Study of second order upwind differencing in a recirculating flow

The accuracy and stability of the second order upwind differencing scheme was investigated. The solution algorithm employed is based on a coupled solution of the nonlinear finite difference equations by the multigrid technique. Calculations have been made of the driven cavity flow for several Reynolds numbers and finite difference grids. In comparison with the hybrid differencing, the second order upwind differencing is somewhat more accurate but it is not monotonically accurate with mesh refinement. Also, the convergence of the solution algorithm deteriorates with the use of the second order upwind differencing

Numerical Investigation of Hot Gas Ingestion by STOVL Aircraft

This report compiles the various research activities conducted under the auspices of the NASA Grant NAG3-1026, "Numerical Investigation of Hot Gas Ingestion by STOVL Aircraft" during the period of April 1989 to April 1994. The effort involved the development of multigrid based algorithms and computer programs for the calculation of the flow and temperature fields generated by Short Take-off and Vertical Landing (STOVL) aircraft, while hovering in ground proximity. Of particular importance has been the interaction of the exhaust jets with the head wind which gives rise to the hot gas ingestion process. The objective of new STOVL designs to reduce the temperature of the gases ingested into the engine. The present work describes a solution algorithm for the multi-dimensional elliptic partial-differential equations governing fluid flow and heat transfer in general curvilinear coordinates. The solution algorithm is based on the multigrid technique which obtains rapid convergence of the iterative numerical procedure for the discrete equations. Initial efforts were concerned with the solution of the Cartesian form of the equations. This algorithm was applied to a simulated STOVL configuration in rectangular coordinates. In the next phase of the work, a computer code for general curvilinear coordinates was constructed. This was applied to model STOVL geometries on curvilinear grids. The code was also validated in model problems. In all these efforts, the standard k-Epsilon model was used

A study of pressure-driven displacement flow of two immiscible liquids using a multiphase lattice Boltzmann approach

The pressure-driven displacement of two immiscible fluids in an inclined channel in the presence of viscosity and density gradients is investigated using a multiphase lattice Boltzmann approach. The effects of viscosity ratio, Atwood number, Froude number, capillary number, and channel inclination are investigated through flow structures, front velocities, and fluid displacement rates. Our results indicate that increasing viscosity ratio between the fluids decreases the displacement rate. We observe that increasing the viscosity ratio has a non-monotonic effect on the velocity of the leading front; however, the velocity of the trailing edge decreases with increasing the viscosity ratio. The displacement rate of the thin-layers formed at the later times of the displacement process increases with increasing the angle of inclination because of the increase in the intensity of the interfacial instabilities. Our results also predict the front velocity of the lock-exchange flow of two immiscible fluids in the exchange flow dominated regime. A linear stability analysis has also been conducted in a three-layer system, and the results are consistent with those obtained by our lattice Boltzmann simulations

Computational fluid dynamics using Graphics Processing Units: Challenges and opportunities

A new paradigm for computing fluid flows is the use of Graphics Processing Units (GPU), which have recently become very powerful and convenient to use. In the past three years, we have implemented five different fluid flow algorithms on GPUs and have obtained significant speed-ups over a single CPU. Typically, it is possible to achieve a factor of 50-100 over a single CPU. In this review paper, we describe our experiences on the various algorithms developed and the speeds achieved

Relative Reactivity of the Metal-Amido versus Metal-Imido Bond in Linked Cp-Amido and Half-Sandwich Complexes of Vanadium

