Streamwise Stations Research Articles

The effect of closed-loop feedback control on scalar mixing in a plane shear layer

The effect of feedback on mixing in a plane shear layer was studied using temperature as an analog to species concentration. Mixing was quantified using temperature measurements made by an array of cold-wire sensors. Upstream of the cold-wire sensors, a schlieren imager measured the cross-stream position of the temperature interface between the two streams before the primary vortical structures had formed. Surface heaters mounted on the flow partition were used as control actuators. Feeding the gained output from the interface position sensor back to the surface heaters closed the loop and created resonance and out-of-resonance conditions in the flow, both of which increased mixing. The feedback gains were adaptively modified in real time to maximize mixing at a given streamwise station. Finally, it was found that deliberately introducing streamwise vorticity, and then choosing feedback gains that strengthen these streamwise vortices, can greatly enhance mixing.

Large Eddy/Reynolds-Averaged Navier-Stokes Simulation of a Mach 5 Compression-Corner Interaction

Simulations of Mach 5 turbulent flow over a 28-deg compression corner are performed using a hybrid large-eddy/ Reynolds-averaged Navier-Stokes method. The model captures the mean-flow structure of the interaction reasonably well, with observed deficiencies relating to an underprediction of the displacement effects of the shock-induced separation region. The computational results provide some support for a recent theory concerning the underlying causes of low-frequency shock-wave oscillation. In the simulations, the sustained presence of a collection of streaks of fluid with lower/higher momentum than the average induces a low-frequency undulation of the separation front. Power spectra obtained at different streamwise stations are in good agreement with experimental results. Downstream of reattachment, the simulations capture a three-dimensional mean-flow structure, dominated by counter-rotating vortices that produce wide variations in the surface skin friction. Predictions of the structure of the reattaching boundary layer agree well with experimental pitot pressure measurements. In comparison with Reynolds-averaged model predictions, the hybrid large-eddy/Reynolds-averaged Navier-Stokes model predicts more amplification of the Reynolds stresses and a broadening of the Reynolds stress distribution within the boundary layer that is probably due to reattachment-shock motion.

Three-Component LDV Measurements in the Wake of a Compressor Cascade With Flow Separation

Measurements were taken of the vortex system and turbulent flow that resulted from the interaction between a stator blade and the approaching endwall boundary layer in a linear cascade of compressor blades. Data were taken at a Reynolds number based on blade chord of 640,000. Five-hole pressure measurements were conducted upstream and downstream of the blade row. The approaching boundary layer was also characterized with the laser-Doppler velocimeter. Downstream three-component laser-Doppler velocimetry surveys were conducted at three streamwise stations to map the location and velocity characteristics of the wake and vortex system. Results clearly showed the extent of the vortex emanating from the separation of the boundary layer on the suction side of the blade. Finally, all components of mean flow velocity and turbulence are documented for the last survey station. These data will form a challenging test case for numerical code validation.

Hydrodynamic stability of rockets with headwall injection

We investigate the hydrodynamic instability of the full-length, cylindrical models of solid and hybrid rockets with headwall injection. Our baseline is the rotational incompressible flowfield proposed in a recent study (Majdalani and Vyas, “Inviscid models of the classic hybrid rocket,” AIAA Paper 2004-3474). The local nonparallel approach is implemented in which the amplitude functions are assumed to be radially dependent at fixed streamwise locations. The usual singularity along the chamber axis is eliminated using Taylor series expansions. As a result, three compatibility relations are derived and substituted for the local boundary conditions along the axis. These depend on whether the tangential wave number q is 0, 1, or larger. Our rotational model is shown to exhibit a range of instability that broadens with successive increases in headwall injection. The lowest frequency below which the flow remains unconditionally stable is observed at ω=28.5 regardless of the headwall injection rate. As usual, the zeroth order tangential mode is found to be the most amplified. Using a representative headwall injection velocity for hybrid rockets, we identify a range of frequencies along which large excursions in pressure and velocity amplitudes are possible. These surges signal the presence of a resonant-like mechanism that is akin to an acoustic instability response. The most excited frequencies vary between 387 and 415 in the vicinity of the headwall. These frequencies are spatially delayed and lowered to 93.8–163.5 when the headwall injection rate is reduced to the level associated with solid rockets. For the most critical streamwise stations, these resurging wave amplitudes are quantified and shown to exhibit spectra that mimic the waterfall data acquired in acoustic instability tests.

