Nozzle Throat Research Articles

Investigation of the Influence of Laval Nozzle Throat Width via Euler-based Flow Simulation

The nozzle is a kind of widely used fluid equipment. It is very important to study its internal flow for improving nozzle performance or improving nozzle design. In this paper, the numerical simulation method based on the Euler equation is used to solve the flow in the nozzle. Euler equations are solved by an explicit finite difference method, including discretization, pre-estimation and correction steps. Boundary treatment for the subsonic inlet and supersonic outlet are discussed. The flow characteristics inside a Laval nozzle are analysed based on the numerical results. The influence of Laval nozzle throat width on the nozzle flow is investigated by comparing three nozzles. It is observed that the dimensionless pressure, temperature, and density of the three nozzles have similar trends. While the maximum Mach number at the outlet decreases with the increase of the throat width. In short, the throat width should be decreased if a larger outlet speed of the flow is needed.

Exploration of laser-induced isotope separation of BCl3

The analytical equations and theoretical calculation methods (proposed by Eerkens in 2005) are used to study the transport mechanics of the excited BCl3 molecules, including the molecular dynamic processes such as the slowing-down of epithermal molecules, the laser-excited molecules and population of epithermals, the pressure of gas source, the minimum temperature of the jet, and the nozzle throat radius. The enrichment factor β and product cuts Θo of the system are also demonstrated. When the temperature is higher, the product cuts is larger. The larger the pressure, the smaller the product cuts, and the enrichment factor is greater. Therefore, the appropriate temperature and pressure must be selected to optimize the isotope separation.

Theoretical Analysis of a Single-Stage Gas-Fired Ejector Heat Pump Water Heater

Abstract Ejector-driven systems have the ability to operate at high efficiencies, utilizing recycled thermal energy as a power source. For a typical ejector heat pump (EHP) system, the increase of the condenser temperature reduces the coefficient of performance (COP). In addition, if the condenser temperature is higher than the critical temperature, the ejector may not function. In this situation, the condenser temperature must be reduced, and an additional heater will be utilized to heat the production water from the condenser temperature to the desired temperature. In this study, a single-stage gas-fired EHP is investigated and thermodynamically modeled to optimize the system COP for the purpose of heating water by utilizing the thermal energy from the ambient air. The effects of the high-temperature evaporator (HTE) and low-temperature evaporator (LTE) on the ejector critical back pressure and the EHP system performance are examined for a HTE temperature range of 120–180 °C and LTE temperatures of 15.5, 17.5, and 19.5 °C. Results show that an optimized COP for the EHP system exists and is dependent on HTE and LTE temperatures and the primary nozzle throat diameter. In addition, it is found that the peak EHP COP does not necessarily coincide with a large ejector COP. From this study, a maximum EHP COP of 1.31 is achieved at a HTE temperature of 170 °C and LTE temperature of 19.5 °C with a total heating capacity of 15.98 kW.

Measurements of Metastable Molecules in Nonequilibrium Supersonic Flows

Nonintrusive laser diagnostics are used for the measurements of metastable nitrogen molecules in the lowest excited electronic state, , in a nonequilibrium flow, blowdown supersonic wind tunnel. The tunnel is operated with nitrogen at plenum pressures of Torr, with the flow expanding through a two-dimensional contoured nozzle to the Mach number of . The steady-state run time of the tunnel is approximately 10 s. The flow is excited by a repetitive nanosecond pulse discharge operated in the plenum or in the nozzle throat. Time-resolved absolute populations in the plenum are measured by single-pass, continuous wave tunable diode laser absorption spectroscopy (TDLAS). In the supersonic test section, absolute populations are measured by cavity ring down spectroscopy (CRDS), using a tunable pulsed laser system operated at 10 Hz. During each run, 50 single-shot ring down traces are acquired, demonstrating good shot-to-shot reproducibility. The results demonstrate that the cavity ring down time is not affected by the supersonic flow. populations and the flow temperature are inferred from the single-shot CRDS data. At the conditions when the flow is excited by the discharge in the nozzle throat, population in the supersonic test section is measured by both CRDS and TDLAS diagnostics. The two diagnostic techniques are complementary and can be used for characterization of nonequilibrium reacting flows over a wide range of pressures, including short-run-time high-enthalpy flow facilities.

