Showing papers on "Hele-Shaw flow published in 1982"

Numerical investigation of turbulent channel flow

Abstract: Fully developed turbulent channel flow was simulated numerically at Reynolds number 13800, based on centerline velocity and channel halt width. The large-scale flow field was obtained by directly integrating the filtered, three dimensional, time dependent, Navier-Stokes equations. The small-scale field motions were simulated through an eddy viscosity model. The calculations were carried out on the ILLIAC IV computer with up to 516,096 grid points. The computed flow field was used to study the statistical properties of the flow as well as its time dependent features. The agreement of the computed mean velocity profile, turbulence statistics, and detailed flow structures with experimental data is good. The resolvable portion of the statistical correlations appearing in the Reynolds stress equations are calculated. Particular attention is given to the examination of the flow structure in the vicinity of the wall.

Curved Ducts With Strong Secondary Motion: Velocity Measurements of Developing Laminar and Turbulent Flow

Abstract: Two orthogonal components of velocity and associated Reynolds stresses are determined in a square-sectioned, 90 degree bend of 2.3 radius ratio by utilizing laser-Doppler velocimetry for Reynolds numbers of 790 and 40,000. Results show that boundary layers at the bend inlet of 0.25 and 0.15 of the hydraulic diameter create secondary velocity maxima of 0.6 and 0.4 of the bulk flow velocity, respectively. It is concluded that the boundary layer thickness is important to the flow development, mainly in the first half of the bend, especially when it is reduced to 0.15 of the hydraulic diameter. Smaller secondary velocities are found for turbulent flow in an identical duct with a radius ratio of 7.0 than in the strongly curved bend, although their effect is more important to the streamwise flow development because of the smaller pressure gradients. In addition, the detail and accuracy of the measurements make them suitable for evaluation of numerical techniques and turbulence models.

Creeping flow in two-dimensional networks

Abstract: We discuss creeping incompressible fluid flow in two-dimensional networks consisting of regular lattice arrays of variable-sized channels and junctions. The intended application is to low-Reynolds-number flow in models of porous media. The flow problem is reduced to an analogue linear-network problem and is solved by numerical matrix inversion. It is found that ‘effective-medium theory’ provides an excellent approximation to flow in such networks. Various qualitative features of such flows are discussed, and an elegant general form for the absolute permeability is derived. The latter, and the effective-medium approximation, are equally applicable to three-dimensional networks.

Low-Reynolds-number flow between converging spheres

Abstract: Two spheres of different radii are approaching each other with equal and opposite velocities, the fluid flow around them being at low Reynolds number. The forces on the spheres can be calculated when they are very close by applying an asymptotic analysis — usually called lubrication theory — to the flow in the gap between the spheres. If the non-dimensional gap width is e, the force is calculated here correct to O(e In e) for all ratios of the two spheres' radii. The analysis can be combined with earlier numerical calculations to find all the constants in the asymptotic expansion correct to O(e).

An experiment on the flow past a finite circular cylinder at high subcritical and supercritical Reynolds numbers

Abstract: The complicated flow in the tip region of a finite circular cylinder in uniform cross flow has been examined at the Reynolds numbers 85,000, 180,000, and 770,000. Simultaneous measurements of the surface-pressure and wake-velocity fluctuations have revealed the existence of a shedding regime in the tip region that is distinct from the one prevailing on the main body of the cylinder. In particular, this regime can be unstable and intermittent, can have a cellular structure in the wake, or can be subcritical when the main flow is supercritical.

Mutations of steady cellular flows in the Taylor experiment

Abstract: Aspects of the various steady states of Taylor-vortex flow between concentric cylinders have been investigated by means of flow visualization. The experiments have focused principally on the evolution of the primary flow, that is, on the continuum of steady states parametrized by the Reynolds number R, beginning at small R where the primary flow is the only one possible. For any particular aspect ratio Γ, the primary flow develops a well-defined pattern of cells at higher R, but then other steady cellular flows (secondary modes) are also possible. The observations presented demonstrate mutations of the primary flow as Γ is varied through critical values: its R-dependent evolution is thereby switched from one to another array of cells realized at higher R. In each of four cases (4–6, 6–8, 8–10 and 10–12 cells), the mutation is shown to involve hysteresis of the primary-flow locus and complicated interactions with secondary modes.Following a description of the apparatus in §2, a discussion of the experimental method used to observe the often delicate hysteresis effects is given in §3. The experimental results in §4 are in broad agreement with abstract mathematical ideas that have been previously shown to bear on the Taylor experiments, but several new and surprising features, such as the coupling between pairs of cells, have been uncovered.

