Critical flow condition in open channel hydraulics

Summary Transition between sub- and supercritical flows in open channel occurs at the so-called critical point, for which critical flow conditions appear. This particular flow state has been originally introduced for flows with parallel streamlines. However, as streamlines are considerably sloped and inclined in the vicinity of the critical point, these effects have to be accounted for. The present investigation explores in detail these effects. In particular, present investigations include i) first order analysis expressing discharge in terms of upstream head and channel geometry (calibration of discharge measurement structures) and ii) determination of surface profiles for transitional flow states by accounting for the effective pressure and velocity distributions. Analysis is based on a first order model with restriction to typical channel bottom and sidewall geometry. Results are compared with observations, and a fair agreement between the two is noted.With 13 Figures     

Granular chute flow regimes:mass flowrates,flowrate limits and clogging

It has previously been shown that the transition from supercritical to subcritical behavior in granular chute flows often results in the formation of stagnant zones which limit the mass flow and eventually clog the chute. This paper reports an analysis of previously unpublished data for the flow of cohesionless granular material in inclined open channels. Three regimes of mass flow behavior, supercritical and two regimes of subcritical flow, were observed and are characterized by their dependence on chute inclination and geometry. (This paper represents the first report of the third flow regime.) Analysis of the experimental findings lead into empirical/mathematical expressions for the mass flow in the first two regimes as well as a prediction of the regime transition points for all three regimes. This last gives insight into the effect of chute geometry on regime transition and the subsequent clogging of chutes.     

Pressure drop measurement on forced flow cable conductors

Forced flow cable conductors being developed for use in LCP coils and other large superconducting magnets utilize supercritical helium flowing through narrow, uneven channels with large cooling surfaces. Extensive measurements on pressure drop of a variety of samples were performed. It is found that the friction factor versus Reynolds number plots of all the data are clustered together and behave in a universal way. A factor of two to three higher in friction factor than the smooth tube value in turbulent helium flow regime can be expected for this type of conductor.     

Review of flow condensation of CO2 as a refrigerant

Carbon dioxide (CO₂) has emerged as an excellent substitute natural refrigerant for low temperature refrigeration applications, but a better understanding of its in-tube flow condensation is needed in order to achieve its full potential. From experimental studies in the open literature we review the effects of mass flux, vapour quality and saturation pressure on CO₂ flow condensation heat transfer, frictional pressure drop and flow regime transition inside smooth, micro-fin and microchannel tubes. Successful condensation models which were developed from experiments with other refrigerants are evaluated against the CO₂ flow condensation experimental data. Comparison between the predicted and experimental data shows that the unique thermophysical properties of CO₂ at high reduced pressure conditions lead to these correlations having high prediction errors on the flow condensation heat transfer inside smooth tubes and microchannels, but have less significant effects on the flow condensation heat transfer and two-phase frictional pressure drop under high mass flux conditions inside micro-fin tubes. Recommendations for condensation and pressure drop models to apply to CO₂ flow condensation in different tubes are made. As there is inconsistency between the experimental data in smooth tubes from different sources, and the effects of microchannel and micro-fin tube geometries, on the flow regime transition and condensation heat transfer of CO₂, are unclear, a more extensive range of the experimental data in different tubes is needed for a fully understanding of in-tube CO₂ flow condensation.     

Incipient motion of gravel and coal beds

An experimental study on incipient motion of gravel and coal beds under unidirectional steady-uniform flow is presented. Experiments were carried out in a flume with various sizes of gravel and coal samples. The critical bed shear stresses for the experimental runs determined using side-wall correction show considerable disagreement with the standard curves. The characteristic parameters affecting the incipient motion of particles in rough-turbulent regime, identified based on physical reasoning and dimensional analysis, are the Shields parameter, particle Froude number, non-dimensional particle diameter and non-dimensional flow depth. Equations of critical bed shear stress for the initial movement of gravel and coal beds were obtained using experimental data. The method of application of critical bed shear stress equations is also mentioned.     

