Experimental investigation of the unsteady structure of a transitional plane wall jet

 A laminar wall jet undergoing transition is investigated using the particle image velocimetry (PIV) technique. The plane wall jet is issued from a rectangular channel, with the jet-exit velocity profile being parabolic. The Reynolds number, based on the exit mean velocity and the channel width, is 1450. To aid the understanding of the global flow features, laser-sheet/smoke flow visualizations are performed along streamwise, spanwise, and cross-stream directions. Surface pressure measurements are made to correlate the instantaneous vorticity distribution with the surface pressure fluctuations. The instantaneous velocity and vorticity field measurements provide the basis for understanding the formation of the inner-region vortex and the subsequent interactions between the outer-region (free-shear-layer region) and inner-region (boundary-layer region) vortical structures. Results show that under the influence of the free-shear-layer vortex, the local boundary layer becomes detached from the surface and inviscidly unstable, and a vortex is formed in the inner region. Once this vortex has formed, the free-shear-layer vortex and the inner-region vortex form a vortex couple and convect downstream. The mutual interactions between these inner- and outer-region vortical structures dominate the transition process. Farther downstream, the emergence of the three-dimensional structure in the free shear layer initiates complete breakdown of the flow. Received: 8 November 1995/Accepted: 6 November 1996     

Application of a Synthetic Jet to Control Boundary Layer Separation under Ultra-High-Lift Turbine Pressure Distribution

The transition and separation processes of the boundary layer developing on a flat plate under a prescribed adverse pressure gradient typical of Ultra-High-Lift low-pressure turbine profiles have been investigated, with and without the application of a synthetic jet (zero net mass flow rate jet). A mechanical piston has been adopted to produce an intermittent flow with zero net mass flow rate. The capability of the device to suppress or reduce the large laminar separation bubble occurring under steady inflow condition at low Reynolds numbers has been experimentally investigated by means of hot-wire measurements. Wall static pressure measurements complement the hot-wire time-resolved velocity results. The paper reports the investigations performed for both steady and controlled conditions. The active device is able to control the laminar separation bubble induced at low Reynolds number conditions by the strong adverse pressure gradient. An overall view of the time-dependent evolution of the controlled boundary layer is provided by the phase-locked ensemble averaging technique, triggered at the synthetic jet frequency. The separated flow transition process, which is detected for the uncontrolled condition, is modified by the synthetic jet in different ways during the blowing and suction phases. Overall, the phase-locked velocity distributions show a reduced separated flow region for the whole jet cycle as compared to the uncontrolled condition. The phase-locked distributions of the random unsteadiness allow the identification of vortical structures growing along the shear layer mainly during the blowing phase.     

Entropy generation in laminar jet: effect of velocity profiles at nozzle exit

Laminar free jet flow finds wide application in industry. Although considerable research studies were carried out in the past, but the irreversibility associated with the flow field due to heat transfer and viscous dissipation needs further investigation. In the present study, laminar free jet is considered and volumetric entropy generation in the flow field is computed. The normalized entropy ratio (entropy ratio generated in one-fourth of the jet length to total entropy generation), irreversibility, and the Merit number are determined for different velocity profiles leaving the nozzle. It is found that the uniform velocity profile results in less entropy generation due to viscous dissipation as compared to its counterpart corresponding to triangular velocity profile; however, the entropy generation due to heat transfer increases for the uniform profile.     

Unsteady flow with heat and mass transfer due to impingement of slot jet on an inclined plate

The unsteady laminar incompressible boundary layer flow due to a two-dimensional slot jet on a flat plate at an angle of attack has been studied. The unsteadiness in the flow field is due to the free stream velocity distribution or wall temperature (concentration) which varies with time. The governing partial differential equations in primitive variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The effect of the variation of the free stream velocity distribution with time is found to be more pronounced on the skin friction than on the heat or mass transfer. The Prandtl number and the variation of the wall temperature with time strongly affect the heat transfer. Similarly, the Schmidt number and the variation of the concentration at the wall with time strongly affect the mass transfer. Beyond a certain critical value of the viscous dissipation parameter, the plate gets heated instead of being cooled.     

Effects of velocity fluctuations on heat transfer enhancement

The three-dimensional velocity fluctuation effects on heat transfer enhancement were experimentally investigated using a wind tunnel system and cylinders placed upstream of the test section in the wind tunnel. The cylinders with different diameters were used as turbulators to generate vortical flow motions with three-dimensional velocity fluctuations. A heated plate, part of the tunnel wall, was placed far downstream of the cylinders such that it was subjected mainly to flows with velocity fluctuations but with negligible steady vortical motions. These studies included three-component velocity measurements to characterize the near-wall and cross-section velocity fields and to obtain the turbulent kinetic energy. The temperatures were measured by thermocouples on the heated plate to obtain the convection heat transfer coefficients and the Nusselt numbers. Results indicate that the heat transfer was enhanced by the velocity fluctuations, which is attributed to the modification of boundary layer velocity profiles without the modification of boundary layer thickness. The resulting normalized Nusselt number was approximately a parabolic function of a dimensionless parameter, the product of Reynolds number and normalized turbulent kinetic energy.     

