Planar Nozzle Research Articles

An evaluation of the hybrid Fokker–Planck-DSMC approach for high-speed rarefied gas flows

The Direct Simulation Monte Carlo (DSMC) method has been widely used for simulations of rarefied gas flows. It has been proven that the numerical solution of the DSMC method converges to the Boltzmann equation, providing a solid physical foundation for high Knudsen numbers. However, many aerospace engineering problems include both low and high-density regions in a single domain, making the DSMC method computationally expensive. Over the past decade, the particle Fokker–Planck (FP) method has been studied as a means to reduce computational costs near the continuum regime. While enhancing efficiency, the FP method loses physical accuracy at high Knudsen numbers. Aiming for universal accuracy and efficiency across the whole range of Knudsen numbers, the hybrid FP-DSMC method has been studied. Nevertheless, consistent comparisons among the DSMC, FP, and hybrid FP-DSMC methods have received limited attention so far. This paper presents a consistent comparative study of the DSMC, FP, and hybrid FP-DSMC methods to assess the accuracy and efficiency of the hybrid FP-DSMC method. The hybrid FP-DSMC solver is developed based on the open-source SPARTA framework. The benchmark problems include supersonic flow in a planar nozzle, hypersonic flow around a cylinder, and hypersonic flow around a THAAD-like missile. The results demonstrate that the hybrid FP-DSMC method can be more efficient than the DSMC method while being more accurate than the FP method. The speed-up achieved by the FP-DSMC method ranged from 1.5 to 14 times compared to the converged DSMC simulation.

Numerical investigation on secondary injection and thrust vector control in a planar double divergent nozzle

In this work, the performance of secondary injection thrust vector control of an altitude adaptive planar double divergent supersonic nozzle is numerically investigated. The compressible turbulent flow is solved using the kT−kL−ω transition-sensitive eddy-viscosity model. An analytical model to predict the separation distance and penetration height due to secondary fluid injection is developed based on the blunt-body theory, and it shows good agreement with the numerical estimation. The computational results indicate that injection pressure, injector location and injection angle significantly impact the thrust vector control performance. The core flow is disrupted by the momentum injection from the secondary fluid, causing the flow field structure to become asymmetrical. The wall pressure imbalance between the upper and lower nozzle increases as the secondary jet pressure elevates. Further, the thrust vectoring amplification factor is improved when the injector is placed downstream near the outlet since the shock reflection is circumvented. Indeed, that resulted in the generation of a large lateral thrust force. Most importantly, for a high injector slot angle, the primary downstream vortex disappears, and a strong secondary upstream vortex is generated, which shifts the primary upstream vortex opposite to the core flow, subsequently the shock separation is advanced. In addition, a secondary injector fitted near the exit with high inclination angles and injection pressure generated a lateral thrust of 20%.

Modeling of separation speed in thick plate cutting with a high-power fiber laser

Most laser cutting operations rely on the operator’s experience and reference data tables to complete the material separation work. This traditional method is time-consuming and labor-intensive, seriously restricting the progress of laser cutting technology toward intelligence and automation. To obtain the material separation speed quickly, this work explores a method to establish a mathematical model of the separation speed by theoretical derivation. Firstly, the energy absorption and consumption in laser cutting of thick plates are analyzed in detail. The laser power density, oxidation reaction power density, and energy consumption per unit volume of material during heat conduction, melting, and heating are modeled, respectively. On this basis, the criterion of separation speed is defined. The theoretical model of separation speed is established through theoretical derivation. Secondly, the effects of laser power, gas pressure, focal plane position, material thickness, and nozzle diameter on the separation speed are investigated. A comparison between the theoretical and experimental values of the separation speed reveals obvious differences in both; however, there are consistent trends in their changes with the process parameters within a certain range. Thirdly, the differences between the theoretical and experimental values of the separation speed are analyzed in detail. This work helps to deepen the understanding of the laser cutting process and improve the laser cutting efficiency.

