Flow Choking Research Articles

Study of mechanical choked Venturi nozzles used for liquid flow controlling

Motivated by the principles of the cavitating Venturi nozzle (CVN) used for controlling fluid flow and addressing limitations of CVN, this paper proposes a mechanical choked Venturi nozzle (MCVN) which achieves choking flow via a mechanical action. The MCVN is constructed by inserting a floating springed blockage into a Venturi nozzle to imitate the bubble dynamics of CVN. First, an initial MCVN design was derived theoretically. Then, using numerical simulation and an iterative procedure, this original design was corrected to build an optimized design. Finally, the optimized design was investigated and tested both numerically and experimentally. The experimental results show that the MCVN can maintain constant flow with a flow control error of 3.8% and a maximum back pressure ratio of 0.97. Since MCVN can achieve constant flow without fluid vaporization, the pressure ratio range for applying a choking flow device is expanded and some limitations of CVN are overcome. The principles and experimental results obtained in this research can be used as a framework for the design of improved constant flow control devices for liquid flow.

Hydraulic Jump and Resultant Flow Choking in a Circular Sewer Pipe of Steep Slope

Urban flood caused by storm-water runoff has been problematic for many regions. There is a need to improve the design and hydraulic performance of storm sewer-pipes, which will help reduce the impact of urban flood. Such a need has motivated the current study. This paper investigates the flow behaviour in a circular pipe of steep slope, in which supercritical flow descends the steep terrain and forms a hydraulic jump under control acting downstream. So far, the jump behaviour and resultant flow choking in a circular pipe are poorly understood. This paper formulates the problem of the hydraulic jump in a circular pipe of slope on the basis of the momentum principle and solves it by using iterative methods. The solutions include the filling ratio and flow field downstream of an undular jump and a direct jump. For the first time, the Froude number’s dependence on the pipe slope has been quantified. For a given slope, it is possible to have two different filling ratios (or equivalently discharges) that associate with the same Froude number value. This paper reports detailed results of the initial versus sequent depth of the hydraulic jumps and quantitatively delineates the slope-filling ratio space between flow-choking and choking-free zones. For the design of storm sewers in a hilly area, it is necessary to correct the current design guidelines, which rely mostly on the uniform flow theory and suggest filling ratios as high as 85%. The corrections are either decreasing the filling ratio or increasing the pipe diameter to achieve choking-free flow in a circular pipe.

A methodology for the preliminary design and performance prediction of high-pressure ratio radial-inflow turbines

Modern power generation technologies, such as organic Rankine cycle power systems, require turboexpanders operating with high-efficiency and high power density. These features often lead to high-pressure ratios machines, characterised by the presence of choking and supersonic flow conditions. This paper proposes a comprehensive methodology for the preliminary design and performance prediction of radial-inflow turbines operating at high-pressure ratios. A steady-state, mean-line model of a radial-inflow turbine is developed including real-gas effects and a detailed modelling strategy for the treatment of choking flow conditions. In addition, a set of loss models tailored to high-pressure ratio radial-inflow turbines is developed. After a global sensitivity analysis, the model is calibrated by means of a multi-objective optimisation with a Genetic Algorithm and using the data of six high-pressure ratio turbines with total-to-total pressure ratios up to 5.8. The calibration method allows a significant reduction in the overall predicted deviation of the turbine isentropic efficiency and mass flow rate. The design model yields predicted deviations in isentropic efficiency within ± 3 %-points and the off-design model within 5%. The methodology and the results are intended to be used as a benchmark for the future development of radial-inflow turbines in high-pressure ratio applications.