An experimental study of a radial wall jet formed by the normal impingement of a round synthetic jet

The flow field of a radial wall jet created by the impingement of a round synthetic jet normal to a flat surface was characterized using hot-wire anemometry. In the synthetic wall jets the width of the outer layer was observed to increase linearly with the radial distance along the wall, while the local maximum velocity varied inversely. The synthetic wall jet exhibits self-similar behavior as distinguished by the collapse of the mean and rms velocity profiles when normalized by the outer layer scaling variables. Increasing the actuator driving amplitude at a fixed frequency (i) increased the growth rate of the outer layer, and (ii) decreased the decay rate of the local velocity maximum. The flow field of the synthetic wall jet was dominated by vortical structures associated with the actuator driving frequency, and harmonics connected with the interaction of the produced vortex structures. For the actuator conditions investigated, neither the classical laminar nor fully turbulent analytical solutions for continuous wall jets were amenable to modeling the synthetic wall jet profile due to the transitional and unsteady nature of the synthetic wall jet.     

Unsteady compressible boundary layer flow in the stagnation region of a sphere with a magnetic field

Summary An analysis is performed to study the unsteady compressible laminar boundary layer flow in the forward stagnation-point region of a sphere with a magnetic field applied normal to the surface. We have considered the case where there is an initial steady state that is perturbed by the step change in the total enthalpy at the wall. The nonlinear coupled parabolic partial differential equations governing the flow and heat transfer have been solved numerically using a finite-difference scheme. The numerical results are presented, which show the temporal development of the boundary layer. The magnetic field in the presence of variable electrical conductivity causes an overshoot in the velocity profile. Also, when the total enthalpy at the wall is suddenly increased, there is a change in the direction of transfer of heat in a small interval of time. Received 15 January 1996; accepted for publication 21 November 1996     

Self-sustained global oscillations in a jet in crossflow

A jet in crossflow with an inflow ratio of 3, based on the maximum velocity of the parabolic jet profile, is studied numerically. The jet is modeled as an inhomogeneous boundary condition at the crossflow wall. We find two fundamental frequencies, pertaining to self-sustained oscillations in the flow, using full nonlinear direct numerical simulation (DNS) as well as a modal decomposition into global linear eigenmodes and proper orthogonal decomposition (POD) modes; a high frequency which is characteristic for the shear-layer vortices and the upright vortices in the jet wake, and a low frequency which is dominant in the region downstream of the jet orifice. Both frequencies can be related to a region of reversed flow downstream of the jet orifice. This region is observed to oscillate predominantly in the wall-normal direction with the high frequency, and in the spanwise direction with the low frequency. Moreover, the steady-state solution of the governing Navier?CStokes equations clearly shows the horseshoe vortices and the corresponding wall vortices further downstream, and the emergence of a distinct counter-rotating vortex pair high in the free stream. It is thus found that neither the inclusion of the jet pipe nor unsteadiness is necessary to generate the characteristic counter-rotating vortex pair.     

LARGE-SCALE VORTICAL STRUCTURES PRODUCED BY AN IMPINGING DENSITY JET IN SHALLOW CROSSFLOW

The large-scale vortical structures produced by an impinging density jet in shallow crossflow were numerically investigated in detail using RNG turbulence model. The scales, formation mechanism and evolution feature of the upstream wall vortex in relation to stagnation point and the Scarf vortex in near field were analyzed. The computed characteristic scales of the upstream vortex show distinguished three-dimensionality and vary with the velocity ratio and the water depth. The Scarf vortex in the near field plays an important role in the lateral concentration distributions of the impinging jet in crossflow. When the velocity ratio is relatively small, there exists a distinct lateral high concentration aggregation zone at the lateral edge between the bottom layer wall jet and the ambient crossflow, which is dominated by the Scarf vortex in the near field.     

Effect of symmetry and asymmetry of turbulent structures on the interaction region of a plane jet

Mean and rms velocity and temperature measurements are made in the near field of a plane jet for two different sets of conditions at the beginning of the interaction region. In the first, the jet has a nearly top-hat velocity profile and laminar boundary layers at the nozzle exit. Schlieren photography and spectral coherence measurements show that the mixing layer structures are strongly organised and symmetric about the centreline. In the second, the jet issues from a two-dimensional duct with a nearly fully developed velocity profile so that, upstream of the interaction region, turbulent structures should be three-dimensional and asymmetric about the jet centreline. The resulting weak interaction obtained in this case contrasts with the strong interaction measured in the first case.     

