Natural convection boiling of water and surfactants in narrow horizontal annular channels

Natural convection boiling of water and surfactants at atmospheric pressure in narrow horizontal annular channels was studied experimentally in the range of Bond numbers Bo = 0.185–1.52. The flow pattern was visualized by high-speed video recording to identify the different regimes of boiling of water and surfactants. The channel length was 24 mm and 36 mm, the gap size was 0.45, 1.2, 2.2, and 3.7 mm. The heat flux was in the range of 20–500 kW/m², the concentration of surfactant solutions was varied from 10 to 600 ppm. For water boiling at Bond numbers Bo < 1 the CHF in restricted space is lower than that in unconfined space. This effect increases with increasing the channel length. For water at Bond number Bo = 1.52, boiling can almost be considered as unconfined. Additive of surfactant led to enhancement of heat transfer compared to water boiling in the same gap size, however, this effect decreased with decreasing gap size. For the same gap size, CHF in surfactant solutions was significantly lower than that in water. Hysteresis was observed for boiling in degraded surfactant solutions.     

Behavior of homogeneous turbulence in channels with variable cross-sectional area

On the basis of the equation describing the behavior of the spectral tensor of the energy of the pulsation velocity for one-dimensional flow in a channel with variable cross-sectional area, we obtained a system of equations for the meansquare components of the pulsation velocity vector and integral scales of the turbulence length in various directions, enabling us to use these parameters in the initial section of the channel for determining their behavior along the channel. We made use of some ideas of A. N. Kolmogorov and J. Rotta concerning the possibility of describing viscous and nonlinear terms in the equations for the components of the tensor of Reynolds stresses in terms of the energy of pulsation motion and the integral scale of the turbulence length. The resulting system, in the special cases of very low intensity of turbulence, leads to the results of the linear theory; for constant cross-sectional area (or for a very high intensity of turbulence, when the damping affects the turbulence much more strongly than does the deformation effect) it describes the known empirical laws of the degeneration of turbulence beyond grids. We made a comparison with the data available in the literature on the behavior of the characteristics of turbulence in channels with variable cross-sectional area.     

Effect of surfactant concentration on saturated flow boiling in vertical narrow annular channels

Saturated flow boiling of environmentally acceptable nonionic surfactant solutions of Alkyl (8–16) was compared to that of pure water. The concentration of surfactant solutions was in the range of 100–1000 ppm. The liquid flowed in an annular gap of 2.5 and 4.4 mm between two vertical tubes. The heat was transferred from the inner heated tube to two-phase flow in the range of mass flux from 5 to 18 kg/m² s and heat flux from 40 to 200 kW/m². Boiling curves of water were found to be heat flux and channel gap size dependent but essentially mass flux independent. An addition of surfactant to the water produced a large number of bubbles of small diameter, which, at high heat fluxes, tend to cover the entire heater surface with a vapor blanket. It was found that the heat transfer increased at low values of relative surfactant concentration C/C₀, reaches a maximum close to the value of C/C₀ = 1 (where C₀ = 300 ppm is the critical micelle concentration) and decreased with further increase in the amount of additive. The dependence of the maximal values of the relative heat transfer enhancement, obtained at the value of relative concentration of C/C₀ = 1, on the boiling number Bo may be presented as single curve for both gap sizes and the whole range of considered concentrations.     

Attractive fixed-point solution study of shell model for homogeneous isotropic turbulence

The attractive fixed-point solution of a nonlinear cascade model is studied for the homogeneous isotropic turbulence containing a parameter C, introduced by Desnyansky and Novikov. With a traditional constant positive external force added on the first shell equation, it can be found that the attractive fixed-point solution of the model depends on both the parameter C and the external force. Thus, an explicit force is introduced to remove the effects of the external force on the attractive fixed-point solution. Furthermore, two groups of attractive fixed-point solutions are derived theoretically and studied numerically. One of the groups has the same scaling behavior of the velocity in the whole inertial range and agrees well with those observed by Bell and Nelkin for the nonnegative parameters. The other is found to have different scaling behaviors of the velocity at the odd and even number shells for the negative parameters. This special characteristic may be used to study the anomalous scaling behavior of the turbulence.     

