The numerical solution of the laminar flow in a constricted channel at moderately high Reynolds number using Newton iteration

The numerical solution of the flow in a stepped channel constricted to half its width has been obtained for Reynolds numbers up to 2000 using Newton's iteration to solve the ensuing algebraic system. In order to avoid high-frequency errors, a locally fine grid is effected near the corner by transformation of the independent variables. The results predict a downstream recirculation region, observed in experiments but not found in earlier numerical calculations. The inclusion of the Dennis–Hudson upwinding, added for stability in SOR methods, whilst giving the same characteristics of the flow, is less accurate by at least an order of magnitude.     

Numerical solution of two-layer,two-dimensional tidal flow in a boundary-fitted orthogonal curvilinear co-ordinate system

A new two-layer, two-dimensional mathematical model employing a finite difference method based on numerically generated boundary-fitted orthogonal co-ordinates and a grid ‘block’ technique for unsteady boundary problems is developed which can be used to simulate flows with density stratification in a natural water-body with complicated topography. In the model the turbulent exchange across the interface is treated empirically and a time-splitting finite difference method with two fractional steps is employed to solve the governing equations. The model is calibrated and verified by comparing the computational results with data measured in Tolo Harbour, Hong Kong. The simulation results mimie the field measurements very closely. The computation shows that the model reproduces the two-layer, two-dimensional tidal flow with density stratification in Tolo Harbour very well. The computed velocity hodographs show that the tidal circulations at various positions in each layer have different patterns and that the features of the patterns are independent of the tidal type except for their scales. The computed Lagrangian pathlines show that the tidal excursion is dependent on the tidal type, especially in the inner harbour and side-coves.     

Wall-modeled large eddy simulation of turbulent channel flow at high Reynolds number using the von Karman length scale

The von Karman length scale is able to reflect the size of the local turbulence structure. However, it is not suitable for the near wall region of wall-bounded flows, for its value is almost infinite there. In the present study, a simple and novel length scale combining the wall distance and the von Karman length scale is proposed by introducing a structural function. The new length scale becomes the von Karman length scale once local unsteady structures are detected. The proposed method is adopted in a series of turbulent channel flows at different Reynolds numbers. The results show that the proposed length scale with the structural function can precisely simulate turbulence at high Reynolds numbers, even with a coarse grid resolution.     

General considerations of numerical stability and accuracy in inviscid,compressible flow calculations employing primitive variables

The numerical stability of a number of computation schemes currently used for three-dimensional, inviscid, compressible flow is analysed using one-dimensional Fourier analysis. Whereas Reference 1 analysed schemes which were modified to render them amenable to simple analysis, the present work analyses the stability of schemes as actually used by Highton,³ Ahrabian,¹ Denton² and Spalding.⁶ The use of current values of the variables as they become available is shown to bring a general improvement to stability margin. The manner of damping introduced by the time marching formulation is shown to be deleterious to modifications which reduce truncation error. Staggered grid schemes can be formulated to second order accuracy with better stability margin than the corresponding first order scheme. While unstaggered grid schemes can be formulated to second order error and remain stable, their stability margin becomes very small. Agreement of the theory with numerical experiments continues to be of a high order for both one and three-dimensional disturbances.     

Obtaining phase averaged turbulence properties in the near wake of a circular cylinder at high Reynolds number using POD

The flow past a circular cylinder at high Reynolds number is studied by means of PIV, 3C-PIV and Time-Resolved PIV techniques. One of the goals of this study was to allow comparisons with numerical simulations on a domain identical to that of the experiment. For this reason, the cylinder was placed in a confined environment, with a high blockage and a low aspect ratio, thereby allowing computations on a mesh of reasonable size, and avoiding “infinite conditions”. This paper deals with the decomposition of the flow in a coherent and random parts. To this aim, phase averaged quantities were first obtained using the wall pressure signal on the cylinder as a trigger signal. This was achieved using both conditional sampling and LSE with similar results. This decomposition is then analysed using the Time Resolved PIV measurements, as well as by comparison of the contributions of the organised and turbulent fluctuations to the time-independent Reynolds stress tensor with those estimated from velocity spectra by interpolation and integration of the continuous part. In agreement with other studies, it is found that the contribution of the turbulent motion is overestimated as a result of the occurence of phase jitter between the trigger and velocity signal. A POD analysis was then performed to extract the coherent motion and to compare this decomposition with that obtained by phase averaging. Similarly to the phase averaging, the POD allows the decomposition of the time-independent stress tensor as the sum of two contributions corresponding to the first N modes, and the rest of the modes. This decomposition is then analysed by comparing these contributions to those obtained from the velocity spectra, according to the value N chosen. It is found that these contributions are strongly dependent on N, and the contribution of the first modes greatly overestimate the coherent motion if N is too large. In order to obtain a good decomposition of the flow in coherent and random parts, the difficulty in this case lies in the choice of the modes. Finally, the POD coefficients of the first two modes are used instead of the pressure signal to determine the phase of the vortex shedding, and the phase averaging is reconsidered. It is found that the phase averaged vortices are less smeared by the averaging process, the turbulent stresses better follow the evolution of the vortices, and the contributions of both coherent and turbulent fluctuations are found to agree well with those evaluated from the velocity spectra. This enhancement is obtained because the phase angle is determined directly from the velocity fields to be averaged, thereby reducing the phase-jitter effect. A comparison with a detached eddy simulation is also briefly shown and demonstrates the high level of agreement obtainable between simulation and experiment, as well as confirming the enhancement of the phase averaging using this procedure.     