Transition mechanisms in laminar separation bubbles with and without incoming wakes and synthetic jet effects

Laminar separation and transition processes of the boundary layer developing under a strong adverse pressure gradient, typical of Ultra-High-Lift turbine profiles, have been experimentally investigated for a low Reynolds number case. The boundary layer development has been surveyed for different conditions: with steady inflow, with incoming wakes and with the synchronized forcing effects due to both incoming wakes and synthetic jet (zero net mass flow rate jet). In this latter case, the jet Strouhal number has been set equal to half the wake-reduced frequency to synchronize the unsteady forcing effects on the boundary layer. Measurements have been taken by means of a single-sensor hot-wire anemometer. For the steady inflow case, particle image velocimetry has been employed to visualize the large-scale vortical structures shed as a consequence of the Kelvin?CHelmholtz instability mechanism. For the unsteady inflow cases, a phase-locked ensemble averaging technique, synchronized with the wake and the synthetic jet frequencies, has been adopted to reconstruct the boundary layer space-time evolution. Results have been represented as color plots, for several time instants of the forcing effect period, in order to provide an overall view of the time-dependent transition and separation processes in terms of ensemble-averaged velocity and unresolved unsteadiness distributions. The phase-locked distributions of the unresolved unsteadiness allowed the identification of the instability mechanisms driving transition as well as the Kelvin?CHelmholtz structures that grow within the separated shear layer during the incoming wake interval and the synthetic jet operating period. Incoming wakes and synthetic jet effects in reducing and/or suppressing flow separation are investigated in depth.     

Heat transfer over an unsteady stretching surface

Similarity solution of the laminar boundary layer equations corresponding to an unsteady stretching surface have been studied. The governing time-dependent boundary layer are transformed to ordinary differential equations containg Prandtl number and unsteadiness parameter. The effect of various govern-ing parameters such as Prandtl number and unsteadiness param-eter which determine the velocity and temperature profiles and heat transfer coefficient are studied.     

Magnetohydrodynamic flow on a half-plane

We investigate the magnetohydrodynamic flow (MHD) on the upper, half of a non-conducting plane for the case when the flow is driven by the current produced by an electrode placed in the middle of the plane. The applied magnetic field is perpendicular to the plane, the flow is laminar, uniform, steady and incompressible. An analytical solution has been developed for the velocity field and the induced magnetic field by reducing the problem to the solution of a Fredholm's integral equation of the second kind, which has been solved numerically. Infinite integrals occurring in the kernel of the integral equation and in the velocity and magnetic field were approximated for large Hartmann numbers by using Bessel functions. As the Hartmann number M increases, boundary layers are formed near the non-conducting boundaries and a parabolic boundary layer is developed in the interface region. Some graphs are given to show examples of this behaviour.     

Analysis of laminar flow forced convection heat transfer in the entrance region of a circular pipe

A numerical solution, for incompressible, steady-state, laminar flow heat transfer in the combined entrance region of a circular tube is presented for the case of constant wall heat flux and constant wall temperature. The development of velocity profile is obtained from Sparrow's entrance region solution. This velocity distribution is used in solving the energy equation numerically to obtain temperature profiles. Variation of the heat transfer coefficient for these two different boundary conditions for the early stages of boundary layer formation on the pipe wall is obtained. Local Nusselt numbers are calculated and the results are compared with those given byUlrichson andSchmitz. The effect of the thermal boundary conditions is studied by comparing the uniform wall heat flux results with uniform wall temperature.     

On the Stability of a Laminar Wall Jet with Heat Transfer

The hydrodynamic stability of a low speed, plane, non-isothermal laminar wall jet at a constant temperature boundary condition was investigated theoretically and experimentally. The mean velocity and temperature profiles used in the stability analysis were obtained by implementing the Illingworth–Stewartson transformation that allows one to extend the classical Glauert solution to a thermally non-uniform flow. The stability calculations showed that the two unstable eigenmodes coexisting at moderate Reynolds numbers are significantly affected by the heat transfer. Heating is destabilizing the flow while cooling is stabilizing it. However, the large-scale instabilities associated with the inflection point of the velocity profile still amplify in spite of the high level of the stabilizing temperature difference. The calculated stability characteristics of the wall jet with heat transfer were compared with experimental data. The comparison showed excellent agreement for small amplitudes of the imposed perturbations. The agreement is less good for the phase velocities of the sub-harmonic wave and this is attributed to experimental difficulties and to nonlinear effects.     

