Showing papers on "Reynolds number published in 1981"
TL;DR: For the zero-pressure-gradient turbulent boundary layer over the Reynolds-number range 500 2000, say, the layer appears to consist very largely of elongated hairpin vortices or vortex pairs, originating in the wall region and extending through a large part of the boundary layer thickness or beyond it; they are for the most part inclined to the wall at a characteristic angle in the region of 40-50°.
Abstract: Flow visualization studies of the zero-pressure-gradient turbulent boundary layer over the Reynolds-number range 500 2000, say) the layer appears to consist very largely of elongated hairpin vortices or vortex pairs, originating in the wall region and extending through a large part of the boundary-layer thickness or beyond it; they are for the most part inclined to the wall at a characteristic angle in the region of 40–50°. Large-scale features, which exhibit a slow overturning motion, appear to consist mainly of random arrays of such hairpin vortices, although there is some evidence of more systematic structures.At low Reynolds numbers (Reθ < 800, say) the hairpin vortices are very much less elongated and are better described as horseshoe vortices or vortex loops; large-scale features now consist simply of isolated vortex loops (at the very lowest Reynolds numbers), or of several such loops interacting strongly, and show a relatively brisk rate of rotation.
947 citations
TL;DR: In this article, the shape and terminal velocities of bubbles rising in viscous liquids have been determined for Morton numbers (M) greater than 4 × 10−3 and R 110.
Abstract: The shapes and terminal velocities of bubbles rising in viscous liquids have been determined. For Morton numbers (M) greater than 4 × 10−3 the drag coefficient and dimensionless bubble shape are functions only of Reynolds number (R). Shape regimes and terminal rise velocities have been correlated. The flow field around a rising bubble was visualized through the hydrogen bubble tracer technique. For M > 4 × 10−3 and R 110 the wake was open and unsteady. Streamlines for the flow were obtained by raising a cine camera at the same speed as the bubble and filming the H2 tracer bubbles. Results are presented for R < 150 and 7·4 × 10−4 < M < 850.
726 citations
TL;DR: A large part of the branching vasculature of the mammalian circulatory and respiratory systems obeys Murray's law, and a functional relationship exists between vessel radius and volumetric flow, average linear velocity of flow, velocity profile, vessel-wall shear stress, Reynolds number, and pressure gradient in individual vessels.
Abstract: A large part of the branching vasculature of the mammalian circulatory and respiratory systems obeys Murray's law, which states that the cube of the radius of a parent vessel equals the sum of the cubes of the radii of the daughters. Where this law is obeyed, a functional relationship exists between vessel radius and volumetric flow, average linear velocity of flow, velocity profile, vessel-wall shear stress, Reynolds number, and pressure gradient in individual vessels. In homogeneous, full-flow sets of vessels, a relation is also established between vessel radius and the conductance, resistance, and cross-sectional area of a full-flow set.
605 citations
TL;DR: In this paper, a two-dimensional airfoil embedded in a uniform low Mach number flow is examined by applying several TE noise theories to the measured data, and the TE noise spectra and directivity are quantitatively determined for the case of a high Reynolds number and a fully turbulent boundary layer.
491 citations
01 Jan 1981
TL;DR: In this paper, a second-order accurate method for solving viscous flow equations has been proposed that preserves conservation form, requires no block or scalar tridiagonal inversions, is simple and straightforward to program (estimated 10% modification for the update of many existing programs), and should easily adapt to current and future computer architectures.
Abstract: Although much progress has already been made In solving problems in aerodynamic design, many new developments are still needed before the equations for unsteady compressible viscous flow can be solved routinely. This paper describes one such development. A new method for solving these equations has been devised that 1) is second-order accurate in space and time, 2) is unconditionally stable, 3) preserves conservation form, 4) requires no block or scalar tridiagonal inversions, 5) is simple and straightforward to program (estimated 10% modification for the update of many existing programs), 6) is more efficient than present methods, and 7) should easily adapt to current and future computer architectures. Computational results for laminar and turbulent flows at Reynolds numbers from 3 x 10(exp 5) to 3 x 10(exp 7) and at CFL numbers as high as 10(exp 3) are compared with theory and experiment.
