Static pressure correction in high Reynolds number fully developed turbulent pipe flow

Measurements are reported of the error in wall static pressure reading due to the finite size of the pressure tapping. The experiments were performed in incompressible turbulent pipe flow over a wide range of Reynolds numbers, and the results indicate that the correction term (as a fraction of the wall stress) continues to increase as the hole Reynolds number $d^+=u_\tau d/\nu$ increases, contrary to previous studies. For small holes relative to the pipe diameter the results follow a single curve, but for larger holes the data diverge from this universal behaviour at a point that depends on the ratio of the hole diameter to the pipe diameter

Turbulence modeling in shock wave/turbulent boundary layer interactions

The research performed was an experimental program to help develop turbulence models for shock wave boundary layer interactions. The measurements were taken in a Mach 3, 16 deg compression corner interaction, at a unit Reynolds number of 63 x 10(exp 6)/m. The data consisted of heat transfer data taken upstream and downstream of the interaction, hot wire measurements of the instantaneous temperature and velocity fluctuations to verify the Strong Reynolds Analogy, and single- and double-pulsed Rayleigh scattering images to study the development of the instantaneous shock/turbulence interaction

The dynamics and control of fluctuating pressure loads in the reattachment region of a supersonic free shear layer

The primary aim is to investigate the mechanisms which cause the unsteady wall-pressure fluctuations in shock wave turbulent shear layer interactions. The secondary aim is to find means to reduce the magnitude of the fluctuating pressure loads by controlling the unsteady shock motion. The particular flow proposed for study is the unsteady shock wave interaction formed in the reattachment zone of a separated supersonic flow. Similar flows are encountered in many practical situations, and they are associated with high levels of fluctuating wall pressure. Wall pressure fluctuations were measured in the reattachment region of the supersonic free shear layer. The free shear layer was formed by the separation of a Mach 2.9 turbulent boundary layer from a backward facing step. Reattachment occurred on a 20 deg ramp. By adjusting the position of the ramp, the base pressure was set equal to the freestream pressure, and the free shear layer formed in the absence of a separation shock. An array of flush-mounted, miniature, high-frequency pressure transducers was used to make multichannel measurements of the fluctuating wall pressure in the vicinity of the reattachment region. Contrary to previous observations of this flow, the reattachment region was found to be highly unsteady, and the pressure fluctuations were found to be significant. The overall behavior of the wall pressure loading is similar in scale and magnitude to the unsteadiness of the wall pressure field in compression ramp flows at the same Mach number. Rayleigh scattering was used to visualize the instantaneous shock structure in the streamwise and spanwise direction. Spanwise wrinkles on the order of half the boundary layer thickness were observed

A new friction factor relationship for fully developed pipe flow

The friction factor relationship for high-Reynolds-number fully developed turbulent pipe flow is investigated using two sets of data from the Princeton Superpipe in the range 31×10^3 ≤ ReD ≤ 35×10^6. The constants of Prandtl’s ‘universal’ friction factor relationship are shown to be accurate over only a limited Reynolds-number range and unsuitable for extrapolation to high Reynolds numbers. New constants, based on a logarithmic overlap in the mean velocity, are found to represent the high-Reynolds-number data to within 0.5%, and yield a value for the von Kármán constant that is consistent with the mean velocity profiles themselves. The use of a generalized logarithmic law in the mean velocity is also examined. A general friction factor relationship is proposed that predicts all the data to within 1.4% and agrees with the Blasius relationship for low Reynolds numbers to within 2.0%

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

Adaptation of WASH Services Delivery to Climate Change and Other Sources of Risk and Uncertainty

This report urges WASH sector practitioners to take more seriously the threat of climate change and the consequences it could have on their work. By considering climate change within a risk and uncertainty framework, the field can use the multitude of approaches laid out here to adequately protect itself against a range of direct and indirect impacts. Eleven methods and tools for this specific type of risk management are described, including practical advice on how to implement them successfully

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

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

Study of the structure of turbulent shear flows at supersonic speeds and high Reynolds number

A major effort to improve the accuracies of turbulence measurement techniques is described including the development and testing of constant temperature hot-wire anemometers which automatically compensate for frequency responses. Calibration and data acquisition techniques for normal and inclined wires operated in the constant temperature mode, flow geometries, and physical models to explain the observed behavior of flows are discussed, as well as cooperation with computational groups in the calculation of compression corner flows

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