Divergent Nozzle Research Articles

Shock-Induced Boundary-Layer Separation in Round Convergent–Divergent Nozzles

The location of shock-induced boundary-layer separation inside the divergent section of convergent–divergent nozzles is studied experimentally. Pressure-sensitive paint technique is used with nozzles of different design Mach numbers in the range 1.4–2.8. Nozzle pressure ratios in the range of 1.12–4.91, corresponding to a “jet Mach number” range of 0.4–1.7 and a Reynolds number range of –, are covered in the experiment. As it is well-known, one-dimensional nozzle flow theory grossly overpredicts the throat-to-shock-location distance at a given nozzle pressure ratio. A correlation from the literature based on rocket nozzle databases is also found to be inadequate for these nozzles of lower design Mach number typical of aircraft applications. For the parametric range covered, a simple correlation for the shock location distance is found. All data collapse in a cluster when plotted as a function of the ratio of jet Mach number to design Mach number. A curve-fit equation representing the average trend is provided.

Effects of Entrainment on Incapability of High Intensity Beam Drilling

The effects of entrainment accompanying mass, momentum, and energy transport from the keyhole wall on keyhole collapse during high-power-density laser or electron beam drilling are theoretically and systematically investigated in this study. High intensity beam drilling is widely used in components, packaging and manufacturing technologies, micro-electromechanical-systems (MEMS), rapid prototyping manufacturing, and keyhole welding. This study proposes a quasi-steady, one-dimensional transport model to predict supersonic and subsonic flow behavior of the two-phase, vapor–liquid dispersion in a keyhole and applies the Young–Laplace equation to calculate the keyhole shape. The results show that the keyhole collapse, representing decreased or vanished radius, is susceptible to mass ejection at the base and entrainment from the side wall. Deposition of a mixture of gas and droplets in the keyhole stabilizes deformation of the keyhole. Enhanced energy and decreased axial component of momentum associated with entrainment are also apt to keyhole collapse. The predicted results agree with axial variations of transport variables of a compressible flow through a divergent and convergent nozzle, and their exact analytical solutions in the absence of friction, energy absorption, and entrainment. An understanding of the effects of ejected and entrained mass in the keyhole on drilling efficiency is therefore provided.

Transfer function of small convergent–divergent (C–D) nozzles and opposite (D–C) devices filled with thermo-viscous fluid at rest

An analytical representation, which involves single integrals, is established for describing the shape of small acoustic elements (slits or tubes) more or less tapered (the shape being governed by only one parameter). This representation includes the ability to create a zero slope (horizontal) at one end and an infinite one (vertical) at the other end, the limiting shapes being small cylindrical tubes or cavities. Then, the results obtained from the analytic procedure presented in a previous paper (Honzík et al., 2013), whereby one expresses the transfer function of such elements filled with a thermo-viscous fluid and, beyond, the transfer function of components obtained when connecting them continuously, are presented and compared to numerical and experimental results. Two prototype components gradually narrowing and widening, and conversely, are considered, namely a convergent–divergent nozzle which makes a symmetric hourglass-shape and the opposite divergent–convergent device, with different loads that end the device. The results show the potentialities of such small components when used in acoustic devices.

Numerical solution of steam flow in a nozzle using different non-equilibrium condensation models

The paper presents three Eulerian models for the two-phase flow of a steam with a non-equilibrium condensation due to the rapid expansion. All models are based on the transport equations for the mass, momentum and total energy of the mixture. The models differ in the number of additional transport equations for the parameters of liquid phase. The models with two and four additional transport equations take into account homogeneous nucleation and growth of existing droplets. The last model with no additional transport equation is based on a “switch” from metastable to equilibrium state, i.e. a “switch” from zero to equilibrium wetness. Although this last model omits the droplet size, it can be particularly interesting for the simplified flow simulations in the first steps of steam turbine design (e.g. simulations of the circumferentially averaged flow in a meridional plane of several turbine stages). Presented numerical results of one- and two-dimensional flowsin a convergent–divergent nozzle have been obtained using in-house codes based on the symmetrical operator splitting with a finite volume method used for the convection and a Runge–Kutta method used for time integration of source terms. The result discussion covers the comparison of three presented models in terms of Mach number, pressure and wetness prediction. It further covers the influence of grid density on the prediction of nucleation zone as well as a new thermodynamic closure alternative to the IAPWS-95 formulation.

