Nozzle Profiles Research Articles

Genetic algorithm based optimization of nozzle profiles for a hydrogen turbo-expander

Liquid hydrogen plays an important role in the large scale storage and long-distance transportation. The development of hydrogen turbo-expander is the key to increase the efficiency of hydrogen liquefaction, reducing the cost of liquid hydrogen production, storage and transportation. In this paper, a numerical model of hydrogen nozzle is established and validated against experimental data. The performance of four traditional nozzle profiles in hydrogen turbo-expanders is simulated and analyzed. The poor uniformity of outlet flow angle is generally found in these nozzle profiles, leading to nozzle passage and impeller incidence losses in turbo-expanders. A genetic algorithm based method is proposed to optimize the nozzle profiles. The optimization objectives involve the nozzle efficiency, the uniformity of the nozzle outlet angle and the uniformity of the outlet Mach number. The deviations in the outlet angle and Mach number of the optimized nozzle are reduced by 50.26 % and 14.03 %, respectively, while the nozzle efficiency reaches 98.64 %. The matching characteristics of the optimized nozzle with the impeller are obtained via simulation of a hydrogen turbo-expander, and the results indicate the expansion efficiency can be increased by 1.53 %.

Developing a predictive model for low-temperature Laval nozzles with applications in chemical kinetics

Laval nozzles are used in the CRESU (“Cinétique de Réaction en Écoulement Supersonique Uniforme”) method to generate a collimated low temperature (5–200 K), low pressure (30–500 Pa), high Mach number (1 < M < 20) supersonic jet. Laval nozzles have been designed using the Method of Characteristics (MOC) since the development of CRESU, which is an analytical method that assumes inviscid, isentropic flow, and is routinely used to design nozzle profiles for a particular gas and temperature with a uniform shock free exit. This study aims to provide a robust computational framework to overcome the limitations of the MOC while also providing recommendations on the numerical model setup required to model a low-temperature supersonic jet. It also discusses the blockage effects when using the Pitot tube method for flow characterization, the influence of inlet turbulence and reservoir size. Numerical results are validated using two different experimental apparatuses from research groups at the University of Leeds and the University of Birmingham. Finally, a MATLAB framework was developed and has been provided as an open source toolbox to allow any user to perform computational fluid dynamics on any Laval nozzle, with the ability to change nozzle geometry, operating conditions and bath gas. The toolbox has been rigorously tested against many benchmark cases, which shows that steady-state Reynolds-averaged Navier–Stokes with the k-omega-shear stress transport turbulence model can be used to accurately predict global quantities, such as average temperature in the stable region of the supersonic jet.

Particle Image Velocimetry and Total Temperature Characterization of Arc-Heated Mach 4.5 Free Jet

Particle image velocimetry (PIV) measurements were conducted in the Arc-Heated Combustion Tunnel (ACT-II) on a high-enthalpy Mach 4.5 nozzle flow. The primary motivation for the current work is to establish the feasibility of PIV as a high-quality flow diagnostic technique in hypersonic arc-heated flows and produce a high-resolution hypersonic nozzle flow characterization, including nozzle free jet shear layer velocity profiles. Due to the uncertain nature of the gas composition in the flowfield of interest, PIV measurements of a supersonic wedge flow were used to couple the flow velocities to the oblique shock relations. This enabled a PIV-derived total temperature calculation that does not require a priori assumptions of the exact gas composition. A PIV expansion module was developed for this study, and proper seed sizing and material were selected for the present flow. An analysis of the seed particle response from the PIV measurements provided an initial validation of the seed performance while revealing potential issues with consistent seed sizing. These measurements and derived conditions represent a means of acquiring high-resolution velocimetry and temperature datasets that consider uncertainties in the experimental generation of hypersonic high-enthalpy flows.

