Spanwise Component Research Articles

Near-grid-scale energy transfer and coherent structures in the convective planetary boundary layer

Coherent structures associated with forward- and backward-scatter energy transfer in the convective planetary boundary layer are studied using large-eddy simulation. A box filter is adopted for calculation of the resolved near-grid-scale stress tensor (Lij), strain-rate tensor (Sij) and dissipation rate (LijSij). Results of conditional sampling at two different heights are presented. The conditional events are resolved dissipation rate and vertical velocity fluctuation. The latter is to distinguish the forward and backward scatter associated with upward and downward motions, respectively. Near the surface, the forward-scatter event with positive vertical velocity fluctuation is physically associated with large-scale elongated updrafts. Therefore, the contribution of spanwise component L22S22 to the resolved dissipation rate is most significant. In the outer layer, the forward-scatter event with positive vertical velocity fluctuation occurs at the top of rising updrafts, consistent with negative S33 and the dominance of L33S33. In like manner, the forward scatter with negative vertical velocity fluctuation is found ahead of downdraft motions where S33 is negative and L33S33 dominates. Near the surface, the off-diagonal component L13S13 becomes dominant as the result of downdraft motions to the surface. For the backward scatter, the vertical diagonal component L33S33 is strongest except near the surface in regions of downward motions where L13S13 tends to be most intense. The strong L33S33 event is embedded within updrafts and is characterized by minimum pressure. Flow visualization suggests that the backward scatter occurs on the upwash side of the vortex where updrafts pass through. It is argued that the diameters of vortices can be effectively increased by nearby updrafts, representing energy transfer from small- to large-scale structures. The backward scatter associated with downward motions near the surface appears to generate small-scale counter-rotating motions, resembling sweeps.

Numerical visualization of vortical structures in a spatially evolving turbulent compressible mixing layer

Large-eddy simulations are performed to numerically visualize the generation of streamwise vortical structures and its interaction with spanwisely rolled-up coherent vortical structure during the spatial development of a turbulent supersonic/subsonic mixing layer at convective Mach number M_c=0.51. Time-dependent three-dimensional compressible conservation equations were solved with a subgrid-scale turbulence model. The numerical code used the finite-volume technique, which adopted alternately in temporal discretization the second-order, explicit MacCormack's and modified Godunov's schemes. Both transverse and spanwise perturbations were imposed initially for promoting the formation of spanwise rollers and counter-rotating streamwise vortices, respectively. Numerical visualizations are presented in terms of time-sequence isopressure surfaces and vorticity contours of spanwise and streamwise components. The results show that the spatial growth of three-dimensional vortical structures, in particular, the formation of chain-link-fence type structures, is adequately captured by the present computations. Vorticity dynamics is further analyzed, for the first time, to identify the dominant roles played by the convection effect followed by the vortex stretching effect on affecting the evolution of streamwise and spanwise vortical structures, respectively, for M_c <0.6.

Direct numerical simulation of a turbulent channel flow with a linear spanwise nonuniformity of time-mean temperature (Examination of the turbulence statistics)

Direct numerical simulation (DNS) was performed for a turbulent channel flow with the time-mean temperature linearly varying in the spanwise direction. Spanwise heat transfer in wall turbulence was explored in this simple case where the turbulent heat flux has only a spanwise component. The computed flow field was confirmed to be in good agreement with the DNS database constructed by Kasagi and colleagues (1992). The general trend of the presently calculated spanwise eddy diffusivity of heat is similar to the experimental data reported by Maekawa and colleagues. However, there is a considerable discrepancy between their results in the vicinity of the wall. The numerical results demonstrate that the spanwise turbulent heat flux is nearly in local equilibrium over the whole channel width excluding the viscous sublayer

Direct numerical simulation of a turbulent channel flow with a linear spanwise nonuniformity of time‐mean temperature (Examination of the turbulence statistics)

