Pipe Of Circular Cross-section Research Articles

Investigation of the strength of a tank container during road transport

Background. Increasing the efficiency of the transport industry leads to the need to introduce modern means of transport with improved technical, economic and environmental characteristics. At present, transportation of liquid cargoes, including those in international traffic, is carried out mainly in tank containers. Therefore, in order to increase the efficiency of tank containers operation it is important to introduce designs with improved performance. Objective. Highlighting the results of improvements to the tank-container design and a study of its strength in road transport. Methods. In order to reduce the material intensity of the tank container, it is proposed to use pipes of circular cross section as frame elements and to create a boiler of composite material. Determination of pipe design parameters has been carried out by optimisation calculations according to material intensity minimum criterion. In order to define strength properties of improved tank-container design the calculation by finite element method has been made which has been implemented by SolidWorks Simulation software. Results. On the basis of the made calculations it is established that at lifting of the container for top corner fittings the maximum equivalent pressure arising in vertical racks of a skeleton are equal 133,6 MPa, and in a boiler – 121,5 MPa, that is below allowed. Under conditions of tank-container transportation by motor transport the maximum stresses in its structure are fixed at influence on it of acceleration 1,2g in a longitudinal direction on a course of movement. The maximum equivalent stresses in the frame were 202.4 MPa, and in the boiler – 122.2 MPa, i.e. do not exceed permissible values. Conclusions. The research carried out will contribute to the development of the design of modern tank container designs and improve the operational efficiency of the transport industry.

An explicit representation for mean profiles and fluxes in forced passive scalar convection

We derive explicit formulae for the mean profiles of passive scalars (either temperature or concentration of a diffusing substance), and their respective wall fluxes (either heat or mass fluxes), in forced turbulent convection, as a function of the Reynolds and Prandtl numbers. Direct numerical simulation data for turbulent flow within a smooth straight pipe of circular cross-section, at friction Reynolds number ${{Re}}_{\tau }=1140$ , in the range of Prandtl numbers from ${{Pr}}=0.00625$ to ${{Pr}}=16$ , are used to infer the proper analytical form of the eddy diffusivity. This is leveraged to derive accurate predictive formulae for the mean passive scalar profiles, and for the corresponding logarithmic offset function. Asymptotic scaling laws result for the thickness of the conductive (diffusive) layer, and for the Nusselt number, which significantly extend the predictive envelope of classical formulae.

Apparatus for calibration of fine-wire sensors at stratospheric conditions

A small-scale, open-circuit wind tunnel was developed to calibrate balloon-born fine-wire anemometers for conditions in the stratosphere. The system enables calibration of hotwire anemometers to test gases at flow velocities between 1 and 5 m/s and pressures between 550 and 5475 Pa. Using a metered inflow of test gas into a long circular cross-section pipe, a parabolic velocity profile is expected at the measurement plane for the fully-developed flow as described by Poiseuille flow theory. Traversal of a commercially available hotwire anemometer within the test section confirms the parabolic profile predicted for Poiseuille flow, with only minor deviations. In conjunction with the experimental testing, numerical simulations are performed to quantify probe support blockage effects on the velocity profile measurements. Test results validate the procedure for calibration of hotwire anemometers and development of forced convection heat transfer relations at stratospheric pressure conditions.

Prandtl number effects on passive scalars in turbulent pipe flow

We study the statistics of passive scalars (either temperature or concentration of a diffusing substance) at friction Reynolds number ${Re}_{\tau }=1140$ , for turbulent flow within a smooth straight pipe of circular cross-section, in the range of Prandtl numbers from ${Pr}=0.00625$ , to ${Pr}=16$ , using direct numerical simulations (DNS) of the Navier–Stokes equations. Whereas the organization of passive scalars is similar to the axial velocity field at ${Pr} = O(1)$ , similarity is impaired at low Prandtl number, at which the buffer-layer dynamics is filtered out, and at high Prandtl number, at which the passive scalar fluctuations become confined to the near-wall layer. The mean scalar profiles at ${Pr} \gtrsim 0.0125$ are found to exhibit logarithmic overlap layers, and universal parabolic distributions in the core part of the flow. Near-universality of the eddy diffusivity is exploited to derive accurate predictive formulas for the mean scalar profiles, and for the corresponding logarithmic offset function. Asymptotic scaling formulas are derived for the thickness of the conductive (diffusive) layer, for the peak scalar variance, and its production rate. The DNS data are leveraged to synthesize a modified form of the classical predictive formula of Kader & Yaglom (Intl J. Heat Mass Transfer, vol. 15, 1972, pp. 2329–2351), which is capable of accounting accurately for the dependence on both Reynolds and Prandtl numbers, for ${Pr} \gtrsim 0.25$ .

