Showing papers on "Incompressible flow published in 1974"
TL;DR: In this paper, a finite element program suitable for solving incompressible, viscous free surface problems in steady axisymmetric or plane flows is presented. But the authors do not consider the non-Newtonian flow, non-zero Reynolds numbers, and transient flow.
Abstract: : The authors discuss the creation of a finite element program suitable for solving incompressible, viscous free surface problems in steady axisymmetric or plane flows. For convenience in extending program capability to non-Newtonian flow, non-zero Reynolds numbers, and transient flow, a Galerkin formulation of the governing equations is chosen, rather than an extremum principle. The resulting program is used to solve the Newtonian die-swell problem for creeping jets free of surface tension constraints. The authors conclude that a Newtonian jet expands about 13%, in substantial agreement with experiments made with both small finite Reynolds numbers and small ratios of surface tension to viscous forces. The solutions to the related stick-slip problem and the tube inlet problem, both of which also contain stress singularities, are also given. (Modified author abstract)
277 citations
TL;DR: In this paper, the decay of two-dimensional, homogeneous, isotropic, incompressible turbulence is investigated both by means of numerical simulation (in spectral as well as in grid-point form), and theoretically by use of the direct-interaction approximation and the test-field model.
Abstract: The decay of two-dimensional, homogeneous, isotropic, incompressible turbulence is investigated both by means of numerical simulation (in spectral as well as in grid-point form), and theoretically by use of the direct-interaction approximation and the test-field model. The calculations cover the range of Reynolds numbers 50 ≤ RL ≤ 100. Comparison of spectral methods with finite-difference methods shows that one of the former with a given resolution is equivalent in accuracy to one of the latter with twice the resolution. The numerical simulations at the larger Reynolds numbers suggest that earlier reported simulations cannot be used in testing inertial-range theories. However, the large-scale features of the flow field appear to be remarkably independent of Reynolds number.The direct-interaction approximation is in satisfactory agreement with simulations in the energy-containing range, but grossly underestimates enstrophy transfer at high wavenumbers. The latter failing is traced to an inability to distinguish between convection and intrinsic distortion of small parcels of fluid. The test-field model on the other hand appears to be in excellent agreement with simulations at all wavenumbers, and for all Reynolds numbers investigated.
206 citations
TL;DR: From the analysis of a conjugate problem of convective heat transfer in a laminar incompressible flow around a flat plate of a finite thickness, the design formulas are suggested for a local Nusselt number Nux(Nux/Nux0)−1 = CBx, (0).
180 citations
TL;DR: In this paper, it was shown that bulk compression or dilatation (i.e., an extra strain rate div U) also appears to affect turbulent shear layers, typical values of Reynolds stress being increased by compression and decreased by dilatations.
Abstract: It is now well known that the turbulence structure of thin shear layers can be strongly affected by the application of extra rates of strain in addition to the shear velocity gradient. Examples of such extra strain rates include lateral divergence or convergence, and streamline curvature in the plane of the mean shear. The changes in Reynolds stress are an order of magnitude larger than would be expected from the explicit extra terms in the Reynolds-stress transport equations, and therefore an order of magnitude larger than predicted by conventional calculation methods. In the present paper, one of a series on ‘complex’ turbulent flows, we show that bulk compression or dilatation (i.e. an extra strain rate div U) also appears to affect turbulent shear layers, typical values of Reynolds stress being increased by compression and decreased by dilatation. The fractional change in Reynolds stress is an order of magnitude larger than the fractional change in volume of a fluid element. The physical mechanism is probably analogous to that responsible for the large effects of divergence or convergence in incompressible flow. Because the phenomenon seems to be of great practical importance we discuss it in the context of engineering calculation methods. An empirical correction formula, analogous to those used to allow for divergence or curvature effects, greatly reduces the large discrepancies found between recent experiments on supersonic boundary layers and calculations by conventional extensions of successful incompressible-flow methods.
154 citations
TL;DR: In this article, the generalization of the Faxen theorem for the force on a sphere in an incompressible fluid to the general nonstationary case derived in a previous paper is further extended to the case of a compressible fluid.
149 citations
TL;DR: In this article, an approximate solution to the problem of incompressible flow through an axisymmetric constriction is presented to simulate an arterial stenosis, and the solution is applicable to both mild and severe stenoses for Reynolds numbers below transition.
103 citations
TL;DR: In this paper, the stability and uniqueness of an incompressible, electrically conducting linear micropolar fluid with rigid microinclusions, in the presence of an arbitrary magnetic field, and in an arbitrary bounded time dependent domain are established.
