Neutrally buoyant bubbles used as flow tracers in air

Research has been performed to determine the accuracy of neutrally buoyant and near-neutrally-buoyant bubbles used as flow tracers in an incompressible potential flowfield. Experimental and computational results are presented to evaluate the quantitative accuracy of neutrally buoyant bubbles using a commercially available helium bubble generation system. A two-dimensional experiment was conducted to determine actual bubble trajectories in the stagnation region of a NACA 0012 airfoil at 0° angle of attack. A computational scheme evaluating the equation of motion for a single bubble was also used to determine the factors which affect a bubble's trajectory. The theoretical and computational analysis have shown that neutrally buoyant bubbles will trace complex flow patterns faithfully in the flowfield of interest. Experimental analysis revealed that the use of bubbles generated by the commercially available system to trace flow patterns should be limited to qualitative measurements unless care is taken to ensure neutral buoyancy.Nomenclature a _c centripetal acceleration - c model chord - c _D bubble drag coefficient - D bubble diameter - g acceleration due to gravity - g _v acceleration due to gravity vector - h trajectory deviation normalization parameter - K nondimensional inertia parameter, - m _f mass of fluid - m _p mass of bubble - p static pressure - r radial distance, bubble radius - R gas constant - Re free-stream Reynolds number, - Re _p bubble slip Reynolds number, - S cross-sectional area of sphere - T temperature - t time - u streamwise velocity component - U free-stream velocity - v _f fluid velocity vector - V _p bubble velocity vector - x _p bubble position vector - y _b bubble trajectory y/c - y _s streamline y/c - model angle of attack - bubble solution surface tension - potential vortex strength - _bfs bubble solution density - fluid density - bubble density - bubble wall thickness - fluid viscosity     

Measurements of thermally stratified pipe flow using image-processing techniques

The cross-correlation technique and Laser Induced Fluorescence (LIF) have been adopted to measure the time-dependent and two-dimensional velocity and temperature fields of a stably thermal-stratified pipe flow. One thousand instantaneous and simultaneous velocity and temperature maps were obtained at overall Richardson numberRi = 0 and 2.5, from which two-dimensional vorticity, Reynolds stress and turbulent heat flux vector were evaluated. The quasi-periodic inclined vortices (which connected to the crest) were revealed from successive instantaneous maps and temporal variation of vorticity and temperature. It has been recognized that these vortices are associated with the crest and valley in the roll-up motion.List of symbols A Fraction of the available light collected - C Concentration of fluorescence - D Pipe diameter - I Fluorescence intensity - L Sampling length along the incident beam - I ₀ Intensity of an excitation beam - I _c (T) Calibration curve between temperature and fluorescence intensity - I _ref Reference intensity of fluorescence radiation - Re _b Reynolds number based on bulk velocity,U _b D/v - Ri Overall Richardson number based on velocity difference,gDT/U ² - t Time - t Time interval between the reference and corresponding matrix - T Temperature - T ₁,T ₂ Temperature of lower and upper layer - T ^* Normalized temperature, (T–T ₁)/T - T _c (I) Inverse function of temperature as a function ofI _c - T _ref Reference temperature - T Temperature difference between upper and lower flow,T ₂ –T ₁ - U ₁ Velocity of lower stream - U ₂ Velocity of upper stream - U _b Bulk velocity - U _c Streamwise mean velocity atY/D=0 - U Streamwise velocity difference between upper and lower flow,U ₁–U ₂ - u, v, T Fluctuating component ofU, V, T - U, V Velocity component of X, Y direction - X Streamwise distance from the splitter plate - Y Transverse distance from the centerline of the pipe - Z Spanwise distance from the centerline of the pipe - Quantum yield - Absorptivity - vorticity calculated from a circulation - Kinematic viscosity - circulation     

Thermofluiddynamic experiments with a heated and rotating circular cylinder in crossflow

Two-dimensional flow fields and temperature boundary layer profiles around a heated and rotating circular cylinder in crossflow were experimentally investigated for a subcritical freestream-Reynolds-number 5.6 · 10⁴ corresponding to a flow velocity of 7 m/s. Test parameter was the ratio of free stream velocity to peripheral speed, which encompasses the range between zero and 2.5. An electronically-controlled hot wire measurement technique, practicable for the requirements of 1–2 mm boundary layer thickness, was used. The numerous reliable test results confirm previous reported experiments. Characteristic features in heat transfer are discussed.List of symbols C _b correction factor for blockage - n rotation rate in rpm - r radial coordinate - R cylinder radius - Re Reynolds-number = U 2R/v - Re _R circumferential Reynolds-number = U _R 2R/v - T local temperature - U velocity - = U · C _b/U _R velocity ratio of air flow and cylinder surface, corrected for blockage - v kinematic viscosity - = T — T /T _w — T non-dimensional temperature Indices undisturbed flow conditions - w wall - R circumferential - c critical Dedicated to Alfred Walz on the occasion of his 80th birthday     

