Solution of 3-dimensional time-dependent viscous flows. Part 2: Development of the computer code

There is considerable interest in developing a numerical scheme for solving the time dependent viscous compressible three dimensional flow equations to aid in the design of helicopter rotors. The development of a computer code to solve a three dimensional unsteady approximate form of the Navier-Stokes equations employing a linearized block emplicit technique in conjunction with a QR operator scheme is described. Results of calculations of several Cartesian test cases are presented. The computer code can be applied to more complex flow fields such as these encountered on rotating airfoils

Solution of 3-dimensional time-dependent viscous flows. Part 3: Application to turbulent and unsteady flows

A numerical scheme is developed for solving the time dependent, three dimensional compressible viscous flow equations to be used as an aid in the design of helicopter rotors. In order to further investigate the numerical procedure, the computer code developed to solve an approximate form of the three dimensional unsteady Navier-Stokes equations employing a linearized block implicit technique in conjunction with a QR operator scheme is tested. Results of calculations are presented for several two dimensional boundary layer flows including steady turbulent and unsteady laminar cases. A comparison of fourth order and second order solutions indicate that increased accuracy can be obtained without any significant increases in cost (run time). The results of the computations also indicate that the computer code can be applied to more complex flows such as those encountered on rotating airfoils. The geometry of a symmetric NACA four digit airfoil is considered and the appropriate geometrical properties are computed

Influence of large-scale motion on turbulent transport for confined coaxial jets. Volume 2: Navier-Stokes calculations of swirling and nonswirling confined coaxial jets

The existence of large scale coherent structures in turbulent shear flows has been well documented. Discrepancies between experimental and computational data suggest a necessity to understand the roles they play in mass and momentum transport. Using conditional sampling and averaging on coincident two-component velocity and concentration velocity experimental data for swirling and nonswirling coaxial jets, triggers for identifying the structures were examined. Concentration fluctuation was found to be an adequate trigger or indicator for the concentration-velocity data, but no suitable detector was located for the two-component velocity data. The large scale structures are found in the region where the largest discrepancies exist between model and experiment. The traditional gradient transport model does not fit in this region as a result of these structures. The large scale motion was found to be responsible for a large percentage of the axial mass transport. The large scale structures were found to convect downstream at approximately the mean velocity of the overall flow in the axial direction. The radial mean velocity of the structures was found to be substantially greater than that of the overall flow

Transverse effects in multifrequency Raman generation

The theory of ultrabroadband multifrequency Raman generation is extended, for the first time, to allow for beam-propagation effects in one and two transverse dimensions. We show that a complex transverse structure develops even when diffraction is neglected. In the general case, we examine how the ultrabroadband multifrequency Raman generation process is affected by the intensity, phase quality, and width of the input beams, and by the length of the Raman medium. The evolution of power spectra, intensity profiles, and global characteristics of the multifrequency beams are investigated and explained. In the two-dimensional transverse case, bandwidths comparable to the optical carrier frequency, spanning the whole visible spectrum and beyond, are still achievable

Calculation of two- and three-dimensional transonic cascade flow field using the Navier-Stokes equations

A Navier-Stokes analysis employing the time-dependent Linearized Block Implicit scheme (LBI) was applied to two-dimensional and three-dimensional transonic turbulent cascade flows. In general, the geometrical configuration of the turbine blade impacts both the grid construction procedure and the implementation of the numerical algorithm. Since modern turbine blades of interest are characterized by very blunt leading edges, rounded trailing edges and high stacking angles, a robust grid construction procedure is required that can accommodate the severe body shape while resolving regions of large flow gradients. A constructive O-type grid generation technique, suitable for cascades with rounded trailing edges, was developed and used to construct the C3X turbine cascade coordinate grid. Two-dimensional calculations were performed employing the Navier-Stokes procedure for the C3X turbine cascade, and the predicted pressure coefficients and heat transfer rates were compared with the experimental data. Three-dimensional Navier-Stokes calculations were also performed

Costs of Chronic Waterborne Zinc Exposure and the Consequences of Zinc Acclimation on the Gill/Zinc Interactions of Rainbow Trout in Hard and Soft Water

Juvenile rainbow trout were exposed to zinc in both moderately hard water (hardness 5 120 mg CaCO3/L, pH = 8.0, Zn = 150 μg/L or 450 μg/L) and soft water (hardness = 20 mg CaCO3/L, pH = 7.2, Zn = 50 μg/L or 120 μg/L) for 30 d. Only the 450 mg/L zinc–exposed fish experienced significant mortality (24% in the first 2 d). Zinc exposure caused no effect on growth rate, but growth affected tissue zinc levels. Whole body zinc levels were elevated, but gills and liver showed no consistent increases relative to controls over the 30-d. Therefore, tissue zinc residues were not a good indicator of chronic zinc exposure. After the 30-d exposure, physiological function tests were performed. Zinc was 5.4 times more toxic in soft water (control 96 h LC50s in hard and soft water were 869 μg/L and 162 μg/L, respectively). All zinc-exposed trout had acclimated to the metal, as seen by an increase in the LC50 of 2.2 to 3.9 times over that seen in control fish. Physiological costs related to acclimation appeared to be few. Zinc exposure had no effect on whole body Ca2+ or Na+ levels, on resting or routine metabolic rates, or on fixed velocity sprint performance. However, critical swimming speed (UCrit) was significantly reduced in zinc-exposed fish, an effect that persisted in zinc-free water. Using radioisotopic techniques to distinguish new zinc incorporation, the gills were found to possess two zinc pools: a fast turnover pool (T1/2 = 3–4 h) and a slow turnover pool (T1/2 = days to months). The fast pool was much larger in soft water than in hard water, but at most it accounted for \u3c3.5% of the zinc content of the gills. The size of the slow pool was unknown, but its loading rate was faster in soft water. Chronic zinc exposure was found to increase the size of the fast pool and to increase the loading rate of the slow pool

Divergence in seasonal hydrology across northern Eurasia: Emerging trends and water cycle linkages

Discharge from large Eurasia rivers increased during the 20th century, yet much remains unknown regarding details of this increasing freshwater flux. Here, for the three largest Eurasian basins (the Ob, Yenisei, and Lena) we examine the nature of annual and seasonal discharge trends by investigating the flow changes along with those for precipitation, snow depth, and snow water equivalent. On the basis of a multiperiod trend analysis and examination of station data, we propose two characteristic regimes to explain the long‐term discharge increase from these large Eurasian rivers. Over the early decades from approximately 1936 to 1965, annual precipitation correlates well with annual discharge, and positive discharge trends are concurrent with summer/fall discharge increases. The latter decades were marked by a divergence between winter/spring flows, which increased, amid summer/fall discharge declines. A comparison of cold season precipitation (CSP) and spring discharge trends across subbasins of the Ob, Yenisei, and Lena shows limited agreement with one precipitation data set but good agreement (R2 \u3e 0.90) when a second is used. While natural variability in the Arctic system tends to mask these emerging trends, spatial and temporal changes can generally be characterized by increased solid precipitation, primarily to the north, along with a drier hydrography during the warm season

Development of a three-dimensional supersonic inlet flow analysis

A method for computing three dimensional flow in supersonic inlets is described. An approximate set of governing equations is given for viscous flows which have a primary flow direction. The governing equations are written in general orthogonal coordinates. These equations are modified in the subsonic region of the flow to prevent the phenomenon of branching. Results are presented for the two sample cases: a Mach number equals 2.5 flow in a square duct, and a Mach number equals 3.0 flow in a research jet engine inlet. In the latter case the computed results are compared with the experimental data. A users' manual is included