DNS of passive scalars in turbulent pipe flow

We study the statistics of passive scalars at $Pr=1$ , for turbulent flow within a smooth straight pipe of circular cross section up to $Re_{\tau } \approx 6000$ using direct numerical simulation (DNS) of the Navier–Stokes equations. While featuring a general organisation similar to the axial velocity field, passive scalar fields show additional energy at small wavenumbers, resulting in a higher degree of mixing and in a $k^{-4/3}$ spectral inertial range. The DNS results highlight logarithmic growth of the inner-scaled bulk and mean centreline scalar values with the friction Reynolds number, implying an estimated scalar von Kármán constant $k_{\theta } \approx 0.459$ , which also nicely fits the mean scalar profiles. The DNS data are used to synthesise a modified form of the classical predictive formula of Kader & Yaglom (Intl J. Heat Mass Transfer, vol. 15 (12), 1972, pp. 2329–2351), which points to some shortcomings of the original formulation. Universality of the mean core scalar profile in defect form is recovered, with very nearly parabolic shape. Logarithmic growth of the buffer-layer peak of the scalar variance is found in the Reynolds number range under scrutiny, which well conforms with Townsend's attached-eddy hypothesis, whose validity is also supported by the spectral maps. The behaviour of the turbulent Prandtl number shows good universality in the outer wall layer, with values $Pr_t \approx 0.84$ , as also found in previous studies, but closer to unity near the wall, where existing correlations do not reproduce the observed trends.

Investigation on the flame and explosion suppression of hydrogen/air mixtures by porous copper foams in the pipe with large aspect ratio

In this work, the flame and explosion suppression performance of copper foams with five apertures of 10 PPI, 20 PPI, 30 PPI, 40 PPI and 60 PPI were investigated. The combustion characteristics of hydrogen/air premixed gas with stoichiometric ratio were investigated under three experimental schemes. The experiments were carried out in a circular cross-sectional pipe with aspect ratio of 108. Under the influence of copper foam, there are four phases of flame propagation, namely, laminar rapid expansion, backflow, rapid turbulence and pulsation deceleration. The results show that continuous copper foam sheets with aperture of 60 PPI can effectively prevent flame from spreading to the downstream of the pipe and make flame quenching. At the same time, the phenomenon of “negative pressure suction” was observed. The upstream overpressure was reduced to 0.06 MPa and the flame velocity was 25 m/s. As the aperture of copper foam decreased, shock wave and flame velocity decreased. The process of deflagration to detonation transition was effectively inhibited. Widely spaced copper foams can effectively prevent the impact of reflected shock wave and hindrance the flame from downstream. The results can provide a significant reference for designing hydrogen flame arrestors to improve the safety of hydrogen pipeline transportations and engineering applications.

One-point statistics for turbulent pipe flow up to

We study turbulent flows in a smooth straight pipe of circular cross-section up to friction Reynolds number $({\textit {Re}}_{\tau }) \approx 6000$ using direct numerical simulation (DNS) of the Navier–Stokes equations. The DNS results highlight systematic deviations from Prandtl friction law, amounting to approximately $2\,\%$ , which would extrapolate to approximately $4\,\%$ at extreme Reynolds numbers. Data fitting of the DNS friction coefficient yields an estimated von Kármán constant $k \approx 0.387$ , which nicely fits the mean velocity profile, and which supports universality of canonical wall-bounded flows. The same constant also applies to the pipe centreline velocity, thus providing support for the claim that the asymptotic state of pipe flow at extreme Reynolds numbers should be plug flow. At the Reynolds numbers under scrutiny, no evidence for saturation of the logarithmic growth of the inner peak of the axial velocity variance is found. Although no outer peak of the velocity variance directly emerges in our DNS, we provide strong evidence that it should appear at ${\textit {Re}}_{\tau } \gtrsim 10^4$ , as a result of turbulence production exceeding dissipation over a large part of the outer wall layer, thus invalidating the classical equilibrium hypothesis.

