Temperature correction for hot-wire anemometers in non-isothermal turbulent boundary layers

The transmission of sound from a source outside a nonisothermal high-speed boundary layer is considered. The sound source is assumed to lie in a uniform stream and matched to a zero velocity at the wall by a linear velocity profile. The unidirectional shear mean flow is assumed to be isentropic but nonhomentropic, so that the entropy, the sound speed, and the temperature can vary fromone streamline to the other. The condition of homoenergetic flow, or constant enthalpy, is used to relate the sound speed to themeanflowvelocity and specify the temperature profile in the boundary layer. Compared with a homentropic boundary layer, for which sound refraction is due to the shear flow alone, a nonhomentropic boundary layer introduces additional refraction due to the nonuniform sound speed and the associated temperature gradients. It is shown that for a high speed, even in isentropic conditions, the nonhomentropic effects of temperature gradients and the nonuniform sound speed can cause significant sound attenuation (viz., for the same sound source outside the boundary layer, the acoustic pressure at the wall can be substantially reduced). This agrees qualitativelywith the results from testingpropfans at high subsonic speeds,which showed significant sound attenuation in the fuselage boundary layer.

Nonequilibrium thermal dissociation in a nonisothermal boundary layer in a mixture of Morse anharmonic oscillators — molecules of a diatomic gas and its atoms — is considered within the framework of the ladder mechanism. The local nonlinear nonequilibrium corrections to the two-temperature macroscopic dissociation rate, which depend, in particular, on the translational and vibrational temperature gradients and the degree of dissociation, are determined.

Effects of weak, small-scale freestream turbulence on turbulent boundary layers with and without thermal convection are experimentally investigated using a wind tunnel. Two experiments are carried out: the first is isothermal boundary layers with and without grid turbulence, and the second is non-isothermal boundary layers with and without grid turbulence. Both boundary layers develop under a small favorable pressure gradient. For the latter case, the bottom wall of the test section is heated at a constant wall temperature to investigate the effects of thermal convection under the effects of freestream turbulence. For both cases, the turbulence intensity in the freestream is Tu = 1.3% ∼ 2.4%, and the integral length scale of freestream turbulence, L∞, is much smaller than the boundary layer thickness δ, i.e., L∞/δ≪1. The Reynolds numbers Reθ based on the momentum thickness and freestream speed U∞ are Reθ = 560, 1100, 1310, and 2330 in isothermal boundary layers without grid turbulence. Instantaneous velocities, U and V, and instantaneous temperature T are simultaneously measured using a hot-wire anemometry and a constant-current resistance thermometer. The results show that the rms velocities and Reynolds shear stress normalized by the friction velocity are strongly suppressed by the freestream turbulence throughout the boundary layer in both isothermal and non-isothermal boundary layers. In the non-isothermal boundary layers, the normalized rms temperature and vertical turbulent heat flux are also strongly suppressed by the freestream turbulence. Turbulent momentum and heat transfer at the wall are enhanced by the freestream turbulence and the enhancement is notable in unstable stratification. The power spectra of u, v, and θ and their cospectra show that motions of almost all scales are suppressed by the freestream turbulence in both the isothermal and non-isothermal boundary layers.

Hot-wire experimental investigation on turbulent Prandtl number in a rotating non-isothermal turbulent boundary layer

This experiment measured the instantaneous temperature and velocity field synchronously in non-isothermal turbulent boundary layer in a rotating straight channel with a parallel-array hot-wire probe. The Reynolds number based on the bulk mean velocity (U) and hydraulic diameter (D) is 19000, and the rotation numbers are 0, 0.07, 0.14, 0.21 and 0.28. The mean velocity u and mean temperature T as well as their fluctuating quantity u’ and T’ were measured at three streamwise locations (x/D = 4.06, 5.31, 6.56). A method for temperature-changing calibration with constant temperature hot-wire anemometers was proposed. It achieved the calibration in operational temperature range (15.5 °C–50 °C) of the hot-wire via a home-made heating section. The measurement system can obtain the velocity and temperature in a non-isothermal turbulent boundary layer at rotating conditions. The result analysis mainly contains the dimensionless mean temperature, temperature fluctuation as well as its skewness and flatness and streamwise turbulent heat flux. For the trailing side, the rotation effect is more obvious, and makes the dimensionless temperature profiles lower than that under static conditions. The dimensionless streamwise heat flux shows a linear decrease trend in the boundary layer. It is hoped that this research can improve our understanding of the flow and heat transfer mechanism in the internal cooling passages of turbine rotor blades.

