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1

Verification of Baffle Factor for Straight Pipe Flow

Artichowicz W., Łuczkiewicz A., Sawicki J. M.

Archives of Hydro-Engineering and Environmental Mechanics

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2018

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Vol. 65, nr 1

31--39

EN

The baffle factor is a parameter widely used to describe flow system characteristics. This indicator is very important in designing disinfection devices. For example, it is used to convert the plug flowtime to the actual fluid residence time in the flowsystem of interest. Its accurate determination is a complex problem requiring tracer experiments or computational fluid dynamics simulations. Therefore, in practice, it is often taken from tables provided in the literature. The literature sources, however, state that the baffle factor for a flow in a straight pipe is equal to unity, which implies the identity between the pipe flow model and the plug flow model. This assumption is doubtful. The aim of the present work is to verify the baffle factor values assumed for the pipe flow. The merit of this study is the analytical derivation of the expression describing the baffle factor value with respect to flow characteristics. To this purpose, the analytical solution of a one-dimensional advection-diffusion equation with a Heaviside initial condition was used. It was demonstrated that the aforementioned assumption is wrong, as the baffle factor for a straight pipe is significantly less than unity.

2

Determination of Mechanical Energy Loss in Steady Flow by Means of Dissipation Power

Artichowicz W., Sawicki J. M.

Archives of Hydro-Engineering and Environmental Mechanics

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2017

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Vol. 64, nr 2

73--85

EN

When systems of simple geometry like pipes or regular channels are considered, the mechanical energy loss of the fluid flow can be expressed by local and longitudinal empirical energy loss coefficients. However, in the case of large spatially distributed objects, there are no simple approaches to this task. In practice, general recommendations addressing different types of objects are used, but they usually provide very coarse estimates of energy loss. In this work, a new methodology for determination of mechanical energy loss in steady flowis proposed. This methodology is based on the observation that the magnitude of the power of energy dissipation in turbulent flow can be determined using the averaged flow velocity and turbulent viscosity coefficient. To highlight this possibility, an analysis of the magnitudes of the power of the main and fluctuating components of turbulent flow is presented. The correctness of the method is verified using an example of laminar and turbulent flows in a circular pipe. The results obtained show clearly that the proposed methodology can be used for mechanical energy loss determination in flow objects. This methodology can be used as a basis for mechanical energy loss determination in different types of flow objects.

3

Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow

Artichowicz W., Prybytak D.

Archives of Hydro-Engineering and Environmental Mechanics

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2015

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Vol. 62, nr 3-4

101--119

EN

In this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study examines the basic properties of numerical methods resulting from different types of averaging.

4

Comparison of Average Energy Slope Estimation Formulas for One-dimensional Steady Gradually Varied Flow

Artichowicz W., Mikos-Studnicka P.

Archives of Hydro-Engineering and Environmental Mechanics

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2014

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Vol. 61, nr 3-4

89–-109

EN

To find the steady flow water surface profile, it is possible to use Bernoulli’s equation, which is a discrete form of the differential energy equation. Such an approach requires the average energy slope between cross-sections to be estimated. In the literature, many methods are proposed for estimating the average energy slope in this case, such as the arithmetic mean, resulting in the standard step method, the harmonic mean and the geometric mean. Also hydraulic averaging by means of conveyance is commonly used. In this study, water surface profiles numerically computed using different formulas for expressing the average slope were compared with exact analytical solutions of the differential energy equation. Maximum relative and mean square errors between numerical and analytical solutions were used as measures of the quality of numerical models. Experiments showed that all methods gave solutions useful for practical engineering purposes. For every method, the numerical solution was very close to the analytical one. However, from the numerical viewpoint, the differences between the methods were significant, as the errors differed up to two orders of magnitude.

5

Numerical Analysis of Open Channel Steady Gradually Varied Flow using the Simplified Saint-Venant Equations

Artichowicz W.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2011

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Vol. 15, No 3-4

317-328

EN

For one-dimensional open-channel flow modeling, the energy equation is usually used. There exist numerous approaches using the energy equation for open-channel flow computations, which resulted in the development of several very efficient methods for solving this problem applied to channel networks. However, the dynamic equation can be used for this purpose as well. This paper introduces a method for solving a system of non-linear equations by the discretization of the one-dimensional dynamic equation for open-channel networks. The results of the computations using the dynamic and energy equations were compared for an arbitrarily chosen problem. Also, the reasons for the differences between the solution of the dynamic and energy equation were investigated.