Wave drag due to lift for transonic airplanes

Lift–dominated pointed aircraft configurations are considered in the transonic range. To make the approximations more transparent, two–dimensionally cambered untwisted lifting wings of zero thickness with aspect ratio of order one are treated. An inner expansion, which starts as Jones's theory, is matched to a nonlinear outer transonic theory as in Cheng and Barnwell's earlier work. To clarify issues, minimize ad hoc assumptions existing in earlier studies, as well as provide a systematic expansion scheme, a deductive rather than inductive approach is used with the aid of intermediate limits and matching not documented for this problem in previous literature. High–order intermediate–limit overlap–domain representations of inner and outer expansions are derived and used to determine unknown gauge functions, coordinate scaling and other elements of the expansions. The special role of switchback terms is also described. Non–uniformities of the inner approximation associated with leading–edge singularities similar to that in incompressible thin airfoil theory are qualitatively discussed in connection with separation bubbles in a full Navier–Stokes context and interaction of boundary–layer separation and transition. Non–uniformities at the trailing edge are also discussed as well as the important role of the Kutta condition. A new expression for the dominant approximation of the wave drag due to lift is derived. The main result is that although wave drag due to lift integral has the same form as that due to thickness, the source strength of the equivalent body depends on streamwise derivatives of the lift up to a streamwise station rather than the streamwise derivative of cross–sectional area. Some examples of numerical calculations and optimization studies for different configurations are given that provide new insight on how to carry the lift with planform shaping (as one option), so that wave drag can be minimized.

GLOBAL INSTABILITIES IN SPATIALLY DEVELOPING FLOWS: Non-Normality and Nonlinearity

▪ Abstract The objective of this review is to critically assess the different approaches developed in recent years to understand the dynamics of open flows such as mixing layers, jets, wakes, separation bubbles, boundary layers, and so on. These complex flows develop in extended domains in which fluid particles are continuously advected downstream. They behave either as noise amplifiers or as oscillators, both of which exhibit strong nonlinearities ( Huerre & Monkewitz 1990 ). The local approach is inherently weakly nonparallel and it assumes that the basic flow varies on a long length scale compared to the wavelength of the instability waves. The dynamics of the flow is then considered as a superposition of linear or nonlinear instability waves that, at leading order, behave at each streamwise station as if the flow were homogeneous in the streamwise direction. In the fully global context, the basic flow and the instabilities do not have to be characterized by widely separated length scales, and the dynamics is then viewed as the result of the interactions between Global modes living in the entire physical domain with the streamwise direction as an eigendirection. This second approach is more and more resorted to as a result of increased computational capability. The earlier review of Huerre & Monkewitz (1990) emphasized how local linear theory can account for the noise amplifier behavior as well as for the onset of a Global mode. The present survey first adopts the opposite point of view by demonstrating how fully global theory accounts for the noise amplifier behavior of open flows. From such a perspective, there is strong emphasis on the very peculiar nonorthogonality of linear Global modes, which in turn allows a novel interpretation of recent numerical simulations and experimental observations. The nonorthogonality of linear Global modes also imposes severe constraints on the extension of linear global theory to the fully nonlinear régime. When the flow is weakly nonparallel, this limitation is so severe that the linear Global mode theory is of little help. It is then much more appropriate to develop a fully nonlinear formulation involving the presence of a front separating the base state region from the bifurcated state region.

