Showing papers on "Incompressible flow published in 1982"

Compressible and incompressible fluids

Abstract: Incompressible fluid: are the fluids with constant density. They could be liquids and gases. Although there is no such thing in reality as an incompressible fluid, we use this term where the change in density with pressure is so small as to be negligible. This is usually the case with liquids. We may also consider gases to be incompressible when the pressure variation is small compared with the absolute pressure. In problems involving water hammer we must consider the compressibility of the liquid. The flow of air in a ventilating system is a case where we may treat a gas as incompressible, for the pressure variation is so small that the change in density is of no importance. But for a gas or steam flowing at high velocity through a long pipeline, the drop in pressure may be so great that we cannot ignore the change in density. For an airplane flying at speeds below 250 mph (100 m/s), we may consider the air to be of constant density. But as an object moving through the air approaches the velocity of sound, which is of the order of 760 mph (1200 km/h) depending on temperature, the pressure and density of the air adjacent to the body become materially different from those of the air at some distance away, and we must then treat the air as a compressible fluid.

Consistent vs. reduced integration penalty methods for incompressible media using several old and new elements

Abstract: SUMMARY The frequently used reduced integration method for solving incompressible flow problems 'a la penalty' is critically examined vis-a-vis the consistent penalty method. For the limited number of quadrilateral and hexahedral elements studied, it is shown that the former method is only equivalent to the latter in certain special cases. In the general case, the consistent penalty method is shown to be more accurate. Finally, we demonstrate significant advantages of a new element, employing biquadratic (2-D) or triquadratic (3-D) velocity and linear pressure over that using the same velocity but employing bilinear (2-D) or trilinear (3-D) pressure approximation.

Sand Stresses Around a Wellbore

Abstract: The authors have studied theoretically the stresses in a poorly consolidated sand around a cylindrical well, assuming axial symmetry. Applying theories of elasticity and plasticity on this three-dimensional (3D) model, analytical solutions for all three stress components have been worked out. The existence of a plastic zone around an uncased wellbore is confirmed, and the size of the zone is determined. When allowing an incompressible fluid to flow radially into the wellbore, a stability criterion describing the failure of the sand is found to exist. This criterion relates fluid flow forces to rock strength properties. Consideration also has been given to the stress distribution around a cased hole. It is shown that a decrease in the size of the plastic zone relative to an uncased hole occurs.

Examples of Turbulence Models for Incompressible Flows

Abstract: The paper describes some currently available models for calculating turbulent stresses and heat or mass fluxes in incompressible flow which are more generally applicable than the Prandtl mixing-length hypothesis. These include models employing transport equations for the intensity and the length scale of the turbulent motion, notably the k-t model, as well as second-order closure schemes based on transport equations for the turbulent stresses and heat or mass fluxes themselves. The individual models are introduced briefly, their merits and demerits are discussed, and typical examples of calculations relevant to aerospace problems are presented.

Creeping flow about a spherical particle

Abstract: We formulate the solution of the linear Navier-Stokes equations for steady, incompressible flow about a spherical particle as an expansion of scattered waves. The amplitudes of the outgoing waves are simply related to a set of spherical force multipoles. These multipoles are found from the amplitudes of the incident waves with the aid of a resistance matrix, which is expressed in terms of the scattering coefficients of the particle.

The touching pair of equal and opposite uniform vortices

Abstract: The shape and speed of a pair of touching finite area vortices are calculated and an error in previous work corrected.

Finite-element solution of the incompressible navier-stokes equations

Abstract: A finite-element procedure is presented for the calculation of two-dimensional, viscous, incompressible flows of a recirculating nature. As in finite-difference procedures, velocity and pressure are uncoupled and the equations are solved one after the other. Velocity fields are determined by first calculating intermediate velocity values based on an estimated pressure distribution and then obtaining appropriate corrections to satisfy the continuity equation. Illustrative examples involving flow in the entrance region between parallel plates, lid-driven cavity flow, and flow around an obstacle demonstrate the accuracy and capabilities of the proposed technique.

A new numerical method for the simulation of three dimensional flow in a pipe

Abstract: A new numerical method has been developed to investigate three-dimensional, unsteady pipe flows using a new velocity-vector expansion method. Each vector function in the expansion set is divergence-free and satisfies the boundary conditions for viscous flow. Other features of the general technique are as follows: (1) pressure is eliminated from the dynamics; (2) only two unknowns per “mesh point” are required; (3) there is rapid convergence of spectral methods; (4) there is implicit treatment of the viscous term at no extra computational cost; and (5) no fractional time-steps are required. In the present application of the method to flow in a pipe, the behavior of each flow variable near the computational singular point is treated rigorously and expansions in Jacobi polynomials have been shown to be particularly advantageous. The method has been tested on the linear stability problem for Poiseuille flow and has demonstrated rapid convergence of the eigenvalues and eigenfunctions as the number of radial modes is increased.

