Slip flow in converging and diverging channels

The classical problem of Jeffery-Hamel flow is considered in which the fluid is allowed to slip along the walls of the channel. The problem is solved analytically and the volumetric flow rate is computed and compared with that of the corresponding no-slip flow. In the converging channel case, it is found that the slip boundary condition enhances flow rates through the channel, although the effect is minimal when the Reynolds number is large.In the case of the diverging channel, the slip boundary condition in some instances actually lowers the flow rate from its no-slip value. In other instances, a stable velocity profile does not even appear to exist. These cases aside, when the mean pressure in the channel is adverse, slip flow solutions exist and increase the flow rate through the channel by at most 15.7%.     

Boiling flow through diverging microchannel

An experimental study of flow boiling through diverging microchannel has been carried out in this work, with the aim of understanding boiling in non-uniform cross-section microchannel. Diverging microchannel of 4° of divergence angle and 146 μm hydraulic diameter (calculated at mid-length) has been employed for the present study with deionised water as working fluid. Effect of mass flux (118–1182 kg/m²-s) and heat flux (1.6–19.2 W/cm²) on single and two-phase pressure drop and average heat transfer coefficient has been studied. Concurrently, flow visualization is carried out to document the various flow regimes and to correlate the pressure drop and average heat transfer coefficient to the underlying flow regime. Four flow regimes have been identified from the measurements: bubbly, slug, slug–annular and periodic dry-out/ rewetting. Variation of pressure drop with heat flux shows one maxima which corresponds to transition from bubbly to slug flow. It is shown that significantly large heat transfer coefficient (up to 107 kW/m²-K) can be attained for such systems, for small pressure drop penalty and with good flow stability.     

Laminar flow in a narrow cylindrical tube

Laminar flows during periodic pressure drops and transverse oscillations of the liquid-solid interface are discussed.     

He II flow in a narrow slit

After a brief review of the relevant He II-flow equations, we report results of our investigations of He II counterflow in the presence of net liquid flow, using a narrow-plane parallel slit. Measurements of the liquid temperature inside the flow channel indicate that with counterflow, there is always some supercomponent vorticity present at least along a part of the channel. With higher velocities, a transition from laminar to turbulent normal-component flow was observed.On leave from Shanghai Institute of Technical Physics, Academia Sinica, 420 Zong Shan Bei Ji Road, Shanghai, People's Republic of China.     

Elastic-plastic flow through a converging conical channel

Summary The flow of an incompressible elastic-perfectly plastic solid through a rough converging conical channel is considered. A solution is obtained using theMises yield condition and thePrandtl-Reuss equations.

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Elastisch-plastische Strömung durch einen konvergierenden kegelförmigen Kanal

Zusammenfassung Es wird die Strömung eines inkompressiblen, ideal elastisch-plastischen Stoffes durch einen rauhen, sich kegelig verengenden Kanal betrachtet. Unter Benützung derMisesschen Fließbedingung und derPrandtl-Reussschen Gleichungen wird eine Lösung erhalten.

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With 6 Figures     

Heat transfer and flow of He II in narrow channels

Heat transfer and fluid flow of He II in a long, narrow channel connected to a bath that supplies a constant supply of heat have been investigated by numerical simulations by using the simplified model of Kitamura et al. [Cryogenics 37 (1) (1997) 1]. Such channels are used to cool compact, stable, low-temperature magnets. The fluid flow is driven by natural convection and the mutual friction between the normal fluid and the superfluid.In this model, the thermomechanical effect and the Goter-Mellink mutual friction balance each other. A consequence of this balance is that the velocity and temperature distributions of He II can be characterized by a dimensionless, dependent parameter equal to the ratio of the fluid speeds of internal convection to the total fluid flow. After a sudden application of heat flux, the internal convection dominates over the total fluid flow until the establishment of steady-state temperature gradients. This predicts that the time required to set up the steady-state total fluid flow is proportional to the total heat capacity in the channel.     