An experimental study of gas-liquid slug flow

Experimental measurements were carried out for upward gas-liquid slug flow in a 50.8 mm diameter pipe. Parallel conductance wires were used to distinguish the Taylor bubbles and liquid slugs and to determine translation velocities and lengths, an electrochemical probe provided the magnitude and direction of the wall shear stress and a radio-frequency local probe was used for the axial and radial distribution of voidage in the liquid slugs. Data are reported over wide range of flow conditions covering slug flow and into the churn flow pattern. Comparison with the Fernandes model predictions are presented. Numerical simulation of slug flow provided information on the structure of flow in a liquid slug and, in particular, on the process of mixing behind a Taylor bubble.List of symbols D pipe diameter - f Taylor bubble frequency - F _Gi (x) gas existence function for i-th liquid slug - g gravitational acceleration - l _A distance for the wall shear stress reversal in a liquid slug - l _B distance for the wall shear stress reversal in a Taylor bubble region - l _LS length of a liquid slug - l _TB length of a Taylor bubble - n number of samples in an ensemble - u axial velocity - U _M superficial mixture velocity (U _SG + U_SL) - U _N translation velocity of the leading Taylor bubble - U _NLS average translation velocity of liquid slugs - U _NTB average translation velocity of Taylor bubbles - U _OT overtaking velocity of the trailing Taylor bubble - U _SG superficial gas velocity - U _SL superficial liquid velocity - v radial velocity - w (y) velocity profile at the inlet to a liquid slug - x axial coordinate - y radial coordinate - void fraction - _LS void fraction in a liquid slug - =l _TB /(l_TB + l_LS) - density - surface tension - shear stress - saturation ratio, = _w / g h - ensemble average     

Experimental investigation of certain aspects of upward vertical bubble and slug flows

The paper describes an installation, and measurements performed with its aid, in which it was possible to observe bubble flows as well as slug flows. Measurements and observations were carried out in vertical upward flow of water, with air injected into it, flowing through a plexiglass tube of 20 mm i.d. and 1500 mm long. The purpose of the investigation was to identify the parameters and influences which determine the observed flow pattern. The results show that there exists a range of values of the superficial velocity U _LS and U _GS in which it is possible to observe both flow patterns depending on the method of air injection employed. The transition zone bubble-slug shows reasonable agreement with the data of Taitel et al., whereas that for the slug-froth transition is close to the data of Oshinowa and Charles, and Griffith and Wallis. The distributions of bubble diameters and plug and Taylor-bubble dimensions are acceptably Gaussian. It is surmised that considerable discrepancies in the delineation of flow-regime boundaries which exist between different investigators are due to hitherto unidentified influences and parameters.List of symbols a distance between aligned bubbles - C ₀ distribution parameter - D inner tube diameter - d _S bubble diamter - L _b length of a Taylor bubble - L _E entrance length - L _S length of liquid plug - U _G actual gas velocity - U _GS superficial gas velocity: - U _L actual liquid velocity - U _LS superficial liquid velocity: - U _S superficial velocity - t time - average void fraction     

Development and evaluation of a new turbulence generator for atomization research

Planar Mie scattering visualizations in compressible mixing layers are used to compute the probability density function of a passive scalar. Mixing layer flows with relative Mach numbers of 0.63 and 1.49 are studied. Ethanol condensation is used to generate both scalar transport seeding and product formation seeding. All PDFs exhibit a marching behavior. The condensation process in the product formation seeding is modeled to provide an estimate of the error embedded in the scalar transport PDFs. The mixing efficiency is found to be 0.56 in the product formation experiments, and the overprediction of mixing efficiency by the scalar PDFs is estimated to be 11% based on results from the ethanol condensation model.List of Symbols _291-01 Damköhler number based on - J droplet nucleation rate - k Boltzmann constant - m _c molecular mass of ethanol - M _r relative Mach number, M _r = 2U/(a₁ + a₂) - N ^* number of nucleated droplets - p(,) probability density function - P _d internal droplet pressure - P _m total mixed fluid probability - P _sat ethanol saturation partial pressure - P _v ethanol vapor partial pressure - r freestream velocity ratio, r=U ₂/U₁; droplet radius - r ^* critical nucleation radius - R gas constant for air - _291-2 Reynolds number based on - s freestream density ratio, s = ₂/₁ - T local static temperature - U ₁ high speed freestream velocity - U ₂ low speed freestream velocity - U _c large structure convection velocity, - U freestream velocity difference, U=U ₁–U₂ - x streamwise coordinate - y transverse coordinate - mixing layer thickness - _i incompressible mixing layer thickness - mixture fraction - similarity variable, = (y–y ₀)/ - _c condensed phase ethanol density - droplet surface tension     

