Nonequilibrium Nozzle Flows Research Articles

State-Specific Study of Air in the Expansion Tunnel Nozzle and Test Section

Thermochemical nonequilibrium in expansion tunnel nozzles is investigated numerically using a state-to-state description in one dimension for representative air conditions. Limiting the multiquantum jumps of vibration–vibration–translation (VVT) transitions to three in both and can accurately simulate the nonequilibrium nozzle flow. The reduction of VVT transitions to vibration–translation transitions works well. State-to-state modeling of an actual expansion tunnel nozzle condition yielded agreement with the measured static pressure. A study on the influence of different thermochemical excitations in the freestream at the test section shows that the postshock radiation emissions can differ by more than 50%. However, the non-Boltzmann distributions in the freestream have no influence. An evaluation of the discrepancy between the two-temperature and state-to-state models shows that the former generally predicts a faster thermochemical relaxation. Furthermore, the state-to-state results indicate that, in general, the molecular species all have a different vibrational temperature.

Kinetics of CO Molecules Taking into Account Resonant VE Exchanges in a Nonequilibrium Nozzle Flow

The kinetics of CO molecules with excited electronic levels for a nonequilibrium flow in nozzles is studied. Three electronic energy levels are taken into account; the VV exchanges of the vibrational energy within each electronic energy level, VT transitions from the vibrational energy to the translational energy, and VE exchanges between the vibrational energy and the electronic terms occur in the system. The system of equations of vibrational level kinetics and gasdynamics, which is written in the zeroth approximation of the Chapman–Enskog method, is solved numerically. Special attention is paid to estimating the effect of the VE exchanges of the vibrational energy on the formation of nonequilibrium populations of the vibrational levels. It is shown that resonant VE transitions considerably affect the relaxation process and noticeably change the population of the upper vibrational levels even in the absence of recombination and dissociation processes; VE exchanges also affect the time dependence of the vibrational temperature.

QCT-based vibrational collisional models applied to nonequilibrium nozzle flows

Thermal and chemical nonequilibrium effects are investigated in hypersonic nozzle expanding flows by means of vibrational collisional models. The rate coefficients for rovibrational dissociation and excitation are provided by two chemical databases for the N + N2 system recently developed at NASA Ames Research Center and the University of Bari. Vibrationally averaged rate coefficients for N + N2 collisions are computed based on the hypothesis of equilibrium between translational and rotational modes. N2 + N2 collisions are also considered based on literature data. Inviscid and quasi 1D governing equations are discretized in space by means of a finite volume method. A fully implicit time integration method is applied to obtain steady state solutions. Results show that, for both N + N2 and N2 + N2 collision dominated flows, the populations of vibrational levels deviate from a Boltzmann distribution. An accurate investigation of vibrational level dynamics shows the different behavior of low and high-lying states. Comparison against experimental data acquired at the EAST facility of NASA Ames Research Center demonstrate good agreement between the computed and experimental results.

2단 초음속 스크램제트 비행체의 개념설계 연구

In this study, two-stage hypersonic scramjet vehicle was designed for the flight condition of Mach number 6. In order to launch at sea level, two stage concept was applied. The first stage of the vehicle is solid rocket-powered and is mounted under the second stage. The second stage is powered by scramjet propulsion system and gas wings. The suggested mission scenario is to deliver 0.2 ton payload to the range of 2,000 km. For the first step of conceptual design, trajectory of air vehicle was calculated by 3-DOF trajectory code. Based on the result of trajectory code, scramjet engine design and mass estimation were performed by non-equilibrium nozzle flow code and NASA`s HASA model, respectively. In order to find best solution, all steps of designing process was iterated until they was reached.

