Axisymmetric Convergent-divergent Nozzle Research Articles

Numerical modelling of flashing flow phase change in convergent-divergent nozzle: A sensitivity analysis

A sensitivity analysis of a computational fluid dynamics (CFD) model of flashing flow phenomenon including the thermal non-equilibrium effect is proposed in the present paper. The model uses a two-phase mixture approach and the phase-change process is based on the difference between the vaporization pressure and the vapour partial pressure. Thermal non-equilibrium effect is included in the model by a sub-routine for the boiling delay. A two-dimensional axisymmetric convergent-divergent nozzle is used as benchmark for the proposed study. Such geometry is representative of well-known applications in nuclear, refrigeration and energy engineering (e.g., primary flow in the motive nozzle of ejectors). The results are compared to experimental data and previous numerical results available in literature. Present results show good agreement with global and local experimental fluid dynamic quantities used to validate the model. The paper includes in the first part a brief description of physical phenomenon of flashing flow, the experimental benchmark geometry and operating conditions. In the second part, the physical model and the numerical modeling approach are reported, showing the validation and the results related to the sensitivity analyses of the artificial coefficients characterizing the modelling approach.

Numerical Solution of Test Problems Using a Modified Godunov Scheme

Modifications of Godunov’s scheme based on V.P. Kolgan’s approach to the construction of second-order accurate schemes in space for smooth solutions are proposed. The gasdynamic parameters linearly interpolated in a mesh cell, but the Riemann problem is solved for parameters at an intermediate point between the center and the boundary of the cell. Properties of Kolgan’s scheme and the proposed modifications, such as monotonicity and entropy nondecrease, are examined as applied to the system of differential equations describing plane sound waves propagation in a resting gas. Test problems in nonlinear gas dynamics are solved, namely, the Riemann problem in a pipe, transformation of an inhomogeneity in a plane-parallel flow, supersonic flow entering an axisymmetric convergent-divergent nozzle with a coaxial central body, and coaxial supersonic flow around a cylinder. The efficiency of schemes with an intermediate point is demonstrated.

Computational Fluid Dynamics Modeling of Flashing Flow in Convergent-Divergent Nozzle

In this paper, a computational fluid dynamics model of flashing flow, which considers the thermal nonequilibrium effect, has been proposed. In the proposed model, based on the two-phase mixture approach, the phase-change process depends on the difference between the vaporization pressure and the vapor partial pressure. The thermal nonequilibrium effect has been included by using ad hoc modeling of the boiling delay. The proposed model has been applied to the case of two-dimensional axisymmetric convergent-divergent nozzle, which is representative of well-known applications in nuclear and energy engineering applications (e.g., the primary flow in the motive nozzle of ejectors). The numerical results have been validated based on a benchmark case from the literature and have been compared with the numerical results previously obtained by different research groups. The proposed approach has shown a good level of agreement as regards the global and the local experimental fluid dynamic quantities. In addition, sensitivity analyses have been carried out concerning (a) grid independency, (b) turbulence modeling approaches, (c) near-wall treatment approaches, (d) turbulence inlet parameters, and (e) semi-empirical coefficients. In conclusion, the present paper aims to provide guidelines for the simulation of flash boiling flow in industrial applications.

CFD study on particle separation performance by shock inception during natural gas flow in supersonic nozzle

Supersonic nozzles with low intensity shock have been reported by oil and gas sectors ideal equipment for eliminating undesired second phases from natural gas during purification process. In this paper, analytical and numerical methods are developed to predict the location of shock for an axisymmetric convergent-divergent nozzle. Six different shapes of nozzle are examined to demonstrate the impact of nozzle shape on shock position. Results are compared to experimental data obtained from subscale testing to demonstrate the limitation of the numerical technique. The computational fluid dynamics simulation analysis predicts shock appearance when nozzle pressure ratio > 1.2 for almost all geometries. Simulation results have also shown that the shockwave predicted by the elliptical nozzle occurs farthest from the throat compared to the other nozzle shapes at relatively small nozzle pressure ratio. However, as nozzle pressure ratio increases, the shockwave using the hexagonal nozzle is shown to occur farthest from the throat.