CFD Analysis of Nozzle Exit Position Effect in Ejector Gas Removal System in Geothermal Power Plant

The single stage ejector is used to extract the Non CondensableGas (NCG) in the condenser using the working principle of the Venturi tube. Three dimensional computational simulation of the ejector according to the operating conditions was conducted to determine the flow in the ejector. Motive steam entering through the convergent – divergent nozzle with increasing flow velocity so that the low pressure exist around the nozzle. Comparison is done also in a two dimensional simulation to know the differences occurring phenomena and flow inside ejector. Different simulation results obtained between two dimensional and three dimensional simulation. Reverse flow which occurs in the mixing chamber made the static pressure in the area has increased dramatically. Then the variation performed on Exit Nozzle Position (NXP) to determine the changes of the flow of the NCG and the vacuum level of the ejector.Keywords: Ejector, NCG, CFD, Compressible flow.

On Global Multidimensional Supersonic Flows with Vacuum States at Infinity

In this paper, we are concerned with the global existence and stability of a smooth supersonic flow with vacuum state at infinity in a 3-D infinitely long divergent nozzle. The flow is described by a 3-D steady potential equation, which is multi-dimensional quasilinear hyperbolic (but degenerate at infinity) with respect to the supersonic direction, and whose linearized part admits the form $\p_t^2-\ds\f{1}{(1+t)^{2(\g-1)}}(\p_1^2+\p_2^2)+\ds\f{2(\g-1)}{1+t}\p_t$ for $1<\g<2$. From the physical point of view, due to the expansive geometric property of the divergent nozzle and the mass conservation of gas, the moving gas in the nozzle will gradually become rarefactive and tends to a vacuum state at infinity, which implies that such a smooth supersonic flow should be globally stable for small perturbations since there are no strong resulting compressions in the motion of the flow. We will confirm such a global stability phenomena by rigorous mathematical proofs and further show that there do not exist vacuum domains in any finite part of the nozzle.

Experimental investigation of flow through planar double divergent nozzles

Dual bell nozzle is one of the feasible and cost effective techniques for altitude adaptation. Planar double divergent nozzle with a rectangular cross section was designed for two different NPR׳s to simulate and investigate the flow regimes similar to those inside the dual bell nozzle. Measurements involved flow visualization using Schlieren technique and wall static pressure measurements. The flow transition between the two nozzles at the respective inflection points and the formation of recirculation region due to flow separation was analyzed in detail. Cold flow tests were performed on the double divergent nozzle in the over-expanded conditions to study the shock wave characteristics. The results obtained from the two independent double divergent nozzles were compared with those obtained from a single divergent nozzle of the same area ratio. From the experiments it was observed that inflection angle played a key role in defining the type of shock structures existing inside the double divergent nozzles.

Existence of global solutions for isentropic gas flow in a divergent nozzle with friction

We study isentropic gas flow in a divergent nozzle with friction. It is physically known that the flow is influenced by friction. In this paper, we investigate the mathematical effect of the friction on solutions. We first construct approximate solutions by using the Godunov scheme and the fractional step procedure. We obtain the bounded estimate by the invariant region. This is the difficult point of the present paper. We use the compensated compactness to prove their convergence. Finally, we prove the existence of global solutions with arbitrary L∞ data.

