Density Ρw Research Articles

Data-driven wall models for Reynolds Averaged Navier–Stokes simulations

This article presents a data-based methodology to build Reynolds-Averaged Navier–Stokes (RANS) wall models for aerodynamic simulations at low Mach numbers. Like classical approaches, the model is based on nondimensional local quantities derived from the wall friction velocity uτ, the wall viscosity μw, and the wall density ρw. A fully-connected neural network approximates the relation u+=f(y+,p+). We consider reference data (obtained with RANS simulations based on fine meshes up to the wall) of attached turbulent flows at various Reynolds numbers over different geometries of bumps, covering a range of wall pressure gradients. After training the neural networks on a subset of the reference data, the paper assesses their ability to accurately recover data for unseen conditions on meshes that have been trimmed from the wall up to an interface height where the learned wall law is applied. The network’s interpolation and extrapolation capabilities are quantified and carefully examined. Overall, when tested within its interpolation and extrapolation capabilities, the neural network model shows good robustness and accuracy. The global error on the skin friction coefficient is a few percent and behaves consistently over all the considered test cases.

On the seawater density in gravity calculations

The bathymetry from the continental margin off the Baja California Peninsula, and across the Tonga Trench, are used to quantify the differences in gravitational attraction, arising by considering a constant density ρw = 1030 kg/m3, typically used in marine geophysical studies, versus two global zonal models that describe the seawater density as a function of depth and geodetic latitude. With precision better than 1 μGal, I found that the maximum difference across the continental margin of the Baja California Peninsula is less than 1.5 mGal in the Cedros Deep away from the Continental Rise, while it is less than 0.05 mGal on the Continental Shelf. The maximum difference across the Tonga trench is about 5.3 mGal. Considering that the overall accuracy achieved in typical marine or satellite gravity surveys is at best of 1 mGal, the calculation of the gravity effect due to the seawater layer by either one of the two zonal models may reduce the error budget in stripping-off the gravity effect in deep waters.

Congruent Chemical Potentials and Insertion Works in Establishing Nonuniform-Fluid Structures via Uniform-Fluid Properties

We propose an effective density ρpseudo that engenders direct mapping of the free energy FU of uniform fluids to the free energy FN of nonuniform fluids by requiring FN = FU (at ρpseudo). The equality is called the congruence condition. It is made possible by considering the statistical mechanical theory: the potential distribution theorem (PDT). The PDT connects three quantities: the work Wins(z) needed for inserting a test particle into the fluid, the chemical potential μ0 of the bulk fluid, and the nonuniform singlet density ρw(1)(z). We use Monte Carlo (MC) data to obtain the insertion work Wins(z) (via the Euler–Lagrange equation) from the probability densities ρw(1)(z). The concept of the congruent effective density ρpseudo is applicable to general interaction potentials, not restricted to the hard sphere type. We examine thus two simple fluids adsorbed on a hard wall: (i) the hard spheres and (ii) the Lennard-Jones fluid for comparison. We discern the difference in behavior of the effective density...

ẢNH HƯỞNG ĐỊA HÌNH ĐÁY BIỂN LÊN DỊ THƯỜNG TRỌNG LỰC TRÊN KHU VỰC BIỂN ĐÔNG VÀ LÂN CẬN

Gravity terrain correction of seafloor topography is very necessary and decisive for effective in interpretation of marine gravity data. In this study, gravity terrain correction is calculated in combination with the methods that given by Nagy (1966) and Kane (1962). A digital terrain model of the seafloor topography (DEM) 2.5 × 2.5km is used in the process of calculating terrain correction. The calculation of the terrain effect is extended to the optimal distance 100km with average density of crustal rocks ρr=2.67g/cm3, and sea water density ρw=1.03 g/cm3. The obtained result of the terrain correction changes from -17.95 to +25.71 mGal in the whole region. By combining the above-mentioned terrain correction result with other data sources, the authors also have built a 2.5 × 2.5 km grid of complete Bouguer gravity anomaly data for East Vietnam Sea and adjacent areas.