Separation from a smooth surface in a slender conical flow

Summary High Reynolds number flow of an incompressible fluid past a smooth surface in a slender conical flow is considered. Attention is focused upon the flow properties in the neighbourhood of the separation line. The analysis incorporates the results of a recent inviscid-flow investigation by Smith [1], and the ideas of Sychev [2] for flow separation in two dimensions.     

Aiding buoyancy driven flow and heat transfer features of converging and diverging trapezoidal cylinders

Numerical computations have been carried out to explore the influence of mixed convection heat transfer from heated trapezoidal geometries of two different configurations namely converging and diverging cylinders in a vertical domain. The recirculation length of the diverging cylinder is found to be more than that of the converging cylinder for all values of Re (5 to 40) considered in this study and this length decreases after introducing buoyancy effect. Drag coefficients decrease with increase in Re for a fixed Ri. However, drag increases for the increasing values of Ri (values considered up to 1). The drag coefficient is found to be the smaller for diverging cylinder than that of converging one. Local Nusselt number shows significant increase as Re and Ri values increase, which results in enhanced heat transfer. Keeping Ri fixed and increasing the value of Re results in the augmentation of heat transfer and is around 15% at Re = 5 and 23% at Re = 40 for Ri = 0 for a square cylinder with respect to diverging cylinder. Under the influence of aiding buoyancy, the values of average Nusselt number (\( \overline{Nu} \)) for the diverging cylinder are higher compared to that of converging cylinder. A correlation expressing functional relationship of \( \overline{Nu} \) with Re and Ri has also been generated.     

Free surface effects on the flow between conical cylinders

Summary An experimental study is presented dealing with free surface effects on the flow between two truncated conical cylinders, the inner being rotated and the outer at rest. For different filling ratios and angular velocities different flow modes are observed. The basic flow and the occurring vortices in the present arrangement show similarities to those observed for the case of a completely liquid-filled annulus. In both systems upwards travelling toroidal cells, steady Taylor vortices and downwards moving helical vortice appear. The variation of the wavelength of toroidal vortices for small filling ratios as well as the occurrence of a helical upward motion are, however, new effects which are solely related to the free surface. In a partially liquid-filled annulus both helical systems may coexist, whereby the helical vortices with opposite inclinations of the vortex axes propagate in opposite directions. The characteristics of the various flow modes are discussed for different Reynolds numbers, filling ratios and initial conditions. A comparison with the case of a completely liquid-filled annulus and with the case of circular cylinders is made.     

Isothermal flow of superfluid helium through narrow channels

The differential pressure across channels has been measured as a function of the flow rate of superfluid helium for two different systems of long narrow channels in the temperature range 1.3–2.2 K. The systems were a wire-filled capillary with a 10-µm gap and a rod of porous Vycor glass with an average pore diameter of 60 Å. A large hysteresis is observed for Vycor, while for the capillary, in the limit of high temperatures and large velocities, the flow characteristics tend to those of a normal fluid with the same viscosity.     

Turbulent helium II flow through different narrow channels

Turbulent helium II flow is investigated in an annular gap of about 10 µm width and in superfilters with a pore size 0.1 µm. Of primary interest is the flow behavior at high mass flow rates. In the cases of both an annular gap and superfilters, deviations from the low-flow-rate behavior are found, which can be attributed to different reasons. Both systems with their separately determined characteristics are then combined in a parallel arrangement in order to study the flow in a channel system with nonuniform dimensions, as is realized, e.g., in a porous plug. The parallel system permits checks of different hypotheses on the flow behavior. The results show that certain simplistic ideas about the internal geometry of a porous plug are inadequate for the hydrodynamic treatment.     

Measurements on isothermal flow of helium II in narrow tubes

Isothermal flow of He II in circular glass and metal tubes of inner diameter 0.2 mm is investigated. Different methods for the generation of the flow are used. The pressure heads required to drive the flow as well as the heat supply require to maintain isothermal conditions are measured. Earlier findings are confirmed and are shown to remain valid for smaller transport rates. The main features may be summarized as follows: (1) the pressure heads at given mass transport are almost independent of bath temperature, (2) they vary almost proportionally to the square of the mass flow rate, and (3) the flow becomes isothermal when there is a small, almost constant slip velocity (2.0 cm/sec) between the superfluid and normal components.     