Direct numerical simulation (DNS) was performed for a turbulent channel flow with the time-mean temperature linearly varying in the spanwise direction. Spanwise heat transfer in wall turbulence was explored in this simple case where the turbulent heat flux has only a spanwise component. The computed flow field was confirmed to be in good agreement with the DNS database constructed by Kasagi and colleagues (1992). The general trend of the presently calculated spanwise eddy diffusivity of heat is similar to the experimental data reported by Maekawa and colleagues (1991). However, there is a considerable discrepancy between their results in the vicinity of the wall. The numerical results demonstrate that the spanwise turbulent heat flux is nearly in local equilibrium over the whole channel width excluding the viscous sublayer. © 1999 Scripta Technica, Heat Trans Asian Res, 28(8): 675–686, 1999

Direct numerical simulation of a turbulent channel flow with a linear spanwise nonuniformity of time-mean temperature (Examination of the turbulence statistics)

Direct numerical simulation (DNS) was performed for a turbulent channel flow with the time-mean temperature linearly varying in the spanwise direction. Spanwise heat transfer in wall turbulence was explored in this simple case where the turbulent heat flux has only a spanwise component. The computed flow field was confirmed to be in good agreement with the DNS database constructed by Kasagi and colleagues (1992). The general trend of the presently calculated spanwise eddy diffusivity of heat is similar to the experimental data reported by Maekawa and colleagues (1991). However, there is a considerable discrepancy between their results in the vicinity of the wall. The numerical results demonstrate that the spanwise turbulent heat flux is nearly in local equilibrium over the whole channel width excluding the viscous sublayer. © 1999 Scripta Technica, Heat Trans Asian Res, 28(8): 675–686, 1999

Small-scale characteristics of a turbulent boundary layer over a rough wall

Measurements of the spanwise and wall-normal components of vorticity and their constituent velocity derivative fluctuations have been made in a turbulent boundary layer over a mesh-screen rough wall using a four-hot-wire vorticity probe. The measured spectra and variances of vorticity and velocity derivatives have been corrected for the effect of spatial resolution. The high-wavenumber behaviour of the spectra conforms closely with isotropy. Over most of the outer layer, the normalized magnitudes of the velocity derivative variances differ significantly from those over a smooth wall layer. The differences are such that the variances are much more nearly isotropic over the rough wall than on the smooth wall. This behaviour is consistent with earlier observations that the large-scale structure in this rough wall layer is more isotropic than that in a smooth wall layer. Isotropy-based approximations for the mean energy dissipation rate and mean enstrophy are consequently more reliable in this rough wall layer than in a smooth wall layer. In the outer layer, the vorticity variances are slightly larger than those over a smooth wall; reflecting structural differences between the two flows.

Coherent structures near the wall in a turbulent channel flow

Coherent structures (CS) near the wall (i.e.y+ ≤ 60) in a numerically simulated turbulent channel flow are educed using a conditional sampling scheme which extracts the entire extent of dominant vortical structures. Such structures are detected from the instantaneous flow field using our newly developed vortex definition (Jeong &amp; Hussain 1995) - a region of negativeλ2, the second largest eigenvalue of the tensorSikSkj+ ΩikΩkj- which accurately captures the structure details (unlike velocity-, vorticity- or pressure-based eduction). Extensive testing has shown thatλ2correctly captures vortical structures, even in the presence of the strong shear occurring near the wall of a boundary layer. We have shown that the dominant near-wall educed (i.e. ensemble averaged after proper alignment) CS are highly elongated quasi-streamwise vortices; the CS are inclined 9° in the vertical (x, y)-plane and tilted ±4° in the horizontal (x, z)-plane. The vortices of alternating sign overlap inxas a staggered array; there is no indication near the wall of hairpin vortices, not only in the educed data but also in instantaneous fields. Our model of the CS array reproduces nearly all experimentally observed events reported in the literature, such as VITA, Reynolds stress distribution, wall pressure variation, elongated low-speed streaks, spanwise shear, etc. In particular, a phase difference (in space) between streamwise and normal velocity fluctuations created by CS advection causes Q4 ('sweep’) events to dominate Q2 ('ejection’) and also creates counter-gradient Reynolds stresses (such as Ql and Q3 events) above and below the CS. We also show that these effects are adequately modelled by half of a Batchelor's dipole embedded in (and decoupled from) a background shearU(y). The CS tilting (in the (x, z)-plane) is found to be responsible for sustaining CS through redistribution of streamwise turbulent kinetic energy to normal and spanwise components via coherent pressure-strain effects.

