Steady Flow Method Research Articles

The Coseismic Fault Weakening Processes Inferred from Frictional and Transport Properties of Fault Rocks, TCDP

No abstract available. doi:10.2204/iodp.sd.s01.06.2007

Quasi-least-squares finite element method for steady flow and heat transfer with system rotation

Two quasi-least-squares finite element schemes based on L2 inner product are proposed to solve a steady Navier–Stokes equations, coupled to the energy equation by the Boussinesq approximation and augmented by a Coriolis forcing term to account for system rotation. The resulting nonlinear systems are linearized around a characteristic state, resulting in linearized least-squares models that yield algebraic systems with symmetric positive definite coefficient matrices. Existence of solutions are investigated and a priori error estimates are obtained. The performance of the formulation is illustrated by using a direct iteration procedure to treat the nonlinearities and shown theoretical convergent rate for general initial guess.

Differential quadrature method for steady flow of an incompressible second-order viscoelastic fluid and heat transfer model

The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a small parameter to get the zeroth- and first-order approximate equations. By using the differential quadrature method with only a few grid points, the high-accurate numerical results were obtained.

Preconditioned lattice-Boltzmann method for steady flows

In this paper we propose a preconditioned lattice Boltzmann (LB) method for steady incompressible flows. For steady flows, the macroscopic equations derived from this LB model are equivalent to those from the standard LB model, but with an improved eigenvalue system. The proposed model can be viewed as an explicit solver for preconditioned compressible Navier-Stokes equations. Linear stability analysis is performed and the results show that the stability of the model is the same as that of the standard LB model for low Mach numbers. The proposed model retains the structure of the standard LB model and, hence, possesses all the advantages. Numerical tests show that the convergence rate can be enhanced as much as an order of magnitude compared to the standard lattice Boltzmann method. The accuracy of the solutions is improved as well.

Investigation of an unstable diffusion process in isothermal three-component gaseous mixtures under steady conditions

The diffusional transport of a ternary gaseous mixture of helium, Freon-12, and argon is studied under isothermal conditions by a steady-flow method. The experiments were done at atmospheric pressure and a temperature of 298 K. The data are compared with the theory. It is shown that the mass transfer of the components is influenced by convective flows.

High-Temperature tests of heat-insulating refractory materials for thermal conductivity

Specialists of D. I. Mendeleev Russian University of Chemical Engineering have created an installation for determining the thermal conductivity of heat-insulating refractory materials in the range of 20–1000°C using a measuring cross. The data obtained for materials tested by the steady-flow method and the hot-wire method (ISO 8894-1:1987 (E)) differ by no more than 12%.

Gel electrophoretic mobility of charged particles in a medium with curved channels.

A model of electrophoretic mobility of small charged particles (for example short DNA fragments) in media with curved channels is proposed. The medium is represented by a dense material embedding the curved channels accessible to the charged particles. The steady flow method is used to obtain an analytical expression of the particles' electrophoretic mobility as a function of the channel's shape. The analogy between the statistical properties of the channels and polymer chains (free-jointed and with the persistent mobility mechanism) is used.

An iterative geostatistical inverse method for steady flow in the vadose zone

An iterative geostatistical inverse approach is developed to estimate conditional effective unsaturated hydraulic conductivity parameters, soil‐water pressure head, and degree of saturation in heterogeneous vadose zones. This approach is similar to the classical cokriging technique, and it uses a linear estimator that depends on covariances and cross covariances of unsaturated hydraulic parameters, soil‐water pressure head, and degree of saturation. The linear estimator is, however, improved successively by solving the governing flow equation and by updating the residual covariance and cross‐covariance functions in an iterative manner. As a result, the nonlinear relationship between unsaturated hydraulic conductivity parameters and head is incorporated in the estimation and the estimated fields are approximate conditional means. The ability of the iterative approach is demonstrated through some numerical examples.

The mean filtration pressure of leukocyte suspensions and its relation to the passage of leukocytes through nuclepore filters and capillary networks.