Hydraulic characteristics of high temperature hydrocarbon liquid jets with various orifice geometries

An experimental study was conducted to investigate the effects of orifice geometry on the hydraulic characteristics of high-temperature aviation fuel jets. Pressurized heated liquid hydrocarbon fuel, simulating fuel used as coolant in the active cooling system of a hypersonic flight vehicle, was injected through a set of plain orifice nozzles of different lengths and diameters. The fuel was heated to close to 573 K (300 °C) using an induction heater at an upstream pressure of up to 1.0 MPa, and discharged to atmospheric downstream pressure conditions. The orifice diameter (D) varies from 0.7 to 1.5 mm and the length (L) from 1.4 to 4.3 mm, which results in length-to-diameter ratios (L/D) from 1.1 to 6.1, and the inlet of the orifice is nominally sharp-edged. Hydraulic characterization in terms of fuel injection temperature (Tinj) was carried out by introducing the discharge coefficient (Cd), and the macroscopic internal flow characteristics were correlated to Reynolds number (Re) and cavitation numbers (K and Ca). The fundamental behaviors of high-temperature liquid fuel jets at the specified operating ranges represented by Cd with respect to Tinj for a given set of injectors revealed that, as Tinj increases above the boiling point, the Cd of the injector with a longer orifice decreases faster than that of a shorter injector of the same orifice diameter, and for injectors of a given orifice length, Cd decreases with Tinj in a similar way irrespective of orifice diameter. Plots of Re vs. Tinj, Cd vs. Re, and Cd vs. K and Ca clearly show the dependence of the cavitation characteristics on the orifice geometry under high temperature injection conditions. In order to quantify the degree of cavitation for various orifice geometries, the Cd vs. Ca curve for each injector configuration has been fitted linearly; the mass flow choking effect in high temperature fuel injection represented by the magnitude of the slope from the linear fit becomes stronger as the orifice is longer in length and/or wider in diameter. This suggests that longer and wider orifices are more susceptible to choked cavitation. It was also found that the geometric effect is maintained for various ΔP, even though the magnitude of the slope increases with ΔP, and the sensitivity of the magnitude to increasing ΔP becomes stronger for longer orifices.

Budgets of Disturbances Energy for Nozzle Flows at Subsonic and Choked Regimes

The noise generated by the passage of acoustic and entropy perturbations through subsonic and choked nozzle flows is investigated numerically using an energetic approach. Low-order models are used to reproduce the experimental results of the hot acoustic test rig (HAT) of Deutsches Zentrum für Luft- und Raumfahrt (DLR), and energy budgets are performed to characterize the reflection, transmission, and dissipation of the fluctuations. Because acoustic and entropy perturbations are present in the flow in the general case, classical acoustic energy budgets cannot be used and the disturbances energy budgets proposed by Myers (1991, “Transport of Energy by Disturbances in Arbitrary Steady Flows,” J. Fluid Mech., 226, pp. 383–400.) are used instead. Numerical results are in very good agreement with the experiments in terms of acoustic transmission and reflection coefficients. The normal shock present in the diffuser for choked regimes is shown to attenuate the scattered acoustic fluctuations, either by pure dissipation effect or by converting a part of the acoustic energy into entropy fluctuations.

Experimental investigation on influence of inlet/outlet pressures on submerged jet flow in common rail injector

The fuel flow in the working chamber of the common rail fuel injector, which is a submerged jet flow, determines the needle movement and causes great effects on the fuel injection performance. This work presents an experimental investigation on the submerged jet flow characteristics of a cylindrical orifice under conditions of varied boundary pressures. A full-scale optical test rig is set up to examine the submerged flow of the cylindrical orifice based on a fuel pump test bench. The optical experimental results reveal that the inner cylindrical orifice flow induces cavitation and causes influences on the submerged jet flow. As the inner cavitation is at the cylindrical orifice outlet, the cylindrical orifice discharge coefficient declines but the mass flow rate becomes choking. The test results also show the boundary pressures (the inlet and outlet pressures) of the cylindrical orifice have great influences on the impingement force of the submerged jet flow. The development process of the impingement force is divided into two periods: the stable period and the fluctuation period. Moreover, the impingement force increases quadratically with the increase in the mass flow rate. Once the choking flow happens, it is useless to increase the jet impingement force by improving the inlet pressure.

CFD Based Prediction of Discharge Coefficient of Sonic Nozzle with Surface Roughness

Due to its simplicity and accuracy, sonic nozzle is widely used in gas flow measurement, gas flow meter calibration standard, and flow control. The nozzle obtains mass flow rate by measuring temperature and pressure in the inlet during choked flow condition and calculate the flow rate using the one-dimensional isentropic flow equation multiplied by a discharge coefficient, which takes into account multiple non-isentropic effects, which causes the reduction in mass flow. Proper determination of discharge coefficient is crucial to ensure the accuracy of mass flow measurement by the nozzle. Available analytical solution for the prediction of discharge coefficient assumes that the nozzle wall is hydraulically smooth which causes disagreement with experimental results. In this paper, the discharge coefficient of sonic nozzle is determined using computational fluid dynamics method by taking into account the roughness of the wall. It is found that the result shows better agreement with the experiment data compared to the analytical result.