Inflow turbulence generation for large eddy simulation in non-isothermal boundary layers

Boundary layer suction is one of the effective methods of intensifying heat and mass transfer and controlling the boundary layer. Many investigations are now being made of a boundary layer with blowing, but the influence of suction on heat and mass transfer in a turbulent boundary layer is studied much less often. Moreover, all known experimental studies [1–5] have been made under nearly isothermal conditions. Under these conditions, the existing theories [6–9] give a fairly good description of the experiments. In the present paper, we report on theoretical and experimental investigation into the influence of uniform suction on heat and mass transfer in a nonisothermal turbulent boundary layer in the presence of chemical reactions on the surface.

Highly reliable measurement of temperature fluctuation in near-wall turbulence by a sophisticated cold-wire technique for considering the frequency response and spatial resolution

Exact solutions of the equations of a stationary laminar boundary layer are reviewed. New exact solutions are presented that depend on arbitrary functions. Newtonian and non-Newtonian liquids are considered. Nonisothermal and diffusion boundary layers are analyzed. A general transformation is presented that preserves the form of the three-dimensional boundary layer equations in an arbitrary orthogonal curvilinear coordinate system. A simple approximate method is proposed for solving the boundary layer problems for flows past slightly deformed smooth surfaces.

The nonlinear, non-isothermal steady-state boundary layer flow and heat transfer of an incompressible tangent hyperbolic non-Newtonian (viscoelastic) fluid from a vertical permeable cone with magnetic field are studied. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using the second-order accurate implicit finite difference Keller-box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely a Weissenberg number (We), rheological power law index (m), surface temperature exponent (n), Prandtl number (Pr), magnetic parameter (M) suction/injection parameter (fw) and dimensionless tangential coordinate (ξ) on velocity and temperature evolution in the boundary layer regime, is examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. It is observed that velocity, surface heat transfer rate and local skin friction are reduced with increasing Weissenberg number, but temperature is increased. Increasing m enhances velocity and surface heat transfer rate but reduces temperature and local skin friction. An increase in non-isothermal power law index (n) is observed to decrease the velocity and temperature. Increasing magnetic parameter (M) is found to decrease the velocity and increase the temperature. Overall, the primary influence on free convection is sustained through the magnetic body force parameter, M, and also the surface mass flux (injection/suction) parameter, fw. The rheological effects, while still prominent, are not as dramatic. Boundary layers (both hydrodynamic and thermal) are, therefore, most strongly modified by the applied magnetic field and wall mass flux effect. The study is pertinent to smart coatings, e.g., durable paints, aerosol deposition processing and water-based solvent thermal treatment in chemical engineering.