Velocity and spanwise vorticity measurements in an excited mixing layer of a plane jet

The mixing layer of a plane jet was subjected to periodic weak excitation at two different frequencies corresponding to shear layer mode (Stθ=0.012) and preferred mode (St D =0.36). The nozzle exit boundary layer was identical for the unexcited and excited flows. Measurements of mean velocity, longitudinal and lateral velocity fluctuations, Reynolds shear stress and spanwise component of fluctuating vorticity were made over a longitudinal distance x/D of 6 for both the unexcited and the excited flows. Even weak excitation was observed to influence the development of the mixing layer. Under shear layer mode of excitation, the width of the layer and longitudinal turbulence level decrease compared to the naturally developing (unexcited) flow whereas preferred mode of excitation results in increase in the width and turbulence levels. The rms spanwise vorticity showed an increase for shear layer mode of excitation whereas the preferred mode of excitation resulted in a decrease compared to the values in an unexcited flow. Spectra of velocity and vorticity fluctuations exhibited subharmonic peaks, suggesting the possible occurrence of vortex pairing in both unexpected and excited flows. The influence of excitation is found to decrease as x/D increases and is not significant at x/D=6.

Measurements of compressible turbulent flow structure in a supersonic mixing layer

Multiple overheat cross-wire, parallel hot-wire, shadowgraph image processing and high-frequency response pitot probe surveys were taken in a two-dimensional, adiabatic, supersonic, free mixing layer, consisting of Mach 1.8 air (Re = 7 x 10 6 /m) injected tangentially into a Mach 4.0 freestream (Re = 67 x 10 6 /m). Mass flux turbulence intensity profiles in three dimensions were acquired, and the axial component was found to be about 25% larger than the transverse and spanwise components. Mean Favre-averaged velocity fluctuation data indicated that the axial component was negative, while both the transverse and span were positive. Turbulent flow structure angles and length scales were measured in the fully developed region of the flow. The structure angles were found to be consistent with previous compressible boundary layer results ; however, the magnitude here was found to decrease across the mixing layer. Mach number fluctuation levels were also measured. The peak Mach number fluctuation level in this flow was about 10%.

Surface pressure measurements on a pitching swept wing in a water channel

We present the results of surface pressure measurements on a swept wing of NACA 0015 profile and a back sweep angle of 15 deg, which was pitched at a uniform angular velocity. The pitching axis was perpendicular to the flow direction so that the experiment simulated the pitch-up maneuver of a fixed-wing aircraft. The experiments were performed in an open-surface water channel. The object of the study was to understand the mechanics of vorticity production and dynamic stall in three-dimensional unsteady flows. The phase-locked pressure data which were obtained at several closely spaced spanwise locations of the wing were used to obtain information on the fluxes of spanwise and chordwise vorticity components, in addition to the usual information on the aerodynamic coefficients. The study showed that the three-dimensional dynamic stall over the slightly swept wing is less catastrophic and more gradual than the two-dimensional process over an unswept wing. Other important effects observed were a spanwise variation of the aerodynamic coefficients and the presence of spanwise periodicity in the production of vorticity following the onset of dynamic stall.

Investigation of Throughflow Hypothesis in a Turbine Cascade Using a Three-Dimensional Navier–Stokes Computation

The results of a computation, performed with a three-dimensional Navier–Stokes computation at ONERA, have been averaged in the blade-to-blade direction; the spatial fluctuations around the averaged flow variables have also been determined. It has then been possible to estimate all terms in the average components of the momentum equations. The comparison of the two-dimensional balances of these three equations shows that the shear stress plays a minor role in the momentum balance, except on the dissipation of the passage vortex kinetic energy downstream of the blade trailing edges. The kinetic energy of the spanwise component of the velocity spatial fluctuations has a very strong influence on the radial pressure gradient; it introduces a convection effect. This is a key effect for all these balances.

