Heat transfer from the heated concave wall of a return bend with rectangular cross section

The characteristics of the turbulent heat transfer along the heated concave walls of return bends which have rectangular cross sections with large aspect ratio have been examined for various clearances of the ducts in detail. The experiments are carried out under the condition that the concave walls are heated at constant heat flux while the convex walls are insulated. Water as the working fluid is utilized. Using three kinds of clearance of 9, 34, and 55 mm, the Reynolds number in the turbulent range are varied from 5×10³ to 8×10⁴ with the Prandtl numbers ranging from 4 to 13. As a result it is elucidated that both the mean and the local Nusselt numbers are always greater than those for the straight parallel plates or for the straight duct, respectively. This is attributed to Görtier vortices, which are visualized here. It is also found that the more the clearance increases, the more both the local and the mean Nusselt numbers increase. Correlation equations for the mean and the local Nusselt numbers are determined in the range of parameters covered. Introducing the Richardson number, it appears that the local Nusselt number,Nu _x , may be described as the following equation:Nu _x =447.745 ·Re _x ^1.497 ·De _x ^?1.596 ·F ^0.960 ·Pr ^0.412     

A transition phenomenon of ice formation in water flow between two horizontal parallel plates

Experiments have been performed to investigate the icetransition profiles and heat-transfer characteristics for water flows between two horizontal parallel plates. The experiments are carried out under the condition that upper plate is cooled at uniform temperature kept less than freezing temperature of water, while the lower plate is heated at uniform temperature kept higher than the temperature of water flow. The temperatures of the upper and lower plates range from ?8 to ?14°C and from 10 to 60 °C, respectively, with inlet-water temperature varied from 1.5 to 4.5 °C. The cooling and heating temperature ratios, θ_c and θ_h, are ranging from 1.78 to 9.33 and from 1.22 to 39, respectively. By using three kinds of heightH of 16, 30 and 40 mm between the horizontal parallel plates, the Reynolds and Grashof numbers are varied from 3.2 × 10² to 1.5 × 10⁴ and from 3.4 × 10³ to 8.97 × 10⁶, respectively. As a result of this investigation two ice-transition modes are observed. The first ice-transition mode is due to an interruption of upper and lower thermal boundary layers, while the second mode is due to an instability of laminar boundary layer formed on water-ice interface. In order to determine the kind of ice-transition mode, criterion correlation formulas including the Reynolds numberRe _H , Grashof numberGr _H , and heating temperature ratio θ_h are determined and may be written as follows: For thermal icetransition mode (th.I.T.M.)Re _H /(Gr _H ·θ _h )^0.23<1.6×10^?3 and for hydrodynamical ice-transition mode (hy.I.T.M.)Re _H /(Gr _H ·θ _h )^0.23>2.3×10^?3 By introducing the freezing parameterB _f , correlation equations for local and mean Nusselt numbers along the water-ice interface at steady-state condition are determined. From the current experimental results it is found that the local Nusselt number may be described as the following equation:Nu _x =0.835 Re _H ^0.278 · B _f ^0.834 ·x/H)^?0.139     

Control of vortex shedding in an axisymmetric bluff body wake

In the present experimental study the effect of a control disc mounted at the rear of an axisymmetric blunt-based body of revolution, first studied by Mair, is investigated in the Reynolds number range 3×10³≤Re_D≤5×10⁴ . As the distance of the control disc from the blunt base is increased, four vortex shedding regimes are identified: at small distances there is no effect, then a sharp increase of vortex shedding activity and total drag is observed, followed by an interval with reduced activity and drag and finally at large distances a regime where the flow around the main body and disc become essentially independent, i.e. where the drag forces of the two elements become additive. The near and far wake velocity fields corresponding to the different regimes are documented with time- and phase-averaged hot-wire and LDA measurements, with spectral analysis of the data and with flow visualizations of the near wake. The results are used to develop an improved understanding of the instability mechanism leading to high vortex shedding activity.     

