Session H04: Turbulence: Wall-Bounded Flows III: Pipe Flows, Channel Flows and Boundary Layers

Direct numerical simulation of turbulent pipe flow up to Reτ=5200

Well-resolved direct numerical simulations (DNSs) of a turbulent pipe flow were conducted at several friction Reynold numbers up to Re_τ=5200. The axial domain has a length  of 10πR, with 12288×1024×5120 grid points in axial, radial, and azimuthal directions, respectively, following standard DNS resolution. We employ the open-source code “OPENPIPE”,  using a Fourier-Galerkin method  in the axial and azimuthal directions, and a central finite difference scheme with a 9-point stencil  in the wall-normal direction. Turbulence statistics have been obtained, and  a clear Reynolds number dependency is documented and  compared with other DNS data  in pipes as well as channels. In particular, the mean pressure is the quantity that found to differ  notably between pipes and channels – linked to the different geometry in the outer wake region.  In addition, the pressure fluctuations in the pipe are higher than that in the channel, but  the difference progressively decreases as Re increases. The inner peak of the axial velocity fluctuation  and the wall-shear stress rms for  the pipe, which is slightly lower than for the channel, continuously increase  with Re_τ as in all other wall flows. Confidence intervals for the the various statistical quantities are also provided to assess  the fidelity of the current data.   

DNS of pipe flow up to Reτ=6000

We present DNS data of turbulent flow in a smooth straight pipe of circular cross-section, up to Re_τ⁼6000. The DNS results highlight mild deviations from Prandtl friction law, amounting to about 2%, which would extrapolate to about 4% at extreme Reynolds numbers. Data fitting of the DNS friction and heat transfer coefficients yields estimated von Karman constants k ≈ 0.387 for the velocity field, and k_θ≈0.459 for the temperature field, which are well in line with those found in all canonical wall-bounded flows. The same constants also apply to the pipe centerline values,  thus providing support for the claim that the asymptotic state of pipe flow at extreme Reynolds numbers should be plug flow. At the Reynolds numbers under scrutiny, no evidence for saturation of the logarithmic growth of the inner peak of the axial velocity variance is found. Although no outer peak of the velocity variance directly emerges in our DNS, we provide strong evidence that it should appear at Re_τ ≥ 10⁴. As a result of turbulence production exceeding dissipation over a large part of the outer wall layer, thus invalidating the classical equilibrium hypothesis.   

A hierarchy of spatially localized, self-similar structures in turbulent pipe flow

Using the data-driven wavelet decomposition (DDWD), we probe experimental data from the Princeton SuperPipe pipe flow facility at Re_τ = 12,000 for the presence of coherent structures. The DDWD has the unique feature that it produces spatially localized structures, as opposed to other analysis methods that produce spatially extended structures. When applied to the SuperPipe data, DDWD reveals a hierarchy of spatially localized structures that are self-similar in a certain range of scales. We will discuss this observation in detail.   

Response and recovery of turbulent pipe flow past a streamlined body of revolution

The response and recovery of a turbulent pipe flow perturbed by a streamlined body of resolution will be presented. The flow upstream of the body is fully developed with a bulk Reynolds number of 167,000. Three body diameters with blockage ratios of 1/9, 2/9 and 1/3 were employed to vary the perturbation strength. PIV data were collected in the region of the body and at downstream distances up to 120 pipe radii to comprehensively characterize the flow behaviors. Over the body, the flow experiences pressure gradients and streamline curvature and divergence/convergence. The responses of the mean flow and turbulent structures in this region are decoupled because the body perturbs the flow with a time scale much shorter than the turbulence time scale. In the wake, the flow development is initially fast by the mean pressure but then undergoes a slow and oscillatory recovery. The latter is a result of the asynchronous recovery between the mean flow and the turbulence, and it has been commonly observed in perturbed wall-bounded flows. A RANS-based model that was developed for recovering pipe flows is examined against the present case to test its validity.   

Response of Turbulent Pipe Flow to an Axisymmetric Body

To better understand the effects of pressure gradient, streamline convergence/divergence, and streamline curvature in wall-bounded flows, a body-of-revolution (BOR) is placed on the axis of the Superpipe at Princeton University. Three different bodies are tested, with blockage ratios of 1/9, 2/9 and 3/9. Measurements using a nano-scale thermal anemometry probe (NSTAP) are made in the flow over the body and in the wake recovery region. The Reynolds numbers of the incoming pipe flow are varied from 0.5x10⁶ to 5x10⁶.   

Examining turbulent length scales and flow correlations in a direct numerical simulation study of a hypersonic boundary layer flow produced by a uniform aspect ratio mesh using a high-resolution low dissipation massively parallel CFD code.

