Prediction of vortex penetration depth at thermal stratification by cavity flow in a branch pipe with closed end (effect of heat radiation condition on temperature fluctuations)

In a branch pipe with one closed end, the cavity flow penetrates into the branch pipe from the main loop and a thermal boundary layer occurs because the cavity flow is a hot fluid, but heat removal causes a colder fluid in the branch pipe. This thermal stratification may affect the structural integrity. Therefore, a pipe design standard to suppress thermal fatigue should be established. The pipe design standard consists of the maximum penetration depth L_sv and the minimum penetration depth L_sh. In order to establish an evaluation method for L_sh, a visualization test and a temperature fluctuation test were carried out. A theoretical formula for thermal stratification was introduced from the heat balance model. Then the model was used to obtain an empirical equation from the map of fluid temperature fluctuation. This method can predict the vortex penetration depth by cavity flow in horizontal branch pipes. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(1):38–55, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20135     

Internal gravity wave resonance of thermal convection fields in a square cavity with heat‐flux vibration

In this paper, the thermal convection field and its resonance phenomena in a square cavity with sinusoidal heat‐flux vibration were numerically investigated. As the angular velocity ω is changed, the thermal convection field at Pr = 0.71,Ra = 10⁶ is found to be classified into 5 regions. In particular, the field has the local maximum relative amplitude of midplane Nusselt's number at ω_c = 350, which corresponds to the angular velocity of internal gravity wave ω_r estimated by a theoretical equation proposed by Thorpe. This shows that the local enhancement is induced by internal gravity wave resonance. Such correspondence is observed for Ra ≥ 10⁵,Ra ≥ 10⁶ for Pr = 0.71, 7.1, respectively. For these ranges of Ra we propose a correlation equation, a function of Pr and Gr only, to estimate the resonant angular velocity. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(5): 309–322, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20122     

Solidification in a water‐saturated porous medium when convection is present (response of solid‐liquid interface due to time‐varying cooling temperature)

A fundamental study on solidifying phenomenon in a rectangular space filled with water‐saturated porous medium has been carried out with a system, cooled from the upper boundary and heated from below, where vigorous convection develops in the un‐solidified liquid layer. The dynamic response of the solid‐liquid interface to the periodical cooling temperature with the bottom boundary kept at constant temperature T_H = 20°C, is investigated experimentally. In particular, the amplitude of the interface and the phase lag in respect to the oscillating cooling temperature have been monitored for various periods and average temperatures. A one‐dimensional numerical model, based on an assumption of constant heat flux from the vigorously convecting liquid regime has been also developed. The numerical model predicts quite well the time‐dependent behavior of the horizontally averaged ice‐layer thickness observed in the experiments. Our general findings are that the amplitude increases proportionally to the temperature fluctuation period and that both the thicker solid layer and the shorter period cause greater phase lags. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(4): 294–308, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20109     

MHD Boundary Layer Flow of a Nanofluid Over an Exponentially Stretching Sheet in the Presence of Radiation

Effects of thermal radiation on the steady laminar magnetohydrodynamic boundary layer flow of a nanofluid over an exponentially stretching sheet is studied theoretically. The governing boundary layer equations of the problem are formulated and transformed into ordinary differential equations, using a similarity transformation. The resulting ordinary differential equations are solved numerically by the shooting method. The effects of the parameters, namely, the magnetic parameter M, radiation parameter N_R, and the solid volume fraction parameter ?, are discussed and presented in detail. Different types of nanoparticles namely, Cu, Ag, Al₂O₃, and TiO₂ with the base fluid water, are studied. It is found that the nanoparticles with low thermal conductivity, TiO₂ have better enhancement on heat transfer, compared to Cu, Ag, and Al₂O₃. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(4): 321–331, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21077     

Optimization of a finned heat sink array based on thermoeconomic analysis

The design and specification of heat sinks for electronic systems is not easily accomplished through the use of standard thermal design and analysis tools since geometric and boundary conditions are not typically known in advance. A second-law based thermoeconomic optimization procedure is presented for a finned heat sink array. This involves including costs associated with material, and irreversible losses due to heat transfer and pressure drop. The influence of important physical, geometrical and unit cost parameters on the overall finned array are optimized for some typical operating conditions that are representative of electronic cooling applications. The optimized cost results are presented in terms of Re_D, Re_L, λ_P / λ_H, and q for a finned system in a graphical form. In addition the methodology of obtaining optimum parameters for a finned heat sink system which will result in minimum operating cost is demonstrated. Copyright © 2006 John Wiley & Sons, Ltd.     