In thermofluid dynamics, free convection flows external to different geometries such as cylinders, ellipses, spheres, curved walls, wavy plates, and cones play a major role in various industrial and process engineering systems. The thermal buoyancy force associated with natural convection flows can exert a critical role in determining skin friction and heat transfer rates at the boundary. In thermal engineering, natural convection flows from cones has gained exceptional interest. A theoretical analysis is developed to investigate the nonlinear, steady-state, laminar, non-isothermal convection boundary layer flows of viscoelastic fluid from a vertical permeable cone with a power-law variation in both temperature and concentration. The Jeffery’s viscoelastic model simulated the non-Newtonian characteristics of polymers, which constitutes a novelty of the present work. The transformed conservation equation for linear momentum, energy, and concentration are solved numerically under physically viable boundary conditions using the finite-difference Keller box scheme. The impact of Deborah number (De), ratio of relaxation to retardation time (λ), surface suction/injection parameter (fw), power-law exponent (n), buoyancy ratio parameter (N), and dimensionless tangential coordinate (ξ) on velocity, surface temperature, concentration, local skin friction, heat transfer rate, and mass transfer rate in the boundary layer regime is presented graphically. It is observed that increasing values of De reduces velocity whereas the temperature and concentration are increased slightly. Increasing λ enhance velocity, however, reduces temperature and concentration slightly. The heat and mass transfer rate are found to decrease with increase in De and increase with increasing values of λ. The skin friction is found to decrease with a rise in De, whereas it is elevated with increasing values of λ. Increasing values of fw and n decelerates the flow and also cools the boundary layer, i.e., reduces temperature and also concentration. The study is relevant to chemical engineering systems, solvent, and polymeric processes.

New classes of exact solutions and transformations of the unsteady-state laminar boundary layer equations are described. Particular attention is given to general solutions that depend on arbitrary functions. Newtonian and non-Newtonian liquids characterized by arbitrary relationships between the shear stress and the shear rate are considered. A transformation is presented that preserves the form of the three-dimensional unsteady-state boundary layer equations in an arbitrary orthogonal curvilinear coordinate system. Three-dimensional nonisothermal and diffusion boundary layers are analyzed.

This chapter firstly describes the necessity of validation study of CFD in relation to pollutant/thermal dispersion in urban areas by comparing CFD results with reliable wind tunnel experimental data. The second section explains a technique for simultaneously measuring fluctuating velocity, temperature, and concentration in non-isothermal turbulent layers. The third section introduces examples of pollutant/thermal dispersion experiments in non-isothermal turbulent boundary layers with different atmospheric stability conditions. This measurement technique was used for the wind tunnel experiments. The fourth section reviews various methods for generating inflow turbulence for large eddy simulation and shows some calculated results by large eddy simulation of pollutant/thermal dispersion that target the wind tunnel experiments mentioned above with the experimental data.

The concentration distribution of massive dilute species (e.g. aerosols, heavy vapours, etc.) carried in a gas stream in non-isothermal boundary layers is studied in the large-Schmidt-number limit, Sc[Gt ]1, including the cross-mass-transport by thermal diffusion (Ludwig–Soret effect). In self-similar laminar boundary layers, the mass fraction distribution of the dilute species is governed by a second-order ordinary differential equation whose solution becomes a singular perturbation problem when Sc[Gt ]1. Depending on the sign of the temperature gradient, the solutions exhibit different qualitative behaviour. First, when the thermal diffusion transport is directed toward the wall, the boundary layer can be divided into two separated regions: an outer region characterized by the cooperation of advection and thermal diffusion and an inner region in the vicinity of the wall, where Brownian diffusion accommodates the mass fraction to the value required by the boundary condition at the wall. Secondly, when the thermal diffusion transport is directed away from the wall, thus competing with the advective transport, both effects balance each other at some intermediate value of the similarity variable and a thin intermediate diffusive layer separating two outer regions should be considered around this location. The character of the outer solutions changes sharply across this thin layer, which corresponds to a second-order regular turning point of the differential mass transport equation. In the outer zone from the inner layer down to the wall, exponentially small terms must be considered to account for the diffusive leakage of the massive species. In the inner zone, the equation is solved in terms of the Whittaker function and the whole mass fraction distribution is determined by matching with the outer solutions. The distinguished limit of Brownian diffusion with a weak thermal diffusion is also analysed and shown to match the two cases mentioned above.

The effect of an inhomogeneous temperature field in a boundary layer on the kinetics of dissociation of diatomic molecules simulated by truncated harmonic oscillators is considered in a multicomponent mixture in the presence of exchange reactions which take place at lower vibrational levels as compared with dissociation.