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Showing papers on "Incompressible flow published in 1981"


Journal ArticleDOI
TL;DR: In this article, a general theory of singular limits in compressible fluid flow and magneto-fluid dynamics is developed, which is broad enough to study a wide variety of interesting singular limits.
Abstract: Many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite. Using classical methods, the authors develop a general theory of such problems. This theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto-fluid dynamics including new constructive local existence theorems for the time-singular limit equations. In particular, the authors give an entirely self-contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the Mach number becomes small. The theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures. Similar results are developed also for the compressible and incompressible Navier-Stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero.

893 citations


Journal ArticleDOI
Michel Fortin1
TL;DR: The conclusion is that the elements introduced here should be quite competitive on a costiprecision scale.
Abstract: SUMMARY This paper presents some seemingly new elements for the computation of two and three-dimensional incompressible flow. We want to obtain elements satisfying the BabGska-Brezzi condition for mixed methods and thus introducing no spurious pressure modes (cf. Sani et al.'). In order to present clearly the advantages and disadvantages of our new elements we compare them on a qualitative basis with more standard ones. Of particular importance for incompressible flow is the size and shape of vortices that can be produced by the elements. We shall try to describe this as precisely as possible. The conclusion is that the elements introduced here should be quite competitive on a costiprecision scale.

238 citations



Journal ArticleDOI
TL;DR: In this paper, exact positive definite expressions for the potential energy density in a continuously stratified incompressible fluid were derived for large displacements or mixing processes in regions of rapidly varying buoyancy frequency.
Abstract: Exact, positive definite expressions both in power series and in closed form are derived for the potential energy density in a continuously stratified incompressible fluid. They are useful for determining the energy of large displacements or mixing processes in regions of rapidly varying buoyancy frequency, such as a sharp pycnocline.

139 citations


Journal ArticleDOI
TL;DR: In this paper, the use of quasi-Newton methods is studied for the solution of the nonlinear finite element equations that arise in the analysis of incompressible fluid flow, and an effective procedure for the application of Broyden's method in finite element analysis is presented.
Abstract: The use of quasi-Newton methods is studied for the solution of the nonlinear finite element equations that arise in the analysis of incompressible fluid flow. An effective procedure for the use of Broyden’s method in finite element analysis is presented. The quasi-Newton method is compared with the commonly employed successive substitution and Newton-Raphson procedures, and it is concluded that the use of Broyden‘s method can constitute an effective solution strategy.

79 citations


Proceedings ArticleDOI
01 Sep 1981
TL;DR: In this article, an unsteady potential flow analysis was developed to predict aerodynamic forces and moments associated with free vibration or flutter phenomena in the fan, compressor, or turbine stages of modern jet engines.
Abstract: An unsteady potential flow analysis, which accounts for the effects of blade geometry and steady turning, was developed to predict aerodynamic forces and moments associated with free vibration or flutter phenomena in the fan, compressor, or turbine stages of modern jet engines Based on the assumption of small amplitude blade motions, the unsteady flow is governed by linear equations with variable coefficients which depend on the underlying steady low These equations were approximated using difference expressions determined from an implicit least squares development and applicable on arbitrary grids The resulting linear system of algebraic equations is block tridiagonal, which permits an efficient, direct (ie, noniterative) solution The solution procedure was extended to treat blades with rounded or blunt edges at incidence relative to the inlet flow

75 citations


Journal ArticleDOI
S. P. Lloyd1
TL;DR: The Navier-Stokes equations for an incompressible viscous fluid admit time translation, time dependent change of the pressure origin, a scale change, rotation of axes, and time dependent spatial translation as discussed by the authors.
Abstract: The Navier-Stokes equations for an incompressible viscous fluid admit time translation, time dependent change of the pressure origin, a scale change, rotation of axes, and time dependent spatial translation. No other transformations appear if dependence on derivatives is allowed.

61 citations


Journal ArticleDOI
TL;DR: In this paper, a quantitative evaluation for the penalty function finite element method for two-dimensional viscous incompressible flow using primitive variables is made, using bilinear and biquadratic elements.

59 citations


Journal ArticleDOI
TL;DR: In this article, the Galerkin finite element method is utilized to obtain quite detailed results for flow through a channel containing a step at Reynolds numbers of 0 and 200, however, this technique is prone to generating wiggles or oscillations when streamwise gradients become too large to be resolved by the mesh.

55 citations


Journal ArticleDOI
TL;DR: The vortex-in-cell (VIC) method as discussed by the authors traces the motion of the vortex filaments in the velocity field which these filaments create, by creating a mesh-record of the vorticity field, then integrating a Poisson's equation via the fast Fourier transform.