Comparative analysis of 2D simulations and isentropic equations for compressible flow in experimental nozzles

Experimental studies for supersonic airflow in different supersonic nozzle geometries are recurrent, and the turbulence of the flow can be reproduced with the CFD tool by applying the RANS model and suitable turbulence models. The objective of this investigation is to carry out a comparative analysis of 2D numerical simulation curves for viscous flow with averaged data against equation curves for quasi-one-dimensional isentropic flow, for three experimental supersonic nozzle geometries that are used in the laboratory, for the flow condition without the presence of shock waves in the divergent. For the numerical simulations, three computational domains were discretized with structured grids, the Spalart-Allmaras turbulence model was used, and the Sutherland's law equation was used for the viscosity as a function of temperature. The results of the curve trajectories for Mach number, pressure and temperature obtained with averaged data from the 2D simulations are close to the curves of the analytical and empirical equations for isentropic flow. It is concluded that the numerical error of the total temperature for the planar nozzle with 𝛼𝛼 = 11.01° and NPR = 8.945 reports 0.008%; for the conical nozzle with 𝛼𝛼 = 15° and NPR = 14.925 it reports 1%; and, finally, for the conical nozzle with 𝛼𝛼 = 4.783° and NPR = 7, it reports 0.04%.

Gas‐kinetic unified algorithm for two‐dimensional planar and axisymmetric nozzle flows

SummaryFor high‐altitude nozzle or micronozzle flows and other gas flows in the slip or transition flow regime, how to solve it reliably has always been a difficult problem. In this paper, a unified gas kinetic expression is presented to describe the two‐dimensional planar and the axisymmetric nozzle flows, and the computable modeling of the Boltzmann equation is developed at the first time for the nozzle flows by introducing the gas molecular collision relaxing parameter and the local equilibrium distribution function integrated in the unified expression with the flow state controlling parameter, including the macroscopic flow variables, the gas viscosity transport coefficient, the thermodynamic effect, the molecular power law, and molecular models, covering a full spectrum of flow regimes. The boundary conditions involved in the nozzle flow have been mathematically expressed at the level of the gas molecular velocity distribution function, and the model equations have been solved uniformly by the gas‐kinetic unified algorithm (GKUA) for rarefied transition to continuum flows. The presented simulated results from the test cases show promising of simulating gas flow from transitional flow to continuum flow in the same flow domain, especially for those flow involving low‐speed gas flow in rarefied regime, which is otherwise practically difficult using direct simulation Monte Carlo (DSMC).

Numerička analiza evolucije udarnog voza u planarnim mlaznicama sa dužinom grla

In the present investigation, the behavior of compressible flow in planar nozzles with throat length is analyzed to determine the flow velocity range and pressure fluctuations in the throat section. The flow field was simulated in 2D computational domains with the ANSYS-Fluent R16.2 code. The RANS model was applied for steady-state flow. The governing equations used are the conservation of mass, momentum, energy, and the ideal gas equation of state. The Sutherland equation was used for the viscosity as a function of temperature. The Spalart-Allmaras turbulence model was used to model the flow turbulence, which was validated with experimental pressure data. In the throat section, for the central region of the flow, as the throat length increases, the flow fluctuates and decelerates. Oblique shock waves are produced, and a shock train region is formed. The flow velocity is transonic and is in the Mach number range of 1 to 1.2, and the static pressure is in the range of 0.37 to 0.52. Therefore, as a result of flow fluctuations, throat length has a significant effect on flow development.