On the convectively unstable nature of optimal streaks in boundary layers

The objective of the study is to determine the absolute/convective nature of the secondary instability experienced by finite-amplitude streaks in the flat-plate boundary layer. A family of parallel streaky base flows is defined by extracting velocity profiles from direct numerical simulations of nonlinearly saturated optimal streaks. The computed impulse response of the streaky base flows is then determined as a function of streak amplitude and streamwise station. Both the temporal and spatio-temporal instability properties are directly retrieved from the impulse response wave packet, without solving the dispersion relation or applying the pinching point criterion in the complex wavenumber plane. The instability of optimal streaks is found to be unambiguously convective for all streak amplitudes and streamwise stations. It is more convective than the Blasius boundary layer in the absence of streaks; the trailing edge-velocity of a Tollmien-Schlichting wave packet in the Blasius boundary layer is around 35% of the free-stream velocity, while that of the wave packet riding on the streaky base flow is around 70%. This is because the streak instability is primarily induced by the spanwise shear and the associated Reynolds stress production term is located further away from the wall, in a larger velocity region, than for the Tollmien-Schlichting instability. The streak impulse response consists of the sinuous mode of instability triggered by the spanwise wake-like profile, as confirmed by comparing the numerical results with the absolute/convective instability properties of the family of two-dimensional wakes introduced by Monkewitz (1988). The convective nature of the secondary streak instability implies that the type of bypass transition studied here involves streaks that behave as amplifiers of external noise.

A Control of a Backward Facing Step Flow by a Vortex Generator Jet The Dynamic Characteristics of the Near-Wall Flow in the Reattachment Region.

The general goal of this study is to construct the closed loop control system of the reattachment process in a backward facing step flow by a row of the vortex generator jets. It is necessary to examine the dynamic characteristics of the injection jet on the reattachment process in the design of the control system. The coherence and the frequency transfer characteristics between the injection jet and the near-wall flow in the reattachment region are examined in the open-loop system. The result shows that the coherence between the jet velocity and the surface static pressure is higher than that with the surface friction velocity and the surface static pressre has better characteristics of the frequency transfer gain at the streamwise station of X/H>7. A step response of the near-wall flow is also conducted in order to find transient characteristics. It is found that the damped oscillation occurs in the surface static pressure immediately after a step change in the jet velocity.

Time-Averaged Mixing Behavior of Circular Jet in Counterflow: Velocity and Concentration Measurements

The time-averaged mixing behavior of a circular jet issuing into a counterflow is investigated in the laboratory at a number of jet-to-current velocity ratios between 3 and 15. The velocity field is obtained from laser Doppler anemometry measurements and the mean concentration field of the jet is measured by laser-induced fluorescence. A similarity analysis is performed on the radial profiles of mean velocity at successive streamwise stations. This is achieved by expressing the mean velocities as jet excess velocities over the ambient counterflow. The agreement of data to the similarity profiles suggested by previous studies is discussed. A similarity analysis is also attempted for the radial distributions of mean concentration. Data are presented on the axial growth of the momentum width and the concentration width of the jet in a counterflow.

On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients

A new approach to the classic closure problem for turbulent boundary layers is presented. This involves, first, using the well-known mean-flow scaling laws such as the log law of the wall and the law of the wake of Coles (1956) together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially closure is achieved here empirically and the potential for achieving closure in the future using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined. Comparisons are made with experiments covering adverse-pressure-gradient flows in relaxing and developing states and flows approaching equilibrium sink flow. Mean velocity profiles, total shear stress and Reynolds stress profiles can be computed for different streamwise stations, given an initial upstream mean velocity profile and the streamwise variation of free-stream velocity. The attached eddy model of Perry & Marusic (1995) can then be utilized, with some refinement, to compute the remaining unknown quantities such as Reynolds normal stresses and associated spectra and cross-power spectra in the fully turbulent part of the flow.

