Steady Separation Research Articles

A simplified formulation of the steady state in gaseous thermal diffusion columns

By introducing a flow pattern weighted average temperature as a reference temperature in a gaseous thermal diffusion column, a simplified formulation for the relevant steady quantities-the maximum separation factor and the optimum pressure-is obtained. This formulation describes within a few per cent all the cases which present in common separation practice and allows us to determine thermal diffusion factors from column steady measurements.

Steady and unsteady separation in an approximately two-dimensional indented channel

Experiments are performed on steady and impulsively started flow in an approximately two-dimensional closed channel, with one wall locally indented. In plan the indentation is a long trapezium which halves the channel width: the inclination of the sloping walls is approximately 5.7°, and these tapered sections merge smoothly into the narrowest section via rounded corners. The Reynolds number (ρ = fluid density), and decays to zero by the time τ ≈ 7.

Heat Transfer From Interrupted Plates

The forced convection heat transfer from two plates aligned with the flow direction in a wind tunnel was measured. The effects of leading edge bluntness, plate spacing distance, and Reynolds number on the leading and trailing plate average heat transfer rate were studied. The low Reynolds number, steady laminar and transitional flow regimes investigated are typical for compact heat exchangers. The measured heat transfer rate from the leading plate agrees well with laminar theory for thin plates when the leading edge is rounded. The heat transfer rate from the leading plate with a blunt nose ranges from slightly below theoretical at a Reynolds number which gives a long, steady separation bubble to well above theoretical under conditions of laminar separation and turbulent reattachment. The heat transfer rate from the second plate is influenced by the leading edge configuration of the first plate only at small plate spacing distances and high Reynolds number. At large spacings the mixing provided by the unsteady wake of the first plate dominates that due to the turbulence formed by leading edge separation on the first plate. The leading edge configuration of the second plate is important only at large values of plate spacing. The heat transfer rate from the second plate is generally higher than that predicted by theory for laminar, steady flow over thin plates and may be higher than that on the leading plate.

Thermo-osmosis of sorbable gases in porous media: Part I: theoretical basis of two methods of mixture separation

The theoretical basis of mixture separation by thermo-osmosis has been developed for two different experimental arrangements. In the first of these two vessels are connected only by a membrane across which a temperature gradient is maintained. Expressions were obtained for the separation factor of binary mixtures in terms of heats of transport, for pressure and composition changes across the membrane, and for determining the heat of transport of each component. In the second arrangement the vessels are connected via the membrane and also by a capillary of appropriate geometry, so that in the steady state there is a constant circulation of each component of the mixture. Expressions have again been derived for the steady state separation factor, and pressure and composition differences for binary mixtures.

Temperature Dependence of Isobaric T.D. Factor by Column

Temperature dependence of thermal diffusion factor, α T , of N 2 -CO (1:1) gas mixture can be assessed from the measurement of the equilibrium steady state separation factor, q e as a function or pressure at 350.1, 378.5 and 413.5 K by a concentric tube type hot wall thermal diffiusion column already calibrated by a gas mixture of known and reliable α T data. Too much attention to the column geometry is, thus, avoided through the use of the existing theoretical formulations for column in calculating α T .

Computer analysis on steady state separation characteristics of hydrogen isotope separation system by cryogenic distillation.

A computer code is developed for effective and exact simulation of cryogenic distillation columns. The simulation model incorporates the differences of latent heat of vaporization among the six molecular species, pressure drop, decay heat of tritium, heat transfer through the column wall, Raoult's law deviation of the solutions of hydrogen isotopes, multiple feeds and multiple sidestreams. The calculational procedure developed by Tomich for general equilibrium stage processes is further modified to match this complicated simulation model. A computer simulation study is performed for the typical cryogenic distillation column cascade and separation characteristics of each column are clarified. The effects of pressure drop are found not significant. If the tritium concentration in the column is considerably high, the lower performance caused by decay heat effects cannot be neglected any longer. Increase of the reflux ratio or refrigeration of the stripping section, is required for improvement. The present study provides a great help to development of exact simulation models and simulation procedures of cryogenic distillation columns.