In-pipe aerodynamic characteristics of a projectile in comparison with free flight for transonic Mach numbers

The transient shock dynamics and drag characteristics of a projectile flying through a pipe 3.55 times larger than its diameter at transonic speed are analyzed by means of time-of-flight and pipe wall pressure measurements as well as computational fluid dynamics (CFD). In addition, free-flight drag of the 4.5-mm-pellet-type projectile was also measured in a Mach number range between 0.5 and 1.5, providing a means for comparison against in-pipe data and CFD. The flow is categorized into five typical regimes the in-pipe projectile experiences. When projectile speed and hence compressibility effects are low, the presence of the pipe has little influence on the drag. Between Mach 0.5 and 0.8, there is a strong drag increase due to the presence of the pipe, however, up to a value of about two times the free-flight drag. This is exactly where the nose-to-base pressure ratio of the projectile becomes critical for locally sonic speed, allowing the drag to be estimated by equations describing choked flow through a converging–diverging nozzle. For even higher projectile Mach numbers, the drag coefficient decreases again, to a value slightly below the free-flight drag at Mach 1.5. This behavior is explained by a velocity-independent base pressure coefficient in the pipe, as opposed to base pressure decreasing with velocity in free flight. The drag calculated by CFD simulations agreed largely with the measurements within their experimental uncertainty, with some discrepancies remaining for free-flying projectiles at supersonic speed. Wall pressure measurements as well as measured speeds of both leading and trailing shocks caused by the projectile in the pipe also agreed well with CFD.

Design of a high-performance centrifugal compressor with new surge margin improvement technique for high speed turbomachinery

This paper presents the design of a centrifugal compressor for high-speed turbomachinery. The main focus of the research is to develop a centrifugal compressor with improved aerodynamic performance. As a meridional frame has a significant effect on overall performance of the compressor, special attention has been paid to the end wall contours. The shroud profile is design with bezier curve and hub profile with circular arc contour. The blade angle distribution has been arranged in a manner that it merges with single value at impeller exit. The rake angle is positive at leading edge and negative at trailing edge with identical magnitude. Furthermore, three-dimensional straight line element approach has been used for this design for better manufacturability. The verification of the aerodynamic performance has been carried out using CFD software with consideration of a single blade passage and vaneless diffuser. The result has been compared with matching size aftermarket compressor stage gas stand data. The compressor stage with Trim 55 provides 34% increase in choke flow at 210000 RPM as compared to gas stand data with 87% peak stage efficiency at 110000 RPM. In addition, new surge margin improvement technique has been proposed by means of diffuser enhancement. This technique provides an average of 16% improvement in surge margin compared to standard diffuser stage with 55 trim compressor impeller. The mechanical integrity has been validated at maximum RPM with the aluminum alloy 2014-T6 as a fabrication material.

Shock dispersal of dilute particle clouds

We present experiments and numerical simulations for an elementary paradigm of disperse multiphase flow: highly dilute, homogeneous, finite-dimension clouds of particles (curtains) hit by shock/blast waves in one dimension. In the experiments (particle volume fraction ${<}1\,\%$) the blasts that follow the shocks vary from low subsonic to supersonic, and we report data on curtain expansions and volume fraction distributions. The particle-resolving numerical simulations, run for the supersonic case, yield excellent agreement with all of these experimental data. We find that the essential feature for these good predictions is a flow choking phenomenon that entails a (particle) dispersive character of the flow down a volume fraction gradient (as at the downstream portions of the curtain). A most basic effective-field model is made to capture this gas dynamics by emulating the wake behind each particle, as seen in the particle-resolving direct Euler simulation (DES). On this basis, standard drag laws yield excellent agreement with the dispersive behaviour found in the experiment/DES, thus revealing a physics-based path to eventual well posedness of the mathematical model.

