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Management of Water Quality and Quantity pp 265–286Cite as

Numerical Modelling of the Fluid Flow at the Outlet from Narrowed Space for a Better Water Management

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Abstract

In the water management, events of significant changes of the running fluid flow space occur very frequently. Such change influences significantly the characteristics of the flow field and thus its effects on the environment. These might be the effects on adjacent objects in the close proximity such as walls of the designated space, or effects on objects bypassed with the running fluid. Such a situation frequently influences the surrounding area. The flow run may affect the terrain of the land or even the ambient climate in some cases. This chapter is dedicated to problems of numerical modelling of Newtonian fluid flows in changing flow space. Showing a particular task, which is solved numerically using computational fluid dynamics (CFD) codes in ANSYS Fluent software, the reader becomes familiar with both problems of the mathematical specification of fluid movements and principles of the correct choice of the numerical model. To resolve this task, four numerical models are selected. Basic turbulent characteristics of the flow field are monitored. Outputs of individual models are evaluated and compared with each other. Selected results are also verified by experimental measuring.

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Abbreviations

A :

Turbulent viscosity function (SST k-ω) (-)

\(C_{ij}\) :

Convection member (RSM) (kg m−1s−3)

\(C_{\mu }\) :

Constant (-)

\(C_{\mu }\) :

Model function for \(\mu_{t}\) calculation (Realisable k-ε) (-)

\(C_{1\varepsilon }\) :

Empiric constant (-)

\(C_{2\varepsilon }\) :

Empiric constant (-)

\(D_{L,ij}\) :

Molecular diffusion member (RSM) (kg m−1s−3)

\(D_{T,ij}^{*}\) :

Turbulent diffusion member (RSM) (kg m−1s−3)

\(D_{\omega }\) :

Mixing member (SST k-ω) (kg m−3s−2)

\(f_{i} ,F_{i}\) :

Force components (N)

\(G_{k}\) :

Generation member of turbulent kinetic energy (kg m−1s−3)

\(G_{\omega }\) :

Generation member of dissipation (SST k-ω) (kg m−3s−2)

k :

Turbulent kinetic energy (m2s−2)

I :

Linear scale factor of turbulence (m)

p :

Compression (Pa)

\(P_{ij}\) :

Compression production member (RSM) (kg m−1s−3)

t :

Time (s)

u :

Momentary velocity (m s−1)

\(u_{i}\) :

I-fold component of momentary velocity (m s−1)

\(u_{i}\) :

Wind velocity at fall in the i-fold building point (m s−1)

\(\overline{u}\) :

Mean velocity (time averaged) (ms−1)

\(\overline{u_{i}}\) :

Mean wind velocity at fall in the i-fold building point (m s−1)

\(\overline{{u_{i,j,k} }}\) :

i, j, k-fold component of mean velocity (m s−1)

\(u_{i,jk}^{\prime }\) :

i, j, k-fold component of fluctuation velocity (m s−1)

\(x_{i}\) :

Cartesian coordinate system [x1, x2, x3] or [x, y, z] (m)

S :

Tensor module of the mean deformation velocity (k-ε) (s−1)

\(S_{i,j}\) :

Deformation velocity tensor (k-ε) (s−1)

\(Y_{k}\) :

Dissipation member for k (SST k-ω) (kg m−1s−3)

\(Y_{\omega }\) :

Dissipation member for ω (SST k-ω) (kg m−3s−2)

\(\delta_{ij}\) :

Kronecker delta symbol (-)

\(\varepsilon\) :

Velocity of kinetic energy dissipation (m2s−3)

\(\varepsilon_{ij}^{*} ,\varepsilon_{ij}\) :

Dissipation member (RSM) (kg m−1s−3)

\(\varPhi_{ij}^{*} ,\varPhi_{ij}\) :

Compressive stress member (RSM) (kg m−1s−3)

\(\kappa\) :

Von Karman constant (-)

\(\mu\) :

Dynamic viscosity (Pa s), (kg m−1s−1)

\(\mu_{t}\) :

Dynamic turbulent viscosity (Pa s), (kg m−1s−1)

\(\nu\) :

Kinematic viscosity (m2s−1)

\(\nu_{t}\) :

Kinematic turbulent viscosity (m2s−1)

\(\rho\) :

Density (kg m−3)

\(\sigma_{k}\) :

Turbulent Prandtl number for k (-)

\(\sigma_{\varepsilon }\) :

Turbulent Prandtl number for ε (-)

\(\sigma_{{v_{i} }}\) :

Turbulent Prandtl number for \(\nu_{t}\) (-)

\(\tau\) :

Viscous stress (Pa)

\(\omega\) :

Dissipation per turbulent kinetic energy (s−1)

\(i\) :

Velocity component index, iteration index, point index (-)

\(i\) :

Summary index (-)

\(j,k,l\) :

Summary Einstein index (-)

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Acknowledgements

Financial support from VŠB-Technical University of Ostrava by means of the Czech Ministry of Education, Youth and Sports through the Institutional support for conceptual development of science, research, and innovations for the year 2018 and by the Scientific Grant Agency of the Ministry of Education of Slovak Republic and the Slovak Academy of Sciences the project VEGA 1/0477/15 and VEGA 1/0374/19 is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Structural Mechanics, Faculty of Civil Engineering, VŠB—Technical University of Ostrava, L. Podéště 1875/17, 708 33, Ostrava-Poruba, Czech Republic

    V. Michalcová

  2. Department of Structural Mechanics, Faculty of Civil Engineering, Institute of Structural Engineering, The Technical University of Kosice, Kosice, Slovak Republic

    K. Kotrasová

Authors
  1. V. Michalcová
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Correspondence to V. Michalcová .

Editor information

Editors and Affiliations

  1. Technical University of Kosice, Kosice, Slovakia

    Martina Zelenakova

  2. Brno University of Technology, Brno, Czech Republic

    Petr Hlavínek

  3. Faculty of Engineering, Zagazig University, Zagazig, Egypt

    Abdelazim M. Negm

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Michalcová, V., Kotrasová, K. (2020). Numerical Modelling of the Fluid Flow at the Outlet from Narrowed Space for a Better Water Management. In: Zelenakova, M., Hlavínek, P., Negm, A. (eds) Management of Water Quality and Quantity. Springer Water. Springer, Cham. https://doi.org/10.1007/978-3-030-18359-2_11

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