Numerical Simulation of Acoustic Resonance Enhancement for Mean Flow Wind Energy Harvester as Well as Suppression for Pipeline

Acoustic resonance in closed side branches should be enhanced to improve the efficiency of wind energy harvesting equipment or thermo-acoustic engine. However, in gas pipeline transportation systems, this kind of acoustic resonance should be suppressed to avoid fatigue damage to the pipeline. Realizable k-ε delayed detached eddy simulations (DDES) were conducted to study the effect of different branch pipe shapes on acoustic resonance. At some flow velocities, the pressure amplitude of the simulation results is twice as large as that of the experimental results, but the simulation can accurately capture the flow velocity range where acoustic resonance occurs. The results prove the feasibility of the method of the equivalent diameter of the circular cross-section pipe and the square cross-section pipe to predict acoustic resonance. The pressure pulsation amplitude of acoustic resonance in a square cross-section pipe is significantly increased than that in a circular square cross-section pipe, indicating that the square cross-section branch configuration can be more conducive to improving the efficiency of wind energy harvesting. The influence of the angle between the branch and the main pipe on the acoustic resonance was studied for the first time, which has an obvious influence on the acoustic resonance. It is found that the design of a square wind energy harvester is better than that of a circular one; meanwhile, changing the branch angle can increase or suppress the acoustic resonance, which can improve the utilization efficiency of the acoustic resonance and provide a new method for suppressing the acoustic resonance.

Hydraulic resistances of derivation channels of hydropower facilities

Currently, many authors have studied the uniform axisymmetric pressure head laminar and turbulent movement of water in hydraulic smooth and rough (with uniform roughness) pipes of circular cross-section. The results obtained in the study of a plane-parallel turbulent flow in pressure channels allow here only to outline the structure of the corresponding dependencies and to clarify the simplest case of unpressurized fluid movement, when this movement can also be reduced to plane-parallel or, in other words, to movement in channel of infinitely large width with a flat bottom. In all other cases, the only way to solve the problem is experiment. But the possibilities of the experiment are limited, as are limited, and in a number of cases debatable, and the information accumulated to date on the uniform free-flow motion of fluid in channels of various cross-sectional shapes. The unpressurized uniform movement of fluid in channels of various cross-sectional shapes has been completely insufficiently studied. The construction of numerous free-flow watercourses, as well as machine channels of pumping stations, requires scientifically based calculation methods. For the correct establishment of hydraulic calculation methods, a sufficiently deep study of the physical essence of the phenomena occurring in the free-flow derivation channels is necessary. The extensive construction of numerous free-flow watercourses, as well as hydroelectric power plant (HPP) derivation channels, requires scientifically based calculation methods. For the correct establishment of hydraulic calculation methods, a sufficiently deep study of the physical essence of the hydraulic phenomena occurring in the free-flow derivation channels of HPPs is necessary.

Transition Problem and Localized Turbulent Structures in Pipes

In the classical experiments of O. Reynolds made in 1883 the critical value of a dimensionless parameter, named now the Reynolds number, $${\text{R}}{{{\text{e}}}_{c}} \approx 2000$$ , was determined. As this value is exceeded in a pipe of circular cross-section, a turbulent flow regime can occur. The attempts to define this value more exactly undertaken during the twentieth century have not met with success. In this study, we present a review of theoretical, experimental, and numerical investigations of flows in a round pipe at the stage of transition to turbulence performed in recent years, which make it possible to formulate a new view on the nature of laminar-turbulent transition in these flows.

