulence flow over the stepped spillway at the Yubeishan reservoir. In order to solve the curved free water surface and to handle the complex boundary conditions, the fractional Volume Of Fluid (VOF) model that is applicable to the solution of the stratified two phase flow is introduced along with k ε turbulence model and the unstructured grid is used for the discretization of the irregular simulation domain. By these methods, the turbulence flow field of the stepped spillway is simulated successfully. The location of the free surface along the spillway, the magnitude and distribution of the velocity, the pressure on the step surface, the turbulence kinetic energy and turbulence dissipation rate are obtained by simulation. The changes and distributions of these characteristics along the width of the spillway are also obtained. The energy dissipation ratio of the stepped spillway is calculated according to the upstream and downstream water depth and velocities

THREE-DIMENSIONAL TURBULENCE NUMERICAL SIMULATION OF A STEPPED SPILLWAY OVERFLOW

In this paper, the k-ε two-equation turbulence model was used to simulatethe three-dimensional turbulent flow of the stepped spillway at the Yubeishan reservoir. In order tosolve the curved free water surface and to handle the complex boundary conditions, the fractionalVolume Of Fluid (VOF) model that is applicable to the solution of the stratified two-phase flow wasintorduced to the k-ε turbulence model and the unstructured grid was used for the discretization ofthe irregular simulation domain. By these methods, the turbulent flow field of the stepped spillwaywas simulated successfully. The location of the free surface along the spillway, the magnitude anddistribution of the velocity, the pressure distribution on the step surface, the turbulence kineticenergy and turbulence dissipation rate were obtained by simulation. The changes and distributions ofthese characteristics along the width of the spillway were also obtained. The energy dissipationratio of the stepped spillway was calculated according to the upstream and downstream water depthand velocities.

Characteristics and generation of elastic turbulence in a three-dimensional parallel plate channel using direct numerical simulation

Direct numerical simulations（DNSs） of purely elastic turbulence in rectilinear shear flows in a three-dimensional（3D） parallel plate channel were carried out,by which numerical databases were established.Based on the numerical databases,the present paper analyzed the structural and statistical characteristics of the elastic turbulence including flow patterns,the wall effect on the turbulent kinetic energy spectrum,and the local relationship between the flow motion and the microstructures＇ behavior.Moreover,to address the underlying physical mechanism of elastic turbulence,its generation was presented in terms of the global energy budget.The results showed that the flow structures in elastic turbulence were 3D with spatial scales on the order of the geometrical characteristic length,and vortex tubes were more likely to be embedded in the regions where the polymers were strongly stretched.In addition,the patterns of microstructures＇ elongation behave like a filament.From the results of the turbulent kinetic energy budget,it was found that the continuous energy releasing from the polymers into the main flow was the main source of the generation and maintenance of the elastic turbulent status.

Numerical study on evolution of subharmonic varicose low-speed streaks in turbulent channel flow

The evolution of two spanwise-aligned low-speed streaks in a wall turbulent flow, triggered by the instability of the subharmonic varicose （SV） mode, is studied by a direct numerical simulation （DNS） method in a small spatial-periodic channel. The results show that the SV low-speed streaks are self-sustained at the early stage, and then transform into subharmonic sinuous （SS） low-speed streaks. Initially, the streamwise vortex sheets are formed by shearing, and then evolve into zigzag vortex sheets due to the mutual induction. As the intensification of the SV low-speed streaks becomes prominent, the tilted streamwise vortex tubes and the V-like streamwise vortex tubes can be formed simultaneously by increasing ＋~. When the SV low-speed streaks break down, new zigzag streamwise vortices will be generated, thus giving birth to the next sustaining cycle of the SV low-speed streaks. When the second breakdown happens, new secondary V-like streamwise vortices instead of zigzag streamwise vortices will be generated. Because of the sweep motion of the fluid induced by the secondary V-like streamwise vortices, each decayed low-speed streak can be divided into two parts, and each part combines with the part of another streak, finally leading to the formation of SS low-speed streaks.