Role of Buoyancy on Instabilities and Structure of Transitional Gas Jet Diffusion Flames

Transitional jet diffusion flames provide the link between dynamics of laminar and turbulent flames. In this study, instabilities and their interaction with the flow structure are explored in a transitional jet diffusion flame, with focus on isolating buoyancy effects. Experiments are conducted in hydrogen flames with fuel jet Reynolds number of up to 2,200 and average jet velocity of up to 54 m/s. Since the fuel jet is laminar at the injector exit, the transition from laminar to turbulent flame occurs by the hydrodynamic instabilities in the shear layer of fuel jet. The instabilities and the flow structures are visualized and quantified by the rainbow schlieren deflectometry technique coupled with a high-speed imaging system. The schlieren images acquired at 2,000 frames per second allowed exposure time of 23 μs with spatial resolution of 0.4 mm. Results identify a hitherto unknown secondary instability in the flame surface, provide explanation for the observed intermittency in the breakpoint length, show coherent vortical structures downstream of the flame breakpoint, and illustrate gradual breakdown of coherent structures into small-scale random structures in the far field turbulent region.     

Second-order effects in unsteady laminar compressible three-dimensional stagnation-point boundary layers

The flow, heat and mass transfer at the stagnation point of a three-dimensional body in unsteady laminar compressible fluid with variable properties have been studied using a second-order boundary-layer theory when the basic potential flow admits selfsimilarity. Both nodal and saddle point regions have been considered. The equations governing the flow have been solved numerically using an implicit finite-difference scheme. It is observed that the enhancement or reduction in the skin friction and heat transfer due to the second-order boundary layers depends upon the values of the parameter characterizing the unsteadiness in the free-stream velocity, the nature of the stagnation point, the variation of the density-viscosity product across the boundary layer, mass transfer and the wall temperature. The suction increases the skin friction and heat transfer whereas injection does the opposite.     

Incompressible fluid flow past a circular cylinder with linear relation between the vorticity and the stream function

Incompressible fluid flow with a linear relationship between the vorticity and the stream function past a circular cylinder is studied.Vortical flows about profiles have been considered in several studies [1–15], but in all these studies with the exception of [15] a constant vorticity was assumed (in [15] an approximate solution is found of the problem of incompressible fluid flow about a Zhukovskii profile with parabolic distribution of the velocities in the approaching stream).A freestream velocity profile similar to that considered below occurs, for example, in a planar jet (laminar or turbulent), in the wake behind a bluff body, in the boundary layer along an infinite plane [4,13], in turbulent jet flows with reverse fluid currents [16]. A similar situation also arises in the flow past an array of cylinders with large spacing which is located in the wake of another array.The author wishes to thank V. E. Davidson for posing the problem and for guidance in its solution.     

Computational modeling of heat transfer over an unsteady stretching surface embedded in a porous medium

The present paper deals with the study of heat transfer characteristics in the laminar boundary layer flow of an incompressible viscous fluid over an unsteady stretching sheet which is placed in a porous medium in the presence of viscous dissipation and internal absorption or generation. Similarity transformations are used to convert the governing time dependent nonlinear boundary layer equations into a system of non-linear ordinary differential equations containing Prandtl number, Eckert number, heat source/sink parameter, porous parameter and unsteadiness parameter with appropriate boundary conditions. These equations are solved numerically by applying shooting method using Runge-Kutta-Fehlberg method. Comparison of numerical results is made with the earlier published results under limiting cases. The effects of the parameters which determine the velocity and temperature fields are discussed in detail.     

Unsteady compressible boundary layer flow over a circular cone near a plane of symmetry

An analysis has been performed to study the unsteady laminar compressible boundary layer governing the hypersonic flow over a circular cone at an angle of attack near a plane of symmetry with either inflow or outflow in the presence of suction. The flow is assumed to be steady at time t=0 and at t>0 it becomes unsteady due to the time-dependent free stream velocity which varies arbitrarily with time. The nonlinear coupled parabolic partial differential equations under boundary layer approximations have been solved by using an implicit finite-difference method. It is found that suction plays an important role in stabilising the fluid motion and in obtaining unique solution of the problem. The effect of the cross flow parameter is found to be more pronounced on the cross flow surface shear stress than on the streamwise surface shear stress and surface heat transfer. Beyond a certain value of the cross flow parameter overshoot in the cross flow velocity occurs and the magnitude of this overshoot increases with the cross flow parameter. The time variation of the streamwise surface shear stress is more significant than that of the cross flow surface shear stress and surface heat transfer. The suction and the total enthalpy at the wall exert strong influence on the streamwise and cross flow surface shear stresses and the surface heat transfer except that the effect of suction on the cross flow surface shear stress is small.