On heat transfer effects of a viscous fluid squeezed and extruded between two parallel plates

The unsteady squeezing and extrusion of a viscous fluid between two parallel plates of constant temperature is examined. The dimensionless extrusion parameter,=U/V, is introduced to represent the effects of the extrusion on the squeezing velocities. The squeezing parameter=VH/, represents the effect of the inertial forces on heat and fluid flow characteristics. It is found that increasing the extrusion parameter will increase both the velocity and the heat transfer rates to the viscous fluid. Increasing the squeezing parameter had also decreased the fluid velocity and enhanced heat transfer rates. Increasing the viscous effects or the Eckert number E=U²/c_p (T_E – T_s) heated the fluid and consequently decreased the heat transfer rates. Different velocity profiles, temperature profiles, and Nusselt numbers against various dimensionless groups are drawn.     

Collision dynamics of bubble pairs moving through a perfect liquid

Equations are derived describing the inertial motion of a bubble pair through a perfect liquid. The relative bubble motion is driven by an interactional force induced by the centre of mass motion. This force can be derived from a potential that is proportional tos ⁿ (n3) and that depends on the bubble pair orientation. The path of two bubbles passing each other is investigated. The angle of deflection of the relative velocity in a two-bubble encounter is calculated numerically as a function of the impact parameter, the relative velocityg and the ratio of the centre of mass velocity componentsc ₂/c ₁. The specific conditions necessary for two bubbles to collide are determined. Ifc ₂/c ₁>1 there is a region with irregular behaviour of the deflection angle. The collision cross-section is calculated and depends smoothly ong, approximately proportional tog ^–1, and has a weak dependence onc ₂/c ₁.     

A theoretical correlation for the Nusselt number in direct contact evaporation of a moving drop in an immiscible liquid

Numerical solutions for the Nusselt number during the direct contact evaporation of a moving drop in a stagnant column of immiscible liquid are presented. The effect of bubble growth rate on the radial component of drop velocity is taken into account in the analysis and the Nusselt number is found to be a function of Peclet number, Jakob number and vapour open angle. A comparison of theoretical and experimental correlations for the Nusselt number shows good agreement. The analysis also yields information on the temperature profile and the thickness of the thermal boundary layer surrounding the evaporating drop.

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Eine theoretische Beziehung für die Nusselt- Zahl bei Verdunstung eines bewegten Tropfens, der in direktem Kontakt zu einer unmischbaren Flüssigkeit steht

Zusammenfassung Es werden numerische Lösungen für die Nusselt-Zahl während der Verdunstung eines bewegten Tropfens, der in direktem Kontakt mit der umgebenden ruhenden Säule aus unmischbarer Flüssigkeit steht, mitgeteilt. In der Berechnung wird der Einfluß der Blasenwachstumsrate auf die radiale Komponente der Tropfengeschwindigkeit berücksichtigt. Es wird festgestellt, daß die Nusselt-Zahl eine Funktion der Peclet-Zahl, der Jakobs-Zahl und des Öffnungswinkels des Dampfes ist. Ein Vergleich der theoretischen und experimentellen Beziehungen für die Nusselt-Zahl zeigt gute Übereinstimmung. Die Berechnung enthält auch Informationen über das Temperaturprofil und die Dicke der thermischen Grenzschicht um den verdampfenden Tropfen.

