Subcritical Flow Region Research Articles

Surface Orientation Effect on Local Heat Transfer by Round Water Jet Impingement

This paper describes local heat transfer for a round water jet on upward-facing and downward-facing static plates. Impinging liquid jets have high heat transfer rates. One of the technological issues in the steel making process is uniformity in cooling between the top and bottom sides of a plate. The objective of this study is to investigate the surface orientation effect on transient heat transfer experimentally. Experiments were conducted for a range of water flow rate, surface orientation. Both surface orientations were conducted on the same apparatus. The heat transfer plate was stainless steel to deal with both supercritical flow and subcritical flow regions. The plate length was wide for laboratory scale. Initial plate temperature was 800 degrees Celsius. Pipe Reynolds numbers were laminar flow regime. Inverse solution was employed to estimate transient local surface temperature and heat flux. Heat transfers between upward-facing and downward-facing surfaces are the same in the order of magnitude at downward-facing surface flow rate from 1.2 times to twice that of upward-facing surface. Local downward-facing surface temperature is higher than that of upward-facing temperature at the same flow rate. The following points can be given as reasons. Downward-flowing impinging jet velocity is larger than that of upward-flowing jet at the same flow rate due to gravity direction. Heat transfer is affected by a geometric arrangement relation of radial spreading liquid film, vapor and hot plate.

The hydrodynamics of two-phase flows in the injection part of a conventional ejector

The characteristics of two-phase flow through a ‘conventional’ convergent-nozzle in an entrainment chamber of an ejector apparatus are described in this paper. A unique data set comprising 350 data points was generated in an air-water horizontal test-rig. Two sets of flow conditions were established, the first one including high liquid - low gas fluids with void fractions less than 0.55, and the second one involving high gas - low liquid fluids with void fractions greater than 0.75. All considered flow-rates lied within the sub-critical flow region. Two-phase flow pressure drop multiplier based empirical correlations were developed to estimate the total mass flow-rates. In the high liquid region, Morris (1985) correlation was modified, resulting in less than 10% error. In the high gas region, two new correlations were proposed, showing less than 10% and 15% of errors, respectively. The established empirical correlations were related to other available multipliers for different geometric configurations including a Venturi, an orifice plate, a gate valve, and a globe valve and were compared to 20 other void fraction correlations. The Chisholm (1983b) and Huq and Loth (1992) correlations showed the highest similarities to the ones proposed for the high liquid and high gas regions, respectively.

Energy harvesting from aeroelastic vibrations induced by discrete gust loads

This article evaluates the amount of energy that can be extracted from a gust using an aeroelastic energy harvester composed of a flexible wing with attached piezoelectric elements. The harvester operates in a subcritical flow region. It is modeled as a linear Euler–Bernoulli beam sandwiched between two piezoceramics. The extended Hamilton’s principle is used to derive the harvester’s equations of motion and an eigenfunction expansion is used to form a three-degree-of-freedom reduced-order model. The degrees of freedom retained in the model are two flexural degrees for the in-plane and out-of-plane displacements, and a torsional degree for the rotational displacement. Wagner and Küssner functions are used to represent the unsteady aerodynamic and gust loading, respectively. The amount of energy extracted from the system is then compared for two different deterministic gust profiles, 1-COSINE and two sharp-edged gusts forming a square gust, for various magnitudes and durations. The results show that the harvester is able to extract more energy from the square gust profile, although for both profiles the harvester extracts more power after the gust has subsided.

Numerical simulations of vortex-induced vibrations on vertical cylindrical structure with different aspect ratios

This paper presents a computational fluid dynamics (CFD) study of vortex-induced vibration (VIV) for different aspect ratio (L/D) cylinder. Of particular interest was to measure hydrodynamic forces and numerically investigate the wake behaviour of VIV while varying the aspect ratio. The simulation models represented the actual experimental conditions with idealised free-surface boundary condition to capture the responses from fluid-structure interaction phenomenon. The simulations were performed in the subcritical flow region (7.4×103 < Re < 2×105), corresponding to a range of reduced velocity (Ur) from 2 to 14. The results of the cases studied were discussed and compared with the experimental data to verify the accuracy and validity of the present simulation. The comparisons have shown a similar curved-shape drag coefficient plot, and however underestimated the value of the drag coefficients over the reduced velocity. Additionally, the simulations seemed to capture a higher lift force response compared with the experimental data for a low aspect ratio. The correlation length was observed to be longer for larger aspect ratio and proportionally decreases as the aspect ratio decreases.

