Non-isothermal Boundary Layer Research Articles

A new equilibrium temperature inflow profile for modelling the non-isothermal atmospheric boundary layer in CFD simulation

The atmospheric boundary layer (ABL) flow in urban morphologies, ranging from micro-scale to local-scale, will become non-isothermal due to the combined effects of solar radiation, wall heat transfer, the urban heat island, and anthropogenic heat, resulting in a mutually coupled urban thermal and wind environment. An appropriate temperature inflow profile is the key prerequisite for Computational Fluid Dynamics (CFD) simulations of the non-isothermal ABL flow and the urban thermal and wind environment, as it must coincide with actual thermal characteristics while being compatible with CFD. Based on the equilibrium ABL model, a new equilibrium temperature inflow profile compatible with the energy equation, the standard gradient diffusion hypothesis, and the turbulence model is derived, which is proportional to the turbulent kinetic energy inflow profile, with the ratio further determined by the wall heat flux, demonstrating that turbulent thermal diffusion is strongly related to turbulent characteristics and atmospheric stability. To address the scaled effect, its full expression is provided based on thermodynamic similarity criteria. Using a numerical model of empty domain based on the SST k-ω model, the horizontal homogeneity of the equilibrium thermal and wind field modeled by the new set of inflow profiles is verified. Taking the flow around a single square building model as an example, its applicability in simulating the urban thermal and wind environment around buildings has been numerically validated, where the comparison of numerical and test results reveals tolerable errors overall.

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

In turbulence measurement of the thermal field in a non-isothermal turbulent boundary layer, it is necessary to use a small-scale temperature sensor that can provide high spatial resolution. Thus, a fine-wire temperature sensor commonly called “cold-wire” is indispensable for capturing small-scale temperature fluctuations near the wall. However, the length-to-diameter ratio of the cold-wire need generally exceed 1000 to minimize the deterioration in dynamic response due mainly to the axial heat conduction of the thin-wire sensor. To meet such a conflicting requirement, the wire diameter of the cold-wire must be extremely thin. In the present study, we have tested experimentally the performance of several cold-wires of different geometrical features, and examined the effects of the temporal and spatial resolutions of the cold-wire on the temperature fluctuation measurements—root-mean-square (rms) values and instantaneous signal traces—in a canonical turbulent thermal boundary layer. As a result, it was found that the previously-reported response compensation technique for the cold-wire outputs enables us to realize sufficiently accurate temperature fluctuation measurement in the immediate vicinity of the wall while avoiding the deterioration in the spatial resolution of the cold-wire. Furthermore, to improve the spatial resolution of the cold-wire probe, we propose a novel temperature sensor consisting of a fine tungsten wire bent at its center to make an apex angle less than about 30 degrees and have named this sensor a “V-shaped” cold-wire. We have verified its measurement performance in reference to the results obtained by a standard cold-wire probe. As a result, it is shown that the V-shaped cold-wire naturally provides high spatial resolution especially for temperature fluctuation measurement near the wall and can take full advantage of the response compensation technique for the normal cold-wire probe.

Estimation of pollutant dispersion around a building within non-isothermal boundary-layer using detached eddy simulation

The paper presents the numerical results of modelling pollutant transport from a low source behind a bluff-body imitating a building within a non-isothermal boundary-layer. The main goal of the study is to estimate the tracer gas dispersion in a complex turbulent separated flow behind a building in the presence of interference of the atmospheric boundary-layer and local flows. In the first part of the study we compare numerical approaches URANS and IDDES for turbulent flow prediction on a configuration for which experimental data are available. It is shown that detached eddy simulation approach predicts correctly the main separated flow features and demonstrates a reliable correlation with the experimental data on mean velocity, pollutant concentration and temperature fields. In the second part of the study, the influence of unstable thermal stratified flow on the tracer gas transport around a building is analyzed using IDDES method. The unstable thermal flow regime considered in the study affects the distribution of the pollutant concentration in the re-circulation zone behind the building. The presence of additional buoyancy effects leads to an increase in the gas concentration on the leeward wall of the body and gas transport from a ground region to a height greater than in the case with the neutral boundary-layer.