To quantitatively evaluate the deformability of bulk suspensions of leukocytes (WBCs), account for the variance of individual cell mechanical properties, and deduce the potential for WBC entrapment within the capillary network in response to alterations in cell properties. The transient washout of WBCs initially trapped under low perfusion pressure in 5-microns pores of Nuclepore filters was analyzed for a 0.2-ml bolus of WBCs (derived from hamsters) with equal numbers of filter pores and cells, to characterize the statistical distribution of pressures, Pyield, required to dislodge the cells. Contributions of the variance in WBC diameter, pore diameter, and cremaster muscle capillary diameter to Pyield were estimated with a WBC cortical shell model and an analysis of the probability function of the ratio of WBC to pore diameter, lambda. For normal WBCs, Pyield exhibited a log-normal distribution with mean (Pyield) of 0.59 cmH2O. Incubation of cells in cytochalasin-B reduced (Pyield) almost 50%, whereas phorbol myristate acetate increased (Pyield) twofold. Incubation in N-formyl-methiolnyl-leucyl-phenylalanine had no significant effect on (Pyield), as polymorphonuclear cells became permanently trapped in the filter. The fluorescent dyes acridine orange, acridine red, and tetramethylrhodamine isothiocyanate increased (Pyield) as much as 10-fold, whereas steady-flow filtration methods showed no alteration. Analysis of the distribution of lambda revealed that due to their smaller pore diameters, in vitro filtration methods may overestimate in vivo values of (Pyield) by almost twofold. The transient filtration of WBC suspensions appears to be much more sensitive to subtle alterations in WBC deformability than steady-flow methods and may provide greater insight into the determinants of capillary perfusion. Estimates of (Pyield) are comparable to those obtained with micropipettes and permit analysis of substantially greater numbers of cells within a sample. Fluorescence labeling techniques should be used with caution, as they may dramatically alter cell properties to an extent undetectable by direct in vivo observations.

A Chebyshev pseudospectral multi-domain method for steady flow past a cylinder up to Re = 150

In this paper, a Chebyshev pseudospectral multi-domain method for solving the symmetric flow past a circular cylinder is considered. Numerical solutions to the Navier-Stokes equations are obtained up to Re = 150. Careful consideration is given to the proper interface condition in the multi-domain method, which decomposes the solution domain into subdomains by overlapping 1 grid point. The utility of this novel technique is demonstrated for the case of a moving shock wave. The Navier-Stokes equations are formulated in terms of the velocity and pressure. These are scaled and the equations are transformed using a stretched logarithmic polar coordinate system which maps the physical domain onto a rectangular domain. The free-stream velocity conditions are imposed on the outer boundaries and the computational boundary method [ Appl. Math. Lett. 6(2), 3 (1993)] is applied to the problem in the transformed domain for obtaining the pressure boundary condition. Finally, our numerical results indicate that the wake bubble has its eddy length proportional to the growth of Re, and its width is approximately O (Re 1 2 ) . These results are in good agreement with those of previous researchers.

Boundary integral method for steady flow in unsaturated porous media : Martinez, M J; McTigue, D F Int J Num Anal Meth GeomechV16, N8, Aug 1992, P581–601

Boundary integral method for steady flow in unsaturated porous media : Martinez, M J; McTigue, D F Int J Num Anal Meth GeomechV16, N8, Aug 1992, P581–601

Explicit Streamline Method for Steady Flows of Non-Newtonian Matter: History-Dependence and Free Surfaces

A new finite-difference method involving a streamline coordinate is developed for analyzing two-dimensional steady non-Newtonian flows with history dependence. The boundary of the material is partially free and partially confined. The proposed method is neither the method of stream function nor the use of convected reference frame. It simply regards streamline as an independent coordinate, thereby retaining the merits of both the Eulerian and Lagrangian schemes. The efficiency of the method is demonstrated in examples of several models' matter steadily discharging from a slit into a free space.

Explicit streamline method for steady flows of non-Newtonian matter: History-dependence and free surfaces

Explicit streamline method for steady flows of non-Newtonian matter: History-dependence and free surfaces

A boundary integral method for steady flow in unsaturated porous media

AbstractThe governing equation for steady flow in a homogeneous, partially saturated, porous medium can be written in a linear form if one adopts a hydraulic conductivity function which varies exponentially with capillary‐pressure head. The resulting linear field equation is a steady Fokker–Planck equation and is well‐suited to numerical solution by the boundary integral equation method (BIEM). The exponential conductivity function is often used in soil physics and is known to be a reasonable approximation over limited ranges of pressure head. A computer code based on the BIEM for obtaining numerical solutions is described and tested. The BIEM is found to exhibit quadratic convergence with element size reduction on smooth solutions and on singular problems, if mesh grading is used. Agreement between results from the BIEM code and a finite element code that solves the fully non‐linear problem is excellent, and is achieved at a substantial advantage in computer processing time. As an illustrative example, the code is applied to determine the distribution of moisture in the vicinity of a tunnel.

