Discharge Coefficient Of Nozzle Research Articles

Analysis of influencing factors and uncertainty assessment of high-pressure natural gas primary standard facility

The mass-time high-pressure natural gas flow standard device is the highest level natural gas flow measurement standard in China. It is mainly used to reproduce the mass flow of high-pressure natural gas and transfer the value. Due to its important position in the value traceability transmission systems, it is of great significance to improve its uncertainty. This article first introduces the working principle and component equipment of mass-time high-pressure natural gas flow standard device, and the influencing factors and control measures of the recurring mass flow uncertainty are given. Then the calculation model and uncertainty evaluation model of the mass flow rate of the standard device and the discharge coefficient of the critical flow nozzle are given. Finally, based on the calculation model, two critical flow nozzles are calibrated and tested, and their repeatability and stability indicators are discussed and analyzed. After analysis, it can be concluded that the measurement performance of the mass-time high-pressure natural gas flow standard device is stable, which can make the uncertainty of the reproduced mass flow rate less than 0.05 % (k = 2), and the uncertainty of the calibrated discharge coefficient of critical flow nozzle is less than 0.1 %(k = 2).

Impact of Installation on the Performance of an Aero-Engine Exhaust at Wind-Milling Flow Conditions

Abstract This paper presents a numerical investigation of the effect of wing integration on the aerodynamic behavior of a typical large civil aero-engine exhaust system at wind-milling flow conditions. The work is based on the dual stream jet propulsion (DSJP) test rig, as will be tested within the transonic wind tunnel (TWT) located at the aircraft research association (ARA) in the UK. The DSJP rig was designed to measure the impact of the installed pressure field due to the effect of the wing on the aerodynamic performance of separate-jet exhausts. The rig is equipped with the dual separate flow reference nozzle (DSFRN), installed under a swept wing. Computational fluid dynamic simulations were carried out for representative ranges of fan and core nozzle pressure ratios (CNPR) for “engine-out” wind-milling scenarios at end of runway (EOR) takeoff, diversion, and cruise conditions. Analyses were done for both isolated and installed configurations to quantify the impact of the installed pressure field on the fan and core nozzle discharge coefficients. The impact of fan and core nozzle pressure ratios, as well as freestream Mach number and high-lift surfaces on the installed suppression effect, was also evaluated. It is shown that the installed pressure field can reduce the fan nozzle discharge coefficient by up to 16%, relative to the isolated configuration for EOR wind-milling conditions. The results were used to inform the design and setup of the experimental activity which is planned for 2023.

Analytical methodology for calculating discharge coefficients of critical flow nozzles for high-pressure hydrogen

Hydrogen is gaining attention as a clean energy source for the sustainable development of the global economy and mitigation of global warming. Flow rate measurements are vital for ensuring the accuracy of hydrogen transaction volumes. As a widely accepted standard for gas flow rate, critical flow nozzles are expected to fulfill this role. However, the discharge coefficient associated with the calibration tests of critical flow nozzles for high-pressure hydrogen does not align with the semi-empirical formula of ISO 9300 (ISO curve). This discrepancy has not yet been resolved. In this study, we conducted 3D numerical simulations of the nozzle discharge coefficients for high-pressure hydrogen. Based on our simulations and experimental results from the previous study, we investigate the cause of the deviation of the discharge coefficient from the ISO curve at high pressure. We also propose a method for calculating the discharge coefficient based on real-gas effects and demonstrate that the discharge coefficient aligns with the ISO curve at high pressures.

PEMODELAN SIKLUS IN-CYLINDER MESIN DIESEL

An engine performance can be predicted through modeling and simulation programs. This paper describes the cycle modeling and breathing process of a four-stroke diesel engine. Calibration of the model parameters to eliminate prediction error. This calibration requires the definition of empirical correlation of two parameters namely mechanical delay and the injector nozzle discharge coefficient. Modeling validation is also given by presenting the result data and evaluating the output parameters of the engine. The result of the diesel engine in-cylinder model produces good predictions by applying a mechanical delay correlation for correction of injection time and correlation coefficient of discharge nozze injector. The parameters for correction of injection duration where the mean temperature and pressure conditions for the duration of the injection are used as input model ignition delay cylinder.