Numerical analysis of the flow field in a planar nozzle for different divergent angles

In the present work, the flow field is analysed for Mach number, pressure and temperature in 2D computational domains for a planar nozzle of symmetrical geometry as used in the experimental tests for cold (air) flow. The study has been considered for three mean angles of the divergent section: α = 9°, α = 11.01° and α = 13°, and for four pressure ratios: NPR = 2.412, NPR = 3.413, NPR = 5.423 and NPR = 8.78. For the numerical simulation of the turbulence in the presence of shock waves, the RANS model, the Sutherland equation and the Spalart-Allmaras turbulence model were used in the ANSYS-Fluent R16.2 code. The results obtained show fluctuations at the intersections of the internal shocks in the divergent, and the fluctuation decreases as the angle of the divergent increases. For NPR = 3.413, NPR = 5.423 and NPR = 8.78, the Mach number at the nozzle exit is the same, where for α = 11.01° Mach 2.00 was obtained, and based on this reference, for α = 13° there is an increase in velocity of 4.15% and for α = 9° a decrease in velocity of 3.78%. The lowest pressure and temperature drop occurs at the nozzle outlet for α = 13°.

Thermal Performance Improvement of Modified Hemispherical Cavity Receiver with Air Curtain

Heat losses from solar cavity receivers degrade the efficiency of solar parabolic dish collector system. Specifically, increased convection losses emulate a significant contribution in decreasing the performance of the modified solar cavity receiver and hence, reducing these convection losses has become a matter of great concern. The Air curtain plays a crucial role in minimizing the convection losses. This work proposes an air curtain-based modified cavity receiver wherein a plane nozzle is placed on the face of receiver to produce air curtain effect. Air curtain will prevent hot air from escaping the modified cavity receiver and increase the stagnation zone inside it to reduce natural convection on the surfaces. Numerical analyses are performed considering different air velocities and receiver orientations to evaluate the effect of air curtains on the convection losses. The impact of plane air nozzle parameters like outlet temperature, inclination, and outlet velocity of the nozzle on convection losses are shown and these parameters’ optimal value is evaluated. Our results state that the air curtain attached to the modified solar cavity receiver significantly improves performance by reducing the convection losses.

Liquid jet stability through elastic planar nozzles

Liquid jet stability through elastic planar nozzles

Computational Investigation of Effects of Side-Injection Geometry on Thrust-Vectoring Performance in a Fuel-Injected Dual Throat Nozzle

Dual-throat Nozzle (DTN) is known as one of the most effective approaches of fluidic thrust-vectoring. It is gradually flourishing into a promising technology to implement supersonic and hypersonic thrust-vector control in aircrafts. The main objective of the present study is numerical investigation of the effects of secondary injection geometry on the performance of a fuel-injected planar dual throat thrust-vectoring nozzle. The main contributions of the study is to consider slot and circular geometries as injector cross-sections for injecting four different fuels; moreover, the impact of center-to-center distance of injection holes for circular injector is examined. Three-dimensional compressible reacting simulations have been conducted in order to resolve the flowfield in a dual throat nozzle with pressure ratio of 4.0. Favre-averaged momentum, energy and species equations are solved along with the standard k- ε model for the turbulence closure, and the eddy dissipation model (EDM) for the combustion modelling. Second-order upwind numerical scheme is employed to discretize and solve governing equations. Different assessment parameters such as discharge coefficient, thrust ratio, thrust-vector angle and thrust-vectoring efficiency are invoked to analyze the nozzle performance. Computationally predicted data are agreed well with experimental measurements of previous studies. Results reveal that a maximum vector angle of 17.1 degrees is achieved via slot injection of methane fuel at a secondary injection rate equal to 9% of primary flow rate. Slot injection is performing better in terms of discharge coefficient, thrust-vector angle and thrust-vectoring efficiency, whereas circular injection provides higher thrust ratio. At 2% secondary injection for methane fuel, vector angle and vectoring efficiency obtained by slot injector is 8% and 34% higher than the circular injector, respectively. Findings suggest that light fuels offer higher thrust ratio, vector angle and vectoring efficiency, while heavy fuels have better discharge coefficient. Increasing center-to-center distance of injector holes improves thrust ratio, while having a negative effect on discharge coefficient, vector angle and vectoring efficiency. A comparison between fuel injectant of current study and inert injectant in the previous studies indicates that fuel reaction could exhibit substantial positive effects on vectoring performance. Secondary-to-primary momentum flux ratio is found to play a crucial role in nozzle performance.