427 citations
TL;DR: In this paper, a plane turbulent mixing between two streams of water which contained dilute chemical reactants was studied in a new blow-down water tunnel and a transition in the mixing was observed in which the aqueous mixing product increased by an order of magnitude.
Abstract: Plane turbulent mixing between two streams of water which contained dilute chemical reactants was studied in a new blow-down water tunnel. In a diffusion-limited reaction, a pH indicator, phenolphthalein, in one stream mixed and reacted with a base, sodium hydroxide, in the other stream to form a visible reaction product. The product was found to exist, as expected, in concentrated regions associated with the large, span-wise-coherent structures of the turbulence. A transition in the mixing was observed in which the aqueous mixing product increased by an order of magnitude. The transition is a consequence of the appearance and development of small-scale three-dimensional motions in the flow. Downstream of the transition, the amount of mixing product was independent of Reynolds number (for an order-of-magnitude increase in the latter) and at most only weakly dependent on Schmidt number.
384 citations
TL;DR: In this article, the influence of surface roughness on the vortex shedding frequency in the wake of a single cylinder has been investigated in an atmospherical and a high-pressure wind tunnel.
Abstract: The influence of surface roughness on the vortex-shedding frequency in the wake of a single cylinder has been investigated. The experiments were carried out in an atmospherical and a high-pressure wind tunnel. The tests were started with a smooth cylinder. Then the wake flow of cylinders with relative roughnesses of ks/d = 75 × 10−5, 300 × 10−5, 900 × 10−5, and 3000 × 10−5 was investigated.For all roughness parameters tested the Strouhal number exhibited an increase in the critical flow regime. With growing roughness parameter the step in the curve became smaller. At transcritical flow conditions the Strouhal number was measured to be in the range of Sr = 0·25 ± 0·018 for all surface roughness tested. No regular vortex shedding could be observed in the critical flow range for the smooth cylinder with l/d = 3·38. When prolonging the test body to l/d = 6·75 the wake fluctuations became periodic.
365 citations
TL;DR: In this paper, direct numerical simulations of three-dimensional magnetohydrodynamic turbulence with kinetic and magnetic Reynolds numbers up to 100 are presented, showing that small-scale helical driving produces strong large-scale nearly force-free magnetic fields.
Abstract: Direct numerical simulations of three-dimensional magnetohydrodynamic turbulence with kinetic and magnetic Reynolds numbers up to 100 are presented. Spatially intermittent magnetic fields are observed in a flow with nonhelical driving. Small-scale helical driving produces strong large-scale nearly force-free magnetic fields.
333 citations
TL;DR: The results of an experimental investigation of a turbulent boundary layer with zero-pressure gradient directed toward extending the data base at low Reynolds numbers are presented in this article, where the data obtained are concerned primarily with mean velocity distributions, skin-friction coefficients, and distributions of intensity of the longitudinal component of the turbulent velocity fluctuations for Reynolds numbers based on momentum thickness as low as 465.
Abstract: The results of an experimental investigation of a turbulent boundary layer with zero‐pressure gradient directed toward extending the data base at low Reynolds numbers are presented. The data obtained are concerned primarily with mean‐velocity distributions, skin‐friction coefficients, and distributions of intensity of the longitudinal‐component of the turbulent‐velocity fluctuations for Reynolds numbers based on momentum thickness as low as 465. The validity, at low Reynolds numbers, of the semi‐empirical laws characterizing the inner and outer regions of the boundary layer is examined.
318 citations
TL;DR: In this article, two-dimensional arrays of circular jets of air impinging on a heat transfer surface parallel to the jet orifice plate are considered, and the air is constrained to exit in a single direction along the channel formed by the surface and the jet plate.