Fluid-to-fluid scaling for convective heat transfer in tubes at supercritical and high subcritical pressures

Following a review of two recent sets of fluid-to-fluid scaling laws for supercritical heat transfer and a discussion of their possible limitations, we have proposed two additional sets of scaling laws, which take into account empirically adjustable versions of the Dittus–Boelter correlation and which are applicable to both the supercritical and the high subcritical flow regions. We have compiled a database of heat transfer measurements in carbon dioxide flowing upwards in vertical heated tubes that are free of deterioration or enhancement. We then applied the four sets of scaling laws to these data to compute values of the water-equivalent heat transfer coefficient and compared these values to predictions of a transcritical look-up table, which was earlier shown to represent well a large compilation of measurements in water at supercritical and high subcritical pressures. It was shown that the two earlier methods systematically overestimated the heat transfer coefficient in water and also introduced significant imprecision. In contrast, the two proposed methods of scaling introduce no bias and have lower precision uncertainties than those of the previous scaling methods.

Tapered-Bean Steam Chokes Revisited

This paper (SPE 144615) was accepted for presentation at the SPE Western North American Regional Meeting, Anchorage, 7–11 May 2011, and revised for publication. Original manuscript received for review 5 July 2011. Paper peer approved 31 August 2011. Summary Controlling and monitoring flow rates at continuousand cyclicsteam-injection wells are important elements of reservoir-heat management. For nearly 30 years, critical flow chokes have proven to be the most reliable and cost-effective means of controlling steam injection into heavy-oil reservoirs. Flow-control efficiency has been further improved with tapered-bore bean inserts to achieve critical flow, with only 10 to 15% pressure loss across the choke. For the past 10 years, the standard steam-choke assembly has consisted of a 1-in.-outer-diameter (OD) and 6-in.-long bean with a 6° tapered bore inserted inside a 2-in.-OD cage nipple or housing. Larger-diameter cage nipples and bean inserts have been required for steam-injection rates exceeding 500 B/D. More recently, a costcutting practice has been employed using shorter tapered beans inserted in standard choke assemblies. This paper presents the results of field tests conducted to evaluate the effectiveness of shorter tapered-bean length for controlling steam-injection rates. Transition from subcritical to critical flow and overall pressure loss for different tapered-bean lengths are presented. A modified Thornhill-Craver flow-rate equation is provided for criticaland subcritical-flow regions. Calculated and measured rates are compared, and their relative uncertainties are assessed.

Dynamics of the outflow and its effect on the hydraulics of two-layer exchange flows in a channel

This paper reports that an experimental study is conducted to examine the dynamics of the outflow in two-layer exchange flows in a channel connecting between two water bodies with a small density difference. The experiments reveal the generation of Kelvin-Helmholtz (KH) instabilities within the hydraulically sub-critical flow region of the channel. During maximal exchange, those KH instabilities develops into large-amplitude KH waves as they escape the channel exit into the reservoir. The propagation speed of those waves, their generation frequency and their amplitudes are studied. The dynamics of the outflow and these waves are directly linked to the hydraulic conditions of the exchange flow within the channel.