Tab Aspect Ratio Effect on Supersonic Jet Mixing

AbstractThe efficacy of introducing mixing promoting small-scale vortices by two rectangular tabs, of aspect ratio 1.0, 1.5 and 2.0, placed at diametrically opposite locations at the exit of a Mach 1.73 convergent–divergent circular nozzle has been experimentally investigated, for NPRs from 4 to 8, covering overexpanded, correctly expanded and underexpanded states of the jet. The area blockage due to the each tab was 2.5% of the nozzle exit area. Keeping the blockage constant, the aspect ratio (defined as the ratio of length to width of the tab) was varied. A maximum core length reduction of 84.6% was caused by the tabs of aspect ratio 1.0, at underexpanded conditions corresponding to NPR (nozzle pressure ratio) 6. At this NPR, tabs of aspect ratio 1.5 and 2.0 caused core length reduction of 76.9% and 61.5%, respectively. The mixing promoting efficiency of aspect ratio 1.0 is found to be better than 1.5 and 2.0, at all NPRs of the present study, except NPR 5. The shadowgraph pictures of the uncontrolled and controlled jets clearly demonstrate the effectiveness of the tabs in weakening the waves in the jet core.

Influence of geometry on the efficiency of convergent–divergent nozzles applied to Tesla turbines

Convergent–divergent (CD) nozzles were designed and manufactured to improve the injection efficiency of the working fluid in Tesla turbines. Ten nozzles have been designed using two different techniques: a one-dimensional approach and a two-dimensional approach with the method of characteristics. All nozzles had rectangular geometry at throat, while 3 had divergent section planar and 2 divergent section circular, considering each mass flow rate (55 and 70kgh−1). Nozzles were analyzed using air as the working fluid. A nozzle exit to throat area ratio (NAR) of 1.35 was used in all nozzles, while the nozzle pressure ratios (NPR) ranged between 2.15 and 3.25. At planar nozzles an (x/H)exit of 2.1 was more suitable for decreased of total pressure losses, while at circular nozzles the shock waves were canceled inside of divergent section.

Numerical Simulation of the Nozzle Angles Effect on the Pressure at Thrustwall and Nozzle Outlet of PDE

In order to investigate the effects of nozzles with different angles on PDE performance, PDE with nozzles of different convergent and divergent angles were simulated and propane-air mixture was used. The simulation results indicated that the effects of nozzles with different angles on the pressure at the thrustwall of PDE and nozzle outlet were not the same. The pressure at the thrustwall and nozzle outlet of PDE with convergent nozzles was higher than that with divergent nozzles, and the pressure peak appeared earlier in the case of convergent nozzles. The peak value of the pressure at the nozzle outlet increased and appeared ahead of time as the convergent angle increased. The peak value of the pressure at the nozzle outlet increased and the evacuation time was prolonged with convergent nozzles. The pressure at the nozzle outlet dropped quickly and the evacuation time was shortened with divergent nozzles.

Experimental and analytical studies on the shock wave length in convergent and convergent–divergent nozzle ejectors

The shock cell structure and the entrainment were investigated for convergent and convergent–divergent nozzle ejectors. The shock wave structures after the nozzle with over-expanded supersonic flow were captured by optical Schlieren measurements at different inlet pressures and temperatures. The first shock wave length was analyzed by using an image processing method. An analytical model was then proposed to predict the wavelength of the first shock wave in both convergent and convergent–divergent nozzle ejectors. The model results agree well with the measurements for the first shock wave length with a maximum difference of 11%. The influence of the first shock wave length on the ejector entrainment performance was analyzed to show that the ejector entrainment performance decreases as the shock wave wavelength is increased at a given primary flow inlet pressure.

Three dimensional investigation of the shock train structure in a convergent–divergent nozzle

Three-dimensional computational fluid dynamics analyses have been employed to study the compressible and turbulent flow of the shock train in a convergent–divergent nozzle. The primary goal is to determine the behavior, location, and number of shocks. In this context, full multi-grid initialization, Reynolds stress turbulence model (RSM), and the grid adaption techniques in the Fluent software are utilized under the 3D investigation. The results showed that RSM solution matches with the experimental data suitably. The effects of applying heat generation sources and changing inlet flow total temperature have been investigated. Our simulations showed that changes in the heat generation rate and total temperature of the intake flow influence on the starting point of shock, shock strength, minimum pressure, as well as the maximum flow Mach number.

