Mean velocity scaling for compressible wall turbulence with heat transfer

2016 ◽  
Vol 28 (2) ◽  
pp. 026102 ◽  
Author(s):  
Andrew Trettel ◽  
Johan Larsson
Keyword(s):  
Heat Transfer ◽  
Wall Turbulence ◽  
Mean Velocity

Rotating Effect on Fluid Flow in a Smooth Duct With a 180-Deg Sharp Turn

2000 ◽  
Author(s):  
Chung-Chu Chen ◽  
Tong-Miin Liou
Keyword(s):  
Heat Transfer ◽  
Kinetic Energy ◽  
Secondary Flow ◽  
Turbulent Kinetic Energy ◽  
Turbine Blades ◽  
Outer Part ◽  
Intensity Level ◽  
Mean Velocity ◽  
High Heat Transfer ◽  
Sharp Turn

Laser-Doppler velocimetry (LDV) measurements are presented of turbulent flow in a two-pass square-sectioned duct simulating the coolant passages employed in gas turbine blades under rotating and non-rotating conditions. For all cases studied, the Reynolds number characterized by duct hydraulic diameter (Dh) and bulk mean velocity (Ub) was fixed at 1 × 104. The rotating case had a range of rotation number (Ro = ΩDh/Ub) from 0 to 0.2. It is found that both the skewness of streamwise mean velocity and magnitude of secondary-flow velocity increase linearly, and the magnitude of turbulence intensity level increases non-linearly with increasing Ro. As Ro is increased, the curvature induced symmetric Dean vortices in the turn for Ro = 0 is gradually dominated by a single vortex most of which impinges directly on the outer part of leading wall. The high turbulent kinetic energy is closely related to the dominant vortex prevailing inside the 180-deg sharp turn. For the first time, the measured flow characteristics account for the reported spanwise heat transfer distributions in the rotating channels, especially the high heat transfer enhancement on the leading wall in the turn. For both rotating and non-rotating cases, the direction and strength of the secondary flow with respect to the wall are the most important fluid dynamic factors affecting local heat transfer distributions inside a 180-deg sharp turn. The role of the turbulent kinetic energy in affecting the overall enhancement of heat transfer is well addressed.

scholarly journals Thermal and Hydrodynamic Phenomena in the Stagnation Zone—Impact of the Inlet Turbulence Characteristics on the Numerical Analyses

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 105
Author(s):  
Tomasz Kura ◽  
Jan Wajs ◽  
Elzbieta Fornalik-Wajs ◽  
Sasa Kenjeres ◽  
Sebastian Gurgul
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Enhancement ◽  
Positive Impact ◽  
Impinging Jets ◽  
Wall Turbulence ◽  
Transfer Enhancement ◽  
Stagnation Region ◽  
Nozzle Orifice ◽  
Inlet Conditions ◽  
Difficult Area

One of the methods of heat transfer enhancement is utilization of the turbulent impinging jets, which were recently applied, for example, in the heat exchangers. Their positive impact on the heat transfer performance was proven, but many questions related to the origin of this impact are still unanswered. In general, the wall-jet interaction and the near-wall turbulence are supposed to be its main reason, but their accurate numerical analysis is still very challenging. The authors’ aim was to construct the numerical model which can represent the real phenomena with good or very good accuracy. Starting with an analysis of single jet and obtaining the agreement with experimental data, it will be possible to extend the model towards the whole minijets heat exchanger. The OpenFOAM software, Bracknell, UK was used for that purpose, with our own implementation of the ζ-f turbulence model. The most difficult area to model is the stagnation region, where the thermal effects are the most intensive and, at the same time, strongly affected by the conditions in the pipe/nozzle/orifice of various size (conventional, mini, micro), from which the jet is injected. In the following article, summary of authors’ findings, regarding significance of the velocity profile and turbulence intensity at the jet place of discharge are presented. In addition, qualitative analysis of the heat transfer enhancement is included, in relation to the inlet conditions. In the stagnation point, Nusselt number differences reached the 10%, while, in general, its discrepancy in relation to inlet conditions was up to 23%.

scholarly journals Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer

2021 ◽  
Vol 118 (34) ◽  
pp. e2111144118 ◽  
Author(s):  
Kevin Patrick Griffin ◽  
Lin Fu ◽  
Parviz Moin
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Flows ◽  
Viscous Sublayer ◽  
Mean Velocity ◽  
General Transformation ◽  
Law Of The Wall ◽  
Velocity Transformation ◽  
Logarithmic Region ◽  
Logarithmic Layer

In this work, a transformation, which maps the mean velocity profiles of compressible wall-bounded turbulent flows to the incompressible law of the wall, is proposed. Unlike existing approaches, the proposed transformation successfully collapses, without specific tuning, numerical simulation data from fully developed channel and pipe flows, and boundary layers with or without heat transfer. In all these cases, the transformation is successful across the entire inner layer of the boundary layer (including the viscous sublayer, buffer layer, and logarithmic layer), recovers the asymptotically exact near-wall behavior in the viscous sublayer, and is consistent with the near balance of turbulence production and dissipation in the logarithmic region of the boundary layer. The performance of the transformation is verified for compressible wall-bounded flows with edge Mach numbers ranging from 0 to 15 and friction Reynolds numbers ranging from 200 to 2,000. Based on physical arguments, we show that such a general transformation exists for compressible wall-bounded turbulence regardless of the wall thermal condition.