Numerical investigation on flow and heat transfer characteristics of corrugated tubes with non-uniform corrugation in turbulent flow

Based on finite volume method, the pressure drop and heat transfer characteristics of one smooth tube and ten different axisymmetric corrugated tubes, including two with uniform corrugation and eight with non-uniform corrugation, have been studied. A physical model of the corrugated tube was built, then the numerical simulation of the model was carried out and the numerical simulation results were compared with the empirical formula.The results show that: the friction factor decreases with the increase of Reynolds number ranging from 6000 to 57000, the value of which in the corrugated tubes with non-uniform corrugation(tube 03–10) are smaller than those with uniform corrugation(tube 01–02). The geometry parameters of tube(01) have advantages on the heat transfer enhancement in low Reynolds number flow region(from 6000 to 13000) and tube(07–08)have advantages on the heat transfer enhancement in high Reynolds number flow region(from 13000 to 57000). The vortex, existed in each area between two adjacent corrugations called second flow region, is the root of the enhancement on heat transfer in the corrugated tubes. The effectiveness factor decreases with the increasing of Reynolds number and the performances of the corrugated tubes with pitch of 12.5 mm have advantages than these of 10 mm under the same corrugation geometric parameter.

Numerical study on three-dimensional CJ detonation waves interacting with isotropic turbulence

The three-dimensional structures of a cellular detonation wave interacting with different turbulent flows were investigated using a one-step irreversible Arrhenius kinetics model. High-resolution bandwidth-optimized WENO scheme of spatial discretization and total variation diminishing temporal integration are used to solve the three dimensional chemically reactive Navier-Stokes equations. The turbulent vertical and entropic forcing effects on the three dimensional detonation wave structures and dynam- ics are analyzed, as well as the detonation effects on tur- bulent vortex structures. It has been found that the turbulence field imposed has created small scale wrinkles embedded in the detonation front, apart from the large scale features of detonation without turbulence. The deto- nation propagating velocity over the leading shock front varies from 0.8 to 1.6 times of CJ velocity and its proba- bility density function （pdf） skews towards sub-CJ velocity and peaks at about 0.9. The recorded detonation velocity always preferentially decays with time, with very rapid accelerations through triple point interactions. Its pdf also skews to sub-CJ velocity, while its overall shape agrees well with W3. The reaction zone is greatly influenced by the vortex, much more irregular and elongated for the turbulent cases. Distributed burning pockets are more likely to be found there. The turbulent kinetic energy is amplified across the detonation, and periodically oscillates downstream the detonation. The off-diagonal components of Reynolds stress also show a rapid rise across the deto- nation and present to be non-zero downstream of detona- tion. Vortex structures are compound results of the convected vortex and the generated vortex by the collision of triple points. The convection term and baroclinic gen- eration term in the transport equation of enstrophy are compared in detail.

A NEW DEPTH-AVERAGED TWO-EQUATION (K-) TURBULENT CLOSURE MODEL AND ITS APPLICATION TO NUMERICAL SIMULATION FOR A RIVER

The paper mainly focuses on describing the modification made to a new depth-averaged two-equation turbulent closure model based on the revised κ-ω model recently. In the case of side discharged jets with tempera- ture difference and transverse current, the new model has been investigated numerically in detail. As a practical example of application to use the new model, the side discharge of the cooling water from three outlets into a natu- ral river on one bank has been simulated, and the geomorphic variation under water has been treated suitably. Two depth-averaged models, and have been used, the later was the unique one up to the present. Emphasis is placed on the comparative research with different models under the same computational conditions. It has been verified that if the discharged flow rates are relatively small, when the pollutant plume in the near and transitional zons is predicted, the agreement with experimental and field data simulated by the model is better than by the model or other methods commonly used in engineering.