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Nomenclature A constant in Eq. (4) - B diameter ratio - C _p specific heat of continuous liquid phase - h instantaneous heat transfer coefficient - h _fg latent heat of evaporation of dispersed phase - Ja system Jakob number, C_p t/(_v h_fg) - k thermal conductivity of continuous liquid phase - m mass of liquid fraction in the evaporating drop - m ₀ total mass of evaporating drop - Nu Nusselt number, 2hR/k - Pe Peclet number, 2UR/ - Pr Prandtl number,/ - q heat transfer rate per unit surface area of evaporating drop - r radial coordinate - R instantaneous radius of evaporating drop - Re Reynolds number, 2UR/ - t time - T temperature - T _c temperature of continuous liquid phase - T _d saturation temperature of dispersed phase - U _r radial component ofU - U tangential component ofU - U bubble translational velocity - x exponent in Eq. (4) - y transformed coordinate, (r–R)/R Greek letters thermal diffusivity of continuous liquid phase - half vapour open angle - non-dimensional bubble growth rate, - T temperature difference, (T _c –T _d ) - density of continuous liquid phase - _v density of dispersed vapour phase - non-dimensional temperature,(T– T _c )/(T _p -T _c ) - spherical polar coordinate - dimensionless time, t/R² - transformed coordinate, (–cos) - kinematic viscosity of continuous liquid phase     

Oscillating convection modes in the surroundings of an air bubble under a horizontal heated wall

The development of different oscillatory modes and their transition into a non-periodic state of convection, initiated by the thermal Marangoni-effect in the vicinity of an air bubble under a horizontal, heated wall, was investigated. In the further surroundings of the air bubble a stably stratified thermal field was maintained. The flow phenomena in the vicinity of the bubble were studied using light sheet and shearing interferometer flow visualization techniques. The observed modes are described with regard to their kinematics. The influence of the Marangoni number and of the bubble geometry on the mode selection is discussed. The boundaries of the different modes and of the non-periodic state are indicated.List of symbols a thermal diffusivity - Bo Bond number, Eq. (4) - c phase velocity, Eq. (6) - g acceleration due to gravity - l characteristic length - Mg Marangoni number, Eq. (1) - n wavenumber - Pr Prandtl number ( = v/a) - r radial coordinate - r _B bubble radius - Ra Rayleigh number ( = ga¦T/r¦l ⁴/va) - Re Reynolds number ( = u _mg l/) - t _p oscillation period - T temperature - T _w wall temperature - u _mg characteristical Marangoni velocity, Eq. (2) - z axial coordinate normal to the heated wall - z _B bubble height Greek letters surface tension - kinematic viscosity - dynamic viscosity Dedicated to Professor Dr.-Ing. Julius Siekmann on the occasion of his 65th birthday     

Interaction between thermocapillary and buoyancy driven convection

Convective flows driven by the variation of surface tension due to a radial temperature gradient along a liquid-gas interface were studied. Three liquids of different viscosities were applied, so that a wide range of Marangoni numbers was encountered. Light sheet technique and differential interferometry were taken to analyse the thermal flows. The mechanism of stationary thermocapillary convection, the influence of the radial temperature gradient and the kinematic viscosity on the Marangoni boundary layer thickness are discussed. Transitions from the steady to the oscillatory Marangoni convection are discovered and the oscillations are visualized with differential interferometry.List of symbols a thermal diffusivity - D cell diameter - f tangential stress - H cell height - Mg Marangoni number, Mg = U · R/a - Pr Prandtl number, Pr = v/a - r radial coordinate tangential to the interface - R cell radius - Re Reynolds number, Re = UR/v - T temperature - T _b, T_m temperature at the boundary and in the centre of the cell, respectively - T temperature difference, T — T _b — T_m - U reference velocity, U = ¦d/dT¦(T/R) R/ - v _r radial stream velocity - v _x velocity at the interface - z axial coordinate normal to the interface - dynamic viscosity - kinematic viscosity - surface tension - d/dT thermal coefficient of surface tension A version of this paper was presented at the 7th Physico-Chemical Hydrodynamics, PCH Conference, June 25–29, 1989, Cambridge, MA, USA     

Temperature-dependent heat sources or sinks in a stagnation point flow

Summary An analytical study has been made to determine the heat transfer characteristics of a stagnation point flow in which there are temperature-dependent heat sources or sinks. Results have been obtained for both strong and weak sources or sinks for a Prandtl number of 0.7. An analytical method, applicable to all Prandtl numbers, was utilized which circumvented the need for extensive numerical solutions and which, at the same time, provided a closed-form representation for the heat transfer. A few numerical solutions were carried out to verify the method.Nomenclature a _i constants depending on Prandtl number - c _p specific heat at constant pressure - f dimensionless velocity variable - g function defined by equation (13) - g _n functions of (n=1, 2, 3,...) - k thermal conductivity - Pr Prandtl number, c _p /k - q heat transfer rate per unit area at surface - Q heat flux parameter, q/k(u ₁/)^1/2 - S rate of heat generation or removal per unit volume (divided by c _p ) - T static temperature; T _w , wall temperature; T , free-stream temperature - u ₁ proportionality constant for free-stream velocity - U free-stream velocity - v normal velocity component - x coordinate measuring distance along surface from stagnation point - y coordinate measuring distance normal to surface - heat generation parameter, equation (3) - dimensionless normal coordinate, - dimensionless temperature - _n functions of (n=1, 2, 3,...) - absolute viscosity - kinematic viscosity - density     