Numerical Analysis of Fluid Stream Division to Supply Multiple Hydraulic Receivers

This article presents a proposal and a numerical analysis of a hydraulic system consisting of one constant capacity pump supplying multiple receivers in the form of hydraulic motors, based on the example of a rail grinder. The proposed approach requires splitting the stream of the working fluid, which was achieved using 2-way flow control valves. As part of the preliminary CFD studies, the pressure and velocity distributions of the flow control valve were obtained, and the discharge coefficient of the valve nozzles was determined as a function of the valve spool position. Then, a mathematical model of the system was formulated, which was used to build a simulation model in the Matlab/Simulink environment. Next, the ability of the system to achieve the assumed operating parameters and its energy efficiency in a given load range were tested. The results indicate that the system can effectively perform the required work cycles with sufficient accuracy.

An experimental study on the in-nozzle cavitating flow and near-field breakup of spirally grooved hole nozzles

To improve liquid atomization for pressure atomizer, a spirally grooved hole (SGH) nozzle was designed, which produces swirling flow inside the nozzle hole and thereby promotes the disturbance in liquid jets, enhancing breakup of liquid jets. In this paper, the optical visualization of the cavitating flow inside nozzles and primary breakup behaviors in the near-nozzle field for three scaled-up transparent nozzles, including two SGH nozzles with different spiral angles, and a non-spiral hole (NSH) nozzle, were performed to clarify the effects of the spirally grooved structures on in-nozzle cavitating flow and near-field fuel breakup. The results show that with an identical K-factor, the cavitation was largely restrained in the SGH nozzles, and the discharge coefficients of the SGH nozzles with spiral angles of 63° and 43° were approximately 13% and 25% lower than that of the NSH nozzle, respectively. Moreover, a liquid column was observed for each of the jets, surrounded with scattering droplets. And the SGH nozzle yields 9–10 times higher number density, 9%–10% smaller Sauter mean diameter of the droplets, and 4–7 times wider spreading angle than those of the NSH nozzle. These facts verified that the use of spirally grooved hole enhanced primary breakup of liquid jets.

Study on cooling performance of rapid cooling system based on vacuum spray flash evaporation

• Vacuum spray flash cooling (VSFC) system was used for the first time with rapid cooling. • VSFC could cool almost six times fast than the freezer. • The cooling process of beverages could be divided into two stages. • The relevant operational parameters that could optimize VSFC cooling performance were studied. • The optimal discharge coefficient of nozzle was found in VSFC. The present study proposes a rapid cooling method based on vacuum spray flash evaporation, and establishes an experimental system to study the cooling performance of this method by taking beverages as an example. The feasibility and superiority of vacuum spray flash cooling (VSFC) are demonstrated by making the comparisons with the existing rapid cooling methods. A cooling performance evaluation is presented concentrating on the influence of the discharge coefficients of nozzle, multi-nozzle array, and vacuum degree of flash chamber. Meanwhile, the relevant operational parameters of VSFC are optimized. Experiments have shown that the VSFC cools almost six times faster than a freezer. Combined with the simulation, it is found that the cooling process of beverages could be divided into the initiating enhancement stage and the gradual decline stage, in accordance with the characteristics of the internal flow of the beverage during rapid cooling. Parametric analysis indicates that there is an optimal discharge coefficient of nozzles in order to achieve maximum cooling rate for VSFC.

