Flow regime transitions due to cavitation in the flow through an orifice

This paper presents both experimental and theoretical aspects of the flow regime transitions caused by cavitation when water is passing through an orifice. Cavitation inception marks the transition from single-phase to two-phase bubbly flow; choked cavitation marks the transition from two-phase bubbly flow to two-phase annular jet flow.

It has been found that the inception of cavitation does not necessarily require that the minimum static pressure at the vena contracta downstream of the orifice, be equal to the vapour pressure liquid. In fact, it is well above the vapour pressure at the point of inception. The cavitation number [σ = (P₃ − P_v)/(0.5 pV²); here P₃ is the downstream pressure, P_v is the vapour pressure of the liquid, ρ is the density of the liquid and V is the average liquid velocity at the orifice] at inception is independent of the liquid velocity but strongly dependent on the size of the geometry. Choked cavitation occurs when this minimum pressure approaches the vapour pressure. The cavitation number at the choked condition is a function of the ratio of the orifice diameter (d) to the pipe diameter (D) only. When super cavitation occurs, the dimensionless jet length [L/(D - d); where L is the dimensional length of the jet] can be correlated by using the cavitation number. The vaporization rate of the surface of the liquid jet in super cavitation has been evaluated based on the experiments.

Experiments have also been conducted in which air was deliberately introduced at the vena contracta to simulate the flow regime transition at choked cavitation. Correlations have been obtained to calculate the critical air flow rate required to cause the flow regime transition. By drawing an analogy with choked cavitation, where the air flow rate required to cause the transition is zero, the vapour and released gas flow rate can be predicted.     

Experimental investigation of heat transfer and pressure drop characteristics of flow through spirally fluted tubes

Spirally fluted tubes are used extensively in the design of tubular heat exchangers. In previous investigations, results for tubes with flute depths e/D_vi < 0.2 were reported, with most correlations applicable for Re ≥ 5000. This paper presents the results of an experimental investigation of the heat transfer and pressure drop characteristics of spirally fluted tubes with the following tube and flow parameter ranges: flute depth e/D_vi = 0.1−0.4, flute pitch p/D_vi = 0.4−7.3, helix angle θ/90° = 0.3−0.65, Re = 500−80,000, and Pr = 2−7. The heat transfer coefficients inside the fluted tube were obtained from measured values of the overall heat transfer coefficient using a nonlinear regression scheme. The friction factor data obtained consisted of 507 data points. The proposed correlation for the friction factor predicts 96% of the database within ±20%. The heat transfer correlation for the range 500 ≤ Re ≤ 5000 predicts 76% of the database (178 data points) within ±20%, and the correlation for the higher Re range predicts 97% of the 342 data points within ±20%. Comparison of heat transfer and friction data show that these tubes are most effective in the laminar and transition flow regimes. The present results show that the increase of flute depth in the range considered does not improve heat transfer.     

Inertial instability of the Stewartson -layer

Inertial stability of a vertical shear layer (Stewartson E^1/4-layer) on the sidewall of a cylindrical tank with respect to stationary axisymmetric perturbations is inverstigated by means of a linear theory. The stability is determined by two non-dimensional parameters, the Rossby number Ro = U/2ΩL and Ekman number E = v/ΩH², where U and L = (E/4)1/4H are the characteristic velocity and width of the shear layer, respectively, Ω the angular velocity of the basic rotation, v the kinematic viscosity and H the depth of the tank.

For a given Ekman number, the flow is more unstable for larger values of the Rossby number. For E = 10⁻⁴, which is a typical value of the Ekman number realized in rotating tank experiments, the critical Rossby number Ro_c for instability and the critical axial wavenumber m_c non-dimensionalized by L⁻¹ are found to be 1.3670 and 8.97, respectively. The value of Ro_c increases and that of m_c decreases with increasing E.     

Condensation from steam—air mixtures in a horizontal annular flow channel

Experiments were performed on the condensation of steam from steam-air mixtures in annular flow at a cooled inner tube. The range of investigation was varied for laminar and turbulent flow for 1.5 × 10³ Re 1.3 × 10⁴ and inlet concentrations 0.59 p_steam/p_total 0.95. The measurements, performed at an open test loop at p_total ≈ 0.96 bar, allowed local heat and mass transfer coefficients to be evaluated for various inlet lengths in the 2 m long annulus. The steam concentration was measured locally inside the annulus with a newly developed dew-point probe. The heat flux was measured locally using the temperature gradient in the cooled inner tube.