Detonation combustion of hydrogen in a convergent-divergent nozzle with a central coaxial cylinder

The feasibility of steady detonation combustion of a hydrogen-air mixture entering at a supersonic velocity in an axisymmetric convergent-divergent nozzle with a central coaxial cylinder is considered. The problem of the nozzle starting and the initiation of detonation combustion is numerically solved with account for the interaction of the outflowing gas with the external supersonic flow. The modeling is based on the gasdynamic Euler equations for an axisymmetric flow. The calculations are carried out using the Godunov scheme on a fine fixed grid which allows one to study in detail the interaction of an oblique shock wave formed in the diffuser with the nozzle axis. It is shown that a central coaxial cylinder ensures the starting with the formation of supersonic flow throughout the entire nozzle and stable detonation combustion of a stoichiometric hydrogen-air mixture in the divergent section of the nozzle.

Starting of an axisymmetric convergent-divergent nozzle in a hypersonic flow

The starting of an axisymmetric convergent-divergent nozzle, with the result that supersonic flow is formed within almost the entire channel, is modeled, as applied to the hypersonic aerodynamic setup of the Institute of Mechanics of Moscow State University. A successful starting is realized when the nozzle is thrown in a uniform supersonic air flow at a fairly high Mach number. The steady flow structure is studied. It is numerically shown that in the convergent section of the channel there arises an oblique shock wave whose interaction with the nozzle axis leads to the formation of a reflected shock and a curvilinear Mach disk with a region of unsteady subsonic flow in the vicinity of the throat. The mathematical model is based on the two-dimensional Euler equations for axisymmetric gas flows.

Contouring optimal three-dimensional nozzles

The contouring of near-optimal three-dimensional nozzles with subsonic flow regions is considered with reference to certain examples. The contouring is carried out in accordance with the earlier-developed direct optimization technique using the approximation of the surfaces of the objects under consideration by the Bernstein-Bezier polynomials and tested against both the solution of the optimization problem for the supersonic region of an axisymmetric convergent-divergent nozzle and the problem of contouring the supersonic region of a nozzle from the dense multi-nozzle maximum-thrust nozzle cluster. The problems of contouring three-dimensional transonic nozzles of an infrared stealth engine and the three-dimensional nozzle of a high-velocity ramjet are considered. The transonic nozzle optimization is realized within the framework of the Reynolds equations. A modified technique for describing the geometry under consideration using the inhomogeneous Bernstein-Bezier surfaces is proposed to more completely describe the set of the possible shapes.

Detonation combustion of hydrogen in a Laval nozzle under rarefied atmosphere conditions

Detonation combustion of a hydrogen-air mixture entering an axisymmetric convergent-divergent nozzle at a supersonic velocity is considered under atmospheric conditions at altitudes up to 24 km. The investigation is carried out on the basis of the two-dimensional gasdynamic Euler equations for a multicomponent reacting gas. The limiting altitude ensuring detonation combustion in a Laval nozzle of given geometry is numerically established for freestream Mach numbers 6 and 7. The possibility of the laser initiation of detonation in a supersonic flow of a stoichiometric, preliminarily heated hydrogen-air mixture is experimentally studied. The investigation is carried out in a shock tube under conditions simulating a supersonic flow in the nozzle throat region.

Nozzle startup in an oncoming flow

Three variants of the startup of an axisymmetric convergent-divergent nozzle are considered with the static pressures at the entry and exit of the nozzle being the same at the beginning of the process. The subsonic startup corresponds to open nozzle acceleration in air. The supersonic startup simulates the sudden opening of a cover at the nozzle inlet under supersonic flight conditions. A successful nozzle startup with the formation of steady supersonic flow along the whole channel is realized in the third variant of supersonic startup with gas injection through a small region of the wall of the divergent nozzle section. The investigation is performed numerically, on the basis of the Euler equations for axisymmetric gas flows.