Research on innovative one-dimensional mathematical model applied to the on-line measurement for transient discharge coefficient of diesel injector nozzle

This paper presents an innovative one-dimensional mathematical model applied to the on-line measurement for transient discharge coefficient of diesel injector nozzle. The state change in the fuel system is abstracted into the transfer and evolution process of the Riemann wave, and a direct mathematical relationship between the pressure and the transient discharge coefficient in a single Riemann wave environment is established. The on-line calibration method of fuel sound velocity is proposed, which avoids the complicated off-line calibration of fuel physical property. The time-domain characteristics recognition method of input signal is put forward and the model is segmented according to time characteristics to improve the applicability. The decoupling algorithm of reflected wave and the correction method of interference wave are proposed to improve the model robustness. The experimental results show that this mathematical model has good accuracy. It is found that the variation of the average discharge coefficient with injection pressure and pulse width is nonlinear due to the cavitation and needle valve average opening.

Structure improvement on turbine guided vane cooling system based on conjugate heat transfer

To improve the cooling performance of the turbine guided vane, conjugate heat transfer is utilized to investigate the internal and external cooling systems in real working conditions. The purpose is to increase the overall cooling effectiveness with limited influence on coolant consumption and cascade pressure loss factors. Firstly, the internal cooling is improved to enhance heat transfer by installing impingement cooling, ribs, dimples, and protrusions. Then, by adopting film holes near the shroud and hub, the coolant coverage of the external cooling is improved. To explain the influence of structure modification, the flow field is analyzed while the blockage effect of various structures on the crossflow is compared. The flow mechanism of conical dimples and protrusions is concluded. Results show that the improvement in internal cooling enhances heat transfer and decreases coolant consumption. However, the external film cooling deteriorates. By installing dimples and protrusions, the effusion condition of jet nozzles deteriorates. Dimples have higher heat transfer performance than protrusions. By improving external cooling, increases in film cooling effectiveness, discharge coefficients of jet nozzles, and heat transfer can be found. However, the coolant consumption increases. At Reynolds number of 15003–19599, the best-performing structure, by combining impingement/effusion cooling with ribs and protrusions, increases overall cooling effectiveness by 0.54–8.01% and 9.81–11.62% on the pressure surface and suction surface respectively. However, changes in coolant consumption (0.63–2.45%) and cascade pressure loss factors (−7.51–4.81%) are limited. The improvement thoughts and influence factors on the cooling performance are concluded, serving as guidance for the vane design.

Impact of installation on a civil large turbofan exhaust system at idle descent conditions

Recent trends in civil aero-engine design aim at lowering specific thrust and improving propulsive efficiency by increasing the bypass ratio and therefore, usually also the fan diameter. The integration of these larger diameter engines with the airframe is critical to exhaust performance, and it is important to include these effects in engine performance analysis. The discharge coefficient of the bypass and core nozzles of a high-bypass ratio aero-engine at idle descent conditions is investigated numerically for an aero-engine in isolation and installed on an airframe. The discharge coefficients influence the engine operating conditions and turbomachinery re-matching at these off-design conditions. The maximum difference in the bypass nozzle discharge coefficient between the installed and isolated aero-engine across the descent phase is ≃1.6%. The differences in the core nozzle discharge coefficient between the installed and the reference isolated configuration are ≃43% and ≃−5.4% at the start and the end of the descent phase, respectively. The nozzle discharge coefficients depend on flight Mach number, incidence angle, and the nozzle pressure ratios of the fan and core nozzles. Multiple competing flow mechanisms govern the static pressure on the core nozzle base, which influences the core nozzle discharge coefficient. A novel reduced-order model is developed to estimate the core nozzle discharge coefficient for the installed configuration in idle descent conditions. This approach is based on the effective nozzle pressure ratio and can be implemented in engine performance simulations.

Behaviors of discharge coefficients of small diameter critical nozzles

The discharge coefficients of 59 small diameter toroidal throat Venturi critical nozzles were measured by the static gravimetric method. The throat diameter is from 0.014 mm to 2.35 mm and the Reynolds number is 4 × 102 to 2 × 105. These nozzles were manufactured by the normally processing method base on the same design drawing, but their discharge coefficients were scattered widely. The purpose of this paper is to explain the behavior of discharge coefficient scattered. In the correction procedure used here, while comparing the discharge coefficient obtained experimentally and the reference theoretical model, the throat diameter is corrected and the optimal radius of curvature of nozzle inlet is determined so that both discharge coefficients match. Resultantly, most of the behaviors of the discharge coefficient of 59 critical nozzles could be explained well.