On the clean numerical simulation(CNS) of chaotic dynamic systems

According to Lorenz, chaotic dynamic systems have sensitive dependence on initial conditions（SDIC）, i.e., the butterfly-effect： a tiny difference on initial conditions might lead to huge difference of computer-generated simulations after a long time. Thus, computer-generated chaotic results given by traditional algorithms in double precision are a kind of mixture of ＂true＂（convergent） solution and numerical noises at the same level. Today, this defect can be overcome by means of the ＂clean numerical simulation＂（CNS） with negligible numerical noises in a long enough interval of time. The CNS is based on the Taylor series method at high enough order and data in the multiple precision with large enough number of digits, plus a convergence check using an additional simulation with even smaller numerical noises. In theory, convergent（reliable） chaotic solutions can be obtained in an arbitrary long（but finite） interval of time by means of the CNS. The CNS can reduce numerical noises to such a level even much smaller than micro-level uncertainty of physical quantities that propagation of these physical micro-level uncertainties can be precisely investigated. In this paper, we briefly introduce the basic ideas of the CNS, and its applications in long-term reliable simulations of Lorenz equation, three-body problem and Rayleigh-Bénard turbulent flows. Using the CNS, it is found that a chaotic three-body system with symmetry might disrupt without any external disturbance, say, its symmetry-breaking and system-disruption are ＂self-excited＂, i.e., out-of-nothing. In addition, by means of the CNS, we can provide a rigorous theoretical evidence that the micro-level thermal fluctuation is the origin of macroscopic randomness of turbulent flows. Naturally, much more precise than traditional algorithms in double precision, the CNS can provide us a new way to more accurately investigate chaotic dynamic systems.

NUMERICAL SIMULATIONS OF TURBULENT FLOW IN AND ABOVE PLANT CANOPIES

The turbulent flow in and above plant canopies is of fundamental importance to the understanding of transport processes of momentum,heat and mass between plant canopies and atmosphere,and to microme- teorology.The Reynolds stress equation model(RSM)has been applied to calculate the turbulence in cano- pies in this paper.The calculated mean wind velocity profiles,Reynolds stress,turbulent kinetic energy and viscous dissipation rate in a corn canopy and a spruce forest are compared with field observed data and with Wilson's and Shaw's model.The velocity profiles and Rynolds stress calculated by both models are in good agreement,and the length scale of turbulence appears to be similar.

NUMERICAL SIMULATION OF TURBULENT DIFFUSION OVER A COMPLEX TERRAIN

A set of hydrostatic atmospheric thermodynamic equations and diffusion equation are solved numerically to simulate the flow,temperature and concentration fields over the Fenhe River Valley,Shanxi Province. The results are compared with the data observed in a tracer experiment carried out in February of 1984. The concentration distributions are calculated by three approaches:ordinary grid numerical model,nested grid model and Gaussian model.The comparison shows that the nested grid model gives the best results and needs only a little more computer time.

LARGE-EDDY SIMULATION OF TURBULENT FLOW CONSIDERING INFLOW WAKES IN A FRANCIS TURBINE BLADE PASSAGE

Turbulent flow in a 3-D blade passage of a Francis hydro turbine was simulated with the Large Eddy Simulation （LES） to investigate the spatial and temporal distributions of the turbulence when strongly distorted wakes in the inflow sweep over the passage, In a suitable consideration of the energy exchanging mechanism between the large and small scales in the complicated passage with a strong 3-D curvature, one-coefficient dynamic Sub-Grid-Scale （SGS） stress model was used in this article. The simulations show that the strong wakes in the inflow lead to a flow separation at the leading zone of the passage, and to form a primary vortex in the span-wise direction. The primary span-wise vortex evolves and splits into smaller vortex pairs due to the constraint of no-slip wall condition, which triggers losing stability of the flow in the passage. The computed pressures on the pressure and suction sides agree with the measured data for a working test turbine model.