THERMO-PNEUMATIC MICROPUMP FOR DRUG DELIVERY APPLICATIONS

Micropumps constitute an essential part of precise delivery and directional volume control of fluid in a microfluidic system. In biomedical applications, micropump is widely used especially in drug delivery, biological fluid transmission, organic analysis, liquid measurement, and many more. In this paper, the concept and design structure hence fabrication of the Thermo pneumatic micropump prototype are explained. The experimental measurement of the micropump employing planar diffuser nozzle in transmits fluid is also presented. Thermopneumatic micropump is comprised of three different components which are the microheater on the bottom, the flexible thin membrane that acts as an actuator, and the planar diffuser nozzle on the top to channel the fluidic. These three components were fabricated separately due to the different materials and techniques used in each component. Finally, the whole micropump system was integrated using an anodic bonding technique. Bulk micromachining technique was used to fabricated the chamber and thin-film membrane, surface micromachining technique for the microheater while replica molding technique was used for the planar diffuser nozzle. The whole diameter size for the micropump was 25 x 20 x 1.6 mm respectively. The microscope image recorded video and data was used during the experimental measurement, to observed and calculate the flow rate of meniscus motion flow in the outlet tube of the micropump. At the end of the experiment, the flow rate range of the micropump measure was approximately 770pL to 12.5nL, when the output of 2-12Vdc was applied to the microheater. This flow rate range is very suitable for drug delivery applications.

Geometry effects on flow characteristics of micro-scale planar nozzles

A numerical investigation of geometry effects on the flow characteristics associated with converging-diverging 2D planar micronozzles is reported. The classical N–S with linear slip model, DSMC method, and a hybrid N–S/DSMC based on the continuum breakdown concept are employed for the simulations. The various methods adopted are validated with available experimental data. The study addresses the issue of heterogeneous findings on optimized half divergence angle recommended by previous studies. The analysis is conducted for various throat dimensions (2–200 µm thoat height), divergence angles (5∘–30∘), and divergence length. The performance and flow characteristics are compared at two distinct operating conditions, i.e. when the flow is mostly subsonic and supersonic in the divergent section. Results show an optimum divergence angle and length, maximizing the performance for a specific operating condition and nozzle size. Literature data suggest various divergence angles for optimum performance. This is due to the differences in operating conditions and the size of the micronozzles used. The current study shows that differences in flow behavior are mainly due to the pressure difference across the nozzle. When the micronozzle is operating under low-pressure differences, the flow is primarily subsonic in the divergent section. However, it accelerates due to the effect created by the growing thick boundary layer. The flow at higher pressure differences is characterized by clear flow separation and the occupation of the separated flow to a considerable portion of the divergent section. The separated phenomenon becomes less pronounced as the pressure difference and nozzle size decreases. As the nozzle size decreases to the nanoscale, Re is very low, and the subsonic layer fully occupies the divergent nozzle section even at very high-pressure differences. The results show that the performance is significantly influenced by the wall thermal conditions. The study highlights the differences in flow behaviour between micro and nano-scale nozzles at various operating conditions. Based on numerical data obtained in this present work, a new correlation is proposed to predict thrust per unit width for micronozzles.

