Reynolds number dependence of streamwise velocity spectra in turbulent pipe flow

Spectra of the streamwise velocity component in fully developed turbulent pipe flow are presented for Reynolds numbers up to 5.7×10^6. Even at the highest Reynolds number, streamwise velocity spectra exhibit incomplete similarity only: while spectra collapse with both classical inner and outer scaling for limited ranges of wave number, these ranges do not overlap. Thus similarity may not be described as complete, and a region varying with the inverse of the streamwise wave number, k1, is not expected, and any apparent k1-1 range does not attract any special significance and does not involve a universal constant. Reasons for this are suggested

Scaling of the streamwise velocity component in turbulent pipe flow

Statistics of the streamwise velocity component in fully developed pipe flow are examined for Reynolds numbers in the range 5.5 x 10^4 ≤ ReD ≤ 5.7 x 10^6. Probability density functions and their moments (up to sixth order) are presented and their scaling with Reynolds number is assessed. The second moment exhibits two maxima: the one in the viscous sublayer is Reynolds-number dependent while the other, near the lower edge of the log region, follows approximately the peak in Reynolds shear stress. Its locus has an approximate (R^+)^{0.5} dependence. This peak shows no sign of ‘saturation’, increasing indefinitely with Reynolds number. Scalings of the moments with wall friction velocity and $(U_{cl}-\overline{U})$ are examined and the latter is shown to be a better velocity scale for the outer region, y/R > 0.35, but in two distinct Reynolds-number ranges, one when ReD 7 x 10^4. Probability density functions do not show any universal behaviour, their higher moments showing small variations with distance from the wall outside the viscous sublayer. They are most nearly Gaussian in the overlap region. Their departures from Gaussian are assessed by examining the behaviour of the higher moments as functions of the lower ones. Spectra and the second moment are compared with empirical and theoretical scaling laws and some anomalies are apparent. In particular, even at the highest Reynolds number, the spectrum does not show a self-similar range of wavenumbers in which the spectral density is proportional to the inverse streamwise wavenumber. Thus such a range does not attract any special significance and does not involve a universal constant

Further observations on the mean velocity distribution in fully developed pipe flow

The measurements by Zagarola & Smits (1998) of mean velocity profiles in fully developed turbulent pipe flow are repeated using a smaller Pitot probe to reduce the uncertainties due to velocity gradient corrections. A new static pressure correction (McKeon & Smits 2002) is used in analysing all data and leads to significant differences from the Zagarola & Smits conclusions. The results confirm the presence of a power-law region near the wall and, for Reynolds numbers greater than 230×10^3 (R+ >5×10^3), a logarithmic region further out, but the limits of these regions and some of the constants differ from those reported by Zagarola & Smits. In particular, the log law is found for 600<y+ <0.12R+ (instead of 600<y+ <0.07R+), and the von Kármán constant κ, the additive constant B for the log law using inner flow scaling, and the additive constant B∗ for the log law using outer scaling are found to be 0.421 ± 0.002, 5.60 ± 0.08 and 1.20 ± 0.10, respectively, with 95% confidence level (compared with 0.436±0.002, 6.15±0.08, and 1.51±0.03 found by Zagarola & Smits). The data also confirm that the pipe flow data for ReD ≤ 13.6×10^6 (as a minimum) are not affected by surface roughness

The response of hot wires in high Reynolds-number turbulent pipe flow

Issues concerning the accuracy of hot-wire measurements in turbulent pipe flow are addressed for pipe Reynolds numbers up to 6 × 106 and hot-wire Reynolds numbers up to Rew ap 250. These include the optimization of spatial and temporal resolution and the associated feature of signal-to-noise ratio. Very high wire Reynolds numbers enable the use of wires with reduced length-to-diameter ratios compared to those typical of atmospheric conditions owing to increased wire Nusselt numbers. Simulation of the steady-state heat balance for the wire and the unetched portion of wire are used to assess static end-conduction effects: they are used to calculate wire Biot numbers, \sqrt{c_0}l , and fractional end-conduction losses, σ, which confirm the 'conduction-only' theory described by Corrsin. They show that, at Rew ap 250, the wire length-to-diameter ratio can be reduced to about 50, while keeping \sqrt{c_0}l\gt3 and σ < 7% in common with accepted limits at Rew ap 3. It is shown that these limits depend additionally on the choice of wire material and the length of unetched wire. The dynamic effects of end-cooling are also assessed using the conduction-only theory