DNS of turbulent thermal boundary layers up to Reθ = 2300

A technique, based on the Lund et al. (1998) [1] approach, is introduced in order to numerically prescribe time-dependent turbulent inflow conditions in spatially-developing thermal boundary layers. A major difference with Lund’s approach is that the new multi-scale approach considers different scaling laws for the inner and outer parts of the boundary layer. Direct numerical simulations (DNS) are performed for incompressible zero (ZPG) and adverse (APG) pressure gradient flows. To the best of our knowledge, the present DNS in ZPG flows at a momentum thickness Reynolds numbers (Re_θ) of 2300 represents the evolving thermal boundary layer simulations at the highest Re_θ in the turbulence community. The temperature is treated as a passive scalar with isothermal walls as a boundary condition and a molecular Prandtl number of 0.71. The predicted Stanton number shows fairly good agreement with empirical correlations, and experimental and numerical data from the literature. Moreover, the influences of the Reynolds number and the APG strength on thermal parameters are also examined. Furthermore, the budget of the temperature variance shows a significant increase of production, turbulent diffusion, and dissipation in the buffer layer at higher Reynolds numbers. The main effects of adverse pressure gradients on the temperature field are manifested by a decreasing trend of thermal fluctuations but an increasing trend of the wall-normal turbulent heat fluxes when normalized by wall units as the APG strength is augmented.     

A numerical study of natural convection in a vertical cylinder bundle

Natural convection in a bundle of vertical cylinders, arranged in equilateral triangular spacing, has been investigated numerically using a boundary‐fitted coordinate system. Numerical calculations for center‐to‐center distance between cylinders S/D = 1.1 to 1.9, 3.0, 4.0, and 7.0 were made of natural convection of air at modified Grashof numbers Gr* from 10 to 10⁸. Local Nusselt number Nu for uniform wall heat flux indicates the same value at the axial locations except for the thermal entrance region. The region for respective cylinder spacing is noted to diminish with decreasing Grashof number. Numerical values of local Nusselt number Nu_i are in relatively good agreement with those obtained from the experiment for air. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 330–341, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10095     

Premixed flames subjected to extreme turbulence: Some questions and recent answers

It has been predicted that several changes will occur when premixed flames are subjected to the extreme levels of turbulence that can be found in practical combustors. This paper is a review of recent experimental and DNS results that have been obtained for the range of extreme turbulence, and it includes a discussion of cases that agree or disagree with predictions. “Extreme turbulence” is defined to correspond to a turbulent Reynolds number (Re_Τ, based on integral scale) that exceeds 2800 or a turbulent Karlovitz number that exceeds 100, for reasons that are discussed in Section 2.1. Several data bases are described that include measurements made at Lund University, the University of Sydney, the University of Michigan and the U.S. Air Force Research Lab. The data bases also include DNS results from Sandia National Laboratory, the University of New South Wales, Newcastle University, the California Institute of Technology and the University of Cambridge.Several major observations are: (a) DNS now can be achieved for a realistic geometry (of the Lund University jet burner) even for extreme turbulence levels, (b) state relations (conditional mean profiles) from DNS and experiments do tend to agree with laminar profiles, at least for methane-air and hydrogen-air reactants that are not preheated, and (c) regime boundaries have been measured and they do not agree with predicted boundaries. These findings indicate that the range of conditions for which flamelet models should be valid is larger than what was previously believed. Additional parameters have been shown to be important; for example, broken reactions occur if the “back-support” is insufficient due to the entrainment of cold gas into the product gas. Turbulent burning velocity measurements have been extended from the previous normalized turbulence levels (u’/S_L) of 24 up to a value of 163. Turbulent burning velocities no longer follow the trend predicted by Shchelkin but they tend to follow the trend predicted by Damköhler. The boundary where flamelet broadening begins was measured to occur at Re_Taylor = 13.8, which corresponds to an integral scale Reynolds number (Re_T) of 2800. This measured regime boundary can be explained by the idea that flame structure is altered when the turbulent diffusivity at the Taylor scale exceeds a critical value, rather than the idea that changes occur when Kolmogorov eddies just fit inside a flamelet. A roadmap to extend DNS to complex chemistry and to higher Reynolds numbers is discussed. Exascale computers, machine learning, adaptive mesh refinement and embedded DNS show promise. Some advances are reviewed that have extended the use of line and planar PLIF and CARS laser diagnostics to studies that consider complex hydrocarbon fuels and harsh environments.     

