Gary N. Coleman

A numerical study of turbulent supersonic isothermal-wall channel flow

A study of compressible supersonic turbulent flow in a plane channel with isothermal walls has been performed using direct numerical simulation. Mach numbers, based on the bulk velocity and sound speed at the walls, of 1.5 and 3 are considered; Reynolds numbers, defined in terms of the centreline velocity and channel half-width, are of the order of 3000. Because of the relatively low Reynolds number, all of the relevant scales of motion can be captured, and no subgrid-scale or turbulence model is needed. The isothermal boundary conditions give rise to a flow that is strongly influenced by wall-normal gradients of mean density and temperature. These gradients are found to cause an enhanced streamwise coherence of the near-wall streaks, but not to seriously invalidate Morkovins hypothesis : the magnitude of fluctuations of total temperature and especially pressure are much less than their mean values, and consequently the dominant compressibility effect is that due to mean property variations. The Van Driest transformation is found to be very successful at both Mach numbers, and when properly scaled, statistics are found to agree well with data from incompressible channel flow results.

Compressible turbulent channel flows: DNS results and modelling

The present paper addresses some topical issues in modelling compressible turbulent shear flows. The work is based on direct numerical simulation (DNS) of two supersonic fully developed channel flows between very cold isothermal walls. Detailed decomposition and analysis of terms appearing in the mean momentum and energy equations are presented. The simulation results are used to provide insights into differences between conventional Reynolds and Favre averaging of the mean-flow and turbulent quantities. Study of the turbulence energy budget for the two cases shows that compressibility effects due to turbulent density and pressure fluctuations are insignificant. In particular, the dilatational dissipation and the mean product of the pressure and dilatation fluctuations are very small, contrary to the results of simulations for sheared homogeneous compressible turbulence and to recent proposals for models for general compressible turbulent flows. This provides a possible explanation of why the Van Driest density-weighted transformation (which ignores any true turbulent compressibility effects) is so successful in correlating compressible boundary-layer data. Finally, it is found that the DNS data do not support the strong Reynolds analogy. A more general representation of the analogy is analysed and shown to match the DNS data very well.

Effect of Roughness on Wall-Bounded Turbulence

Direct numerical simulation of turbulent incompressible plane-channel flow between a smooth wall and one covered with regular three-dimensional roughness elements is performed. While the impact of roughness on the mean-velocity profile of turbulent wall layers is well understood, at least qualitatively, the manner in which other features are affected, especially in the outer layer, has been more controversial. We compare results from the smooth- and rough-wall sides of the channel for three different roughness heights of h+= 5.4, 10.8, and 21.6 for Reτ of 400, to isolate the effects of the roughness on turbulent statistics and the instantaneous turbulence structure at large and small scales. We focus on the interaction between the near-wall and outer-layer regions, in particular the extent to which the near-wall behavior influences the flow further away from the surface. Roughness tends to increase the intensity of the velocity and vorticity fluctuations in the inner layer. In the outer layer, although the roughness alters the velocity fluctuations, the vorticity fluctuations are relatively unaffected. The higher-order moments and the energy budgets demonstrate significant differences between the smooth-wall and rough-wall sides in the processes associated with the wall-normal fluxes of the Reynolds shear stresses and turbulence kinetic energy. The length scales and flow dynamics in the roughness sublayer, the spatially inhomogeneous layer within which the flow is directly influenced by the individual roughness elements, are also examined. Alternative mechanisms involved in producing and maintaining near-wall turbulence in rough-wall boundary layers are also considered. We find that the strength of the inner/outer-layer interactions are greatly affected by the size of the roughness elements.