Effect of Low ALR on the Spray Characteristics of a Pressure-swirl Duplex Nozzle

The objective of this study is to investigate the effect of the air-to-liquid ratio (ALR) in a low range on the characteristics of the spray issuing from a pressure-swirl duplex nozzle. In this study, the pressure-swirl duplex nozzle was used as an atomizer with non-swirl shroud air. The shroud air was radially discharged inward across the nozzle face to avoid the contamination of the nozzle tip. Jet A-1 fuel was used as the working fluid. The analysis of the spray characteristics was carried out by using a phase Doppler anemometry (PDA) system and a laser based planer imaging system. The flow rate, discharge coefficient, spray structure, spray cone angle, velocity and drop size distributions were analyzed. The results show that the discharge coefficient of the pilot nozzle is higher than that of the main nozzle and the combined pilot and main nozzles. The spray angle tends to decrease almost linearly with increasing ALR. The shape of the spray gradually changes from a hollow cone to a full cone with increasing ALR, as revealed in the axial velocity distributions with an increase in the axial distance. The weighted mean SMD (WMSMD) increases by 1.2 as the ALR increases, but thereafter, it decreases again.

Numerical investigation of heat transfer and flow characteristics of a double-wall cooling structure: Reverse circular jet impingement

• The reverse jet impingement is shown to be more resistant to the crossflow effect. • The extended nozzles minimize the crossflow effect. • Increasing the internal heat transfer surface area improves the total heat transfer rate. • To maximise Nu, optimum nozzle-to-target spacing is around 3 jet diameter. Double-wall cooling structures are commonly used to enhance the heat transfer in combustor liner and aerofoil internal cooling within gas turbine engines and other industrial applications. This is the first study to adopt a novel reverse jet impingement technique into a double-wall cooling structure in order to achieve a higher heat transfer rate with relatively lower pressure drop. This paper uses the computational fluid dynamics to study crossflow, nozzle configuration, inlet orientation, and jet-to-target spacing distance effects on the heat transfer rate and the discharge coefficient. In this study, jet-to-target spacing was varied from 1.6 to 7 jet diameter, jet-to-jet spacing was 3.4 jet diameter, the reverse tube diameter was 3.2 jet diameter, and jet Reynolds number was set at 23,000. Procedural optimisation throughout the study initially evaluated that nozzles extended through the crossflow channel are more effective than the square-edged nozzles in eliminating the crossflow effect and promoting higher heat transfer. Variation of inlet condition yielded no significant optimisation was found. Jet-to-target spacing was optimised at jet-to-target spacing around 3 jet diameter. The most significant variable affecting nozzle discharge coefficient was the flow area of the outlet. The reverse jet impingement design showed capacity to enhance heat transfer by increasing the internal surface area, and minimise negative crossflow effects, without excessive reduction in the discharge coefficient.

Accurate theoretical calculation of the discharge coefficient for sonic nozzle using geometric parameter measurements in Re=(7.33×104–1.26×106)

In order to improve the measurement accuracy and efficiency of sonic nozzles (SNs) in laminar boundary layer, a correlation model for theoretical discharge coefficient of sonic nozzle taking into account the viscous effects on the boundary layer along the nozzle wall (Cd,th,1), and the multi-dimensional characteristic effect of the core region (Cd,th,2) was proposed. The theoretical discharge coefficient is related to the measurement of geometric parameters, such as the throat diameter, d, and curvature radius, Rc. The detailed geometric measurements of sonic nozzle by 3D coordinate measuring machine were conducted. Then, the evaluation procedures of parameters d and Rc including roundness and waviness profile for designed SNs of d = 7.453 mm and d = 1.919 mm were presented in detail. The effect of waviness profile on the discharge coefficient and boundary layer transient was investigated. It indicated that waviness effect is quite complex. Finally, the validation of the theoretical calculation model of discharge coefficient was verified by the experimental data of National Institute of Metrology (NIM) and National Metrology Institute of Japan (NMIJ) based on the accurate measurements of the geometric parameters. The result showed that the consistency between the Cd,exp and the Cd,th is better than 0.11% when the effect of the heat transfer was considered within the range of Re= (7.33 × 104–1.26 × 106).