Equation-oriented methods for design optimization and performance analysis of radial inflow turbines

This paper presents methods for design optimization and performance analysis of radial inflow turbines. Both methods are formulated in an equation-oriented manner and involve a single mathematical problem that is solved by an efficient, gradient-based optimization algorithm. In addition, the comparison of the model output with experimental data showed that the underlying mean-line flow model accurately predicts the variation of mass flow rate and isentropic efficiency as a function of the pressure ratio, rotational speed, and nozzle throat area. Moreover, the capabilities of the proposed methods were demonstrated by carrying out the preliminary design and performance prediction of the radial inflow turbine of an organic Rankine cycle. The results indicate that the design optimization method converges to the global optimum solution, regardless of the start values for the independent variables. In addition, the performance maps generated by the performance analysis method are physically consistent and agree with general findings from experimental data reported in the open literature. Considering the accuracy, robustness and low computational cost of the proposed methods, they can be regarded as a powerful tool for the preliminary design and performance prediction of radial inflow turbines, either as a standalone component or as part of a larger system.

Experimental investigations on cylindrical critical flow Venturi nozzles with roughness

In an attempt to redefine and improve the ISO9300 norm, it is possible to see the emergence of a universal (Cd) curve. For this, all the influential factors must be correctly understood within their range of variation. In recent discussions, the experimental calibration point could be limited, and a low-pressure measurement could be sufficient to extrapolate the higher part of the curve with a relatively good level of confidence. For that purpose, the cylindrical shape gives more variations and needs a higher level of measurement to understand the behavior of the curve. Roughness level is a key parameter to this understanding. Experiments have been carried out to determine the impact of cylindrical nozzle throat roughness on Cd and to demonstrate the need for precise dimensional parameters, such as diameter and roughness characterization. The results show that an increase in roughness may lead to a significant decrease in Cd, particularly at high Reynolds numbers (Red). A theorization is introduced based on Colebrook & White’s formulation which allows the thickness boundary layer to be quantified. This study highlights the need for further investigation into both cylindrical nozzles and roughness effects on the discharge coefficient in order to improve the norm.

A fluidic thrust vector control using the bypass flow in a dual throat nozzle

A fluidic thrust vector control using the bypass flow in a dual throat nozzle

Experimental Investigation on Cavity Pressure Inside Sheet Cavitation

Abstract The gas content is one of the important factors in cavitation, which may increase the pressure inside the cavity through the diffusive mass transfer of the dissolved gas into the cavity. In the present study, we try to directly measure the cavity pressure inside the sheet cavity at the throat of a converging-diverging nozzle. Then the influences of the flow velocity and the gas content (amount of dissolved oxygen) on the gas partial pressure are investigated. It is found that, even in low gas content level, the cavity pressure is slightly but apparently higher than the saturated vapor pressure, indicating the presence of gas partial pressure. It is observed that the gas partial pressure in significantly developed cavitation is almost constant regardless of the flow velocity but slightly increases against the increase of the saturation level of dissolved gas. It is also found that the gas partial pressure inside cavity depends on the degree of cavitation development; the gas partial pressure decreases with the development of cavitation.

Multiparameter Optimization of Thrust Vector Control with Transverse Injection of a Supersonic Underexpanded Gas Jet into a Convergent Divergent Nozzle

The optimal design of the thrust vector control system of solid rocket motors (SRMs) is discussed. The injection of a supersonic underexpanded gas jet into the diverging part of the rocket engine nozzle is considered, and multiparameter optimization of the geometric shape of the injection nozzle and the parameters of jet injection into a supersonic flow is developed. The turbulent flow of viscous compressible gas in the main nozzle and injection system is simulated with the Reynolds-averaged Navier–Stokes (RANS) equations and shear stress transport (SST) turbulence model. An optimization procedure with the automatic generation of a block-structured mesh and conjugate gradient method is applied to find the optimal parameters of the problem of interest. Optimization parameters include the pressure ratio of the injected jet, the angle of inclination of the injection nozzle to the axis of the main nozzle, the distance of the injection nozzle from the throat of the main nozzle and the shape of the outlet section of the injection nozzle. The location of injection nozzle varies from 0.1 to 0.9 with respect to the length of the supersonic part of the nozzle; the angle of injection varies from 30 to 160 degrees; and the shape of the outlet section of the injection nozzle is an ellipse with an aspect ratio that varies from 0.1 to 1. The computed fluid flow in the combustion chamber is compared with experimental and computational results. The dependence of the thrust as a function of the injection parameters is obtained, and conclusions are made about the effects of the input parameters of the problem on the thrust coefficient.

