Prediction of friction and heat transfer for viscoelastic fluids in turbulent pipe flow

Experimental measurements of the friction factor and the dimensionless heat-transfer j-factor were carried out for the turbulent pipe flow of viscoelastic aqueous solutions of polyacrylamide. The studies covered a wide range of variables including polymer concentration, polymer and solvent chemistry, pipe diameter, and flow rate. Degradation effects were also studied. It is concluded that the friction factor and the dimensionless heat transfer are functions only of the Reynolds number, the Weissenberg number, and the dimensionless distance, provided that the rheology of the flowing fluid is used.Nomenclature cp Specific heat of fluid, J · kg^–1 · K^–1 - d Diameter of tube, m - f Fanning friction factor, _w/(V²/2) - h Convective heat-transfer coefficient, q _w(T _w{T _b), W · m^–2 · K^–1 - k Thermal conductivity of fluid, W · m^–1 · K^–1 - j _H Heat-transfer j-factor, StPr _a ^2/3 - L _e Entrance length, m - Nu Nusselt number, hd/k - Pr _a Prandtl number based on apparent viscosity at the wall, c _p/k - q _w Heat flux at the wall, W · m^–2 - Re _a Reynolds number based on apparent viscosity at the wall, Vd/ - St Stanton number, Nu/(Re _a Pr _a) - T Temperature, K - T _b Bulk temperature of fluid, K - T _w Inside-wall temperature, K - V Average velocity, m · s^–1 - Ws Weissenberg number, V/d - x Axial coordinate, m Greek symbols g Shear rate, s^–1 - Apparent viscosity evaluated at the wall, P⁵ - ₀ Zero shear-rate viscosity, P⁵ - Apparent viscosity at infinite shear rate, P⁵ - Characteristic time of fluid, s - Density of fluid, kg · m^–3 - _w Wall shear stress, N · m^–2 Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Skin friction and heat transfer in turbulent flow of structurally viscous fluids

Relations which contain no new empirical turbulence constants are proposed for calculation of the resistance coefficient and the Nusselt number in turbulent flow of structurally viscous fluids.     

The effect of the physical parameters of polymer solutions on the reduction of drag in turbulent flow

By measurements in the ultracentrifuge, rotational viscosimeter, photogoniodiffusometer and in an apparatus with coaxial cylinders, it is shown that in solutions which possess the Toms effect, particles of the polymer have an asymmetric shape with an elongation equal to 5 approximately. A model of a medium with anisotropic viscosity is demonstrated for explaining the phenomenon.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 6, pp. 1039–1044, December, 1973.     

Influence of polymer molecular-weight distribution on hydrodynamic drag reduction in a turbulent stream of solution

The molecular weights of polyethylene oxide specimens, their distributions and dispersion coefficients, and the dependence of the Thoms effect on the polymer concentration in the solution are measured. Values of the Thoms effect of the specimens are compared with their dispersion coefficients.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 1, pp. 40–43, July, 1977.     

Direct Monte Carlo simulation of turbulent drag reduction by rigid fibers in a channel flow

A two-way coupled simulation technique for a dilute suspension of rigid fibers in turbulent flows is proposed. It is based on an Eulerian direct numerical simulation of the incompressible Navier–Stokes equations and a Lagrangian direct Monte Carlo simulation of the fiber orientational conformation. The numerical methods are explained in detail. The developed simulation tool is employed to study the turbulent drag reduction by rigid fibers in a fully developed channel flow at a nominal shear Reynolds number Re _τ = 180. We use 128³ grid cells to resolve the Eulerian field and 6.55 × 10⁷ Lagrangian particle clusters each of which containing 100 fibers to compute the fiber conformation. This results in a total number of 6.55 × 10⁹ fibers. Turbulence statistics of the fibrous drag-reduced channel flow using a direct solver are reported for the first time. Previously reported features of a fibrous drag-reduced channel flow are confirmed by our simulation. We present the mean flow quantities. In particular, turbulence intensities are investigated by considering the probability density function of the fluctuating velocities.     

The friction drag of a turbulent flow reduced on the surface with a molecular film of foleox polymer

We have experimentally studied the possibility of reducing the friction drag of a flow over a metal surface by applying a fluorine-containing polymer (foleox) onto the surface. It is shown that the foleox coating significantly decreases the friction drag of a turbulent flow.     

Experimental study of the effect of single-layer viscoelastic coatings on turbulent friction and pressure pulsation on a wall

Information is given on the change in turbulent friction and pressure pulsations on a wall with the application of single-layer monolithic coatings. The viscoelastic properties of the materials used are characterized.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 2, pp. 189–196, August, 1984.     

Thermal convection waves in viscoelastic fluids

We demonstrate that undamped and weakly damped thermal convection waves, in particular, thermal and transverse waves, can be propagated in viscoelastic heat-conducting fluids. We have found the frequency spectrum and the wavelengths for such waves. We indicate the possibility of developing a mechanical generator of thermal oscillations.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 16, No. 5, pp. 780–785, May, 1969.     