This work reports the initial analysis of a direct numerical simulation (DNS) of a hypersonic turbulent boundary layer (TBL). The simulation uses an aspect ratio unity mesh allowing the better-conditioned capture of flow structures near the wall in all coordinate directions. The focus of this work is on the spatial organization of the primitive variable fields, density, velocity energy, and pressure, across multiple scale ranges within the TBL. A particular emphasis is on the impact of the small-scale turbulent flow structures on the evolution of the larger turbulent scales, such as the ones modeled in a large-eddy simulation (LES) of a TBL. A discussion of the examined turbulent time-series data extracted from the DNS, taken at numerous points and spanwise lines in the configuration, i.e., the only homogeneous time-series data possible for this otherwise highly inhomogeneous flow. This analysis was then used to comment on the treatment of small-scale thermodynamic processes in various previously-developed subgrid-scale (SGS) models for compressible turbulent flows.   

Numerical investigation of the effect of wall cooling on hypersonic turbulent boundary layers

The interest in transitional and turbulent compressible boundary layers has been revitalized in recent years due to an increasing interest in minimizing the frictional drag of hypersonic vehicles. At low and moderate supersonic freestream Mach numbers, experimental and numerical results revealed that the validity of Morkovin's hypothesis (referring to the resemblance between incompressible and compressible wall turbulence structures) cannot be disputed. However, as the Mach number is increased towards high supersonic and hypersonic regimes, turbulent flow structures are modified and enhanced by intense fluctuations of density and pressure, which can be even more pronounced if the wall temperature varies adiabatically. In this work, we study the effect of wall cooling on a hypersonic turbulent boundary layer by direct and large eddy simulations, via a simple and robust re-scaling and recycling method. We considered both constant and localized wall cooling in our analysis and monitor both statistical and structural characteristics of turbulence evolving at the wall.   

Slot film cooling downstream of misaligned plates

In a turbine engine,  an inter-platform gap often exists between the combustor and the turbine annulus because they are created as separate parts and assembled.  The gap must be supplied with leakage air to prevent ingestion of the hot combustion gases into the engines' interior. Moreover, misalignments often arise between the combustor and the turbine annulus due to their different thermal expansion and assembly tolerance. Herein, we present direct numerical simulation results of two misaligned plates with cross-flow and a leakage flow simulated as a slot jet. The study focuses on forward misalignment, backward misalignment, and plain configurations and reports the corresponding cooling effectiveness, flow statistics such as the turbulent fluxes and kinetic energy. Our results show that negative viscosity exists at regions where the incoming boundary layer starts to mix with the leakage jet and it takes time, or travel-distance, before the eddies in the incoming boundary layer and those in the leakage jet to come to an equilibrium, thereby favoring a transport Reynolds stress model over a local eddy viscosity type model.   

Thermally-driven secondary flows in turbulent channel flow: Prandtl's secondary flow of the third kind

Turbulent secondary flows are classified as Prandtl's secondary flow of the first or second kind, where the former is produced by stretching and/or tilting of vorticity while the latter is produced by spatial heterogeneity in the Reynolds stresses. While previous studies have focused on spanwise variability in surface roughness, which can produce heterogeneity in Reynolds stresses (Prandtl's secondary flow of the second kind), turbulent secondary flows driven by thermal gradients have received less attention. Using large eddy simulations of unstably-stratified turbulent channel flow with uniform aerodynamic roughness, but spanwise-variable surface heat flux, we demonstrate that spanwise thermal heterogeneity can produce turbulent secondary flows, defined hereafter as Prandtl's secondary flow of the third kind. Shear and buoyancy production over elevated heat flux regions necessitates lateral entrainment of low-TKE fluid, inducing mean counter-rotating cells aligned such that upwelling and downwelling occur over high and low heat flux regions, respectively. This result illustrates that buoyancy production of TKE alters aggregate flow response and thus is a distinctly different mechanism responsible for sustenance of secondary flows than others identified previously.   

A Study of Langmuir Turbulence based on Statistical State Dynamics

Roll circulations are commonly observed in the ocean surface mixed layer. Traditionally, formation of these rolls has been ascribed to the Langmuir modal instability arising from Stokes drift included by the surface wave field. 

However, it has also been shown that in turbulent wall bounded shear flows rolls also form by direct destabilization of the roll structure by Reynolds stress torque. Understanding roll formation in the turbulent mixed layer under the influence of both Stokes drift and mean Eulerian shear, in which both the Langmuir modal instability and the Reynolds stress torque induced roll instability are supported, remains to be understood. Because both of these roll formation mechanisms are supported by the associated representation of the dynamics using statistical state dynamics (SSD), a comprehensive understanding of

the roll formation mechanism can be obtained by studying the associated SSD. 

By analyzing the SSD we find parameter regimes for which both the Langmuir destabilization mechanism and the Reynolds stress torque mechanism contribute to the formation and maintenance of rolls in mixed layer.