Two Fluid Modeling of Microbubble Turbulent Drag Reduction

2003 ◽  
Author(s):  
Robert F. Kunz ◽  
Steven Deutsch ◽  
Jules W. Lindau
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Drag Reduction ◽  
Flat Plate ◽  
Skin Friction ◽  
High Reynolds Number ◽  
Fluid Modeling ◽  
Wall Shear ◽  
High Reynolds ◽  
Two Fluid

An unstructured 3D multiphase CFD method has been adapted and applied for the modeling of high Reynolds number external flows with microbubble drag reduction (MDR). An ensemble averaged multi-field two-fluid baseline differential model is employed. Interfacial dynamics models are incorporated to account for drag, lift, virtual mass and dispersion. Wall kinematic constraints, porous-wall shear apportionment, coalescence, breakup and attendant turbulence attenuation are also accounted for. The results of several high Reynolds number applications are presented, including quasi-1D analysis of an equilibrium bubbly boundary layer, 2D analysis of flat plate flow across a range of gas injection flow rates, and 3D analysis of a notional high lift hydrofoil with MDR. For the flat plate analyses, quantitative comparisons are made with available experimental skin friction measurements, and qualitative comparisons are made with available volume fraction profile measurements. Though some accuracy shortcomings remain, the generally good agreement observed serves to validate the appropriateness of two-fluid modeling in these flows, while elucidating areas where modeling improvements can be made. It is observed that the extraction of turbulent kinetic energy from the liquid phase by the action of bubble breakup can be a significant source of skin friction reduction. Also, the role of mixture density in the boundary layer on wall shear stress is discussed in the context of the homogenous mixture and two-fluid simulations presented.

Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to 13650

2014 ◽  
Vol 743 ◽  
pp. 202-248 ◽  
Author(s):  
Sébastien Deck ◽  
Nicolas Renard ◽  
Romain Laraufie ◽  
Pierre-Élie Weiss
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Flat Plate ◽  
Skin Friction ◽  
High Reynolds Number ◽  
Large Scale ◽  
Wall Shear ◽  
High Reynolds

AbstractA numerical investigation of the mean wall shear stress properties on a spatially developing turbulent boundary layer over a smooth flat plate was carried out by means of a zonal detached eddy simulation (ZDES) technique for the Reynolds number range $3060\leq Re_{\theta }\leq 13\, 650$. Some asymptotic trends of global parameters are suggested. Consistently with previous findings, the calculation confirms the occurrence of very large-scale motions approximately $5\delta $ to $6 \delta $ long which are meandering with a lateral amplitude of $0.3 \delta $ and which maintain a footprint in the near-wall region. It is shown that these large scales carry a significant amount of Reynolds shear stress and their influence on the skin friction, denoted $C_{f,2}$, is revisited through the FIK identity by Fukagata, Iwamoto & Kasagi (Phys. Fluids, vol. 14, 2002, p. L73). It is argued that $C_{f,2}$ is the relevant parameter to characterize the high-Reynolds-number turbulent skin friction since the term describing the spatial heterogeneity of the boundary layer also characterizes the total shear stress variations across the boundary layer. The behaviour of the latter term seems to follow some remarkable self-similarity trends towards high Reynolds numbers. A spectral analysis of the weighted Reynolds stress with respect to the distance to the wall and to the wavelength is provided for the first time to our knowledge and allows us to analyse the influence of the largest scales on the skin friction. It is shown that structures with a streamwise wavelength $\lambda _x >\delta $ contribute to more than $60\, \%$ of $C_{f,2}$, and that those larger than $\lambda _x >2\delta $ still represent approximately $45\, \%$ of $C_{f,2}$.

Bubble friction drag reduction in a high-Reynolds-number flat-plate turbulent boundary layer

2006 ◽  
Vol 552 (-1) ◽  
pp. 353 ◽  
Author(s):  
WENDY C. SANDERS ◽  
ERIC S. WINKEL ◽  
DAVID R. DOWLING ◽  
MARC PERLIN ◽  
STEVEN L. CECCIO
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Drag Reduction ◽  
Flat Plate ◽  
High Reynolds Number ◽  
Friction Drag ◽  
High Reynolds ◽  
Friction Drag Reduction

Flow-induced degradation of drag-reducing polymer solutions within a high-Reynolds-number turbulent boundary layer

