Flow In Convergent-divergent Nozzle Research Articles

Simulation of nozzle flow based on Euler equations

The nozzle is a widely used device in daily life, such as water fountains to rocket engines. It is important to find out the influence of the position of the nozzle throat for the application or the design of the nozzle. To that end, the finite difference method was employed to solve the 1D Euler equations to obtain the flow inside the nozzle. To implement the method, an in-house python code was developed. The relationship among the velocity, pressure and density in the convergent-divergent nozzle flow was found. It is observed that: the velocity rose quickly along with the nozzle and reached the top before a rapid decrease; pressure remained constant initially, which eventually began to drop; density dropped steadily and had a turning point. Moreover, the influence of the nozzle throat position is investigated thoroughly. It is observed that the position of the nozzle throat influences the velocities at the nozzle exit. The faster the flow reaches the throat, the higher the velocity or Mach number at the exit boundary.

Two-Phase Flow Analysis and Design of Geothermal Energy Turbine

A two-phase geothermal turbine generates mechanical energy by means of a total flow system. Literature references are available for experimental investigation of such flow machines but there is no validated numerical model for prediction of flow field and flashing for optimal design of the turbine’s flow channels. This paper presents a test reaction-turbine design study with two-phase flow using CFD. An Eulerian-Eulerian multiphase model with the Thermal Phase-Change criteria for two-phase heat, mass and momentum transfer has been used. Phase change validation has been conducted on published experimental data on a converging-diverging nozzle flow at various operating conditions. The stationary nozzle model was then extended to curved nozzle turbine and the results of flow and power has been validated with the data available in literature. Liquid water and vapour distribution due to flash evaporation was predicted by the analysis. Two-phase turbine model so established has been used further to re-design and optimise turbine nozzle by evaluating its cross section, area ratio, throat design, specific torque variation and curvature. Two new channel geometries, square and blended, were compared with the base circular channel and it was found that a blended channel offers on an average 6% higher specific power at 4623rpm. For the same rotor diameters and feed water flow rate, the power output could thus be improved by 4.5%. Isentropic efficiency in the range of 10 to 19% was estimated. Final design will be prototyped and tested in the laboratory for validation of design and deployment in eastern Africa.

Prediction of critical mass rate of flashing carbon dioxide flow in convergent-divergent nozzle

The prediction of a critical mass flow rate of flashing flow is of crucial importance for many applications in chemical and processing apparatus. One of the most prosperous application is the two-phase ejector as a device with flashing liquid phase as a motive fluid and vapour phase as a secondary fluid. In that case the prediction of critical flashing flow mass flow rate is necessary. A new generalised procedure of the transonic trajectory determination that uses enhanced Possible-Impossible Flow algorithm is proposed. The procedure is much faster than the commonly used Newton Critical Point (NCP) approach. The approach was applied in modelling of carbon dioxide transonic two-phase flow through the convergent-divergent nozzle by means of Homogeneous Equilibrium Model (HEM) and Delayed Equilibrium Model (DEM). These models were used to simulate flows that were experimentally and theoretically investigated in literature. The application of DEM model for determination of the supersonic trajectory part for CO2 flow is a novel contribution provided in the paper. The comparison with literature experimental data revealed that the original closure equations developed for water are improper for CO2 transonic flows, thus the adjusting attempts were demonstrated. It was revealed that the applied Darcy friction factor determination approach significantly influences on the results. Moreover, an effective DEM adjustment is impossible until Lockhart–Martinelli approach is utilised. It was shown that for CO2 case Darcy friction factor calculated by means of Friedel approach is more appropriate than the one calculated by means of the commonly used Lockhart–Martinelli approach. Nevertheless, it was demonstrated that using a frictionless approach would still give better results while adjusting DEM to better approximate the experimental pressure distributions.

Analysis of high-speed photography of cavitating flow in convergent-divergent nozzle

Cavitation is a phenomenon that is difficult to observe, as well as to analyse. Many methods are being applied in order to study cavitation – high-speed photography is one of them. Analysis of images that were obtained in this way gives the possibility of superficial assessment of the phenomenon, but the use of digital image analysis allows obtaining more information on the studied series of images. In the paper, we propose two methods intended for such analysis - they are destined specifically for obtaining variability maps of cavitating flow based on series of high-speed photography. The work is based on the analysis of three different cavitating flows induced in convergent-divergent nozzles. Obtained results show that described methods can be helpful in analysis of cavitation - variability maps can be used for example as reference images for validation of results of numerical simulations of cavitating flow, which is not possible in case of a direct use of high-speed photographs.