Simulation of mixed convection heat transfer in a horizontal channel with an open cavity containing a heated hollow cylinder

The objective of this paper is to numerically investigate the mixed convective flow and heat transfer controlled by a heated hollow cylinder inside an open cavity attached with a horizontal channel. All the boundaries of the channel and cavity are perfectly insulated while the inner surface of the cylinder is heated uniformly by heat flux q. The equations of conservation of mass, momentum, and energy were solved using adequate boundary conditions by Galarkin's weighted residual finite element technique. The solution has been performed in the computational domain as a whole with proper treatment at the solid/fluid interface. Computations have been conducted for Ra = 10³–10⁵, Prandtl number Pr varying from 0.7 to 7 and ratio of solid to fluid thermal conductivities from 0.2 to 50. Results are presented in terms of streamlines, isotherms, heat transfer rate in terms of the average Nusselt number (Nu_av), drag force (D), and maximum bulk temperature (θ_max). © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21002     

Simple method to support optimization of layouts for vacuum insulation panels (VIPs) for refrigerators

We proposed a technique of analysis that supports the optimization of layouts for vacuum insulation panels (VIPs) for refrigerators, using a one‐dimensional technique of calculation to simulate the heat loss caused by VIP envelope materials. VIP thermal characteristics were described by approximating system efficiency by using the panels' average length (L_p). We compared this simplified method to three‐dimensional numerical analysis of 1 to 6µm thick, vacuum‐packed aluminum foil and 1.5 to 6 mW/mK thermally conductive heat‐insulated core materials, and verified them to be within a 1% margin of error. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(7): 451–463, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20132     

Influence of Lewis number on double‐diffusive convection in a square cavity filled with binary gas

This paper presents double‐diffusive convection in a square cavity filled with binary gas, due to horizontal opposing temperature and concentration gradients. The effect of Lewis number was considered under the conditions of Prandtl number Pr = 1, buoyancy ratio N = 1, and thermal Rayleigh number Ra_T = 10⁴ and 10⁵. Numerical solutions are obtained by a Chebyshev collocation technique with high resolution. Depending on the Lewis number, three kinds of flow structures are identified: symmetric steady flow, asymmetric oscillatory flow, and symmetric oscillatory flow. Oscillatory flow occurs in the regime of thermal dominant flow and it leads to a periodic change between stable and unstable states in species stratification due to the thermo‐solutal interaction. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1): 85–97, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10073     

Internal gravity wave resonance of thermal convection fields in rectangular cavities with heat‐flux vibration (effects of aspect ratio on the fields)

In this paper the thermal convection field and its resonance phenomena in a rectangular cavity with heat‐flux vibration are numerically examined and the results are compared with those of a square cavity. As in the case of α=1, the critical angular velocity at which the relative amplitude of the midplane Nusselt number α_m has a local maximum agrees very well with the resonance angular velocity of the internal gravity wave ω_r, estimated by the theoretical equation proposed by Thorpe, even when the aspect ratio is α=5 and the Prandtl number is Pr=0.71 for a range of the Rayleigh number Ra. However, α_m has two local maxima for a larger Ra, which is peculiar to the case of larger α. The time variation of sub‐components of the fluctuating component of the midplane Nusselt number shows that the phase at the maximum value of α_m agrees well with that of the sub‐component of velocity for the first resonance angular velocity ω_r. For the other angular velocity ω_r2, the phase of α_m agrees with that of the sub‐component of temperature. Moreover, we found that the boundary angular velocity ω₀ between the first two of the five ω regions, which classify the thermal convection fields against ω, can be expressed by a function of α, Ra, and Pr and that α_m is independent of α and Ra for a relatively wide range of ω/ω₀. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(3): 158– 171, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20149     

Flashing characteristics in a pipe downstream from a depressurizing tank and temperature fluctuation characteristics at a mixing tee junction with cold water injection