Computation and Experiment of a Nonequilibrium Nozzle Flow of Arc-heated Air

Numerical simulations of a nonequilibrium nozzle flow of are-heated air were carried out using an eight-temperature model composed of translational, N 2 -rotational, O 2 -rotational, NO-rotational, N 2 -vibrational, O 2 -vibrational, NO-vibrational, and electron temperatures. The on-axis profile of each temperature in the nozzle is shown and the thermal characteristics of the nozzle flow are discussed. Measurements of NO emission spectra were also made at wavelengths 220-265 nm at the nozzle exit to determine NO rotational temperature by a curve-fitting method. Computed rotational temperature of NO at the nozzle exit was compared with the experimental temperature to discuss the nozzle flow model introduced to the present numerical analysis. Moreover, the present computation was applied to a nozzle flow in another arcjet facility

On two-phase frozen and flashing flows in safety relief valuesRecommended calculation method and the proper use of the discharge coefficient

Abstract Many relief scenarios involve the discharge of a two-phase fluid mixture, and the proper method for sizing the relief valve for these conditions is the subject of considerable discussion. Sizing a valve is based on the flow through an isentropic nozzle, the pressure–density relation for the fluid properties, and a discharge coefficient ( K d ) to match the calculated mass flux to that measured for the flow of air or water in the actual valve. For single-phase flow, this is straightforward, since the fluid properties are simple and measured values of K d are available. For two-phase flow, the density–pressure relation is complex and no values of K d are available, so a variety of “models” have been proposed in the literature to address this problem. Since the various models produce various results, the appropriate value of K d required to match the model to the actual valve will depend on the model. This paper utilizes a simple, rigorous method for sizing relief valves for two-phase flow that utilizes the fluid properties directly and hence does not require a “model” for these properties. It is shown how this method can be applied to two-phase frozen or flashing (equilibrium or non-equilibrium) nozzle flows, and how the available values for K d for single-phase flow can be used directly with this method, depending on the critical state of flow in the nozzle, to accurately predict two-phase flow in any valve. The calculations are compared with data from the literature for frozen air/water and flashing steam/water flows in actual safety relief valves.

Numerical and experimental studies of an arc-heated nonequilibrium nozzle flow

The arc-heated high-temperature gas is rotationally and vibrationally excited, and partially dissociated and ionized. When such gas flows inside a nozzle, energy transfers from rotational and vibrational energy modes to translational energy mode, and, in addition, recombination reactions occur. These processes are in thermal and chemical nonequilibrium. The present computations treat arc-heated nonequilibrium nozzle flows using a six temperature model (translational, rotational, N2 vibrational, O2 vibrational, NO vibrational and electron temperatures), and nonequilibrium chemical reactions of air. From the calculated flow properties, emission spectra at the nozzle exit were re-constructed by using the code for computing spectra of high temperature air. On the other hand, measurements of N2+ (1−) emission spectra were conducted at the nozzle exit in the 20 kW arc-heated wind tunnel. Vibrational and rotational temperatures of N2 were determined using a curve fitting method on N2+ (1−) emission spectra, with the vibrational and rotational temperatures for N2 and N2+ being assumed equal. Comparison of the measured and computed results elucidated that the experimental temperatures were larger than the computed ones. At present, we are trying to reveal the main reason for the discrepancy between the computed and measured N2 vibrational and rotational temperatures.

Effects of blowing/suction on vortex instability of horizontal free convection flows

Stollery, J. L., and Park, C., Computer Solution to the Problem of Relaxation in Hypersonic Nozzle Flows, Journal of ' Fluid Mechanics, Vol. 19, 1964, pp. 113-123. Ericson, W. D., Vibrational Non-Equilibrium Flow of Nitrogen in Hypersonic Nozzles, NASA TN-D-1810, June 1963. Der, J. J., Theoretical Studies of Supersonic Two-Dimensional and Axisymmetric Non-Equilibrium Flow Including Calculation of Flow Through a Nozzle, NASA TR-R-164, 1963. Olynick, D. P., Moss, J. N., and Hassan, H. A., Monte Carlo Simulation of Relaxation in Nitrogen, Journal of Thermophysics and Heat Transfer, Vol. 6, No. 1, 1992, pp. 22-26. Reddy, N. M., and Daum, F. L., Solutions in Nonequilibrium Nozzle Flows, AIAA Journal, Vol. 9, No. 8, 1971, pp. 1622-1624. Park, C., Nonequilibrium Hypersonic Aerothermodynamics, Wiley, New York, 1989. Anderson, J. D., Jr., Hypersonic and High Temperature Gas Dynamics, McGraw-Hill, New York, 1989. Marble, F. E., Dynamics of a Gas Containing Small Solid Particles, 5th AGARD Combustion and Propulsion Colloquia, Pergamon, Oxford, England, UK, 1963, pp. 175-214. Hultberg, J. A., and Soo, S. L., Two-Phase Flow Through a Nozzle, Astronautica Acta, Vol. 11, No. 3, 1965, pp. 207-216. R. K., Solutions and General Correlating Parameters in Non-Equilibrium Nozzle Flows, Ph.D. Dissertation, Indian Inst. of Science, Bangalore, India, March 1990. Thulasiram, R. K., and Reddy, N. M., Gas-Particle Non-Equilibrium Nozzle Flows: Concept of Virtual Speed of Sound and Similar Solutions, AIAA Journal, Vol. 30, No. 8, 1992, pp. 2047-2055.