Vortical Structures in Homogeneously Sheared Turbulence Subjected to Background Rotation

The homogeneously sheared turbulence subjected to a background rotation that cancels the shear vorticity is investigated numerically. The vortex structures that appear in the rotating flow are only longitudinal vortex tubes which are highly elongated in the streamwise direction. The vertical components of fluid velocity and particle diffusion are activated compared with spanwise components, reflecting the arrangement of the vortical structures, which leads to a large particle diffusion in the streamwise direction as well.

Effects of Embedded Vortices on Injectant From Film Cooling Holes With Large Spanwise Spacing and Compound Angle Orientations in a Turbulent Boundary Layer

Experimental results are presented that describe the effects of embedded, longitudinal vortices on heat transfer and film injectant downstream of a single row of film cooling holes with compound angle orientations. Holes are spaced 7.8 hole diameters apart in the spanwise direction so that information is obtained on the interactions between the vortices and the injectant from a single hole. The compound angle holes are oriented so that their angles with respect to the test surface are 30 deg in a spanwise/normal plane projection, and 35 deg in a streamwise/normal plane projection. A blowing ratio of 0.5 is employed and the ratio of vortex core diameter to hole diameter is 1.6–1.67 just downstream of the injection holes (x/d=10.2). At the same location, vortex circulation magnitudes range from 0.15 m2/s to 0.18 m2/s. The most important conclusion is that local heat transfer and injectant distributions are strongly affected by the longitudinal embedded vortices, including their directions of rotation and their spanwise positions with respect to film injection holes. To obtain information on the latter, clockwise rotating vortices R0–R4 and counterclockwise rotating vortices L0–L4 are placed at different spanwise locations with respect to the central injection hole located on the spanwise centerline. With vortices R0–R4, the greatest disruption to the film is produced by the vortex whose downwash passes over the central hole (R0). With vortices L0–L4, the greatest disruption is produced by the vortices whose cores pass over the central hole (L1 and L2). To minimize such disruptions, vortex centers must pass at least 1.5 vortex core diameters away from an injection hole on the upwash sides of the vortices and 2.9 vortex core diameters away on the downwash sides of the vortices. Differences resulting from vortex rotation are due to secondary flow vectors, especially beneath vortex cores, which are in different directions with respect to the spanwise velocity components of injectant after it exits the holes. When secondary flow vectors near the wall are in the same direction as the spanwise components of the injectant velocity (vortices R0–R4), the film injectant is more readily swept beneath vortex cores and into vortex upwash regions than for the opposite situation in which near-wall secondary flow vectors are opposite to the spanwise components of the injectant velocity (vortices L0–L4). Consequently, higher Stanton numbers are generally present over larger portions of the test surface with vortices R0–R4 than with vortices L0–L4.

Dynamics of vortical structures in a homogeneous shear flow

The mechanism of generation, development and interaction of vortical structures, extracted as concentrated-vorticity regions, in homogeneous shear turbulence is investigated by the use of the results of a direct numerical simulation of the Navier-Stokes equation with 1283 grid points. Among others, a few of typical vortical structures are identified as important dynamical elements, namely longitudinal and lateral vortex tubes and vortex layers. They interact strongly with each other. Longitudinal vortex tubes are generated from a random fluctuating vorticity field through stretching of fluid elements caused by the mean linear shear. They are inclined toward the streamwise direction by rotational motion due to the mean shear. There is a small (about 10°) deviation in direction between the longitudinal vortex tubes and vorticity vectors therein, which makes the vorticity vectors turn toward the spanwise direction (against the mean vorticity) until the spanwise components of the fluctuating vorticity become comparable in magnitude with the mean vorticity. These longitudinal vortex tubes induce straining flows perpendicular to themselves which generate vortex layers with spanwise vorticity in planes spanned by the tubes and the spanwise axis. These vortex layers are unstable, and roll up into lateral vortex tubes with concentrated spanwise vorticity through the Kelvin-Helmholtz instability. All of these vortical structures, through strong mutual interactions, break down into a complicated smallscale random vorticity field. Throughout the simulated period an oblique stripe structure dominates the whole flow field: initially it is inclined at about 45° to the downstream and, as the flow develops, the inclination angle decreases but eventually stays at around 10°–20°.