Hydraulic resistances experimental and field studies of supply canals and pumping stations structures

Currently, many authors have studied the uniform axisymmetric pressure head laminar and turbulent movement of water in hydraulic smooth and rough (with uniform roughness) pipes of circular cross-section. The results obtained in the study of a plane-parallel turbulent flow in pressure canals allows here only to outline the structure of the corresponding dependencies and to clarify the simplest case of unpressurized fluid movement, when this movement can also be reduced to plane-parallel or, in other words, to movement in a canal of infinitely large width with a flat bottom. In all other cases, the only way to solve the problem is an experiment. The construction of numerous free-flow watercourses and machine canals of pumping stations requires scientifically based calculation methods.

Movement of an Open-Ended Pipe with a Soil Plug Under a Longitudinal Impact

The process of horizontal immersion into soil of an open-ended steel pipe of circular cross section containing a soil plug is under study. The effect of both single and multiple longitudinal strikes is considered. A one-dimensional mathematical model of the movement of the pipe and soil plug is proposed that takes into account changes in radial stress caused by the lateral interaction of the pipe and soil plug. In this model, the interaction of the pipe with internal and external soil is described by the law of external dry friction. The resistance of the soil in front of the pipe is taken into account by specifying viscous conditions at the pipe end. The influence of the parameters of the pipe and soil on the process of immersing an open-ended pipe into the soil is studied numerically by the finite-difference method. In addition, the results of a field experiment are given which was carried out by the authors in dense urban environment. As a result of comparing the data obtained in numerical and field experiments, it is concluded that the proposed model can be used to describe the results of field experiments.

Flow and heat transfer investigation of a circular jet issuing on different types of surfaces

In the present study, flow and heat transfer characteristics of an impinging jet issuing from a circular cross-sectional pipe on a rectangular plate, convex and concave hemispheres were investigated numerically for various Reynolds numbers and jet-to-plate distances. Steady and three-dimensional Reynolds-Averaged Navier-Stokes equations were solved iteratively utilizing finite volume method. Turbulence model assessment study reveals that the transitional Shear Stress Transport k-ω turbulence model can be used for such a problem. Regardless of the geometry of the impinging surfaces, two different flow regions were detected around y/D = 3. The first region starts from the stagnation point (y/D = 0) to the edge of the rectangular plate and hemispheres (y/D = 3). In this region, the maximum heat transfer is obtained for the jet impinging on the rectangular plate. However, in the second region that covers the wall jet zone the impinging jet on the convex hemisphere provides the maximum while the concave causes the minimum heat transfer. The most efficient jet-to-plate distance is found as H/D = 2 in the first region while heat transfer does not change with distance in the wall jet zone. It was shown that Nusselt number increases with Reynolds number when the jet impinges on the concave and convex hemispheres as observed for the impinging jet on a flat plate.

A robust optimization design method for sheet metal roll forming and its application in roll forming circular cross-section pipe

Sheet metal roll forming (SMRF) is affected by many factors, including forming speed, forming passes, roller diameter, and material properties. It is easy to produce quality defects, such as longitudinal bending, edge wave, and springback, which eventually lead to poor quality stability of SMRF. At present, SMRF design relies mainly on the experience of engineers and its technological parameters must be adjusted repeatedly through experiments, resulting in a long product design cycle and difficult quality stability control. This paper discusses a mathematical model for a robust optimization design for SMRF. Support vector machine (SVM) classification and support vector regression (SVR) are adopted to construct a model of the response surface and to separate feasible variables and infeasible variables. High-dimensional robust optimization problems in SMRF are solved. Using roll forming of a circular cross-section pipe as an example, the result shows that the roundness error standard deviation of the robust optimization design method is 62.2% less than the roundness error standard deviation of the deterministic optimization design method, along with significant improvement in reliability probability. The method is validated as effective in reducing quality defects, including longitudinal bending, edge wave, and springback. This robust optimization design method can improve the quality stability of SMRF.