Theoretical and Experimental Investigation of Subcooled Flashing Flow through Simulated Steam Generator Tube Cracks

ABSTRACTFlow models and experiments were developed to predict the choking flow of subcooled flashing water through steam generator tube crack. Experiments were conducted for vessel pressures up to 7 MPa with various subcoolings through 7 sets of simulated crack geometries with channel length to diameter ratios from 1.3 to 2, and channel length of 1.3 mm. Mass flux data with respect to subcooling are presented for all seven sets of crack specimens. As the subcooling increased for each specimen the mass flux increased. In general as the mass flux increased the area of the specimens increased. Experimental data were compared with homogeneous equilibrium and non-equilibrium mechanistic models for two-phase choking flow. A comparison of the model results with experimental data shows that the homogeneous equilibrium-based models grossly underpredict choking flow rates in such geometries, while homogeneous non-equilibrium models greatly increase the accuracy of the predictions.

A closed-form analytical model for predicting 3D boundary layer displacement thickness for the validation of viscous flow solvers

A closed-form analytical model is developed for estimating the 3D boundary-layer-displacement thickness of an internal flow system at the Sanal flow choking condition for adiabatic flows obeying the physics of compressible viscous fluids. At this unique condition the boundary-layer blockage induced fluid-throat choking and the adiabatic wall-friction persuaded flow choking occur at a single sonic-fluid-throat location. The beauty and novelty of this model is that without missing the flow physics we could predict the exact boundary-layer blockage of both 2D and 3D cases at the sonic-fluid-throat from the known values of the inlet Mach number, the adiabatic index of the gas and the inlet port diameter of the internal flow system. We found that the 3D blockage factor is 47.33 % lower than the 2D blockage factor with air as the working fluid. We concluded that the exact prediction of the boundary-layer-displacement thickness at the sonic-fluid-throat provides a means to correctly pinpoint the causes of errors of the viscous flow solvers. The methodology presented herein with state-of-the-art will play pivotal roles in future physical and biological sciences for a credible verification, calibration and validation of various viscous flow solvers for high-fidelity 2D/3D numerical simulations of real-world flows. Furthermore, our closed-form analytical model will be useful for the solid and hybrid rocket designers for the grain-port-geometry optimization of new generation single-stage-to-orbit dual-thrust-motors with the highest promising propellant loading density within the given envelope without manifestation of the Sanal flow choking leading to possible shock waves causing catastrophic failures.

Flow characteristics of gaseous flow through a microtube discharged into the atmosphere

Flow characteristics for a wide range of Reynolds number up to turbulent gas flow regime, including flow choking were numerically investigated with a microtube discharged into the atmosphere. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The LB1 turbulence model was used in the turbulent flow case. Axis-symmetric compressible momentum and energy equations of an ideal gas are solved to obtain the flow characteristics. In order to calculate the underexpanded (choked) flow at the microtube outlet, the computational domain is extended to the downstream region of the hemisphere from the microtube outlet. The back pressure was given to the outside of the downstream region. The computations were performed for adiabatic microtubes whose diameter ranges from 10 to 500 μm and whose aspect ratio is 100 or 200. The stagnation pressure range is chosen in such a way that the flow becomes a fully underexpanded flow at the microtube outlet. The results in the wide range of Reynolds number and Mach number were obtained including the choked flow. With increasing the stagnation pressure, the flow at the microtube outlet is underexpanded and choked. Although the velocity is limited, the mass flow rate (Reynolds number) increases. In order to further validate the present numerical model, an experiment was also performed for nitrogen gas through a glass microtube with 397 μm in diameter and 120 mm in length. Three pressure tap holes were drilled on the glass microtube wall. The local pressures were measured to determine local values of Mach numbers and friction factors. Local friction factors were numerically and experimentally obtained and were compared with empirical correlations in the literature on Moody’s chart. The numerical results are also in excellent agreement with the experimental ones.