Development of a Linear Unsteady Aerodynamic Analysis for Finite-Deflection Subsonic Cascades

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 (i.e., noniterative) solution. The solution procedure was extended to treat blades with rounded or blunt edges at incidence relative to the inlet flow.

Calculations of laminar viscous flow over a moving wavy surface

Abstract: The steady, laminar, incompressible flow over a periodic wavy surface with a prescribed surface-velocity distribution is found from the solution (via Newton's method) of the two-dimensional Navier–Stokes equations. Validation runs have shown excellent agreement with known analytical (Benjamin 1959) and analytico-numerical (Bordner 1978) solutions for small-amplitude wavy surfaces: For steeper waves, significant changes are observed in the computed surface-pressure distribution (and consequently in the nature of the momentum flux across the interface) when a surface orbital velocity distribution, of the type found in water waves, is included,

A numerical method for the dynamics of non-spherical cavitation bubbles

Abstract: A boundary integral numerical method for the dynamics of nonspherical cavitation bubbles in inviscid incompressible liquids is described. Only surface values of the velocity potential and its first derivatives are involved. The problem of solving the Laplace equation in the entire domain occupied by the liquid is thus avoided. The collapse of a bubble in the vicinity of a solid wall and the collapse of three bubbles with collinear centers are considered.

Fundamentals of Compressible Flow

Abstract: COURSE OUTLINE : “Gas Dynamics” is a topic of fundamental interest to Mechanical and Aerospace engineers that provides a link between core subjects i.e. “Fluid Mechanics and Thermodynamics”. It pertains the basic theory of compressible flow, formation of shock waves and expansion waves, nozzle flows. The treatment of the syllabus becomes the backbone of aerodynamic engineers towards research in the design of high-speed vehicles. The contents of the course starts with fluid and thermodynamic fundamentals followed by governing theories of compressible flow phenomena. Many aerodynamic high-speed facilities and their measurement diagnostics governed by these theories, are also covered in this course.

Spectral Computation of Triple-Deck Flows

Abstract: In recent times the most common means of solving (numerically) Prandtl’s boundary-layer equations has been finite-difference marching methods. Despite the nonlinearity of these equations, these techniques (incorporating Newton iteration) can provide rapid accurate solutions on modern computers. The marching method was applied successfully, for example, by Jobe and Burggraf [2.14] in their solution of the triple-deck problem of interaction between boundary layer and freestream near a trailing edge. Nevertheless, there are several types of flow for which these marching techniques either fail or become difficult to implement. Of these difficult types, perhaps separated flow is the most obvious. The physical cause of the difficulty is the region of reversed flow, in which the fluid travels in the direction opposite to that of the main body of fluid. As a result there is a change of character of the governing boundary-layer equations. Usually these are of parabolic type for which marching techniques are valid; however, the flow reversal due to separation changes the boundary-layer equations to quasielliptic type, with information being propagated both upstream and downstream. Any attempt to obtain an accurate solution by marching through such reversed-flow regions must fail due to the improper direction of information flow.

Oscillating stagnation point flow

Abstract: A solution of the Navier-Stokes equations is given for an incompressible stagnation point flow whose magnitude oscillates in time about a constant, non-zero, value (an unsteady Hiemenz flow). Analytic approximations to the solution in the low and high frequency limits are given and compared with the results of numerical integrations. The application of these results to one aspect of the boundary layer receptivity problem is also discussed.

Subsonic panel method for the efficient analysis of multiple geometry perturbations

Abstract: An accurate and efficient method was developed for the aerodynamic analysis of a series of arbitrary small geometry perturbations to a given baseline configuration. The method is appropriate for wing-fuselage configurations in incompressible potential flow. Mathematical formulations are presented for three computer programs that are employed. The first program is a conventional surface panel method for calculating the baseline singularity distribution. The second program calculates a partial derivative matrix. Each element of the matrix is the rate of change of singularity strength at one point with respect to a surface coordinate of a different point. For each baseline configuration, the calculated quantities from the first two programs establish an input file for the third. The third program calculates the surface pressure distribution and forces and moments for a series of geometry perturbations.

The effect of Hall currents on MHD flow and heat transfer between two parallel porous plates

Abstract: The effect of Hall currents on magneto hydrodynamic (MHD) flow of an incompressible viscous electrically conducting fluid between two non-conducting porous plates in the presence of a strong uniform magnetic field is studied. The flow is generated by a small uniform suction at the plates. Solutions are obtained for suction Reynolds number R≪1, considering two cases for the imposed magnetic field, viz. (i) when the magnetic field is perpendicular to the plates (parallel to y-axis), and (ii) when the magnetic field is parallel to the plates and perpendicular to the primary flow direction (parallel to z-axis). The effect of the Hall currents on the flow as well as on the heat transfer is studied. It is observed that in the absence of Hall currents, the change of the direction of the applied magnetic field does not affect the primary flow.