РАСЧЕТ КОНСТРУКТИВНЫХ ПАРАМЕТРОВ ЗАГРУЗОЧНОГО УЗЛА ДЕЗИНТЕГРАТОРА ПРИ УСТАНОВКЕ ПАТРУБКА РЕЦИКЛА МАТЕРИАЛА

Currently, disintegrators are equipment used for grinding, mixing and activation of a number of materials. The possibility of obtaining a grinding product with a given granulometric composition is one of the advantages of disintegrators. An experimental unit with a recycling pipe is created to obtain a narrow granulometric composition of the grinding product. It provides unloading of the finished product and returning the grits for additional grinding to the chamber. The branch pipe of the recycle is a rubber-fabric pipe of circular cross-section with a radius of curvature, which ensures the movement of a two-phase medium from the discharge zone to the loading part of the disintegrator. When performing theoretical studies of the grinding process, it is necessary to coordinate the throughput of the loading unit and the node of the disintegrator recycle. In addition, the mass flow rate of the material through the feeder and the mass flow rate of the material (throughput) passing through the rows of percussion elements must be the same for the balanced operation of the disintegrator and the feeder. The mass flow capacity of the coarse material moving in the recycling pipe is determined based on the assumption of the linear nature of the change in bulk density when the material moves inside the recycling pipe. In result of theoretical researches, the analytical expression is received allowing to define a radius of a pipe of the modernized feeder proceeding from constructive and technological parameters of a disintegrator with a branch pipe of a recycle. A calculation scheme for determining the radius of the pipe of an improved disintegrator is presented. The analysis of obtained analytical expression allows to conclude that the radius of the pipe of the modernized unit is associated with the design and technological parameters of the disintegrator

Analytic representations of dissipation in partially-submerged reciprocating pipe flow

Abstract A series of analytic models are presented of a partially-submerged, straight circular cross-section pipe subjected to reciprocating flow, incorporating viscous and turbulent boundary-layer dissipation. This pipe is the most elementary paradigm for a fixed-type Oscillating Water Column (OWC), and its analysis more generally addresses one aspect of reciprocating pipe flow. The derivation of the dissipation terms in the momentum conservation equations from their origin in the Navier–Stokes equation are explicitly identified. The contribution of different damping sources to the overall energy loss is compared. The flow inside the pipe is assumed fully developed along the entire length, neglecting the effect of the flow development region. For relevance to engineering applications, a power take-off system is modelled assuming that the air compresses and expands isentropically in an air chamber at the top of the pipe. Existing theory is adapted into the current models for computing the hydrodynamic coefficients related to the scattered wave and radiation wave. A novel contribution of this paper is the inclusion of damping due to the wall shear stress, modelled for the reciprocating flow system inside the pipe. Comparison between the damping factors in relatively short OWCs confirms the findings in the literature that the major part of the damping is due to the radiation wave. However, it is found that with the increase of the draft length, the wall shear stress damping may also become an important factor in the resulting dynamics.

Modelling and analysis of the unsteady flow and heat transfer of immiscible micropolar and Newtonian fluids through a pipe of circular cross section

This study deals with the unsteady flow and heat transfer of micropolar and Newtonian fluids, flowing immiscibly through a circular pipe. The micropolar and Newtonian fluids occupy core and peripheral regions, respectively. Initially, the pipe and fluids in both regions are at rest; after an instant of time, a constant pressure gradient is applied to generate the flow. The equations governing the flow are time dependent, coupled and nonlinear. The solutions for velocity, microrotation and temperature are acquired numerically employing Crank–Nicolson finite difference approach. Volume flow rate is also obtained numerically and presented in tabular form. At fluid–fluid interface, continuity of velocities, shear stresses, temperatures and heat fluxes are considered. The results for velocity, microrotation and temperature are displayed graphically. It is seen that the fluid velocities, microrotation and temperatures are increasing with time and attain a steady state after a particular time level. The micropolarity parameter has a decreasing effect on the fluid velocities and temperatures.