Abstract: Two-dimensional arrays of circular jets of air impinging on a heat transfer surface parallel to the jet orifice plate are considered. The air, after impingement, is constrained to exit in a single direction along the channel formed by the surface and the jet plate. The downstream jets are subjected to a crossflow originating from the upstream jets. Experimental and theoretical results obtained for streamwise distributions of jet and crossflow velocities are presented and compared. Measured Nusselt numbers resolved to one streamwise hole spacing are correlated with individual spanwise row jet Reynolds numbers and crossflow-to-jet velocity ratios. Correlations are presented for both inline and staggered hole patterns including effects of geometric parameters: streamwise hole spacing, spanwise hole spacing, and channel height, normalized by hole diameter. The physical mechanisms influencing heat transfer coefficients as a function of flow distribution and geometric parameters are also discussed.
314 citations
01 Apr 1981
TL;DR: In this paper, the authors presented data for lift coefficients from near zero through maximum values at Mach numbers from 0.30 to 0.86 and Reynolds numbers of 3.0 x 10 to the sixth power with transition fixed.
Abstract: Data are presented for lift coefficients from near zero through maximum values at Mach numbers from 0.30 to 0.86 and Reynolds numbers of 3.0 x 10 to the sixth power with transition fixed. A limited amount of data is presented near zero and maximum lift for a Reynolds number of 6.0 x 10 to the sixth power with transition fixed. In addition, transition free data is presented through the Mach number range from 0.30 to 0.86 for near zero lift and a Reynolds number of 3.0 x 10 to the sixth power.
TL;DR: In this article, the stability of three dimensional rotating disk flow and the effects of Coriolis forces and streamline curvature were investigated and it was shown that this analysis gives better growth rates than Orr-Sommerfeld equation.
Abstract: The stability of three dimensional rotating disk flow and the effects of Coriolis forces and streamline curvature were investigated It was shown that this analysis gives better growth rates than Orr-Sommerfeld equation Results support the numerical prediction that the number of stationary vortices varies directly with the Reynolds number
TL;DR: In this article, hot-wire measurements of second-and third-order mean products of velocity fluctuations have been made in the flow behind a backward-facing step with a thin, laminar boundary layer at the top of the step.
Abstract: Hot-wire measurements of second- and third-order mean products of velocity fluctuations have been made in the flow behind a backward-facing step with a thin, laminar boundary layer at the top of the step. Measurements extend to a distance of about 12 step heights downstream of the step, and include parts of the recirculating-flow region: approximate limits of validity of hot-wire results are given. The Reynolds number based on step height is about 105, the mixing layer being fully turbulent (fully three-dimensional eddies) well before reattachment, and fairly close to self-preservation in contrast to the results of some previous workers. Rapid changes in turbulence quantities occur in the reattachment region: Reynolds shear stress and triple products decrease spectacularly, mainly because of the confinement of the large eddies by the solid surface. The terms in the turbulent energy and shear stress balances also change rapidly but are still far from the self-preserving boundary-layer state even at the end of the measurement region.
TL;DR: A non-orthogonal helical co-ordinate system is introduced and it is found that both curvature and torsion induce non-negligible effects when the Reynolds number is less than about 40.
Abstract: A non-orthogonal helical co-ordinate system is introduced to study the effect of curvature and torsion on the flow in a helical pipe. It is found that both curvature and torsion induce non-negligible effects when the Reynolds number is less than about 40. When the Reynolds number is of order unity, torsion induces a secondary flow consisting of one single recirculating cell while curvature causes an increased flow rate. These effects are quite different from the two recirculating cells and decreased flow rate at high Reynolds numbers.
TL;DR: In this paper, an exact solution to the Navier-Stokes equations for the flow in a channel or tube with an accelerating surface velocity is presented, where the equations of motion are reduced to a single ordinary differential equation for the similarity function which is solved numerically.
