High enthalpy nozzle flow sensitivity study and effects on heat transfer

The sensitivity of the flow along the nozzle and in the test section of high enthalpy wind tunnels to the thermochemical response of the nozzle expansion process, as well as effects on the pressure and heat transfer distributions over the Electre blunt cone standard test model, are examined in the framework of properly characterizing the test section flow field in such facilities. Particularly sensitive to the thermochemical behaviour of the nozzle flow, in the facilities under consideration, are the static pressure, static temperature and Mach number, whereas stagnation point (pitot) pressure and heat transfer data or freestream velocity are inadequate for the characterization of the thermochemical state of the flow. The Electre and nozzle wall pressure data in the F4 arc jet wind tunnel suggest, in contrast to nonequilibrium computations, that the flow in the F4 nozzle is close to equilibrium. In the HEG and, to some extent, the T5 piston-driven shock tunnels, there are indications that significant heat losses occur in the reservoir. Lastly, simple semi-empirical formulations for stagnation point heating are shown to perform reasonably well in high enthalpy flow conditions.     

The influence of sidewall cooling on boundary layer pressure fluctuations for a two-dimensional supersonic nozzle

Broadband root-mean-square (rms) values and frequency spectra for pressure fluctuations in the supersonic boundary layer on a Mach 3 DeLaval nozzle sidewall and in the freestream are reported for both adiabatic and cooled surface conditions. The flat sidewall of the nozzle contained four sections independently cooled by liquid nitrogen. During the experiments, the flat sidewall was operated (1) adiabatically, (2) cooled in an approximately uniform manner to ?40°C, and (3) cooled in a nonuniform manner. For all thermal boundary conditions on the sidewall, a dynamic pitot probe was traversed through the boundary layer and into the freestream to measure the broadband pressure fluctuations from 30 Hz to 100 kHz. The influence of sidewall cooling on the measured pressure fluctuations was dependent on the unit Reynolds number. Compared with the pressure fluctuations measured with an adiabatic sidewall, uniform cooling of the sidewall was found to reduce the rms pressure fluctuations in both the boundary layer and the freestream by approximately 50% at the highest stagnation pressures used (unit Reynolds numbers above 44,000/cm). Uniform cooling of the sidewall increased rms pressure fluctuations for lower stagnation pressures (unit Reynolds numbers below 44,000/cm). A reduction in the pressure fluctuation amplitude within the boundary layer resulted in a corresponding reduction in the pressure fluctuation amplitude in the test section freestream. Tests using a nonuniform temperature distribution on the sidewall indicated that cooling the portion of the sidewall covering the nozzle throat had the most influence on the pressure fluctuations in the boundary layer and in the freestream.     

On the conditions of formation of population inversion of atomic levels in a thermally heated recombining plasma

A theoretical investigation is made into the recombination of a thermally heated plasma of a monatomic gas which undergoes gas-dynamic cooling in a supersonic nozzle. A method of approximate analytic calculation makes it possible to determine the necessary conditions for the existence of an effective recombination regime of the flow out of the nozzle that makes possible population inversion of the excited electronic levels of the atom. The conditions of occurrence of inversion are studied as functions of the parameters characterizing the state of the plasma in the reservoir in front of the entrance to the nozzle, the shape of size of the nozzle, and the working substance. Use of the method of blocks of levels made it possible to calculate the degree of expansion needed for the formation of inversion between transitions with different wavelengths, and also to estimate the gain and the specific radiation energy in these transitions. Numerical estimates of the values of the parameters for the case of an argon plasma are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 91–97, November–December, 1979.We thank S. A. Losev for discussing the results and for helpful comments.     

Experimental research on the rotating detonation in gaseous fuels�Coxygen mixtures

An experimental study on rotating detonation is presented in this paper. The study was focused on the possibility of using rotating detonation in a rocket engine. The research was divided into two parts: the first part was devoted to obtaining the initiation of rotating detonation in fuel–oxygen mixture; the second was aimed at determination of the range of propagation stability as a function of chamber pressure, composition, and geometry. Additionally, thrust and specific impulse were determined in the latter stage. In the paper, only rich mixture is described, because using such a composition in rocket combustion chambers maximizes the specific impulse and thrust. In the experiments, two kinds of geometry were examined: cylindrical and cylindrical-conic, the latter can be simulated by a simple aerospike nozzle. Methane, ethane, and propane were used as fuel. The pressure–time courses in the manifolds and in the chamber are presented. The thrust–time profile and detonation velocity calculated from measured pressure peaks are shown. To confirm the performance of a rocket engine with rotating detonation as a high energy gas generator, a model of a simple engine was designed, built, and tested. In the tests, the model of the engine was connected to the dump tank. This solution enables different environmental conditions from a range of flight from 16 km altitude to sea level to be simulated. The obtained specific impulse for pressure in the chamber of max. 1.2 bar and a small nozzle expansion ratio of about 3.5 was close to 1,500 m/s.     