A homogeneous relaxation model algorithm in density-based formulation with novel tabulated method for the modeling of CO2 flashing nozzles

Accurate prediction of the flow physics within nozzles and ejectors working with two-phase carbon dioxide remains particularly challenging. Indeed, the flashing phenomenon in the device often comes along with the formation of the metastable phase, which can severely affect both the flow physics, and the flow rate. Due to the particular challenges associated with building and operating two-phase carbon dioxide experimental setups, computational fluid dynamics constitutes a compelling alternative to study and predict nozzle and ejector flows. In this work, the metastability effects are modeled through a Homogeneous Relaxation Model for the first time expressed in density-based formulation, within the SU2 solver. The thermodynamic relations for the equation of state are tabulated using a novel quad-tree algorithm and directly coupled to the solver, ensuring fast and accurate predictions. The simulation tool is then validated against experimental nozzle pressure profiles and used to compare the commonly used Homogeneous Equilibrium Model to the Homogeneous Relaxation Model in terms of local flow topology and mass flow rates. Most notably, it was found that the Homogeneous Relaxation Model was able to better fit the experimental pressure profiles within the first part of the expansion.

A streamlining method for ejector nozzle profile optimization based on polynomial function

In this study, ejector performance was optimized by streamlining the primary nozzle profile using polynomial functions. Thirteen streamline nozzle profiles with different initial and exit expansion half-angles which determined by quadratic and cubic functions were established, and their performance are discussed. The results indicate that the nozzle profiles designed by cubic function have the best performance than quadratic function. To improve the effective working range, the ejector should have an initial expansion half-angle that is as small as possible and an exit expansion half-angle that is as large as possible. To enhance the entrainment ratio, the ejector should have a constant exit expansion half-angle and a minimum initial expansion half-angle of 1°. An excessive initial expansion half-angle caused a sealed Mach number contour inside the nozzle, which wasted energy to reduce the velocity and increase the static pressure, decreasing the working efficiency of the primary flow. In addition, the entrainment ratio significantly decreased with a large exit expansion half-angle (greater than 17°).

Role of process parameters on microstructure, mechanical properties and erosion performance of HVAF sprayed Cr3C2-NiCr coatings

In this study, Cr3C2-NiCr coatings of two different particle sizes (fine: 10–30 and coarse: 15–45 μm) were deposited by variable nozzle lengths (long, medium and short) and profiles (convergent-divergent, over-expanding and straight barrel) using high-velocity air-fuel (HVAF) and oxygen augmented air-fuel (HVAF(O)) spray mode. A comparative analysis of the generated coating specimen was performed through the microstructural features, phases present, properties and erosion performance. Additionally, the deposition efficiency (DE) was evaluated to assess the techno-economic feasibility of HVAF/HVAF(O) sprayed Cr3C2-NiCr coatings. All the deposited coatings were dense, uniform and displayed a homogenous distribution of carbides. The convergent-divergent-based long and medium nozzle sprayed coatings displayed better mechanical properties, whereas coatings deposited by short-length nozzles showed relatively inferior properties. In terms of particle size, fine Cr3C2-NiCr sprayed using HVAF and coarse Cr3C2-NiCr sprayed using HVAF(O) displayed improved coating characteristics and properties. Erosive studies implied coatings with improved intersplat adhesion exhibited ductile eroding behavior like “ploughing” and “micro-cutting” rather than “splat flaking/chipping.” Overall, employing a medium-length, convergent-divergent nozzle deposited Cr3C2-NiCr coatings with an ideal combination of DE, mechanical properties and erosion performance. Besides, short-length nozzles were inappropriate for spraying Cr3C2-NiCr since they displayed compromised coating characteristics and performance.