Vibration relaxation in gas-particle nozzle flows - A study of the effect of particles

Nonequilibrium nozzle flows of pure gases is common in many aerospace applications such as rocket nozzles, and hypersonic simulation facilities such as wind-tunnel/shock-tunnel nozzles. The basic problems, including the problem of obtaining numerical solutions for nozzle flows with vibrational energy relaxation, have been studied by several authors. With the advent of metallized propellants for solid rocket motors, the nozzle flow consists not only of pure gases. The metallized propellant burnt in the combustion chamber becomes metal oxide particles and are dragged out of the combustion chamber by the nozzle expansion process of the gas. Arc-heated test gas in hypersonic wind tunnels also contains large numbers of particles flowing with the gas. It is a known fact from earlier studies that the presence of particles in the flow can modify the flow expansion process. The effects of such particles on the internal energy nonequilibrium phenomena during the nozzle expansion process is studied in this investigation.

Gas-particle nonequilibrium nozzle flows - Concept of virtual speed of sound and similar solutions

An attempt is made to obtain similar solutions for gas-particle nonequilibrium nozzle flows. Modified definitions for speed of sound and Mach number are proposed. The governing equations are transformed into a similar form and a single correlating parameter is obtained. The limiting (equilibrium and frozen) speeds of sound are shown to be derivable from the modified definition.

Tests of certain approximations in computations modeling the formation of clusters in supersonic flow

Two approximations made in previous treatments modeling the nucleation and growth of molecular clusters generated in nonequilibrium nozzle flow are examined along with the sensitivity of results to uncertainties in input parameters. The first approximation, namely, the assignment of identical temperatures to all clusters at a given point in the flow, was found to be not seriously in error. The kinetics of mass and heat transfer must be suitably taken into account, however, to obtain the correct difference between the cluster temperature and that of the surronding carrier gas. The second approximation, according to which the Kelvin equation is applied to critical nuclei but not subsequently to growing clusters, has an appreciable effect

Numerical analysis of gas-solid two-phase nonequilibrium nozzle flows.

Numerical simulation of the steady two-phase flow field of gas-particle inside a JPL nozzle is described in this paper. The computations use a time-dependent technique using the TVD-MacCormack algorithm for both gas and particle phases. The nozzle flows considered here are inviscid, and spherical particles of 1-5μm in diameter are treated. Numerical results show that the nozzle expansion is delayed as the interaction between gas and particle phases becomes strong. In addition, it is seen that there exists a particle-free zone in the divergent section of the nozzle.

Exhaust of NOx from High-Temperature Wind Tunnels

Theoretical calculations were performed in order to estimate the concentrations of three main constituents of NOx (NO, NO2 and N2O) in the exhaust gas produced by two kinds of hypersonic wind tunnels. One of them had an arc-heater, and the other a pebble-heater. Estimations were performed for the equilibrium air in the plenum chamber, for the equilibrium and nonequilibrium nozzle flows, and for the final exhaust gas. Measurements in the exhaust gas of the arc-heated wind tunnel show that the total concentration of NOx (NO and NO2) was of the order of 10,000 ppm, depending on the conditions of operation. Two simple models are proposed to explain the origin of such a high level of NOx in the exhaust. It is shown that a model taking account of the isothermal compression of the exhaust gas in rotary pumps of the vacuum system can predict the formation of high concentrations of NOx.

