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Micro-nozzles are essential for enabling precise satellite attitude control and orbital maneuvers. Accurate prediction of performance parameters, including thrust and specific impulse, is critical, necessitating careful design of these nozzles. Given the high Knudsen numbers associated with micro-nozzle flows, rarefied gas dynamics often dominate, and conventional computational fluid dynamics (CFD) methods fail to capture accurate flow expansion behavior. The Direct Simulation Monte Carlo (DSMC) method, developed by Bird, is widely used for modeling rarefied flows; however, it has been primarily implemented on platforms like OpenFOAM and FORTRAN, with limited exploration in MATLAB. This study presents the development of a viscosity-based DSMC (μDSMC) simulation framework in MATLAB for analyzing rarefied gas expansion through micro-nozzles. Key boundary conditions, including upstream and downstream pressure conditions and thermal wall treatments with diffuse reflection, are incorporated into the code. The μDSMC results are validated against traditional DSMC outcomes, showing strong agreement. Grid convergence studies indicate that the radial grid size must be less than one-third of the mean free path, with a more relaxed requirement on axial grid size. Flow characteristics within micro-nozzles are evaluated across varying ambient pressures and gas species in terms of the back pressure ratio, effective exit flow ratio, and exit flow velocity. Studies indicated that a minimum back pressure ratio is required, beyond which the effective nozzle flow expansion is achieved. Parametric analysis further suggests that gases with lower molecular weights are preferable for achieving optimal expansion in micro-nozzles under low ambient pressures. [ABSTRACT FROM AUTHOR]

Micro-nozzles are essential for enabling precise satellite attitude control and orbital maneuvers. Accurate prediction of performance parameters, including thrust and specific impulse, is critical, necessitating careful design of these nozzles. Given the high Knudsen numbers associated with micro-nozzle flows, rarefied gas dynamics often dominate, and conventional computational fluid dynamics (CFD) methods fail to capture accurate flow expansion behavior. The Direct Simulation Monte Carlo (DSMC) method, developed by Bird, is widely used for modeling rarefied flows; however, it has been primarily implemented on platforms like OpenFOAM and FORTRAN, with limited exploration in MATLAB. This study presents the development of a viscosity-based DSMC (μDSMC) simulation framework in MATLAB for analyzing rarefied gas expansion through micro-nozzles. Key boundary conditions, including upstream and downstream pressure conditions and thermal wall treatments with diffuse reflection, are incorporated into the code. The μDSMC results are validated against traditional DSMC outcomes, showing strong agreement. Grid convergence studies indicate that the radial grid size must be less than one-third of the mean free path, with a more relaxed requirement on axial grid size. Flow characteristics within micro-nozzles are evaluated across varying ambient pressures and gas species in terms of the back pressure ratio, effective exit flow ratio, and exit flow velocity. Studies indicated that a minimum back pressure ratio is required, beyond which the effective nozzle flow expansion is achieved. Parametric analysis further suggests that gases with lower molecular weights are preferable for achieving optimal expansion in micro-nozzles under low ambient pressures.

Micro-nozzles play a critical role in various applications, such as micro-/nano-satellites in aerospace and heat dissipation and cooling in microelectronic systems (MEMS). The flows inside micro-nozzles can experience both continuum and rarefied flow due to their small size. In this research, we explore the optimal geometry configuration of micro-nozzles to achieve comprehensive performance and size, as well as background pressure compensation. Using classical computational fluid dynamics (CFD) and direct simulation Monte Carlo methods (DSMC), we investigate the effects of the expansion ratio, cross-profile shape, and plug on the performance of micro-nozzles operating over a wide range of pressures (0. 5 − 100 kPa). The results reveal that micro-nozzle performance is influenced by the interplay between flow expansion and viscous loss induced by the subsonic layer next to the micro-nozzle wall. The findings show that micro-nozzle performance improves with increasing expansion ratio in slip and continuum flow regimes, but decreases in the transition flow regime. Additionally, the results indicate that the axisymmetric micro-nozzle (with a circular cross-profile) outperforms the linear micro-nozzle (with a rectangular cross-profile) in terms of both performance and size when subject to the same conditions, making it the recommended choice for practical applications. We also find that plugs designed at the throat decrease performance, but increase stability under diverse background pressures. This study provides valuable insights for the design of high-efficiency micro-nozzles in applications such as nanosats and MEMS heat dissipation units. • Geometry configuration effects on micro-nozzle performance are studied numerically. • Viscous loss and flow expansion degree are pivotal for micro-nozzle performance. • Low expansion ratio micro-nozzle is better for comprehensive performance and size. • The axisymmetric micro-nozzle surpasses the linear micro-nozzle. • The plug micro-nozzle performs well in variable pressure ambient. [ABSTRACT FROM AUTHOR]