Taylor vortices between two concentric rotating spheres

Abstract: The laminar viscous flow in the gap between two concentric spheres is investigated for a rotating inner sphere. The solution is obtained by solving the Navier-Stokes equations by means of finite-difference techniques, where the equations are restricted to axially symmetric flows. The flow field is hydrodynamically unstable above a critical Reynolds number. This investigation indicates that the critical Reynolds number beyond which Taylor vortices appear is slightly higher in a spherical gap than for the flow between concentric cylinders. The formation of Taylor vortices could be observed only for small gap widths s ≤ 0·17. The final state of the flow field depends on the initial conditions and the acceleration of the inner sphere. Steady and unsteady flow modes are predicted for various Reynolds numbers and gap widths. The results are in agreement with experiment if certain accuracy conditions of the finite-difference methods are satisfied. It is seen that the equatorial symmetry is of great importance for the development of the Taylor vortices in the gap.

Supersonic jet noise generated by large scale instabilities

Abstract: The role of large scale wavelike structures as the major mechanism for supersonic jet noise emission is examined With the use of aerodynamic and acoustic data for low Reynolds number, supersonic jets at and below 70 thousand comparisons are made with flow fluctuation and acoustic measurements in high Reynolds number, supersonic jets These comparisons show that a similar physical mechanism governs the generation of sound emitted in he principal noise direction These experimental data are further compared with a linear instability theory whose prediction for the axial location of peak wave amplitude agrees satisfactorily with measured phased averaged flow fluctuation data in the low Reynolds number jets The agreement between theory and experiment in the high Reynolds number flow differs as to the axial location for peak flow fluctuations and predicts an apparent origin for sound emission far upstream of the measured acoustic data

Numerical Simulation of Separated Flows

Abstract: A new numerical method, based on the Vortex Method, for the simulation of two-dimensional separated flows, was developed and tested on a wide range of gases. The fluid is incompressible and the Reynolds number is high. A rigorous analytical basis for the representation of the Navier-Stokes equation in terms of the vorticity is used. An equation for the control of circulation around each body is included. An inviscid outer flow (computed by the Vortex Method) was coupled with a viscous boundary layer flow (computed by an Eulerian method). This version of the Vortex Method treats bodies of arbitrary shape, and accurately computes the pressure and shear stress at the solid boundary. These two quantities reflect the structure of the boundary layer. Several versions of the method are presented and applied to various problems, most of which have massive separation. Comparison of its results with other results, generally experimental, demonstrates the reliability and the general accuracy of the new method, with little dependence on empirical parameters. Many of the complex features of the flow past a circular cylinder, over a wide range of Reynolds numbers, are correctly reproduced.

Flow Oscillations of Spike-Tipped Bodies

Abstract: The oscillating flow field around a spike-tipped body has been simulated by the numerical solution of the 3-D compressible Navier-Stokes equations at a Mach number of 3.0 and a nominal Reynolds number of 7.87 x 10 to the 6th/m. Computations were performed using a vectorized 3-D Navier-Stokes program on the STAR 100 computer. Numerical solutions confirmed the experimental result that the self-sustained oscillation occurs within a limited range of the protruded spike length to shoulder height ratio. The numerical result predicted correctly the discrete frequency range as well as the rms pressure intensity. The detailed flow structure is also presented and discussed.

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.

The origin of polymer migration in a nonhomogeneous flow field

Abstract: Flow-induced polymer migration is treated in a rather intuitive though mathematically formal way. It is important to incorporate hydrodynamic interaction effects as well as flow geometry effects in studying polymer migration perpendicular to the flow direction. Simple examples, circular Couette flow in the free-draining limit and plane Poiseuille flow in the nondraining limit, are chosen to illustrate the importance of such effects.

Asymmetric Flow in Symmetric Expansions

Abstract: Asymmetric flow patterns may occur in perfectly symmetric abrupt expansions, in which the main flow deflects and attaches arbitrarily to one wall of the expansion. With the notable exception of “fluidic” devices, asymmetric flow patterns are detrimental in most civil engineering applications. The adverse effects include lengthening of the distance to full-width flow in expansions, inefficient operation of screens in screen channels, and increasing the potential for vortexing in pump intakes. No good explanation or prediction of the onset of asymmetric flow patterns is known to exist. This paper attributes the asymmetric behavior to a static instability of the system occurring under certain conditions of expansion geometry. The stability is investigated by analyzing the forces acting on the system when it undergoes a small deflection from its symmetric position. A mathematical stability criterion is developed and applied to subcritical, horizontal, rectangular expansions. The results are in excellent agreement with experimental observations (limited to small Froude Numbers). The predictive method is extended theoretically to the analysis of certain preventive and corrective measures. Means of extending the analyses to more complex two-dimensional and three-dimensional configurations are examined.