95 citations
TL;DR: In this paper, the authors compared the elasticity of a particle moving slowly through a two-dimensional incompressible fluid with the viscous damping of a falling wire, showing that the elastic restoring force opposing particle displacements approaches zero with increasing crystal size, leading to a logarithmically diverging rms displacement in the large-system limit.
Abstract: The mathematical analogy between the elastic stress due to particle displacements in Hooke's law solids and the viscous stress due to velocity gradients in incompressible fluids correlates two interesting phenomena. In a two‐dimensional crystal the elastic restoring force opposing particle displacements approaches zero with increasing crystal size, leading to a logarithmically diverging rms displacement in the large‐system limit. The vanishing of the solid‐phase force is mathematically analogous to the lack of viscous damping for a particle moving slowly through a two‐dimensional incompressible fluid. These two continuum results are compared with discrete‐particle computer simulations of two‐dimensional solids and fluids. The divergence predicted by macroscopic elasticity theory agrees quantitatively with computer results for two‐dimensional harmonic crystals. These same results can also be correlated with White's experimental study of the viscous resistance to a cylinder (a falling wire) moving slowly th...
85 citations
TL;DR: In this article, an analysis of two-dimensional steady flow of an incompressible, viscous, electrically conducting fluid past an infinite vertical porous plate is carried out under the following assumptions: (i) the suction velocity normal to the plate is constant, (ii) the plate temperature is constant and (iii) the difference between the temperatures of the plate and the free stream is moderately large, causing free convection currents, and (iv) the transversely applied magnetic field and magnetic Reynolds number are very small and hence the induced magnetic field is negligible.
Abstract: An analysis of two-dimensional steady flow of an incompressible, viscous, electrically conducting fluid past an infinite vertical porous plate is carried out under the following assumptions: (i) that the suction velocity normal to the plate is constant, (ii) that the plate temperature is constant, (iii) that the difference between the temperatures of the plate and the free stream is moderately large, causing free convection currents, (iv) that the transversely applied magnetic field and magnetic Reynolds number are very small and hence the induced magnetic field is negligible.Approximate solutions to the coupled nonlinear equations governing the steady velocity and temperature are derived. They are shown graphically. During the course of discussion, the effects of positive and negative G (the Grashof number: G > 0 implies cooling of the plate, G < 0 heating of the plate), of P (the Prandtl number), of positive and negative E (the Eckert number) and of M (the magnetic field parameter) are presented quantitatively.
64 citations
TL;DR: In this paper, the authors derived an equation for the fluctuation correlation in an incompressible shear flow, utilizing the two-point distribution function which obeys the BBGKY hierarchy equation truncated with the hypothesis of "ternary" molecular chaos.
Abstract: Equations for the fluctuation correlation in an incompressible shear flow are derived on the basis of kinetic theory, utilizing the two‐point distribution function which obeys the BBGKY hierarchy equation truncated with the hypothesis of “ternary” molecular chaos. The step from the molecular to the hydrodynamic description is accomplished by a moment expansion which is a two‐point version of the thirteen‐moment method, and which leads to a series of correlation equations, viz., the two‐point counterparts of the continuity equation, the Navier‐Stokes equation, etc. For almost parallel shearing flows the two‐point equation is separable and reduces to two Orr‐Sommerfeld equations with different physical implications. Solution of an eigenvalue problem for the Blasius boundary layer is obtained in a certain parallelism to the classical stability theory, and is used for predicting the transition Reynolds number of a “quiescent” Blasius flow in which thermodynamic fluctuations alone are the initiating mechanism. Also, the calculated spatial growth rate of fluctuation agrees with the Schubauer‐Klebanoff experiment, which gives an account of unexplained experimental evidence that the fluctuation complex (turbulence bursts plus the Tollmien‐Schlichting wave), as a whole, obeys a certain linear theory.
57 citations
TL;DR: In this article, the Navier-Stokes equations for both the stationary and the freely rotating case were solved numerically for values of the Reynolds number R in the range from 0.047 to 70.
Abstract: The two-dimensional steady flow of an incompressible viscous fluid past a circular cylinder, placed symmetrically in a simple shear field, has been studied for both the stationary and the freely rotating case by solving numerically the Navier-Stokes equations for values of the Reynolds number R in the range from 0.047 to 70. At R = 0.047, the results obtained are in substantial agreement with the analytic small-R perturbation solution given by Robertson and Acrivos (1970). Inertia effects were found, however, to play a significant role even at R = 1, and hence the calculated flow pattern for R greater than or equal to 1 differs significantly from that of the creeping-flow solution. Specifically, for the freely rotating case, the region of closed streamlines decreases rapidly in extent with increasing R, two symmetrically placed wakes are formed on either side of the cylinder, and the dimensionless rotational speed of the freely suspended cylinder decreases as the reciprocal of the square root of R.
