Commercial Steel Pipe Research Articles

Application of maximum statistical entropy in formulating a non-gaussian probability density function in flow uncertainty analysis with prior measurement knowledge

In mechanical, civil and chemical engineering systems the accuracies of flow measurement instruments is conventionally specified by certified measurement capabilities (CMCs) that are symmetric, however it is physically possible for some flow instruments and equipment to exhibit asymmetric non-Gaussian behaviour. In this paper the influence of non-Gaussian uncertainties is investigated using direct Monte Carlo simulations to construct a probability density function (PDF) using representative non-Gaussian surface roughness data for a commercial steel pipe friction factor. Actual PDF results are compared and contrasted with a symmetric Gaussian PDF, and reveal inconsistencies in the statistical distributions that cannot be neglected in high accuracy flow measurements. The non-Gaussian PDF is visualized with a kernel density estimate (KDE) scheme to infer an initial qualitative shape of the actual PDF using the approximate locations of the normalized peaks as a initial metrologist estimate of the measurement density. This is then utilized as inputs in a maximum statistical entropy functional to optimize the actual non-Gaussian PDF using a nonlinear optimization of Lagrange multipliers for a mathematically unique PDE. Novelties in the present study is that a new methodology has been developed for statistical sampling from non-monotonic non-Gaussian distributions with accompanying Python and Matlab/GNU Octave computer codes, and a new methodology for utilizing metrologist's expert prior knowledge of PDF peaks and locations for constructing an a priori estimate of the shape of unknown density have been incorporated into the maximum statistical entropy nonlinear optimization problem for a faster and more efficient approach for generating statistical information and insights in constructing high accuracy non-Gaussian PDFs of real world messy engineering measurements.

Computational parametric analysis of the design of cross-flow turbines under constraints

Abstract The cross-flow turbine is an attractive technology for small-scale hydropower generation thanks to its low capital cost and relatively high efficiency even under partial discharge operating conditions. It has been proposed that this kind of turbine can be manufactured from standard steel pipe sections given its simple geometry, an alternative that would further decrease the turbine’s capital cost compared to highly engineered cross-flow designs. This article explores the trade-offs encountered during the design of cross-flow turbines under the constrains imposed by the discrete set of dimensions available for commercial steel pipes. First, the computational model is presented, analyzed in terms of its convergence behavior, and validated with experimental data. Then, a parametric analysis is performed to understand the relative importance of the design variables and their optimum value in regard to the turbine efficiency. Based on the design guidelines derived from the parametric analysis, an example cross-flow turbine design is presented and thoroughly characterized, demonstrating that it is possible to engineer a cross-flow turbine of competitive efficiency out of commercial steel pipes. These guidelines may encourage the use of cross-flow turbines as an appropriate technology for off-grid regions.

Experimental Investigation Into the Relationship Between the Roughness Height in Use With Nikuradse or Colebrook Roughness Functions and the Internal Wall Roughness Profile for Commercial Steel Pipes

The relationships between the sand grain roughness height (ks) in use with Nikuradse or Colebrook correlations for the roughness function (RF) and the internal pipe wall roughness element described by the root-mean-square (RMS) of the roughness profile (Rq) for turbulent flow in pipes are experimentally examined. Flow tests were conducted on a total of 13 commercial steel pipes of two sizes: 168.3 mm and 114.3 mm outer diameter (OD). The aim was to provide further insight into relationship between ks and Rq, for use with either RF correlations. The tests were conducted on high-pressure pipeline quality natural gas in the range of Reynolds number (based on pipe internal diameter) of 9 × 106–16 × 106. For commercial carbon steel pipes, the relationship between ks and Rq was found in the form ks=1.306 Rq+0.078 Rq2 and ks=2.294 Rq (both ks and Rq in μm), for use with Colebrook and Nikuradse RF correlations, respectively. These correlations cover a wide range of Rq from 2.7 μm to 12.5 μm which is typically found in commercial carbon steel pipes. For stainless steel (SS) pipes, preliminary results indicate that other surface roughness profile parameters need to be employed to better define the values of ks for these types of commercial steel pipes.

Pipe Sizing of District Cooling Distribution Network Using Implicit Colebrook-White Equation

An implicit solution of Colebrook-White equation was used in calculating the friction factor for commercial steel pipes using Newton-Raphson method with Reynolds number ranging from 4.0 × 103to 1.3 × 107. Initial value for iterative friction factor estimation was based on expanded form of Colebrook-White equation for larger values of Reynolds number with tolerance value of 1.0 × 10-8. Numerical results were compared with known explicit solutions and iterative procedure proposed by Lester in which, their mean difference, root-mean square deviation, mean relative error and correlation coefficient were evaluated. Correlation coefficients equal to unity and overall mean relative error of 4.821 × 10-8were achieved for all fifteen (15) pipe cases with nominal diameters ranging from 100 mm to 1,500 mm when compared with iterative solution suggested by Lester. Student’s t-test for paired data was also used which yielded a calculated t-value of -5.406 × 10-4. Combining the piping network design criteria with the logical structure of friction factor calculation determines the pipe size of distribution network and defines the boundaries of chilled-water velocities at different pressure drop limits as a function of commercial steel pipe diameter according to ANSI B36.1.