Embedded LES of thermal stratification effects on the airflow and concentration fields around an isolated high-rise building: Spectral and POD analyses

Non-isothermal stratification conditions can alter the airflow pattern and pollutant dispersion process within urban areas. The present study is focused on the impact of various stratification conditions, namely, stable, isothermal (neutral), and unstable, on the airflow and concentration fields around an isolated high-rise building. Zonal Reynolds-averaged Navier-Stokes (RANS)-large eddy simulation (LES), also known as embedded large eddy simulation (ELES), is employed for simulating the airflow and concentration fields under non-isothermal boundary layers in order to make a balance between computational costs and accuracy. Comparing the results predicted by the present ELES with an available LES study, with almost similar computational settings (i.e., the inflow turbulence generation method, grid resolution, etc.) shows better performance of ELES in predicting the concentration field. The findings also illustrate that the impact of the unstable stratification condition on turbulence statistics is more pronounced than that of the stable stratification condition. The present article also investigates the effect of thermal stratification conditions on the mechanisms of pollutant dispersion, namely, convective and turbulent diffusion fluxes. The findings reveal that an increase in turbulence kinetic energy (TKE), caused by the unstable thermal stratification condition, increases the concentration fluctuations, which causes the pollutant concentration to be decreased. Furthermore, spectral and proper orthogonal decomposition (POD) analyses are performed for all stratification scenarios. The results show that by altering the thermal condition from isothermal to non-isothermal, either stable or unstable conditions, the contribution of the primary dominant modes to total TKE increases.

Nonsimilar boundary layer flow of Cross fluid induced by a heated stretched sheet

AbstractThis paper deals with the nonisothermal boundary layer flow of Cross fluid due to a stretching sheet. Unlike previous studies on boundary layer flow of Cross fluid, a nonsimilar formulation is adopted to transform the boundary layer equations into nondimensional form. The problem is characterized by three dimensionless parameters, namely, the Deborah number, the Prandtl number, and dimensionless distance along the sheet. The transformed equations are simulated by a numerical scheme with the help of MAPLE software. The velocity and temperature profiles inside the boundary layer are calculated and shown graphically. The skin friction coefficient and Nusselt number at various axial stations are also tabulated for several values of Deborah number and Prandtl number.

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

This experiment used a parallel array of hot wire probes to simultaneously measure the temperature and velocity fields in the non-isothermal turbulent boundary layer of a rotating straight channel. The Reynolds numbers are 15,000 and 25,000, respectively. The rotation numbers are 0, 0.07, 0.14, 0.21 and 0.28, respectively. The purpose of this study is to calculate the turbulent Prandtl number in a rotating non-isothermal turbulent boundary layer. Due to the difficulty in measuring local turbulent Prandtl numbers, this study focuses on the average turbulent Prandtl numbers in the logarithmic region instead. Under static conditions, this value is taken as 0.9 normally. This research finds that rotation conditions can affect the turbulent Prandtl number by affecting the properties of velocity and temperature boundary layers. The change range of the turbulent Prandtl number is roughly 0.6–1.1. The influence of the leading side is greater than that of the trailing side, especially at high rotation numbers. This can provide validation and guidance for numerical simulation. Other information within the turbulent boundary layer is also discussed. It is hoped that this study would enhance our understanding of the mechanism of turbulent flow in the turbulent layer at rotating conditions.

Effect of ablation at the inlet of submerged nozzle on discharge characteristics

The effect of ablation on the discharge characteristics of solid rocket engines with submerged nozzles is examined. State-of-the-art computational fluid dynamics software package ANSYS Fluent is employed for simulation. The ablation is considered from the standpoint of the effect caused by uniform blowing of degradation products on the boundary layer developing over the entrance length of the submerged nozzle. Different masses of injected substance are considered. The impact of injection on velocity profiles is estimated. The discharge coefficient is affected by the non-isothermal boundary layer when degraded thermal protection material is injected and chemical reactions are neglected. The effect of injection on the profiles of velocity and temperature, and hence, on discharge characteristics is revealed.