Turbulent flow field structure of initially asymmetric jets

The near field structure of round turbulent jets with initially asymmetric velocity distributions is investigated experimentally. Experiments are carried out using a constant temperature hot-wire anemometry system to measure streamwise velocity in the jets. The measurements are undertaken across the jet at various streamwise stations in a range starting from the jet exit plane and up to a downstream location of twelve diameters. The experimental results include the distributions of mean and instantaneous velocities, vorticity field, turbulence intensity, and the Reynolds shear stresses. The asymmetry of the jet exit plane was obtained by using circular cross-section pipes with a bend upstream of the exit. Three pipes used here include a straight pipe, and 90 and 160 degree-bend pipes. Therefore, at the upstream of the pipe exit, secondary flow through the bend and mean streamwise velocity distribution could be controlled by changing the curvature of pipes. The jets into the atmosphere have two levels of initial velocity skewness in addition to an axisymmetric jet from a straight pipe. In case of the curved pipe, a six diameter-long straight pipe section follows the bend upstream of the exit. The Reynolds number based on the exit bulk velocity is 13,400. The results indicate that the near field structure is considerably modified by the skewness of an initial mean velocity distribution. As the skewness increases, the decay rate of mean velocity at the centerline also increases.

An experimental investigation of the vertical temperature structure of homogeneous stratified shear turbulence

The vertical temperature structure of homogeneous stratified shear turbulence is investigated using new rapid vertical temperature measurements in a thermally stratified wind tunnel. Six cases of gradient Richardson number, Rig = N 2 /(dU/dz) 2 , where N is the Brunt-Vaisala frequency (N 2 = (g/T)dT/dz), are studied, spanning a range 0.015 ≤ Ri g ≤ 0.5. Three- to five-hundred high-resolution temperature profiles are made for several streamwise stations for each case of Ri g . These measurements are supplemented with standard fixed-point, Eulerian measurements of streamwise and vertical velocity fluctuations and temperature fluctuations and with an eight-point vertical rake of temperature probes using standard hot-wire and cold-wire techniques. Vertical profiles uniquely enable the computation of available potential energy (APE), Thorpe scales (L Th ), and the diapycnal flux (o d ), as well as one-dimensional vertical wavenumber temperature spectra. These quantities are compared with Eulerian measurements of turbulent kinetic energy (KE), potential energy (PE), and buoyancy flux. It is found that the one-dimensional vertical wavenumber temperature spectrum contains more energy at smaller scales compared to the horizontal spectrum, owing in part to shear distortion, which leads to larger mean square vertical gradients of fluctuating temperature as compared to mean square horizontal gradients. The combination of shear and stratification, especially for cases where the turbulence decays with evolution, accelerates the evolution toward small-scale anisotropy compared to just shear or just stratification. It is found that in highly stratified cases, the diapycnal flux can persist after buoyancy flux has collapsed to negligible values, indicating enhanced heat transfer without turbulent mixing. For low Rig, large-scale vertical advection creates both high local temperature gradients and regions of static instability. Associated with the regions of instability is APE, which grows relative to KE for the least stratified cases. For high Ri g , the turbulence evolves to a wavelike state, containing some counter gradient fluxes and unstable patches. This wavelike state has higher heat flux efficiency than the more turbulent states owing to the low dissipation but relatively high diapycnal flux.

Viscous simulation of F-16 like configuration at high AoA

A viscous simulation of the flow over an F-16A model with inlet and the ventral fins, which were normally not considered in previous studies, is described. The method uses a patch grid multi-block, multi-grid Navier-Stokes solver. A novel method to grid the intake and diverter is used. The arrangement of the gridding system adopted minimises the number of grids needed particularly for viscous computations. A modified form of the Baldwin-Lomax algebraic turbulence model was used for the high AoA studies. To simplify the incorporation of turbulence model, the blocking arrangement is such that it allows a thin-layer Navier-Stokes equation formulation in the calculation of the eddy viscosity. A series of four flow conditions were studied; M = 0.9, AoA = 4°, 6.0°; and M = 1.2 at AoA = 6.0°; and M = 1.85 at AoA = 16°. Extensive comparisons with experimental data of the pressure distribution on the wing and on different streamwise stations show the modelling to be reasonably accurate. For the results presented here, the wing tip missile is ignored.