수치해석기법을 적용하여 3 MW급 소형 폐압 증기 터빈의 성능 분석 및 설계

In this study, the design of an axial steam turbine that is installed for a using waste pressure. Airfoils and flow fields are designed based on 1D and 2D meridional plane design techniques. The 3D geometry of the steam turbine is designed considering the 1D and 2D design parameters. The turbine is designed with an average radius of 287 mm and rotates at 8,300 re v/min. The inlet boundary condition of the steam turbine was applied in consideration of the installation condition of the waste pressure turbine. When analyzing the results of the numerical simulation, the performance of the steam turbine is predicted with an output of 3.5 MW and isentropic efficiency of 88.4%. The choked flow in the nozzle throat and the flow separation in the suction side on the blades are predicted numerically, and it is expected to be a study to determine the cause of the reduction in efficiency of the steam turbine.

Thermal Structure Strength Analysis of Nozzle of Solid Rocket Motor with the Coupled Algorithm

In order to achieve the thermal structural integrity analysis of the solid rocket motor nozzle accurately and efficiently, the multifield (flow-thermal-mechanical) coupled numerical investigation was carried out based on the mesh-based parallel code coupled interface. The numerical simulation process and finite element model of the coupled algorithm and engineering algorithm were obtained, while the physical model was simplified appropriately. The coupled interface parameters, internal flow field, temperature field, and stress field of the coupled algorithm were compared with the engineering algorithm results, and the effectiveness and accuracy of the numerical simulation were validated. The numerical investigations shown that both the temperature field and stress field obtained by the coupled algorithm were slightly lower than which obtained by the engineering algorithm. These were considered to be impacted by the Bartz empirical formula and the one-dimensional isentropic flow assumption. Further experimental investigations shown that the exterior surface temperature and strain of the nozzle throat obtained by the coupled algorithm were much closer to the experimental results, which further verified the accuracy of the coupled algorithm.

Investigation on Flow Characteristics and Parameters Optimization of a New Concept of TC Nozzle

Lighter weight, simpler structure and throat area controllable are the developing trends of aircraft engine exhaust system. To meet these challenges, a new concept of hybrid throat control (TC) nozzle was proposed to improve the control efficiency of throat area (η) by using a rotary valve with secondary injection. The flow mechanism of the hybrid TC nozzle and the effect of aerodynamic and geometric parameters on nozzle performance were investigated numerically. Then the approximate model characterizing the hybrid TC nozzle was established with design of experiment and response surface methodology. The approximate model was used to analysis the coupling effect between parameters and optimized the parameter combination. The results show that the flow area of the nozzle can be restricted effectively by the rotary valve and the secondary flow, and η is bigger than 5.24. Nozzle pressure ratio and secondary pressure ratio are the dominant factors for the nozzle throat area control performance. The optimization of the parameter combination was carried out with penalty function approach, with ratio of throat area control being 30 percent and corrected mass flow ratio of secondary flow being 5 percent The maximize error of the optimization result is 4.13 percent and it verifies the validity and feasibility of the approximate model.

Scaling law for supersonic core length in circular and elliptic free jets

We present here the experiments demonstrating the scaling law for supersonic core length in circular and elliptic free jets. A proper scale for the supersonic core length of free jets is found as Lc*AR e−0.11γMj2, where Lc* is the core length normalized by nozzle throat diameter Dth, AR is the aspect ratio of the elliptic nozzle, γ is the specific heats ratio, and Mj is the ideally expanded jet Mach number. The scaling law developed for supersonic core length shows a close dependence with nozzle expansion ratio pe/pa and agrees well with the results reported in open literature, including the data reported for γ = 1.28–1.67. In spite of their uniqueness, the present results refer to circular and elliptic jets only. Thus, other similar studies on rectangular and square jets for a wide range of parameters are needed for a full comprehension of the universality of the scaling law for non-circular jets.

Design of a Throat-extended FDM Extruder for Multi-axis 3D Printing

Multi-axis fused deposition modelling (FDM) 3D printing technology has been paid attention to by more and more people. However, existing FDM extruders are usually short and fat, which significantly restricts the popularization of multi-axis FDM 3D printing technology because one significant trend of additive manufacturing is the use of long and thin extruders to avoid collisions between extruders and workpieces in the printing process. This paper presents the design of a throat-extended FDM extruder to print complex-shaped workpieces with details. The main contributions in this paper include: (i) presenting a novel extruder structure including an extended-throat, a smaller heater block, and a cooling mini-fan; (ii) designing an optimized heater block using the shapes of its components and the milling tool as constraints to make its volume as little small as possible; (iii) Construct experimental and simulation methods to examine the temperature distribution of the throat to optimize the shapes of the heat dams of nozzle throats and the wind speed of the heat-dissipation fan. Based on the throat-extended FDM extruder, a five-axis FDM 3D printer has been developed, and various complex-shaped workpieces have been printed without any support.