Numerical study of secondary mass flow modulation in a Bypass Dual-Throat Nozzle

The fluidic thrust-vectoring modulation on a Bypass Dual-Throat Nozzle (BDTN) is studied numerically. The thrust vectoring modulation is obtained by varying the secondary mass flow, introducing different area contraction ratios of the bypass duct. The scope of present study is twofold: (i) to set up a model for the control of the secondary mass flow that is consistent with the resolution of the nozzle main flow and (ii) to derive a simplified representation of a valve system embedded in the bypass channel. The simulations of the turbulent airflow inside the BDTN and its efflux in the external ambient have been simulated by using RANS approach with RNG [Formula: see text] turbulence modeling. The numerical results have been validated with experimental and numerical data available in the open literature. The nozzle performance and thrust vector angle are computed for different values of the bypass area contraction ratio. The effects of different secondary mass flow rates on the system resultant thrust ratio and discharge coefficient of the bypass dual-throat nozzle have been investigated. By using the proposed approach to the secondary mass flow modulation, the thrust pitch angle has been controlled up to 27°.

Civil turbofan engine exhaust aerodynamics: Impact of fan exit flow characteristics

It is envisaged that future civil aero-engines will operate with greater bypass ratios compared to contemporary configurations to lower specific thrust and improve propulsive efficiency. This trend is likely to be accompanied with the implementation of a shorter nacelle and bypass duct for larger engines. However, a short bypass duct may result in an aerodynamic coupling between the exit flow conditions of the fan Outlet Guide Vanes (OGVs) and the exhaust system. Thus, it is imperative that the design of the exhaust is carried out in combination with the fan exit profile. A parabolic definition is used to parameterise and control the circumferentially-averaged radial profiles of stagnation pressure and temperature at the fan OGV exit. The developed formulation is coupled with a parametric exhaust design approach, an automatic computational mesh generator, and a compressible flow solution method. A global optimisation strategy is devised comprising methods for Design of Experiment (DOE), Response Surface Modelling (RSM), and genetic optimisation.A combined Design Space Exploration (DSE) comprising both geometric, as well as fan exit profile variables, is performed to optimise the exhaust geometry in conjunction with the fan exit profile. The developed approach is used to derive optimum exhaust geometries for a tip, mid, and hub-biased fan blade loading distribution. It is shown that the proposed formulation can ameliorate adverse transonic flow characteristics on the core after-body due to a non-uniform bypass inflow. The hub-loaded profile was found to be most penalising in terms of exhaust performance compared to the mid and tip-loaded variants. It is demonstrated that the combined fan exit profile and exhaust geometry optimisation offers significant performance improvement compared to the fixed inflow cases. The predicted performance benefits can reach up to 0.19% in terms of exhaust velocity coefficient, depending on fan loading characteristics. A notable improvement is also noted in terms of bypass nozzle discharge coefficient. This suggests that the combined optimisation can lead to an exhaust design that can satisfy the engine mass-flow rate demand with a reduced geometric throat area, thus potentially offering further exhaust size and weight benefits.