On slip effect in free coating of non-Newtonian fluids

The failure of the current theories to predict the coating thickness of non-Newtonian fluids in free coating operations is shown to be a result of the effective slip at the moving rigid surface being coated. This slip phenomenon is a consequence of stress induced diffusion occurring in flow of structured liquids in non-homogeneous flow fields. Literature data have been analysed to substantiate the slip hypothesis proposed in this work. The experimentally observed coating thickness is shown to lie between an upper bound, which is estimated by a no-slip condition for homogeneous solution and a lower bound, which is estimated by using solvent properties. Some design considerations have been provided, which will serve as useful guidelines for estimating coating thickness in industrial practice.fa exponent in eq. (15) - b n/(4 –n)(n + 1) - Ca Capillary number - D diffusivity - De Deborah number - g acceleration due to gravity - G Goucher number - h thickness profile - h ₀ final coating thickness - K consistency index - L length available for diffusion - L _t tube length - n power-law index - P pressure drop - Q flow rate - R cylinder radius - R _t tube radius - t time available for diffusion - T ₀ dimensionless thickness without slip - T _s dimensionless thickness with slip - U _c theoretically calculated withdrawal velocity to match the film thickness - u _s slip velocity - U withdrawal velocity - U _w theoretically calculated withdrawal velocity based on solvent properties - U ^* effective withdrawal velocity - x distance in the direction of flow - y distance transverse to the flow direction - curvature coefficient - slip coefficient - curvature coefficient - rate of deformation tensor - u _s /U - relaxation time - density - surface tension - shear stress in tube flow - _w wall shear stress in tube flow - stress tensor - _w wall shear stress - T _s /T ₀ NCL-Communication No. 2818     

The interaction of two opposing,asymmetric curved wall jets

An experimental investigation was made of a two dimensional flow formed by the interaction of two asymmetric turbulent curved wall jets past a circular cylinder. Measurements were made of velocity and turbulence intensity profiles of the two curved wall jets before the interaction, and those of the merged jet after the interaction. The location of the interaction region of the two opposing curved wall jets and the flow direction of the merged jet were found to depend primarily on the ratio of initial momentum fluxes. The velocity and turbulence intensity profiles of the merged jet were similar to those of the plane turbulent jet. However, the growth rate of the merged jet was approximately 1.5 times larger than that of the plane jet. The influence of the momentum flux ratio on the growth rate appeared to be insignificant.List of symbols C _f friction coefficient - h slot height - J _p, J _c initial momentum flux of a power jet and of a control jet, respectively - P, Pa wall static and atmospheric pressure, respectively - Re Reynolds number based on slot height - Re _m local Reynolds number U _m y _m /v - U local mean velocity - U _c velocity along the center line of the merged jet - U _m local maximum velocity of the curved wall jet - u r.m.s. value of velocity fluctuations - u _u friction velocity - U ⁺ U/u_t - x distance along the cylinder surface - x distance along the center line of the merged jet - y _1/2, y _1/2 position of y and y where U = U _m /2 and U = U _c /2, respectively - y ⁺ yu _t/V - deflection angle of the merged jet (Fig. 4) - interaction angle (Fig. 4) - merged jet angle (Fig. 4) - angle measured from the center line of the cylinder (Fig. 4) - interception angle (Fig. 8) - , normalized coordinates, y/y _1/2 and y/y _1/2, respectively     