The effect of the Reynolds number on the Reynolds stresses and vorticity in a turbulent far-wake

Using two orthogonal arrays of 16 X-wires, eight in the (x,y)-plane and eight in the (x,z)-plane, the effect of the Reynolds number in a turbulent plane far-wake has been investigated for two values of Re_θ (based on the free stream velocity and the momentum thickness), i.e. 1350 and 4600. It is observed that as the Reynolds number increases the magnitudes of the measured Reynolds stresses increase, as does the size of two-point vorticity correlation iso-contours. Discernible differences are also observed in probability density function, spectra and three-dimensional topologies. The Reynolds number dependence seems to vanish when Re_θ5000.     

Phase-averaged measurements of the turbulence properties in the near wake of a circular cylinder at high Reynolds number by 2C-PIV and 3C-PIV

The near wake of a circular cylinder at high Reynolds number is investigated by means of 2D-PIV and stereoscopic PIV. Phase-averaged measurements of the instantaneous fields have been performed. The linear stochastic estimation (LSE) has been adapted to estimate the phase-averaged quantities. This avoids the long time acquisition and the large storage needed for phase averaging. A good comparison is achieved between the results of the conditional sampling and those of LSE. Therefore, the estimation has been applied to the three-component datas and allowed evaluation of the whole phase-averaged turbulent stress tensor.     

The numerical solution of Stokes flow in a domain with re-entrant boundaries by the boundary element method

Numerical solutions are presented for two-dimensional low Reynolds number flow in a rotating tank with stationary barriers. The boundary element method is employed, assuming straight panels and quadratic source distribution. The feasibility of repositioning the nodes as a way to minimize the error is explored. A stretching parameter places smaller elements near the re-entrant regions. Elementary error analysis shows uniform improvement in the solution with stretching. The changing eddy pattern for different numbers and sizes of the barriers is compared with experimental results.     

A numerical study of the vortex motion in oscillating flow around a circular cylinder at low and middlieKc numbers

A new hybrid model, which is based on domain decomposition and proposed by the authors, is used for calculating the flow around a circular cylinder at low and middle Keulegan-Carpenter numbers (Kc=2−18) respectively. The vortex motion patterns in asymmetric regime, single pair (or transverse) regime and double pair (or diagonal) regime are successfully simulated. The calculated drag and inertial force coefficients are in better agreement with experimental data than other recent computational results. The project supported by the National Natural Science Foundations of China and the LNM, Institute of Mechanics, Academia Sinica     

The rheological behavior of flexible-chain polymers in the region of high shear rates and stresses,the critical process of spurting,and supercritical conditions of their movement at T > Tg

Methods of capillary viscometry were used in studying the rheological properties and behavior of a broad range of rubbers, including polymers with narrow and wide molecular-weight-distribution as well as commercial rubber grades, at widely varying shear rates and stresses. As is shown, in full conformity with the previously conducted experiments, during transition from a fluid to highelastic (quasi-cross-linked) state, they are chracterized by spurting followed by sliding over the channel walls. This relaxation transition is characterized by a critical shear stress value invariant with respect to the molecular weight, molecularweight distribution and temperature. The parameters defining spurting of polymer flow as a function of molecular-weight characteristics, temperature, and channel geometry have been investigated in detail. It is shown for the first time that under supercritical conditions the rate of polymer flow through channels does not depend, in the first approximation, on the molecular weight of the polymer, its molecularweight distribution, temperature, and filling, but is determined only by the shear stress.