Numerical study of choked cavitation in high temperature hydrocarbon liquid jets

A numerical study was conducted on a practical plain orifice injector issuing pressurized high-temperature aviation fuel, in order to simulate injection of fuel after use as a coolant in the active cooling system of a hypersonic vehicle. A three-dimensional unstructured mesh inside the orifice was created using ICEMCFDTM S/W, and the CFD analysis was performed using FLUENTTM S/W. A multiphase mixture model was used to simulate cavitating two-phase flow, and the full cavitation model was activated to predict the mechanism and effects of cavitation induced by the high fuel vapor pressures at elevated temperature conditions. The simulation was performed for fuel heated up to 553 K (280 °C) at an upstream pressure (Pinj) of up to 1.0 MPa, and various ambient pressures (P∞). The results were compared with experimental data, and the simulation was found to predict the discharge coefficient (Cd) with respect to the fuel injection temperature (Tinj) quite well at the given conditions. The CFD analyses for high fuel temperature conditions revealed that the mainstream flow inside the injector separates from the orifice wall at the vena contracta due to the generated fuel vapor cavity, and the attached flow at the end of the cavity separates again to produce a very small recirculation zone. In addition, for a given pressure drop, the sharply decreasing trend of the mass flow rate (or Cd) with increasing Tinj varies depending on P∞, because the mass flow choking is determined by the relationship between P∞ and the vapor pressure (Psat) at Tinj. Finally, Cd with respect to cavitation number was found to follow an almost identical line, even at different P∞. This confirms that choked cavitation at high fuel temperature conditions depends on the downstream pressure of the orifice, and the effect of cavitation on Cd at high Tinj is well represented by the cavitation numbers, regardless of Pinj, P∞, and Tinj.

Thermodynamic Modelling of Supersonic Gas Ejector with Droplets

This study presents a thermodynamic model for determining the entrainment ratio and double choke limiting pressure of supersonic ejectors within the context of heat driven refrigeration cycles, with and without droplet injection, at the constant area section of the device. Input data include the inlet operating conditions and key geometry parameters (primary throat, mixing section and diffuser outlet diameter), whereas output information includes the ejector entrainment ratio, maximum double choke compression ratio, ejector efficiency, exergy efficiency and exergy destruction index. In single-phase operation, the ejector entrainment ratio and double choke limiting pressure are determined with a mean accuracy of 18 % and 2.5 % , respectively. In two-phase operation, the choked mass flow rate across convergent-divergent nozzles is estimated with a deviation of 10 % . An analysis on the effect of droplet injection confirms the hypothesis that droplet injection reduces by 8 % the pressure and Mach number jumps associated with shock waves occuring at the end of the constant area section. Nonetheless, other factors such as the mixing of the droplets with the main flow are introduced, resulting in an overall reduction by 11 % of the ejector efficiency and by 15 % of the exergy efficiency.

Toward gene expression programming for accurate prognostication of the critical oil flow rate through the choke: correlation development

AbstractIn this study, gene expression programming (GEP) was employed to develop a new equation for calculating choke flow rate as a function of fluid properties and wellhead choke characteristics. For this reason, a comprehensive databank was adopted from the petroleum industry, and then, the databank was split into three groups of training set for model construction (70% of database), test set for model evaluation (15% of database), and validation set for avoiding over‐fitting problem (15% of database). For assessing of GEP model, numerous statistical and graphical tools were applied, and then, it was compared with widely applied literature correlations. Consequently, the proposed tool in this study gives the best fit with the actual flow rate data with the average absolute relative deviation of 11.0872% and determination coefficient (R2) of 0.9695. Additionally, cumulative frequency plot demonstrates that the GEP model has the highest frequency over the database. The outcomes of the GEP model were also compared with the outputs of the artificial neural network (ANN) revealing the higher precision of the ANN than the proposed GEP model in this study. At the end, it is worthwhile that the suggested model can be used as reliable tool for choke performance modeling. © 2017 Curtin University and John Wiley & Sons, Ltd.