Experimental study of atmospheric pressure surface discharge in helium

The surface discharge generated at atmospheric pressure in helium was examined by monitoring the current and voltage at the discharge electrode. The discharge generated in helium behaves differently when compared to that generated in other gases (e.g. air). The single discharge duration and the time between consecutive discharges are longer because there is a different mechanism of discharge evolution. The metastable helium atoms play the most important role for discharge generation. Streamer-like and glow types of discharge were observed. The decay of helium metastables concentration determines the discharge regime. Hence, operation conditions have strong influence on the discharge regime. The introduction of gas flow removes metastable quenchers (gaseous products from dielectric and electrode surfaces) and transition to glow discharge is observed. Also covering the discharge electrode with thin dielectric foil to suppress Auger de-excitation of metastables at metal surface leads to generation of atmospheric pressure glow surface discharge. Properties of this discharge are comparable with properties of glow discharge at low pressure (e.g. the electron concentration).     

Experimental study of atmospheric pressure surface discharge in helium

The surface discharge generated at atmospheric pressure in helium was examined by monitoring the current and voltage atthe discharge electrode. The discharge generated in helium behaves differently when compared to that generated in other gases (e.g. air). The single discharge duration and the time between consecutive discharges are longer because there is a different mechanism of discharge evolution. The metastable helium atoms play the most important role for discharge generation. Streamer-like and glow types of discharge were observed. The decay of helium metastables concentration determines the discharge regime. Hence, operation conditions have strong influence on the discharge regime. The introduction of gas flow removes metastable quenchers /gaseous products from dielectric and electrode surfaces) and transition to glow discharge is observed. Also covering the discharge electrode with thin dielectric foil to suppress Auger de-excitation of metastables at metal surface leads to generation of atmospheric pressure glow surface discharge. Properties of this discharge are comparable with properties of glow discharge at low pressure (e.g. the electron concentration).     

Modified neural network correlation of refrigerant mass flow rates through adiabatic capillary and short tubes: Extension to CO2 transcritical flow

This paper presents a modified dimensionless neural network correlation of refrigerant mass flow rates through adiabatic capillary tubes and short tube orifices. In particular, CO₂ transcritical flow is taken into account. The definition of neural network input and output dimensionless parameters is grounded on the homogeneous equilibrium model and extended to supercritical inlet conditions. 2000 sets of experimental mass flow-rate data of R12, R22, R134a, R404A, R407C, R410A, R600a and CO₂ (R744) in the open literature covering capillary and short tube geometries, subcritical and supercritical inlet conditions are collected for neural network training and testing. The comparison between the trained neural network and experimental data reports 0.65% average and 8.2% standard deviations; 85% data fall into ±10% error band. Particularly for CO₂, the average and standard deviations are −2.5% and 6.0%, respectively. 90% data fall into ±10% error band.     

Changes in the NPL orifice conductance on a transition from molecular gas flow to transitional flow

The conductance of an NPL orifice in the molecular regime is constant and can be exactly calculated from the geometric dimensions. For smaller Knudsen numbers the conductance increases and correction functions are employed to reduce the uncertainty in this range of pressures. The conductance is also constant in the viscous regime during flow into a vacuum and can also be calculated. A suitable function has been chosen with one free parameter, which is constant for both very low and sufficiently high pressures and the parameter was determined on the basis of the experimentally measured course of the conductance at the borderline between molecular and transitional flow. The function fits the experimental data very well and can be used to calculate the conductance of the orifice up to Knudsen number ≈1.     

Theoretical and experimental investigation of rarefied gas flow in molecular pumps

The article presents a theoretical model for calculating the gas flow through channels with moving walls in the molecular flow regime. The analytical equations are solved by iteration techniques. The calculated data for the pumping speed and the compression ration of a molecular pump are compared with the experimental results. The agreement between calculated and measured values is good.     