Modeling and Simulation of Supersonic Flow in 2D Nozzle Using MacCormack’s and Upwind Methods

In this work, two-dimensional inviscid supersonic flow in nozzle has been investigated using CFD schemes and characteristics method. The employed scheme is MacCormack’s finite volume method. Our own code CHARMAC, was written using MATLAB environment. Standard boundary conditions and the grid parameters were considered to solve the problem. Before analyzing the flow by CFD method, we obtained the ideal nozzle geometry using the method of characteristics for a 2D divergent Nozzle. Using 2D nozzle flow relations, an optimal throat area is found. At the end we compare the results with the advection upstream splitting Method (Ausm) and Fluent.

Mechanical and microstructural behavior of nanocomposites produced via cold spray

Cold spraying is an innovative coating technology mainly based on the high speed impact of metals and ceramic particles on different substrates. Through the employment of low temperature gases (Air, He, N2) spray particles (usually 1–50μm in diameter) are accelerated to a high velocity (typically 300–1200m/s) that is generated through a convergent–divergent de Laval type nozzle. Severe plastic deformation of particles impacting on the substrate occurs at temperature well below the melting point leading to the unique mechanical properties experienced by such kinds of coatings. In the present paper the main processing parameters affecting the microstructural and mechanical behavior of metal–metal cold spray deposits are described. The effect of processing parameters on grain refinement and mechanical properties were analyzed for different particles (Ti–TiAl3, Al–Al2O3, Ni–Cr3C2, Ni–BN, Cu–Al2O3, Co–SiC). The results belonging to the properties of the formed nanocomposites were compared with those of the pure parent materials sprayed in the same conditions. Many experimental conditions have been analyzed in terms of particle dimensions and composition, substrate temperature and composition, gas temperature and pressure, nozzle properties. In particular, those conditions leading to a strong grain refinement with an acceptable level of the mechanical deposit properties such as porosity, adhesion strength and hardness were underlined.

Analysis of One-Dimensional Inviscid and Two-Dimensional Viscous Flows Using Entropy Preserving Method

In this paper, the entropy preserving (EP) scheme (which is introduced recently by Jameson) has been considered deeply and compared with the other artificial viscosity and upwind schemes. The discretization of the governing equations in the EP scheme is performed in such a way that the entropy is conserved in all those points with no shock. The purpose of this study was to introduce a stable numerical method that enters a minimum artificial dissipation only in the vicinity of shocks. In this paper, an inviscid one-dimensional flow through a convergent–divergent nozzle and a viscous two-dimensional flow with axial symmetry are considered. It is shown that the EP scheme is more accurate if the number of mesh points is increased; and in contrast to other schemes, there is no limit in increasing the number of points.

Non-equilibrium condensation of water vapor in sonic nozzle

The non-equilibrium condensation phenomenon during the operation of sonic nozzle is very complicated, and will affect the flow measurement and control of sonic nozzle. Two-dimensional multi-fluid k–ε turbulence models for both homogeneous and heterogeneous nucleation of condensation were constructed to investigate the effect of vapor condensation on mass flow-rate of sonic nozzle. These models were validated by experimental data of homogeneous nucleation in the moist nitrogen flow through a convergent–divergent nozzle by Wyslouzil and the numerical solutions of heterogeneous nucleation in wet steam flow by Dykas respectively. Finally, both models above were applied to study the condensation flow in sonic nozzle. It was showed that the discharge coefficient of sonic nozzle is affected by both homogeneous and heterogeneous nucleation. When the flow is homogeneous, there is significant influence on discharge coefficient with high inlet relative humidity, which agrees with the thermal choking theory. The discharge coefficient deviation reaches 0.275% when the inlet relative humidity is 95%, which is close to the Lim's experimental data with accuracy of 0.15%. However, under low relative humidity condition, the experimental discharge coefficient deviation is larger, which is explained by the heterogeneous nucleation fortunately.