Rheology on the drawing zone in glass spinning

Summary Among investigations concerning the rheology of spinning materials from melt, or in other terms the problem of spinnability, glasses perform an example of fibre forming without crystallization along the spinning way and with surface tension playing an important role. Furthermore glasses show aNewtonian behaviour at least in the upper part of the drawing zone.As the absence of crystallization simplifies the formulation of the governing energy equation, on the other hand, the surface tension makes the applied motion equations quite complex to solve, above all in the two-dimensional analysis.The present paper shows that only a two-dimensional approach can give reliable results on the temperature, velocity and stress distribution in the drawing zone by a comparison of the theoretical and the experimental diameter profile of the forming fibre.The temperature profile has been obtained by a numerical solution of the energy equation, only after gaining experimentally the heat transfer coefficient. The results shown in the one-dimensional analysis cannot be applied in the opper part of the drawing zone.The velocity and stress distribution can be obtained by very complex numerical solutions in the very upper part of the drawing zone where the one-dimensional approach is shown unreliable. This can be thought an asymptotic solution of two-dimensional approach, reliable only after a certain distance of the spinning way from the exit of the nozzle.Furthermore, an analysis of the dimensionless numbers involved in the spinning phenomena brings up some information concerning the instability of the glass jet in comparison with that shown by materials as molten polymers or metals.As far as the rheological behaviour of glasses in the elongational shear rate is concerned, some conclusions can be drawn. F _r Froude numberU ₀ ² /gR₀ withg acceleration gravity (cm/sec²) - N _u Nusselt number 2Rh/Ka withh heat transfer coefficient (cal/cm² sec °C) andK _a air thermal conductivity (cal/cm sec °C) around the forming fibre - Q Volume rate of flow (cm³/sec) - r Radial distance from the central axis of the fibre (cm) - R Cross section radius of the fibre (cm) - R ₀ Inside diameter of the nozzle (cm) - t Quenching time (sec) - T _aT_s Temperature of fibre at the centre (°C) - T _i Initial temperature at the distancex = 0 (°C) - T ₀ Mean value of temperature of air surrounding the forming fibre (°C) - U ₀ Mean value of velocity of glass atx = 0 (cm/sec) - V Local velocity of fibre in the axial direction (cm/sec) - x Axial distance of the fibre from the nozzle exit (cm/sec) - W Weight rate of flow (g/minute) - W _e Weber numberU ₀ ² R₀/ - Glass surface tension (dynes/cm) - Angle between the fibre axis and the tangent to the fibre surface in ther, x plane (radiant). - v Air kinematic viscosity (cm²/sec) - Glass density (g/cm³) - Glass viscosity (poises) - _i Glass viscosity atT _i. - Maxwell relaxation time/G (sec) withG (dynes/cm²) elastic shear modulus of glass With 10 figures and 2 tables     

Vaporization of single liquid drops in an immiscible liquid part II: Heat transfer characteristics

Heat transfer characteristics during the vaporization process of a pentane or furan drop in an aqueous glycerol of high viscosity has been studied. With the progress of vaporization, the overall heat transfer coefficient related to the liquid-liquid interfacial area of a two-phase bubble increases monotonically, and influences of initial drop diameter and temperature difference reduce. Some convection or circulation seems to occur in the unvaporized-liquid phase.

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Verdampfung einzelner Flüssigkeitstropfen in einer nicht mischbaren Flüssigkeit. Teil II: Der Wärmeübergang

Zusammenfassung In dieser Arbeit wird der Wärmeübergang während der Verdampfung von Pentan- und Furan-Tropfen in einer wässerigen Glyzerinlösung hoher Viskosität untersucht. Mit fortschreitender Verdampfung steigt der Wärmeübergangskoeffizient, bezogen auf die Grenzfläche flüssig-flüssig der zweiphasigen Blase monoton an, wobei Einflüsse des anfänglichen Tropfendurchmessers und der Temperaturdifferenz abnehmen. In der nichtverdampften Flüssigkeitsphase scheint Konvektion oder Zirkulation aufzutreten.

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Nomenclature A total surface area of two-phase bubble - A_L liquid-liquid interfacial area of two-phase bubble - D equivalent spherical diamter of two-phase bubble - D_i initial drop diameter - h average overall heat transfer coefficient related to A - h_c average outside heat transfer coefficient related to A - q local outside heat transfer coefficient - h_L average overall heat transfer coefficient related to A_L - h_Lc average outside heat transfer coefficient related to A_L - k_c thermal conductivity of continuous-phase liquid - k_dl thermal conductivity of dispersed-phase liquid - k_v correction factor of velocity [cf. Eq.(2)] - Nu_c =h_c D/k - Nu_c =h_c D/k_c - Pe_c =UD/_c - Pr_c =_c/_c - Q cumulative heat transferred into two-phase bubble - q local heat flux - r radial distance in spherical co-ordinates - R radius of two-phase bubble - T temperature - T_L interface temperature between continuousphase and dispersed-phase component in liquid phase - T bulk temperature - T temperature difference - T nominal temperature difference - U velocity of rise of two-phase bubble - u velocity gradient in r direction [cf. Eq.(9)] - u_r velocity component in r direction - u velocity component in direction - V volume of two-phase bubble - V_dl volume of dispersed-phase component in liquid phase - X defined in Eq.(7) - Y defined in Eq.(8) - Z defined in Eq.(12) - _c thermal diffusivity of continuous-phase liquid - half opening angle of vapor phase in two-phase bubble - average thickness of dispersed-phase component in liquid phase [cf. Eq.(22)] - angle in spherical co-ordinates - vaporization ratio - time     