The micro-nozzle allows small spacecraft to realize the orbital maneuvering and precise station-keeping. Due to the rarefaction effect of the gas flow in micro-nozzles, the velocity-slip and temperature-jump exists near inner wall, and thus, affecting the operating characteristics of micro-nozzles. Various gas-solid theories and models have been developed to describe the velocity slip and temperature jump in computational fluid dynamics (CFD). In this study, numerical simulations of a micro-nozzle with five classical slip boundary models, which are based on the Maxwell scattering and Langmuir adsorption, are conducted to analyze the applicability of these models through comparing with the results obtained by direct simulated Monte Carlo (DSMC) method. The results show that the inlet pressure dramatically influences the flow regime of the micro-nozzle. The lower the inlet pressure, the higher the influence of the rarefaction effect. The results also indicate that the Langmuir slip model can accurately simulate the flow field in the transition regime. However, the modified Maxwell and Langmuir models proposed by Agrawal et al. (2008) and Le et al. (2012), respectively, are valid in the slip regime. • Applicability of five slip models in micro-nozzle were validated. • The results obtained by various slip models were compared with that of DSMC. • The effects of slip and jump upon the behavior of micro-nozzle flow were analyzed. • Two slip models were recommended for the slip regime. [ABSTRACT FROM AUTHOR]

Featured Application: Surface modification of mini- and micro-nozzles for dispensing systems. Miniature products and components must be surface treated to improve their wear resistance and corrosion toughness. Among various processes, low-temperature plasma nitriding was employed to harden the outer and inner surfaces of micro-nozzles and to strengthen the micro-springs. A table-top nitriding system was developed even for simultaneous treatment of nozzles and springs. A single AISI316 micro-nozzle was nitrided at 673 K for 7.2 ks to have a surface hardness of 2000 HV0.02 and nitrogen solute content up to 10 mass%. In particular, the inner and outer surfaces of a micro-nozzle outlet were uniformly nitrided. In addition, the surface contact angle increased from 40° for bare stainless steels to 104° only by low-temperature plasma nitriding. A stack of micro-nozzles was simultaneously nitrided for mass production. Micro-springs were also nitrided to improve their stiffness for medical application. [ABSTRACT FROM AUTHOR]

