Temperature spectra from a turbulent thermal plume by ultrasound scattering

This paper reports the results of a study on temperature inhomogeneities conducted on a thermal plume by using ultrasound scattering as a non-intrusive measurement technique. The plume rises from a metallic disk which can be heated up to 800 °C. The working fluid is air at atmospheric pressure. In the measurement technique, an incoming ultrasound wave is emitted towards the thermal plume. The incident wave is scattered because of non-linear couplings with the flow instabilities present in the measurement region. The scattered wave carries information about those flow instabilities. The technique allows for the retrieving of this information. The shape of the obtained spectrum of temperature fluctuations as a function of wave vector modulus is consistent with previous theoretical analysis. Three qualitatively different regions were identified: first, a production region characterized by a q² law; secondly, a region with behavior as per q⁻³ associated with a buoyancy region and; finally, a dissipation region associated with a q⁻⁷ law. These spectral regions characterize the energy transfers mechanisms among the length scales of flow investigated here. A coefficient of anisotropy γ was defined to analyze anisotropic features of the flow.     

Experimental study of transition to turbulence of a round thermal plume by ultrasound scattering

In this study, we carried out the characterization of the transition to turbulence of a thermal pure plume by using ultrasound scattering. For this, the position, amplitude and broadening of the scattering peak are analyzed. The technique is based upon the scattering of an ultrasound wave coupling with an unstable flow. The coupling between the acoustic mode with both vorticity and entropy modes is derived from non-linear terms of Navier–Stokes and energy equations. When the scattering mechanism occurs, the characteristic length scale of the flow structure under observation is comparable with the wavelength of incoming sound. Thus, the flow can be probed at different length scales by only changing the frequency of incoming sound. The thermal plume rises from a heated disk immersed into a quiescent medium and can reach transition and fully turbulent regimes. Criteria allowing the identification of both the beginning and the end of transition are derived from the results. The characteristics of the scattering process show evidence that allows us to discern the beginning of transition. The analysis of the amplitude of the scattering peak revealed a homogeneous behavior and led us to think of a possible principle of similarity. The evolution of both thermal and velocity fluctuations has made it possible to establish the limits of both the beginning and the end of transition, in terms of local Grashof number Gr_z and position of the measurement zone z/D. The limits for transition reported in this work are comparable in its magnitude order with those of the literature. It was verified that thermal and velocity transition are phenomena that begin and finish almost simultaneously.     

Experiments on turbulent natural convection in an enclosed tall cavity

Experiments have been undertaken to investigate the natural convection of air in a tall differentially heated rectangular cavity (2.18 m high by 0.076 m wide by 0.52 m in depth). They were performed with temperature differentials between the vertical plates of 19.6°C and 39.9°C, giving Rayleigh numbers based on the width of 0.86×10⁶ and 1.43×10⁶. Under these conditions the flow in the core of the cavity is fully turbulent and property variations with temperature are comparatively small. A previously used experimental rig has been modified, by fitting partially conducting top and bottom walls and outer guard channels, to provide boundary conditions which avoid the inadequately defined sharp changes in temperature gradient and other problems associated with insufficient insulation on nominally adiabatic walls. Mean and turbulent temperature and velocity variations within the cavity have been measured, together with heat fluxes and turbulent shear stresses. The temperature and flow fields were found to be closely two-dimensional, except close to the front and back walls, and anti-symmetric across the diagonal of the cavity. The partially conducting roof and floor provide locally unstable thermal stratification in the wall jet flows there, which enhances the turbulence as the flow moves towards the temperature controlled plates. The results provide a greatly improved benchmark for the testing of turbulence models in this low turbulence Reynolds number flow.     

Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions

Numerical simulations have been undertaken for the benchmark problem of natural convection flow in a square cavity. The control volume method is used to solve the conservation equations for laminar and turbulent flows for a series of Rayleigh numbers (Ra) reaching values up to 10¹⁰. The k-? model has been used for turbulence modelling with and without logarithmic wall functions. Uniform and non-uniform (stretched) grids have been employed with increasing density to guarantee accurate solutions, especially near the walls for high Ra-values. ADI and SIP solvers are implemented to accelerate convergence. Excellent agreement is obtained with previous numerical solutions, while some discrepancies with others for high Ra-values may be due to a possibly different implementation of the wall functions. Comparisons with experimental data for heat transfer (Nusselt number) clearly demonstrates the limitations of the standard k-? model with logarithmic wall functions, which gives significant overpredictions.     