Helium jets discharging normally into a swirling air flow

The characteristics of helium jets injected normally to a swirling air flow are investigated experimentally using laser Doppler and hot-wire anemometers. Two jets with jet-to-crossflow momentum flux ratios of 0.28 and 12.6 are examined. The jets follow a spiral path similar to that found in the swirling air flow alone. Swirl acts to decrease jet penetration, but this is being counteracted by the lighter jet fluid density which is being pressed towards the tube center by the inward pressure gradient. Consequently, in spite of the large variation in momentum flux ratio, jet penetration into the main flow for the two jets investigated is about the same. The presence of the jet is felt only along the spiral path and none at all outside this region. Upstream of the jet, the oncoming swirling flow is essentially unaffected. These characteristics are quite different from jets discharging into a uniform crossflow at about the same momentum flux ratios, and can be attributed to the combined effects of swirl and density difference between the jet fluid and the air stream. Finally, the jets lose their identity in about fifteen jet diameters.List of symbols C mean volume concentration of helium - C _j mean volume concentration of helium at jet exit - c fluctuating volume concentration of helium - instantaneous volume concentration of helium - c RMS volume concentration of helium - D _j jet nozzle diameter - D _T diameter of tube - F flatness factor of c - J = _j U _j ² / _a U _a ^{gn 2} jet-to-crossflow momentum flux ratio - P(c) probability density function of c - r radial coordinate measured from tube centerline - R = D _T /2 radius of tube - Re _j = D _j U _j / _j jet Reynolds number - S = = tan swirl number - Sk skewness of c - instantaneous axial velocity - u RMS axial velocity - U mean axial velocity - local average mean axial velocity across tube - U _j jet exit velocity - U _a overall average mean axial velocity across tube - instantaneous circumferential velocity - w RMS circumferential velocity - W mean circumferential velocity - x axial coordinate measured from exit plane of swirler - x ₁ axial coordinate measured from centerplane of normal jet - y normal distance measured from tube wall - _j jet fluid kinematic viscosity - _a air density - _j jet fluid density - vane angle (constant)     

Mixing enhancement in axisymmetric turbulent isothermal and buoyant jets

Measurements of the velocity and concentration in axisymmetric, turbulent, isothermal and buoyant jets have been performed with laser-Doppler velocimetry and planar and point laser-induced fluorescence to quantify the mixing enhancement achieved by periodic forcing when the jet exit has a fully-developed turbulent pipe flow, a situation less well-studied than the case of laminar initial conditions. It was found that forcing at Strouhal numbers around 0.6 enhances mixing in the developing region of the jet and this enhancement increased with increasing amplitude of excitation, consistent with results of initially-laminar jets. The initial turbulence intensity did not have any effect, but an increase in the initial lengthscale of the turbulence, controlled by a perforated plate inside the nozzle, caused faster mixing. In agreement with previous experiments, the initial conditions of the jet did not affect the far-field rate of decay, but the jet-fluid concentration there was significantly reduced by forcing due to the increased mixing during the early stages of development, an effect that can be described by a smaller virtual origin in decay laws of jet decay. These results are independent of the Froude number because the initial conditions have an influence only in the early stages where the flow is still momentum dominated.List of Symbols A normalised excitation amplitude, defined by A = u'/U ₀ - D nozzle diameter - f jet-fluid concentration - F mean f - f r.m.s. f - Fd Froude number, defined by Fd=U ₀ ² /(gDT ₀) - g acceleration of gravity - I fluorescent intensity - I _inc incident light intensity - I _ref light intensity of the reference flow - K decay constant - L _hf concentration halfwidth - M mixing enhancement, defined by U _cl/U _cl,st=0 at x/D=5 - r radial coordinate - Re Reynolds number, defined by Re=U ₀ D/v - [Rh] concentration of Rhodamine B - St Strouhal number, defined by St=D/U ₀ - T ₀ temperature of jet fluid - T temperature of outer fluid - T ₀ temperature difference (= T ₀–, T ) - u r.m.s. axial velocity - u r.m.s. of the sinusoidal velocity fluctuation due to forcing - U mean axial velocity - U _cl mean axial centreline velocity - U _cl,st=0 mean axial centreline velocity for an unforced jet - U _max U at the centre of the nozzle exit - U ₀ bulk velocity at nozzle exit - x streamwise coordinate - X ₀ virtual origin Greek coefficient of thermal expansion - kinematic viscosity of the jet fluid - forcing frequency The experiments described here have been performed together with Mr. J. Sakakibara. Acknowledgments are also due to Prof. H. Longmire, of the University of Minnesota, for helpful discussions on forcing. This work was done while E.M. visitied Keio University with the financial assistance of TEPCO.     