Interaction of a streamwise vortex with a free surface

An experimental investigation on the flow structure resulting from the interaction of a single tip vortex with a deformable free surface is described. The results have shown that the free surface redistributes part or all of the normal turbulent kinetic energy into streamwise and spanwise components. The turbulent kinetic energy first decrease sharply with increasing vertical distance from the vortex and then remains nearly constant within a thin layer below the «roughened» free surface. The results lend further credence to the simulation of near-surface structures by a decaying two-dimensional turbulence via vortex or contour dynamics

On the simultaneous measurements of two velocity components in the turbulent spot

Measurements of spanwise and streamwise velocity components in a turbulent spot artificially initiated in a Blasius boundary layer are described. A special hot-wire rake consisting of 8 ‘V’ shaped arrays was built for this purpose. This multi-probe rake also enabled one to align the individual realizations in both streamwise and spanwise directions and to form more representative ensemble-averages near the tip of the spot. The data reveals the existence of a strong spanwise component of velocity which attains its maximum value at the tip of the spot and is centered around an elevation equivalent to the displacement thickness of the unperturbed boundary layer. This perturbation velocity resembles a wave which follows the leading interface of the spot and may therefore be amenable to analysis.

On the mechanism of sinuous and varicose modes in three-dimensional viscous secondary instability of nonlinear Görtler rolls

The present study begins with the solution of the linearized partial differential equations for viscous, secondary instabilities of nonlinearly developed primary Görtler rolls. A global energy balance verifies the amplification rates obtained from secondary instability analysis and confirms that the sinuous mode would dominate. This therefore explains the strong resemblance between the rms-streamwise u-velocity structure obtained by hot-wire measurements [Swearingen and Blackwelder, J. Fluid Mech. 182, 255 (1987)] in the cross-sectional yz plane and that of the sinuous mode. The u contours of the secondary disturbance have peaks at locations corresponding to the shoulder regions of the mushroom-like primary streamwise U-velocity structure and even more intense regions surrounding the mushroom stem near the wall. This structure is explained by detailed analysis of the energy-balancing mechanisms for u2/2 in yz plane: the Reynolds stress-conversion mechanism predominantly affects the primary spanwise rate of shear strain ∂U/∂z, whereas of less importance is the effect on the normal rate of shear strain ∂U/∂y; these are delicately balanced by the isotropizing mechanism of pressure rate of strain correlation and viscous dissipation. The appropriate pressure rates of strain correlation then provide the sources for the vertical v2/2 and spanwise w2/2 contributions to the kinetic energy. The sinuous mode can be identified with streamwise-propagating structures having spanwise waviness in flow visualization studies. The spanwise-antisymmetric w, which has intense regions in the upper and lower levels of the boundary layer, tends to wag the primary mushroom structure both at the upper domed region and in the stem region near the wall, not necessarily in phase, in the spanwise direction in the y,z plane, as shown in the flow-visualization work of Peerhossaini and Wesfreid [Intl. J. Heat Fluid Flow 9, 12 (1988)]. On the other hand, the infrequency of the varicose mode can be attributed to its relatively lower amplification rate for its most amplified mode. When observed, it is identifiable with the spanwise-symmetric streamwise propagating, repetitive ‘‘horseshoe’’ structures appearing in flow visualization. Energy balance analysis reveals that this mode is attributable mainly to the Reynolds stress-conversion mechanism associated with rate of strain ∂U/∂y in the high shear layer in the peak region, although the mechanism associated with ∂U/∂z is not dramatically smaller. Viscous dissipation, though not large enough to overcome the production mechanisms, is nevertheless prominent in the global balance as well as in the detailed structural balances in the yz plane. The secondary instability vorticity structure indicates that the sinuous mode is dominated by its vertical component ηs and the varicose mode by its spanwise component ζv.