The flashing characteristics in a pipe downstream from a depressurizing tank were experimentally and analytically investigated on the basis of the transient test and two‐phase flow analysis. The following conclusions were obtained. (1) When the pressure margin of the pump inlet side and the distance to obtain an isothermal condition were sufficient, flashing phenomena did not occur in spite of the decreasing pressure. (2) When the ratio of the cold water injection flow rate to the hot water flow rate M_c/M_h increased, the peak distance of the water temperature fluctuation moved from L/D = 1 to 0, and the maximum water temperature fluctuation ratio was about 40% of the temperature difference between hot and cold water near the mixing tee junction. Because no problem occurred regarding the pipe material thermal fatigue, reliability of the mixing tee junction was assured. (3) Due to suppression of flashing phenomena of the mixing pipe system, the decision diagram on the flashing occurrence was obtained from the test and the analytical results, taking into consideration three factors: the depressurizing ratio in the tank; the cold water injection flow rate due to remaining subcooling; and the delay time of thermal mixing. The simplified analytical equation was used to decrease the cold water injection flow rate by the optimized pipe length between the mixing tee junction and the drain pump. The cold water injection flow rate was minimized when the pipe length was about 15 to 20 times the pipe inner diameter. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(5): 411–429, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10096     

Investigation of flow behind vortex generators by stereo particle image velocimetry on a thick airfoil near stall

Stereoscopic Particle Image Velocimetry measurements investigating the effect of vortex generators (VGs) on the flow near stall were carried out in a purpose‐built wind tunnel for airfoil investigations on a DU 91‐W2‐250 profile. Measurements were conducted at Re = 0.9?10⁶, corresponding to free stream velocity U_∞ = 15 m s^?1. The objective was to investigate the flow structures induced by the vortex generators and study their separation controlling behavior on the airfoil. The uncontrolled flow (no VGs) displayed unsteady behavior with separation as observed from large streamwise velocity variations. The corresponding controlled flow (with VGs) showed the same unsteadiness, where the appearance of the vortex structures alternated with a much less separated or even attached boundary layer as also seen in the measured airfoil data: C_L = 1.56, C_D = 0.116 with VGs and C_L = 1.16, C_D = 0.135 without. On average, the controlled flow left an attached flow as opposed to the uncontrolled one. Mixing close to the wall, transferring high momentum fluid into the near wall region, was observed, and the hypothesis of variations in the streamwise velocity component in the boundary layer was supported by a Snapshot Proper Orthogonal Decomposition analysis. This analysis also revealed some of the dynamics of the induced vortices. Copyright © 2012 John Wiley & Sons, Ltd.     

Large eddy simulation of flow and scalar transport in a round jet

Large eddy simulation (LES) was performed for a spatially developing round jet and its scalar transport at four steps of Reynolds number set between 1200 and 1,000,000. A simulated domain, which extends 30 times the nozzle diameter, includes initial, transitional, and established stage of jet. A modified version of convection outflow condition was proposed in order to diminish the effect of a downstream boundary. Tested were two kinds of subgrid scale (SOS) models: a Smagorinsky model (SM) and a dynamic Smagorinsky model (DSM). In the former model, parameters are kept at empirically deduced constants, while in the latter, they are calculated using different levels of space filtering. Data analysis based on the decay law of jet clearly presented the performance of SGS models. Simulated results by SM and DSM compared favorably with existing measurements of jet and its scalar transport. However, the quantitative accuracy of DSM was better than that of SM at a transitional stage of flow field. Computed parameters by DSM, coefficient for SGS stresses, C_R and SGS eddy diffusivity ratio, Γ_SGS, were not far from empirical constants of SM. Optimization of the model coefficient was suggested in DSM so that coefficient C_R was nearly equal in the established stage of jet but it was reduced in low turbulence close to the jet nozzle. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(3): 175–188, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20001     

Analysis of energy technology changes and associated costs

An integrated mathematical model constituting of interlinked submodels on technology costs, progress and market penetration has been developed. The model was applied to a few new energy technologies to investigate the economic boundary conditions for a full market breakthrough and corresponding market impact on a 50 years time scale. The model shows that public subsidies amounting to slightly over 220 billion € in total worldwide would be necessary over the next 30–40 years to bring wind and photovoltaics to a cost breakthrough in the market and to reach a 20 and 5% share of all electricity at t = 50 years, respectively. These up‐front learning investments would be partly amortized toward the end of the interval as the new technologies become cost competitive but could be fully paid off earlier if CO₂ emission trading schemes emerge even with modest CO₂ price levels. The findings are sensitive to changes in the parameter assumptions used. For example, a 2% uncertainty in the main parameters of the model could lead to a spread of tens of per cents in the future energy impact and subsidy needs, or when related to the above subsidy estimate, 155–325 billion €. This underlines the overall uncertainty in predicting future impacts and resource needs for new energy technologies. Copyright © 2006 John Wiley & Sons, Ltd.     