Effects of viscous dissipation on heat transfer in an oscillating flow past a flat plate

Theoretical investigation has been carried out of laminar thermal boundary layer response to harmonic oscillations in velocity associated with a progressive wave imposed on a steady free stream velocity and convected in the free stream direction. Series solutions are derived both to velocity and temperature field and the resulting equations are solved numerically. The functions affecting the temperature field are shown graphically for different values of Prandtl number. It is observed that there is more reduction in the rate of heat transfer for P _r<1 and a rise in the rate of heat transfer for P _r>1 due to the presence of oscillatory free-stream.Nomenclature u, v velocity components in the x and y direction - x, y Cartesian coordinate axes - t time - U, U ₀ instantaneous value of and mean free stream velocity - density of fluid - kinematic viscosity - T, T _w, T temperature of the fluid, wall and free stream fluid - c _p specific heat at constant pressure - thermal diffusivity - amplitude of free stream velocity - frequency - _p non-dimensional temperature (T–T /T _w–T ) - P _r Prandtl number (c _p/K) - E _c Eckert number (U ₀ ² /c _p(T _w–T )) - a parameter ( ) - ₀ boundary layer thickness of the oscillation of a harmonic oscillation of frequency ( ) - ordinary boundary layer thickness ( ) - time-averaged, time-independent external velocity - A, B, C, D, E, K, L, M, N, P functions used in expansion for u and - Nu Nusselt number (hx/k) - T _w–% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8V4rqqrFfpeea0Jc9yq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepGe9fr-xfr-x% frpeWZqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaacIcadaGcaa% qaaiaadAhacaWG4bGaai4laiqadwfagaqeaaWcbeaakiaacMcaaaa!3CA6!\[(\sqrt {vx/\bar U} )\] - k thermal conductivity     

An experimental investigation of separating flow on a convex surface

The mean and turbulent characteristics of an incompressible turbulent boundary layer developing on a convex surface under the influence of an adverse pressure gradient are presented in this paper.The turbulence quantities measured include all the components of Reynolds stresses, auto-correlation functions and power spectra of the three components of turbulence. The results indicate the comparative influence of the convex curvature and adverse pressure gradient which are simultaneously acting on the flow. The investigation provides extensive experimental information which is much needed for a better understanding of turbulent shear flows.Nomenclature a, b constants in equation for velocity defect profile (Fig. 6) - c _f skin-friction coefficient (= _w/F _1/2 U ₁ ² ) - E(k ₁) one-dimensional wave number spectra - f frequency in Hz - G Clauser's equilibrium parameter = (H–1)/H(c _f /2) - H shape parameter (= ₁/ ₂) - k ₁ wave number (=2f/U) - L _u, L _v, L _w length scales of u, v and w fluctuations - p _s static pressure on the measurement surface - p _w reference tunnel wall static pressure - q ² total turbulent kinetic energy - R radius of curvature of the convex surface - R() auto-correlation function - T _u, T _v, T _w time scales of u, v and w fluctuations - U local mean velocity - U ₁ local free stream velocity - U _* friction velocity - u, v, w velocity fluctuations in x, y and z directions respectively - X streamwise coordinate measured along the surface from A (Fig. 1b) - x streamwise coordinate measured along the surface reckoned from station 9 - y coordinate normal to the surface - z spanwise coordinate - ₁/ _w · dp/dx - - boundary layer thickness - ₁ displacement thickness - ₂ momentum thickness - ₃ energy thickness - kinematic viscosity - density - time delay - _w wall shear stress