Combined effects of nozzle hole variation and piston bowl geometry modification on performance characteristics of a diesel engine with energy and exergy approach

This experimental work aims to address the challenges of waste management. Biomass waste is converted into useful fuel and considered as a replacement to conventional fuel in CI engines. In this context, the grape marc and grape pomace are crushed and further processed to produce grapeseed oil. The grapeseed oil is further trans esterified to produce grapeseed seed oil methyl ester. The present study aims in examining the effect of varying piston shapes and nozzle profile on energy and exergy rates of a CI engine run with grapeseed oil methyl ester (GSME) blended with cerium oxide nano particles. The CeO2 nano particles were suspended in the base fuel at a concentration of 100 ppm and stability tests were conducted. The experiments were performed on a single cylinder, water cooled diesel engine with rated power of 5.2 kW. The research work includes two additional piston shapes namely, toroidal and shallow deep and two additional nozzle profiles viz. 4 hole and 5-hole nozzle. The hemispherical shape and 3-hole nozzle were considered as the standard one. Energy and exergy analysis were done on the experimental data to understand the exergy associated with cooling water, exhaust gas and unaccounted losses. The energy and exergy rates show that increase in nozzle hole number, decreases the destructive availability of the system. The exergetic efficiency of 32.8% is higher proving that toroidal shape and 5-hole nozzle profile is comparatively better and suitable for effective engine operation. HC, CO and smoke emissions reduced considerably by 14.4%–30% by the engine modification. Brake thermal efficiency was improved from 28.2% to 31.02% for CI engine with biodiesel. The paper addresses the gap in fuel modification clubbed with engine modification using biomass waste derived fuel. Exergy and energy analysis further add value to this current experimental work.

Impact of changing nozzle profiles on thermal and structural loads acting on nozzle wall

A nozzle of rockets is a window for the combustion chamber to the ambient air. It is subjected to several thermal and mechanical loads acting on the internal wall. So, the nozzle structural behavior has a significant impact on the mission achievement. The aim of this paper is studying a variety of nozzle profiles shape and its influences on structural behavior. Computational fluid dynamics software was applied to investigate the temperature and pressure on the internal wall of the nozzle while observing if there is any change at nozzle ballistic performance or not. Four different convergent profiles had been investigated to study its effect on structural stresses acting on nozzle wall. The results showed body temperature distribution, static pressure and thermal-structural stresses at nozzle wall. Changing the internal profile of the nozzle convergent caused significant change in pressure and temperature loads acting on nozzle wall structure. Conical shape convergent profile produced less stresses at throat section by 19.8% compared to original profile.

Numerical investigation of quenching technique for steel alloy hardening process using twins liquid jets

Quenching is one of the most common phenomena for hardening steel. The present study is focused on investigating the hardening of stainless-steel plates by single as well as twin liquid jets. To this end, flow interaction of twin jets on hot stainless-steel plate and consequent thermal characteristics (especially temperature profile) on the latter has been studied via commercial CFD software, ANSYS FLUENT 18. A steady-state, two- dimensional, and turbulent (standard k-epsilon) model has been developed by taking jet-based Reynolds number ranges between 3800 and 17,000 for the different nozzle to stainless steel plate distance, whereas the latter’s temperature is fixed for 700 °C in the beginning. The results were compared with the help of stagnation heat transfer coefficient, stagnation Nusselt number, and turbulence effect near hot plate for the different nozzle to plate distance. Fluid interaction from twin jets also affects the cooling phenomena strongly, especially at the stagnation point. The local variation of heat transfer at the stagnation point was qualitatively different for different nozzle outlet velocity profiles near the plate.

Performance analysis and optimization of a steam ejector through streamlining of the primary nozzle

A steam ejector uses high-pressure vapor as the power for operating in steam cycles. The ejector geometry and pressure of the motive flow significantly influence its performance. Here, a steam ejector used in a distilled water preparation system for medical injection was numerically studied to improve its performance under insufficient motive source, in the meantime, to guarantee its high efficiency under the designed motive pressure of 6.0 bar. Owing to the temporary insufficiency of the motive pressure of around 4.5 bar in a specific time period, the most convenient and inexpensive approach was to fine-tune the primary nozzle and replace it with no further changes in the ejector structure. Fifteen streamline nozzle profiles were established and the performance effect of the different structures is discussed. The entrainment ratio of the ejector with a streamlined nozzle could reach up to 19.79% and 8.04% higher than the original one under the motive pressures of 4.5 and 5.5 bar, respectively. In addition, their performance was similar under a designed motive pressure of 6.0 bar. The proposed ejector extends the high efficiency operating range of the on-site steam ejector and the results may contribute to the streamline ejector design.