Comparison of non‐reflective boundary conditions for a free‐rising turbulent axisymmetric plume

The stability and accuracy of radiation type non‐reflective outflow boundary conditions, as well as the standard Neumann boundary condition with zero normal derivative, have been compared for the numerical simulation of a turbulent axisymmetric plume with Reynolds number of 7700 and Prandtl number of 0.71. Comparison of the performance of the boundary conditions with respect to each other, and to the results obtained for an extended domain, shows that a one‐dimensional scheme in which advection and diffusion terms are included in the radiation equation is the optimum approach for the plume simulation. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental observations of the thermal flow around a square obstruction on a vertical wall in a differentially heated cavity

The transient thermal boundary layer flow around a square obstruction placed at the middle of the hot wall in a differentially heated cavity is visualized using a shadowgraph technique. The results show that the thermal boundary layer flow, which is blocked by the obstruction, firstly forms an intrusion head under the obstruction (the lower intrusion head). Subsequently, the lower intrusion head bypasses the obstruction and reattaches to the down-stream boundary. During the reattachment process, a more complicated flow is induced, and eventually both the lower intrusion head and the thermal boundary layer destabilize. After the lower intrusion head is convected away, the thermal boundary layer flow re-stabilizes. At the quasi-steady state, the thermal boundary layer forms a double-layer structure, which is split into two sections by the obstruction. It is demonstrated that both the transient processes and the quasi-steady state flow structures of the thermal boundary layer are significantly altered by the obstruction in comparison with the case without the obstruction.     

Large-eddy simulation of buoyancy-driven natural ventilation in an enclosure with a point heat source

Rising buoyant plumes from a point heat source in a naturally ventilated enclosure have been investigated using large-eddy simulation (LES). The aim of the work is to assess the performance and the accuracy of LES for modelling buoyancy-driven displacement ventilation of an enclosure and to shed more light on the transitional behaviour of the plume and the coherent structures involved. The Smagorinsky sub-grid scale model is used for the unresolved small-scale turbulence. The Rayleigh number, Ra is chosen to be in the range where spatial transition from laminar to turbulent flow takes place (Ra = 1.5 × 10⁹). The plume properties (source strength and rate of spread) as well as the ventilation properties (stratification height and temperature of stratified layer) estimated using the theory of Linden et al. are found to agree reasonably well with the LES results. The variation of the plume width with height indicates a linear variation of the entrainment coefficient rather than a constant value used by Linden et al. for a fully turbulent thermal plume. Flow visualisation revealed the nature of the large-scale coherent structures involved in the transition to turbulence in the plume. The most excited modes observed in the velocity, pressure and temperature fields spectra correspond to Strouhal number in the range 0.3 ≤ St ≤ 0.55 which is in agreement with those observed by Zhou et al. for a turbulent forced plume. Excited modes less than thisvalue (St = 0.2) were observed and may be due to low-frequency motions felt throughout the flow.     

Effects of variable viscosity and thermal conductivity of Al2O3–water nanofluid on heat transfer enhancement in natural convection

Heat transfer enhancement in horizontal annuli using variable properties of Al₂O₃–water nanofluid is investigated. Different viscosity and thermal conductivity models are used to evaluate heat transfer enhancement in the annulus. The base case uses the Chon et al. expression for conductivity and the Nguyen et al. experimental data for viscosity which take into account the dependence of these properties on temperature and nanoparticle volume fraction. It was observed that for Ra  10⁴, the average Nusselt number was reduced by increasing the volume fraction of nanoparticles. However, for Ra = 10³, the average Nusselt number increased by increasing the volume fraction of nanoparticles. For Ra  10⁴, the Nusselt number was deteriorated every where around the cylinder surface especially at high expansion ratio. However, this reduction is only restricted to certain regions around the cylinder surface at Ra = 10³. For Ra  10⁴, the difference in Nusselt number between the Maxwell Garnett and Chon et al. model prediction is small. But, there was a deviation in prediction at Ra = 10³ and this deviation becomes more significant at high volume fraction of nanoparticles. The Nguyen et al. data and Brinkman model gives completely different predictions for Ra  10⁴ where the difference in prediction of Nusselt number reached 30%. However, this difference was less than 10% at Ra = 10³.     

Experimental investigation of turbulent natural convection flow in a channel

This paper presents the results of velocity measurements of natural convection in symmetrically heated vertical channel using the particle image velocimetry (PIV) system. Velocity measurements were conducted at three different sections on the horizontal plane to validate the flow two-dimensionality and at three different heights in the vertical plane to establish vertical mean velocity profiles. The results indicate a considerable influence of the Rayleigh number and aspect ratio on the mean velocity profile. The results also indicate significant diffusion rates of the vertical mean velocity component and normal Reynolds stresses towards the center of the channel.     