Space-time description of stationary and homogeneous turbulence

A system of two functional equations is derived, describing turbulence that is stationary in time and homogeneous in space. A theory of perturbations is formulated and the character of hypotheses concerning termination of the series involved is sharpened.     

Nucleate and transition boiling in narrow horizontal spaces

Nucleate and transition boiling are performed in a horizontal narrow space between a heated upward-facing copper disk and an unheated surface for saturated n-pentane. The heat flux and the wall temperature are determined by mean of an inverse heat conduction method. The influence of the confinement on the boiling curves and the flow patterns are analysed. Characteristic instabilities are observed at low heat flux and during the transition regime.     

A theory of homogeneous isotropic turbulence

Summary Homogeneous and isotropic turbulence has been discussed in the present paper. An attempt has been made to find the simplifying hypothesis for connecting the higher order correlation tensor with the lower ones. Starting from the Navier-Stokes equations of motion for an incompressible fluid and following the usual method of taking the averages, a differential equation in Q and X, the defining scalar of the second order correlation tensor Q _x and the defining scalar of a third order isotropic tensor X _ijk , has been derived. The tensor X _ijk stands for a tensorial expression containing the derivatives of the third and the fourth order tensors. Then the hypothesis is used that X=F(Q), where F is an unknown function. To find the forms of F, Kolmogoroff's similarity principles have been used, and thus two forms for F(Q) corresponding to two regions of the validity of these principles have been deduced.     

Modeling of pressure-strain rate in homogeneous turbulence

Direct numerical simulations were used to study the slow pressure strain rate term in homogeneous, axisymmetric turbulence during its relaxation towards isotropy. A strong Reynolds number dependence was found on the relaxation rate. A model for the rapid pressure strain rate tensor was developed using the classical approach of expansion in the Reynolds stress tensor. The model is tensorially complete and satisfies strong realizability. Rapid distortion analysis has been used to calibrate the model coefficients. The range of applicability of the model has been tested using direct numerical simulations.     

The self-preservation of homogeneous shear flow turbulence

An analysis of the equations governing homogeneous shear flow shows the possibility of solutions which are self-preserving at all scales of motion, and that these solutions are dependent on the initial conditions. The appropriate velocity scale is the one obtained from the turbulence kinetic energy, q ²/2, while the length scale is the Taylor microscale, . Two cases of self-preserving flow are identified: one corresponding to constant mean shear, the other to a mean shear which is inversely proportional to time. For the first case (the only one considered in detail) the principal results of the postulated similarity are that is constant, while q ² varies exponentially with time. The ratio of the turbulence energy production rate to its dissipation rate remains constant. It is also shown that the energy spectra scale over all wavenumbers with q ² and , and that they have shapes determined by the initial conditions. The experimental evidence is generally consistent with the theory.     

On the generation of large-scale homogeneous turbulence

An active turbulence generating grid, based on the rotating-vane design of Makita (1991), was developed for a large wind tunnel. At 2.14 m square, the grid is the largest of this type ever developed. To improve the isotropy of the turbulence generated, the grid was placed in the wind tunnel contraction. Measurements show that the grid produces a closely uniform mean flow and homogeneous isotropic turbulence to within two integral scales from the wall. By systematically varying the flow speed and parameters controlling the random motion of the vanes, grid turbulence with a wide variety of characteristics was produced and the dependence of those characteristics on the operating parameters of the grid revealed. Taylor Reynolds numbers of the grid turbulence varied from 100 to 1,360 and integral scales from 5 to almost 70 cm. The extreme cases represent some of the highest Reynolds number and largest scale homogeneous turbulent flows ever generated in a wind tunnel.     