Abstract: An exact solution to the Navier–Stokes equations for the flow in a channel or tube with an accelerating surface velocity is presented. By means of a similarity transformation the equations of motion are reduced to a single ordinary differential equation for the similarity function which is solved numerically. For the two-dimensional flow in a channel, a single solution is found to exist when the Reynolds number R is less than 310. When R exceeds 310, two additional solutions appear and form a closed branch connecting two different asymptotic states at infinite R. The large R structure of the solutions consists of an inviscid fluid core plus an O(R−1) thin boundary layer adjacent to the moving wall. Matched-asymptotic-expansion techniques are used to construct asymptotic series that are consistent with each of the numerical solutions.For the axisymmetric non-swirling flow in a tube, however, the situation is quite different. For R [Lt ] 10[sdot ]25, two solutions exist which form a closed branch. Beyond 10[sdot ]25, no similarity solutions exist within the range 10[sdot ]25 0. These solutions, however, do not evolve from the R = 0 state nor do they bifurcate from the non-swirling solutions at any finite value of R.
TL;DR: In this paper, error estimates for splitting algorithms are developed which are uniform in the viscosity v as it becomes small for either two or three-dimensional fluid flow in all of space.
Abstract: Viscous splitting algorithms are the underlying design principle for many numerical algorithms which solve the Navier-Stokes equations at high Reynolds number. In this work, error estimates for splitting algorithms are developed which are uniform in the viscosity v as it becomes small for either twoor three-dimensional fluid flow in all of space. In particular, it is proved that standard viscous splitting converges uniformly at the rate C^lAt, Strang-type splitting converges at the rate CP(At)2, and also that solutions of the Navier-Stokes and Euler equations differ by Cp in this case. Here C depends only on the time interval and the smoothness of the initial data. The subtlety in the analysis occurs in proving these estimates for fixed large time intervals for solutions of the Navier-Stokes equations in two space dimensions. The authors derive a new long-time estimate for the two-dimensional NavierStokes equations to achieve this. The results in three space dimensions are valid for appropriate short time intervals; this is consistent with the existing mathematical theory.
TL;DR: The applicability of the Taylor hypothesis to large-scale coherent structures in turbulent shear flows has been evaluated by comparing the actual spatial distributions of the structure properties with those deduced through the use of the hypothesis.
Abstract: The applicability of the Taylor hypothesis to large-scale coherent structures in turbulent shear flows has been evaluated by comparing the actual spatial distributions of the structure properties with those deduced through the use of the hypothesis. This study has been carried out in the near field of a 7[sdot ]62 cm circular air jet at a jet Reynolds number of 3[sdot ]2 x 104, where the coherent structures and their interactions have been organized through controlled excitation. Actual distributions of the structure properties have been obtained through phase-average hot-wire data, the measurements having been repeated at different spatial points over the extents of the structure crosssections at a fixed phase. The corresponding ‘spatial’ distributions of these properties obtained (by using the Taylor hypothesis) from the temporal data at appropriate phases and locations, show that the hypothesis works quite well for an isolated coherent structure if a constant convection velocity, equal to the structure centre velocity, is used in the hypothesis everywhere across the shear flow. The popular use of the local time-average or even the instantaneous streamwise velocity produces unacceptably large distortions. When structure interactions like pairing are involved, no convection velocity can be found with which the hypothesis works. Distributions of the terms in the Navier–Stokes equation contributing to the phase-average vorticity, but neglected by the hypothesis, have been quantitatively determined. These show that the terms associated with the background turbulence field, but not those associated with the coherent motion field, can be neglected. In particular, the pressure term due to the coherent motion field is large and cannot be neglected.
TL;DR: In this article, the steady, incompressible, isothermal, developing flow in a square-section curved duct with smooth walls was investigated, and the mean velocity and Reynolds tensor were measured with a laser-Doppler anemometer at a Reynolds number of 4 × 104 and in various cross-stream planes.