Interactions Between Embedded Vortices and Injectant From Film Cooling Holes With Compound Angle Orientations in a Turbulent Boundary Layer

Experimental results are presented that describe the effects of embedded, longitudinal vortices on heat transfer and film injectant downstream of two staggered rows of film cooling holes with compound angle orientations. Holes are oriented so that their angles with respect to the test surface are 30 deg in a spanwise/normal plane projection, and 35 deg in a streamwise/normal plane projection. A blowing ratio of 0.5, nondimensional injection temperature parameter θ of about 1.5, and free-stream velocity of 10 m/s are employed. Injection hole diameter is 0.945 cm to give a ratio of vortex core diameter to hole diameter of 1.6–1.67 just downstream of the injection holes (x/d = 10.2). At the same location, vortex circulation magnitudes range from 0.15 m2/s to 0.18 m2/s. By changing the sign of the angle of attack of the half-delta wings used to generate the vortices, vortices are produced that rotate either clockwise or counterclockwise when viewed looking downstream in spanwise/normal planes. The most important conclusion is that local heat transfer and injectant distributions are strongly affected by the longitudinal embedded vortices, including their directions of rotation and their spanwise positions with respect to film injection holes. Differences resulting from vortex rotation are due to secondary flow vectors, especially beneath vortex cores, which are in different directions with respect to the spanwise velocity components of injectant after it exits the holes. When secondary flow vectors near the wall are in the same direction as the spanwise components of the injectant velocity (clockwise rotating vortices R0–R4), the film injectant is more readily swept beneath vortex cores and into vortex upwash regions than for the opposite situation in which near-wall secondary flow vectors are opposite to the spanwise components of the injectant velocity (counter-clockwise rotating vortices L0–L4). Consequently, higher St/St0 are present over larger portions of the test surface with vortices R0–R4 than with vortices L0–L4. These disruptions to the injectant and heat transfer from the vortices are different from the disruptions that result when similar vortices interact with injectant from holes with simple angle orientations. Surveys of streamwise mean velocity, secondary flow vectors, total pressure, and streamwise mean vorticity are also presented that further substantiate these findings.

Length scales and the energy balance for turbulence near a free surface

The structure of turbulence near a free surface is examined by using results obtained from a direct simulation of flow between a no-slip wall and a shear free boundary, which serves as a model of a waveless free surface. An energy balance analysis shows that the pressure-strain term is the dominant producing term for the spanwise component of the turbulent kinetic energy. In addition, the dissipation rates for the horizontal components of the turbulence are reduced near the free surface, whereas the dissipation rate for the vertical component remains approximately constant. Two-point correlations, energy spectra, and length scales reveal important free surface induced effects. The length scales near the free surface are compared with the scales near the centerline of normal turbulent channel flow. This comparison reveals an increase by a factor of three in the streamwise length scales associated with the spanwise velocity fluctuations and an increase by a factor of two in the spanwise length scales for the streamwise velocity fluctuations. The length scales normal to the free surface are decreased for all velocity components. This indicates a more pancake-like eddy structure near the free surface compared with the structure near the centerline of a normal channel. The energy spectra show qualitative agreement with the Hunt-Graham model, though higher resolution calculations will be required to make more quantitative comparisons. The streaky structure in free surface bounded turbulent channel flow is noticeably more persistent than in normal turbulent channel flow. This is principally due to the attachment of streamwise oriented wall eddies to the free surface.

Experimental Study of an Embedded Longitudinal Vortex Interacting with a Three-Dimensional Turbulent Boundary Layer. 2nd Report, Reynolds Stress Profiles.

The paper presents the Reynolds stress data for the two cases. Case 1 in which the vortex sign is opposite that of the near-wall vorticity of the three-dimensional boundary layer and Case 2 in which the vortex sign is the same as the near-wall vorticity. The value of U2 is initially large in the vortex core region but decays rapidly for both Cases through the third measurement slot. Regions of high U2 develop on upwash side of the vortex and above the vortex center, in Case 2. The first region is the vicinity of the cross-flow separation point. The contours of V2 and W2 show an elliptic shape centered on the peak vorticity point. The difference between the vertical and spanwise normal stress component shows increasing distortion going downstream, in Case 2.