Outer Flow Field Research Articles

Turbulent velocity field in heterogeneously drag reduced pipe flow

Two-dimensional Laser Doppler Velocimetry and pressure drop measurements were carried out in a heterogeneously drag reduced turbulent pipe flow of 20 000 < Re < 30 000. A polymer solution of 0.75 wt.% PAMH was injected in the centerline of a 30 mm × 30 mm quadrangular duct. A detailed statistical analysis consisting of mean velocity, second and higher moments, discrete Fourier analysis, and correlation of the recorded velocity signals is presented. The results are consistent with the assumption that the heterogeneous drag reduction system is due to the entangled polymer molecules present in the flow and not due to a large scale interaction of the polymer thread with the outer flow field. Following the assumption that the achieved drag reduction is due to dissolved polymer, the differences in the onset of the effect and in the mean velocity profile is explained by an agglomerate model. That means that, the active drag reducing elements are entanglements of multiple polymer molecules capable of affecting the entire pipe diameter even at low drag reduction levels. It is also shown that the velocity signals for drag reduced flow are affected mainly in the buffer layer whereas the injected polymer thread practically never approaches the wall closer than γ + = 100.

Chemical effects of CF 3H in extinguishing counterflow CO/air/H 2 diffusion flames

The relative importance of introducing CF 3 H as a fire suppressant with the oxidizer or the fuel stream, and its chemical and thermal effects on the extinction condition of counterflow CO/air/H 2 diffusion flames, are investigated both experimentally and numerically. In experiments, the extinction strain rate is evaluated by measuring the jet exit velocities at extinction and the jet separation distance. In numerical calculations, the potential flow approximation is introduced to describe the outer flow field and the strain rate at extinction is determined from the axial velocity gradient on the oxidizer side. By employing mixture fraction concepts, the shift in flame location within the mixing layer caused by increasing the CF 3 H mole fraction or switching CF 3 H from air to fuel stream is shown to affect the measured and predicted extinction strain rates significantly. Flame structure and reaction pathway analyses have been used to identify the ratecontrolling reactions and the influence of introducing the supressing agent from the oxidizer or fuel side on the finite-rate chemistry. Subsequent sensitivity analysis has shown that two alternate CF 3 -consumption reaction pathways can either increase or decrease the extinction strain rate, similar to the sensitivities found in a recent premixed burning velocity study. Finally, based on the numerical calculations, the overall chemical and thermal effects of CF 3 H are demonstrated by freezing the CF 3 H chemistry and by replacing the heat capacity of CF 3 H with that of N 2 for the frozen case.

Matched Asymptotic Solutions of Impulsive Flow over an Elliptic Cylinder

The initial flow field of an impulsively started incompressible viscous flow over an elliptic cylinder is analyzed by the method of matched asymptotic expansions. Analytical solutions for the outer and inner flow fields are obtained to the third order. The Symbolic Manipulation Program is used to facilitate the work. Flow separation is studied in some detail, as are the surface quantities such as the vorticity, the pressure distribution, the drag, and the lift coefficients.

Shock wave/boundary layer interaction with heat addition by nonequilibrium phase transition

This investigation deals with the interaction of a turbulent boundary layer and a normal shock wave caused by supercritical heat addition in homogeneously condensing flows. The method used is a combination of analytical and numerical procedures, which is based on the perturbation method of Bohning & Zierep for the shock/boundary layer interaction in adiabatic flow. The homogeneous condensation process is described by the classical nucleation theory of Volmer together with the molecular droplet growth law of Hertz and Knudsen. The cooling rate, the nucleation rate, the surface-averaged droplet radius and the condensate mass fraction are analyzed along several streamlines in the boundary layer. The strength of the shock wave caused by supercritical heat addition in the outer flow field weakens and ultimately vanishes near the boundary edge by the influence of viscous effects. Comparison is made of the integral boundary layer variables and the friction coefficient in adiabatic flow with those in diabatic flow.