Near the inlet region the experiments showed a slightly higher heat flux at the bottom of the tube compared to the top, although it is expected to be smaller there owing to a thicker liquid film. Far downstream from the inlet region the heat transfer at the top was higher than at the bottom. The reasons for these effects are discussed, yielding a better understanding of the thermal and fluid processes involved in condensation from vapor-gas mixtures. The measured data allow the development of correlations for predicting the local Nusselt and Sherwood numbers in a horizontal annular-flow chanbel.     

Measurement and correlation of volumetric heat transfer coefficients of cellular ceramics

The volumetric heat transfer coefficients (h_v) between cellular ceramics and a stream of air were measured using the single-blow transient experimental technique in conjunction with an inverse analysis. Test specimen made of mullite, YZA, SiC, cordierite and cordierite with LS-2 coating was studied. The number of pores per centimeter (PPC) ranged from 4 to 26 and the specimen thickness ranged from 6 to 12 mm. Based on the experimental data, the volumetric heat transfer coefficients were generalized by developing Nusselt number vs. Reynolds number correlations of the form Nu_v=C Re^m for the materials studied. The effects of pore length-scale and specimen thickness on the volumetric heat transfer coefficients are presented and discussed.     

Experiments on the local heat transfer characteristics of a circulating fluidized bed

The role of particle diameter in the heat transfer of a gas–solid suspension to the walls of a circulating fluidized bed was studied for particles of uniform size. This work reports and analyzes new experimental results for the local bed to wall heat transfer coefficient, not including the radiation component, in a long active heat transfer surface length laboratory bed, which extend previous findings and clear up some divergences. The research included determining the effects of extension and location of the heat transfer surface, circulating solids mass flux and average suspension density. An experimental set-up was built, with a 72.5 mm internal diameter riser, 6.0 m high, composed of six double pipe heat exchangers, 0.93 m high, located one above the other. Five narrow sized diameter quartz sand particles − 179, 230, 385, 460 and 545 μm − were tested. Temperature was kept approximately constant at 423 K and the superficial gas velocity at 10.5 m/s. The major influence of suspension density on the wall heat transfer was confirmed, and contrary to other authors, a significant effect of particle size was found, which becomes more relevant for smaller particles and increasing suspension density. It was observed that the extension of the heat transfer surface area did not influence the heat transfer coefficient for lengths greater than 0.93 m.The heat transfer surface location did not show any effect, except for the exchanger at the botton of the riser. A simple correlation was proposed to calculate the heat transfer coefficient as a function of particle diameter and suspension density.     

Thermo-mechanical modeling of turbulent heat transfer in gas–solid flows including particle collisions

A thermo-mechanical turbulence model is developed and used for predicting heat transfer in a gas–solid flow through a vertical pipe with constant wall heat flux. The new four-way interaction model makes use of the thermal k_θ–τ_θ equations, in addition to the hydrodynamic k–τ transport, and accounts for the particle–particle and particle–wall collisions through a Eulerian/Lagrangian formulation. The simulation results indicate that the level of thermal turbulence intensity and the heat transfer are strongly affected by the particle collisions. Inter-particle collisions attenuate the thermal turbulence intensity near the wall but somewhat amplify the temperature fluctuations in the pipe core region. The hydrodynamic-to-thermal times-scale ratio and the turbulent Prandtl number in the region near the wall increase due to the inter-particle collisions. The results also show that the use of a constant or the single-phase gas turbulent Prandtl number produces error in the thermal eddy diffusivity and thermal turbulent intensity fields. Simulation results also indicate that the inter-particle contact heat conduction during collision has no significant effect in the range of Reynolds number and particle diameter studied.     

Gas–liquid mass transfer in the gas–liquid–solid mini fluidized beds

The gas–liquid–solid mini fluidized bed (GLSMFB) combines the advantages of fluidized bed and micro-reactor, and meets the requirements for safety and efficiency of green development of process industry. However, there are few studies on its flow performance and no studies on its mass and heat transfer performance. In this paper, the characteristics of gas–liquid mass transfer in a GLSMFB were studied in order to provide basic guidance for the study of GLSMFB reaction performance and application. Using CO₂ absorption by NaOH as the model process, the gas–liquid mass transfer performance of GLSMFB was investigated. The results show that the liquid volumetric mass transfer coefficient and the gas–liquid interfacial area both increase with the increase of the superficial gas velocity within the experimental parameter range under the same given superficial liquid velocity. At the same ratio of superficial gas to liquid velocity, the liquid volumetric mass transfer coefficient increases with the increase of the superficial liquid velocity. Fluidized solid particles strengthen the liquid mass transfer process, and the liquid volumetric mass transfer coefficient is about 13% higher than that of gas–liquid mini bubble column.     