Numerical solutions for high Reynolds number separated flow past a semi-infinite compression corner

The present paper addresses the high Reynolds number, two-dimensional, steady laminar flow separation phenomenon near an interior (concave) corner. A very fast Alternating Direction Implicit finite difference approach is used to solve the Interacting Boundary Layer approximation to the Navier Stokes equations in a conformal plane. Solutions are presented for corner angles up to 18° for Reynolds numbers (based on forebody length) up to 10 8. Convergence properties and accuracy levels are identified in order to provide reliability estimates of the results. Limitations to the numerical algorithm for large separation regions at high Reynolds numbers are identified.

Flow over a body with development of a steady separation zone as re ? ?

This paper discusses formulation of the “total” problem of flow of an incompressible liquid over a body, with formation of a closed stationary separation zone as Re → ∞. The scheme used is based on the method of matched asymptotic expansions [1]. Following [1], it is postulated that the separated zone is developed (i.e., it is not infinitely fragmented and does not vanish as Re → ∞), and the flow inside it has a definite degree of regularity with respect to Re. With these hypotheses we can use the Prandtl-Batchelor theorem [2], which states that, in the limit as Re → ∞, a region of circulating flow becomes vortex flow of an inviscid liquid with constant vorticity ω. Therefore, a basis for constructing matched asymptotic expansions is the vortex-potential problem (the problem of determining a stream function ψ, satisfying the equation Δψ = 0 in the region of translational motion and the equation Δψ = ω in a certain region, unknowna priori, of circulating motion). In the general case the solution of the vortex-potential problem depends on two parameters: the total pressure po and the vorticity ω in the separated zone. These parameters appear in the condition for matching the solutions of the first and second boundary-layer approximations (at the boundary of the separated zone for the end Re values) with the corresponding solutions for the inviscid flow. It is shown in the present paper that the conditions for matching the cyclic boundary layer with the external translational flow are the same additional relations which allow us to close the total problem. Thus, in using the method of matched asymptotic expansions to solve the problem of flow over a body with closed stationary separation zones one must simultaneously consider no less than two approximations.

Analytic description of steady separation from curved surfaces

Effects of wall curvature on steady separation phenomena are examined by exact analysis for Stokes flow between eccentric cylinders. Curvature alone, convex or concave, determines nothing in the stagnation regions for all features depend upon the total flow field, including the angle of departure of the separation streamline. However, the angular relationships among the curves streamfunction Ψ=0, vorticity ζ=0, and along-wall velocity component vβ=0 at the stagnation point are universal. They are valid for all Reynolds number, internal or external laminar flow.

The 1976 Freeman Scholar Lecture: Some Current Research in Unsteady Fluid Dynamics

Important unsteady fluid dynamic effects occur in a wide range of modern engineering problems. A review and critical appraisal has been made of the current research activities on topics that contain essential and unique unsteady features, especially those which cannot be approximated by quasi-steady analyses. A synopsis of the main areas covered in this paper is given below. Linear potential theory is well advanced and most of the fundamental concepts are well understood. The theory has been specially adapted for engineering purposes to many complex geometries and flow environments, but its limitations are not well established in most cases. Transonic flows have received considerable attention in recent years, and the profusion of numerical analyses of nonlinear unsteady flows has outstripped measurements. However, new experimental investigations are underway. Numerical codes are becoming much more efficient, and efforts are being made to incorporate viscous effects into them. Unsteady boundary layers have been computed with almost no complementary experimental guidance, and this deficiency is particularly acute in the turbulent case. A major conceptual difference between steady and unsteady separation has been identified and is continuing to be studied. Unsteady stall is currently under detailed examination, and recent experiments have shed considerable new insight on the fundamental mechanisms of dynamic stall on oscillating airfoils. New attempts to treat unsteady stall as a strong viscous-inviscid interaction problem are needed. Vortex shedding from bluff bodies is difficult to predict, especially in cases where body oscillations are self-induced by the fluctuating fluid dynamic forces. Nonlinear oscillator models are limited by a lack of understanding of the basic fluid dynamic phenomena. The trailing edge condition of Kutta and Joukowski for thin airfoils has been called into question recently for unsteady flows at high frequencies or with trailing-edge separation. The correct modeling of this condition is important in predicting the fluid dynamic forces on all thin lifting surfaces that fluctuate. Considerable progress has been made in each of these subjects, but none of them has been mastered. The questions that remain unanswered pose intriguing challenges to the fluid dynamics community.