Aerodynamics of laminar separation flutter at a transitional Reynolds number

Experimental observations of self-sustained pitch oscillations of a NACA 0012 airfoil at transitional Reynolds numbers were recently reported. The aeroelastic limit cycle oscillations, herein labelled as laminar separation flutter, occur in the range 5.0×10⁴≤Re_c≤1.3×10⁵. They are well behaved, have a small amplitude and oscillate about θ=0°. It has been speculated that laminar separation leading to the formation of a laminar separation bubble, occurring at these Reynolds numbers, plays an essential role in these oscillations. This paper focuses on the Re_c=7.7×10⁴ case, with the elastic axis located at 18.6% chord. Considering that the experimental rig acts as a dynamic balance, the aerodynamic moment is derived and is empirically modelled as a generalized Duffing–van-der-Pol nonlinearity. As expected, it behaves nonlinearly with pitch displacement and rate. It also indicates a dynamically unstable equilibrium point, i.e. negative aerodynamic damping. In addition, large eddy simulations of the flow around the airfoil undergoing prescribed simple harmonic motion, using the same amplitude and frequency as the aeroelastic oscillations, are performed. The comparison between the experiment and simulations is conclusive. Both approaches show that the work done by the airflow on the airfoil is positive and both have the same magnitude. The large eddy simulation (LES) computations indicate that at θ=0°, the pitching motion induces a lag in the separation point on both surfaces of the airfoil resulting in negative pitching moment when pitching down, and positive moment when pitching up, thus feeding the LCO.     

Non-symmetric bi-stable flow around the Ahmed body

The flow around the Ahmed body at varying Reynolds numbers under yawing conditions is investigated experimentally. The body geometry belongs to a regime subject to spanwise flow instability identified in symmetric flow by Cadot and co-workers (Grandemange et al., 2013b). Our experiments cover the two slant angles 25° and 35° and Reynolds numbers up to 2.784 × 10⁶. Special emphasis lies on the aerodynamics under side wind influence. For the 35° slant angle, forces and moments change significantly with the yawing angle in the range 10° ≤ |β| ≤ 15°. The lift and the pitching moment exhibit strong fluctuations due to bi-stable flow around a critical angle β of ±12.5°, where the pitching moment changes sign. Time series of the forces and moments are studied and explained by PIV measurements in the flow field near the rear of the body.     

Effect of the use of the balance and gradient methods as a result of experimental investigations of natural convection action with regard to the conception and construction of measuring apparatus

Measurement apparatus designed and constructed according to conceptions of the authors, enabled a more precise calculation of the heat transfer coefficient with the balance and gradient methods. Construction and use of the apparatus and devices are described below, results of experimental investigations for horizontal and vertical, isothermal, flat plates obtained independently with the balance and gradient methods, are also presented. The following equations were found:Nu=0.612 · (Ra)^1/4 10⁴ ≦Ra ≦ 10⁸ for vertical platesNu=0.766 · (Ra)^1/5 10⁴ ≦Ra ≦ 10⁷ Nu=0.173 · (Ra)^1/3 10⁵ ≦Ra≦ 10⁸ for horizontal plates. On the basis of the results obtained from both these methods, differences of natural convection acting from vertical and horizontal plates are discussed. The usefulness of the balance and gradient methods have been considered for qualitative and quantitative investigations of heat transfer by natural convection.     

Effect of magnetic field on 3D flow and heat transfer during solidification from a melt

We present the effect of a magnetic field on three-dimensional fluid flow and heat transfer during solidification from a melt in a cubic enclosure. The walls of the enclosure are considered perfectly electrically conducting and the magnetic field is applied separately in three directions. The finite-volume method with enthalpy formulation is used to solve the mathematical model in the solid and liquid phases. The results obtained by our computer code are compared with the numerical and experimental data found in the literature. For Gr = 5 × 10⁵ and Ha = 0, 25, 50, 75, and 100 (where Gr and Ha are the Grashof and Hartmann numbers, respectively), the effects of magnetic field on flow and thermal fields, and on solid/liquid interface shape are presented and discussed. The interface is localized with and without magnetic field. The results show a strong dependence between the interface shape and the intensity and orientation of magnetic field. When the magnetic field is applied along the X-direction, the magnetic stability diagrams (V_max–Ha) and (Nu_avg–Ha) show the strongest stabilization of the flow field and heat transfer.     