The 2-D plasma thermal jet simulations with substrate interaction

This paper presents plasma thermal jet simulations with substrate interaction. In this work, 2-D plasma thermal jet simulations will be presented using the ANSYS-CFX code with taking into account the interaction fluid-substrate during thermal spraying. Two models of turbulence are used such as the shear stress transport k-? (SST-k-?) and Re-normalization group (RNG-k-?). The governing parameters of the problem under study are the plasma gas power, the nozzle exit temperature and velocity profiles, the plasma jet temperature and velocity fields and the substrate temperature. The experimental and numerical results are presented in order to carry out a comparison between these results. Moreover, transient simulations will be also treated for different x-positions and different values of time. The distribution of temperature of the substrate will be also presented.

Nozzle Flow Influence on Forebody Aerodynamics

In this study, the nozzle flow influence on the forebody aerodynamics has been numerically investigated and validated with experiment. To understand the nozzle flow aerodynamics on the forebody, five different nozzle-exit profiles, which are often encountered in the experiments, are considered one at a time. One flow condition is considered at a nominal freestream Mach number of 4. The CFD simulations are performed using a two-dimensional axisymmetric four-equation transition shear stress transport (SST) turbulence model. The numerical results are compared with the Ludwieg tube Mach 4 experimental data and showed good agreement. The numerical results showed that despite the slight effect on the wall static pressure depending on the nozzle profiles considered, the physical flow phenomena such as shock shape are directly influenced. With the undeveloped nozzle flow profile case, however, significant pressure differences are observed. The distance between the model and the nozzle exit may significantly affect the forebody aerodynamic characteristics, and so, the consideration of the distance between the model and nozzle exit needs to be placed during the model setup to reduce the unwanted uncertainty in the measurement.

Numerical simulation of an over-expanded supersonic and subsonic industrial nozzle flow relevant to flaring system

Flaring in oil and gas production is the controlled burning of unwanted exhaust gases to enhance safety. To improve flare combustion, gas flares are equipped with air nozzles that introduce extra oxygen and improve mixing in the combustion zone. These nozzles are operated in the subsonic, sonic, or supersonic regimes. In this paper, we are concerned with turbulence modeling of the jet flow exiting from a particular convergent–divergent nozzle used in flare systems. That nozzle has convergent and divergent sections that are connected via a throat section with a finite length and constant diameter. The Realizable k – ε and SST k – ω models are used to study the compressible flow within the nozzle. The velocity profiles, turbulent kinetic energy, Mach number profiles, and entrainment rate coefficients predicted by both turbulence models are compared for nozzle pressure ratios in the range 1.18 ≤ NPR ≤ 1.78. It is shown that both turbulence models predict nearly identical flow evolution along the nozzle. When the flow becomes supersonic, the shock surface, and consequently nozzle outlet velocity profiles, predicted by the SST k – ω model deviates slightly from the other model. The differences, however, become negligible a couple of diameters downstream of the nozzle outlet.