Evolution and convection of large-scale structures in supersonic reattaching shear flows

Double-pulsed Mie scattering studies were performed to characterize the evolution of large-scale structures embedded within a planar supersonic base flow. Images were obtained at several streamwise stations along the shear layers, at reattachment, and in the near-wake regions. From these time-correlated images, the evolution characteristics of the large-scale structures were examined over a range of nondimensional time delays, as defined by local integral length and velocity scales. The double-pulsed images indicated that for short time delays (i.e., less than the representative eddy rollover time), the structures exhibited a simple translation in the streamwise direction. As the time delay was increased, rotation and elongation of the structures were observed in addition to the translation feature. Time delays that appreciably exceeded the local eddy rollover time generally resulted in a dramatic loss of structure identity. No eddy interactions, such as pairing, were observed at any of the imaging locations. Images obtained near reattachment provided evidence of shocklets moving in concert with the local eddies. In the initial portions of the shear layers, the mean convection velocity was measured to be significantly higher than the isentropic estimate, which is consistent with the results of previous convection velocity studies using mixing layers composed of supersonic/subsonic freestream combinations. The eddies decelerate through the recompression and reattachment regions, presumably due to the influence of the adverse pressure gradient. Downstream of reattachment, the large-scale structures accelerate as the wake develops.

Direct excitation of small-scale motions in free shear flows

The conventional approach to small-scale mixing enhancement in free shear flows by the manipulation of global flow instabilities and the ensuing large-scale vortical structures depends on the classical cascading mechanism to transfer the control influence to the scales at which molecular mixing takes place. Thus the manipulation of mixing at the smallest scales is indirect and only weakly coupled to the control input. The present work focuses on direct excitation of the small scales within the dissipation range of a free shear flow. This approach is demonstrated in a shear layer segment of an air jet emanating from a square conduit. The flow is forced at a frequency that is approximately an order of magnitude lower than the passage frequency of eddies at the Kolmogorov scale using cantilevered piezoelectric actuators. Cross-stream distributions of the streamwise velocity component are measured at a number of streamwise stations downstream of the actuator using hot wire anemometry. Direct small scale excitation results in enhanced energy transfer from the large to the small scales and in a substantial increase in the dissipation and in the decay rate of turbulent kinetic energy.

Ultrasound scattering by a swirling jet

Recent analytical work has shown that when an acoustic plane wave propagates through a rotational flow field there is a linear relationship between the Fourier component of the scattered acoustic pressure and the Fourier transform in space and time of the vorticity component that is normal to the plane defined by the wave vectors of the incident and scattered acoustic waves. Hence, ultrasound scattering can be used as a non-intrusive spectral probe of vorticity and potentially as a tool for direct measurements of vorticity distributions. Some aspects of this technique have been tested in a swirling air jet emanating from a 2.54 cm diameter nozzle where the swirl is generated upstream of the jet nozzle by a rotating paddle. For a given exit volume flow rate, swirl numbers up to 0.4 are realized. Radial distributions of the streamwise and tangential velocity components downstream of the jet exit plane are measured using two-component hot-wire anemometry and the corresponding distributions of streamwise vorticity are computed. A nominally plane ultrasonic wave field is generated normal to the jet axis by a transmitter having a 16 cm square aperture. The scattered ultrasound in the radial direction is measured at a number of streamwise and azimuthal stations. In accord with the theory, the normalized amplitude of the scattered acoustic wave is a linear function of the magnitude of the centerline vorticity at the exit plane of the jet, and is independent of the intensity of the incident wave field. Fourier components of the vorticity distribution are directly measured by varying the scattering angle and are in good agreement with theoretical predictions.

