A multi-state description of roughness effects in turbulent pipe flow

Abstract

Despite persistent efforts over the last century, a theory for predicting the effects of surface roughness on the mean flow is still missing. Here, we extend a recently proposed multi-state theory to incorporate roughness effects. A formula for the roughness function is constructed by applying the Lie-group invariance theory, giving excellent agreement with the fully collapsed data of both the Nikuradze sand-coated and Princeton honed pipes. A major advantage of the theory is its ability to successfully describe the non-universality-either inflectional or monotonic variations-in a transitionally rough regime with a single sharpness parameter. This model then yields an analytic prediction for the friction factor and mean velocity profiles in rough pipes, agreeing with the empirical data. Consistent with classical understanding (e.g. Townsend's similarity hypothesis), our results confirm the multi-layer theory of wall turbulence, regardless of smooth or rough surfaces.

Numerical and theoretical investigation of pulsatile turbulent channel flows

“…The results are also compared with earlier published data, which for the pulsating channel flow come from the DNS of Scotti & Piomelli (2001) with Re τ = 350 and ω + f = 0.04, and for the steady channel flow the DNS of Moser, Kim & Mansour (1999) with Re τ = 395. We also present the mean flow profile computed using an algebraic EVM based on the ν T proposed by She et al (2012) (see appendix A). To validate the algebraic EVM, the mean velocity profile is computed from (2.3) and (A 1), by setting ∂p/∂x = −(Re τ /Re cl ) 2 .…”

“…In this paper, we use the algebraic model proposed by She et al (2012) to compute the eddy viscosity ν T . The details of the model are given below.…”

Probability Density Functions of Vorticities in Turbulent Channels with Effects of Blowing and Suction

“…A range of blowing and suction conditions is covered with A = 0.05, 0.1, 0.2. While the mean velocity profile, the RMS, skewness and flatness are all altered severely, the PDFs for (spanwise) vorticity are found to satisfy the GHD of Birnir [9,10] above the buffer layer thickness [19]. The latter leads to accurate descriptions of all PFDs with four parameters depending on the wall distances y + and perturbation strength A.…”

“…Actually all other components of vorticity tensor can be studied in a similar way. Figure 5 shows the PDF of − Ω z (positive mean) with blowing effects at positions y + = 40, 200 and 390, representing PDFs at the buffer layer, the logarithmic layer and the centerline of channel, respectively [18,19]. Note that for a better display, we just compare the PDF at two blowing strengths, i. e. A = 0.05 (square) and A = 0.2 (circle), where the PDF at A = 0.1 is similar.…”

Similarity transformation for equilibrium boundary layers, including effects of blowing and suction

“…Note that the expansion is key to the success of the transformation, which means that blowing/suction conditions can be effectively described by the relative variation (ratio) of length functions. Such a procedure (by characteristic lengths) has been introduced by [21] as a new way to quantify turbulent wall flows (with more results to be presented). Note that all of the mean flow quantities (U + , V + and R + ) are calculated from the single profile U + * (y + ) with high accuracy.…”