EVALUATION OF THE HYDRAULICS MODULE OF THE WQRRS MODEL FOR LOW FLOW SIMULATIONS

The in-stream water quality model, Water Quality for River-Reservoir Systems, (WQRRS) was applied to a 68 kilometre section of the Bow River, much of which through the City of Calgary. Steady and unsteady low flow conditions were examined using four of the six different hydraulic routing methods contained in the Stream Hydraulics Package (SHP). The steady flow methods considered were simple backwater and stage flow. The unsteady flow methods considered were a finite element solution of the complete form of the St. Venant equations and the kinematic wave method. A sensitivity analysis was performed which examined variations of water surface elevations with changes in the number of channel cross-sections used to define the study section, the element lengths used in the discretization scheme of the study section, and the time step. The ability of the finite element solution of the St. Venant equations and the kinematic wave technique to simulate rapid changes in flow rate was also evaluated. The result...

Constructing physics-based numerical schemes for viscous-inviscid interactions

It was the belief of the late Professor R. Thomas Davis that numerical methods should honor, and in fact be based on, the fundamental physics of the flows in question. This philosophy was perhaps best exemplified in his work during the 1970s and 1980s in the areas of interacting boundary-layer theory (IBLT) and parabolized Navier-Stokes (PNS) methodologies. In this paper we would like to review some of Professor Davis' fundamental contributions to these two fields within the context of his philosophical approach to computational fluid mechanics. We will also discuss how this work has impacted more recent developments in the field of IBLT and PNS methods for steady flows.

Explicit streamline method for steady flows of non-Newtonian matter.

A computational method, which explicitly employs a streamline coordinate as an independent variable, is proposed for analyzing steady flows of non-Newtonian matter.

Modeling the Transport of Inorganic Ions Through Undisturbed Soil Columns from Two Contrasting Watersheds

AbstractThe transport of several inorganic cations and anions (i.e., Mg2+ NH+4, Br−, NO−3), via saturated flow, through large undisturbed soil columns from two contrasting watersheds was investigated. The mobility of nonreactive tracers was described well with the convection‐dispersion (CD) equation using flux‐averaged solute detection in the effluent. Reactive tracers were also modeled well using various linear and nonlinear, equilibrium and nonequilibrium, transport codes based on the CD equation. Appropriate independent estimates of model predicted chemical retardation were possible only through experimental development of “dynamic isotherms” using a steady flow method on small undisturbed soil columns. The latter condition can accurately predict solute retardation on large soil columns, since tracer movement is largely controlled by the physical aspects of the soil (e.g., preferential flow zones). Adsorption isotherms generated on disturbed soils using a batch equilibration method, overestimated the amount of solute retardation from displacement experiments on the large undisturbed soil columns. The use of batch adsorption measurements in curve‐fitting transport models to describe data from saturated column displacement experiments on undisturbed soils, may result in erroneous transport parameter estimates.

Calculation of three-dimensional flowfields by the unsteady method of characteristics

A numerical algorithm based on the unsteady three-dimensional method of characteristi cs is presented for calculating unsteady three-dimensional subsonic/transonic inviscid flowfields. The flowfield unit processes are based on a local network consisting of six bicharacteristics and the pathline. The algorithm is an explicit secondorder accurate predictor-corrector procedure. An inverse-march ing method is employed, wherein the solution grid in physical space is prespecified. Steady flow solutions are obtained as the asymptotic solution in time. Results are presented for spherical supersonic source flow, for axisymmetric supersonic flow in a conical nozzle, for three-dimensional supersonic flow in a superelliptical nozzle, and for three-dimensional subsonic/transonic flow in a superelliptical nozzle. Solutions obtained by the present method agree well with solutions obtained by steady flow method of characteristi cs algorithms and experimental data.

Mixed finite element method for analysis of viscoelastic fluid flow

In the present paper, numerical analysis of incompressible viscoelastic fluid flow is discussed using mixed finite element Galerkin method. Because Maxwellian viscoelasticity is assumed as the constitutive equation, stress components could not be eliminated from the governing equation system. Because of this, mixed finite element method is utilized to discretize the basic equations. For the solution procedures to solve discretized equation system, Newton-Raphson method for steady flow and perturbation method for unsteady flow is employed. As the numerical examples, comparison was made on the finite element computational results between by direct method and by mixed method. Effects of the viscoelasticity is analyzed for the flows at Reynold's numbers 30, 50 and 70.