The nonunique rate of spread of the two‐dimensional mixing layer

Abstract: The rate of spread of a plane, incompressible, turbulent shearlayer was determined experimentally. The velocity ratio was constant, while the actual velocities were altered. It was established that the divergence of the flow with downstream distance was not uniquely determined by the velocity ratio in the range of variables considered. It is believed that an instability is responsible for this behavior.

Solutions of the compressible Navier-Stokes equations using the integral method

Abstract: The integral representation method was used to obtain numerical solutions of the compressible, unsteady, two-dimensional Navier-Stokes equations for subsonic flows. The equations were written with the vorticity, the dilatation, the density, and the enthalpy as the dependent variables. The method was tested by solving the following problems: the flow over a flat plate, around a circular cylinder, and around a Joukowski airfoil. The last two problems involved massive flow separation. The approach offers the capability of confining the domain of computations to the region where two quantities, the vorticity and the difference in dilatation between the real flow and the potential flow around the body, are non-negligible.

Theoretical Analysis of Parachute Inflation Including Fluid Kinetics

Abstract: An analysis is presented for predicting parachute inflation. Equations of motion for the complete system are developed from first principles, and are solved with no experimental inputs. Ballistic equations of motion are derived for the canopy, payload, and suspension line masses. However, the enclosed fluid mass is not lumped with the canopy as an apparent mass term. Instead, the fluid conservation equations for a deforming, accelerating control volume are solved to determine the behavior of the captured fluid and its interaction with the canopy. Only first-order effects are included, and the analysis is limited to inviscid, incompressible flow. Results for both porous and nonporous canopies are compared with experimental data.

An experimental study of a turbulent round two-phase jet

Abstract: The effect of solid particles on the flow structure of an axisymmetric turbulent incompressible jet has been studied. A two-color laser anemometer was used to measure the mean and fluctuating velocity components along the axial and radial directions as well as the corresponding component of the shear stress. 50 μ and 200 μ glass beads were used. Results for the 200 μ case are presented for moderate mass loadings (mass ratio = 0.8, volumetric ratio = 3.5 × 10-4)which indicates ignificant influence of the solid phase on the flow structure. Results for the 50 μ. case are reported elsewhere.1 When compared with the single-phase measurement, the spread rate of the two-phase jet was found to be smaller and a lower level of turbulence was observed.

Marginal stability of impulsively initiated Couette flow and spin‐decay

Abstract: A viscous, incompressible fluid is contained within an infinitely long circular cylinder or between a pair of infinitely long concentric cylinders. In both cases, the entire system is in a state of rigid‐body rotation. At time t = 0 the outer flow boundary is impulsively brought to rest, giving rise to a potentially unstable, unsteady swirl flow. The stability of these flows is examined by employing energy theory with a marginal stability criterion to obtain lower bounds on the onset times for instability. In some cases, the asymptotic steady‐state flow will be stable, with any instability merely a transient, while in other cases, stability of the asymptotic state is not guaranteed.

Effect of an infinite plane wall on the motion of a spherical Brownian particle

Abstract: The motion of a spherical Brownian particle in an incompressible fluid bounded by an infinite plane wall is studied on the basis of the linearized Landau–Lifshitz equations for the fluctuating hydrodynamics. The asymptotic forms for large time t of the autocorrelation function Φdj(t) for the random force acting on the particle and the autocorrelation function Ψij(t) for its velocity are discussed for the case that the distance l between the wall and the particle is finite but much larger than the particle radius a. It is shown that Φii and Ψii fall off as t−3/2 for a2/ν≪t≪l2/ν, but for t≫l2/ν they fall as t−5/2 or t−7/2, accordingly, as the direction i is parallel or perpendicular to the wall, where ν is the kinematic shear viscosity of the fluid.

Free convection and mass transfer effects on the oscillatory flow past an infinite moving vertical isothermal plate with constant suction and heat sources

Abstract: An analysis of the two-dimensional flow of an incompressible, viscous binary fluid past an infinite, porous, vertical plate is presented under the following conditions: (i) the suction velocity is constant; (ii) the free stream oscillates in time about a constant mean; (iii) the plate moves in the upward direction in its own plane; (iv) the temperature of the plate is constant; (v) there are heat generation (absorption) in the fluid.

An existence theorem for non-homogeneous incompressible fluids

Abstract: We prove an existence theorem for weak solutions of non-homogeneous, incompressible fluids moving in an arbitrary region Ω. In the case Ω unbounded, the theorem does not require the initial density distribution to be strictly positive in Ω.