Heat transfer in the flow of low-density air in narrow channels

Results are given from measurements on air flow in narrow channels; relationships in dimensionless terms are derived for the heat transfer over a wide range in speed (1–120 m/sec) and in pressure (1 · 10⁵ > P > 1.33 · 10³) N/m².Notation V volume flow rate of air - N total number of buret divisions - P₀ pressure in measuring tank - l length of measuring section of buret - t time of oil column rise to the height h_i - n number of buret division corresponding to_i - _o, _m specific weights of oil and mercury - c scale division of buret - h₂ height of oil drop in measuring cylinder - v₀ total volume of system from needle throttle to heat exchanger inlet - P_p pressure at heat exchanger inlet - T_p, T₀ temperature at heat exchanger inlet and of surrounding air - G flow rate in mass terms - c_p mean specific heat of air - t temperature variation over measuring section - Nu, Re Nusselt and Reynolds numbers - l, d length and diameter of channel Translated from Inzhenerno-Fizicheskii Zhurnal, vol. 20, No. 5, pp. 879–883, May, 1971.     

Viscous liquid flow in a narrow gap between two nonplanar surfaces

The effect of gap median surface form on the character of Hill-Show type flow (Re 1) is demonstrated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 52, No. 4, pp. 569–575, April, 1987.     

Asymptotic flow of a monatomic dilute gas in narrow gap channels

The asymptotic flow of a dilute gas in gap channels is constructed within the ES-model. Flow with slow condensation (sublimation) on the channel flow is considered as an example.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 51, No. 2, pp. 207–217, August, 1986.     

Experimental study of the flow rectification performance of conical diffuser valves

Flow rectification performance of conical diffuser valves has been investigated experimentally. In order to quantify the valving capability of the diffuser, a diffuser performance test cell is designed. The main feature of the test cell is that the volume change of the pumping chamber is independent of the diffuser geometry and actuation frequency. Experiments have been carried out over a range of diffuser angles varying from 10° to 35° and Roshko numbers (based on diffuser throat diameter and actuation frequency) from 25 to 300. Results show that the valving performance of the diffuser is significantly affected by the tapered angle and Roshko number. The diffuser valve with diverging angle of 10° exhibits the best performance. This is consistent with our recent simulations. The maximum flow rectification efficiency that has been attained at condition of zero backpressure is around 48%. In addition, we have simultaneously measured the time-dependent pressure inside the actuation chamber. It is found that the variations of the pressure amplitude with the Roshko number are qualitatively similar to those of the valving efficiency; high rectification efficiencies are always associated with large actuation pressures. However, for a large actuation volume, the valve performance declines, even though the actuation pressure increases. A possible explanation for this phenomenon is also provided.     

Film flow of a nonlinear viscoelastic fluid along a conical rotor

Film flow of a nonlinear viscoelastic fluid, whose deformed behavior is described by using kinematic matrices, is considered along the surface of a rotating conical rotor.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 2, pp. 231–236, August, 1976.     

Superfluid turbulence in converging and diverging rectangular channels

We have extended the earlier work of Kafkalidis, Klinich, and Tough (KKT) on the effect of nonuniform flow on superfluid turbulence. The same high aspect ratio rectangular cross section flow channel is used as before, but now reversed to produce converging flow. Temperature difference data are obtained as a function of heat current for eight different positions along the channel, at four bath temperatures. After all of the data had been obtained, the channel was removed from the apparatus and cut into sections so that the actual geometry could be determined. Although designed to have a uniform height, it was found that the channel actually had a substantial height variation along its length. Incorporating this new information, we are able to show that the Schwarz theory of homogeneous turbulence in uniform flow can be simply extended to fit the weakly nonuniform flow in our channel. Data from both converging and diverging flow agree with calculations based upon the Schwarz theory applied locally but using a slightly modified value of the vortex line parameterc _L . The correction toc _L is about 10% independent of temperature and independent of flow direction.