A survey of experimental heat transfer data for nucleate pool boiling of liquid metals and a new correlation

The experimental data for heat transfer during nucleate pool boiling of saturated liquid metals on plain surfaces are surveyed and a new correlation is presented. The correlation is h = Cq^0.7p_r^m, where C and m are, respectively, 13.7 and 0.22 p_r < 0.001 and 6.9 and 0.12 for p_r > 0.001 (h is in W/m² K and q in W/m²). This correlation has been verified with data for K, Na, Cs, Li, and Hg from 17 sources over the reduced pressure (p_r) range of 4.3 × 10⁻⁶ to 1.8 × 10⁻². The correlation of Subbotin et al. was found unsatisfactory, but a modified correlation was developed that also gives good agreement with most of the data.     

Heat transfer to air–water annular flow in a horizontal pipe

Two-phase air–water flow and heat transfer in a 25 mm internal diameter horizontal pipe were investigated experimentally. The water superficial velocity varied from 24.2 m/s to 41.5 m/s and the air superficial velocity varied from 0.02 m/s to 0.09 m/s. The aim of the study was to determine the heat transfer coefficient and its connection to flow pattern and liquid film thickness. The flow patterns were visualized using a high speed video camera, and the film thickness was measured by the conductive tomography technique. The heat transfer coefficient was calculated from the temperature measurements using the infrared thermography method. It was found that the heat transfer coefficient at the bottom of the pipe is up to three times higher than that at the top, and becomes more uniform around the pipe for higher air flow-rates. Correlations on local and average Nusselt number were obtained and compared to results reported in the literature. The behavior of local heat transfer coefficient was analyzed and the role of film thickness and flow pattern was clarified.     

Direct contact heat transfer from an immiscible liquid jet

Temperature distribution and transfer of heat in a vertical, immiscible, liquid jet in direct contact with a liquid matrix are analyzed. A theoretical model for plug and parabolic flow is adopted from the literature, the treatment of a special V-shaped velocity distribution expected in the experiment and suitable for reactor application is calculated. Two common surface conditions, i.e. constant heat flux or constant temperature are considered. An experiment was performed in which a high Prandtl number fluid (oil) formed the jet and a low Prandtl number fluid (water) formed the matrix. The experimental results fall within theoretical results obtained for a V-type velocity distribution and plug flow. It was determined that the heat transfer characteristics of a direct contact jet flow in most cases have definite advantages over those of flow in a pipe beyond the obvious advantage of removal of the pipe wall's thermal resistance. These advantages result from the more flat velocity distribution encountered in jet flow as compared to a corresponding Laminar pipe flow. The likeliness of having a particular flow shape is discussed. Advantages of a central wire, leading to the V-type flow, are the enhancement of heat transfer and the stabilisation of the jet for any desired length. The jet flow is laminar.     

Rime- and glaze-ice accretion due to freezing rain falling vertically on a horizontal thermally insulated overhead line conductor

A theory of atmospheric icing due to freezing rain on an overhead line conductor (OHLC) is developed. The rain falls vertically on a horizontal OHLC that is thermally insulated. It is assumed that the collection efficiency of the accretion surface is unity and that this surface is in thermodynamic equilibrium with the environment.

For air temperature T_A 0°C and raindrop temperature T_D 0°C, the freezing rain accretes as rime ice, provided that the temperature of the ice surface T_l < 0°C. The evolution equation governing the mass transfer at the accretion surface is solved analytically, yielding the shape of the rime-ice surface. Equations governing the thermal state of the rime-ice deposit are also given. These determine the onset of wet growth or glaze accretion at the upper stagnation line during suitable environmental conditions.

For environmental conditions producing an ice surface at temperature T_l = 0°gC, the freezing accretes as glaze. Equations governing the heat and mass transfer at the surface determine the shape of the glaze surface and the downward viscous motion of the unfrozen water. For T_D < 0°C, glaze evolution equations are developed for T_A 0°C and T_A 0°C. Analytical solutions of these equations are obtained. In particular, when T_D < −T_A < 0°C, the evolution equation predicts a novel limiting growth that is triangular in shape. Further study of the mass and heat transfer conditions, in the neighborhood of this final stage of glaze accretion, shows that it is maintained in thermodynamic equilibrium with its warm air environment.     