Treatment of (η5-C5H4C2H4NR)V(N-t-Bu)Me (R = Me, i-Pr) and CpV(N-p-Tol)(N-i-Pr2)Me (Cp = η5-C5H5) with B(C6F5)3 or [Ph3C][B(C6F5)4] results in formation of the corresponding cations, [(η5-C5H4C2H4NR)V(N-t-Bu)]+ and [CpV(N-p-Tol)(N-i-Pr2)]+. The latter could also be generated as its N,N-dimethylaniline adduct by treatment of the methyl complex with [PhNMe2H][BAr4] (Ar = Ph, C6F5). Instead, the analogous reaction with the linked Cp-amido precursor results in protonation of the imido-nitrogen atom. Sequential cyclometalation of the amide substituents gave cationic imine complexes [(η5-C5H4C2H4NCR'2)V(NH-t-Bu)]+ (R' = H, Me) and methane. Reaction of cationic [(η5-C5H4C2H4NR)V(N-t-Bu)]+ with olefins affords the corresponding olefin adducts, whereas treatment with 1 or 2 equiv of 2-butyne results in insertion of the alkyne into the vanadium-nitrogen single bond, affording the mono- and bis-insertion products [(η5-C5H4C2H4N(i-Pr)C2Me2)V(N-t-Bu)]+ and [(η5-C5H4C2H4N(i-Pr)C4Me4)V(N-t-Bu)]+. The same reaction with the half-sandwich compound [CpV(N-p-Tol)(N-i-Pr2)]+ results in a paramagnetic compound that, upon alcoholysis, affords sec-butylidene-p-tolylamine, suggesting an initial [2+2] cycloaddition reaction. The difference in reactivity between the V-N bond versus the V=N bond was further studied using computational methods. Results were compared to the isoelectronic titanium system CpTi(NH)(NH2). These studies indicate that the kinetic product in each system is derived from a [2+2] cycloaddition reaction. For titanium, this was found as the thermodynamic product as well, whereas the insertion reaction was found to be thermodynamically more favorable in the case of vanadium.

Boundary-Layer Transition on Broad Cones rotating in an Imposed Axial Flow

We present stability analyses for the boundary-layer flow over broad cones (half-angle > 40◦) rotating in imposed axial flows. Preliminary convective instability analyses are presented that are based on the Orr–Sommerfeld equation for a variety of axial-flow speeds. The results are discussed in terms of the limited existing experimental data and previous stability analyses on related bodies. The results of an absolute instability analysis are also presented which are intended to further those by Garrett & Peake21 through the use of a more rigorous steady-flow formulation. Axial flow is seen to delay the onset of both convective and absolute instabilities

A Very High-Order Accurate Staggered Finite Volume Scheme for the Stationary Incompressible Navier–Stokes and Euler Equations on Unstructured Meshes

International audienceWe propose a sixth-order staggered finite volume scheme based on polynomial reconstructions to achieve high accurate numerical solutions for the incompressible Navier-Stokes and Euler equations. The scheme is equipped with a fixed-point algorithm with solution relaxation to speed-up the convergence and reduce the computation time. Numerical tests are provided to assess the effectiveness of the method to achieve up to sixth-order con-2 Ricardo Costa et al. vergence rates. Simulations for the benchmark lid-driven cavity problem are also provided to highlight the benefit of the proposed high-order scheme

Argonne National Laboratory Reports

The accuracy of the finite analytic method of discretizing fluid flow equations is assessed through calculations of multidimensional scalar transport. The transport of a scalar function in a uniform velocity flow field inclined with the finite-difference grid lines is calculated for a range of grid Peclet numbers and flow skewness. The finite analytic method is observed to be superior to the approach of constructing finite-difference analogs from locally one-dimensional resolution of the flow vector. However, the finite analytic method also produces appreciable errors locally in regions of steep variations, under conditions of large grid Peclet numbers, and skewness of the streamlines

Argonne National Laboratory Reports

A fully coupled solution algorithm for pressure-linked fluid flow equations earlier found to be rapidly convergent in laminar flows has been extended to calculate turbulent flows. The governing mean flow equations are solved in conjunction with a two-equation (k - epsilon) turbulence model. A number of two-dimensional recirculating flows have been computed and it is shown that the calculation procedure is rapidly convergent in all the cases. The calculations have been compared with published experimental data; their agreement is in accord with other published experiences with the (k - epsilon) model in similar flows

Argonne National Laboratory Reports

The report describes and demonstrates the performance of a modification to an earlier solution algorithm for the calculation of multidimensional fluid flow, heat transfer, and combustion processes. The modification significantly reduces the computer storage required by the earlier algorithm without degrading the rate of convergence. The modification called as telescoping subdomain analysis (TSDA) splits the flow domain into overlapping subregions and solves them in a sequence, with known conditions on the boundaries of the subregions. The procedure has been tested in four different two-dimensional recirculating flows and the convergence rates have been equivalent to the rates with full-domain analysis. The modification offers significant savings of computer storage and cost and permits calculations with larger finite-difference grids