Direct numerical simulation of the Ekman layer : A step in Reynolds number, and cautious support for a log law with a shifted origin

Results at Ekman Reynolds numbers Re ranging from 1000 to 2828 expand the direct numerical simulation (DNS) contribution to the theory of wall-bounded turbulence. An established spectral method is used, with rules for domain size and grid resolution at each Reynolds number derived from the theory. The Re increase is made possible by better computers and by optimizing the grid in relation to the wall shear-stress direction. The boundary-layer thickness in wall units δ+ varies here by a factor of about 5.3, and reaches values near 5000, or 22 times the minimum at which turbulence has been sustained. An equivalent channel Reynolds number, based on the pressure gradient in wall units, would reach about Reτ=1250. The principal goal of the analysis, the impartial identification of a log law, is summarized in the local “Karman measure” d(ln z+)/dU+. The outcome differs from that for Hoyas and Jimenez [Phys. Fluids 18, 011702 (2006)] and for Hu et al. [AIAA J. 44, 1541 (2006)] in channel-flow DNS at similar Reynolds numbers, for reasons unknown: Here, the law of the wall is gradually established up to a z+ around 400, with little statistical scatter. To leading order, it is consistent with the experiments of Osterlund et al. [Phys. Fluids 12, 1 (2000)] in boundary layers. With the traditional expression, a logarithmic law is not present, in that the Karman measure drifts from about 0.41 at z+≈70 to the 0.37–0.38 range for z+≈500, with Re=2828. However, if a virtual origin is introduced with a shift of a+=7.5 wall units, the data support a long logarithmic layer with κ=0.38 a good fit to d(ln[z++a+])/dU+. A determination of the Karman constant from the variation of the skin-friction coefficients with Reynolds numbers also yields values near 0.38. The uncertainty is about ±0.01. These values are close to the boundary-layer experiments, but well below the accepted range of [0.40,0.41] and the experimental pipe-flow results near 0.42. The virtual-origin concept is also controversial, although nonessential at transportation or atmospheric Reynolds numbers. Yet, this series may reflect some success in verifying the law of the wall and investigating the logarithmic law by DNS, redundantly and with tools more impartial than the visual fit of a straight line to a velocity profile.Results at Ekman Reynolds numbers Re ranging from 1000 to 2828 expand the direct numerical simulation (DNS) contribution to the theory of wall-bounded turbulence. An established spectral method is used, with rules for domain size and grid resolution at each Reynolds number derived from the theory. The Re increase is made possible by better computers and by optimizing the grid in relation to the wall shear-stress direction. The boundary-layer thickness in wall units δ+ varies here by a factor of about 5.3, and reaches values near 5000, or 22 times the minimum at which turbulence has been sustained. An equivalent channel Reynolds number, based on the pressure gradient in wall units, would reach about Reτ=1250. The principal goal of the analysis, the impartial identification of a log law, is summarized in the local “Karman measure” d(ln z+)/dU+. The outcome differs from that for Hoyas and Jimenez [Phys. Fluids 18, 011702 (2006)] and for Hu et al. [AIAA J. 44, 1541 (2006)] in channel-flow DNS at similar Reyno...

Direct numerical simulation of vortex ring evolution from the laminar to the early turbulent regime

Direct numerical simulation is used to study the temporal development of single vortex rings at various Reynolds numbers and core thicknesses. Qualitative differences between the evolution of thin- and thick-core rings are observed leading to a correction factor to the classical equation for the ring translational velocity. We compare the obtained linear modal growth rates with previous work, highlighting the role of the wake in triply periodic numerical simulations. The transition from a laminar to a turbulent ring is marked by the rearrangement of the outer core vorticity into a clearly defined secondary structure. The onset of the fully turbulent state is associated with shedding of the structure in a series of hairpin vortices. A Lagrangian particle analysis was performed to determine the ring entrainment and detrainment properties and to investigate the possibility of an axial flow being generated around the circumference of the core region prior to the onset of turbulence.