Characteristics of flow field and water concentration in a horizontal deadleg

Deadlegs are defined as the inactive portion of the pipe where the flow is stagnant. Corrosion in deadlegs occurs as a result of water separation due to the very low flow velocity. The present work provides an investigation of the effect of deadleg geometry and average flow velocity on flow field and oil/water separation in deadlegs. The investigation is based on the solution of the mass and momentum conservation equations of an oil/water mixture together with the volume fraction equation for the secondary phase. A fluid flow model based on the time-averaged governing equations of 3-D turbulent flow has been developed. An algebraic slip mixture model is utilized for the calculation of the two immiscible fluids (water and crude oil). The model solves the continuity and momentum equations for the mixture, and the volume fraction equation for the secondary phase utilizing an algebraic expression for the relative velocity. Flow visualization experiments were conducted in order to validate the numerical procedure. Good agreement was obtained between the calculated and measured flow patterns. Results are obtained for different lengths of the deadleg. The considered fluid mixture contains 90% oil and 10% water (by volume). The inlet flow velocity ranges from 0.2 to 10 m/s and the deadleg length to diameter ratio (L/D) ranges from 1 to 10. The results showed that the size of the stagnant fluid region increases with the increase of L/D and decreases with the increase of inlet velocity. The results also indicated that the water volumetric concentration increases with the increase of L/D and influenced by the deadleg geometry.     

Convective heat transfer for cold tube bundles with ice formations in a stream of water at steady state

Experiments were conducted on cold-tube banks subjected to a cross-flow of water. The tubes were internally cooled below the freezing temperature and became enveloped in ice. The resulting ice shapes, which formed on the outside surfaces of the tubes, were allowed to stabilize, and their impact on the total steady-state rate of energy exchange between the tubes and the flowing water was investigated.

Both in-line and staggered tube-bank geometries were considered, with tests conducted in the low to moderate Reynolds number range (Re_d = 100−2,000) and for cooling-temperature ratio variations of 0.5 < Θ < 8. The ice formations were directly observed and photographed, and the total heat transfer rate for the tube bank was inferred from a simple energy balance on the system.

The ice shapes that formed around the tubes were described by one of three distinct categories: ice formutions with no linkage occurring between any adjacent tubes; ice formations with partial linkage of some adjacent tubes; and, for the staggered tube bank, a complete linkage of a majority of the tubes.

The experiments showed that the ice formations dramatically affected the convective heat transfer rate of the tube banks (when compared to nonicing tube banks at the same Re_d) and that the change in heat transfer rate is dependent on the tube-bank geometry. In the no-link category, the ice formations were found to either increase or decrease the tube-bank heat transfer rate depending on the amount of ice-build accumulation, the staggered configuration showing a greater overall rise with Θ than the in-line geometry. Ice linkage between adjacent tubes was found to be detrimental to the heat transfer rate of the staggered bank; however, the same phenomenon on the in-line tube bank did not seriously impede its heat transfer rate. Correlations expressing the heat transfer behavior of both in-line and staggered tube banks with ice formations at steady state have been developed.     

Experimental study on convective heat transfer of TiO2 nanofluids

In this study, nanofluids with different TiO₂ nanoparticle concentrations were synthesized and measured in different constant heat fluxes for their heat transfer behavior upon flowing through a vertical pipe. Addition of nanoparticles into the base fluid enhances the forced convective heat transfer coefficient. The results show that the enhancement of the convective heat transfer coefficient in the mixture consisting of ethylene glycol and distilled water is more than distilled water as a base fluid.     

Drag coefficient and upstream influence in three-dimensional stratified flow of finite depth

A numerical study of the three-dimensional stratified flow past a vertical square flat plate in a channel of finite depth is described. Particular attention is paid to the anomalous dependence of the drag coefficient C_D on parameter K( = ND/-πU), where N is the Brunt-Väisälä frequency, D is the half depth of the channel and U is the upstream velocity. It is shown that C_D generally increases with K, while it decreases locally at integral values of K. Time development of the upstream columnar disturbance and the corresponding variation of C_D reveals that the periodic variation of C_D with time for K > 1 comes from the successive upstream radiation of the columnar disturbances of the first internal wave mode. Although the propagation speed of the columnar disturbance is consistent with the prediction of linear theory, its time-dependent structure is different from the weakly nonlinear theory as has been shown by laboratory experiments.     