Performance improvement of ejector refrigerator–based water chiller working with different mixing chamber profiles

This paper proposes the performance improvement of the ejector refrigerator based water chiller (ejector-based chiller) by means of using different mixing chamber profiles. Two different ejector mixing chamber profiles are constructed which are based on the conventional method (CONV–ejector) and the constant rate of momentum change method (CRMC–ejector). With the different design methods, the ejectors have different flow areas along the ejector’s axis; however, they have identical ejector throat diameters of 9 mm. Both ejectors are equipped with two primary nozzles, and hence, they have the same ejector area ratio of 6.3 and 7.9, respectively. The refrigerator is powered by hot water at a temperature of 94–98 °C while the condenser is cooled by cooling water at 29–31 °C. The chilled water temperature (Tchill) under various cooling loads and COP is assessed. It is found that the CRMC–ejector produces a much lower chilled water temperature than the CONV–ejector at identical cooling load. The system COP can be increased by 27–63% via the CRMC–ejector. With the change in Thot, both ejectors produce identical Tchill; however, the CRMC–ejector still produces much lower Tchill at an identical cooling load. A larger primary nozzle throat yields a higher Tchill.

Dynamic simulation method of adjustable nozzle considering clearance fit

Aiming at the motion stagnation and local damage failure of a 2D needled Cf/SiC adjustable nozzle during operation, the motion performance of the nozzle and the contact stress at the key parts were studied. A dynamic simulation method of the nozzle with adjustable nozzle considering clearance fit was established, and the throat contraction process was analyzed by a simulation example. Firstly, the critical analysis positions of the nozzle were determined by trial calculation, and the model was simplified and the mesh was optimized. Then, the simulation was carried out under the boundary conditions involving multiple fields. The motion characteristics of the nozzle throat during the throat contraction process were analyzed due to the velocity results, and the stress state and failure state at the key position of the nozzle during the impact process were finally determined.

Design and optimization strategy for ejectors applied in refrigeration cycles

Implementation of an ejector for expansion work recovery in transcritical Carbon Dioxide (CO2) cycles provides an opportunity to improve the efficiency of these environmentally-friendly refrigeration systems. However, literature outlining an approach to ejector design for a given application is lacking. This paper presents a tool to design a complete ejector applied in a vapor compression cycle. In this work, the developed design tool was validated using experimentally-derived polynomials at air conditioning conditions, then efficiencies were input to broaden the analysis to study a transcritical CO2 system with an ejector operating in the evaporating temperature range of −15 °C to 20 °C and gas cooler pressure in the range of 80–110 bar. The design tool allows for the calculation of the motive and suction nozzle throat diameters, the mixing section diameter, and the diffuser outlet diameter, as well as the lengths of each section, to output a full internal geometry of the ejector based on performance requirements. Individual component sub-models are presented within the proposed model structure. The model which forms the basis of the design tool was experimentally validated with a mean absolute error (MAE) between 3% and 4%. Additionally, the sensitivity of the ejector geometry and performance to component efficiencies, operating conditions, and component versus system optimization was investigated. The optimization and parametric studies conducted provided novel insights into the impact of desired efficiency and operating conditions on ejector geometry, thus allowing a designer to make decisions based on the tradeoff between ejector size and performance. For example, as the diffuser length increased by 5.1 mm to obtain an efficiency increase, to obtain a further efficiency increase of the same amount would require a 17.1 mm length increase in diffuser length. Potential model improvements and other future work are also discussed.