A numerical study of three-dimensional wall-bounded flows

Abstract Nonequilibrium three-dimensional (3-D) turbulent boundary layers are studied using direct numerical simulation (DNS). Time-developing flows are used to investigate the physics of spatial-developing ones. We find that application of a spanwise shear leads to the reduction of both the turbulent kinetic energy and drag, with the most dramatic reduction of the latter occurring when the shear is applied between y + ≈ 5 and 15. When the three-dimensionality is produced by transverse skewing, the resulting alteration of the relationship between the Reynolds stresses is associated in large part with the effect of the pressure gradient upon the amplification or attenuation of the turbulent kinetic energy.

A numerical study of strained three-dimensional wall-bounded turbulence

Channel flow, initially fully developed and two-dimensional, is subjected to mean strains that emulate the effect of rapid changes of streamwise and spanwise pressure gradients in three-dimensional boundary layers, ducts, or diffusers. As in previous studies of homogeneous turbulence, this is done by deforming the domain of a direct numerical simulation (DNS); here however the domain is periodic in only two directions and contains parallel walls. The velocity difference between the inner and outer layers is controlled by accelerating the channel walls in their own plane, as in earlier studies of three-dimensional channel flows. By simultaneously moving the walls and straining the domain we duplicate both the inner and outer regions of the spatially developing case. The results are used to address basic physics and modelling issues. Flows subject to impulsive mean three-dimensionality with and without the mean deceleration of an adverse pressure gradient (APG) are considered: strains imitating swept-wing and pure skewing (sideways turning) three-dimensional boundary layers are imposed. The APG influences the structure of the turbulence, measured for example by the ratio of shear stress to kinetic energy, much more than does the pure skewing. For both deformations, the evolution of the Reynolds stress is profoundly affected by changes to the velocity–pressure-gradient correlation [Pi]ij. This term – which represents the finite time required for the mean strain to modify the shape and orientation of the turbulent motions – is primarily responsible for the difference (lag) in direction between the mean shear and the turbulent shear stresses, a well-known feature of perturbed three-dimensional boundary layers. Files containing the DNS database and model-testing software are available from the authors for distribution, as tools for future closure-model testing.

Near-wall turbulence structures in three-dimensional boundary layers

We examine the structure of near-wall turbulence in three-dimensional boundary layers (3DBLs), which we approximate by applying an impulsive spanwise motion to the lower wall of a turbulent channel flow. Direct numerical simulation (DNS) data are analysed using probability density functions (PDFs), conditional-averaged quadrant analysis about Reynolds-stress-producing events, and visualization of vortices with the ?2-criterion. The evidence suggests that mean three-dimensionality breaks up the symmetry and alignment of near-wall structures, disrupting their self-sustaining mechanisms, and thereby causing a reduction in the turbulence kinetic energy (TKE).

Direct numerical simulation of a decelerated wall-bounded turbulent shear flow

A fully developed turbulent channel flow is subjected to a mean strain that approximates that in a spatially developing adverse-pressure-gradient (APG) boundary layer. This is done by applying uniform irrotational temporal deformations to the flow domain of a conventional direct numerical simulation channel code. The velocity difference between the inner and outer layer is also controlled by accelerating the walls in the streamwise plane, in order to duplicate the defining features of both the inner and outer regions of an APG boundary layer. Eventually, the flow reverses at the wall. We address basic physics and modelling issues, and create a database that makes detailed testing of turbulence models easy. As in the corresponding spatial layers, distinct inner- and outer-layer dynamics are observed: a decrease in turbulence intensity near the wall is accompanied by increased energy in the outer layer. The ‘extra strain’ effect associated with the diverging outer-layer streamlines is documented, particularly in the Reynolds-stress budgets.

Rapid distortion theory for compressible homogeneous turbulence under isotropic mean strain

Isotropic compressible turbulence subjected to rapid isotropic compression is studied using inviscid rapid distortion theory (RDT) and direct numerical simulation. An exact solution to the rapid distortion problem is given. Comparisons are made between the simulation results and the RDT solution, as well as previously studied limiting cases of the RDT solution. The comparisons illustrate the range of applicability of the RDT solutions. Implications for the use of RDT results in modeling compressible turbulent flows are briefly discussed.