Longitudinal spin-relaxation in nitrogen-vacancy centers in electron irradiated diamond

We present systematic measurements of longitudinal relaxation rates ($1/T_1$) of spin polarization in the ground state of the nitrogen-vacancy (NV$^-$) color center in synthetic diamond as a function of NV$^-$ concentration and magnetic field $B$. NV$^-$ centers were created by irradiating a Type 1b single-crystal diamond along the [100] axis with 200 keV electrons from a transmission electron microscope with varying doses to achieve spots of different NV$^-$ center concentrations. Values of ($1/T_1$) were measured for each spot as a function of $B$.Comment: 4 pages, 8 figure

The Primordial Abundance of He4: An Update

We include new data in an updated analysis of helium in low metallicity extragalactic HII regions with the goal of deriving the primordial abundance of He4 (Y_P). We show that the new observations of Izotov et al (ITL) are consistent with previous data. However they should not be taken in isolation to determine (Y_P) due to the lack of sufficiently low metallicity points. We use the extant data in a semi-empirical approach to bounding the size of possible systematic uncertainties in the determination of (Y_P). Our best estimate for the primordial abundance of He4 assuming a linear relation between He4 and O/H is Y_P = 0.230 \pm 0.003 (stat) based on the subset of HII regions with the lowest metallicity; for our full data set we find Y_P = 0.234 \pm 0.002 (stat). Both values are entirely consistent with our previous results. We discuss the implications of these values for standard big bang nucleosynthesis (SBBN), particularly in the context of recent measurements of deuterium in high redshift, low metallicity QSO absorption-line systems.Comment: 26 pages, latex, 6 ps figure

The He abundance in the metal-deficient blue compact dwarf galaxies Tol 1214-277 and Tol 65

We present high-quality Keck telescope spectroscopic observations of the two metal-deficient blue compact dwarf (BCD) galaxies Tol 1214-277 and Tol 65. These data are used to derive the heavy-element and helium abundances. We find that the oxygen abundances in Tol 1214-277 and Tol 65 are the same, 12+logO/H=7.54+/-0.01, or Zsun/24, despite the different ionization conditions in these galaxies. The nitrogen-to-oxygen abundance ratio in both galaxies is logN/O=-1.64+/-0.02 and lies in the narrow range found for the other most metal-deficient BCDs. We use the five strongest HeI emission lines 3889, 4471, 5876, 6678 and 7065, to correct self-consistently their intensities for collisional and fluorescent enhancement mechanisms and to derive the He abundance. Underlying stellar absorption is found to be important for the HeI 4471 emission line in both galaxies, being larger in Tol 65. The weighted He mass fractions in Tol 1214-277 and Tol 65 are respectively Y=0.2458+/-0.0039 and 0.2410+/-0.0050 when the three HeI emission lines, 4471, 5876 and 6678, are used, and are, respectively, 0.2466+/-0.0043 and 0.2463+/-0.0057 when the HeI 4471 emission line is excluded. These values are in very good agreement with recent measurements of the He mass fraction in others of the most metal-deficient BCDs by Izotov and coworkers. We find that the combined effect of the systematic uncertainties due to the underlying HeI stellar absorption lines, ionization and temperature structure of the HII region and collisional excitation of the hydrogen emission lines is likely small, not exceeding ~2% (the error is 2sigma). Our results support the validity of the standard big bang model of nucleosynthesis.Comment: 22 pages, 3 Postscript figures, accepted for publication in the Astrophysical Journa

Radiation-Resistant Solar Cells - A Panel Discussion

Radiation resistant silicon cells for solar energy conversio