TL;DR: In this paper, it was proved that cylindrical shells and two-dimensional flat panels constrained to zero displacement at their leading and trailing edges, and exposed to subsonic flow, can lose their stability by divergence (buckling) while in supersonic flow two dimensional panels can only flutter.
TL;DR: In this article, a new and direct approach for calculating the first higher order potential flow along an axial corner is presented, where displacement effects in the corner may be visualized as the superposition of the displacement effects for the two intersecting semi-infinite plates forming the corner.
Abstract: A new and direct approach for calculating the first higher order potential flow along an axial corner is presented. For the incompressible potential flow, the present approach demonstrates that the displacement effects in the corner may be visualized as the superposition of the displacement effects for the two intersecting semi-infinite plates forming the corner. The compressible subsonic potential flow is then obtained by the Prandtl-Glauert rule. Linearized airfoil theory is used to determine the potential flow for the supersonic case. The asymptotic viscous flow, to lowest order, for the corner problem has been calculated for general compressible flow. The analysis presented here recovers all the previously obtained lowest order asymptotic solutions. Cross flow velocity profiles have been given for M f between 0.001 to 4 for an adiabatic wall as well as for a prescribed temperature at the wall. The behavior of the cross flow skin-friction coefficient is shown to be quite different from that of the skin friction coefficient due to classical axial flow.
TL;DR: In this paper, the complete Navier-Stokes equations have been used to analyze the symmetric laminar incompressible flow past a class of semi-infinite bodies including the family of parabolas and rectangular slabs as special cases.
Abstract: The complete Navier-Stokes equations have been used to analyze the symmetric laminar incompressible flow past a class of two-dimension al semi-infinite bodies including the family of parabolas and rectangular slabs as special cases. The problem is formulated in terms of coordinates obtained from the Cartesian coordinates by a conformal transformation. Similarity-type variables are used for the vorticity and stream functions. In these variables, the solution approaches the Blasius solution far downstream and the correct inviscid flow transversely far from the body surface. The formulation also produces the correct starting solution along the stagnation streamline. An alternating direction implicit finite-difference method is used to obtain the numerical solution. Results are presented for the skin-friction function and the surface pressure distributions for various values of the problem parameters. For the rectangular slab with a sharp shoulder, the wall shear is unbounded at the shoulder; however, the vorticity function employed remains bounded. For large Reynolds number, separation and reattachment are observed aft of the region of the shoulder, resulting in a separation bubble of finite, sometimes quite large extent. The flow structure in the separation region is carefully analyzed. Finally, it is shown that a certain boundary-layer-type simplified form of the vorticity equation may be used in separation studies if the displacement effects are correctly accounted for through the complete stream function equation.
TL;DR: In this paper, a new fluid dynamics computing technique is described for the solution of time-varying multifluid flows in several space dimensions, referred to as the GILA method.
TL;DR: In this article, the authors consider the possibility of modifying the Sonnerup solution for incompressible fluid flow about an X-type re-connexion line, to include fields and flows parallel to the X line.
Abstract: We consider the possibility of modifying the Sonnerup solution for incompressible fluid flow about an X-type re-connexion line, to include fields and flows parallel to the X line. We find that such fields and flows may change across the discontinuities of the Sonnerup solution. By considering the requirements imposed by a proper matching across the various regions of flow, and by the integral conservation properties of the diffusion region, we seek to find the restrictions that are imposed on this parallel field and flow, and on the arrangement of the discontinuity planes around the diffusion region. We find that four types of such arrangements are possible, each corresponding to a different set of restrictions on the parallel field and flow. In one case, where all the discontinuity planes intersect at a common line, the ‘ parallel’ parameters of the in-flow and out-flow regions may be arbitrarily and independently chosen. Of the remaining three cases, one contains solutions with uniform parallel fields ad flows, while the other two depend for their existence on large fluid flow or magnetic field shears across the two in-flow regions.
TL;DR: In this article, the steady, two-dimensional incompressible MHD flow past a circular cylinder with an applied magnetic field parallel to the main flow was calculated using the method of series truncation.
Abstract: The steady, two-dimensional incompressible MHD flow past a circular cylinder with an applied magnetic field parallel to the main flow is calculated using the method of series truncation. The differential equations are solved analytically and the Oseen approximation is made. The magnetic Reynolds number is assumed to be small. The results show that with an applied magnetic field the flow stays attached to the cylinder longer and in some cases does not separate until the rear stagnation point.
TL;DR: In this paper, the flow of a highly conducting incompressible fluid in the convection region surrounding an X-type neutral line is considered and the Sonnerup solution is generalized to include cases in which the in-flowing anti-parallel magnetic fields are of unequal magnitude, and in which plasmas of the two in-flow regions have unequal density.