A potential distribution induced mapping of free energies for simple fluids

The potential distribution theorem (PDT) is utilized to construct an effective density, the pseudo-densityρpseudo(z), that enables mapping of the free energies of the uniform fluid exactly onto the nonuniform system values. In addition, a similar quantity, the pseudo-chemical potentialμpseudo(z), is given as the chemical potential produced by the uniform equation of state upon using the nonuniform density ρw(1)(z) as input. The PDT connects three quantities: the work Wins(z) for inserting a test particle into the fluid, the chemical potential μ0 of the bulk fluid, and the nonuniform singlet density ρw(1)(z). We perform Metropolis NVT ensemble Monte Carlo (MC) simulations to obtain the insertion work Wins(z) (via Widom’s particle insertion) and the densities ρw(1)(z). We illustrate the mapping on two simple fluids adsorbed on a hard wall: the Lennard-Jones and the attractive Yukawa fluids. The pseudo-density is determined via an accurate uniform-fluid equation of state for the Lennard-Jones system, and for the Yukawa fluid via direct MC simulations. We characterize the behavior of the effective density and the pseudo-chemical potential vis-à-vis the cases of enhancement and depletion of the fluid density near the wall. These quantities (ρpseudo&μpseudo) are found to exhibit for enhanced adsorption out-of-phase oscillations compared to ρw(1)(z) and βWins(z). For depleted adsorption, we do not observe oscillations and the trends of ρpseudo and μpseudo are in good agreement with those of ρw(1)(z) and βWins. We analyze the differences in behavior in terms of the concavity of the chemical-potential function. We also show the equivalence of the potential distribution theorem to the Euler–Lagrange equation of the density functional theory.

Prediction of Drag Coefficient and Secondary Motion of Free-Falling Rigid Cylindrical Particles with and without Curvature at Moderate Reynolds Number

Laboratory experiments have been conducted to understand the behavior of negatively buoyant cylindrical particles of density ρ, length L, diameter d, with and without curvature, freely falling in a fluid of density ρw at Reynolds numbers based on d of 200–6,000. The paper proposes a parameter based on the cylinder density ratio S=ρ/ρw and aspect ratio E=L/d that is able to predict the onset of different modes of secondary motion ranging from oscillations to tumbling. The same parameter can also predict the maximum amplitude of the oscillations of the cylinder, on the basis of comparing the magnitudes of the oscillation velocity with the fall velocity. Contrary to previous work that has treated the oscillations and drag coefficient dependence as independent phenomena, this paper argues that the secondary motion reduces the time-averaged projected surface area of the cylinder during its descent, leading to a lower observed drag coefficient CD computed using the nominal projected area of length times diamete...

Large-Eddy Simulation of Langmuir Turbulence in Pure Wind Seas

Abstract The scaling of turbulent kinetic energy (TKE) and its vertical component (VKE) in the upper ocean boundary layer, forced by realistic wind stress and surface waves including the effects of Langmuir circulations, is investigated using large-eddy simulations (LESs). The interaction of waves and turbulence is modeled by the Craik–Leibovich vortex force. Horizontally uniform surface stress τ0 and Stokes drift profiles uS(z) are specified from the 10-m wind speed U10 and the surface wave age CP/U10, where CP is the spectral peak phase speed, using an empirical surface wave spectra and an associated wave age–dependent neutral drag coefficient CD. Wave-breaking effects are not otherwise included. Mixed layer depths HML vary from 30 to 120 m, with 0.6 ≤ CP/U10 ≤ 1.2 and 8 m s−1 < U10 < 70 m s−1, thereby addressing most possible oceanic conditions where TKE production is dominated by wind and wave forcing. The mixed layer–averaged “bulk” VKE 〈w2〉/u*2 is equally sensitive to the nondimensional Stokes e-folding depth D*S/HML and to the turbulent Langmuir number Lat = u*/US, where u* = |τ0|/ρw in water density ρw and US = |uS|z=0. Use of a D*S scale-equivalent monochromatic wave does not accurately reproduce the results using a full-surface wave spectrum with the same e-folding depth. The bulk VKE for both monochromatic and broadband spectra is accurately predicted using a surface layer (SL) Langmuir number LaSL = u*/〈uS〉SL, where 〈uS〉SL is the average Stokes drift in a surface layer 0 > z > − 0.2HML relative to that near the bottom of the mixed layer. In the wave-dominated limit LaSL → 0, turbulent vertical velocity scales as wrms ∼ u*La−2/3SL. The mean profile (z) of VKE is characterized by a subsurface peak, the depth of which increases with D*S/HML to a maximum near 0.22HML as its relative magnitude /〈w2〉 decreases. Modestly accurate scalings for these variations are presented. The magnitude of the crosswind velocity convergence scales differently from VKE. These results predict that for pure wind seas and HML ≅ 50 m, 〈w2〉/u*2 varies from less than 1 for young waves at U10 = 10 m s−1 to about 2 for mature seas at winds greater than U10 = 30 m s−1. Preliminary comparisons with Lagrangian float data account for invariance in 〈w2〉/u*2 measurements as resulting from an inverse relationship between U10 and CP/U10 in observed regimes.