Boundary layer growth on two circular cylinders

This paper deals with the problem of boundary layer growth on two circular cylinders in a flow with large Reynolds and Strouhal numbers. Analytic solutions for the stream function of the inner and outer flow field are obtained to the second order by using the method of matched asymptotic expansions. The dependence of the movement of the detachment points and the drag coefficients of the two cylinders on (i) the distance between them, (ii) the ratio of their radii, (iii) the Reynolds number and (iv) the acceleration parameter of the flow is investigated. The results obtained indicate that the mutual hydrodynamic interaction between two cylinders leads to some new relations and findings.

Instability and particle agglomeration in acoustically driven flows

The mechanism responsible for instability and turbulence generated by high amplitude acoustic waves has been of interest of in acoustic agglomeration of particles. When a low-frequency oscillation is used in conjunction with a higher frequency acoustic wave, localized unstable boundary layer disturbances can be used to drive the outer flow field. By virtue of the Reynolds stress, the harmonic spectrum of the unstable vortical disturbance serves to modulate the acoustic wave amplitude. This process enhances the ability of the acoustic wave to agglomerate particles. A theoretical model of the instability mechanism and the interaction process will be presented. [Work supported by Analog Devices Professorship.]

Experiments with an adaptable-wall wind tunnel for large lift

Experiments have been carried out in a demonstration wind tunnel of the adaptable-wall type designed for the testing of high-lift configurations, such as powered-lift V/STOL aircraft. The simulated flight vector makes a large angle (30-40 deg) relative to the tunnel axis, so that the model's wake lies in a benign position. Simulation of flight at the desired speed and angle is accomplished by iteratively matching conditions at an interface within the tunnel to the calculated, updated outer flowfield. Measurements were made with a traversing laser-Doppler-anemometer system. The test model in these experiments was a V/STOL transport aircraft model with lower-surface blown wing flaps. Under test conditions, the powered wing-wake made a large angle with the flight direction, and wake positions were measured and are shown. Results show that the iterative procedure successfully reduced matching discrepancies at the interface. Typically, the best match was reached after about six or eight iterations, and this match represents precise simulation at the model to within 1% of stream speed.

Inverse design of multiholed internally cooled turbine blades

AbstractA methodology is described for the inverse design and/or analysis of coolant flow passage shapes in multiholed internally cooled turbine blades. The user of this technique may specify the temperature (or heat flux) distribution along the aerofoil outer surface. In addition, the temperature on the surface of each of interior coolant flow passages (holes) may be specified. The numerical solution of the outer hot gas flow field determines the remaining unspecified aerofoil outer surface quantity—surface heat flux if temperature was originally specified or vice versa. The position and shape of each turbine blade coolant hole is then found iteratively by solving the heat conduction problem within the solid portions of the blade. This solution procedure involves satisfying the dual Dirichlet and Neumann specified boundary conditions of temperature and heat flux on the outer boundary of the aerofoil. The inner hole geometry is then modified using an optimization procedure in such a way as to minimize the error in satisfying the specified Dirichlet temperature boundary condition on the surface of each of the evolving interior holes. Results are shown for single‐hole and double‐hole configurations that have analytic solutions and for a realistic turbine blade design problem.

Visualization of the viscous flow induced by a round jet

The flow induced by a laminar round glycerol jet emerging from a plane wall is investigated. The flow field (jet region as well as outer flow field) is visualized by means of very small bubbles suspended in the fluid. For slender jets the observed flow pattern disagrees with both potential-flow theory and Squire's ‘exact’ solution, but it is in excellent agreement with results of an asymptotic analysis by Schneider (1981). At a downstream distance that depends exponentially on the square of the Reynolds number, the jet develops into a toroidal eddy as predicted by Schneider (1985). In an apparatus of reasonable size the eddy can be observed only in a very limited Reynolds-number regime.