Numerical Model of Turbidity Currents with a Deforming Bottom Boundary

A numerical model of turbidity currents with a deforming bottom boundary has been developed. The model predicts the vertical structure of the flow velocity and concentration as well as change in the bed level due to erosion and deposition of suspended sediment. The Reynolds-averaged Navier-Stokes equations for dilute suspension have been solved using a finite volume method. The bottom boundary and the grid system are allowed to adjust in response to sediment deposition and entrainment during the computation. The model has been applied to simulate the evolution of a conservative saline density current and turbidity currents along an 11.6 m long flume that includes a slope followed by a horizontal bed. The model successfully simulates the evolution of the currents. Model results have been compared with the experimental data. Good similarity profiles of velocity and excess density or suspended sediment concen- tration are obtained at both the upstream supercritical and the downstream subcritical flow regions. A turbulent Schmidt number larger than one has been found to be appropriate for providing a good match with the experimental data. Changes in bed level predicted by the model have also been found to be in agreement with the experiment data.

Control Variability and Internal Bore Evolution in the Strait of Gibraltar: A 2-D Two-Layer Model Study

A two-dimensional, high-resolution, non-linear, two-layer, free-surface, boundary-fitted co-ordinate, hydrostatic model was applied to study the time–space variability of hydraulic controls and the development of internal bores in the Strait of Gibraltar. The model predicts the occurrence of four averaged (over a tropical month) controls located to the west of the Spartel Sill, at the Spartel and Camarinal Sills and in the Tarifa Narrows. The last of these controls is apparent in the sense that it consists of discrete fragments alternating with subcritical flow regions. The only control which extends over the whole width of the strait is the control at the Camarinal Sill, but it breaks down during neap tide, too. This control exists concurrently with the control in the Tarifa Narrows for short periods, while for much of the tropical month there is either just one or neither of the controls. The model predicts the development of a hydraulic jump and a jump-drop pair near the Camarinal Sill; the appearance of bulges of Mediterranean water to the east and west of the sill; the large-amplitude and small-amplitude internal bores released from the Camarinal Sill, which travel, respectively, eastward and westward, and their transformation due to radial spreading and dissipative effects. Also presented here are the results illustrating the effects of earth's rotation on the internal bores in the Strait of Gibraltar.

Gas injection from the surface of a triangular plate in a hypersonic flow

The flow formed as a result of gas injection through the permeable surface of a triangular plate is investigated in the regime of strong viscous-inviscid interaction between the hypersonic flow and the laminar boundary layer. The features of the flow past strongly cooled surfaces with the formation of supercritical and subcritical flow regions in the boundary layer are studied. The injected gas distribution ensuring the existence of self-similar solutions in the supercritical flow regions is obtained.

Quasi‐steady current sheet structures with field‐aligned flow

General properties of field‐aligned plasma flow in quasi‐steady ideal MHD configurations are discussed, and explicit solutions, modeling compressible flow around a plasmoid in the distant magnetotail, are presented. The explicit solutions are based on the assumption that plasma and field gradients along the x and y directions parallel to the tail current sheet are typically much smaller than those in the z direction perpendicular to the current sheet. In contrast to the incompressible case, two different flow solutions exist in the compressible case in the subalfvénic regime. The different regimes are distinguished by whether the flow speed is below or above a critical speed υo, which represents the group velocity of a slow magnetosonic wave (aligned with the magnetic field) in the limit of phase propagation perpendicular to the magnetic field, where the phase speed vanishes. In the incompressible case, only the subcritical flow solution is realized in the subalfvénic regime. In the compressible case, both regimes may exist simultaneously in the flow around the plasmoid. They are separated by a tangential discontinuity which may be considered as the limit of a slow shock for vanishing normal flow and normal magnetic field. The subcritical flow region surrounding the plasmoid inside of a supercritical region possibly corresponds to the layers of tailward streaming ions observed adjacent to the plasmoid proper. The signatures of a passage from the supercritical through the subcritical flow region in the vicinity of the plasmoid can be similar to those of a passage through the plasmoid itself: a reduction of Bx followed by a local enhancement in the middle of the encounter, as observed, for instance, by Hones et al. (1984) and Slavin et al. (1989). This enhancement is found for a simple loop structure within the plasmoid and hence need not be associated with multiple loops or a tail flapping as suggested by Hones et al. Field signatures outside the plasmoid are typically those of encounters of a traveling compression region: an enhancement of Bx accompanying a north‐south signature of Bz. In certain parameter regimes, however, unusual signatures are also possible: a reduction of Bx with a north‐south Bz signature for a close plasmoid encounter (without penetration) and a south‐north signature of Bz accompanying a Bx enhancement for a distant plasmoid encounter at high latitudes.

