Ejector-Nozzle Flow and Thrust

1960 ◽  
Vol 82 (1) ◽  
pp. 120-129 ◽  
Author(s):  
H. E. Weber
Keyword(s):  
Nozzle Exit ◽  
Turbulent Mixing ◽  
Basic Assumption ◽  
Small Distance ◽  
Momentum Thickness ◽  
Flow Properties ◽  
Thrust Coefficient ◽  
Ejector Nozzle ◽  
Momentum Integral ◽  
Secondary Stream

An analysis for predicting the secondary and primary flows and the thrust coefficient of ejector nozzles is presented. Particular attention is given to the diverging shroud ejector in which the throat of the secondary stream is formed at a small distance down-stream of the primary nozzle exit; i.e., near the plane of the minimum shroud area. The basic assumption in the analysis is that the shroud is sufficiently short so that the mixing of the two streams is incomplete, and that both streams have isentropic cores. The momentum thickness of the mixing region is obtained from the momentum-integral equation for the turbulent mixing region assuming that momentum and temperature diffuse at the same rate. The momentum thickness at the nozzle exit is related to the initial momentum thickness created by the wall separating the two streams. The exit-momentum thicknesses of the mixing region and the wall are used to obtain the actual thrust coefficient. Experimental data on primary-secondary flow properties and thrust coefficients of a divergent-shroud ejector nozzle show good correlation with the theory.

The Mixing of Turbulent Supersonic Fuel-Air Streams

1965 ◽  
Vol 16 (4) ◽  
pp. 377-387
Author(s):  
J. M. Forde
Keyword(s):  
Mach Number ◽  
Turbulent Mixing ◽  
Integral Form ◽  
Spreading Rate ◽  
External Flow ◽  
Supersonic Combustion ◽  
Mixing Zone ◽  
Mixing Conditions ◽  
Momentum Integral ◽  
Air Streams

SummaryAn integral part of the study of supersonic combustion is the investigation of supersonic turbulent mixing of dissimilar fluids. Experimental results obtained in the course of investigating the turbulent mixing zone between supersonic streams of CO3 and air are presented. Good correlation between observation and available theories has been obtained in terms of the parameter ξ=σy/x. The correlating parameter σ defines the spreading rate of the mixing zone. The available theories, though not developed for these specific conditions, are shown to be applicable to the turbulent mixing of supersonic streams.The correlating parameter σ was determined for three different combinations of internal and external flow Mach numbers. The values found for σ were 18, 16·3, 15·3 for constant external Mach number 1·62 and internal Mach number 1·62, 1·53, 1·47 respectively. The magnitudes of σ showed the expected trend, that is the higher value implies the least divergence of the mixing boundaries.The reasonable agreement with experiment and the simplicity of application of the momentum integral form of solution would appear to favour the use of this approach for the theoretical prediction of the mixing conditions.

Improved Linearized Velocity Profiles for Turbulent Free Shear Layers

1969 ◽  
Vol 36 (4) ◽  
pp. 657-663
Author(s):  
J. P. Lamb ◽  
T. F. Greenwood ◽  
J. L. Gaddis
Keyword(s):  
Figure Of Merit ◽  
Velocity Profiles ◽  
Shear Layers ◽  
Density Field ◽  
Longitudinal Motion ◽  
Nonlinear Analyses ◽  
Free Shear Layers ◽  
Inductive Theory ◽  
Momentum Integral ◽  
Secondary Stream

The longitudinal motion equation for turbulent boundary layers is linearized in a manner which retains the spirit of Reichardt’s inductive theory. The resulting approximate velocity profiles for isobaric free shear layers are found to be functions of the density field as well as the velocity of the secondary stream. Using the amount of transverse shift, which is required to satisfy the momentum integral equation, as a figure of merit, it is shown that the alternate profiles are generally better representations of the flow field than distributions obtained with the classic Oseen linearization for both developing and fully developed free layers. The alternate velocity distributions, in combination with integral conservation equations, are shown to yield characteristic velocities in the midpart of the profile which are in agreement with those obtained from more elaborate nonlinear analyses.