Analytical and numerical studies of mass flux dispersed from tapered swirl atomizer with various nozzle cut profiles

Spraying dispersed fluid by swirl atomizer into a main gas stream in order to obtain homogeneous blended flow within a restricted distance from the atomizer position is a significant issue. The dispersal of sprayed fluid mass-flux from the atomizer should be correlated to mass flux distribution of the main flow gas. Consequently, it is essential to control the distribution of liquid mass flux from the injector to match the distribution of main gas flux to attain perfect mixing with identical liquid/gas mass flux ratio all over the pipe. The present study examines the liquid mass flux pattern injected from tapered swirl atomizer having various cut shapes. A mathematical approach to circumferentially evaluate the outlet mass fraction distribution from generalized tapered nozzle cut was analyzed. The derived mass fraction distribution equation is dependent on the flow-angle, the cut-angle, and the arc-angle. A CFD simulation was performed to evaluate the flow angle at the outlet from the nozzle cut. The finding of the present work delivers a guide for researchers and engineers to the preferred injector cut profile to give the best mass flux uniformity. The simulated spray pattern relied on circumferential mass flux at nozzle outlet has been in great coincidence with what depicted by imaging. More studies could be performed to have the most appropriate cut shape of the injector with various flow profiles of the main gas stream.

Theoretical Analysis of the Composition and Thermodynamic Parameters of Products Formed in Combustion of 2,2'-Bis(bicyclo[2.2.1]heptane) in Oxygen

Theoretical analysis was made on the composition and thermodynamic parameters of combustion products of 2,2'-bis(bicyclo[2.2.1]heptane) in oxygen in a wide range of temperatures and pressures. 2,2'-Bis(bicyclo[2.2.1]heptane) can potentially be used as a fuel component in combustion chambers of liquid rocket engines for the first-stage launch vehicles. The average molar mass of approximately 26 amu., obtained for products formed in combustion of 2,2'-bis(bicyclo[2.2.1]heptane) in oxygen is close to similar values for methane in oxygen, whereas its density is more than twice the density of liquid methane. This circumstance makes it possible to hope that the mass of storage tanks can be made smaller if 2,2'-bis(bicyclo[2.2.1]heptane) is used for rockets, compared with the mass of storage tanks containing an equivalent amount of methane. The results obtained can be used to calculate nozzle profiles and combustion chamber parameters of a liquid jet propulsion engines.

Modeling Multiphase Effects in CO2 Compressors at Subcritical Inlet Conditions

An advanced numerical framework to model CO2 compressors over a wide range of subcritical conditions is presented in this paper. Thermodynamic and transport properties are obtained through a table look-up procedure with specialized features for subcritical conditions. Phase change is triggered by the difference between the local values of pressure and saturation pressure, and both vaporization and condensation can be modeled. Rigorous validation of the framework is presented for condensation in high pressure CO2 using test data in a De Laval nozzle. The comparisons between computations and test data include: condensation onset locations, Wilson line, and nozzle pressure profiles as a function of inlet pressures. The framework is applied to the Sandia compressor that has been modeled over broad range of conditions spanning the saturation dome including: near critical inlet conditions (305.4 K, and 7.843 MPa), pure liquid inlet conditions (at 295 K), pure vapor inlet conditions (at 302 K), and two-phase inlet conditions (at 290 K). Multiphase effects ranging from cavitation at the liquid line to condensation at the vapor line have been simulated. The role of real fluid effects in enhancing multiphase effects at elevated temperatures closer to the critical point has been identified. The performance of the compressor has been compared with test data; the computational fluid dynamics (CFD) results also show that the head-flow coefficient curve collapses with relatively minor scatter, similar to the test data, when the flow coefficient is defined on the impeller exit meridional velocity.

Numerical and experimental study of the thermochemical erosion of a graphite nozzle in a hybrid rocket motor with a star grain