Abstract: The steady, incompressible, isothermal, developing flow in a square-section curved duct with smooth walls has been investigated. The 40 × 40 mm duct had a radius ratio of 2·3 with long upstream and downstream straight ducts attached. Measurements of the longitudinal and radial components of mean velocity, and corresponding components of the Reynolds-stress tensor, were obtained with a laser-Doppler anemometer at a Reynolds number of 4 × 104 and in various cross-stream planes. The secondary mean velocities, driven mainly by the pressure field, attain values up to 28% of the bulk velocity and are largely responsible for the convection of Reynolds stresses in the cross-stream plane. Production of turbulent kinetic energy predominates close to the outer-radius wall and regions with negative contributions to the production exist. Thus, at a bend angle of 90° and near the inner-radius wall, is positive and represents a negative contribution to the generation of turbulent kinetic energy.In spite of the complex mean flow and Reynolds stress distributions, the cross-stream flow is controlled mainly by the centrifugal force, radial pressure gradient imbalance. As a consequence, calculated mean velocity results obtained from the solution of elliptic differential equations in finite difference form and incorporating a two-equation turbulence model are not strongly dependent on the model; numerical errors are of greater importance.
TL;DR: In this article, the evolution of a vortex ring in an ideal fluid under self-induction from a flat and elliptic configuration is followed numerically using the cut-off approximation (Crow 1970) for the velocity at the vortex.
Abstract: The evolution of a vortex ring in an ideal fluid under self-induction from a flat and elliptic configuration is followed numerically using the cut-off approximation (Crow 1970) for the velocity at the vortex. Calculations are presented for four different axes ratios of the initial ellipse. A particular choice is made for the core size and vorticity distribution in the core of the vortex ring. When the initial axes ratio is close to 1, the vortex ring oscillates periodically. The periodicity is lost as more eccentric cases are considered. For initial axes ratio 0·2, the calculations suggest a break-up of the ring through the core at one portion of the ring touching that at another, initially distant, portion of the ring.Results from quantitative experiments, conducted at moderate Reynolds number with the vortex rings produced by puffing air through elliptic orifices, are compared with the calculations. The agreement is fairly good and it is found that a vortex ring produced from an orifice of axes ratio 0·2 breaks up into two smaller rings. The relevance of the results to the vortex trail of an aircraft is discussed.
TL;DR: In this article, a theory of flow resistance for large-scale roughness is developed, the main points of which are supported by a flume study from which the outline of a process-based resistance equation is determined.
Abstract: A theory of flow resistance for large-scale roughness is developed, the main points of which are supported by a flume study from which the outline of a process-based resistance equation is determined. Rivers with large-scale roughness have steep slopes and depths of the same order of magnitude as the bed material size. Flow resistance depends on the form drag of the roughness elements and their disposition in the channel. Theoretical considerations show resistance to be a function of Reynolds number, Froude number, roughness geometry, and channel geometry. These processes are examined using the results of flume experiments based on five different roughness beds and a wide range of flows. Semi-empirical analysis supports the theory and allows the development of a theoretical power law resistance equation which accounts for most of the processes. A summary of the data is presented for use in other research studies.
TL;DR: In this paper, a simplified stage average pitchline approach is employed so that the procedure can be used during a preliminary design effort before detailed radial distributions of blading geometry and fluid parameters are established.
Abstract: A procedure for estimating the maximum pressure rise potential of axial flow compressor stages is presented. A simplified stage average pitchline approach is employed so that the procedure can be used during a preliminary design effort before detailed radial distributions of blading geometry and fluid parameters are established. Semi-empirical correlations of low speed experimental data are presented that relate the stalling static-pressure-rise coefficient of a compressor stage to cascade passage geometry, tip clearance, bladerow axial spacing and Reynolds number. Blading aspect ratio is accounted for through its effect on normalized clearances, Reynolds number and wall boundary layer blockage. An unexpectedly strong effect of airfoil stagger and of the resulting flow coefficient of the stage’s vector triangle is observed in the experimental data. This is shown to be caused by the differing ability of different types of stage vector triangles to re-energize incoming low-momentum fluid. Use of a suitable “effective” dynamic head in the pressure rise coefficient gives a good correlation of this effect. Stalling pressure rise data from a wide range of both low speed and high speed compressor stages are shown to be in good agreement with these correlations.