Interaction of an Oscillating Control Surface with am Unsteady Separated Region

The results of experiments involving an airfoil with an oscillating fence-type spoiler are utilized in the development of a semiempirical flow model capable of describing the surface effects of a dynamically separating region. Founded on an extension of steady flow separation concepts, the model incorporates a prediction of growth lag and modifications to the pressure field of the separation bubble as its essential features. The model is employed in the equation of motion for a system involving a mechanically and aerodynamically coupled spoiler/control surface combination undergoing oscillations. Resultant system behavior was predicted adequately, as verified by subsequent experiments. Limit cycle motion, which may be thought of as a subsonic analog of control surface buzz, was observed to correlate with analytical estimates.

Steady flow separation along a straight streamwise corner

This note considers the steady incompressible flow of a laminar or turbulent boundary layer along a straight streamwise corner, formed by two flat plates intersecting each other at an arbitrary included angle. It is assumed that the undisturbed freestream is parallel or roughly parallel to the cornerline and that the intersecting corner-walls are impermeable. Attention is focussed on the necessary and sufficient conditions for steady flow separation from the sharp cornerline.

Isotopic and nonisotopic thermal diffusion factors from column measurements

Experimental steady state separation data obtained in a concentric tube type Clusius–Dickel column for seven He–Ar mixtures, five Ne–Xe mixtures, and the isotopic natural Ne mixture at ?=340±5 K are presented. The results show that thermogravitational columns are able to furnish correct values for the thermal diffusion factors of the mixtures examined when any one of them is used as a calibration mixture.

Non-Steady Separation of Multicomponent Isotopic Mixtures in Clusius-Dickel Columns

Analytical expressions for the non steady separation factor of an isotopic multicomponent mixture in a thermal diffusion column are given. The results, which are appropiate for column operation at total reflux and cover the real case in which small non active end volumes are present, show a simple exponential rising of the logarithm of the reduced separation factor independent of the initial mixture composition. This fact is confirmed by experimental transient data previously reported by Brun et al. and by new experimental work presented here. It is shown that the relative variations of the relaxation time with the hot wire temperature and with the operation pressure are just those predicted by the Furry, Jones and Onsager theory. It is concluded that two experimental operations: steady-separation vs pressure and non-steady separation vs time, and the use of FJO theory will allow us the qualitative prediction of the column operation in the usual temperature and pressure range in laboratory operation

Unsteady Separation Phenomena in a Two-Dimensional Cavity

Introduction I is generally recognized that the problem of separation is very important in practical aerodynamics and in many other fluid flowfields. Although a great deal of theoretical work has been done on steady separation, mostly through the use of the boundary-layer equations, the unsteady situation has received little attention in spite of its significance. Because the boundarylayer approximation is incomplete, recourse has been made to the full momentum equation. A two-dimensional oscillatory cavity flow presents a tractable model for approximate finite-difference solution of the equation to study the unsteady separation process. Although other workers have used steady cavity flow models, this is the first time an oscillatory cavity.flow solution has been published. The results are first compared to the steady case where there is only one fixed separation streamline along the line of symmetry. Then a dynamic pattern of separation and reattachment is illustrated.

Separated flow over a body of revolution

A method is developed to determine the flowfield of a body of revolution in separated flow. The technique employed is the use of the computer to integrate various solutions and solution properties of the sub-flowfields which make up the entire flowfield without resorting to a finite difference solution to the complete Navier-Stokes equations. The technique entails the use of the unsteady cross flow analogy and a new solution to the required two-dimensional unsteady separated flow problem based upon an unsteady discrete-vorticity wake. Data for the forces and moments on bodies of revolution at high angle of attack (outside the range of linear inviscid theories) such that the flow is substantially separated are produced which compare well with experimental data at low speeds. In addition, three-dimensional steady separation regions and wake vortex patterns are determined.