Graphical abstract The contribution of effective forces acting on the bubble near detachment moment on 450 mm nozzle and 0.5 ml/min gas flow rate. Highlights • This research investigated bubble formation on submerged micrometer-sized nozzles in Newtonian/non-Newtonian fluids. • Bubble volume obeys a U-shaped trend with increasing gas flow rate in both Newtonian/non-Newtonian fluids. • It was found that necking process is not observable in non-Newtonian fluids and it is predicted that happen somewhere inside the nozzle. • It was observed that the micrometer-sized scale of the nozzles significantly influences the bubble formation process based on the "cube-squared law". Abstract This research presents detailed formation of air bubbles on different submerged micrometer-sized nozzles in Newtonian and non-Newtonian fluids. An experimental study is performed using the high-speed camera on three nozzles with diameters of 150, 450, and 600 μm under relatively low gas flow rate conditions (0.1∼1 ml/min). Distilled water and various concentrations of Carboxymethyl cellulose (CMC) aqueous solutions are utilized as the continuous phase for each type of fluid. Different characteristics of the bubble formation such as volume change, frequency, height, maximum width, and instantaneous contact angle are obtained using an image processing technique and the Young-Laplace equation. Effect of different parameters including gas flow rate, nozzle diameter, concentration, and rheological properties of the continuous phases are investigated. Also, a detailed dynamic force analysis is performed to survey the role of fluid properties on the effective forces. The force balance reveals that the surface tension force is dominant in the smallest orifice, while its influence decreases as the orifice diameter increases. Moreover, it was observed that the drag and hydrostatic forces have relatively noticeable contributions in this low gas flow rates. Furthermore, results show that under the conditions of this research, the characteristics of the bubble are weakly dependent on the gas flow rate. On the other hand, the concentration of the CMC and the rheological behavior of the non-Newtonian fluids so-obtained have a significant influence on bubble formation process. Also, observations made and predictions done as to the bubble's curvature (say, based on Young-Laplace equation) suggest that the necking phenomenon does not exhibit itself at the top of the nozzle in non-Newtonian liquids flowing through micron-sized nozzles. [ABSTRACT FROM AUTHOR]

Abstract Micro-abrasive jet machining (AJM) is an advanced subtractive machining technology with ample opportunities to form regular micro-patterns on freeform surfaces. AJM removes material mainly through erosion and abrasion, which transform kinetic energy to fracture and deform substrates. The kinetic energy of a solid particle is tightly connected to its velocity, which is the most significant source of error in precise prediction of a machined feature. The present study involves both theoretical analysis and two-dimensional axisymmetric numerical simulation of particle velocity fields at the lower end of the micro-scale. The developed model represents the finest particles in a cylindrical nozzle down to an inner diameter of 100 μm. The computed results agree well with the experimental data. It is shown that, due to viscous friction, such nozzles are significantly less efficient in terms of particle saturation with kinetic energy. The study highlights the effects of nozzle diameter and length, air pressure, particle size and density on particle velocity development through the jet field. Finally, practical recommendations and multiple regression models of maximum particle velocity, location from the nozzle exit and simplex velocity profile approximation are offered for management of particle kinetic energy. Graphical abstract Unlabelled Image Highlights • Miniaturisation of nozzle diameter below 1 mm leads to decrease of air velocity • Particle's velocity increment after the end of potential core is insignificant • Drag/Resistance Transition occurs on distance from 10 to 20 of nozzle diameters • Drag/Resistance force acting on central and peripheral particles are comparable [ABSTRACT FROM AUTHOR]

Miniature products and components must be surface treated to improve their wear resistance and corrosion toughness. Among various processes, low-temperature plasma nitriding was employed to harden the outer and inner surfaces of micro-nozzles and to strengthen the micro-springs. A table-top nitriding system was developed even for simultaneous treatment of nozzles and springs. A single AISI316 micro-nozzle was nitrided at 673 K for 7.2 ks to have a surface hardness of 2000 HV0.02 and nitrogen solute content up to 10 mass%. In particular, the inner and outer surfaces of a micro-nozzle outlet were uniformly nitrided. In addition, the surface contact angle increased from 40° for bare stainless steels to 104° only by low-temperature plasma nitriding. A stack of micro-nozzles was simultaneously nitrided for mass production. Micro-springs were also nitrided to improve their stiffness for medical application.

To improve the jetting performance of liquid metals, an electromagnetic micro-jetting (EMJ) valve that realizes drop-on-demand (DOD) jetting while not involving any valve core or moving parts was designed. The influence of the lead angle of the nozzle on the jetting of liquid metal gallium (Ga) was investigated. It was found that the Lorentz force component parallel to the nozzle that jets the electrified liquid Ga is always larger than its internal friction; thus, jet can be generated with any lead angle but with different kinetic energies. Experimental results show that the mass of the jetting liquid, the jetting distance, the initial velocity of the jet, and the resulting kinetic energy of the jet increase first and then decrease. When the lead angle is 90°, the mass of the jetting liquid and the kinetic energy are at their maximum. When the angle is 80°, the initial velocity achieves its maximum, with a calculated value of 0.042 m/s. Moreover, very close and comparatively high kinetic energies are obtained at 80° and 90°, indicating that angles in between this range can produce a preferable performance. This work provides an important theoretical basis for the design of the EMJ valve, and may promote the development and application of micro electromagnetic jetting technology. [ABSTRACT FROM AUTHOR]