Non-conservative pressure-based compressible formulation for multiphase flows with heat and mass transfer

A pressure-based compressible multiphase flow solver has been developed based on non-conservative discretization of the mixture continuity equation. The formulation is an extension of the single phase incompressible pressure-correction approach, such that it can be applied to both two-phase flows using interface resolving methods and general n-phase ensemble-averaged mixture flows. The formulation is currently presented with the single pressure and single temperature assumption, but extension to multiple temperatures is straightforward. A robust treatment of phase change allows the method to model conditions with rapid phase change such as expansion through nozzles and valves. The method has been validated thoroughly using canonical single phase problems such as the shock tube, tank filling and sudden valve closure problems. Multiphase flow validation has been carried out for sound propagation in mixtures using the ensemble-averaged model and pressure wave transmission and reflection across an air-water interface, using the level set interface tracking method. The method has been used to study sound propagation in saturated steam-water systems under thermodynamic non-equilibrium, where the expected drastic reduction in the speed of sound is reproduced. Finally the method is applied to the problem of critical (choked) flow in a nozzle for a saturated steam-water system.

Comparative evaluation of phase-change mechanisms for the prediction of flashing flows

A numerical study is presented, evaluating in a comparative manner the capability of various mass-transfer rate models to predict the evolution of flashing flow in various geometrical configurations. The examined models comprise phase-change mechanisms based on the kinetic theory of gases (Hertz–Knudsen equation), thermodynamic-equilibrium conditions (HEM), bubble-dynamics considerations using the Zwart-Gerber-Belamri model (ZGB), as well as semi-empirical correlations calibrated specifically for flash boiling (HRM). Benchmark geometrical layouts, i.e a converging-diverging nozzle, an abruptly contracting (throttle) nozzle and a highly-pressurized pipe, for which experimental data are available in the literature have been employed for the validation of the numerical predictions. Consideration on additional aspects associated with phase-change processes, such as the distribution of activated nucleation sites, as well as the deviation from thermodynamic-equilibrium conditions have also been taken into account. The numerical results have demonstrated that the onset of flashing flow in all cases is associated with the occurrence of compressible flow phenomena, such as flow choking at the constriction location and expansion downstream, accompanied by the formation of shockwaves. Phase-change models based on the kinetic theory of gases produced more accurate predictions for all the cases investigated, while the validity of the HRM and ZGB models was found to be situational. Furthermore, it has been established that the inter-dependence between intrinsic physical factors associated with flash boiling, such as the nucleation-site density and the phase-change rate, has a significant, yet not clearly distinguishable influence on the two-phase flow characteristics.

Hierarchical Immersed Boundary Method with Smeared Geometry

This paper presents a low-order model applying the immersed boundary method on smeared geometry. It is thus able to represent the effect of turbomachinery within a complex system. Assessment of this model on the NASA rotor 67 has been made under clean flow conditions. Good agreement has been achieved between the immersed boundary method on smeared geometry model, experiments, and a high-fidelity computational fluids dynamics model. For high-speed conditions, about within 0.5, 1, and 1% agreements are achieved on the pressure ratio, efficiency, and choking flow, respectively, between immersed the boundary method on smeared geometry model and the experiment. The capability of the model capturing the fan’s behavior under inlet distortion has also been assessed under the flow with a level of 10% distortion of the total pressure, which covers a 120 deg sector. The nonuniform work input of the fan, which is one of the key features of the fan–distortion interaction, has been captured by the immersed boundary method on smeared geometry model. Finally, the model also helps to shed light on the physical understanding of fan–distortion interaction. It provides evidence suggesting that the tangential pressure gradient is one of the mechanisms causing the induced nonuniform work input of the fan subjected to the inlet distortion.

Characterization of high-pressure cavitating flow through a thick orifice plate in a pipe of constant cross section

To validate the applicability of basic cavitating flow theory for high-pressure flow systems, this paper presents a systematic study of high-pressure flow through a thick orifice plate in a constant cross-section pipe over a wide range of operating conditions. A combined theoretical, numerical and experimental approach was employed to explore the two-phase flow characteristics of both the non-choked and choked flows with a maximum upstream pressure of 5000 psi and a maximum Reynolds number of 2 × 106. For the flow configuration used in this work, a critical downstream-to-upstream pressure ratio of 0.45 was identified below which cavitation and flow choking will occur. Furthermore, it was found from the numerical models that the conventional one-dimensional analysis is inadequate in predicting the discharge coefficient and the condition for the onset of cavitation. Subsequently, new theoretical corrections suitable for high-pressure conditions were proposed, based on the numerical simulation results, and validated by the experimental measurements.