Thwaites' Method In Laminar Boundary Layer

1989 ◽  
pp. 5-13 ◽  
Author(s):  
Prof. Amer Nordin ◽  
Lim Chee Wah
Keyword(s):  
Boundary Layer ◽  
Coefficient Of Friction ◽  
Momentum Thickness ◽  
Flow Properties ◽  
Local Coefficient ◽  
Simple Boundary ◽  
Displacement Thickness ◽  
Different Types ◽  
Naca 0012 ◽  
Complex Curvature

Thwaites' method can be applied to find the boundary layer characteristics for either similar or nonsimilar flow for a variety of boundaries ranging from a simple flat plate (Blasius's Solution(1)) to a symmetrical airfoil. The flow properties to be determined include potential flow velocity distribution, displacement thickness, momentum thickness and coefficient of friction. Furthermore,the location of flow separation is readily obtainable from the numeric value of local coefficient of friction. Thwaites' Method is able to provide satisfactory approximate solution to different types of simple boundary as long as the flow is laminar and not separated. For a complex curvature such a an airfoil Thwaite' Method is yet to be tested. In this context, we will look into the applicability of Thwaites' Method for a particular symmetrical airfoil, NACA 0012.

scholarly journals Propulsion and Thermodynamic Parameters of van der Waals Gases in Rocket Nozzles

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Fernando S. Costa ◽  
Gustavo A. A. Fischer
Keyword(s):  
Thermodynamic Parameters ◽  
High Pressures ◽  
Specific Impulse ◽  
Van Der Waals ◽  
Combustion Products ◽  
Ideal Gas ◽  
Flow Properties ◽  
Thrust Coefficient ◽  
Analysis And Design ◽  
Specific Heats

Propellants or combustion products can reach high pressures and temperatures in advanced or conventional propulsion systems. Variations in flow properties and the effects of real gases along a nozzle can become significant and influence the calculation of propulsion and thermodynamic parameters used in performance analysis and design of rockets. This work derives new analytical solutions for propulsion parameters, considering gases obeying the van der Waals equation of state with specific heats varying with pressure and temperature. Steady isentropic one-dimensional flows through a nozzle are assumed for the determination of specific impulse, characteristic velocity, thrust coefficient, critical flow constant, and exit and throat flow properties of He, H2, N2, H2O, and CO2 gases. Errors of ideal gas solutions for calorically perfect and thermally perfect gases are determined with respect to van der Waals gases, for chamber temperatures varying from 1000 to 4000 K and chamber pressures from 5 to 35 MPa. The effects of covolumes and intermolecular attraction forces on flow and propulsion parameters are analyzed.

scholarly journals Effects of nozzle-exit boundary-layer profile on the initial shear-layer instability, flow field and noise of subsonic jets

2019 ◽  
Vol 876 ◽  
pp. 288-325 ◽  
Author(s):  
Christophe Bogey ◽  
Roberto Sabatini
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Shear Layer ◽  
Nozzle Exit ◽  
Momentum Thickness ◽  
Shear Layer Instability ◽  
Instability Waves ◽  
Exit Velocity ◽  
Exit Boundary ◽  
Boundary Layer Profile

The influence of the nozzle-exit boundary-layer profile on high-subsonic jets is investigated by performing compressible large-eddy simulations (LES) for three isothermal jets at a Mach number of 0.9 and a diameter-based Reynolds number of $5\times 10^{4}$, and by conducting linear stability analyses from the mean-flow fields. At the exit section of a pipe nozzle, the jets exhibit boundary layers of momentum thickness of approximately 2.8 % of the nozzle radius and a peak value of turbulence intensity of 6 %. The boundary-layer shape factors, however, vary and are equal to 2.29, 1.96 and 1.71. The LES flow and sound fields differ significantly between the first jet with a laminar mean exit velocity profile and the two others with transitional profiles. They are close to each other in these two cases, suggesting that similar results would also be obtained for a jet with a turbulent profile. For the two jets with non-laminar profiles, the instability waves in the near-nozzle region emerge at higher frequencies, the mixing layers spread more slowly and contain weaker low-frequency velocity fluctuations and the noise levels in the acoustic field are lower by 2–3 dB compared to the laminar case. These trends can be explained by the linear stability analyses. For the laminar boundary-layer profile, the initial shear-layer instability waves are most strongly amplified at a momentum-thickness-based Strouhal number $St_{\unicode[STIX]{x1D703}}=0.018$, which is very similar to the value obtained downstream in the mixing-layer velocity profiles. For the transitional profiles, on the contrary, they predominantly grow at higher Strouhal numbers, around $St_{\unicode[STIX]{x1D703}}=0.026$ and 0.032, respectively. As a consequence, the instability waves rapidly vanish during the boundary-layer/shear-layer transition in the latter cases, but continue to grow over a large distance from the nozzle in the former case, leading to persistent large-scale coherent structures in the mixing layers for the jet with a laminar exit velocity profile.

