Publication detail

Analytical Formula for the Mean Velocity Profile in a Pipe Derived on the Basis of a Spatial Polynomial Vorticity Distribution

ŠTIGLER, J.

English title

Analytical Formula for the Mean Velocity Profile in a Pipe Derived on the Basis of a Spatial Polynomial Vorticity Distribution

Type

journal article in Web of Science

Language

en

Original abstract

The derivation of the mean velocity profile for a given vorticity distribution over the pipe cross-section is presented in this paper1. The velocity profile and the vorticity distribution are axisymmetric, which means that the radius is the only variable. The importance of the vortex field for the flow analysis is discussed in the paper. The polynomial function with four free parameters is chosen for the vorticity distribution. Free parameters of this function are determined using boundary conditions. There are also two free exponents in the polynomial. These exponents are determined based on the comparison of this analytical formula with experimental data. Experimental data are taken from the Princeton superpipe data which consist of 26 velocity profiles for a wide range of Reynolds numbers (Re). This analytical formula for the mean velocity profile is more precise than the previous one and it is possible to use it for the wide range of Reynolds number <31,577; 35,259,000>. This formula is easy to use, to integrate, or to derivate. The empirical formulas for the profile parameters as a function of Re are also included in this paper. All information for the mean velocity profile prediction in the mentioned Re range are in the paper. It means that it is necessary to know the average velocity v((av)), the pipe radius R, and Re to be able to predict the turbulent mean velocity profile in a pipe.

English abstract

The derivation of the mean velocity profile for a given vorticity distribution over the pipe cross-section is presented in this paper1. The velocity profile and the vorticity distribution are axisymmetric, which means that the radius is the only variable. The importance of the vortex field for the flow analysis is discussed in the paper. The polynomial function with four free parameters is chosen for the vorticity distribution. Free parameters of this function are determined using boundary conditions. There are also two free exponents in the polynomial. These exponents are determined based on the comparison of this analytical formula with experimental data. Experimental data are taken from the Princeton superpipe data which consist of 26 velocity profiles for a wide range of Reynolds numbers (Re). This analytical formula for the mean velocity profile is more precise than the previous one and it is possible to use it for the wide range of Reynolds number <31,577; 35,259,000>. This formula is easy to use, to integrate, or to derivate. The empirical formulas for the profile parameters as a function of Re are also included in this paper. All information for the mean velocity profile prediction in the mentioned Re range are in the paper. It means that it is necessary to know the average velocity v((av)), the pipe radius R, and Re to be able to predict the turbulent mean velocity profile in a pipe.

Keywords in English

fluid flow in pipe; turbulent mean velocity profile; vorticity

Released

14.05.2021

Publisher

MDPI

Location

BASEL

ISSN

2073-4441

Volume

13

Number

10

Pages from–to

1–27

Pages count

27

BIBTEX


@article{BUT172540,
  author="Jaroslav {Štigler},
  title="Analytical Formula for the Mean Velocity Profile in a Pipe Derived on the Basis of a Spatial Polynomial Vorticity Distribution",
  year="2021",
  volume="13",
  number="10",
  month="May",
  pages="1--27",
  publisher="MDPI",
  address="BASEL",
  issn="2073-4441"
}