The Inverse Design of Internally Cooled Turbine Blades

A methodology is developed for the inverse design and/or analysis of interior coolant flow passage shapes in internally cooled configurations with particular applications to turbine cascade blade design. The user of this technique may specify the temperature (or heat flux) distribution along the blade outer fixed surface shape and the unknown interior coolant/blade interface. The numerical solution of the outer gas flow field determines the remaining unspecified blade outer surface quantity—surface heat flux if temperature was originally specified or vice versa. Along the unknown coolant flow passage shape the designer has the freedom to specify the desired temperature distribution. The hollow blade wall thickness distribution is then found from the solution of Laplace’s equation governing the temperature field within the solid portion of the hollow blade, while satisfying both boundary conditions of temperature and heat flux at the fixed outer blade surface, and the specified temperature boundary condition on the evolving inner surface. A first order panel method, coupled with Newton’s N-dimensional interation scheme, is used for the iterative solution of the unknown coolant/blade interface shape. Results are shown for a simple eccentrical bore pipe cross section and a realistic turbine blade cross section. The inverse design procedure is shown to be efficient and stable for all configurations that have been tested.

Analysis of two-dimensional viscous flow over cylinders in unsteady motion

The two-dimensional, viscous flow around elliptic cylinders undergoing prescribed rotary and translational motions is analyzed. The fluid is taken to be incompressible and initially at rest. Departing from conventional numerical formulations, the body is replaced by fluid which has a rigid motion exactly the same as the actual solid body. This is achieved by placing a uniform vorticity field within the body (equal to twice the instantaneous angular velocity), and bound vorticity on the body surface in the form of a vortex sheet. The latter distribution is governed by an integral equation. The solution is made unique by the principle of conservation of total vorticity. This depends on the instantaneous angular velocity of the body, the new ingredient to this analysis. The free vorticity in the outer flowfield is governed by the usual vorticity transport equation, which is solved numerically. The velocity field is determined by the velocity induction law. Transient flow results are presented for 1) an elliptic cylinder started impulsively from rest with constant angular velocity, and 2) a pitching elliptic cylinder moving with constant translational velocity. Results for case 1 are compared with those from a previous numerical analysis. Previous results for case 2 are not known. Predictions for the drag, lift, and moment coefficients are given over two complete cycles of oscillation.

On the converging flow of viscoelastic fluids through cones and wedges

A novel approximation method for obtaining solutions to the slow flow of viscoelastic fluids through converging cones and wedges is presented. The method involves considering two distinct regions in the flow field divided by a streamline: an inner irrotational sink flow occupying most of the flow field and an outer highly sheared self-lubricating layer adjacent to the walls. This procedure greatly simplifies the governing equations and allows analytic expressions to be obtained. Since the two regions are seperated by a streamline, different constitutive equations can be used for the inner and outer flow fields. This enables constitutive models to be used which model polymer melt rheology reasonably accurately and still retain analytic solutions. The method is applied to both wedges and cones; extensions to converging annuli are straightforward. Finally, an example flow field is considered in relation to a typical die-entry flow in polymer proccessing.

A compatibility assessment method for adaptive-wall wind tunnels

A new method is described for assessing the compatibility between inner and outer flow regimes in adaptive-wall wind tunnels. The method is applicable to both two- and three-dimensional flows, and unlike other schemes, requires the measurement of only one velocity component. Moreover, a complete solution to the outer flowfield is not required with the new method. Computer simulations of two- and three-dimensional flows are presented along with data from a two-dimensional pilot wind tunnel test using the new method.

The flow field of Newtonian fluids in cone and plate viscometers with small gap angles

The flow of a Newtonian fluid in cone-plate viscometers is determined by solving the Navier-Stokes equations. It is shown in an order-of-magnitude analysis that the governing equations can be simplified and that the flow field can be split into two parts, if the angle between cone and plate is small. A closedform solution for the inner flow field is established through an iteration procedure. The zeroth-order solution in which the convective terms are neglected is inserted into the governing equations which then can be integrated again. The outer flow field is also described analytically. The solution satisfies the boundary condition of the vanishing radial velocity component at the free surface. The flow is described throughout the whole gap. Velocity components, pressure distributions, torque and normal force due to inertia are calculated. Pressure distributions and the maximum radial velocity are measured. The free surface boundary condition is experimentally examined.