Calculation of Three-Dimensional Boundary Layers on Rotor Blades Using Integral Methods

1993 ◽  
Vol 115 (2) ◽  
pp. 342-353 ◽  
Author(s):  
M. T. Karimipanah ◽  
E. Olsson
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Rotor Blades ◽  
Rotating Flow ◽  
Momentum Thickness ◽  
Transonic Compressor ◽  
Integral Methods ◽  
Momentum Integral

The important effects of rotation and compressibility on rotor blade boundary layers are theoretically investigated. The calculations are based on the momentum integral method and results from calculations of a transonic compressor rotor are presented. Influence of rotation is shown by comparing the incompressible rotating flow with the stationary one. Influence of compressibility is shown by comparing the compressible rotating flow with the incompressible rotating one. Two computer codes for three-dimensional laminar and turbulent boundary layers, originally developed by SSPA Maritime Consulting AB, have been further developed by introducing rotation and compressibility terms into the boundary layer equations. The effect of rotation and compressibility on the transition have been studied. The Coriolis and centrifugal forces that contribute to the development of the boundary layers and influence its behavior generate crosswise flow inside the blade boundary layers, the magnitude of which depends upon the angular velocity of the rotor and the rotor geometry. The calculations show the influence of rotation and compressibility on the boundary layer parameters. Momentum thickness and shape factor increase with increasing rotation and decrease when compressible flow is taken into account. For skin friction such effects have inverse influences. The different boundary layer parameters behave similarly on the suction and pressure sides with the exception of the crossflow angle, the crosswise momentum thickness, and the skin friction factor. The codes use a nearly orthogonal streamline coordinate system, which is fixed to the blade surface and rotates with the blade.

Effects on Momentum Thickness and Density Ratio for Side-Jet Formation in Round Jets With Variable-Density

2011 ◽  
Author(s):  
Yasuhiro Kaneda ◽  
Akinori Muramatsu
Keyword(s):  
Nozzle Exit ◽  
Mass Density ◽  
Laser Sheet ◽  
Density Ratio ◽  
Variable Density ◽  
Momentum Thickness ◽  
Hot Wire ◽  
Jet Formation ◽  
Ambient Gas ◽  
Density Ratios

If the mass density of an issuing gas is sufficiently lower than that of the ambient gas, radial ejections of the jet gas may be generated near the nozzle exit. These radial ejections are referred to as side jets. The parameters for side-jet formation have been reported to be the density ratio of the jet gas and the ambient gas and the momentum thickness at the nozzle exit. In the present experimental study, gases with variable density were discharged into still air. Two round nozzles having different area contraction ratios were used in order to vary the momentum thickness. The momentum thicknesses were obtained after the velocity profiles at the nozzle exit were measured by a hot-wire probe and a hot-wire concentration probe for jets with various density ratios and issuing velocities. The existence of side jets was confirmed by flow visualization of the jets using a laser sheet. The domain for side-jet formation is illustrated using the non-dimensional momentum thickness and the density ratio.

Momentum Diffusion From a Slot Jet Into a Moving Secondary

1956 ◽  
Vol 23 (3) ◽  
pp. 437-443
Author(s):  
A. S. Weinstein ◽  
J. F. Osterle ◽  
W. Forstall
Keyword(s):  
Turbulent Mixing ◽  
Isotropic Turbulence ◽  
Single Parameter ◽  
Spreading Coefficient ◽  
Homogeneous Isotropic Turbulence ◽  
University Of Illinois ◽  
Secondary Stream ◽  
The University ◽  
Initial Turbulence ◽  
Tube Study

Abstract Results are presented for an experimental, impact-tube study of the diffusion of momentum for the isothermal, incompressible, turbulent mixing of a slot jet issuing into a slower moving secondary region. The symmetric spread of the jet into a uniformly flowing secondary stream of low initial turbulence is well correlated by phenomenological expressions based on assumptions suggested by the Engineering Experiment Station of the University of Illinois and extended in this paper to include the case of the slot jet issuing into a moving secondary. The single parameter upon which this correlation is based, the spreading coefficient, is shown to have an interesting interpretation in terms of the diffusion of a stream of fluid “particles” into uniformly flowing fields of homogeneous isotropic turbulence.

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