Influence of wall roughness on boundary layer transition position of the sonic nozzles

The discharge coefficient of sonic nozzle is mainly dependent on the viscous boundary layer which is affected by the Reynolds number, wall roughness and turbulence intensity. Six sonic nozzles with various throat diameter of (1.921–9.086) mm and the average roughness of 0.6 μm in NIM were designed and calibrated to experimentally analyze the influences of wall roughness on the discharge coefficient and boundary layer transition by two pVTt gas flow standard facilities. Furthermore, a series of numerical simulations through the transition SST model for the axisymmetric nozzles were established to research the discharge coefficients of the sonic nozzles with the throat diameter of 3.808 mm, 5.350 mm and 7.453 mm when the Reynolds numbers ranges from 2.5 × 104 to 4.4 × 107 and the relative equivalent sand roughness Ks/d from 1.3 × 10−5 to 1.3 × 10−3. The calculating results of the simulation model were validated by the ISO 9300 empirical equation and the experimental data of NIM, PTB and UK. Finally, the relationships between the displacement thickness of boundary layer, namely the discharge coefficient and the relative roughness of the wall were obtained in detail. The starting positions of boundary layer transition with different Reynolds number and relative roughness were also analyzed.

A comprehensive understanding of enhanced condensation heat transfer using phase separation concept

A comprehensive analysis of enhanced condensation with phase separation concept is presented, for which mesh-membrane-tube (MMT) is suspended in a tube. A twill Dutch weaved mesh screen and two plain Dutch weaved mesh screens are used to fabricate MMT. Our study reveals that liquid leakage across MMT not only keeps better condensation on condenser wall, but also decreases pressure drop rise penalty. To modulate stratified-flow, the #1 MMT with smallest dp has the largest capillary force to pump liquid towards core region to expose more condenser surface with vapor, where dp is pore diameter. To modulate annular-flow, finest mesh wires of #1 MMT ensure the best wetting to liquid to prevent condenser wall from being impacted by satellite droplets. These mechanisms explain the best performance of #1 MMT, reaching a maximum heat transfer enhancement ratio of 1.82. The three MMTs share a single curve of nozzle discharge coefficient versus Reynolds number. The similar performance of #2 and #3 MMTs is due to identical dp/φ, where φ is mesh open porosity. Fine mesh wires and small mesh pores are suggested to enhance condensation heat transfer. MMT are recommended to be used in condenser tube upstream when vapor mass qualities larger than 0.1.

A Novel Method to Determine the Discharge Coefficient of Constant Section Nozzles Under Compressible Dynamic Flow Conditions

The present paper introduces a novel transient experimental method employed to determine the discharge coefficient of constant section nozzles of small diameters of 1–3 mm and with a length/diameter ratio of around one. Flow is considered to be real and compressible; the discharge process was analyzed at relatively high pressures, the fluid used was N2. Based on the experimental data, a generalized expression characterizing the discharge coefficient for nozzles of different diameters, lengths, and fluid conditions was developed. In order to check the precision of the analytical equation presented, experimental upstream reservoir pressure decay was compared with the temporal pressure decay obtained using the new analytical equation. Good correlation was achieved for pressure differentials up to 7.6 MPa. Despite the fact that the procedure established can be extended to other gases and nozzle configurations, so far the equation presented to estimate the discharge coefficient, can only be applied to orifices with length to diameter ratios of around one.

Re-definition of the discharge coefficient of throat-tapped flow nozzle and investigations on the influence of geometric parameters

The objective of this paper is to obtain a useful equation which gives a discharge coefficient of a throat-tapped flow nozzle. Experiments for throat-tapped flow nozzles with several different geometric parameters were performed using highly accurate flow facilities at the National Metrology Institute of Japan (NMIJ). The effects of some geometric parameters on the discharge coefficient were experimentally investigated. The parameters include the ratio of the diameter of the pressure taps located at the throat to the throat diameter, the diameter of the pressure taps located at upstream pipe and the roughness of the nozzle surface. Also, the effectiveness of a flow conditioner prescribed in ASME PTC 6 was examined. Although a limitation to the proposed equations was found, the discharge coefficient is affected by the geometric parameters smaller than the measurement uncertainty. Finally, new equations for the discharge coefficient, which cover all experimental results within 0.5%, have been proposed as a set of functions of the Reynolds number.