Upstream propagation of unsteady disturbances in supersonic boundary layers

It is shown that weak harmonic waves can propagate upstream in a supersonic stream along a plane wall over distances that are very large in comparison with the boundary-layer thickness. These waves are characterized by small reduced frequencies, large wavelengths and small phase velocities. Results are presented for the flow along a single plane wall and alsoforthe flow between two plane parallel plates (channel flow).The progressive-wave solutions are found by asymptotic expansions for small disturbances, large Reynolds numbers of the basic flow, and small reduced frequencies of the unsteady disturbances. It turns out that, as in the corresponding steady theory, four flow regions have to be distinguished: a middle layer which embraces most of the boundary layer; an inner layer near the wall; the outer flow field; and a transition layer between the middle layer and the outer layer. A quasi-steady treatment of the middle, transitional and outer layers is appropriate. Unsteady effects originate in the inner layer.The relative importance of viscosity and unsteady effects with regard to the waves is characterized by a dimensionless parameterNwhich is the product of certain powers of the reduced frequency and the Reynolds number. ForN→ ∞ and a single wall, Lighthill's steady theory of upstream influence in supersonic boundary layers is recovered as a limiting case of the present theory.

Slow flow of an elastic- viscous fluid past an immersed body

The slow flow of an elastico-viscous fluid past an immersed body is examined analytically. A method is outlined using successive integral transform techniques which provide solutions for both steady and unsteady cases. The Oseen equations for the outer flow field are solved and the solutions are matched asymptotically with the Stokes solutions near the body. A detailed calculation is presented for the two-dimensional flow past a circular cylinder and three-dimensional flow past a sphere. The departure of the drag coefficient and the stream function from the purely viscous value is discussed. The results for the sphere agree qualitatively with previous analyses and the new results for the flow past a cylinder predict a departure from the Newtonian drag as a quadratic function of the velocity.

Calculation of the laminar boundary layer on the flow-spreading line of the frontal surface of a segmental body in supersonic gas flow

The pressure increase behind the bow wave in this region and the reduction of the boundary layer thickness as a result of transwave spreading of the flow lead to an increase of the heat fluxes on the flow-spreadingline. Numerous experiments and some exact eaicuIations of the equations of the boundary layer, made for flows about pointed cones at an angle of attack, have shown that the thermal fluxes at this region exceed those at other points of the cone severalfold. In turn, the thermal fluxes depend significantly on the angle of attack a, the freestream Mach number Mo~, and the wall temperature T w. The flow in the boundary layer on the flow-spreading line for blunt bodies has received less study in view of the complexity of the analysis of the system of differential equations for the threedimensional boundary layer, which do not reduce to a system of ordinary differential equations, as is the case, for example, for a conical outer flowfield. In the following we present the equations of the laminar boundary layer on the flow-spreading line lying in the plane of symmetry of an immersed body. Restilts are presented of a numerical calculation of the boundary layer on the flow-spreading line on the frontal portion of a spherical segment.

The stress generated in a non-dilute suspension of elongated particles by pure straining motion