Abstract: We consider the flow of a highly conducting incompressible fluid in the convection region surrounding an X-type neutral line. The Sonnerup solution is generalized to include cases in which the in-flowing anti-parallel magnetic fields are of unequal magnitude, and in which the plasmas of the two in-flow regions have unequal density. It is found that there exists no unique solution for a given set of in-flow plasma parameters, but that the out-flowing plasma may exit within a certain range of angles with respect to the in-flow direction, depending on in-flow parameters.
TL;DR: In this paper, the Navier-Stokes equations were solved iteratively for two-dimensional, incompressible flow in a rectangular cavity where the fluid motion of the stable vortices was driven by the action of a boundary layer moving above the crop canopy surface.
TL;DR: In this paper, the laminar radically outward flow of Newtonian incompressible fluid between parallel corotating disks has been used to calculate the performance of multiple-disk pumps using such flow passages as the rotor.
Abstract: Earlier analyses of the laminar radically outward flow of Newtonian incompressible fluid between parallel corotating disks have been used to calculate the performance of multiple-disk pumps using such flow passages as the rotor. Such pumps are characterized by certain dimensionless parameters and a large number of computerized calculations have enabled preparation of pump performance maps for pumps idealized as having no losses external to the rotor; these maps show the quantitative dependence of pump efficiency, pressure change and required power on the pump geometry, speed, and on fluid properties. Conventional loss information for the pump entrance and diffuser flows, and conventional bearing, seal, and “disk friction” loss information, must be applied in the design process to provide prediction of actual pump performance and comparison with conventional pumps. The design information is also applicable to low-pressure gas blowers.
TL;DR: In this paper, the nominal and actual length of the potential core of an axi-symmetric jet have been determined experimentally and estimated analytically, and the analysis based on similar solutions shows that the nominal potential core length is proportional to the Reynolds number in the laminar region, and it is independent of the Reynolds numbers in the turbulent region.
TL;DR: In this article, a method for calculating three-dimensional incompressible laminar and turbulent boundary layers is proposed with respect to its applicability to attachment line flow on an infinite swept wing.
Abstract: A proposed method for calculating three-dimensional incompressible laminar and turbulent boundary layers is investigated with respect to its applicability to incompressible attachment line flow on an infinite swept wing. The calculation results obtained exhibit satisfactory agreement with experimental data.
TL;DR: In this article, the authors used matched asymptotic expansions to simplify the procedure of calculating the lift and pressure distribution induced on an infinite-span thin wing interacting with an oblique sinusoidal gust in subsonic flow.
Abstract: The techniques of Galilean-Lorentz transformation and matched asymptotic expansions are used to simplify the procedure of calculating the lift and pressure distribution induced on an infinite-span thin wing interacting with an oblique sinusoidal gust in subsonic flow. This technique requires that the product of the flow Mach number and the reduced frequency be small. Under this condition, the inner region of the transformed space behaves as an incompressible flow, so that existing incompressible flow theories can be used as a basis to construct closed-form solutions for the airload induced on the wing. This approach is an extension of the GASP approximation developed by Amiet and Sears (1970). Results are obtained for both the magnitude and the phase of the unsteady lift due to interaction with gust. These results are compared with available numerical results. Some discrepancies are noted and discussed.
TL;DR: In this paper, the applicability of Bradshaw's interaction hypothesis to two-dimensional free shear flows was investigated and the empirical functions of the turbulence model were found correlated with the spreading rate of the shear layer.
Abstract: The applicability of Bradshaw's interaction hypothesis to two-dimensional free shear flows was investigated. According to it, flows with velocity extrema may be considered to consist of several interacting layers. The hypothesis leads to a new expression for the shear stress which removes the usual restriction that shear stress vanishes at the velocity extremum. The approach is based on kinetic energy and the length scale equations. The compressible flow equations are simplified by restriction to low Mach numbers, and the range of their applicability is discussed. The empirical functions of the turbulence model are found here to be correlated with the spreading rate of the shear layer. The analysis demonstrates that the interaction hypothesis is a workable concept.
Journal Article•
01 Jul 1974
TL;DR: A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates.
Abstract: A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates. A study has been made of the effect on the relative efficiency of several numerical methods applied to a particular fluid flow problem when they are implemented on a vector computer. The method of Brailovskaya, the alternating direction implicit method, a fully implicit method, and a new method called partial implicitization have been applied to the problem of determining the steady state solution of the two-dimensional flow of a viscous imcompressible fluid in a square cavity driven by a sliding wall. Results are obtained for three mesh sizes and a comparison is made of the methods for serial computation.