Separation in a thermoelectrogravitational electrophoresis column without reservoirs: Part I. Theoretical development of the transport equation and its application to the analysis of steady state batch operation

AbstractThe thermoelectrogravitational electrophoresis column without reservoirs has been conceived following the principle of the Clusius‐Dickel thermal diffusion column. The transport equation approach in thermal diffusion developed by Jones and Furry to explain the behavior of a conventional thermogravitational thermal diffusion column has been applied to describe the electrophoretic separation in the thermoelectrogravitational electrophoresis column. Equations have been established for a system in which one single or one hypothetically single component is mobile and the other species are at their isoelectric points.Theoretical calculations for the velocity profiles, temperature distribution, and the steady state batch separation factors have been made with field strength, temperature difference, membrane spacing, and electric mobility as variables, and expected trends of the results are discussed using the steady state solution of the transport equation for batch operation.

Sepration in a thermoelectrogravitational electrophoresis column without reservoirs: Part II. Steady state operation of continuous flow column: Theory and experiment

AbstractIn Part I of this paper, a thermoelectrogravitational electrophoresis column without reservoirs was proposed for preparative electrophoretic separations. The Furry, Jones, and Onsager procedure in thermal diffusion was applied to develop a transport equation, and its solution for the steady state batch case was employed to demonstrate some typical effects of temperature difference, electric field strength, and membrane spacing on the predicted steady state batch separation in the column.In this part, a theory is first developed from mathematical analysis of a continuous‐flow thermoelectrogravitational column without reservoirs by modification of the transport equation to take into account the bulk flow through the column.An experimental center‐fed thermoelectrogravitational electrophoresis column and the related equipment used to obtain experimental data to test the theory are described. Further, experimental separation factors as a function of flow rates ranging from 0 to 10 g/min for the bovine albumin system at two pH values (8.6 and 6.0) were obtained using two membrane spacings (0.1354 and 0.3018 cm respectively) at four different electric field strengths (0.0423 to 0.423 volt/cm) and for three different temperature differences of 0°C, 8.5°C, and 16°C. Experimental data indicated that meaningful separations could be obtained using thermoelectrogravitational columns but that the temperature difference has an adverse effect on electrophoretic separation.Analysis of the experimental flow data showed that theory and experiment are not in quantitative agreement. However, there was general, qualitative agreement between theory and experiment for the dependence of separation on field strength, temperature difference, membrane spacing and mobility of the component.

On turbulent boundary-layer separation

An experimental and analytical study of the separation of a turbulent boundary layer is reported. The turbulent boundary-layer separation model proposed by Sandborn & Kline (1961) is demonstrated to predict the experimental results. Two distinct turbulent separation regions, an intermittent and a steady separation, with correspondingly different velocity distributions are confirmed. The true zero wall shear stress turbulent separation point is determined by electronic means. The associated mean velocity profile is shown to belong to the same family of profiles as found for laminar separation. The velocity distribution at the point of reattachment of a turbulent boundary layer behind a step is also shown to belong to the laminar separation family.Prediction of the location of steady turbulent boundary-layer separation is made using the technique employed by Stratford (1959) for intermittent separation.

Magnetohydrodynamic species separation in a gaseous nuclear rocket

This analytical study deals with the possibility of steady flow separation of U 235 from hydrogen by magnetohydrodynamically spinning the fluid in a cylindrical vortex A gaseous nuclear rocket configuration is described and its model analyzed The hydromagnetic equations are solved for the velocity distribution, pressure field, concentration of uranium and hydrogen, electrical power required, and dissipation rates as a function of Hartmann number and radial Reynold's number Some properties of a hydrogen plasma at a temperature of 1 ev are presented and potential rocket performance given