48 citations


Journal ArticleDOI
TL;DR: In this article, the Hartmann number has been used to measure the acceleration of the particles in the laminar motion of an electrically conducting, viscous and incompressible dusty fluid between two infinitely extended nonconducting parallel plates.
Abstract: The unsteady laminar motion of an electrically conducting, viscous and incompressible dusty fluid between two infinitely extended non-conducting parallel plates under a uniform transverse magnetic field, fixed relative to the fluid has been considered. The lower and the upper plate are started impulsively from rest and thereafter move with different but uniform velocities. The velocity fields for the conducting dusty fluid and non-conducting dust particle have been obtained in terms of three non-dimensional parametersl (concentration), σ (relaxation time parameter) andM (Hartmann number). The expressions for the discharge per unit breadth of the plate and the skin-friction at the lower plate are calculated. It is observed, from numerical calculations, that as the Hartmann number increases velocities of the dusty gas and dust particle increase when both the plates are in motion (velocity of the upper plate being equal to, greater than and less than that of the lower plate in the same direction) and decrease in case of Couette motion.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the effects of inertia forces by constructing regular perturbation series for the stream function, of which the leading term is the known similarity solution, and obtained analytically the first-order inertial effect.
Abstract: When viscous fluid is contained in the corner between two planes intersecting at an 0 angle a, a flow may be ‘forced’ either by relative motion of the two planes keeping a constant (the ‘paint-scraper ’ problem- Taylor 1960) or by relative rotation of the planes about their line of intersection (the hinged-plate problem -Moffatt 1964). In either case, a similarity solution is available describing the flow sufficiently near the corner, where inertia forces are negligible. In this paper, we investigate the effects of inertia forces, by constructing regular perturbation series for the stream function, of which the leading term is the known similarity solution. The first-order inertial effect is obtained analytically, and, for the Taylor problem with a = Qn, 25 terms of the perturbation series for the wall stress are generated numerically. Analysis of the coefficients suggests that the radius of convergence of the series is given by r 1 U( /v z 9.1, where r is distance from the corner, U is the relative speed of the planes, and v is the kinematic viscosity of the fluid. For the hinged-plate problem, discussed in 5 5, the unsteadiness of the flow contributes to an inertial effect which is explicitly incorporated in the analysis. For both problems, streamline plots are presented which indicate the first influence of inertia forces at distances from the corner at which these become significant.

Journal ArticleDOI
TL;DR: In this article, the effects of a uniform transverse magnetic field on the free-convection flow of a viscous incompressible and electrically conductive fluid past an accelerated vertical infinite plate with variable suction or injection and heat flux are analyzed.

Journal ArticleDOI
TL;DR: In this paper, explicit basis functions are constructed for 9-node biquadratic velocity fields which guarantee that a weak form of the continuity equation is satisfied, and corresponding pressure approximations are either piecewise constant, piecewise linear or piecewise bilinear.
Abstract: Explicit basis functions are constructed for 9-node biquadratic velocity fields which guarantee that a weak form of the continuity equation is satisfied. The corresponding pressure approximations are either piecewise constant, piecewise linear or piecewise bilinear. These results are extended to give bases for bilinear velocity/piecewise constant pressure elements and also to some three-dimensional brick elements.

Journal ArticleDOI
TL;DR: In this article, a method is presented for computation of performance of two-dimensional (planar) diffusers with steady turbulent inflow of an incompressible fluid, using a one-dimensional flow model for the potential core.
Abstract: A method is presented for computation of performance of two-dimensional (planar) diffusers with steady turbulent inflow of an incompressible fluid. Previous methods can predict one regime of flow. The present method gives accurate predictions covering three flow regimes: unstalled flow, transitory stall, and fully developed stall. The method is a considerable extension of the procedure given by Ghose and Kline [5]; it also uses some ideas from the method for fully stalled flows given by Woolley and Kline [4]. The flow model is zonal and steady. It uses a one-dimensional flow model for the potential core. A momentum integral equation and an entrainment equation are employed for the boundary layer zone. Simultaneous solution is employed to model the different zones where the flow is separating or separated. Improved correlations of flow detachment and of the boundary layer flow state approaching detachment are presented as part of the work and employed in the computations. These will be reported more fully in a separate paper. This model is too simple for the full representation of the physics of transitory stall, which is not symmetric, steady, or one-dimensional in the core. Despite this, the main features of the mean flow, including wall pressure as a function of streamwise location, are accurately represented with very modest computation times, typically tenths of a second on an IBM 3033. The results again indicate that the key features in modeling separated flows are: • correct representation of blockage of shear layers and stalled zones, • adequate modeling of the interaction of potential and viscous zones.