Roughness effects of commercial steel pipe in turbulent flow: universal scaling

The mean turbulent flow over a transitional rough commercial steel pipe is considered in terms of alternate inner roughness variables. The matching of inner layer and outer layer in the overlap region leads to the universal log laws for velocity profile and friction factor, explicitly independent of surface roughness of all kinds. The roughness function, for commercial steel pipe differs from inflectional (sand grain) roughness. The traditional wall law and friction factor depends on type of surface roughness.

Control and Management of Particulate Emissions using Improved Reverse Pulse-Jet Cleaning Systems

Abstract The control of particulate emissions from various applications such as power generation, cement plants, minerals processing etc. is essential to meet government regulatory standards. Filter bags and cartridge elements are typical common mediums used to separate particulates. A common method used to clean filters in the extraction of particulate matter from a fluid stream, is Reverse Pulse-Jet (RPJ) cleaning systems. The operation of the RPJ cleaning system relies on stored energy in the form of compressed gas, which is usually air. In this paper, the design and application of an efficient cleaning system to minimise the use of compressed gas to achieve the required filter cleaning is described. In an RPJ cleaning system, a high-energy pulse of compressed gas is delivered into the filter medium to rapidly increase the internal pressure and, in the case of filter bags, accelerate the filter material to force the break-up of dust cakes that form on the filter surface. One key component of the cleaning system is an extremely fast acting valve that controls the flow of the high pressure gas, the other is the blowtube. The blowtube is a commercial steel pipe with a number of outlet orifices distributed along the longitudinal axis and centrally located above each filter. The cleaning system improvements have been achieved by advances in valve and blowtube design that have enabled increases in the peak pressures developed in the filters whilst minimising the response rate of the system to decrease the air consumption. The store of potential energy must be effectively and efficiently converted into kinetic energy to utilise the available energy to build pressure in the filter. Thus, by improving the RPJ cleaning system the operating costs associated with the compressors are reduced thereby decreasing the environmental impact of operating filter cleaning systems, to more efficiently remove particulate matter from fluid streams.

Flow in a commercial steel pipe

Mean flow measurements are obtained in a commercial steel pipe with krms/D = 1/26 000, where krms is the roughness height and D the pipe diameter, covering the smooth, transitionally rough, and fully rough regimes. The results indicate a transition from smooth to rough flow that is much more abrupt than the Colebrook transitional roughness function suggests. The equivalent sandgrain roughness was found to be 1.6 times the r.m.s. roughness height, in sharp contrast to the value of 3.0 to 5.0 that is commonly used. The difference amounts to a reduction in pressure drop for a given flow rate of at least 13% in the fully rough regime. The mean velocity profiles support Townsend's similarity hypothesis for flow over rough surfaces.

Unsteady state mass transfer coefficients controlling steel pipe corrosion under isothermal flow conditions

Corrosion tests of commercial steel pipe in aerated natural water under variable flow isothermal conditions were made by weight loss determinations over periods up to 210 days. The porosity, density, and the average thickness of the corrosion product layer were determined. Friction coefficients were evaluated through precise pressure drop measurements as a function of exposure time for the various flow rates (Reynolds number range 4000–25,000). The corrosion mechanism was analysed as a mass transfer operation by considering all the plausible unsteady state process characteristics, involving growth of corrosion product on the metal surface and change of surface roughness. The general mathematical model postulated from that analysis fitted the experimental data with acceptable precision. The model permitted, using corrosion data only, the prediction of values for the porosity and friction coefficient which were in good agreement with the experimental data. The average thickness of the damped turbulence layer for the smooth pipe was also calculated from the corrosion data, using the same model, and showed an excellent agreement with values estimated from usual hydrodynamic relationships. The effect of the surface roughness on the mass transfer coefficients in the damped turbulence layer, K L, and in the corrosion product layer, K s, were examined in detail. It was found that K L controls the overall mass transfer process for the time range and flow rate range examined.

Drag reduction and velocity distribution in developing pipe flow

Drag reduction and mean velocity measurements obtained for polymer injection into a developing axisymetric boundary layer in the inlet region of a pipe are reported. Experiments were conducted in a 12-in. diam commercial steel pipe. Concentrated solutions of Polyox WSR 301 were injected into the pipe at 3.5 diam for the pipe entrance. Injection concentrations varied from 100 ppm to 2400 ppm with Reynolds number varying from 2.8x10 to fifth power to 3.0x10 to the sixth power. Data for the inlet and fully developed regions of this study indicate that high drag reductions can be obtained in the inlet region. Drag reduction was found to depend on polymer flow rate, wall shear stress, and distance, but not to depend significantly on injection velocity or injection concentration. A four-layer mean velocity model is shown to describe the velocity profile in the developing polymeric region. The polymer interactive layer is dependent on flow and polymer characteristics. The upward shift of the turbulent layer is directly related to the dimensionless drag reduction parameter (V/u)(hu sub p/hu sub w). The velocity profile in the outer flow of the developing region is described by a velocity defect law with a constant profile parameter.