TL;DR: In this paper, effective thermal conductivities of neutrally buoyant solid-fluid mixtures were measured in a rotating Couette flow apparatus, where low Reynolds numbers were used to avoid the effects of turbulence.
Abstract: Eddy transport associated with microscopic flow fields in shearing two-phase flows was investigated. Although such microconvective effects are expected to be present in all disperse two-phase flows, usually they are masked by other collateral mechanisms and could not be studied critically. In the present study, effective thermal conductivities of neutrally buoyant solid-fluid mixtures were measured in a rotating Couette flow apparatus. Low Reynolds numbers were used to avoid the effects of turbulence. Significant enhancement in effective thermal conductivity was observed when the Pe/sub d/ = ed/sup 2//..cap alpha../sub f/ where e is the local mean shear rate, d is the particle diameter, and ..cap alpha../sub f/ is the thermal diffusivity of the fluid. Volume fractions employed were phi = 0.15 and 0.30 for polyethylene beads (2.9 mm in diameter) in a mixture of silicone oil and kerosene, and phi = 0.15 for polystyrene particles (0.3 mm in diameter) in a mixture of silicone oil and Freon-113. Single-phase liquid mixtures were also measured in various shear rates to show that the thermal conductivity was independent of shear rate and hence the observed phenomenon was not an instrumental artifact. The dependence of conductivity on particle Peclet number appeared to approach a powermore » law relationship k/sub e/proportionalPe/sub d//sup 1/2/ for high Peclet numbers (300« less
TL;DR: The coherent “starting structure” of poststenotic flow disturbances may have relevance in reducing the threshold of recognition of developing atherosclerotic plaques.
TL;DR: In this paper, the authors examined the dependence of the configuration of the vortices on various end constructions and found that the three-dimensional structure of the wake depends strongly on the flow configuration at each end of the cylinder.
Abstract: At low Reynolds numbers, three-dimensional features are frequently observed in the vortices shed behind a basically two-dimensional circular cylinder. This paper deals with the dependence of the configuration of the vortices on various end constructions. The cylinder is towed at a uniform speed in a water tank and simple flow visualization is used. It is found that the three-dimensional structure of the wake depends strongly on the flow configuration at each end of the cylinder. The boundary condition imposed on the nascent vortex lines determines the subsequent behaviour of the shed vortices. Consequently, the vortex street can be rendered more nearly two-dimensional by allowing the vortices to link outside the boundary as they approach that boundary normally. This is the case for the water–air interface when the water surface is clean. In the case of a contaminated water surface or of a solid surface acting as a boundary to the vortex street, the vortices link between themselves underneath the water surface and a strong interaction takes place behind the end of the cylinder. The subsequent effect is a bowing of the vortices towards the end of the cylinder. The free-end effect at the bottom end of the cylinder induces a strong bowing of the vortices towards that end and causes the wake to contract. It follows from the effect of surface contamination that the study of vortex wakes by the spreading of some surface contaminants might not necessarily show the true behaviour of the wake below the surface. It is postulated that slantwise shedding arises from a difference in the two end effects.
TL;DR: In this paper, the authors investigated the spontaneous oscillations observed when a high-viscosity fluid jet flows vertically against a flat surface, and the minimum distance from the jet orifice to the flat surface for which these oscillations are observed, termed the buckling height, was determined experimentally.
Abstract: Experimental results are presented concerning the spontaneous oscillations observed when a high-viscosity fluid jet flows vertically against a flat surface. The two jet shapes investigated were the axisymmetric jet and the plane jet. The minimum distance from the jet orifice to the flat surface for which these oscillations are observed, termed the ‘buckling height’, was determined experimentally. The frequency of the subsequent oscillations was also determined. Both were measured as functions of fluid and flow variables. It is found that surface tension effects are the dominant factors influencing the buckling height, while the rate of oscillation is affected by both surface tension effects and by viscous, gravity and inertia effects. The major results are presented in non-dimensional form. Photographs of the buckling phenomenon are provided for representative jet geometries. It is also established experimentally that there is an upper limit to the flow Reynolds number above which buckling does not occur.
