Power Velocity Profile Research Articles

Assessing theoretical flow velocity profile and resistance in gravel bed rivers by field measurements

Previous studies showed that integrating a power velocity profile, deduced applying dimensional analysis and the incomplete self-similarity condition, the flow resistance equation for open channel flow can be obtained. At first, in this paper the relationship between the Γ function of the power velocity profile, the channel slope and the Froude number, which was already empirically introduced in a previous paper, is now theoretically deduced. Then this relationship is calibrated using the field measurements of flow velocity, water depth and bed slope carried out in 101 reaches of gravel bed rivers available by literature. The proposed relationship for estimating Γ function and the theoretical flow resistance equation are also tested by an independent dataset of 104 reaches of some gravel bed rivers (Fiumare) in Calabria region. Finally, the theoretically-based relationship for estimating the Γ function is calibrated by the overall available database (205 reaches). In this way the three coefficients of the theoretically based Γ function are estimated for a wide range of slopes (0.1%-6.19%) and hydraulic conditions (Froude number values ranging from 0.08 to 1.25). In conclusion, the analysis shows that the Darcy-Weisbach friction factor for gravel bed rivers can be accurately estimated by the approach based on a power-velocity profile and the theoretically-based relationship proposed for estimating Γ function. The analysis also points out a performance in estimating mean flow velocity better than that obtained in a previous study carried out by the authors.

Testing a new rill flow resistance approach using the Water Erosion Prediction Project experimental database

AbstractIn this paper, a recently theoretically deduced rill flow resistance equation, based on a power‐velocity profile, was tested using the Water Erosion Prediction Project database. This database includes measurements of flow velocity, water depth, cross section area, wetted perimeter, and bed slope that were made in rills shaped on experimental sites distributed across the continental United States. In particular, three different experimental conditions (only rainfall, only flow, and rain with flow) were examined, and for each condition, the theoretically based relationship for estimating the Γ function of the power velocity profile was calibrated. The results established that (a) the Darcy‐Weisbach friction factor can be accurately estimated using the proposed theoretical approach, and (b) the flow resistance increases with the effect of rainfall impact.

Comment on “Rill erosion processes on steep colluvial deposit slope under heavy rainfall in flume experiments with artificial rain by F. Jiang et al.”

Since rill flows are characterized by small water depths and steeply sloping channels, the corresponding hydraulic conditions are very different to those which are typically found in channels of streams and rivers. Furthermore, limited information is currently available on the effect of rainfall on flow resistance. The objective of this comment was to investigate the applicability of a recently theoretically deduced rill flow resistance equation, based on a power-velocity profile, using measurements carried out by Jiang et al. for both different slope steepness conditions and rainfall intensity. The relationship between the velocity profile parameter Γ, the channel slope and the flow Froude number was calibrated using the data by Jiang et al. The theoretical approach and the measurements carried out in the investigated conditions allowed to state that a) the Darcy-Weisbach friction factor can be accurately estimated using the proposed theoretical approach, b) the data were supportive of the slope independence hypothesis of rill velocity stated by Govers and c) the Darcy-Weisbach friction factor varies with rainfall intensity.

Experiments for testing soil texture effects on flow resistance in mobile bed rills

In this paper a recently theoretically deduced rill flow resistance equation, based on a power-velocity profile, was tested experimentally on plots of varying slopes and soil texture in which mobile bed rills are incised. Measurements of flow velocity, water depth, cross section area, wetted perimeter and bed slope conducted in rill reaches incised on experimental plots, having different slope values (9, 14, 22, 24 and 26%) and soil texture (clay fraction ranging from 42 to 73%), and literature data were used to calibrate the flow resistance equation. In particular, the relationship between the velocity profile parameter Γ, the channel slope, the flow Froude number and texture fractions was firstly calibrated using 147 rill reach data. Then this relationship was tested using 126 measurements carried out with soils having different texture (percentage of clay ranging from 9.6 to 73%) and slopes (6.9%–26%). The measurements allowed to establish that a) the Darcy-Weisbach friction factor can be accurately estimated using the proposed theoretical approach, and b) the data were supportive of the soil texture influence on rill velocity and flow resistance.

Assessing flow resistance in gravel bed channels by dimensional analysis and self-similarity

In this paper a new flow resistance equation for open channel flow, based on the integration of a power velocity profile, was tested for gravel bed channels. First this flow resistance equation, theoretically deduced by dimensional analysis and incomplete self-similarity condition, was reported. Then a relationship between the Γ function of the velocity profile, the channel slope and the Froude number was calibrated by the available laboratory measurements of flow velocity, water depth and bed slope carried out in 416 flume experimental runs with a gravel bed. Then the relationship for estimating Γ function and the theoretical resistance equation was tested by 83 independent flume measurements. The analysis also showed that the proposed flow resistance equation allows an estimate of the Darcy-Weisbach friction factor which is more reliable and accurate than that obtained by a semi-logarithmic flow resistance law or a variable-power resistance equation, calibrated with the same gravel bed measurements. For testing the applicability of the proposed Γ function (Eq. (17)), whose coefficients were estimated by flume measurements, available fields measurements were used. The analysis demonstrated that a scale factor (equal to 0.7611) is necessary to convert Γ values obtained by flume measurements into those corresponding to gravel bed rivers. The similitude between flow resistance in a gravel bed flume and in a gravel bed river is governed by the Γ function and a scale factor, equal to 1.6, is required to upscale the Darcy-Weisbach friction factor values obtained by flume measurements to the river case. In conclusion, the analysis showed that the Darcy-Weisbach friction factor for gravel bed channels can be accurately estimated by the proposed theoretical approach based on a power-velocity profile.