Effects of turbulence and secondary flows on subcooled flow boiling

Experiments are conducted on the influence of turbulence and longitudinal vortices on subcooled flow boiling in a vertical, rectangular channel. Different flow inserts are used to create turbulence and vortices in the channel. Studied boiling regimes range from the onset of nucleate boiling over the critical heat flux up to fully developed film boiling. A wide range of measuring techniques is applied: time averaged particle image velocimetry (PIV) is used in cold flows for the evaluation of the effects the inserts have on the flow, high speed PIV and photography are used to determine the effects on the fluid and vapor movement in boiling experiments. Digital Holographic Interferometry is used for the evaluation of temperature distributions in the boiling flow. Furthermore, optical microprobes are used to obtain pointwise measurements in areas inaccessible to the imaging techniques. The experiments show that the flow inserts can have considerable impact on the heat fluxes and the distribution of vapor and temperature along the channel. All used inserts lead to an increase in critical heat flux, which is more pronounced for stronger turbulence and higher flow rates and fluid subcoolings. The measuring techniques reveal both a better transport of vapor from the heater surface as well as an increase in mixing in the liquid phase with flow inserts.     

Direct numerical simulation of homogeneous stratified rotating turbulence

The effects of the Prandtl number on stratified rotating turbulence have been studied in homogeneous turbulence by using direct numerical simulations and a rapid distortion theory. Fluctuations under strong stable-density stratification can be theoretically divided into the WAVE and the potential vorticity (PV) modes. In low-Prandtl-number fluids, the WAVE mode deteriorates, while the PV mode remains. Imposing rotation on a low-Prandtl-number fluid makes turbulence two-dimensional as well as geostrophic; it is found from the instantaneous turbulent structure that the vortices merge to form a few vertically-elongated vortex columns. During the period toward two-dimensionalization, the vertical vortices become asymmetric in the sense of rotation. Communicated by S. Obi PACS 47.55.Hd     

Prediction of flow and heat transfer in narrow rotating rectangular channels using Reynolds stress model

A computational study is performed on three-dimensional turbulent flow and heat transfer in a rotating rectangular channel with aspect ratio (AR) of 10:1, oriented 120° from the direction of rotation. The Focus is on high rotation and high-density ratios effects on the heat transfer characteristics of the 120° orientation. The Reynolds stress model (RSM), which accounts for rotational effects are used to compute the turbulent flow and heat transfer in the rotating channel. The effects of rotation and coolant-to-wall density ratio on the fluid flow and heat transfer characteristics is reported on a range of rotation numbers and density ratios (0 < Ro < 0.25 and 0.07 < Δρ/ρ < 0.4). The computational results are in good agreement with experimental data within ±15%. The results show that the density ratio, rotation number and channel orientation significantly affect the flow field and heat transfer characteristics in the rotating rectangular channel. Flow reversal occurs at high rotation number and density ratio.     

Creating homogeneous and isotropic turbulence without a mean flow

A novel method of creating homogeneous and isotropic turbulence with small mean flow has been developed. Eight synthetic jet actuators on the corners of a cubic chamber can create energetic turbulence with root-mean-square (rms) velocities as large as 0.87 m/s, corresponding to a Taylor microscale Reynolds number, Re , of 218. Stationary turbulence results show that the turbulence was isotropic, with the rms velocity ratio equal to 1.03, and also homogeneous within the region of interest. Natural decaying turbulence measurements confirmed the power-law decay of the turbulent kinetic energy, with the decay exponent n equal to 1.86 for an initial Re of 224.     

A solution of the E-ε model for nearly homogeneous turbulence with a mean shear

An analytical solution of the E-ε model for the downstream evolution of a stationary and nearly homogeneous turbulent shear flow is presented. In case that the turbulent time scale has adjusted itself to the time scale imposed by the shear, an asymptotic solution can be derived from the full solution, which shows that both E and ε increase downstream exponentially. By comparing this asymptotic solution with experimental data a value for the unknown constant c _lε , in the ε-equation, is derived. Moreover, we find an expression for the downstream development of the variance of a scalar, which is also compared with experimental data. The analytical solution shows that a homogeneous shear flow with a uniform velocity gradient can only be obtained if the shear is sufficiently small. In the experiments this condition is not always satisfied. A discussion is given on how a nearly homogeneous shear flow can be obtained over a limited downstream interval by changing the initial conditions in E and ε, and a comparison is made with experimental data. Finally it is shown that better transverse homogeneity can be obtained by taking an exponential velocity profile instead of a linear profile.