Inviscid transonic flow field analysis

This paper describes a method for analysing inviscid transonic flow. This method is based on the fact that the angle made by the streamline of the transonic flow and of the corresponding incompressible flow is usually small. By using curvilinear coordinates, the differential equation of the stream function of an inviscid compressible flow is simplified and a general solution of the equation obtained. As examples of the method, transonic solutions are given for flow through twodimensional and axisymmetric Laval nozzles of different throat wall radii together with sonic lines and iso-Mach lines. To determine the discharge coefficients of Laval nozzles, an integral relation is developed. The general behaviour of the transonic flow in the throat region is presented, and the effect of the mass discharge on the Mach number distribution in the nozzle analysed. The effects of the ratio of the specific heats on the characteristics of the flow in the throat region are discussed. For transonic flow around a circular cylinder and a sphere, sonic lines and iso-Mach lines are presented for free-stream Mach number varying from the subcritical to the supercritical, including a free-stream Mach number of one. Part of the results obtained are compared with those available in current literature. For the two-dimensional hyperbolic Laval nozzles, the iso-Mach lines are compared with those given by Cherry (1959) and Serra (1972). For, axisymmetric Laval nozzles, the discharge coefficient and the Mach number at the throatsection for various throat wall radii are compared with those given by Sauer (1944), Hall (1962), Kliegel & Levine (1969), and Klopfer & Holt (1975). The theoretical discharge coefficients are compared with the experimental results by Backet al (1975), Durham (1955), Norton & Shelton (1969) etc. For the transonic flow around a circular cylinder, the iso-Mach lines are compared with Cherry’s exact solution for the quasi-circular cylinder for.M∞ equal to 0.51. The. Mach number distributions on the surface of the circular cylinder are compared with those given by Imai (1941) forM∞ equal to 0.4, by Cherry (1947) forM∞ equal to 0.51, by Dorodnicyn (1956) forM∞ equal to 1, and by Hafez, South & Murman (1979) forM∞ equal to 0.51. The present method has a much wider scope of application, requires simpler computation and gives results with good accuracy. It is being used to analyse supercritical wings and cascades, and we expect to extend its application to the field of transonic unsteady flow.     

Flow structure and heat transfer during the separation of a pulsating flow

The results of experimental studies of heat transfer in the separation region and the kinematic structure of the air flow in a channel behind a rib under superimposed discharge pulsations are presented. The effect of heat transfer enhancement of up to1.5 times in comparison with the stationary regime has been established. In the near wake behind the obstacle, it was up to five times. An observable decrease in the reat-tachment length (of up to two times) has been revealed under the pulsating flow regimes. The mechanism of these phenomena has been established, and typical features of the structure of pulsating separated flows have been described on the basis of the results of visualization experiments. The classification of these flows is proposed, and a regime map has been drawn up.     

A hybrid numerical model for predicting segregation during core flow discharge

A continuum numerical model is presented that parameterizes the interactions between particles at the microscopic level and predicts the development of moving stagnant zone boundaries during core flow discharge of granular material. The model is then employed for the prediction of segregation of multi-component granular mixtures during discharge from core flow hoppers and its capability to accurately simulate the behavior of the granular mixture is demonstrated through comparisons with experimental data.     

Two-phase flow in a horizontal rectangular microchannel

Two-phase flow in a rectangular short horizontal channel 200 μm high was studied experimentally. The use of the fluorescent method made it possible to reveal flow of liquid in the channel and to determine its characteristics quantitatively. The existence of the regime of separate (stratified) flow is established. Based on analysis of previous investigations and newly obtained data, it is shown that a change in the height of the horizontal channel has a substantial effect on the boundaries between the regimes. The region of the churn regime increases with decreasing thickness of the channel.     

Fuel ignition and flame front stabilization in supersonic flow using electric discharge

Recent achievements in the field of stabilization of the front of high speed combustion using electric discharge are presented. Near-surface discharge at the plane wall between electrodes installed in the plane of the wall is applied in this study. Hydrogen and ethylene directly injected from the wall to the flow with a Mach number M = 2 and an air total temperature T ₀ = 300–760 K are used as fuel. The excess fuel coefficient calculated by the total air flow rate in the channel does not exceed ER = 0.1. The value of electric power input into the discharge is W _pl/H _tot < 2% of the total flow enthalpy, while the thermal power due to combustion exceeds W _com/H _tot > 100% at a low initial gas temperature. Electric discharge is first applied to stabilize combustion under conditions of a fixed separated zone and on the plane wall of the combustion chamber. A two-stage combustion regime is demonstrated. It is shown that the application of electric discharge makes it possible to achieve complete fuel combustion η > 0.9 in a wide range of experimental parameters.     