The inertial effect on the natural convection flow within a fluid-saturated porous medium

The general momentum equation for fluid flow within a porous medium is supposedly valid for any fluid-porous medium configuration. One of the main concerns of using the general equations refers to the inclusion of both inertia terms, namely, the convective inertia term and the Forchheimer term. In this study, we go beyond the important discussion about the correctness of including both terms in the general momentum equations by focusing upon the effect of the convective inertia term on the heat transfer results. The fluid-porous medium system considered here is a cavity bounded by solid surfaces with vertical walls maintained at constant but different temperatures. The natural convection problem is solved numerically, and the results are compared with a general theory developed by using the method of scale analysis. It is demonstrated that the convective inertia term effect upon the heat transfer results is minor for 0.01 ≤ Pr ≤ 1, 10 ≤ Ra_D ≤ 10⁴, 10⁻⁸ ≤ Da ≤ 10⁻², and porosities 0.4 and 0.8. It is also shown that, contrary to the general belief, the convective inertial effect upon the heat transfer within the cavity is minimized when the Prandtl number is reduced.     

Experimental study of turbulence in isothermal and stably stratified homogeneous shear flows: Mean flow measurements

The evolution of freestream turbulence under the combined action of linear shear and stable linear temperature profile is investigated. The experiment is carried out in a small, open circuit, low-speed test cell that uses air as working fluid. The temperature gradient formed at the entrance to the test section by means of an array of 24 horizontal, differentially heated elements is varied to get a maximum Brunt-Vaisala frequency N_o[=({g/T_m}{∂T/∂y})^1/2] of 3.1⁻¹. Linear velocity profiles are produced using screens of variable mesh size. The Reynolds number Re_M based on centre-line velocity and mesh size is varied from 80 to 175. Isothermal studies are carried out in four different experiments with varying velocity gradients. The effect of inlet turbulence level on growth of turbulence is studied in these flows by keeping the shear parameter Sh (=(x/u)(∂u/∂y)) constant. The range of shear parameters considered is 2.5–7.0. Shear and stratification combined produce a maximum gradient Richardson number Ri_g (= N_o²/(∂u/∂y)²) of 0.0145. Results have been presented in terms of evolution of variance of velocity fluctuations, Reynolds shear stress and temperature fluctuations. Measurements show the following: In isothermal flows the growth rate of turbulence quantities depends on both shear parameter and inlet turbulence level. There are distinct stages in the evolution of the flow and that can be identified by the power-law exponent of growth of turbulence. Shear is seen to promote the growth of turbulence and accelerate it towards a fully developed equilibrium state. Stratification initially suppresses the growth of turbulence and, hence, enhances the degree of underdevelopment. Under these conditions shear becomes active and subsequently enhances the growth rate of turbulence quantities.     

Measurement of heat transfer at the phase interface of condensing bubbles

Using holographic interferometry and high-speed cinematography the heat transfer at the phase interface of vapor bubbles condensing in a subcooled liquid of the same substance was measured with ethanol, propanol, refrigerant R113 and water. To evaluate the axisymmetric temperature field around the bubble from the interference fringe field, the Abel integral method is not sufficient. A correction procedure considering the light deflection caused by the local temperature gradient has been developed and applied to calculate the heat transfer coefficient. The measurements were performed in the range 2 < Pr < 15 and I < Ja < 120. Measured data could be well-correlated as functions of the Prandtl and Reynolds numbers for the heat transfer coefficient and as functions of the Reynolds, Prandtl and Jacob numbers for the bubble collapse time.     

Experimental investigation of natural convection heat transfer in horizontal and inclined annular fluid layers

In the present study, an experimental investigation of heat transfer and fluid flow characteristics of buoyancy-driven flow in horizontal and inclined annuli bounded by concentric tubes has been carried out. The annulus inner surface is maintained at high temperature by applying heat flux to the inner tube while the annulus outer surface is maintained at low temperature by circulating cooling water at high mass flow rate around the outer tube. The experiments were carried out at a wide range of Rayleigh number (5 × 10⁴ < Ra < 5 × 10⁵) for different annulus gap widths (L/D _o = 0.23, 0.3, and 0.37) and different inclination of the annulus (α = 0°, 30° and 60°). The results showed that: (1) increasing the annulus gap width strongly increases the heat transfer rate, (2) the heat transfer rate slightly decreases with increasing the inclination of the annulus from the horizontal, and (3) increasing Ra increases the heat transfer rate for any L/D _o and at any inclination. Correlations of the heat transfer enhancement due to buoyancy driven flow in an annulus has been developed in terms of Ra, L/D _o and α. The prediction of the correlation has been compared with the present and previous data and fair agreement was found.