Journal ArticleDOI
TL;DR: In this article, the authors considered two-dimensional unsteady free convection and mass transfer, flow of an incompressible viscous dissipative and electrically conducting fluid past an infinite, vertical porous plate, when the flow, is subjected in the action of uniform transverse magnetic field.
Abstract: Two-dimensional unsteady free convection and mass transfer, flow of an incompressible viscous dissipative and electrically conducting fluid, past an infinite, vertical porous plate, is considered, when the flow, is subjected in the action of uniform transverse magnetic field. The magnetic Reynolds number is taken to be small enough so that the induced magnetic field is negligible. The solution of the problem is obtained in the form of power series of Eckert numberE, which is very small for incompressible fluids. Analytical expressions for the velocity field and temperature field are given, as well as for the skin friction and the rate of heat transfer for the case of the mean steady flow and for the unsteady one. The influence of the magnetic parameter,M, modified Grashof numberG c , Schmidt numberS c and frequency ω, on the flow field, is discussed with the help of graphs, when the plate is being cooled, by the free convection currents (G r ,E>0), or heated (G r ,E<0). A comparative study with hydrodynamic case (M=0) and the hydromagnetic one (M≠0) is also made whenever necessary.

Journal ArticleDOI
TL;DR: In this paper, the authors developed a reduced form of the Navier-Stokes equations that is regular at the separation point, and the resulting formulation is a semi-elliptic model comprised of the parabolized momentum equations together with an elliptic equation for the pressure distribution.

Journal ArticleDOI
TL;DR: In this paper, an inviscid, rotational flow model for incompressible jet impingement is formulated in terms of vector and scalar potentials and the vector vorticity.
Abstract: An inviscid, rotational flow model for incompressible jet impingement is formulated in terms of vector and scalar potentials and the vector vorticity. The set of four elliptic partial-differential equations governing the kinematics of the flow and three coupled hyperbolic equations for the vorticity are solved numerically for the impingement of fully developed round jets upon a plane wall at incidence angles of 90 (normal), 75, and 60 deg. The finite-difference computations are consistent with both existing rotational stagnation point analysis and reported data on stagnation point location, wall pressure, and, to a lesser extent, azimuthal distribution of momentum efflux.

Journal ArticleDOI
TL;DR: In this paper, the aerodynamic forces of a flexible cylinder with pinned ends immersed in axial subsonic flow, either bounded or unconfined, are investigated and a number of distinct formulations of these forces, involving different approximations, are presented.
Abstract: This paper examines the dynamics of a flexible cylinder with pinned ends immersed in axial subsonic flow, either bounded or unconfined. The problem proves to be surprisingly resistant to exact solution, as compared to the incompressible flow case, because of difficulties in determining precisely the inviscid aerodynamic forces. This paper presents a number of distinct formulations of these forces, involving different approximations: (1) a slender-body approximation; (2) an approximate three-dimensional formulation where, in the determination of the aerodynamic forces, the axial shape is prescribed in advance; and (3) an exact integral formulation of the generalized aerodynamic forces. In each case, Galerkin-type solutions yield the system eigenfrequencies which describe the dynamical behavior of the system. It is found that for sufficiently high flow velocities, divergence and flutter are possible. The different methods yield similar, but not quantitatively identical results. Interestingly, dependence of the dynamical characteristics on Mach number is shown to be weak for slender cylinders; for nonslender ones, it is stronger. Finally, a brief discussion of wave propagation in an unconstrained cylinder indicates the existence of a cutoff flow velocity for backward propagating waves, followed by wave amplification at higher flow, which is closely related to loss of stability inmore » the constrained system.« less