Effect of modulation on onset of thermal convection of a second-grade fluid layer

This study examines the stability of a horizontally extended second-grade fluid layer heated from below, when a steady temperature difference between the walls is superimposed on sinusoidal temperature perturbations. A linear stability analysis proposed by Venezian (J. Fluid Mech. 35 (1969) 243) is employed to obtain the critical Rayleigh numbers for different types of temperature modulation. The free–free and isothermal boundary conditions are considered so as to allow analytic solutions. The stability characterized by the shift in critical Rayleigh number R_2c is calculated as a function of the modulation frequency ω, the Prandtl number Pr, and the viscoelastic parameter Q. It is found that the onset of convection can be delayed or advanced by these parameters.     

Bifurcation analysis for thermal convection in a rotating porous layer

The linear and weakly nonlinear thermal convection in a rotating porous layer is investigated by constructing a simplified model involving a system of fifth-order nonlinear ordinary differential equations. The flow in the porous medium is described by Lap wood-Brinkman-extended Darcy model with fluid viscosity different from effective viscosity. Conditions for the occurrence of possible bifurcations are obtained. It is established that Hopf bifurcation is possible only at a lower value of the Rayleigh number than that of simple bifurcation. In contrast to the non-rotating case, it is found that the ratio of viscosities as well as the Darcy number plays a dual role on the steady onset and some important observations are made on the stability characteristics of the system. The results obtained from weakly nonlinear theory reveal that, the steady bifurcating solution may be either sub-critical or supercritical depending on the choice of physical parameters. Heat transfer is calculated in terms of Nusselt number.     

Stability analysis of thermosolutal convection in a horizontal porous layer using a thermal non-equilibrium model

A stability analysis is carried out to investigate the onset of thermosolutal convection in a horizontal porous layer when the solid and fluid phases are not in a local thermal equilibrium, and the solubility of the dissolved component depends on temperature. To study how the reaction and thermal non-equilibrium affect the double-diffusive convection, the effects of scaled inter-phase heat transfer coefficient H and dimensionless reaction rate k on thermosolutal convection are discussed . The critical Rayleigh number and the corresponding wave number for the stability and overstability convections are obtained. Specially, asymptotic analysis for both small and large values of H and k is presented, and the corresponding asymptotic solutions are compared with numerical results. At last, a nonlinear stability analysis is presented to study how H and k affect the Nusselt number.     

The effect of thermal dispersion on free convection film condensation on a vertical plate with a thin porous layer

An analytical solution to the problem of condensation by natural convection over a thin porous substrate attached to a cooled impermeable surface has been conducted to determine the velocity and temperature profiles within the porous layer, the dimensionless thickness film and the local Nusselt number. In the porous region, the Darcy–Brinkman–Forchheimer (DBF) model describes the flow and the thermal dispersion is taken into account in the energy equation. The classical boundary layer equations without inertia and enthalpyterms are used in the condensate region. It is found that due to the thermal dispersion effect, the increasing of heat transfer is significant. The comparison of the DBF model and the Darcy–Brinkman (DB) one is carried out.     

Heat transfer enhancement in a turbulent natural convection boundary layer along a vertical flat plate

An experimental study on heat transfer enhancement for a turbulent natural convection boundary layer in air along a vertical flat plate has been performed by inserting a long flat plate in the spanwise direction (simple heat transfer promoter) and short flat plates aligned in the spanwise direction (split heat transfer promoter) with clearances into the near-wall region of the boundary layer. For a simple heat transfer promoter, the heat transfer coefficients increase by a peak value of approximately 37% in the downstream region of the promoter compared with those in the usual turbulent natural convection boundary layer. It is found from flow visualization and simultaneous measurements of the flow and thermal fields with hot- and cold-wires that such increase of heat transfer coefficients is mainly caused by the deflection of flows toward the outer region of the boundary layer and the invasion of low-temperature fluids from the outer region to the near-wall region with large-scale vortex motions riding out the promoter. However, heat transfer coefficients for a split heat transfer promoter exhibit an increase in peak value of approximately 60% in the downstream region of the promoter. Flow visualization and PIV measurements show that such remarkable heat transfer enhancement is attributed to longitudinal vortices generated by flows passing through the clearances of the promoter in addition to large-scale vortex motions riding out the promoter. Consequently, it is concluded that heat transfer enhancement of the turbulent natural convection boundary layer can be substantially achieved in a wide area of the turbulent natural convection boundary layer by employing multiple column split heat transfer promoters. It may be expected that the heat transfer enhancement in excess of approximately 40% can be accomplished by inserting such promoters.     