Hybrid Double-Divergent Nozzle as a Novel Alternative for Future Rocket Engines

The efficiency of a rocket engine is dependent on altitude adaptability of its nozzle. In this context, double-divergent nozzles (DDNs) have drawn immense interest. The DDNs explored till now comprise of two nozzles of the same contour such as double conical and dual bell. In such DDNs, although the issue of altitude compensation may be partially addressed, the losses associated with the particular type of nozzle contour may get aggravated. This work proposes a novel concept of a hybrid double-divergent rocket nozzle (HDDN) as an alternative to mitigate certain undesirable characteristics of fluid flow through the nozzle. Two types of HDDNs, having extensions of planar minimum length nozzle and planar thrust-optimized parabolic, have been studied. A planar double conical nozzle is taken as reference. The flow analysis is performed using commercially available software ANSYS Fluent for various nozzle pressure ratios. The realizable turbulence model is used for closing the Reynolds-averaged Navier–Stokes equations. The side loads, moments, coefficient of thrust (), and thrust-to-weight ratio have been investigated. At the highest nozzle pressure ratio, the conical thrust-optimized parabolic HDDN exhibits an increase of by 4% and an increase of thrust-to-weight ratio by about 18% vis-à-vis the reference design.

On the unsteady dynamics of partially shrouded compressible jets

We experimentally investigate a partially shrouded sonic jet (a sonic free-jet shielded by a solid wall-extension on one side) exiting from a planar nozzle at two different nozzle pressure ratio ($\zeta=4$ and $5$). We experimentally show that the inherent jet unsteadiness from the shock-induced flow separation on the wall and the emitted noise in the far-field is strongly coupled through a series of experiments like high-speed schlieren, wall-static pressure, unsteady pressure spectra, and microphone measurements. The partially shrouded jet's lateral free expansion is also identified to be complicated, three-dimensional, and the produced noise is directional. The emitted acoustic pulses from the flapping-jet, the radiated noise from the shock-induced separation on the wall, and the shock-shear layer interaction on the other side of the wall are responsible for the generated acoustic disturbances. The non-uniform aeroacoustic forcing on the top and bottom portion of the partially wall-bounded jet shear layer leads to a self-sustained jet oscillation and a discrete sound emission. The vital features are identified through the proper orthogonal decomposition of high-speed schlieren images and supplemented by other measurements.

Large-Eddy Simulation of Compressible Flow in Asymmetric and Symmetric Planar Nozzles

Large-eddy simulations of supersonic, turbulent flow in asymmetric and symmetric planar nozzles are carried out using high-order finite difference schemes and a large-eddy simulation approach based on explicit filtering. The inflow to the nozzles is from supersonic, fully developed turbulent channel flows at and 360 with centerline Mach number 1.2. The combined effects of expansion and acceleration of the flow in this geometry result in reductions of mean pressure, density, and temperature as well as a reduction of Reynolds stresses. The asymmetry of the nozzle leads to notable differences in the aforementioned effects near the straight and the curved walls. It is shown that the decay in Reynolds stresses is more near the curved wall than near the straight wall of asymmetric nozzle, and it is nearly the same near both walls of the symmetric nozzle. Effects of longitudinal streamline curvature are found to be localized near the curved wall of the asymmetric nozzle and are quantified. The aforementioned effects of acceleration, expansion, and streamline curvature are found to be similar in the flow cases with two different Reynolds numbers, although with increasing Reynolds number, subtle differences in these effects are found.

Visualization of flow through planar double divergent nozzles by computational method

The double divergent nozzle is a type of altitude adaptive nozzle. The double divergent nozzle does not have any mechanical parts, leading to reduced nozzle weight and requires minimum modifications to the existing launch system. The planar double divergent nozzle is a type of double divergent nozzle, having a rectangular cross section. The present study involved the numerical analyses of a single divergent nozzle, and five double divergent nozzle geometries. The flow is simulated on five different double divergent sections having the same area ratio, but with different inflection angles/extension length. All geometries are studied with similar boundary conditions. Flow pattern, wall static pressure, side load, and specific impulse are studied for pressure ratios ranging from 1.5 to 8.5 with cold air as working fluid. The results obtained are compared with a single divergent nozzle having the same area ratio. It is inferred that the flow pattern, side load, and specific impulse of a double divergent nozzle have a strong dependence on the inflection angle.