Prediction of flow stress in dynamic strain aging regime of austenitic stainless steel 316 using artificial neural network

Flow stress during hot deformation depends mainly on the strain, strain rate and temperature, and shows a complex nonlinear relationship with them. A number of semi empirical models were reported by others to predict the flow stress during deformation. In this work, an artificial neural network is used for the estimation of flow stress of austenitic stainless steel 316 particularly in dynamic strain aging regime that occurs at certain strain rates and certain temperatures and varies flow stress behavior of metal being deformed. Based on the input variables strain, strain rate and temperature, this work attempts to develop a back propagation neural network model to predict the flow stress as output. In the first stage, the appearance and terminal of dynamic strain aging are determined with the aid of tensile testing at various temperatures and strain rates and subsequently for the serrated flow domain an artificial neural network is constructed. The whole experimental data is randomly divided in two parts: 90% data as training data and 10% data as testing data. The artificial neural network is successfully trained based on the training data and employed to predict the flow stress values for the testing data, which were compared with the experimental values. It was found that the maximum percentage error between predicted and experimental data is less than 8.67% and the correlation coefficient between them is 0.9955, which shows that predicted flow stress by artificial neural network is in good agreement with experimental results. The comparison between the two sets of results indicates the reliability of the predictions.     

A generalized dimensionless local power-law correlation for refrigerant flow through adiabatic capillary tubes and short tube orifices

This paper presents a new method to obtain generalized dimensionless correlation of refrigerant mass flow rates through adiabatic capillary tubes and short tube orifices. The dimensionless Pi groups were derived from the homogeneous equilibrium model, which is available for different refrigerants entering adiabatic capillary tubes or short tube orifices as the subcooled liquid, two-phase mixture, or supercritical fluid. To mitigate the potential over-fitting risk in neural network, a new “local” power-law correlation reformed from the homogeneous equilibrium model was proposed and compared with the conventional “global” power-law correlation and recently developed neural network model. About 2000 sets of experimental mass flow rate data of R12, R22, R134a, R404A, R407C, R410A, R600a and CO₂ (R744) in the open literature covering capillary and short tube geometries, subcritical and supercritical inlet conditions were collected for the model development. The comparison between the recommended six-coefficient correlation and experimental data reports 0.80% average and 8.98% standard deviations, which is comparable with the previously developed neural network and much better than the “global” power-law correlation.     

Plasma aerodynamics in a supersonic gas flow

We perform an experimental study and numerical simulation of the process of periodic initiation of spark extended discharge in air flow with a Mach number M = 2. Critical parameters of the discharge are measured in a high velocity air flow, and visualization of the gas flow in the presence of the discharge is performed. The influence of the discharge on the flow near the body surface streamlined by the supersonic flow is studied.     

Analysis of a convective fluid flow with a concurrent gas flow with allowance for evaporation

The paper presents a theoretical analysis of a convective fluid flow with a concurrent gas flow accompanied by evaporation at the interface. The analysis of two-layer flows is based on a mathematical model taking into account evaporation at a thermocapillary boundary and effects of thermal diffusion and diffusion heat conduction in the gas–vapor layer. New exact solutions describing steady two-layer flows in a channel with the interface remaining undeformed and examples of velocity and temperature profiles for the HFE-7100 (liquid)–nitrogen (gas) system are presented. The influence of longitudinal temperature gradients along the channel boundaries, the gas flow rate, and the height of the fluid layer on the flow regime and evaporation rate is studied. A comparison of the calculated data with experimental results is performed.     

Two-phase flow regimes in round, square and rectangular tubes during condensation of refrigerant R134a

An experimental investigation of two-phase flow mechanisms during condensation of refrigerant R134a in six small diameter round (4.91 mm), square (D_h=4 mm, α=1), and rectangular (4×6 and 6×4 mm: D_h=4.8 mm, α=0.67 and 1.5; 2×4 and 4×2 mm: D_h=2.67 mm, α =0.5 and 2) was conducted. Unique experimental techniques and test sections were developed to enable the documentation of the flow mechanisms during phase change. For each tube under consideration, flow mechanisms were recorded over the entire range of qualities for five different refrigerant mass fluxes between 150 and 750 kg m⁻² s⁻¹. The flow mechanisms were categorized into four different flow regimes: intermittent flow, wavy flow, annular flow, and dispersed flow. In addition, the large amount of data enabled the delineation of several different flow patterns within each flow regime, which provides a clearer understanding of the different modes of two-phase flow. Transition lines between the respective flow patterns and regimes on these maps were established based on the experimental data. It was found that for similar hydraulic diameters, flow regime transitions are not very strongly dependent on tube shape or aspect ratio. These maps and the transition lines can be used to predict the particular flow pattern or regime that will be established for a given mass flux, quality and tube geometry.