CFD analysis of convergent-divergent nozzle flow and base pressure control using micro-JETS

This paper presents numerical study was undertaken to identify the use of the micro-jets to regulate the pressure in the region from two-dimensional convergent-divergent (CD) Nozzle. At the exit of the divergent nozzle in the base region 1 mm of two micro-jets orifice diameter has been arranged at ninety degrees at pcd 13 mm to control base pressure. The inertia level at the inlet to suddenly expanded duct was 1.87. The micro-jets are suddenly expanded into a two-dimensional planar area ratio of 3.24. The L/D of the duct was 1, 2, 4, 5, 6, 8 and 10. The total wall pressure distribution from inlet to the outlet too was recorded. The results indicate that the micro-jets can oblige as the effective regulators of the pressure in the base area. The duct wall pressure field is not negatively affected by the dynamic control. Nozzles were operated with the NPR in the range from 3 to 11. The results show that we can fix the flow parameter which will result in the maximum gain in the base pressure, velocity and temperature. The convergent-divergent nozzle geometry has been modeled and simulated employing turbulence models: K-ε standard wall function turbulence model from the code was validated with the commercial computational fluid dynamics.

Accuracy of non-resonant laser-induced thermal acoustics (LITA) in a convergent–divergent nozzle flow

Non-resonant laser-induced thermal acoustics (LITA) was applied to measure Mach number, temperature and turbulence level along the centerline of a transonic nozzle flow. The accuracy of the measurement results was systematically studied regarding misalignment of the interrogation beam and frequency analysis of the LITA signals. 2D steady-state Reynolds-averaged Navier–Stokes (RANS) simulations were performed for reference. The simulations were conducted using ANSYS CFX 18 employing the shear-stress transport turbulence model. Post-processing of the LITA signals is performed by applying a discrete Fourier transformation (DFT) to determine the beat frequencies. It is shown that the systematical error of the DFT, which depends on the number of oscillations, signal chirp, and damping rate, is less than $$1.5\%$$ for our experiments resulting in an average error of $$1.9\%$$ for Mach number. Further, the maximum calibration error is investigated for a worst-case scenario involving maximum in situ readjustment of the interrogation beam within the limits of constructive interference. It is shown that the signal intensity becomes zero if the interrogation angle is altered by $$2\%$$ . This, together with the accuracy of frequency analysis, results in an error of about $$5.4\%$$ for temperature throughout the nozzle. Comparison with numerical results shows good agreement within the error bars.

Experience using pressure-based CFD methods for Euler–Euler simulations of cavitating flows

The paper is devoted to different approaches of a pressure–velocity coupling method to account for density variations in cavitating two-phase flow simulations. Results obtained from two strategies are investigated in detail. A simpler engineering approach associated the variations of the local density solely with the changes of the vapor-volume fraction computed by a cavitation model and assumes incompressible vapor and water phases. A more elaborate method additionally accounts for the compressibility of the two individual fluid phases. Numerical issues of significance for engineering applications are discussed in the paper, such as the occurrence of ill-conditioned matrices or cavitation-model dependencies. The single-phase verification and validation study refers to prominent aerodynamic benchmarks, i.e. a convergent-divergent nozzle flow and the flow over a bump in a channel. Cavitating flow validations are concerned with a stationary flow over a hydrofoil. An unsteady cavitating flow over a NACA0015 hydrofoil is computed to demonstrate merits of the implemented compressible fluid method to simulate sheet and vapor cavitation including the collapse of a vapor cloud followed by a shock wave formation and propagation. Results demonstrate that the predicted cavitation pattern of the two approaches are very similar and the compressible flow model is only required when attention is directed to the evolution of pressure waves of the collapsing cavities, e.g. in erosion studies.

Characterization of the cavitating flow in converging-diverging nozzle based on experimental investigations

Cavitation phenomena occuring in converging-diverging nozzle (Venturi tube) are described in the paper. A closed test circuit with possibility to control both flow rate and pressure level were used. Loss coefficient was evaluated for different sigma numbers resulting in full static characterization of the nozzle. Visualizations of the cavitation pattern development were acquired and matched with evolution of the loss coefficient. Three cavitation regimes are described: partial cavitation, fully developed cavitation, supercavitation.

Experimental measurement and numerical modeling of cavitating flow in converging-diverging nozzle

Paper presents results of the experimental research and computational modeling aimed on cavitating vortical structures induced by swirling flow. An experimental circuit was built with swirl generator and converging-diverging nozzle made of plexiglass. Cavitating zone develops along the nozzle axis due to balance of pressure and centrifugal forces. Resulting vortical structure is unstable, which is manifested by pulsations. Computational modelling of the one-phase flow is carried out and results are confronted with experimental data and the different modelling approaches are discussed.