Experimental characterization of nozzle flow expansions of siloxane MM for ORC turbines applications

This paper reports extensive experimental results characterizing the supersonic expansion of organic vapor MM (hexamethyldisiloxane, C6H18OSi2) in conditions representative of actual Organic Rankine Cycle turbine operation, in the close proximity of the liquid-vapor saturation curve. Experiments were conducted on the Test Rig for Organic VApors, at the Laboratory of Compressible fluid dynamics for Renewable Energy Applications of Politecnico di Milano. A planar nozzle featuring a design exit Mach number of 1.6 was characterized by measuring total pressure, total temperature, static pressures along the nozzle axis and by schlieren visualizations. The non-ideal influence of inlet total conditions on nozzle expansions was verified by gathering data exhibiting total compressibility factor ZT ranging from 0.39 (strongly non-ideal) to 0.98 (almost ideal conditions). Pressure ratio measured at the lowest ZT exceeded by 10%–20% the one at highest ZT along the whole nozzle. An extensive experimental dataset was analyzed to assess the influence of both total compressibility factor ZT and total fundamental derivative of gasdynamics ΓT on the non-dimensional pressure distribution along the nozzle axis. It was investigated whether one parameter only can univocally identify a non-dimensional nozzle expansion. Significant validation data for simulation codes and design tools are provided for MM and for siloxanes in general.

On the fluidic behavior of an over-expanded planar plug nozzle under lateral confinement

The present work aims to study the fluidic behavior on lateral confinement by placing sidewalls on the planar plug nozzle through experiments. This study involves two cases of nozzle pressure ratio (NPR = 3, 6), which correspond to over-expanded nozzle operating conditions. Steady-state pressure measurements, together with schlieren and surface oil flow visualization, reveal the presence of over-expansion shock and subsequent interaction and modification of the flow field on the plug surface. The flow remains attached to the plug surface for NPR = 3; whereas for NPR = 6, a separated flow field with a recirculation bubble is observed. Spectral analysis of the unsteady pressure signals illustrates a clear difference between the attached and the separated flow. Besides, other flow features with a distinct temporal mode associated with and without lateral confinement are observed. The absence of lateral confinement reduces the intensity of low-frequency unsteadiness; however, on the contrary, the interaction region is relatively reduced under lateral confinement.

Analysis of shock-wave unsteadiness in conical supersonic nozzles

Large Eddy Simulations (LES) of an over-expanded conical nozzle are performed to study the complex interaction between the turbulent boundary layer, the internal shock wave and the separated mixing layer. Both wall-modeled (WM) and wall-resolved (WR) LES strategies are employed to investigate the three-dimensional unsteady aspect of shock-wave boundary-layer interaction (SWBLI). First, a comparison of flow behavior in a conical nozzle against an equivalent planar nozzle is made. It was found that whilst both configurations may share common flow features such as large-scale turbulent structures and shock-wave patterns, they show contrasts on the symmetry of the flow and the shock dynamics. In particular, the latter was found to have a shorter excursion length in conical nozzle compared to the planar one. The strong adverse pressure gradient tends to reduce the amplitude of the shock movements in conical flows. Additionally, the dynamic mode decomposition (DMD) analysis showed the existence of two unsteady modes; the non-helical modes which are low-frequency based, appearing mainly in the streamwise forces and the helical modes which are high frequency dominated modes and are largely responsible for the side side-loads generation.

The Thermal State of a Packet of Cooled Microrocket Gas-Dynamic Lasers

A complex physicomathematical model of heat transfer in packets of cooled microrocket gas-dynamic planar nozzles used for the pumping of gas-dynamic lasers is presented. A small size (~15 mm), due to which they are quickly heated up and require intense heat removal, is a specific feature of such rocket nozzles. The complex physicomathematical model of heat transfer and gas dynamics, as well as heating and cooling, is new, since all the physical processes are coupled at the boundary of a multiply connected domain. The cooling of high-temperature gas-dynamic lasers is one of the main problems in designing them. Numerical results for gas temperatures, the heat transfer coefficient, and cooler temperatures, as well as temperatures in the critical section of the nozzle, are obtained.