The influence of near-wall density and viscosity gradients on near-wall turbulence in a channel are studied by means of Direct Numerical Simulation (DNS) of the low-Mach number approximation of the Navier-Stokes equations. Different constitutive relations for density ρ and viscosity µ as a function of temperature are used in order to mimic a wide range of fluid behaviours and to develop a generalised framework for studying turbulence modulations in variable property flows. Instead of scaling the velocity solely based on local density, as done for the van Driest transformation, we derive an extension of the scaling that is based on gradients of the semi-local Reynolds number, defined as Re * τ ≡ (ρ/ρ w )/(µ/µ w ) Re τ (bar and subscript w denote Reynolds averaging and wall value, respectively, while Re τ is the friction Reynolds number based on wall values). This extension of the van Driest transformation is able to collapse velocity profiles for flows with near-wall property gradients as a function of the semi-local wall coordinate. However, flow quantities like mixing length, turbulence anisotropy and turbulent vorticity fluctuations do not show a universal scaling very close to the wall. This is attributed to turbulence modulations, which play a crucial role on the evolution of turbulent structures and turbulence energy transfer. We therefore investigate the characteristics of streamwise velocity streaks and quasi-streamwise vortices and found that, similar to turbulent statistics, the turbulent structures are also strongly governed by Re * τ profiles and that their dependence on individual density and viscosity profiles is minor. Flows with near-wall gradients in Re * τ (dRe * τ /dy = 0) showed significant changes in the inclination and tilting angles of quasi-streamwise vortices. These structural changes are responsible for the observed modulation of the Reynolds stress generation mechanism and the intercomponent energy transfer in flows with strong near-wall Re * τ gradients.

When high voltage is applied to distilled water filled into two glass beakers which are in contact, a stable water connection forms spontaneously, giving the impression of a floating water bridge. A detailed experimental analysis reveals static and dynamic structures as well as heat and mass transfer through this bridge.

We theoretically and numerically investigate the effect of temperature dependent density and viscosity on turbulence in channel flows. First, a mathematical framework is developed to support the validity of the semi-local scaling as proposed based on heuristic arguments by Huang, Coleman, and Bradshaw ["Compressible turbulent channel flows: DNS results and modelling," J. Fluid Mech. 305, 185-218 (1995)]. Second, direct numerical simulations (DNS) of turbulent channel flows with different constitutive relations for density and viscosity are performed to assess and validate the semi-local scaling for turbulent statistics. The DNS database is obtained by solving the low-Mach number approximation of the Navier-Stokes equation. Finally, we quantify the modulation of turbulence due to changes in fluid properties. In the simulations, the fluid is internally heated and the temperature at both channel walls is fixed, such that the friction Reynolds number based on wall quantities is Re τ = 395 for all cases investigated. We show that for a case with variable density ρ and viscosity µ, but constant semi-local Reynolds number Re * τ ≡  (ρ/ρ w )/(µ/µ w )Re τ (where bar and subscript w, denote Reynolds averaging and averaged wall quantity, respectively), across the whole channel height, the turbulent statistics exhibit quasi-similarity with constant property turbulent flows. For cases where Re * τRe τ across the channel, we found that quasi-similarity is maintained for cases with similar Re * τ distributions, even if their individual mean density and viscosity profiles substantially differ. With a decrease of Re * τ towards the channel center (Re * τ < Re τ ), we show that the anisotropy increases and the pre-multiplied stream-wise spectra reveal that this increase is associated with strengthening of the large scale streaks in the buffer layer. The opposite effect is observed when Re * τ increases towards the channel center. The present results provide an effective framework for categorizing turbulence modulation in wall-bounded flows with variable property effects, and can be applied to any Newtonian fluid that is heated or cooled. C 2015 AIP Publishing LLC. [http://dx