Four-sensor hot-wire probe measurements of the isothermal flow in a model combustion chamber at different levels of swirl

Measurements of the isothermal flowfield in a model combustion chamber at three different levels of swirl were carried out with a four-sensor hot-wire measurement technique. The new four-sensor hot-wire probe allows the measurement of all three components of the instantaneous velocity vector simultaneously at high data rates. The three mean velocity components and all six Reynolds stress components are subsequently calculated from an appropriate number of instantaneous-velocity measurements. The four-sensor measurement technique is described in the first part of the paper. The main feature of the flowfields measured is the existence of two distinct regions: a supercritical region in which disturbance do not influence the upstream flow and a subcritical region in which disturbances have a strong upstream influence. The transition from the supercritical flow at the inlet of the combustion chamber to the subcritical flow is associated with vortex breakdown and the formation of recirculation zones. With increasing swirl strength, the flow in the subcritical region approaches a one-dimensional state; that is, the mean velocity components are a function of only the radial' coordinate. Measurements of the Reynolds stress components are consistent with the mean velocity measurements. In the subcritical flow region the turbulent momentum transport nearly vanishes; similar to the mean velocities, the turbulent intensities approach one-dimensional behavior in the subcritical flow region.

Fluid Flow and Heat Transfer around Two Circular Cylinders of Different Diameters in Cross Flow

The heat transfer mechanism in separated region of a cylinder immersed in a free stream with non-homogeneous and unisotropic turbulence was made clear experimentally in relation to the wake formation process near the cylinder and the flow behavior in the layer close to the cylinder wall. An experiment was conducted in the subcritical flow region. The appearance of a second peak of heat transfer coefficients in separated region is due to the existence of a three-dimensional unsteady flow close to the cylinder surface and the decrease of heat transfer coefficients in near stagnation region is caused by the formation of an apparent turbulent separation point.

Effect of shroud eccentricity on suppression of flow induced vibrations

The object of the research described was to examine the vibrational characteristics (amplitude and frequency) and the resulting drag for an eccentrically shrouded cylinder. The results revealed that an eccentricity in any direction and of any magnitude always reduces the amplitude of vibration in the subcritical flow region in comparison with that of a concentrically shrouded cylinder. This trend was terminated within the transitional region where there was a converging of the concentric and eccentric vibrational responses. The drag of the cylinder enclosed in the axial-rod shroud was found to be less than the drag of the plain cylinder in the subcritical region but the opposite effect was obtained in the transitional region. The drag was measured on the eccentrically shrouded cylinder for various upstream, lateral and downstream eccentricities and the results were compared with those for the concentrically shrouded cylinder.

Thermal Conduction in Liquid Helium II. II. Effects of Channel Geometry

The critical heat-current density W/sub c/ in liquid helium II has been measured as a function of temperature in channels of various geometries. For channels of both circular and rectangular cross section W/sub c/ varies almost inversely with channel diameter, but for the same hydraulic diameter W/sub c/ is almost 25% smaller in rectangular channels. In channels with more irregular cross sections, W/sub c/ is much smaller than in cylindrical channels of the same hydraulic diameter. The hydraulic diameter is thus not a useful parameter for comparing data obtained in channels of different shape. The temperature dependence of W/sub c/ is in all cases similar to that reported in I for a cylindrical channel, and suggests that W/sub c/ may be associated with ordinary turbulence below about 1.7 deg K but at higher temperatures is caused by some other mechanism. The effects of varying the channel length and shape of orifice were also studied. Shortening one of the channels to 60% of its original length had no observable effect on W/sub c/. W/sub c/ was also unaffected by moderate changes in orifice shape, but a severe constriction apparently disrupted the subcritical flow region so completely that W/sub c/ could notmore » be measured at all. Various theories of the origin of the critical velocity are discussed in the light of these measurements. (auth)« less