SIMULATION OF THE PROCESS OF CONTINUOUS FORMING OF STRAIGHT-SEAM WELDED PIPES ON THE BASIS OF “TESA 10-50 TRAINER”

One of the most productive and reliable methods for studying the processes of metal forming is direct physical modeling on a real metal. The limitations of this method, as applied to the production of electric welded pipes, are generally related only to the lack of specialized equipment for modeling the continuous roll forming process. In 2014, a laboratory for modeling the most common processes of forming welded straight-seam pipes produced by continuous or discrete methods was established at the “Metal Forming” Department of NUST “MISIS”. The laboratory includes a specialized “TESA10-50TRAINER” (TRAINER), which allows simulation of continuous processes of electric welded pipes of small diameter. At the TRAINER, it is possible to simulate the processes of continuous forming of pipes of small and medium diameter by the basic production schemes of the pipe-electric welding manufactory: obtaining welded pipes of circular cross-section from strand; production of profiled pipes from sheet billet; obtaining profiled pipes from a preformed round or oval billet. In the research part of the article, the focus of deformation of the pipe blank, including the non-contact focus of the folding, the contact deformation center and the sprung portion, is considered. Initially, the shaping parameters of pipe billet in monotonous and roll forming centers were calculated by the adopted methods. The obtained results were compared by dynamics of the change in the width of billet from fixed sections of the deformation center. Further, the parameters of the roller tool were checked for compliance with the calculated dimensions. For the first roll stand of a continuous focus, an experiment was organized and conducted for the same conditions, but in a real roll center. The obtained experimental sample, marked out in eight sections, was measured after the billet had left the drive stand and the obtained data are listed in the table. Analysis of the results showed that the shape change of the cross-section parameters corresponds to the accepted provisions on geometry nature of the billet in the roller drive calibers. The discrepancy between the theoretical and experimental data for the roll center does not exceed 1.5 %.

A particle distribution function approach to the equations of continuum mechanics in Cartesian, cylindrical and spherical coordinates: Newtonian and non-Newtonian fluids

The evolution equations for the particle distribution functions are written in a divergence form applicable in three dimensions. From this set, it is shown that the continuity equation and the equations of motion are satisfied in Cartesian, cylindrical and spherical coordinates for all fluids when additional source terms are added to the equations of evolution in the latter two coordinate systems. If the body forces are present, a new set of source functions is required in each coordinate system and these are described as well. Next, the energy equation is derived by using a separate set of particle distribution functions. Modifications of the relevant equations to be applicable to incompressible fluids is described. The incorporation of boundary conditions and the description of the numerical scheme for the simulation of the flows employing the new approach is given. Validation results obtained through the modelling of a mixed convection flow of a Bingham fluid in a lid-driven square cavity, and the steady flow of a Bingham fluid in a pipe of square cross-section are presented. Next, using the cylindrical coordinate version of the evolution equations, numerical modelling of the steady flow of a Bingham fluid and the Herschel–Bulkley fluid in a pipe of circular cross-section have been performed and compared with the simulation results using the augmented Lagrangian method as well as the analytical solutions for the velocity field and the flow rate. Finally, some comments on the theoretical differences between the present approach and the existing formulations regarding Lattice Boltzmann Equations are offered.

Characterization of exchange flow in vertical pipes of circular and square cross-sections under unstable density gradient

The exchange flows in a buoyancy driven forced flow in vertical pipes of circular and square cross-sections were studied experimentally and the flow structure was examined by proper orthogonal decomposition (POD) analysis. The experiments were carried out in the vertical pipes issuing into a still brine water environment and the flow fields were visualized by the laser-induced fluorescence (LIF) technique. The flow visualization study showed that the critical inflow condition was deviated from the purging boundary due to the influence of hysteresis, and they are shifted to the high Froude numbers in the square pipe compared to the circular one. The POD analysis of the exchange flow indicates that the fluctuating energy is increased in the lower POD modes due to the formation of large-scale structure of the exchange flow. It is found from the analysis that the exchange flow in the low Reynolds number is promoted at the corners of the cross section in the square pipe, while it is randomly distributed in the circular pipe. This corresponds to an increased critical Froude number in the square pipe than that of the circular pipe, which is due to the presence of exchange flow through the corners. With increasing the Reynolds numbers, the flow becomes turbulent and the scale of the exchange flow is decreased and restricted to the near-wall region, while the location of the exchange flow becomes random along the pipe wall irrespective of the cross-sectional shape of the pipes.