Quantifying the dynamics of flow within a permeable bed using time-resolved endoscopic particle imaging velocimetry (EPIV)

This paper presents results of an experimental study investigating the mean and temporal evolution of flow within the pore space of a packed bed overlain by a free-surface flow. Data were collected by an endoscopic PIV (EPIV) technique. EPIV allows the instantaneous velocity field within the pore space to be quantified at a high spatio-temporal resolution, thus permitting investigation of the structure of turbulent subsurface flow produced by a high Reynolds number freestream flow (Re _s in the range 9.8?×?10³?C9.7?×?10⁴). Evolution of coherent flow structures within the pore space is shown to be driven by jet flow, with the interaction of this jet with the pore flow generating distinct coherent flow structures. The effects of freestream water depth, Reynolds and Froude numbers are investigated.     

Turbulent film boiling from a vertical non-isothermal surface

The turbulent film boiling from a vertical non-isothermal surface is formulated with due consideration to thermal radiation from its lateral face. It is observed that the application of Reynolds analogy together with thermal conduction in the test surface has yielded a conjugate solution from which the case of an isothermal condition can be generated as a special case. The analysis has further paved the way in establishing a functional relation between the Nusselt numberNu, radiation parameterN _R , fin parameterM, temperature ratio termT _s /(T _w,0?T _s ), and a product of characteristic modified Grashof, Prandtl and superheating parameter defined as (Gr ² Pr S). In a fully developed turbulent film boiling i.e., modified Grashof number being greater than 10¹⁰, the temperature ratio term accounts for the non-linearities arising due to the inclusion of radiation from the lateral face of the fin. The results are in good agreement with experimental data over a wide range of system conditions.     

Heat transfer in asymmetric transverse flows over bundles of tubes

Heat transfer was studied on a separate transverse row of tubes with the relative pitch ofs ₁/d=1.5 and a staggered bundle with the relative pitches ofs ₁/d×s ₂/d=1.15×0.98. A test tube in the transverse row was used with a variable displacement from the symmetric position. The tube bundle was placed at different gaps from the shell wall. Experiments were performed in air and water in the range ofRe from 10³ to 6×10⁵. Asymmetric flows over transverse rows are accompanied by augmented heat transfer rates and steady state lift force which becomes higher with the amount of displacement. The presence of the shell wall introduces alterations in the thermal and fluid dynamics over outside tubes in a bundle.     

Analytical solutions for laminar fully developed flows in double-sine shaped ducts

Fully developed, constant property, laminar flows in double-sine shaped ducts are considered. This cross section represents a limiting inter-plate channel geometry in plate heat exchangers. Accurate analytical solutions based on the Galerkin integral method are presented. Heat transfer with both T and H1 thermal boundary conditions is analyzed; they simulate the most fundamental practical heating/cooling applications. Velocity and temperature distributions, along withfRe, Nu _T , andNu _H1 results for flows in double-sine ducts of different aspect ratios (1/8 ≤γ ≤ 8) are presented. Effects of the relative cross-sectional geometry and thermal boundary conditions are delineated. A comparison of the thermal-hydraulic performance with that of other compact channel geometries is made. The results suggest an optimum (Nu/fRe) performance in a double-sine duct of aspect ratio near unity.     

Leray-α Regularization of the Smagorinsky-Closed Filtered Equations for Turbulent Jets at High Reynolds Numbers

The article reports on blending of the Leray-α regularization with the conventional Smagorinsky subgrid-scale closure as an option for large-eddy-simulation of turbulent flows at very high Reynolds number on coarse meshes. The model has been tested in the self-similar far-field region of a jet at a range of Reynolds numbers spanning over two decades (4×10³, 4×10⁴ and 4×10⁵) on two very coarse meshes of 2×10⁵ and 3×10⁴ mesh cells. The results are compared with the well-resolved DNS for $Re_D=4\times 10^3$ on 15 million cells and experimental data for higher Re numbers. While the pure Leray-α can fail badly at high Re numbers on very coarse meshes, a blending of the two strategies by adding a small amount of extra-dissipation performs well even at a huge jet Reynolds number of $Re_D=4\times 10^5$ on a very coarse mesh (2×10⁵ cells), despite the ratio of the typical mesh spacing to the Kolmogorov length exceeding 300. It is found that the main prerequisite for successful LES, both for the classic Smagorinsky and the blended Leray-α/Smagorinsky model, is to resolve the shear-length $L_s=\sqrt{\varepsilon/{\cal S}^3}$ (where ${\cal S}$ is the shear-rate modulus), defined by the constraint Δ/L _s ?<?1, where Δ is the typical mesh-cell size. For the mixed Leray-α/Smagorinsky model the regularization parameter should also be related to the shear-length rather than the local mesh size or Reynolds number, for which we propose a guide criterion α?=?0.15÷0.3 L _s .     