Machined surface roughness has significant effects on the performance of micro-nozzles, which are fabricated by micro-machining. Machining process parameters greatly affect surface roughness, for that the manufacturers need to obtain optimal operating parameters. In this paper, machining parameters are optimized for micro-machining nozzle based on the characteristics of surface roughness. First, roughness model of nozzle milling with ball-end mill is presented. A case of nozzle surface is then given to verify the reliability of the roughness model proposed. Second, influences of surface roughness on nozzle average outlet velocity and thrust efficiency are investigated through computational fluid dynamics (CFD) analysis. It is found that vortical flow generates gradually with increasing of surface roughness, which leads to wasted energy increasing. When roughness value reaches a certain threshold, vortical flow is formed, which significantly reduces nozzle performances of velocity and thrust efficiency. Finally, micro-orthogonal machining experiments are performed. It is shown that the remarkable factor influencing the surface roughness of micro-nozzle is axial depth of cut. [ABSTRACT FROM AUTHOR]

In the last 25 years a number of Micro Electro Mechanical System (MEMS) were developed. These MEMS devices not only include the mechanical systems but also the fluids. Knowledge about fluid flows in this scale is not as mature as the mechanical properties of the MEMS. As their dimensions are between 1 mm and 1 micron, gas flows related with the MEMS devices have high Knudsen numbers (Kn) similar to high atmosphere flights. If Kn is higher than 0.1, instead of the classical continuum based Euler or Navier-Stokes (N-S) equations, higher order continuum based equations like Burnett equations or molecular models like DSMC should be used. This is due to the departure from local thermodynamic equilibrium with increasing Kn number. First velocity slip and temperature jump are formed on the boundaries. Next, low order constitutive equations are lost their validity because relations both between shear stress and velocity gradient and heat conduction and temperature gradient are not linear any more. Additionally the ratio of flow surface area to flow volume is dramatically increased in micro gas flow conditions. So surface forces dominate the volume forces. Consequently, compressibility and viscous heating (dissipation) effects become more important in micro gas flows in addition to rarefaction effects. Even in low Mach numbers, large density and temperature gradients prevail. It is found that a micro scale gas flow can behave differently from the large-scale one, which is generally studied with hydrodynamic models. Our application of DSMC starts with the division of the computational domain into smaller cells. Linear dimensions of these cells are of the same order as the mean-free-path (λ) of the gas. A group of physical gas molecules are represented by one representative molecule that called DSMC molecule in this study. Every DSMC molecule carries position, velocity, cell number and if applicable internal energy information on it. In DSMC method molecule movements and collisions are separated from each other. As a first step, molecules move according to their velocities and initial conditions. Their velocities, positions and cell numbers are updated. In the collision step, stochastic approach is used and molecule velocities are updated according to the collision model chosen. Next step is the calculation of the macroscopic gas flow properties for each cell from the microscopic molecule information. For steady flows, time averaging is used for the calculation of macroscopic properties. DSMC method is computationally expensive. To shorten the computation time new approaches are needed.. Generally molecule movements are traced cell-by-cell in DSMC solvers both in structural and unstructured meshes. At each time step DSMC molecules move to a new position. Then each DSMC molecule is checked whether they left the cell or not. If it is determined that DSMC molecules left the cell then which cell they stopped is calculated. To do this either all the neighbor cells should be searched or which edge molecule left the origin cell should be determined. And then new cell is found. This procedure requires many mathematical calculations and time. If non-rectangular physical flow geometry can be converted a rectangular computational domain, then it is possible to calculate the DSMC molecule cell information in a very short time with a very simple mathematical operation. Additionally current DSMC solvers use complex and time consuming indexing mechanism to realize molecule collisions. All the molecules put in order 1-Dimensional arrays at the end of each time step. Molecule collision partners are selected from this array, which are required to be in the same cell. In this study using a new data structure which consist of a cell number and a molecule number in that cell. Each molecule completing its movement is renumbered according to its new cell information and what number in this cell. This new data structure is copied onto old data structure at the end of each time step. Consequently complex indexing mechanism is found to be obsolete now. A cold gas micro-nozzle test problem is chosen from the literature. In this problem working medium is Argon. A test study is performed with Argon gas flow through a convergent-divergent micro-nozzle to determine the efficiency of the new method. Both macro properties of Argon gas flow through the micro- nozzle and solution times of each method is reported. Cold gas flow through a micro-nozzle is chosen because they are thought important for micropropulsion systems. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a method to generate three-dimensional surfaces with micro-electrolyte jet machining and discusses how to determine the nozzle path and scanning speed. In order to verify the effectiveness of the proposed method, calculated and machined results were compared. It was found that three-dimensional surfaces can be generated by superimposing elemental curved grooves, and good agreement between the cross-sectional shapes of the superimposed and machined surfaces with those of the target surface proves the effectiveness of the proposed method. In addition, layer-by-layer machining with optimized interval of the nozzle path is an effective way to reduce machining errors. [Copyright &y& Elsevier]