The internal flow in the HyShot II scramjet is investigated through numerical simulations. A computational infrastructure to solve the compressible Reynolds-averaged Navier-Stokes equations on unstructured meshes is introduced. A combustion model based on tabulated chemistry is considered to incorporate detailed chemicalkinetics mechanics while retaining a low computational cost. Both nonreactive and reactive simulations have been performed, and results are compared with ground test measurements obtained at DLR, German Aerospace Center. Different turbulence models were tested, and the dependence on the mesh is assessed through grid refinement. The comparison with experimental data shows good agreement, although the computed heat fluxes at the wall are higher than measurements for the reactive case. A sensitivity analysis on the turbulent Schmidt and Prandtl numbers shows that the choice of these parameters has a strong influence on the results. In particular, variations of the turbulent Prandtl number lead to large changes in the heat flux at the walls. Finally, the inception of thermal choking is investigated by increasing the equivalence ratio, whereby a normal shock is created locally and moves upstream, leading to a large increase in the maximum pressure. Nevertheless, a large portion of the flow is still supersonic. Nomenclatureproportionality constant between turbulence and scalar time scales c p = specific heat capacity at constant pressure D = scalar diffusion coefficient d = injector diameter E = total specific energy e = specific internal energy F = convective flux vector F v = viscous flux vector h = specific enthalpy I = identity matrix k = turbulent kinetic energy Le = Lewis number Ma = Mach number N = number of species n = outward-pointing unit vector normal to surface P ref = reference pressure Pr = Prandtl number p = pressure Q = vector of primitives variables Q ref = reference wall heat flux R = residuum R = gas constant R u = universal gas constant r f = vector connecting cell center and center of cell face S = source-term vector S = wave speed in approximate Riemann solver S i = source term for scalar i Sc = Schmidt number T = temperature t = time U = vector of conserved variables U = inflow velocity V = cell volume v = Cartesian velocity vector W = species molecular weight x = Cartesian position vector Y = species mass fraction y = wall-normal direction Z = mixture fraction = exponent for the pressure correction of the source term of the progress variable = ratio of specific heat capacity h 0 = heat of formation ij = Kronecker delta @ = boundary of the physical domain = thermal diffusivity = viscosity = approximation of the triple correlation = stress tensor = density k = turbulent kinetic-energy Schmidt number ij = viscous stress tensor R ij = Reynolds stress tensor = generic scalar ' = equivalence ratio = scalar dissipation rate = slope limiter = physical domain ! = specific turbulent dissipation _ ! C = source term of the progress variable Subscripts F = fuel f = cell face inj = injector k ...

Heated or cooled fluids at supercritical pressure show large variations in thermophysical properties, such as the density, dynamic viscosity and molecular Prandtl number, which strongly influence turbulence characteristics. To investigate this, direct numerical simulations were performed of a turbulent flow at supercritical pressure (CO$_{2}$at 8 MPa) in an annulus with a hot inner wall and a cold outer wall. The pseudo-critical temperature lies close to the inner wall, which results in strong thermophysical property variations in that region. The turbulent shear stress and the turbulent intensities significantly decrease near the hot inner wall, but increase near the cold outer wall, which can be partially attributed to the mean dynamic viscosity and density stratification. This leads to decreased production of turbulent kinetic energy near the inner wall and vice versa near the outer wall. However, by analysing a transport equation for the coherent streak flank strength, it was found that thermophysical property fluctuations significantly affect streak evolution. Near the hot wall, thermal expansion and buoyancy tend to decrease streak coherence, while the viscosity gradient that exists across the streaks interacts with mean shear to act as either a source or a sink in the evolution equation for the coherent streak flank strength. The formation of streamwise vortices on the other hand is hindered by the torque that is the result of the kinetic energy and density gradients. Near the cold wall, the results are reversed, i.e. the coherent streak flank strength and the streamwise vortices are enhanced due to the variable density and dynamic viscosity. The results show that not only the mean stratification but also the large instantaneous thermophysical property variations that occur in heated or cooled fluids at supercritical pressure have a significant effect on turbulent structures that are responsible for the self-regeneration process in near-wall turbulence. Thus, instantaneous density and dynamic viscosity fluctuations are responsible for decreased (or increased) turbulent motions in heated (or cooled) fluids at supercritical pressure.

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We investigate the hydrodynamic stability of compressible boundary layers over adiabatic walls with fluids at supercritical pressure in the proximity of the Widom line (also known as the pseudo-critical line). Depending on the free-stream temperature and the Eckert number that determines the viscous heating, the boundary-layer temperature profile can be either sub-, trans-or supercritical with respect to the pseudo-critical temperature, T pc . When transitioning from sub-to supercritical temperatures, a seemingly continuous phase change from a compressible liquid to a dense vapour occurs, accompanied by highly non-ideal changes in thermophysical properties. Using linear stability theory (LST) and direct numerical simulations (DNS), several key features are observed. In the sub-and supercritical temperature regimes, the boundary layer is substantially stabilized the closer the free-stream temperature is to T pc and the higher the Eckert number. In the transcritical case, when the temperature profile crosses T pc , the flow is significantly destabilized and a co-existence of dual unstable modes (Mode II in addition to Mode I) is found. For high Eckert numbers, the growth rate of Mode II is one order of magnitude larger than Mode I. An inviscid analysis shows that the newly observed Mode II cannot be attributed to Mack's second mode (trapped acoustic waves), which is characteristic in high-speed boundary-layer flows with ideal gases. Furthermore, the generalized Rayleigh criterion (also applicable for non-ideal gases) unveils that, in contrast to the trans-and supercritical regimes, the subcritical regime does not contain an inviscid instability mechanism.