Hybrid rocket motors is a promising propulsion system because of its intrinsic advantages over a conventional solid rocket motor and liquid rocket engine. However, serious nozzle erosion is a key problem that prevents hybrid rocket motors from being widely used, especially for propulsion systems with long operating times. In this paper, the erosion of a graphite-based nozzle coupled with a combustion flow field is studied in a hybrid rocket motor with a star grain. As the oxidizer and fuel, 90% hydrogen peroxide and hydroxide-terminated polybutadiene are adopted, respectively. The nozzle erosion was simulated coupled with the flow field in a typical hybrid rocket motor through three-dimensional numerical simulations. The simulations are based on a pure-gas steady numerical model considering turbulence, fuel pyrolysis, oxidizer/fuel reactions, thermal conduction and solid-gas boundary interactions on the fuel and nozzle surfaces. The results indicate that the nozzle erosion is greatly influenced by the inner flow field. The flame near the grain trough is thicker than that near the grain peak. Therefore, the maximum erosion rate (0.042 mm/s) occurs near the nozzle throat corresponding to the grain trough. The OH and H2O contribute 49.8% and 45.5% to the erosion rate, respectively, in this area. Furthermore, 56.6% and 31.9% contributions are made by OH and H2O, respectively, in the area corresponding to the grain peak. The O, CO2 and O2 make much lower contributions to the total erosion. In addition, a firing test is carried out to characterize the graphite nozzle erosion on a full-scale hybrid rocket motor with star grain. The nozzle inner profiles before and after test show that the erosion behavior of the graphite material is strictly related to the fuel shape.

Investigation into Off-Design Performance of a S-CO2 Turbine Based on Concentrated Solar Power

Research on concentrated solar power (CSP) plants has been increasing in recent years. Supercritical carbon dioxide (S-CO2) has been applied to solar power plants due to its promising physical properties. S-CO2 has a relatively low critical temperature of 31.1 °C and owns high density in the supercritical region. Hence, it is a vital working fluid in the application of low temperature heat source and miniature power equipment. Due to the fact that solar power system has a constantly changing heat source according to season and weather, a satisfactory off-design performance is necessary for the turbine in a solar power system. In this work, a S-CO2 radial-inflow turbine based on CSP is designed. A thorough numerical analysis of the turbine is then performed. To investigate the off-design performance of this turbine, three types of nozzle profiles with different leading edge diameters are adopted. Mach number, temperature and pressure distribution are covered to present the off-design effect with different nozzle profiles. Moreover, the relation of output power, mass flow rate and efficiency with different leading edge diameter (LED) are analyzed. Results show that different LED has a vital influence on the aerodynamic characteristics and off-design performance of the S-CO2 turbine based on CSP. In addition, the designed turbine with LED = 4 mm can obtain the highest mass flow rate and output power. While the turbine with LED = 10 mm provides slightly better off-design efficiency for CSP plants.

Supersonic Nozzle Optimization Design with Spline Curves Fitting the Nozzle Profiles

Supersonic nozzle contour optimization design was applied to 0.6m×0.6m continuous transonic wind tunnel to improve flow quality in the test section. The Mach number root mean square deviation with the design value was chosen as optimization target. And the CFD results were verified with experimental results. Cubic spline curves with the optimal interpolating point distribution scheme were used to fit the nozzle contour. Efficient global optimization based on the Gaussian process surrogate model was used to reduce the times of evaluation. Results indicate that, the optimization framework can generate a supersonic nozzle contour with better flow quality and more accurate Mach number and that the optimal Mach number root mean square deviation is 0.001.

Experimental and Computational Exploration of Underexpanded Jets from Conical, Bell and Double Parabolic Nozzles

The flow structure of the jet emanating from supersonic nozzle with different profiles at underexpanded condition were investigated systematically. Experiments were carried out on conical, bell and double parabolic nozzle at Nozzle Pressure Ratios (NPR) of 4.5, 5 and 5.5. For the sake of comparison, the divergent length was the same for all the nozzles. Numerical simulations were also conducted in a two dimensional computational domain taking a density-based solver with RANS equations and SST k-ω turbulence model. The experimental and numerical results matched well all NPRs. The shock cell length, potential core length and supersonic core length at different NPRs were determined from experiments and compared to numerical predictions. These values are also compared to the predicted values based on the equations previously developed by researchers. It is observed that there is not much influence in nozzle profiles in the shock cell length, potential core length and supersonic core length.