TL;DR: In this paper, the transition between laminar and turbulent flow in a round jet flame is studied experimentally and a comparison is made between transition in non-burning and burning jets and between jet flames with systematic variation in initial Reynolds number and equivalence ratio.
Abstract: The transition between laminar and turbulent flow in a round jet flame is studied experimentally. Comparison is made between transition in nonburning and burning jets and between jet flames with systematic variation in initial Reynolds number and equivalence ratio. Measurements are made using laser anemometry, miniature thermocouples, ionization probes, laser Schlieren, and high-speed cine films. Compared with the cold jet, the jet flame has a longer potential core, undergoes a slower transition to turbulence, has lower values of fluctuating velocity near the burner with higher values further downstream, and contains higher velocity gradients in the mixing layer region although the total jet width does not alter greatly in the first twenty diameters. As in the cold jet, transitional flow in the flame contains waves and vortices and these convolute and stretch the initially laminar interface burning region. Unlike the cold jet, which has Kelvin-Helmholtz instabilities, the jet flame can contain at least two initial instabilities: an inner high-frequency, combustion-driven instability and an outer, low-frequency instability that may be influenced by buoyancy forces.
TL;DR: The linear stability of the spiral motion induced between concentric cylinders by an axial pressure gradient and independent cylinder rotation is studied numerically and experimentally for a wide gap geometry as mentioned in this paper.
Abstract: The linear stability of the spiral motion induced between concentric cylinders by an axial pressure gradient and independent cylinder rotation is studied numerically and experimentally for a wide-gap geometry. A three-dimensional disturbance is considered. Linear stability limits in the form of Taylor numbers TaL are computed for the rotation ratios μ, = 0, 0·2, and -0·5 and for values of the axial Reynolds number Re up to 100. Depending on the values of μ and Re, the disturbance which corresponds to TaL can have a toroidal vortex structure or a spiral form. Aluminium-flake flow visualization is used to determine conditions for the onset of a secondary motion and its structure at finite amplitude. The experimental results agree with the predicted values of TaL for μ [ges ] 0, and low Reynolds number. For other cases in which agreement is only fair, apparatus length is shown to be a contributing influence. The comparison between experimental and predicted wave forms shows good agreement in overall trends.
TL;DR: In this article, the authors surveyed available experimental data on the turbulent burning velocity of premixed gases and discussed the accuracy of experimental measurements and the means of ascertaining relevant turbulent parameters.
Abstract: Available experimental data on the turbulent burning velocity of premixed gases are surveyed. There is discussion of the accuracy of experimental measurements and the means of ascertaining relevant turbulent parameters. Results are presented in the form of the variation of the ratio of turbulent to laminar burning velocities with the ratio of r.m.s. turbulent velocity to laminar burning velocity, for different ranges of turbulent Reynolds number. A two-eddy theory of burning is developed and the theoretical predictions of this approach, as well as those of others, are compared with experimentally measured values.
TL;DR: In this article, the authors presented a complete procedure for successful matching of an unsteady low-Reynolds number flow past a sphere when a constant rectilinear velocity is suddenly imparted to the sphere, and the drag of the sphere is calculated up to the term of O(Re2 In Re) using the new procedure.
Abstract: This paper complements an earlier paper by Bentwich & Miloh in which the matched asymptotic expansion type of solution is presented for an unsteady low-Reynolds-number flow past a sphere when a constant rectilinear velocity is suddenly imparted to the sphere. It is shown that the matching procedure proposed in the earlier paper is incomplete. The present paper represents a complete procedure for successful matching; the drag of the sphere is calculated up to the term of O(Re2 In Re) using the new procedure.
TL;DR: In a slightly heated turbulent boundary layer, this paper showed that the extent of these regions, as a proportion of the boundary layer thickness, is approximately constant, independent of the momentum thickness Reynolds number when R m ⪞ 3100.