Friction drag of turbulent finely dispersed air mixtures

On the basis of a theoretical analysis of the turbulent stresses due to momentum transfer the author determines the excess drag coefficient in a finely dispersed air-mixture flow. The results obtained are checked against the experimental data.     

Numerical evaluation of the heat transfer and the friction drag in a pipe with a turbulent flow of a gas with variable physical properties

The temperature field and the velocity field as well as the local coefficients of heat transfer and friction are determined in the entrance segment of a pipe where a turbulent flow of a gas with variable physical properties stabilizes thermally.Translated from Inzhenerno-Fizteheskii Zhurnal, Vol. 24, No. 4, pp. 730–734, April, 1973.     

On turbulent flow of micropolar fluids

Equations of motion for turbulent parallel flows are derived for a class of fluids named micropolar fluids by Eringen[3]. Turbulent microstress couples in addition to the conventional Reynolds stresses are identified. Conditions for flow stability are examined. Necessary conditions for turbulent flow of an ‘inviscid’ micropolar fluid are also studied. Empirical relations for fully developed turbulent flow are proposed.     

Hydraulic drag in turbulent coolant flow in a porous cable

The hydrodynamics and heat transfer in the cooling of an electrical cable by radical coolant filtration are studied.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 51, No. 3, pp. 375–383, September, 1986.     

Analysis of the drag of two discs in a turbulent incompressible fluid flow

The effect of reducing the drag of two discs is investigated by using difference modeling of their flow by using the two-parameter k — turbulence model.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 2, pp. 251–256, February, 1985.     

On a deformable superconductor model for the vortex viscoelastic drag coefficient

A deformable superconductor model for a velocity-dependent vortex visco-elastic drag coefficient is discussed. New integral identities for energy dissipation are derived, avoiding previously employed approximations. This approach provides a suitable basis for further extension and improvement of the deformable superconductor model.     

Flow of viscoelastic fluids under high shearing stresses

Some characteristics of viscoelastic fluid flow under high shearing stresses are analyzed here.Notation _w tangential shearing stress at a channel wall - h half-height of a channel - L channel length - =w/¯w flow velocity, dimensionless - ¯w mean flow velocity at a given section - fluidity of viscoelastic fluid - P_xx-P_yy first difference of normal stresses, N/m² - =y/h distance from channel wall, dimensionless Translated from Inzhenerno-Fizicheskii Zhurnal, vol. 20, No. 5, pp. 918–920, May, 1971.     

Turbulent mass transfer and diffusion in polymer solutions reducing friction drag

A comparison is presented between the computed and experimental data on turbulent mass transfer and diffusion in the near-wall domain of a channel and plate.Translated from Inzhernerno-Fizicheskii Zhurnal, Vol. 54, No. 6, pp. 963–970, June, 1988.     

Property dependence of onset of instability in viscoelastic respiratory fluids

This paper deals with the modelling of viscoelastic respiratory fluids in the mucus layer of the human trachea with a view toward the design of improved inhaled medication. The problem of instability and droplet formation in this layer, specifically aimed at problems of both cough particle suppression as well as reduction of disease transmission, is studied. Rayleigh–Taylor type analysis is performed on the suitably chosen viscoelastic model to investigate temporal instabilities and their relation to the fluid properties. Several physiologically important conclusions are obtained in support of potential treatments that work by adjusting the mucus layer properties. An important result from the analysis shows that the two potential treatment approaches are mutually incompatible.     

On propagation of small non-stationary disturbances in linear viscoelastic fluids

Summary A representation is given for the solutions of linearized equations describing a flow of compressible viscoelastic fluids, the spherical part of tensor of stresses corresponding to the rheological Voigt body, while the deviator part corresponds to the Maxwell, Oldroyd and Kelvin-Voigt body of any order. Two independent equations for the propagation of longitudinal and transverse disturbances are obtained.The Laplace transform is applied to study the propagation of plane non-stationary longitudinal and transverse waves in linear viscoelastic fluids, where the spherical part of the tensor of stresses corresponds to the elastic body, while the deviator part corresponds to the Maxwell body. The problem of inversion is reduced to the numerical solution of the linear homogeneous Volterra integral equation of the second kind with a discontinuous kernel.     

Heat exchange and drag in a turbulent boundary layer with pressure gradient

On the basis of a semiempirical Prandtl model of turbulence, the heat transfer and drag coefficients are determined in a turbulent boundary layer with longitudinal pressure gradient.     

Numerical simulations of Rayleigh-Taylor front evolution in turbulent stratified fluids

We present state-of-the-art numerical simulations of a two-dimensional Rayleigh-Taylor instability for a compressible stratified fluid. We describe the computational algorithm and its implementation on the QPACE supercomputer. High resolution enables the statistical properties of the evolving interface that we characterize in terms of its fractal dimension to be studied.