▪ AbstractWe review the experimental evidence on turbulent flows over rough walls. Two parameters are important: the roughness Reynolds number ks+, which measures the effect of the roughness on the buffer layer, and the ratio of the boundary layer thickness to the roughness height, which determines whether a logarithmic layer survives. The behavior of transitionally rough surfaces with low ks+ depends a lot on their geometry. Riblets and other drag-reducing cases belong to this regime. In flows with δ/k ≲ 50, the effect of the roughness extends across the boundary layer, and is also variable. There is little left of the original wall-flow dynamics in these flows, which can perhaps be better described as flows over obstacles. We also review the evidence for the phenomenon of d-roughness. The theoretical arguments are sound, but the experimental evidence is inconclusive. Finally, we discuss some ideas on how rough walls can be modeled without the detailed computation of the flow around the roughness element...

Turbulent flows over rough walls

Publication in late 1993 by the International Organization for Standardization (ISO) of the Guide to the Expression of Uncertainty in Measurement in the name of ISO and six other international organizations has, in everything but name only, established a new international experimental uncertainty standard. In this article, an analysis of the assumptions and approximations used in the development of the methods in the ISO guide is presented, and a comparison of the resulting equation with previously published uncertainty analysis approaches is made. Also discussed are the additional assumptions necessary to achieve the less complex large sample methodology that is recommended in AIAA Standard S-071-1995, Assessment of Wind Tunnel Data Uncertainty, issued in 1995. It is shown that these assumptions are actually less restrictive than those associated with some previously accepted methodologies. The article concludes with a discussion of some practical aspects of implementing experimental uncertainty analysis in engineering testing.

Engineering application of experimental uncertainty analysis

A laboratory study on the hydraulics of flow in an open channel with circular cylindrical roughness is presented. The laboratory study consists of an extensive set of flume experiments for flows with emergent and submerged cylindrical stems of various sizes and concentrations. The results show that the flow resistance varies with flow depth, stem concentration, stem length, and stem diameter. The stem resistance experienced by the flow through the vegetation is best expressed in terms of the maximum depth-averaged velocity between the stems. Physically based formulas for flow resistance, the apparent channel velocity, and flow velocities in the roughness and surface layers are developed. The formulas are validated with the flume data from the present study as well as those from past studies. A method for calculating channel hydraulic conditions using these formulas is presented.

Hydraulic resistance of flow in channels with cylindrical roughness

The paper describes the process of induction of equations for the description of vegetation-induced roughness from several angles. Firstly, it describes two approaches for obtaining theoretically well-founded analytical expressions for vegetation resistance. The first of the two is based on simplified assumptions for the vertical flow profile through and over vegetation, whereas the second is based on an analytical solution to the momentum balance for flow through and over vegetation. In addition to analytical expressions the paper also outlines a numerical 1-DV k–e turbulence model which includes several important features related to the influence plants exhibit on the flow. Last but not least, the paper presents a novel way of applying genetic programming to the results of the 1-DV model, in order to obtain an expression for roughness based on synthetic data. The resulting expressions are evaluated and compared with an independent data set of flume experiments

On inducing equations for vegetation resistance

A review of predictive methods used to determine the frictional drag on a rough surface is presented. These methods utilize a wide range of roughness scales, including roughness height, pitch, density, and shape parameters. Most of these scales were developed for regular roughness, limiting their applicability to predict the drag for many engineering flows. A new correlation is proposed to estimate the frictional drag for a surface covered with three-dimensional, irregular roughness in the fully rough regime. The correlation relies solely on a measurement of the surface roughness profile and builds on previous work utilizing moments of the surface statistics. A relationship is given for the equivalent sandgrain roughness height as a function of the root-mean-square roughness height and the skewness of the roughness probability density function. Boundary layer similarity scaling then allows the overall frictional drag coefficient to be determined as a function of the ratio of the equivalent sandgrain roughness height to length of the surface. DOI: 10.1115/1.4001492

https://www.usna.edu/NAOE/_files/documents/Faculty/schultz/Flack,%20Schultz%20-%20Hydraulic%20Roughness%20Scales,%202010.pdf

Review of Hydraulic Roughness Scales in the Fully Rough Regime

Prediction of Turbulent Rough-Wall Skin Friction Using a Discrete Element Approach

A Re-Evaluation of Schlichting’s Surface Roughness Experiment

The determination of precision uncertainty is described for experiments where the test measurements are obtained from single readings or from a limited number of independent readings. For these cases, the limits of precision uncertainty are best determined from previous experience based on larger sample sizes over the full range of variations that occur for a specific test. We describe the appropriate procedures to determine the limits of precision uncertainty based on previous experience for small sample experiments. A Monte Carlo simulation technique is used to model the experiments to demonstrate the effectiveness of using the precision uncertainty to determine the range that covers the true test result

Use of previous experience to estimate precision uncertainty of small sample experiments

: A discrete element model for turbulent flow over rough surfaces has been rigorously derived from basic principles. This model includes surface roughness effects as a constitutent part of the partial differential equations which describe momentum and energy transport in turbulent flows. The model includes the necessary empirical information on the interaction between the roughness elements and the flow around and between the elements in a general way which does not require experimental data on each specific surface. This empirical information is input via algebraic models for the local element drag coefficient and Nusselt number. These models were calibrated by comparison with base data sets from surfaces with three-dimensional (distributed) roughness elements. Calculations using the present model have been compared with experimental data from 118 separate experimental runs. The results of these comparisons ranged from good to excellent. The calculations compared equally well with both transitionally rough and fully rough turbulent flow results without modification of the roughness model. (Author)

A discrete element prediction approach for turbulent flow over rough surfaces

The procedures for determining experimental uncertainty contained in the current version of the ANSI/ASME Standard (PTC19.1-1985) Measurement Uncertainty are compared with the procedure presented in the 1993 ISO Guide to the Expression of Uncertainty in Measurement. A Monte Carlo technique is used to stimulate several example experiments to demonstrate the effectiveness of the models for predicting an appropriate uncertainty interval at a given confidence level, either 95% or 99%. The simulation results show that the ISO model is more consistent in providing an uncertainty interval at the desired level of confidence. The simulations also show that if a determined results has degrees of freedom of nine or more, simplified models using values of t95 = 2.0 for a 95% confidence level and t99 = 2.6 for a 99% confidence level can be used to determine the uncertainty to a good approximation.

R. P. Taylor

Papers

Prediction of Turbulent Rough-Wall Skin Friction Using a Discrete Element Approach

A Re-Evaluation of Schlichting’s Surface Roughness Experiment

Use of previous experience to estimate precision uncertainty of small sample experiments

A discrete element prediction approach for turbulent flow over rough surfaces

Comparison of ANSI/ASME and ISO models for calculation of uncertainty