Analytical and numerical study of double diffusive convection in a vertical enclosure

This paper presents an analytical and numerical study of natural convection of a double-diffusive fluid contained in a rectangular slot subject to uniform heat and mass fluxes along the vertical sides. Governing parameters of the problem under study are the thermal Rayleigh number, Ra _T ; buoyancy ratio, N; Lewis number, Le; Prandtl number, Pr and aspect ratio of the cavity, A. In the first part of the analytical study a scale analysis is applied to the two extreme cases of heat-transfer and mass-transfer-driven flows. In the second part, an analytical solution, based on the parallel flow approximation, is reported for tall enclosures (A?1). Solutions for the flow fields, temperature and concentration distributions and Nusselt and Sherwood numbers are obtained in terms of the governing parameters of the problem. In the limits of heat-driven and solute-driven flows a good agreement is obtained between the prediction of the scale analysis and those of the analytical solution. The numerical solutions are based on the complete governing equations for two-dimensional flows, and cover the range 1≤Ra _T ≤10⁷, 0≤N≤10⁵, 10^-3≤Le≤10³, 1≤A≤20 and Pr=7. A good agreement is found between the analytical predictions and the numerical simulation.     

Transient natural convection cooling of a high Prandtl number fluid in a cubical cavity

This work presents a numerical analysis of the effects of thermal boundary conditions, fluid variable viscosity and wall conduction on transient laminar natural convection of a high Prandtl number (Pr=4×10⁴) fluid (Golden Syrup) in a cubical cavity. The simulations consider physical situations realizable at laboratory scale using a cavity with Plexiglas walls of 1 cm of thickness, and inside dimension of L=20 cm. The initial Rayleigh (Ra) number is 10⁶. The cavity is initially full of fluid at rest and at constant temperature (T _i =45°C) higher than the temperature of the walls (T _w =25°C). The time evolution of the flow patterns, the temperature contours, the mean temperature of the fluid and the Nusselt number (Nu) of eight different cases of cooling are presented and analyzed.     

Scalar dispersion in the near wake of a simplified model car

Experimental results on tracer gas diffusion within the near wake of a simplified model car (Ahmed model with a rear slant angle of 25°) are presented. Pollutant emission is simulated using heated air injected through a small pipe at one side of the model base. Fine cold wire thermometry is used to measure instantaneous temperature excess in the near wake. Characteristics of the temperature field over the Reynolds number range (1.3×10⁴<Re _L<7×10⁴) show strong differences as a result of transition in the wake at a critical Reynolds number Re _Lc=2.7×10⁴.     

Heat transfer characteristics of staggered wing-shaped tubes bundle at different angles of attack

An experimental and numerical study has been conducted to clarify heat transfer characteristics and effectiveness of a cross-flow heat exchanger employing staggered wing-shaped tubes at different angels of attack. The water-side Re_w and the air-side Re_a were at 5 × 10² and at from 1.8 × 10³ to 9.7 × 10³, respectively. The tubes arrangements were employed with various angles of attack θ_1,2,3 from 0° to 330° at the considered Re_a range. Correlation of Nu, St, as well as the heat transfer per unit pumping power (ε) in terms of Re_a and design parameters for the studied bundle were presented. The temperature fields around the staggered wing-shaped tubes bundle were predicted by using commercial CFD FLUENT 6.3.26 software package. Results indicated that the heat transfer increased with the angle of attack in the range from 0° to 45°, while the opposite was true for angles of attack from 135° to 180°. The best thermal performance and hence the efficiency η of studied bundle occurred at the lowest Re_a and/or zero angle of attack. Comparisons between the experimental and numerical results of the present study and those, previously, obtained for similar available studies showed good agreements.     