LES and Hybrid RANS/LES of a Fundamental Trailing Edge Slot

2014 ◽  
Author(s):  
Elizaveta Ivanova ◽  
Gregory M. Laskowski
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Numerical Study ◽  
Mixing Layer ◽  
Detached Eddy Simulation ◽  
Trailing Edge ◽  
Adiabatic Wall ◽  
Mean Velocity ◽  
Eddy Simulation ◽  
Delayed Detached Eddy Simulation

This paper presents the results of a numerical study on the predictive capabilities of Large Eddy Simulation (LES) and hybrid RANS/LES methods for heat transfer, mean velocity, and turbulence in a fundamental trailing edge slot. The geometry represents a landless slot (two-dimensional wall jet) with adjustable slot lip thickness. The reference experimental data taken from the publications of Kacker and Whitelaw [1] [2] [3] [4] contains the adiabatic wall effectiveness together with the velocity and the Reynolds-stress profiles for various blowing ratios and slot lip thicknesses. The simulations were conducted at three different lip thickness and several blowing ratio values. The comparison with the experimental data shows a general advantage of LES and hybrid RANS/LES methods against unsteady RANS. The predictive capability of the tested LES models (dynamic ksgs-equation [5] and WALE [6]) was comparable. The Improved Delayed Detached Eddy Simulation (IDDES) hybrid method [7] also shows satisfactory agreement with the experimental data. In addition to the described baseline investigations, the influence of the inlet turbulence boundary conditions and their implication for the initial mixing layer and heat transfer development were studied for both LES and IDDES.

On the size of the energy-containing eddies in the outer turbulent wall layer

2012 ◽  
Vol 702 ◽  
pp. 521-532 ◽  
Author(s):  
Sergio Pirozzoli
Keyword(s):  
Outer Part ◽  
Eddy Diffusivity ◽  
Wall Layer ◽  
Wall Turbulence ◽  
Normal Velocity ◽  
Mixing Length ◽  
Mean Velocity ◽  
Local Mean ◽  
Turbulent Wall ◽  
Good Agreement

AbstractWe investigate the scaling of the energy-containing eddies in the outer part of turbulent wall layers. Their spanwise integral length scales are extracted from a direct numerical simulation (DNS) database, which includes compressible turbulent boundary layers and incompressible turbulent Couette–Poiseuille flows. The results indicate similar behaviour for all classes of flows, with a general increasing trend in the eddy size with the wall distance. A family of scaling relationships are proposed based on simple dimensional arguments, of which the classical mixing length approximation constitutes one example. As in previous studies, we find that the mixing length is in good agreement with the size distribution of the eddies carrying wall-normal velocity, which are active in establishing the mean velocity distribution. However, we find that the eddies associated with wall-parallel motions obey a different scaling, which is controlled by the local mean shear and by an effective eddy diffusivity ${\nu }_{t} = { u}_{\tau }^{\ensuremath{\ast} } \delta $, where ${ u}_{\tau }^{\ensuremath{\ast} } $ is the compressible counterpart of the friction velocity, and $\delta $ is the thickness of the wall layer. The validity of the proposed scalings is checked against DNS data, and the potential implications for the understanding of wall turbulence are discussed.

The Effects of Localized Blade Endwall Suction on Secondary Flows and Heat Transfer

2010 ◽  
Author(s):  
Rebecca Hollis ◽  
Jeffrey P. Bons
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
High Surface ◽  
Surface Heat ◽  
Secondary Flows ◽  
Surface Shear Stress ◽  
Mean Velocity ◽  
Surface Shear ◽  
Surface Heat Transfer ◽  
High Heat Transfer

Two methods of flow control were designed to mitigate the effects of the horseshoe vortex structure (HV) at an airfoil/endwall junction. An experimental study was conducted to quantify the effects of localized boundary layer removal on surface heat transfer in a low-speed wind tunnel. A transient infrared technique was used to measure the convective heat transfer values along the surface surrounding the juncture. Particle image velocimetry was used to collect the time-mean velocity vectors of the flow field across three planes of interest. Boundary layer suction was applied through a thin slot cut into the leading edge of the airfoil at two locations. The first, referred to as Method 1, was directly along the endwall, the second, Method 2, was located at a height ∼1/3 of the approaching boundary layer height. Five suction rates were tested; 0%, 6.5%, 11%, 15% and 20% of the approaching boundary layer mass flow was removed at a constant rate. Both methods reduced the effects of the HV with increasing suction on the symmetry, 0.5-D and 1-D planes. Method 2 yielded a greater reduction in surface heat transfer but Method 1 outperformed Method 2 aerodynamically by completely removing the HV structure when 11% suction was applied. This method however produced other adverse effects such as high surface shear stress and localized areas of high heat transfer near the slot edges at high suction rates.

