scholarly journals Turbulence Intensity and the Friction Factor for Smooth- and Rough-Wall Pipe Flow

Fluids ◽  
2017 ◽  
Vol 2 (2) ◽  
pp. 30 ◽  
Author(s):  
Nils T. Basse
Keyword(s):  
Friction Factor ◽  
Turbulence Intensity ◽  
Pipe Flow ◽  
Rough Wall

scholarly journals Turbulence Intensity Scaling: A Fugue

Fluids ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 180 ◽  
Author(s):  
Nils T. Basse
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Turbulence Intensity ◽  
Pipe Flow ◽  
Rough Wall ◽  
Flow Measurements ◽  
Flow Turbulence ◽  
Intensity Scaling ◽  
Grain Roughness ◽  
Made In

We study streamwise turbulence intensity definitions using smooth- and rough-wall pipe flow measurements made in the Princeton Superpipe. Scaling of turbulence intensity with the bulk (and friction) Reynolds number is provided for the definitions. The turbulence intensity scales with the friction factor for both smooth- and rough-wall pipe flow. Turbulence intensity definitions providing the best description of the measurements are identified. A procedure to calculate the turbulence intensity based on the bulk Reynolds number (and the sand-grain roughness for rough-wall pipe flow) is outlined.

Heat Transfer in Turbulent Pipe Flow for Liquids Having a Temperature-Dependent Viscosity

1978 ◽  
Vol 100 (2) ◽  
pp. 224-229 ◽  
Author(s):  
O. T. Hanna ◽  
O. C. Sandall
Keyword(s):  
Heat Transfer ◽  
Friction Factor ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Analytical Approximations ◽  
Constant Viscosity ◽  
Dependent Viscosity

Analytical approximations are developed to predict the effect of a temperature-dependent viscosity on convective heat transfer through liquids in fully developed turbulent pipe flow. The analysis expresses the heat transfer coefficient ratio for variable to constant viscosity in terms of the friction factor ratio for variable to constant viscosity, Tw, Tb, and a fluid viscosity-temperature parameter β. The results are independent of any particular eddy diffusivity distribution. The formulas developed here represent an analytical approximation to the model developed by Goldmann. These approximations are in good agreement with numerical solutions of the model nonlinear differential equation. To compare the results of these calculations with experimental data, a knowledge of the effect of variable viscosity on the friction factor is required. When available correlations for the friction factor are used, the results given here are seen to agree well with experimental heat transfer coefficients over a considerable range of μw/μb.

Extended Models for Transitional Rough Wall Boundary Layers With Heat Transfer: Part I—Model Formulations

2008 ◽  
Author(s):  
M. Stripf ◽  
A. Schulz ◽  
H.-J. Bauer ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Boundary Layers ◽  
Turbulence Model ◽  
Turbulence Intensity ◽  
Discrete Element ◽  
Rough Wall ◽  
Test Cases ◽  
Wall Boundary ◽  
Turbine Vane

Two extended models for the calculation of rough wall transitional boundary layers with heat transfer are presented. Both models comprise a new transition onset correlation, which accounts for the effects of roughness height and density, turbulence intensity and wall curvature. In the transition region, an intermittency equation suitable for rough wall boundary layers is used to blend between the laminar and fully turbulent state. Finally, two different submodels for the fully turbulent boundary layer complete the two models. In the first model, termed KS-TLK-T in this paper, a sand roughness approach from Durbin et al., which builds upon a two-layer k-ε-turbulence model, is used for this purpose. The second model, the so-called DEM-TLV-T model, makes use of the discrete-element roughness approach, which was recently combined with a two-layer k-ε-turbulence model by the present authors. The discrete element model will be formulated in a new way suitable for randomly rough topographies. Part I of the paper will provide detailed model formulations as well as a description of the database used for developing the new transition onset correlation. Part II contains a comprehensive validation of the two models, using a variety of test cases with transitional and fully turbulent boundary layers. The validation focuses on heat transfer calculations on both, the suction and the pressure side of modern turbine airfoils. Test cases include extensive experimental investigations on a high-pressure turbine vane with varying surface roughness and turbulence intensity, recently published by the current authors as well as new experimental data from a low-pressure turbine vane. In the majority of cases, the predictions from both models are in good agreement with the experimental data.

A Review of Explicit Friction Factor Equations

1985 ◽  
Vol 107 (2) ◽  
pp. 280-283 ◽  
Author(s):  
D. J. Zigrang ◽  
N. D. Sylvester
Keyword(s):  
Friction Factor ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Explicit Equation ◽  
Flow Friction ◽  
Friction Factors ◽  
High Degree ◽  
Very High

A review of the explicit friction factor equations developed to replace the Colebrook equation is presented. Explicit friction factor equations are developed which yield a very high degree of precision compared to the Colebrook equation. A new explicit equation, which offers a reasonable compromise between complexity and accuracy, is presented and recommended for the calculation of all turbulent pipe flow friction factors for all roughness ratios and Reynold’s numbers.

An Alternative (Preferable) Friction Factor

2006 ◽  
Author(s):  
Richard A. Gaggioli
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Pipe Flow ◽  
Incompressible Flows ◽  
Flow Regimes ◽  
Relative Roughness ◽  
Curve Fit ◽  
Moody Diagram ◽  
Approximate Formulas

An alternative to the traditional friction factor for pipe flow is presented (φ = [R]f). For incompressible flows, the correlation of this new friction factor with Reynolds Number [R] and Relative Roughness [ε] is presented graphically, and appears much simpler and more intuitive than the Moody Diagram (or other equivalents). Moreover, relatively simple curve-fit formulas for representing φ explicitly as a function of R and ε are presented for various flow regimes, along with measures of error associated with these approximate formulas.

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