The development of a lumped parameter model is described for the performances prediction of a solid propellant micro-scale rocket. A micro-scale rocket consists of a combustion chamber containing the propellant, a converging and a diverging part to accelerate the gas generated by the propellant combustion. The input modelling parameters are the geometrical features of the rockets, the propellant characteristics and the ambient conditions. The output results are the temperature, the pressure, the volumic mass of the gas in the combustion chamber and the resulting thrust as a function of time. To illustrate the computational results, the performances of one micro-rocket investigated at LAAS for micro-propulsion application have been evaluated. The micro-rocket has a throat diameter of 108 μm, a chamber diameter of 850 μm, a chamber length of 1500 mm, a convergent length of 500 μm and a diverging length of 500 μm. The computational results give a chamber pressure of ∼5 bar and a thrust value of ∼3 mN at steady state. To illustrate the capabilities of the model, discussed two points:

Coupled Navier-Stokes and Direct Simulation Monte Carlo (NS-DSMC) simulations of gas flow in micro-nozzles for various wall thermal conditions and geometrical aspects are presented. Micro-thrusters employed in miniature spacecraft and microsatellites experience substantial changes in wall thermal conditions. This can influence the internal boundary layer development and the exit plume structure of a micro-nozzle. These changes in flow physics differ with the nozzle divergence angle and the proximity of a similar nozzle in the cluster. Continuum solvers often fail to analyze the micro-nozzles operating in vacuum conditions as the flow in micro-nozzles experiences continuum, transitional, and rarefied regimes. Coupled NS-DSMC solver is an effective alternative that can simulate the non-equilibrium effects in a micro-nozzle flow field. A steady solution of the entire flow field has been obtained using a non-linear Harten-Lax-van Leer-Contact (HLLC) scheme based finite volume solver with a higher order slip boundary condition. Continuum breakdown regions are identified based on the gradient-length local (GLL) Knudsen number condition. This initial steady solution on the flow transition boundary is implemented in the DSMC solver as a Dirichlet boundary condition. The present computations are useful in calibrating micro-propulsion controllers to adapt to the substantial momentum changes associated with various nozzle wall thermal conditions and the proximity of similar nozzles in the cluster. • Coupled NS-DSMC simulations is performed for gas flow in micro-nozzles. • Computations have been performed to study the effect of nozzle divergence and wall heat transfer. • Wall heat transfer alter the developing boundary layer in miniature nozzle and plume structure. [ABSTRACT FROM AUTHOR]