Flow resistance equation for rills

AbstractIn this paper, a new flow resistance equation for rill flow was deduced applying dimensional analysis and self‐similarity theory. At first, the incomplete self‐similarity hypothesis was used for establishing the flow velocity distribution whose integration gives the theoretical expression of the Darcy–Weisbach friction factor. Then the deduced theoretical resistance equation was tested by some measurements of flow velocity, water depth, cross section area, wetted perimeter, and bed slope carried out in 106 reaches of some rills shaped on an experimental plot. A relationship between the velocity profile, the channel slope, and the flow Froude number was also established. The analysis showed that the Darcy–Weisbach friction factor can be accurately estimated by the proposed theoretical approach based on a power–velocity profile.

Flow and Heat Transfer in an Industrial Rotor-Stator Rim Sealing Cavity

Flow and heat transfer in the row-1 upstream rotor-stator disk cavity of a large 3600-rpm industrial gas turbine was investigated using an integrated approach. A two dimensional axisymmetric transient thermal analysis using aeroengine-based correlations was performed to predict the steady-state metal temperatures and hot running seal clearances at ISO rated power condition. The cooling mass flow and the flow pattern assumption for the thermal model were obtained from the steady-state two dimensional axisymmetric CFD study. The CFD model with wall heat transfer was validated using cavity steady-state air temperatures and static pressures measured at inlet to the labyrinth seal and four cavity radial positions in an engine test which included the mean annulus static pressure at hub radius. The predicted wall temperature distribution from the matched thermal model was used in the CFD model by incorporating wall temperature curve-fit polynomial functions. Results indicate that although the high rim seal effectiveness prevents ingestion from entering the cavity, the disk pumping flow draws air from within the cavity to satisfy entrainment leading to an inflow along the stator. The supplied cooling flow exceeds the minimum sealing flow predicted from both the rotational Reynolds-number-based correlation and the annulus Reynolds number correlation. However, the minimum disk pumping flow was found to be based on a modified entrainment expression with a turbulent flow parameter of 0.08. The predicted coefficient of discharge (Cd) of the industrial labyrinth seal from CFD was confirmed by modifying the carryover effect of a correlation reported recently in the literature. Moreover, the relative effects of seal windage and heat transfer were obtained and it was found that contrary to what was expected, the universal windage correlation was more applicable than the aeroengine-based labyrinth seal windage correlation. The CFD predicted disk heat flux profile showed reasonably good agreement with the free disk calculated heat flux. The irregular cavity shape and high rotational Reynolds number (in the order of 7×107) leads to entrance effects that produce a thicker turbulent boundary layer profile compared to that predicted by the 1/7 power velocity profile assumption.

Applying Hypothesis of Self-Similarity for Flow-Resistance Law of Small-Diameter Plastic Pipes

In this paper the writer reports the results of an investigation carried out to test the applicability of the self-similarity hypothesis for determining the flow-resistance law in small-diameter plastic pipes. The incomplete self-similarity (ISS) hypothesis is applied for establishing both the flow-resistance law and the velocity distribution. The analysis shows that the head loss per unit length can be accurately estimated using a theoretical approach based on the ISS hypothesis for the velocity profile in a circular smooth pipe. A new relationship between the Γ coefficient of the power-velocity profile and the flow Reynolds number, based on previous measurements carried out in plastic polyethylene (PE) pipes with nominal diameter equal to 16, 20, and 25 mm and for flow Reynolds numbers ranging from 3,037 to 36,112, is also established.

Effects of Nonuniform Surface Heat Flux and Uniform Volumetric Heating on Blanket Design for Fusion Reactors

An analytical solution for the temperature profile and film temperature drop for fully-developed, laminar flow in a circular tube is provided. The surface heat flux varies circcimferentally but is constant along the axis of the tube. The volulmetric heat generation is uniform in the fluid. The fully developed laminar velocity profile is approximated by a power velocity profile to represent the flattening effect of a perpendicular magnetic field when the coolant is electrivally conductive. The presence of volumetric heat generation in the fluid adds another component to the film temperature drop to that due to the surface heat flux. The reduction of the boundary layer thickness by a perpendicular magnetic field reduces both of these two film temperature drops. A strong perpendicular magnetic field can reduce the film termperatiure drop by a factor of two if the fluid is electrically conducting. The effect of perpendicualr magnetic field )or the flatness of the velocity profile) is less pronounced on teh film termperature drop due to nonuniform surfacae heat flux than on that due to uniform surface heat flux. An example is provided to show the relative effects on these two film temperd