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.     

Freestream effects on base pressure development of an annular plug nozzle

An experimental investigation has been carried out to study the effect of freestream flow and cowl-length variation on (i) upstream flow interference effects and (ii) the base wake-closure nozzle pressure ratio. It is observed that for supersonic freestream Mach numbers the nozzle exhaust seems to only slightly influence the upstream interference effects for M = 1.2 but shows significant influence for M = 1.6. Increasing the cowl-length further reduces the upstream flow interference effects significantly. Further, the reduced momentum thrust from the inner nozzle in the presence of freestream for similar nozzle pressure ratio (relative to static tests) delays the downstream movement of the system of shocks on the plug surface. In the case of the plug truncated at 40% length, this delays the onset of base-wake closure and hence, increases the base-wake closure nozzle pressure ratio with increasing freestream Mach number. Increasing the cowl-length also helps to increase the base pressure thrust contribution at all operating conditions.     

Effect of Sudden Expansion on Entrainment and Spreading Rates of a Jet Issuing from Asymmetric Nozzles

Turbulent free jets issuing from five different nozzle geometries; smooth pipe, contracted circular, rectangular, triangular, and square, are experimentally investigated by using TSI 2-D laser Doppler velocimetry (LDV) to assess the effect of nozzle geometry and quarl (i.e. a cylindrical sudden expansion) on jet entrainment and spreading. The centerline mean velocity decay and the jet half-velocity width, which are indicators of jet entrainment and spreading rates, are determined for each nozzle’s flow configuration, i.e. with and without sudden expansion. Furthermore, turbulence quantities, such as the flow mean velocities and their mean fluctuating components, as well as Reynolds shear stresses, are all measured along the centerline plane of the jet to facilitate understanding the extent of the effect of nozzle’s geometry (i.e. nozzle’s orifice shape and sudden expansion) on jet’s entrainment and spreading. The main results show that the jet flow with the presence of sudden expansion exhibits higher rates of entrainment and spreading than without. In addition, these results reveal that sudden expansion exercises a greater effect on the asymmetric jet characteristics, especially for the triangular and rectangular nozzles compared to their axisymmetric counterparts (i.e. circular contracted nozzle).     

A fundamental study of a variable critical nozzle flow

Critical nozzle is defined as a device to measure the mass flow rate with only the nozzle supply conditions, making use of the flow choke phenomenon at the nozzle throat. Recently, such critical nozzles have been extensively utilized to measure the mass flow rate in a variety of industrial applications. For the measurement of mass flow rates in a wide range of operation conditions, the critical nozzle is required to be designed with different diameters. The objective of the present study is to investigate the effectiveness of a variable critical nozzle. A rod with a small diameter is inserted into the critical nozzle to change the effective cross-sectional area of the critical nozzle. Experimental work is performed to measure the mass flow rate of the critical nozzle with rod. Computational work is carried out using the two-dimensional, axisymmetric, compressible Navier–Stokes equations which are discretized using a fully implicit finite volume method. The diameter of the rod is varied to obtain different mass flow rates through the variable critical nozzle. Computational results predict well the measured mass flow rates. The boundary layer displacement and momentum thickness at the throat of the critical nozzle are given as a function of Reynolds number. The discharge coefficient of the critical nozzle is given as an empirical equation.     

Heating enhancement caused by a transverse control jet in hypersonic flow

Experiments are reported in which the heat flux distribution near a single circular, sonic transverse jet on a flat plate exposed to a hypersonic (Mach 6.7) freestream flow was quantitatively measured using thermochromic liquid crystals. The freestream conditions were such that the boundary layer growth on the plate ahead of the jet was laminar. The results indicate that the interaction of the jet with the freestream flow created a complex flowfield with regions of separation and reattachment which caused localised enhancements to the heat flux upstream and to the side of the jet, the magnitudes of which were sensitive to both jet plenum pressure and jet gas composition. Received 28 August 1996 / Accepted 6 June 1997     

Inflow broadband noise from an isolated symmetric airfoil interacting with incident turbulence