Probability density function treatment of turbulence/chemistry interactions during the ignition of a temperature-stratified mixture for application to HCCI engine modeling

Homogeneous charge compression ignition (HCCI) engine technology promises to reduce NO_x and soot emissions while achieving high thermal efficiency. Temperature and mixture stratification are regarded as effective means of controlling the start of combustion and reducing the abrupt pressure rise at high loads. Probability density function methods are currently being pursued as a viable approach to modeling the effects of turbulent mixing and mixture stratification on HCCI ignition. In this paper we present an assessment of the merits of three widely used mixing models in reproducing the moments of reactive scalars during the ignition of a lean hydrogen/air mixture (Φ=0.1, p=41 atm, and T=1070 K) under increasing temperature stratification and subject to decaying turbulence. The results from the solution of the evolution equation for a spatially homogeneous joint PDF of the reactive scalars are compared with available direct numerical simulation (DNS) data [E.R. Hawkes, R. Sankaran, P.P. Pébay, J.H. Chen, Combust. Flame 145 (1-2) (2006) 145-159]. The mixing models are found able to quantitatively reproduce the time history of the heat release rate, first and second moments of temperature, and hydroxyl radical mass fraction from the DNS results. Most importantly, the dependence of the heat release rate on the extent of the initial temperature stratification in the charge is also well captured.     

Effect of viscosity variation on natural convection flow of water–alumina nanofluid in an annulus with internal heat generation

Heat transfer enhancement in a horizontal annulus using the variable viscosity property of an Al₂O₃–water nanofluid is investigated. Two different viscosity models are used to evaluate heat transfer enhancement in the annulus. The base case uses the Pak and Cho model and the Brinkman model for viscosity which take into account the dependence of this property on temperature and nanoparticle volume fraction. The inner surface of the annulus is heated uniformly by a constant heat flux q_w and the outer boundary is kept at a constant temperature T_c. The nanofluid generates heat internally. The governing equations are solved numerically subject to appropriate boundary conditions by a penalty finite‐element method. It is observed that for a fixed Prandtl number Pr = 6.2, Rayleigh number Ra = 10⁴ and solid volume fraction ? = 10%, the average Nusselt number is enhanced by diminishing the heat generation parameter, mean diameter of nanoparticles, and diameter of the inner circle. The mean temperature for the fluids (nanofluid and base fluid) corresponding to the above mentioned parameters is plotted as well. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21016     

Thermophysical properties of molten tungsten measured with an electrostatic levitator

Thermophysical properties of liquid and supercooled tungsten were measured using non‐contact techniques in combination with an electrostatic levitator. Over the 3125–3707 K temperature range, the density measurements can be expressed as ρ (T) = 16.7(± 0.33)× 10³ ? 1.08(± 0.08) (kg? m^?3) with T_m = 3695 K, leading to a volume expansion coefficient of 6.6×10^?5 K^?1. In addition, over the 3398–3695 K temperature range, the surface tension (γ) and viscosity (η) data can be expressed respectively as γ (T) = 2.48× 10³(± 75) ? 0.31(± 0.08) (T ? T_m) (10^?3 N? m^?1) and η (T) = 0.11(± 0.02) exp[12.8(± 4.1) × 10⁴/(RT)] (10^?3 Pa? s). © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(2): 152–164, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20101     

Thermal Radiation and Heat Source Effects on a MHD Nanofluid Past a Vertical Plate in a Rotating System with Porous Medium

This article studies the effect of thermal radiation on a MHD free convection flow of a nanofluid bounded by a semi‐infinite vertical plate with a constant heat source in a rotating frame of reference. The plate is assumed to oscillate in time with constant frequency so that the solutions of the boundary layer are the same oscillatory type. The dimensionless governing equations for this investigation are solved analytically using the regular perturbation method. The effect of various important parameters entering into the problem on velocity and temperature fields within the boundary layer are discussed for three different water‐based nanofluids such as Cu, Al₂O₃, and TiO₂ with the help of graphs. The predicted results clearly indicate that the presence of nanoparticles in the base fluid enhances the heat transfer process significantly. The present work shows the need for immediate attention in next‐generation solar film collectors, heat‐exchanger technology, material processing exploiting vertical surface, geothermal energy storage, and all those processes which are greatly exaggerated by heat‐enhancement concepts. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21101