Study on supersonic rectangular microjets using molecular tagging velocimetry

In the present study, the characteristics of supersonic rectangular microjets are investigated experimentally using molecular tagging velocimetry. The jets are discharged from a convergent–divergent rectangular nozzle whose exit height is 500 μm. The jet Mach number is set to 2.0 for all tested jets, and the Reynolds number Re is altered from 154 to 5,560 by changing the stagnation pressure. The experimental results reveal that jet velocity decays principally due to abrupt jet spreading caused by jet instability for relatively high Reynolds numbers (Re > ~450). The results also reveal that the jet rapidly decelerates to a subsonic speed near the nozzle exit for a low Reynolds number (Re = 154), although the jet does not spread abruptly; i.e., a transition in velocity decay processes occurs as the Reynolds number decreases. A supersonic core length is estimated from the streamwise distribution of the centerline velocity, and the length is then normalized by the nozzle exit height and plotted against the Reynolds number. As a result, it is found that the normalized supersonic core length attains a maximum value at a certain Reynolds number near which the transition in the velocity decay process occurs.

Mitigating Operating Room Fires

Operating room fires are sentinel events that present a real danger to surgical patients and occur at least as frequently as wrong-sided surgery. For fire to occur, the 3 points of the fire triad must be present: an oxidizer, an ignition source, and fuel source. The electrosurgical unit (ESU) pencil triggers most operating room fires. Carbon dioxide (CO2) is a gas that prevents ignition and suppresses fire by displacing oxygen. We hypothesize that a device can be created to reduce operating room fires by generating a cone of CO2 around the ESU pencil tip. One such device was created by fabricating a divergent nozzle and connecting it to a CO2 source. This device was then placed over the ESU pencil, allowing the tip to be encased in a cone of CO2 gas. The device was then tested in 21%, 50%, and 100% oxygen environments. The ESU was activated at 50 W cut mode while placing the ESU pencil tip on a laparotomy sponge resting on an aluminum test plate for up to 30 seconds or until the sponge ignited. High-speed videography was used to identify time of ignition. Each test was performed in each oxygen environment 5 times with the device activated (CO2 flow 8 L/min) and with the device deactivated (no CO2 flow-control). In addition, 3-dimensional spatial mapping of CO2 concentrations was performed with a CO2 sampling device. The median ± SD [range] ignition time of the control group in 21% oxygen was 2.9 s ± 0.44 [2.3-3.0], in 50% oxygen 0.58 s ± 0.12 [0.47-0.73], and in 100% oxygen 0.48 s ± 0.50 [0.03-1.27]. Fires were ignited with each control trial (15/15); no fires ignited when the device was used (0/15, P < 0.0001). The CO2 concentration at the end of the ESU pencil tip was 95%, while the average CO2 concentration 1 to 1.4 cm away from the pencil tip on the bottom plane was 64%. In conclusion, an operating room fire prevention device can be created by using a divergent nozzle design through which CO2 passes, creating a cone of fire suppressant. This device as demonstrated in a flammability model effectively reduced the risk of fire. CO2 3-dimensional spatial mapping suggests effective fire reduction at least 1 cm away from the tip of the ESU pencil at 8 L/min CO2 flow. Future testing should determine optimum CO2 flow rates and ideal nozzle shapes. Use of this device may substantially reduce the risk of patient injury due to operating room fires.

Cavitation regime detection through Proper Orthogonal Decomposition: Dynamics analysis of the sheet cavity on a grooved convergent–divergent nozzle

The unsteady character of the sheet cavity dynamics on the suction side of hydrofoils, on convergent–divergent nozzles or on blades in turbines and propellers is responsible for many issues like erosion, noise and vibrations. This two-phase flow dynamics is investigated using a robust method based on Proper Orthogonal Decomposition (POD). This method is applied to sequences of sheet cavity images, in order to identify the cavitation regimes (sheet cavity or cloud cavitation regimes). Once this method is validated on a reference case, POD calculation is used to evaluate the efficiency of a passive control method. Different longitudinal grooved surfaces are machined on the diverging wall of a Venturi. The grooves geometry allows to change the cavitation regime for a fixed cavitation number, and even to avoid the cloud cavitation shedding, which may damage structures.