Journal ArticleDOI
TL;DR: In this paper, the final stages of the cratering flow along the symmetry axis are described, using the incompressible flow formalism proposed by Maxwell, where the amplitude of the particle velocity field decreases with time as kinetic energy is converted into heat and gravitational potential energy.
Abstract: Upon impact of a meteorite with a planetary surface the resulting shock wave both ‘processes’ the material in the vicinity of the impact and sets a larger volume of material than was subjected to high pressure into motion. Most of the volume which is excavated by the impact leaves the crater after the shock wave has decayed. The kinetic energy which has been deposited in the planetary surface is converted into reversible and irreversible work, carried out against the planetary gravity field and against the strength of the impacted material, respectively. By using the results of compressible flow calculations prescribing the initial stages of the impact interaction (obtained with finite difference techniques) the final stages of cratering flow along the symmetry axis are described, using the incompressible flow formalism proposed by Maxwell. The fundamental assumption in this description is that the amplitude of the particle velocity field decreases with time as kinetic energy is converted into heat and gravitational potential energy. At a given time in a spherical coordinate system the radial velocity is proportional to R^(−z), where R is the radius (normalized by projectile velocity) and z is a constant shape factor for the duration of flow and a weak function of angle. The azimuthal velocity, as well as the streamlines, is prescribed by the incompressibility condition. The final crater depth (for fixed strength Y) is found to be proportional to R_0[2(z + 1)u_(or)²/g]^(1/(z+1)), where u_(or) is the initial radial particle velocity at (projectile normalized) radius R_0, g is planetary gravity, and z (which varied from 2 to 3) is the shape factor. The final crater depth (for fixed gravity) is also found to be proportional to [ρu_(or)^2/Yz]^(1/(z+1)), where ρ and Y are planetary density and yield strength, respectively. By using a Mohr-Coulomb yield criterion the effect of varying strength on transient crater depth and on crater formation time in the gravity field of the moon is investigated for 5-km/s impactors with radii in the 10- to 10^7-cm range. Comparison of crater formation time and maximum transient crater depth as a function of gravity yields dependencies proportional to g^(−0.58) and g^(−0.19), respectively, compared to g^(−0.618) and g^(−0.165) observed by Gault and Wedekind for hypervelocity impact craters in the 16- to 26-cm-diameter range in a quartz sand (with Mohr-Coulomb type behavior) carried out over an effective gravity range of 72–980 cm/s².

Journal ArticleDOI
TL;DR: In this article, an evolution equation for the motions of patches of vorticity (vortex) was derived, and steady state solutions of this equation that include those of Kirchhoff and Moore & Saffman are established.
Abstract: We derive an evolution equation for the motions of patches of vorticity (vortex). Steady state solutions of this equation that include those of Kirchhoff and Moore & Saffman are established. The m-fold symmetric, m≧3, hypotrochoid is an exact steady solution of this equation when rotation and strain are present. When strain is absent but rotation is present, the m-fold symmetric, m≧2, hypotrochoid is a perturbation solution with a dispersion relation extending that of Lamb. The case of m=2 is exact and is the Kirchhoff elliptical vortex.

Journal ArticleDOI
TL;DR: In this paper, the shape of a three-dimensional bubble in an axially symmetric shear flow of an inviscid incompressible fluid is calculated numerically, and it is found that there is a maximum Weber number above which there is no steady solution.
Abstract: The shape of a three‐dimensional bubble in an axially symmetric shear flow of an inviscid incompressible fluid is calculated numerically. The shape depends upon a single dimensionless constant related to the Weber number. It is found that there is a maximum Weber number above which there is no steady solution.

Journal ArticleDOI
TL;DR: In this paper, a new variational principle is derived through the construction of the action in terms of a new set of canonical coordinates, which contain exclusively information concerning the Eulerian description of the flow.
Abstract: A new variational principle is derived through the construction of the action in terms of a new set of canonical coordinates. The main advantage of this set of coordinates is that they contain exclusively information concerning the Eulerian description of the flow.

Journal ArticleDOI
TL;DR: In this article, the viscous incompressible rotating flow in a shrouded rotor geometry is solved by the finite element method, using the complete three-dimensional (axisymmetric) Navier-Stokes equations.
Abstract: The viscous incompressible rotating flow in a shrouded rotor geometry is solved by the finite element method, using the complete three-dimensional (axisymmetric) Navier-Stokes equations. Solutions to classical as well as to previously unsolved rotating flow problems are given and discussed.

Journal ArticleDOI
Osamu Inoue1
TL;DR: In this paper, the MRS criterion for flow separation over moving walls was investigated with respect to three types of flows, one of which is quite similar to that treated by Tsahalis.
Abstract: Steady, incompressible, laminar boundary-layer flows over moving walls are numerically investigated with special regard to the MRS criterion for flow separation. To analyze separated flows without meeting any singularity at the separation point, a set of approximate equations (instead of the boundary-layer equations) is solved under the condition of prescribed external velocity distributions. Three different types of flows are considered, one of which is quite similar to that treated by Tsahalis. It is found that, at least for the flows treated in the present paper, the MRS criterion is not satisfied for the case of upstream-moving walls, although it is satisfied for the case of downstream-moving walls.

Journal ArticleDOI
TL;DR: In this paper, the work in steady, viscous, incompressible flows is extended to general variably inclined, but nowhere aligned, flows with the objective of obtaining some exact solutions.
Abstract: By a variably inclined MHD plane flow we mean a flow in which the magnetic and velocity fields are coplanar, the angle between these vector fields is variable and all the flow variables are functions of two coordinates and time. No work seems to have been done for these general plane MHD flows, even in the steady case. In the present paper the work in steady, viscous, incompressible flows is extended to general variably inclined, but nowhere aligned, flows with the objective of obtaining some exact solutions. We employ the hodograph transformation, one of the strong analytical methods, to find these solutions.