In a pure straining motion, elongated rigid particles in suspension are aligned parallel to the direction of the greatest principal rate of extension, provided the effect of Brownian motion is weak. If the suspension is dilute, in the sense that the particles are hydrodynamically independent, each particle of length 2l makes a contribution to the bulk deviatoric stress which is of roughly the same order of magnitude as that due to a rigid sphere of radius l. The fractional increase in the bulk stress due to the presence of the particles is thus equal to the concentration by volume multiplied by a factor of order l2/b2, where 2b is a measure of the linear dimensions of the particle cross-section. This suggests that the stress due to the particles might be relatively large, for volume fractions which are still small, with interesting implications for the behaviour of polymer solutions. However, dilute-suspension theory is not applicable in these circumstances, and so an investigation is made of the effect of interactions between particles. It is assumed that, when the average lateral spacing of particles (h) satisfies the conditions b [Lt ] h [Lt ] l, the disturbance velocity vector is parallel to the particles and varies only in the cross-sectional plane. The velocity near a particle is found to have the same functional form as for an isolated particle, and the modification to the outer flow field for one particle is determined by replacing the randomly placed neighbouring particles by an equivalent cylindrical boundary. The resulting expression for the contribution to the bulk stress due to the particles differs from that for a dilute suspension only in a minor way, viz. by the replacement of log 2l/b by log h/b, and the above suggestion is confirmed. The relative error in the expression for the stress is expected to be of order (log h/b)−1. Some recent observations by Weinberger of the stress in a suspension of glass-fibre particles for which 2l/h = 7·4 and h/2b = 7·8 do show a particle stress which is much larger than the ambient-fluid stress, although the theoretical formula is not accurate under these conditions.

The Theory of Viscous Hypersonic Flow

The flow of gas at hypersonic speed near a solid surface leads to the forma­ tion of a boundary layer whose thickness significantly exceeds (at the same Reynolds number) the thickness of the boundary layer formed at moderate supersonic speeds. The reason for this is the high temperature level and the consequent low density and high coefficient of viscosity in the hypersonic boundary layer. As a result, the effect of viscosity at high supersonic speeds is not confined to the interior of the boundary layer, and leads to substantial changes in the entire flow field. In the first place this is associated with the displacement effect of the boundary layer, which changes the effective shape of the body. Furthermore, thickening of the boundary layer can pro­ duce changes in the character of the flow in the boundary layer itself, as a result of the effect of the vorticity of the outer stream, the increased role of the transverse curvature of the surface, etc. All these effects are usually studied on the basis of the theory of inter­ action of the boundary layer with the outer stream, that is, on the basis of simultaneous consideration of the flow field in the boundary layer and the outer inviscid stream. In cases when the boundary-layer thickness is of an order of magnitude significantly smaller than the thickness of the body, the situation in the first approximation does not differ from the classical one, that is, the outer stream may, in the first approximation, be regarded as independent of the boundary layer. In this case of so-called weak interaction, the problem of studying the influence of the boundary layer upon the outer flow field and secondary effects in the boundary layer itself reduces to the investigation of higher approximations in boundary-layer theory. However if the body is so slender that the boundary layer has comparable or greater thickness, the effects of interaction may determine all functions of the flow field in their leading terms. The study of such cases constitutes the theory of moderate or strong interaction of the boundary layer with the outer stream. This last development has a central place in the present survey, because the theory of higher approximations for a boundary layer is treated in detail in the article by Van Dyke in the first volume of Annual Review of Fluid Mechanics ( 1969). We devote attention primarily to investigations carried out within the last decade, since the earlier period of development of the theory of viscous hypersonic flow is described in detail in the book of Hayes & Probstein (1959a).

An investigation of vorticity amplification in stagnation flow

Recently a theory which could explain satisfactorily the strong sensitivity of stagnation-point heat transfer and skin friction on cylinders in cross flow to relatively small turbulent fluctuations in the free-stream was put forth by Sutera et al. [11. This mathematical model proposed that vorticity amplification due to stretching of vortex filaments in the strongly diverging flow near the stagnation point is the underlying mechanism. The basic physical ideas and mathematical formulations relating to vorticity amplification by stretching and the resulting effects on flow, heat transfer and skin friction at a two-dimensional stagnation point were set forth in Reference 1 and in a subsequent paper by Sutera E2]. This theory was later extended to the outer flow field, i.e., outside and far from the boundary layer, by Sadeh et al. I31. Thus, a detailed review of the vorticity-amplification theory need not be repeated here. The primary purpose of the present investigation was the experimental verification of the vorticity-amplification theory presented in References 1, 2 and 3. The experimental work was designed mainly to obtain quantitative evidence of vorticity amplification by stretching and its effects on the average boundary-layer profile. A search for the prezlicted vortex structure near the wall was also carried out.