Film Cooling From Spanwise-Oriented Holes in Two Staggered Rows

Adiabatic effectiveness and iso-energetic heat transfer coefficients are presented from measurements downstream of film-cooling holes inclined at 30 deg. with respect to the test surface in spanwise/normal planes. With this configuration, holes are spaced 3d apart in the spanwise direction and 4d in the streamwise direction in two staggered rows. Results are presented for an injectant to free-stream density ratio near 1.0, and injection blowing ratios from 0.5 to 1.5. Spanwise-averaged adiabatic effectiveness values downstream of the spanwise/normal plane holes are significantly higher than values measured downstream of simple angle holes for x/d < 25–70(depending on blowing ratio) when compared for the same normalized streamwise location, blowing ratio, and spanwise and streamwise hole spacings. Spanwise-averaged iso-energetic Stanton number ratios range between 1.0 and 1.41, increase with blowing ratio at each streamwise station, and show little variation with streamwise location for each value of blowing ratio tested.

Performance evaluation of vaned pipe bends in turbulent flow of liquid propellants

Computational fluid dynamics techniques were used to analyze turbulent, incompressible flow in a vaned pipe bend that is being considered for use in the liquid propellant feed lines of the space shuttle main engine. The design is an 80° bend that incorporates two turning vanes. Computations were performed using a finite difference code for solving the Navier-Stokes equations in three dimensions using the method of pseudocompressibility, a flux-splitting upwind differencing scheme, and a Baldwin-Barth one-equation turbulence model. To compare and evaluate the performance of the bend under consideration, two other bend designs—an unvaned 80° bend and a simplified 80° vaned bend—were also analyzed. Evaluation of the bend designs was accomplished by comparing the predicted streamwise and cross-stream velocity distributions at the symmetry plane at several streamwise stations and the predicted mean pressure drops. It was observed that the vaned bend under consideration effectively provides uniform streamwise velocity distributions downstream of the bend, reduces cross-stream velocities, and significantly reduces pressure losses.

Supersonic flow mixing and combustion using ramp nozzle

A special supersonic nozzle that features five swept ramps on its expansion side, called the RAMP nozzle, was used to enhance Mach 2 jet mixing with the surrounding air either at rest or flowing at Mach 1.3. The total pressure profiles of the supersonic jets were measured at several streamwise stations and the initial shearlayer growth rates were deduced from the measurements. The results showed that the special growth rate was significantly increased with the RAMP nozzle in comparison with axisymmetric supersonic jets discharging from reference circular nozzles. The increase was 44% at the convective Mach number of 0.23 and 110% at 0.86. Also, the supersonic jets were visualized using a planar Mie-scattering technique. Instantaneous images of the RAMP-expanded-jet showed large-scale well-organized structures that resembled axial vortices in the shear layers. The appearance of these structures was linked to the increase in the initial shear-layer growth rate. Lastly, for an afterburning fuel-rich supersonic jet, the RAMP nozzle changed the afterburning characteristics significantly. This suggests that the supersonic mixing is affected.

Effect of concentrated wall suction on a turbulent boundary layer

The effect of suction, applied through a short porous wall strip, on a low Reynolds number self-preserving turbulent boundary layer has been quantified by measuring the local wall shear stress and the main Reynolds stresses downstream of the strip. When the suction rate is sufficiently high, pseudo-relaminarization occurs almost immediately downstream of the strip. Farther downstream, transition occurs followed by a slow return to a fully turbulent self-preserving state. During relaminarization, the measured skin friction coefficient cf falls below the level corresponding to the no suction value, reaching a minimum where transition begins. An empirical cf distribution is proposed that groups together results obtained at different streamwise stations and different suction rates. Of all the measured Reynolds stresses, the longitudinal turbulence intensity recovers relatively quickly from the change in boundary conditions while the wall-normal turbulence intensity and the Reynolds shear stress are significantly affected by the suction. The Reynolds shear stress, which is negligible during relaminarization, has the slowest recovery.