Stability of detonation combustion with respect to the variation in the hydrogen concentration at the supersonic nozzle inlet

Detonation combustion of hydrogen-air mixtures entering an axisymmetric convergent-divergent nozzle at a supersonic velocity is considered. The nozzle geometry does not ensure gas self-ignition; for this reason, forced ignition is used, which, under certain conditions, leads to the formation of stationary detonation combustion in the case of both uniform and nonuniform hydrogen distribution at the channel entry. The nonlinear problem of the stability of these combustion regimes against periodic disturbances of the hydrogen concentration in the oncoming flow is numerically solved. The study is performed on the basis of the two-dimensional gasdynamic Euler equations for a multicomponent reacting gas. A detailed model of chemical reactions is used.

A numerical simulation on the infrared radiation of hot exhausting nozzles with a coupled flow and heat transfer model

A coupled model among flow field, solid temperature, species concentration and gas radiation, which was based on statistical narrow-band correlated-k model, was employed to predict the infrared radiations from hot exhausting nozzles. The parameters of narrow-band model were deduced from HITEMP line-by-line database. Several methods to increase computational efficiency and to save computational resources were employed, thus all the complicated computations could be operated on a personal computer. The predictions for three cases have been conducted to validate the accuracy of the methods mentioned above, including the temperature distribution of a water-cooling nozzle in rocket engines, the carbon dioxide absorptivity at the wavelength of 4.3 micron and the infrared radiation of a cylindrical furnace. Finally, the aerothermodynamic and infrared characteristics of two nozzles were predicted. It was shown that the infrared radiation intensity of chevron ejecting nozzle were obviously smaller than that of common axisymmetric convergent-divergent nozzle.

Numerical modeling of detonation combustion of hydrogen-air mixtures in a convergent-divergent nozzle

The flow of igniting hydrogen-air mixtures entering an axisymmetric convergent-divergent nozzle at a supersonic velocity is considered. A possibility of stabilizing detonation combustion is numerically investigated at different freestream Mach numbers with account for nonuniform distribution of hydrogen concentration at the nozzle entry. The investigation is performed on the basis of the two-dimensional gasdynamic Euler equations for a multicomponent reacting gas. A detailed model of chemical reactions is used. The calculated thrust is compared with the drag of a conical housing containing the supersonic nozzle considered.

Analysis of particle behavior in High-Velocity Oxy-Fuel thermal spraying process

This paper analyzes the behavior of coating particle as well as the gas flow both of inside and outside the High-Velocity Oxy-Fuel (HVOF) thermal spraying gun by using quasi-one-dimensional analysis and numerical simulation. The HVOF gun in the present analysis is an axisymmetric convergent-divergent nozzle with the design Mach number of 2.0 followed by a straight passage called barrel. In the present analysis it is assumed that the influence of the particles injected in the gas flow is neglected, and the interaction between the particles is also neglected. The gas flow in the gun is assumed to be quasi-one-dimensional adiabatic flow. The velocity, temperature and density of gas in the jet discharged from the barrel exit are predicted by solving Navier-Stokes equations numerically. The particle equation of motion is numerically integrated using three-step Runge-Kutta method. The drag coefficient of the particle is calculated by linear interpolation of the experimental data obtained in the past. Particle mean temperature is calculated by using Ranz and Marchalls’ correlation for spherical particles. From the present analysis, the distributions of velocity and temperature of the coating particles flying inside and outside the HVOF gun are predicted.

Computation of supersonic jet mixing noise for an axisymmetric convergent-divergent nozzle

The turbulent mixing noise of a supersonic jet is calculated for an axisymmetric convergent-divergent nozzle at the design pressure ratio. Aerodynamic computations are performed using the PARC code with a k-e turbulence model. LighthiU's acoustic analogy is adopted. The acoustics solution is based upon the methodology followed in the MGB code. The source correlation function is expressed as a linear combination of second-order tensors (Ribner's assumption). Assuming separable second-order correlations and incorporating Batchelor's isotropic turbulence model, the source term was calculated from the kinetic energy of turbulence. A Gaussian distribution for the time-delay of correlation was introduced. The CFD solution was used to obtain the source strength as well as the characteristic time-delay of correlation. The effect of sound/flow interaction was incorporated using the high frequency asymptotic solution to Lilley's equation for axisymmetric geometries. Acoustic results include sound pressure level directivity and spectra at different polar angles. The aerodynamic and acoustic results demonstrate favorable agreement with experimental data.