Inflow noise from a symmetric airfoil interacting with homogeneous and isotropic turbulence is investigated focusing on the effects of airfoil geometry. The numerical method employed is based on computational aeroacoustic techniques using the high-order dispersion-relation-preserving finite-difference schemes for solving two-dimensional linearized Euler equations. Effects on inflow noise of the airfoil thickness, leading-edge radius, and freestream Mach number are examined by comparing the acoustic power spectrum of the airfoils and their flow field characteristics. Acoustic power levels of airfoils are found to exponentially decrease in the high-frequency range as airfoil thickness increases because incident turbulent velocities are more distorted in the larger stagnation region near the leading edge. This distortion is shown to be related to the slope angle of the streamline of steady mean flow near the leading edge. However, this high-frequency reduction weakens as the Mach number increases due to the decreasing slope angle. In addition, the chordwise velocity component in the incident turbulence contributes more to the radiating acoustic pressure level as the freestream Mach number increases, which also results in less high-frequency reduction at higher freestream Mach number. At fixed airfoil thickness, increasing the leading-edge radius leads to decreases in the acoustic power level, which may also be explained by size variation of the stagnation region around the leading edge. An approximate algebraic formula for acoustic power spectra is derived on the basis of these observations. Acoustic power spectra predicted using this formula are shown to closely follow the numerical results. Finally, the applicability of the algebraic formula and the current numerical methods to more realistic problems are confirmed by comparing their predictions with the measured data.     

Thermodynamic properties of equilibrium air by an exact two-equation model for Euler and Navier–Stokes CFD algorithms

This paper details an exact two-equation procedure to generate pressure, temperature and mass and mole fractions as well as their thermodynamic and Jacobian partial derivatives for five-species neutral equilibrium air. Applicable for arbitrary forms of equilibrium constants and especially designed for explicit and implicit CFD algorithms, the procedure algebraically reduces to two equations the six-equation thermodynamic system comprising the equations for internal energy, law of mass action and conservation of species mass and ratio of oxygen and nitrogen nuclei. This exact algebraic reduction explicitly expresses four mass fractions in terms of nitric oxide mass fraction and temperature, which are then determined through a rapidly converging numerical solution of the internal energy and nitric oxide mass action equations. The procedure then exactly determines the partial derivatives of pressure, temperature and mass fractions analytically. The mathematical formulation also introduces a convenient system non-dimensionalization that makes the procedure uniformly applicable to flows ranging from shock tube flows with zero initial velocity to aerothermodynamic flows with supersonic/hypersonic freestream Mach numbers. Over a wide range of density and internal energy the predicted distributions of mole fractions for the model five species agree with independent published results, while pressure and temperature as well as their partial derivatives remain continuous, smooth and physically meaningful. © 1997 John Wiley & Sons, Ltd.     

Gas dynamic ozone generator

The formation of ozone when partially dissociated oxygen flows out of a supersonic nozzle has been investigated experimentally and theoretically. The supersonic flow of a chemically reacting gas mixture containing excess O atoms is calculated in the one-dimensional approximation for a class of plane wedge-shaped nozzles. It is shown that for initial gas pressures ahead of the nozzle inlet of about 10 atm and a temperatureT ₀=1000 K in nozzles with a total vertex angle of 30°C and a throat dimensionh.=1 mm it is possible to obtain an ozone concentration of about 1%, which is comparable with ordinary ozonizers, while the output of the device is two to three orders greater. Experiments on a shock tube fitted with a nozzle to measure the absorption of UV radiation by oxygen recombining in the nozzle under highly nonoptimal conditions revealed the presence in the flow of ozone molecules formed as a result of O+O₂ recombination.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 139–148, November–December, 1994.     

Comparison of the Eulerian and Lagrangian approaches in studying the flow pattern and heat transfer in a separated axisymmetric turbulent gas-droplet flow

The Eulerian and Lagrangian approaches are used to perform a numerical study of the disperse phase dynamics, turbulence, and heat transfer in a turbulent gas-droplet flow in a tube with sudden expansion with the following ranges of two-phase flow parameters: initial droplet size d ₁ = 0–200 µm and mass fraction of droplets M _L1 = 0–0.1. The main difference between the Eulerian and Lagrangian approaches is the difference in the predictions of the droplet mass fraction: the Eulerian approach predicts a smaller value of M _L both in the recirculation region and in the flow core (the difference reaches 15–20%). It is demonstrated that the disperse phase mass fraction calculated by the Lagrangian approach agrees better with measured data than the corresponding value predicted by the Eulerian approach.     

Self-sustained oscillation and cavitation characteristics of a jet in a Helmholtz resonator

Self-sustained oscillations resulting from a sudden expansion in geometry, as encountered in cavities, occur in a broad array of engineering applications. In the present study, the turbulent flow past a 120°-impinging edge Helmholtz nozzle was investigated. A modified theoretical model accompanied by numerical simulation was proposed to obtain the range of the oscillation frequency and was verified using experimental results. It was found that the cavitation clouds in the chamber dominate the oscillating frequency under the low pressure-high flowrate condition. Based on the simulation results, the details of cavitation development, the motion of vortex structures, and the fluid injection and reinjection were investigated in one typical cycle. The interaction between the cavitation and the vortex formation was analyzed with the vortex transport equation. The dilatation term, which is related to the mass transfer rate through the linkage of velocity divergence, has a high value only around the bulk flow; while the baroclinic torque is predominant due to the unremitting collapse and coalescence of the cavitation clouds.     