Onset of convection in a horizontal porous channel with uniform heat generation using a thermal nonequilibrium model

This paper considers the onset of free convection in a horizontal fluid-saturated porous layer with uniform heat generation. Attention is focused on cases where the fluid and solid phases are not in local thermal equilibrium, and where two energy equations describe the evolution of the temperature of each phase. Standard linearized stability theory is used to determine how the criterion for the onset of convection varies with the inter-phase heat transfer coefficient, H, and the porosity-modified thermal conductivity ratio, γ. We also present asymptotic solutions for small values of H. Excellent agreement is obtained between the asymptotic and the numerical results.     

Natural convection flow of a viscous incompressible fluid in a rectangular porous cavity heated from below with cold sidewalls

We consider the flow, which is induced by differential heating on the boundaries of a porous cavity heated from below. In particular we allow the sidewalls to have the same cold temperature as the upper surface, and thus the problem is a variant of the Darcy-Bénard convection problem, but one where there is flow at all non-zero Grashof numbers. Attention is focused on how the flow and heat transfer is affected by variations in the cavity aspect ratio, the Grashof number and the Darcy number. The flow becomes weaker as the Darcy number decreases from the pure fluid limit towards the Darcy-flow limit. In addition the number of cells which form in the cavity varies primarily with the aspect ratio and is always even due to the symmetry imposed by the cold sidewalls.     

Characteristic turbulent structure of a modified drag-reduced surfactant solution flow via dosing water from channel wall

The modification of the near-wall structure is very important for the control of wall turbulence. To ascertain the effect of near-wall modulation on the viscoelastic drag-reduced flow, the modified characteristics of a surfactant solution channel flow were investigated experimentally. The modulation was conducted on the boundary of the channel flow by injecting water from the whole surface of one side of the channel wall. The diffusion process of the injected water was observed by using the planar laser-induced fluorescence technique. The velocity statistics and characteristic structure including the spatial distributions of instantaneous streamwise velocity, swirling strength, and Reynolds shear stress were analyzed based on the velocity vectors acquired in the streamwise wall-normal plane by using the particle imaging velocimetry technique. The results indicated that the disturbance of the injected water was constricted within a finite range very near the dosing wall, and the Reynolds shear stress was increased in this region. However, the eventual drag reduction rate was found to be increased due to a relatively large decrement of viscoelastic shear stress in this near-wall region. Moreover, the flow structure under this modulation presented obvious regional characteristics. In the unstable disturbed region, the mixing of high-speed and low-speed fluids and the motions of ejection and sweep occurred actively. Many clockwise vortex cores were also found to be generated. This characteristic structure was similar to that in the ordinary turbulence of Newtonian fluid. Nevertheless, outside this disturbed region, the structure still maintained the characteristics of the drag-reduced flow with non-Newtonian viscoelastic additives. These results proved that the injected Newtonian fluid associated with the modified stress distribution creates a diverse characteristic structure and subsequent enhanced drag reduction. This investigation can provide the experimental basis for further study of turbulence control.     

The influence of natural convection on the temperature decay of a porous thermal layer

Temperature decay in sealed rockbeds has been recorded. The rockbeds lost energy through the top surface and the results indicated that different natural convective flows occurred in beds of fixed depth and rock size but different lateral dimensions. However, the different flows had no effect on the mean power density dissipated through the top of the beds. A simple numerical conduction model based on the power integral method was used to calculate the temperature decay. The experimental results suggested that an insulated porous lower boundary was appropriate for the model and this gave the best agreement with the experiments.     

Natural convection from a vertical cylinder in a thermally stratified porous medium

The problem of non-Darcy natural convection adjacent to a vertical cylinder embedded in a thermally stratified porous medium has been analyzed. Nonsimilarity solutions are obtained for the case that the ambient temperature increases linearly with height of the cylinder. A generalized flow model was used in the present study to include the effects of the macroscopic viscous term and the microscopic inertial force. Also, the thermal dispersion effect is considered in the energy equation. Thus, the main aim of this work is to examine the effects of thermal stratification and non-Darcy flow phenomena on the free convection flow and heat transfer characteristics. It was found that the present problem depends on six parameters, namely, the local thermal stratification parameter ξ, the boundary effect parameter Bp, the modified Grashof number Gr^*, wall temperature exponent m, the curvature parameter ω, and the modified Rayleigh number based on pore diameter Ra _d . The impacts of these governing parameters on the local heat transfer parameter are discussed in great detail. Also, representative velocity and temperature profiles are presented at selected values of the thermal stratification parameter. In general, the local heat transfer parameter is increased with increasing the values of m, ω, and Ra _d ; while it is decreased with increasing the values of ξ, Bp, and Gr^*. Received on 19 May 1998