scholarly journals Natural logarithms

2013 ◽  
Vol 718 ◽  
pp. 1-4 ◽  
Author(s):  
B. J. McKeon
Keyword(s):  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Significant Advance ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Logarithmic Scaling ◽  
The Mean ◽  
High Reynolds

AbstractMarusic et al. (J. Fluid Mech., vol. 716, 2013, R3) show the first clear evidence of universal logarithmic scaling emerging naturally (and simultaneously) in the mean velocity and the intensity of the streamwise velocity fluctuations about that mean in canonical turbulent flows near walls. These observations represent a significant advance in understanding of the behaviour of wall turbulence at high Reynolds number, but perhaps the most exciting implication of the experimental results lies in the agreement with the predictions of such scaling from a model introduced by Townsend (J. Fluid Mech., vol. 11, 1961, pp. 97–120), commonly termed the attached eddy hypothesis. The elegantly simple, yet powerful, study by Marusic et al. should spark further investigation of the behaviour of all fluctuating velocity components at high Reynolds numbers and the outstanding predictions of the attached eddy hypothesis.

Rotating Effect on Fluid Flow in Two Smooth Ducts Connected by a 180-Degree Bend

2003 ◽  
Vol 125 (1) ◽  
pp. 138-148 ◽  
Author(s):  
Tong-Miin Liou ◽  
Chung-Chu Chen ◽  
Meng-Yu Chen
Keyword(s):  
Heat Transfer ◽  
Kinetic Energy ◽  
Secondary Flow ◽  
Turbulent Kinetic Energy ◽  
Separation Bubble ◽  
Turbine Blades ◽  
Outer Part ◽  
Intensity Level ◽  
Mean Velocity ◽  
Sharp Turn

Laser Doppler velocimetry (LDV) measurements are presented of turbulent flow in a two-pass square-sectioned smooth duct simulating the coolant passages employed in gas turbine blades under rotating and nonrotating conditions. For all cases studied, the Reynolds number characterized by duct hydraulic diameter and bulk mean velocity was fixed at 1×104. The rotation number Ro was varied from 0 to 0.2. It is found that as Ro is increased, both the skewness (SK) of streamwise mean velocity and magnitude of secondary-flow velocity increase linearly, SK=2.3 Ro and U2+V2¯/Uh=2.3 Ro+0.4, and the magnitude of turbulence intensity level increases exponentially. As Ro is increased, the curvature induced symmetric Dean vortices in the turn for Ro=0 is gradually dominated by a single vortex most of which impinges directly on the outer part of leading wall. The high turbulent kinetic energy is closely related to the dominant vortex prevailing inside the 180-deg sharp turn. The size of separation bubble immediately after the turn is found to diminish to null as Ro is increased from 0 to 0.2. A simple correlation is developed between the bubble size and Ro. A critical range of Ro responsible for the switch of faster moving flow from near the outer wall to the inner wall is identified. For both rotating and nonrotating cases, the direction and strength of the secondary flow with respect to the wall are the most important fluid dynamic factors affecting local the heat transfer distributions inside a 180-deg sharp turn. The role of the turbulent kinetic energy in the overall enhancement of heat transfer is well addressed.

Relationship between the heat transfer law and the scalar dissipation function in a turbulent channel flow

2017 ◽  
Vol 830 ◽  
pp. 300-325 ◽  
Author(s):  
Hiroyuki Abe ◽  
Robert Anthony Antonia
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Channel Flow ◽  
Dissipation Rate ◽  
Turbulent Channel Flow ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate ◽  
Mean Velocity ◽  
The Mean ◽  
Logarithmic Dependence

Integration across a fully developed turbulent channel flow of the transport equations for the mean and turbulent parts of the scalar dissipation rate yields relatively simple relations for the bulk mean scalar and wall heat transfer coefficient. These relations are tested using direct numerical simulation datasets obtained with two isothermal boundary conditions (constant heat flux and constant heating source) and a molecular Prandtl number Pr of 0.71. A logarithmic dependence on the Kármán number $h^{+}$ is established for the integrated mean scalar in the range $h^{+}\geqslant 400$ where the mean part of the total scalar dissipation exhibits near constancy, whilst the integral of the turbulent scalar dissipation rate $\overline{\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}}$ increases logarithmically with $h^{+}$. This logarithmic dependence is similar to that established in a previous paper (Abe & Antonia, J. Fluid Mech., vol. 798, 2016, pp. 140–164) for the bulk mean velocity. However, the slope (2.18) for the integrated mean scalar is smaller than that (2.54) for the bulk mean velocity. The ratio of these two slopes is 0.85, which can be identified with the value of the turbulent Prandtl number in the overlap region. It is shown that the logarithmic $h^{+}$ increase of the integrated mean scalar is intrinsically associated with the overlap region of $\overline{\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D703}}}$, established for $h^{+}$ (${\geqslant}400$). The resulting heat transfer law also holds at a smaller $h^{+}$ (${\geqslant}200$) than that derived by assuming a log law for the mean temperature.

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