Nusselt-Rayleigh correlations for free convection in 2D air-filled parallelogrammic enclosures with isothermal active walls

In the present study Nu-Ra-α correlations are proposed to calculate the steady-state natural convection heat transfer taking place in 2D air-filled cavities of parallelogrammic section. The thermal conditions and the dimensions of the enclosures permit to cover a large range of Rayleigh numbers, 1.7 × 10³  ≤ Ra ≤ 3.0 × 10⁹, suitable for diverse engineering applications. The two active walls of the cavities are kept vertical and isothermal at hot and cold temperatures T _h and T _c respectively. Separated by a horizontal distance H, they have the same height H and are connected by a closed adiabatic channel whose upper and lower walls can be inclined at an angle α with respect to the horizontal, varying between −60° to +60°. That gives rise to a conducting or insulating cavity, in the convective sense of the term (diode cavity). A computational model based on the finite volume method is used to solve the governing equations. The large number of treated configurations led to propose Nu-Ra-α correlations for large ranges of Ra and α which can be applied to many engineering areas. The results of this numerical study have been successfully compared with calculated and measured available data.     

Numerical computation of natural convection in an isosceles triangular cavity with a partially active base and filled with a Cu–water nanofluid

This paper discusses the results of a study related to natural convection cooling of a heat source located on the bottom wall of an inclined isosceles triangular enclosure filled with a Cu water-nanofluid. The right and left walls of the enclosure are both maintained cold at constant equal temperatures, while the remaining parts of the bottom wall are insulated. The study has been carried out for a Rayleigh number in the range 10⁴ ≤ Ra ≤ 10⁶, for a heat source length in the range 0.2 ≤ ε ≤0.8, for a solid volume fraction in the range 0 ≤ ?≤0.06 and for an inclination angle in the range 0° ≤ δ≤45°. Results are presented in the form of streamline contours, isotherms, maximum temperature at the heat source surface and average Nusselt number. It is noticed that the addition of Cu nanoparticles enhances the heat transfer rate and therefore cooling effectiveness for all values of Rayleigh number, especially at low values of Ra. The effect of the inclination angle becomes more noticeable as one increases the value of Ra. For high Rayleigh numbers, a critical value for the inclination angle of δ = 15° is found for which the heat source maximum temperature is highest.     

Modeling of vibration-dissociation oxygen kinetics at temperatures of 4,000-11,000 K

The time profiles of vibrational molecular oxygen temperature T _v measured earlier in experiments behind a strong shock wave were used for testing the theoretical and empirical models of thermal nonequilibrium dissociation of molecules. To do this, dissociating gas flows behind the strong shock wave front were calculated with account for these models. If the initial gas temperature behind the wave front T ₀ < 6.5×10³ K, the models well describe changing the temperature with time. However, for T ₀ > 7×10³ K neither of the models tested describes the measured temperature profiles satisfactorily. Using the empirical model proposed in the present study made it possible to satisfactorily describe the vibrational temperature evolution observed in experiments at temperatures up to 11×10³ K.     

Transient natural convection between concentric and vertically eccentric spheres with mixed boundary conditions

Transient analysis has been investigated numerically to determine heat transfer by natural convection between concentric and vertically eccentric spheres with constant heat flux on the inner wall and a specified isothermal temperature on the outer wall. The governing equations, in terms of vorticity, stream function and temperature are expressed in a spherical polar coordinate system. The alternating direction implicit method and the successive over-relaxation techniques are applied to solve the finite difference form of governing equations. A physical model is introduced which accounts for the effects of fluid buoyancy as well as eccentricity of the outer sphere. Transient solutions of the entire flow field are obtained for a range of modified Rayleigh number (10³<Ra?<5×10⁵), for a Prandtl number of 0.7 and a radius ratio of 2.0, with the outer sphere near the top and bottom of the inner sphere (ε=±0.625). Results of the parametric study conducted further reveal that the heat and flow fields are primarily dependent on the modified Rayleigh number and the eccentricity of the spherical annulus. The results of average Nusselt numbers are also compared with the results obtained for flow between two isothermal spheres.