2011 ◽  
Vol 670 ◽  
pp. 337-364 ◽  
Author(s):  
BRIAN R. ELBING ◽  
MICHAEL J. SOLOMON ◽  
MARC PERLIN ◽  
DAVID R. DOWLING ◽  
STEVEN L. CECCIO
Keyword(s):  
Boundary Layer ◽  
Molecular Weight ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Drag Reduction ◽  
High Reynolds Number ◽  
Polymer Degradation ◽  
Rheological Analysis ◽  
Downstream Distance ◽  
High Reynolds

Polymer drag reduction, diffusion and degradation in a high-Reynolds-number turbulent boundary layer (TBL) flow were investigated. The TBL developed on a flat plate at free-stream speeds up to 20ms−1. Measurements were acquired up to 10.7m downstream of the leading edge, yielding downstream-distance-based Reynolds numbers up to 220 million. The test model surface was hydraulically smooth or fully rough. Flow diagnostics included local skin friction, near-wall polymer concentration, boundary layer sampling and rheological analysis of polymer solution samples. Skin-friction data revealed that the presence of surface roughness can produce a local increase in drag reduction near the injection location (compared with the flow over a smooth surface) because of enhanced mixing. However, the roughness ultimately led to a significant decrease in drag reduction with increasing speed and downstream distance. At the highest speed tested (20ms−1) no drag reduction was discernible at the first measurement location (0.56m downstream of injection), even at the highest polymer injection flux (10 times the flux of fluid in the near-wall region). Increased polymer degradation rates and polymer mixing were shown to be the contributing factors to the loss of drag reduction. Rheological analysis of liquid drawn from the TBL revealed that flow-induced polymer degradation by chain scission was often substantial. The inferred polymer molecular weight was successfully scaled with the local wall shear rate and residence time in the TBL. This scaling revealed an exponential decay that asymptotes to a finite (steady-state) molecular weight. The importance of the residence time to the scaling indicates that while individual polymer chains are stretched and ruptured on a relatively short time scale (~10−3s), because of the low percentage of individual chains stretched at any instant in time, a relatively long time period (~0.1s) is required to observe changes in the mean molecular weight. This scaling also indicates that most previous TBL studies would have observed minimal influence from degradation due to insufficient residence times.

scholarly journals Persistence of the laminar regime in a flat plate boundary layer at very high Reynolds number

2006 ◽  
Vol 10 (2) ◽  
pp. 63-96 ◽  
Author(s):  
Jovan Jovanovic ◽  
Bettina Frohnapfel ◽  
Emir Skaljic ◽  
Milenko Jovanovic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Flat Plate ◽  
High Reynolds Number ◽  
Plate Boundary ◽  
Laminar Regime ◽  
High Reynolds ◽  
Very High ◽  
Flat Plate Boundary Layer

Flat-Plate Frictional-Drag Reduction with Polymer Injection

1971 ◽  
Vol 15 (04) ◽  
pp. 278-288
Author(s):  
Justin H. McCarthy
Keyword(s):  
Reynolds Number ◽  
Drag Reduction ◽  
Flat Plate ◽  
High Reynolds Number ◽  
Leading Edge ◽  
Flat Plates ◽  
Frictional Drag ◽  
Polymer Injection ◽  
High Reynolds ◽  
Reynolds Number Flows

A method is developed for prediction of frictional-drag reduction in high Reynolds number flows past smooth flat plates with polymer injection near the leading edge. Numerical results are given for water-Polyox WSR 301 solutions with either uniform concentration or injection.

Skin Friction Measurements of Transition in High Reynolds Number, Adverse Pressure Gradient Flow

2018 ◽  
Author(s):  
Brian M. Holley ◽  
Larry W. Hardin ◽  
Gregory Tillman ◽  
Ray-Sing Lin ◽  
Jongwook Joo
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Skin Friction ◽  
High Reynolds Number ◽  
Gradient Flow ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Data Set ◽  
High Reynolds

A combined experimental and analytical modeling effort has been carried out to measure the skin friction response of the boundary layer in high Reynolds number adverse pressure gradient flow. The experiment was conducted in the United Technologies Research Center (UTRC) Acoustic Research Tunnel, an ultra-low freestream turbulence facility capable of laminar boundary layer research. Boundary layer computational fluid dynamics and stability modeling were used to provide pre-test predictions, as well as to aid in interpretation of measured results. Measurements were carried out at chord Reynolds numbers 2–3 × 106, with the model set at multiple incidence angles to establish a range of relevant leading edge pressure gradients. The combination of pressure gradient and flight Reynolds number testing on a thin airfoil has produced a unique data set relevant to propulsion system turbomachinery.

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