Effect of Curvature on Gas-Particle Flow in Converging and Diverging Supersonic Nozzle

A cold spray process is a relatively new process using high velocity metallic particles for surface modifications. Metallic powder particles which are injected into a converging-diverging nozzle are accelerated to supersonic velocities. In this study a comparative study was performed to figure out the effect of curvature on gas and particle flow in converging-diverging nozzle. And, the critical radius of curvature in converging and diverging section of nozzle and the behavior of the gas and particle flow were determined and calculated, respectively.

Theoretical Prediction of Resonance in Nozzle Flows

Resonance and damping in the shock movement induced either by a low-pressure ratio in a transonic convergent-divergent nozzle flow or by a supersonic or hypersonic flow in an overexpanded nozzle subject to external pressure fluctuations have been studied experimentally and numerically in the past. The underlying mechanisms for this resonance phenomenon in both cases are not fully understood. A perturbative quasi-one-dimensional model, coupled with a dual-oscillator concept, is given to explore the physical parameters that govern the shock excursion and the wave transport in the subsonic domain downstream of the shock. It is shown that the standing wave (strong resonance) in the former case is a consequence of superimposing two almost identical in amplitude but in opposite direction traveling waves through the subsonic domain inside the separated boundary layer. In the latter case, a relatively weak resonance is encountered as a result of the phasing in the convective energy transported between the energy dissipation due to the shock movement and the energy supply due to external pressure fluctuations. Resonant frequencies and pressure fluctuations compare well with the available experimental data and numerical solutions.

臨界状態にある末広ノズル内気液二相の流動(流体工学XI)

臨界状態にある末広ノズル内気液二相の流動(流体工学XI)

Head-on collision of two compressible vortex rings

The flow field induced by two vortex rings approaching each other at a high speed has been experimentally and numerically studied. The two vortex rings have been generated after shock waves are emitted into the atmosphere at the same time from two nozzles connected to a shock tube, after which they follow a jet flow. The flow field, where the vortex rings come close to each other, has been clarified from optical shadowgraph and numerical results. As the vortex rings approach each other, a supersonic region grows upstream of the rings and a high-pressure region occurs downstream of the rings. As these approach more closely, an inward-facing shock is generated in the narrow region between the two vortex rings. It has been shown that the formation of the shock is due to the same mechanism as that in the convergent-divergent nozzle flow.

Momentum Variable Procedure for Solving Compressible and Incompressible Flows

Navier-Stokes equations are solved for both compressible and incompressible flows using momentum component variables instead of the usual velocity variables as the dependent variables. The numerical procedure is developed in a control-volume-based, finite element context. The procedure is determined in a pressure-based algorithm rather than the density-based algorithms, which compressible methods normally use. The proper selection of the connections between the variables on control volume surfaces and the main nodal values allow the use of a collocated grid arrangement. The compressible and incompressible results of this algorithm are investigated by testing a number of test cases including the driven cavity, an entrance region flow, and a converging-diverging nozzle flow. The results indicate that the momentum component procedure is quite successful for solving compressible and incompressible flows within a single algorithm

A coupled implicit method for chemical non-equilibrium flows at all speeds

A time-accurate, coupled solution procedure is described for the chemical nonequilibrium Navier-Stokes equations over a wide range of Mach numbers. This method employs the strong conservation form of the governing equations, but uses primitive variables ( p g, u, v, h, Y i ) as unknowns. Real gas properties and nonequilibrium chemistry are considered. Numerical tests include steady convergent-divergent nozzle flows with air dissociation/recombination chemistry, dump combustor flows with n-pentane-air chemistry, and nonreacting unsteady driven cavity flows. Numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for Mach numbers ranging from the incompressible limit to supersonic speeds.C 1993 Academic Press, Inc.

Fluctuation characteristics of bubbly liquid flow in converging-diverging nozzle

The pressure fluctuation characteristics in bubbly liquid flow in a converging-diverging nozzle are interpreted on the basis of the previous theoretical results concerning the possible wave modes in bubbly liquid flow and their properties. The experiment is performed in a visual blowdown facility using water and nitrogen gas. The intensity and power spectrum density of the pressure fluctuations are measured, as well as the velocities of liquid and bubbles, the void fraction and the chord length of bubbles. All the fluctuation characteristics and their relation with the main stream condition are compatible with the theoretical predictions. The instability of the convection mode in the presence of the velocity slip and the cut off of the propagation modes in moderate frequency are demonstrated.

Some numerical results on viscous low-density nozzle flows in the slender-channel approximation

Viscous convergent-divergent nozzle flow slender channel approximations, discussing roles of nozzle geometry, Reynolds number and wall temperature, calculating velocity, enthalpy, etc

Convergent-divergent nozzle flows.

Convergent-divergent nozzle flow field solution obtained in form of perturbation about one dimensional flow field