Analysis of Gain Coefficients for CO2-N2-He Nozzle Flows with Boundary Layer

Experimental measurements and theoretical calculation of gain coefficients were made for vibrationally nonequilibrium nozzle flows, with relatively low reservoir pressure. A simple and semi-empirical method to estimate the effective cross section of the expansion core was proposed and applied to the calculations. Gain coefficients versus the reservoir pressure, throat height, and the distance along a nozzle were measured. Experimental results agreed well with the theoretical ones.

Comment on "Nonequilibrium nozzle flow of a nitrogen-hydrogen mixture"

Clarence J. Harris* General Electric Company, Philadelphia, Pa. Ebrahim, N.A. and Hornung, H.G., Nozzle Expansion of Carbon Dioxide from a High Enthalpy Reservior, Journal, Vol. 11, Oct. 1973, pp. 1369-1370. MacDermott, W.N. and Dix, R.E., Mass Spectrometric Analysis of Nonequilibrium Airflows, Journal, Vol. 10, April 1972, pp. 494-499. Young, W.S., Correlation of Chemical Freezing in a Freejet Expansion, AIAA Journal, Vol. 13, Nov. 1975, pp. 1478-1482.

Nonequilibrium Nozzle Flow of a Partially Ionized Two-Temperature Nitrogen

A set of equations governing the quasi-one-dimensional, nonequilibrium flow of partially ionized nitrogen gas is formulated, where the inelastic sources of both the electron-catalyzed ionization-recombination and the exchange with vibrational energy of N 2 are taken into account in the electron energy equation. The set of equations is applied to the study of the flow properties of partially ionized nitrogen gas in a convergent-divergent nozzle. Calculations show that at a low plenum temperature, the exchange with N 2 vibration is the primary source of electron energy in the nonequilibrium expansion through the nozzle, and at a high plenum temperature, the electron-catalyzed ionization-recombination reaction becomes an important source of the electron energy.

Entropy in Nonequilibrium Nozzle Flows of Vibrationally Relaxing Diatomic Gases

Entropy in Nonequilibrium Nozzle Flows of Vibrationally Relaxing Diatomic Gases

Anharmonic Effects on the Rate of Relaxation of Vibrational Energy in Rapidly Expanding Flows

Detailed numerical results are presented for the time dependent vibrational relaxation process in the rapid expansion of anharmonic oscillators in nonequilibrium nozzle flows. Calculations for the expansion of CO, CO/Ar, and CO/N2 mixtures from high stagnation temperatures, in the range 2000–4500°K, are compared with previously reported experimental results. It is concluded that the effects of the anharmonicity of the molecules are unlikely to lead to an increase of more than a factor of 2 in the vibrational energy relaxation rate. A simple analytical result is derived in terms of the molecular constants and the expansion temperature ratio to predict the degree of distortion of the low level ``vibrational temperature'' which results from the anharmonicity.

Population Inversions in an Expanding Gas: Theory and Experiment

It is well established that population inversions between the (001) and (100) vibrational energy levels of CO1 can be created by rapid expansions of CO2-N2-H2O or He mixtures through supersonic nozzles. New experimental results are presented for such inversions. These experiments were conducted in both the 3-MW arc tunnel and the 12.7-cm shock tunnel at the Naval Ordnance Laboratory. The results support previously published theoretical predictions obtained with a numerical, time-dependent, nonequilibrium nozzle flow analysis employing a simplified vibrational kinetic model. This theory is also compared with experimental data obtained by other investigators.

Similar Solutions in Vibrational Nonequilibrium Nozzle Flows

Abstract : The problem of obtaining similar solutions in pseudo-one-dimensional nozzle flows with vibrational relaxation is considered. The governing equations are transformed into a similar form by using a new similarity parameter eta so that the nonequilibrium flow solutions depend on two parameters for a given kind of gas. However, the similar equations are further reduced to a universal form by a transformation of the independent variable ETA to xi such that the similar solutions, for all combinations of initial conditions and for a defined family of nozzle shapes, depend on a single parameter chi which are then presented in a single graph. It is also shown that the equilibrium solutions depend on only one parameter xi. The parameters xi and chi are also the exact, general correlating parameters. With the present similar solutions the flow quantities in a nozzle are readily determined without resorting to complex computer programs.