Modeling the Effect of Freestream Turbulence on Unsteady Boundary Layer Flow

We present a new version of the two-equation turbulence model, which makes it possible to calculate continuously the entire flow range from laminar to turbulent, including transition, in the case of a time-periodic, high-turbulence-level freestream. The influence of the parameters characterizing the harmonic fluctuations of the external velocity and the freestream turbulence intensity and scale on the parameters of the flat-plate flow are analyzed. A comparison of the numerical solutions with the experimental and theoretical data indicates the possibility of describing the wall flow properties on the basis of a quasi-stationary turbulence model, as the Reynolds number varies from low to high values.     

Foam flowing vertically upwards in pipes through expansions and contractions

The drift-flux analysis of one-dimensional two-phase flow of Wallis (Wallis, G.B., 1969. One-dimensional two-phase flow. McGraw-Hill Book Company, New York.) is utilised for the first time to model the behaviour of pneumatic foam flowing vertically through an expansion or an contraction. It is demonstrated that, although a sudden contraction of flow area decreases the liquid fraction, it does not affect the volumetric liquid over-flow rate. It is also demonstrated that a sudden expansion of flow area decreases both the liquid fraction and the volumetric liquid over-flow rate. The liquid fraction of a foam stabilised by 2.92 g/L sodium dodecyl sulphate (SDS) solution flowing through a sudden contraction or expansion was measured by an improved pressure gradient method. The results were found to be consistent with the theoretical analysis. This study has implications for foam fractionation device design, optimisation and process intensification.     

Theory of two-component gasdynamic laser

In the present paper a numerical calculation is made of the vibrational relaxation of a binary mixture of molecular nitrogen and carbon dioxide gas. The calculation is performed for the entire range of variation of the concentrations of the components and over a wide range of mixture temperatures and pressures for various geometries of the supersonic part of the nozzle (throat dimensions, degree of expansion). It is shown that population inversion of the CO₂ molecules exists within a certain range of variation of the parameters of the mixture and the nozzle. The population inversion of the vibrational levels and the gain of the gaseous mixture are calculated as functions of these parameters and of distance measured from the critical cross section of the nozzle. The energy characteristics of the two-component gasdynamic laser are optimized.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 23–30, May–June, 1974.     

Quantitative visualization of compressible turbulent shear flows using condensate-enhanced Rayleigh scattering

This paper describes several flow visualization experiments carried out in Mach 3 and Mach 8 turbulent shear flows. The experimental technique was based on laser scattering from particles of H₂O or CO₂ condensate that form in the wind tunnel nozzle expansion process. The condensate particles vaporize extremely rapidly on entering the relatively hot fluid within a turbulent structure, so that a sharp vaporization interface marks the outer edge of the rotational shear layer fluid. Calculations indicate that the observed thin interface corresponds to a particle size of 10 nm or less, which is consistent with optical measurements, and that particles of this size track the fluid motions well. Further, calculations and experiments show that the freestream concentration of condensate required for flow visualization has only a small effect on the wind tunnel pressure distribution. Statistics based on the image data were compared to corresponding results from probe measurements and agreement was obtained in statistical measures of speed, scale, and orientation of the large-scale structures in the shear layer turbulence. The condensate-enhanced Rayleigh scattering technique is judged to be a useful tool for quantitative studies of shear layer structure, particularly for identifying the instantaneous boundary layer edge and for extracting comparative information on the large-scale structures represented there.     

Viscoelasticity in inkjet printing

We investigate the effects of viscoelasticity on drop generation in inkjet printing. In drop-on-demand printing, individual ink ‘drops’ are ejected from a nozzle by imposed pressure pulses. Upon exiting the nozzle, the shape of each ‘drop’ is that of a nearly spherical bead with a long thin trailing ligament. This ligament subsequently breaks up under the Rayleigh instability, typically into several small droplets (known as satellite drops). These satellite drops can create unwanted splash on the target substrate and a reduction in printing quality. Satellite drops can potentially be eliminated by adding polymer to the ink; elastic stresses can act to contract the trailing ligament into the main drop before capillary breakup occurs. However, elasticity can also reduce the drop velocity and can delay or even prevent the break-off of the drop from the ink reservoir within the nozzle. To achieve optimal drop shape and speed, non-Newtonian parameters such as the polymer concentration and molecular weight must be chosen correctly. We explore this parameter space via numerical simulations, using the Lagrangian–Eulerian finite-element method of Harlen et al. (J Non-Newtonian Fluid Mech 60:81–104, 1995). Results are compared with experimental observations taken from real printheads.