Experimental Investigation on Velocity and Temperature Field in a Rotating Non-isothermal Turbulent Boundary Layer using Hot-wire

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.

Effects of ramped wall temperature and concentration on viscoelastic Jeffrey’s fluid flows from a vertical permeable cone

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.

Large eddy simulation of thermal stratification effect on convective and turbulent diffusion fluxes concerning gaseous pollutant dispersion around a high-rise model building

In this paper, the large eddy simulation (LES) approach is employed to investigate the role of different thermal stratification conditions (stable, neutral and unstable) in the air flow and gaseous pollutant dispersion processes around a high-rise non-isolated model building with 1:1:2 shape placed within a non-isothermal boundary layer. The simulation results are initially validated with available experimental measurements and then applied to study the characteristics of pollutant dispersion. Predictions show a low-velocity zone behind the model building. The major effect of a stable stratification on flow field is the formation of a weak recirculation flow in the wake region. Results represent an intense temperature gradient close to the sides of the model building for both stable and unstable conditions. Moreover, the convective and turbulent diffusion fluxes are compared under different thermal stratification conditions, and it is shown that the LES approach is capable of predicting the counter-gradient mechanism.

Magnetohydrodynamic free convection boundary layer flow of non-Newtonian tangent hyperbolic fluid from a vertical permeable cone with variable surface temperature

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.

Lie group analysis and numerical solutions for non-Newtonian nanofluid flow in a porous medium with internal heat generation

A mathematical model is presented and analysed for steady two-dimensional non-isothermal boundary layer flow from a heated horizontal surface which is embedded in a porous medium saturated with a non-Newtonian power-law nanofluid. It is assumed that the wall temperature and nanoparticle volume fraction vary nonlinearly with the axial distance. By applying appropriate group transformations, the governing transport equations are reduced to a system of coupled, nonlinear ordinary differential equations with associated boundary conditions. The reduced equations are then solved numerically using the Runge–Kutta–Fehlberg fourth–fifth-order numerical method with Maple 13 software. The effects of several thermophysical parameters including rheological power-law index, non-isothermal index, Lewis number, Brownian motion parameter, thermophoresis parameter, buoyancy ratio and internal heat generation/absorption parameter on the non-dimensional velocity, temperature, nanoparticle volume fraction (concentration) and also on the friction factor, heat and mass transfer rates are investigated. A comparison of the present results with the existing published results shows excellent agreement, verifying the accuracy of the present numerical code. The study finds applications in nano biopolymeric manufacturing processes and also thermal enhancement of energy systems employing rheological working fluids.

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

Many studies have presented the importance of turbulent inflow data for large eddy simulation, and several techniques have been proposed for generating inflow fluctuations for LES in a neutral boundary layer, but few studies have considered non-isothermal cases. In this study, first wind tunnel experiments were conducted to generate both unstable and stable turbulent thermal boundary layers in a thermally stratified wind tunnel at Tokyo Polytechnic University. The decrease of turbulence due to the effect of buoyancy was clearly observed in a stable boundary layer. Then a precursor method using a long domain and a recycling procedure using a short domain to generate the turbulence statistics corresponding to the experimental data were investigated for both unstable and stable conditions. The characteristics of the generated flow (mean profiles and fluctuation profiles) by both methods agreed relatively well with those of the wind tunnel experimental data. When a recycling procedure was adopted to generate turbulence statistics in a stable boundary layer, large damping was necessary to decrease the turbulence level. For the temperature field, giving only a mean profile (no temperature fluctuation) as an inflow boundary condition of the driver region was the simplest way. Even if the inflow temperature fluctuation was not given, temperature fluctuation gradually developed in the downstream direction with velocity fluctuation in the turbulent boundary layer.

Effects of small-scale freestream turbulence on turbulent boundary layers with and without thermal convection

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.