Flow electrification through porous media

Abstract This paper deals with streaming current generated by water flow through 4 geological porous media. These experimental measurements and a theoretical model allow us to determine the space charge density ρW at the wall in these 4 cases and to compare these values to previous ones obtained with glass capillaries and glass porous samples. The results show that ρW is effectively the intrinsic parameter of the solid–liquid interface because it is not a function of the geometry of the fluid flow paths but it only depends on the physico–chemical properties of the solid and the liquid.

Ion association of dilute aqueous sodium hydroxide solutions to 600�C and 300 MPa by conductance measurements

The limiting molar conductances Λ0 and ion association constants of dilute aqueous NaOH solutions (<0.01 mol-kg−1) were determined by electrical conductance measurements at temperatures from 100 to 600°C and pressures up to 300 MPa. The limiting molar conductances of NaOH(aq) were found to increase with increasing temperature up to 300°C and with decreasing water density ρw. At temperatures ≥400°C, and densities between 0.6 to 0.8 g-cm−3, Λ0 is nearly temperature-independent but increases linearly with decreasing density, and then decreases at densities <0.6 g-cm−3. This phenomenon is largely due to the breakdown of the hydrogen-bonded, structure of water. The molal association constants K Am for NaOH( aq ) increase with increasing temperature and decreasing density. The logarithm of the molal association constant can be represented as a function of temperature (Kelvin) and the logarithm of the density of water by $$\begin{gathered} log K_{Am} = 2.477 - 951.53/T - (9.307 \hfill \\ - 3482.8/T)log \rho _{w } (25 - 600^\circ C) \hfill \\ \end{gathered} $$ which includes selected data taken from the literature, or by $$\begin{gathered} log K_{Am} = 1.648 - 370.31/T - (13.215 \hfill \\ - 6300.5/T)log \rho _{w } (400 - 600^\circ C) \hfill \\ \end{gathered} $$ which is based solely on results from the present study over this temperature range (and to 300 MPa) where the measurements are most precise.

The Dissipation Range of Wind-Wave Spectra Observed on a Lake

Based on an interpretation of a field experiment it is argued that, due to breaking of wind waves in deep water, the dissipation of energy is restricted to a range of frequencies ω > ωg, much higher than the frequency ωm of the dominant waves. In this dissipation range the spectrum has the form S(ω) = βg2ω−5 where g is the acceleration due to gravity and β = 0.025. For spectral wave components at ω ≤ ωg, only a local balance between energy input from the wind and the weak, third-order, nonlinear interaction is important. Asymptotically as ω ≫ ωm the wind input becomes unimportant, and the wave spectrum has the Kitaigorodskii form of a Kolgomorov analog S(ω) = 2aε0⅓ g4/3 ω−4 where ε0 is a constant flow of mean energy per unit surface area through the spectrum dissipated at high frequencies (when multiplied by g and water density ρw). From a method of M. S. Longuet-Higgins we estimate the magnitude of the dissipation (due to wave breaking) and find the Kolmogorov constant to be a ≈ 0.6. When a model, explained by Phillips, for wind energy input to the wave spectrum is applied to a simplified spectral model prescribing the scales of dissipation and growth of spectral wave components, good agreement is found with measurements by Donelan et al. of the coefficient 2aε0⅓ and its dependence on the frequency ωm of the dominant waves at the spectral peak.

Atmosphere of Mercury

THE recently released news concerning the possible atmosphere surrounding Mercury seems to have taken the astronomical community by surprise. It had generally been expected that because of the high temperatures (of the order of 450 K) existing there and also because of the low surface gravity, any atmosphere originally present, or any released from subsequent events on the surface would quickly evaporate since the random thermal speed of the atoms would be greater than the escape velocity. If VE is the escape velocity from Mercury, ρA the density of its atmosphere and A the surface area, then a simple computation indicates1,2 that the rate of mass loss from this atmosphere is where β = m/2 kT, k being Boltzmann's constant and m the atomic mass. All this ignores the solar wind which carries mass into the atmosphere. In reality the problem becomes a boundary layer problem in which the magnetic field of Mercury plays a part, but we can see simply that the main effect is to generate an atmosphere. If the wind has a density ρw and a velocity Vw, then it adds matter to Mercury at the rate and the stead state situation is given when Inserting the appropriate numerical values, β≈10−11, VE2≈ 2 × 1010, and Vw≈ 108 (all in c.g.s. units gives) There should therefore be a very tenuous atmosphere, basically composed of hydrogen being maintained in this way. Any helium and argon released by radioactivity would become trapped in this atmosphere and should be detected.