arXiv subjects

Fazle Hussain

Publications and source records attributed to Fazle Hussain.

23 records · Page 2Linked to original sources

arXiv2015

Quantifying wall turbulence via a symmetry approach. Part I. A Lie group theory

First principle based prediction of mean flow quantities of wall-bounded turbulent flows (channel, pipe, and turbulent boundary layer - TBL) is of great importance from both physics and engineering standpoints. Here (Part I), we present a symmetry-based approach which derives analytic expressions governing the mean velocity profile (MVP) from an innovative Lie-group analysis. The new approach begins by identifying a set of order functions (e.g. stress length, shear-induced eddy length), in analogy with the order parameter in Landau's mean-field theory, which aims at capturing symmetry aspects of the fluctuations (e.g. Reynolds stress, dissipation). The order functions are assumed to satisfy a dilation group invariance - representing the effects of the wall on fluctuations - which allows us to postulate three new kinds of invariant solutions of the mean momentum equation (MME), focusing on group invariants of the order functions (rather than those of the mean velocity as done in previous studies). The first - a power law solution - gives functional forms for the viscous sublayer, the buffer layer, the log-layer, and a newly identified central `core' (for channel and pipe, but non-existent for TBL). The second - a defect power law of form $1-r^{m}$ ($r$ being the distance from the center line) - describes the `bulk zone' (the region of balance between production and dissipation). The third - a relation between the group invariants of the stress length function and its first derivative - describes scaling transition between adjacent layers. A combination of these three expressions yields a multi-layer formula covering the entire flow domain, identifying three important parameters: scaling exponent, layer thickness, and transition sharpness. All three kinds of invariant solutions are validated, individually and in combination, by data from direct numerical simulations (DNS).

physics.flu-dyn↗

arXiv2014

Prediction of temperature distribution in turbulent Rayleigh-Benard convection

A quantitative theory is developed for the vertical mean temperature profile (MTP) in turbulent Rayleigh-Benard convection (RBC), which explains the recent experimental and numerical observations of a logarithmic law by Ahlers et al.(Phys. Rev. Lett., 2012). A multi-layer model is formulated and quantified, whose predictions agree with DNS and experimental data for the Rayleigh-number (Ra) over seven decades. In particular, a thermal buffer layer follows a 1/7 scaling like the previously postulated mixing zone (Procaccia et al, Phys. Rev. A,1991), and yields a Ra-dependent log law constant. A new parameterization of Nu(Ra) dependence is proposed, based on the present multi-layer quantification of the bulk MTP.

physics.flu-dyn↗

arXiv2012

A multi-layer model for turbulent kinetic energy in pipe flows

A multi-layer model of an energy length function is developed by employing recent results of the authors. The theory predicts the complete, mean streamwise turbulent kinetic-energy profile (MKP), in good agreement with empirical data for a wide range of Reynolds numbers (Re). In particular, a critical $Re_τ$ is predicted, beyond which a scaling anomaly appears and MKP develops a second peak.

physics.flu-dyn↗

arXiv2012

Logarithmic distribution of mean velocity and turbulent kinetic energy in a pipe flow

A Lie-group based similarity theory is developed for both momentum and energy distributions in a turbulent pipe flow, leading to asymptotic logarithmic profiles of mean velocity and turbulent kinetic energy. Both channel and pipe data over a wide range of Re yield 0.45 to be the universal Karman constant. A new spatial invariant characterizing outer dynamics is discovered and validated by reliable experimental data. The theory predicts the mean velocity profile (MVP) with 99% accuracy for high Re experimental data (up to 40 millions), and offers a quantitative explanation for recent observation of logarithmic kinetic energy distribution by Hullmak et al. (Phys. Rev. Lett. 108, 094501).

physics.flu-dyn↗

arXiv2011

Karman constant and accurate mean flow prediction in a turbulent pipe

The Karman constant κ- widely used in atmospheric science and engineering turbulence modelling, and proposed by Prandtl in 1925 and von Karman in 1930 to describe the mean velocity of a turbulent wall-bounded flow - leads to a logarithmic profile in an overlap region near the wall. For over eighty years, its value was believed to be ~0.41. But more recently, many argue that it is not a constant, because of measured variations in different flows and at different Reynolds numbers (Re). Here, a multi-layer analytic theory is shown to lead to a re-interpretation of κas a global constant for both the overlap region and outer flow, and to yield a new method for its measurement. The newly determined value is 0.45 for both channel and pipe. It is shown that this new κ, together with other wall constants, yields a 99% accuracy in the prediction of mean velocity data at all points in high Re (up to 40 million) pipe flow. The theory also describes finite Re effect, and discovers a transition at the friction Re (i.e. Re_τ)=5000. An accurate model for the prediction of turbulent transport in canonical pipe and channel flows is achieved here, and we propose the model to be valid for a wide class of turbulent flows.

physics.flu-dyn↗