Heat transfer enhancement for boundary layer flow over a wedge by the use of electric fields

The effect of an electric field is investigated for heat transfer properties in a laminar, incompressible, non-isothermal boundary layer gas flow over a wedge. The governing boundary layer equations are reduced to an ordinary differential equation system using similarity transformations. The reduced equations are solved numerically for different values of electric and flow field parameters characterizing the ratio of electric force to fluid inertia force, Joule heating and ion kinetic work. For specific electric field function forms, leading to similarity solutions, velocity boundary layers are observed to become thinner and heat transfer properties are shown to be enhanced near the wall. The level of enhancement is controlled by the electric body force with additional effects of Joule heating and ion kinetic work on the bulk flow. The effects of low and high Prandtl numbers are also demonstrated. Heat transfer enhancement is observed to increase with increasing Prandtl number.

CFD simulations of gas dispersion around high-rise building in non-isothermal boundary layer

Urban heat island phenomena and air pollution become serious problems in weak wind regions such as behind buildings and within street canyons, where buoyancy effect cannot be neglected. In order to apply CFD techniques for estimation of ventilation and thermal and pollutant dispersion in urban areas, it is important to assess the performance of turbulence models adopted to simulate these phenomena. As the first step of this study, we carried out wind tunnel experiments and CFD simulations of gas and thermal dispersion behind a high-rise building in an unstable non-isothermal turbulent flow. The standard k– ε model and a two-equation heat-transfer model as RANS models, and LES, were used for the CFD simulation. One of the important purposes of this study was to clarify the effect of inflow turbulence (both velocity and temperature) on flow field and gas/thermal dispersion for the LES calculation. Thus, LES calculations with/without inflow turbulence were conducted. The inflow turbulence was generated through a separate precursor simulation. The calculated results showed that both RANS models overestimated the size of the recirculation region behind the building and underestimated the lateral dispersion of the gas. Turbulent flow structures of LES with and without inflow turbulence were completely different. The LES result with inflow turbulence achieved better agreement with the experiment.

Sound Transmission from a Source Outside a Nonisothermal Boundary Layer

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.

Soret‐modified hydrocarbon mass transport across compressed nonisothermal gases

AbstractWhile engineering methods employed to predict mass transport rates across carrier fluids are often limited to either ideal gas mixtures or constant density liquids, we deal here with species mass transport across nonisothermal compressed gas “films”, with special reference to hydrocarbon fuel vapor transport across nonisothermal N2 or H2O boundary layers at pressures up to ca. 300 atm, and at temperatures often above 1000 K. We show that because of the pressure sensitivity of the Soret factor (which quantifies the relative importance of mass transfer due to temperature gradients compared to that due to concentration gradients) mass transfer coefficients become far more sensitive to pressure level than would have been anticipated from the pressure sensitivity of ρD. Motivated, in part, by combustion applications, we first examine the expected pressure dependence of the binary Soret factor, αT,12 for each of the n‐alkanes (CH4 to C20H42) dilute in compressed N2 or H2O, exploiting a rational formulation for “correcting” Chapman‐Enskog‐derived Soret factors (α) to higher pressures based on the Thermodynamics of Irreversible Processes (TIP) combined with a Virial Equation of State (VES). Our TIP‐VES‐predicted Soret factors are used to demonstrate the pressure sensitivity of expected “Soret‐modified” mass transfer coefficients (Sherwood numbers) for the illustrative case of C12H26(g) transport across N2(g) at temperature ratios between 0.3 (“cold”‐wall) and 2.0 (“hot”‐wall) at pressures up to 300 atm. Because of the growing importance of compact, high‐pressure systems in fields beside combustion, including supercritical fluid extraction and even distillation, our present results suggest that reliable mass transfer rate predictions in nonisothermal dense vapor systems of engineering importance will generally require systematic inclusion of non‐Fickian molecular mass transport. © 2007 American Institute of Chemical Engineers AIChE J, 2007

Equations of an Unsteady-State Laminar Boundary Layer: General Transformations and Exact Solutions

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.

Exact Solutions and Transformations of the Equations of a Stationary Laminar Boundary Layer

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.