Closed-cavity laminar flows at moderate Reynolds numbers

Abstract: The paradox reported by Brady & Acrivos (1981) of the non-existence of similarity solutions in the Reynolds-number range 10·25 < R < 147 for the flow in a tube with an accelerated surface velocity is resolved. It is shown that the source of the difficulty lies in the assumption that the tube is infinite in extent. For a finite tube, it is demonstrated that the presence of the closed end, even though far removed from the origin, affects in a fundamental way the structure of the flow throughout the entire tube. The change in the flow structure that occurs in a finite tube at R = 10·25 is caused by the fluid which is returning from the downstream end; it is shown further that the problem of determining the motion in a long finite tube is equivalent to that of selecting the initial condition for the boundary-layer equations that properly takes into account the presence of the reverse flow. By applying a method originally developed by Klemp & Acrivos (1976) for selecting this condition, the flow in a finite tube is determined numerically for Reynolds numbers up to 70. In addition, it is shown that the same change in structure brought about by the returning fluid occurs in a finite two-dimensional channel at R = 57, even though the corresponding similarity solutions exist for all values of R. The results suggest that similarity solutions should be viewed with caution because they may not represent a real flow once a critical Reynolds number is exceeded.

A network flow analysis of extrusion dies and other flow systems

Abstract: A method is presented to calculate the slow viscous flow distribution in systems of passages, for which the major velocity components are substantially parallel to the axes of those passages. That condition is generally satisfied in flat extrusion dies, disc filters, in-line filters, and other now devices. A finite difference matrix method is initially used to determine the flow distribution for an assumed viscosity distribution. That flow distribution is next used to determine a new distribution of resistances, now based on a specified rheological equation. This process is iterated until there is no significant change in the flow distribution. The passages are subdivided in this method and replaced by a network of resistances. A few unknowns are introduced at one end of the network, which are solved at the other end, using a matrix marching routine. The method is described for newtonian flow through a flat die with equalizing channel, for which the analytic solution is known. Results are shown for that die for flow of power law liquids.

Stokes drag on a flat annular ring

Abstract: A surface distribution of point forces has been used to calculate the Stokes flow drag on a thin flat ring moving either parallel to or perpendicular to the axis of rotational symmetry. The results for motion parallel to the axis are confirmed by experiment. The drag is found to depend primarily upon the outside diameter of the ring and to be relatively insensitive to the inside diameter, in contrast to measurements at high Reynolds number. When the inside diameter is zero, the results agree with the known exact solutions for the circular disk.

A Suggested Mechanism for Nonlinear Wall Roughness Effects on High Reynolds Number Flow Stability

Abstract: The interactions between an uneven wall and free stream unsteadiness and their resultant nonlinear influence on flow stability are considered by means of a related model problem concerning the nonlinear stability of streaming flow past a moving wavy wall. The particular streaming flows studied are plane Poiseuille flow and attached boundary-layer flow, and the theory is presented for the high Reynolds number regime in each case. That regime can permit inter alia much more analytical and physical understanding to be obtained than the finite Reynolds number regime; this may be at the expense of some loss of real application, but not necessarily so, as the present study shows. The fundamental differences found between the forced nonlinear stability properties of the two cases are influenced to a large extent by the surprising contrasts existing even in the unforced situations. For the high Reynolds number effects of nonlinearity alone are destabilizing for plane Poiseuille flow, in contrast with both the initial suggestion of earlier numerical work (our prediction is shown to be consistent with these results nevertheless) and the corresponding high Reynolds number effects in boundary-layer stability. A small amplitude of unevenness at the wall can still have a significant impact on the bifurcation of disturbances to finite-amplitude periodic solutions, however, producing a destabilizing influence on plane Poiseuille flow but a stabilizing influence on boundary-layer flow.

Numerical simulation of wall-bounded turbulent shear flows

Abstract: Developments in three dimensional, time dependent numerical simulation of turbulent flows bounded by a wall are reviewed Both direct and large eddy simulation techniques are considered within the same computational framework The computational spatial grid requirements as dictated by the known structure of turbulent boundary layers are presented The numerical methods currently in use are reviewed and some of the features of these algorithms, including spatial differencing and accuracy, time advancement, and data management are discussed A selection of the results of the recent calculations of turbulent channel flow, including the effects of system rotation and transpiration on the flow are included