Experimental study of internal forces and moments generated by strut injection in a supersonic cross-flow in a C-D nozzle

An experimental investigation was conducted to obtain wall pressure distribution in a convergent divergent nozzle with a strut inserted through the diverging wall and to find out the possible generation of side force. The strut inserted through the nozzle wall represented an active control method for thrust vector control. Laboratory tests were carried out to examine whether this type of strut injection would be effective and serve as an alternative thrust vector control method for the other widely used such as secondary injection thrust vector control. The nozzle model used in the experiments had a design Mach number of 1.84 with a corresponding area ratio of 1.48. The solid strut which was inserted through the diverging wall of the nozzle had a square cross section. Experiments were conducted for identifying three different strut positions from the nozzle throat, i.e. at Ld/3, Ld/2, and 2Ld/3, where Ld was the length of the diverging section of the nozzle. At each strut position, the strut height was varied and the maximum strut height corresponded to the radius of the local cross section where the strut was inserted. The nozzle was operated at overexpansion conditions such as nozzle pressure ratios of 3.4 and 5. The strut side and the opposite side of the nozzle wall had eight wall pressure tappings each and the wall pressure data were obtained using a pressure scanner. The asymmetrical pressure distributions of the strut side and the non-strut side (opposite side) of nozzle wall were used for the calculation of side force and pitching moment in the nominal plane through the wall pressure ports of both sides. The calculated two-dimensional side force, axial force, and pitching moment coefficients were plotted against strut height at each strut position from the nozzle throat. From the experimental data and calculations, it was found that the axial force varied more or less linearly with strut height irrespective of the strut position. However, the side force and pitching moments varied nonlinearly with strut height and the nature of variation of the two was similar. Both the side force and pitching moment exhibited maximum and minimum values at two specific values of the strut height. The change in the strut position did not alter the nature of the above variations and the strut height values for maximum and minimum. The magnitude of the side force was found to be 1–10% of the axial force generated as a fluid dynamic pressure drag. Both positive and negative side force and pitching moments were produced with increase in the strut height.

Investigation on Pressure Build-Up and Blowing Processes by Multipoint Pressure Measurement and Fluid Analysis for Self-Blast-Type High-Voltage Circuit Breaker

In high-voltage gas circuit breakers, processes to blow high-pressure and low-temperature gas into an arc are important for efficient fault current interruption. Self-blast-type gas circuit breakers obtain a high pressure by using arc energy to blow the high-pressure gas into the arc. In order to understand the self-blast phenomenon, we carried out multipoint pressure measurements to investigate the pressure build-up mechanism and blowing processes quantitatively. Because the pressure in the nozzle throat was particularly high around the arc area, the nozzle throat with a narrow cross-sectional area and high-current density works as a pressure source at a high-current condition. Blowing gas from a thermal puffer chamber becomes dominant when interrupting current decreases, and then a switch is made to the blowing process a few milliseconds before current zero. The pressure ratio between the thermal puffer chamber and nozzle throat agreed well with the pressure ratio calculated from the sound speed condition thereafter around current zero. Therefore, we confirmed the formation of sound speed flow in the nozzle throat, and supersonic flow was established in the nozzle diverging section. It was possible to use the pressure distribution and influence of pin position around current zero in the nozzle diverging section to evaluate gas flow by a theoretical calculation, and the pressure measurement found the influence of stagnation flow by pin contact. The influence of pin contact could be evaluated from the comparison of measurement and gas flow analyses, and it was confirmed that the evaluation of gas flow and interrupter design was possible.

Port diameter design of multiport solid fuel in hydrogen peroxide hybrid rockets

A feasibility study of the design of multiport solid fuel using the ratio of the nozzle throat area to the port area was performed in a hydrogen peroxide/high-density polyethylene hybrid rocket. The port diameters of the multiport solid fuel according to the change of the number of ports were designed by setting the ratio of the nozzle throat area to the port area at 0.25, 0.3, 0.5, and 1. To obtain the design point of the multiport solid fuel, the final port diameter and performance parameters were analyzed using a numerical estimation code based on the regression rate equation. The numerical estimation indicated that the solid fuel with nine circular ports with a length of 400 mm, and a port diameter designed with ratio of 0.5 between the nozzle throat area and the port area, had an oxidizer-to-fuel ratio (O/F) close to the design value and high specific impulse efficiency. To verify the value calculated using the numerical estimation, a 2500-N-class hydrogen peroxide/high-density polyethylene hybrid rocket with multiport solid fuel was designed, and experiments were performed. The specific impulse and overall regression rate calculated from the experiments and numerical estimation were compared. The maximum differences of less than 10.7% and 4.38% were observed in the comparison. Based on the small difference, the estimation results calculated using numerical estimation at ratios (the nozzle throat area to the port area) of 0.25, 0.3, 0.5, and 1 were demonstrated. The design method of the multiport solid fuel in a hydrogen peroxide/high-density polyethylene hybrid rocket using the ratio of the nozzle throat area to the port area and the numerical estimation based on the regression rate equation was feasible.