Fully Expanded Supersonic Flow Inside Conical and Contour Nozzle

A simple analytical model is developed for optimum ejector steady-state performance under the assumption that the driver gas mass flow rate exceeds the suction side mass flow rate. This requires the mixing to be at constant pressure and the suction side inlet Mach number to be small. Since the model is formulated in terms of enthalpy, it is applicable to arbitrary motive and suction gases. For purposes of verification, the model is compared with exact numerical results, and with the experimentally determined entrainment ratio used to correct the suction side mass flow rate for changes in temperature or molecular weight. The effect on ejector performance of the pertinent dimensionless parameters is considered. For example, it is shown that the use of a motive fluid with a ratio of specific heats near unity is detrimental to performance. I. Introduction O VER the past few decades there have been many fluid mechanic studies of ejector pumps. Currently, there is renewed interest in ejectors for pumping the subatmospheric effluent of cw chemical lasers,1-4 with primary emphasis on optimized ejector performance. Since an ejector is a pump, performance is in terms of a compression ratio, in particular, the ratio of the exhaust gas stagnation pressure divided by the stagnature pressure of the inlet suction gas. (The suction gas is referred to as the secondary flow; the motive gas is referred to as the primary flow.) Optimum performance is defined here as the largest compression ratio for given primary and secondary flow rates and for a given secondary stagnation pressure. An objective of this work is to derive simple, approximate formulas for the optimum compression ratio in terms of a minimum number of key dimensionless parameters. This approach provides a simple estimate of the maximum possible compression ratio, given the primary and secondary fluids, their stagnation conditions, and their flow rates. Conversely, it does not determine such fundamental characteristics as the transition1 between the mixed and super sonic regimes. Some generality is retained in the choice of parameters for the thermodynamic properties of both primary and secondary gases. This is important for laser application where the-composition of both gases often differs considerably from steam or air. Because of its analytical simplicity, the derivation provides useful insight into the dominant process in an ejector, e.g., a natural consequence of the analysis is an ejector figure of merit. The assumptions underlying the derivation, the derivation itself, and its method of application are presented in Sec. II. The effect on ejector performance of changes in primary gas stagnation enthalpy, ejector nozzle Mach number, etc., are discussed in Sec. III. Of particular interest are the sections which show that a value near unity for the ratio of specific heats of the primary gas leads to a small compression ratio, and that a low subsonic Mach number is required for the secondary inlet flow for optimum compression. To establish the validity of the analysis, a comparison is provided in Sec. Ill with exact computer solutions for a steam and air ejector pumping a chemical laser flow. A simple derivation is also given for the entrainment ratio used by the Heat Exchange In

Axial and vectored flow behavior of an axisymmetric confined jet thrust vector control (CJTVC) nozzle is studied experimentally under steady-state and dynamic conditions. Pressurized secondary air injection is used to vector the nozzle at various levels of primary (chamber) air pressure. Attention is focused on internal flow characterization, nozzle instability, and the influence of secondary mass flow rate on vectored side force. The overexpanded flow separation point is located during axial test runs and compared to empirical predictions. Side force and mass flow rate measurements suggest that choked secondary mass flow occurs prior to the secondary mass flow rate that generates a maximum side force. Cavity pressure oscillations and nozzle side force response times are investigated to further characterize the dynamic behavior of the CJTVC nozzle. Nomenclature A = area a = cavity acoustic speed D = throat diameter d = cavity diameter F = force / = eigenfrequencies L = nozzle length from throat to exit M = Mach number m = mass flow rate P = stagnation pressure p = static pressure St = cavity Strouhal number, /Trd/a x = axial distance from throat a = conical half-angle y = ratio of specific heats Subscripts a = axial b = cavity downstream of separation e = exit m = circle nodal parameter n = radial nodal parameter p = primary s = side/separation/secondary w = wall

+− ⎫ ⎛⎞ ⎧ ⎡⎤ =+ − ⎨ ⎬ ⎜⎟ ⎣⎦ + ⎩ ⎝⎠ ⎭ Despite the importance of this relation and recurrence in engineering applications, only numerical root finding and/or tabulation have been so far utilized to calculate the exit Mach number corresponding to a given design area ratio. Our asymptotic solution will preclude the need for numerical iteration; it will be based on the assumptions that the flow is a perfect gas undergoing isentropic expansion through a practical size nozzle. While current techniques utilized to solve the preceding equation will only generate numerical values, our solution will produce the Mach numbers explicitly as a function of the area ratio and the ratio of specific heats. Furthermore, both subsonic and supersonic solutions will be obtained explicitly. This will help to gain deeper physical insight into the dependence of the flow Mach number on these two important geometric and thermodynamic ratios.

The problem of supersonic streamlining of an aerodynamic (AD) body, “a plate blunted by a cylinder”, by a flow with the freestream Mach number M = 4 containing an external energy source has been studied, taking into account physicochemical transformations. The results of the effect of the ratio of specific heats γ changing in the range from 1.1 to 1.4 on the dynamics of triple-shock configurations and vortex-contact structures are presented for the interaction of an energy source with the bow shock wave. The energy source is modeled via the heated rarefied layer (filament). The angles in the triple-shock configurations, the stagnation pressure, together with the frontal drag force, have been studied dependent on the specific heats ratio γ, the characteristics of the energy source, and also on the angle of the incident shock. Vortex-contact structures have been researched for the Mach numbers 7, 8, 9, as well as the generation of the Richtmyer-Meshkov instability accompanying the formation of a triple-shock configuration. The results show a strong influence of the specific heats ratio of the gas medium and the parameters of the energy source on the triple-shock configuration and aerodynamic characteristics of the body. This conclusion can be useful for aerospace applications in the area of the design of nozzles, intakes, and high speed flying vehicles. Additionally, the results show the possibility of flow control in the atmospheres of other planets using external energy deposition.

A theoretical analysis of the performance of normal shock inlets having sweptback faces is presented. The analysis, which is based on a continuity and stream-thrust balance without regard to the internal shock patterns, permits the prediction of the critical total pressure recovery of a sweptback normal shock inlet as a function of face angle, angle of attack, and free-stream Mach Number. The theory shows that the performance of a normal shock inlet at positive angles of attack can be significantly improved without penalizing the performance at zero angle of attack by sweeping back the inlet face. The theory also shows tha t the supercritical mass-flow ratio for the normal shock inlets is independent of Mach Number and depends only upon the geometry of the inlet and the angle of attack. A series of normal shock inlets having face angles of 0°, 10°, 20°, 30°, and 40° was tested at Mach Numbers of 1.62 and 1.99. The experimental results are shown to be in good agreement with the theory. A D f F g m m M Ps Pt R Tt V W a 0 7 P 0 ibsc 0 = 1 = 2 = 3 = NOMENCLATURE = area = diameter = stream thrust per unit area = stream thrust = acceleration due to gravity = mass flow = Mach Number parameter defined in Eq. (3) = Mach Number = static pressure = total pressure = gas constant = total temperature = velocity = airflow = angle of attack = inlet face, angle = ratio of specific heats = density = parameter defined in Eq. (14) and tabulated in reference 1 ripts = free stream = inlet station = exit station at end of constant-area passage = end of subsonic diffuser

: An investigation was conducted to determine the diffuser-ejector performance for five different driving fluids--air, nitrogen, argon, helium, and hydrogen--having different ratios of specific heats. Two diffuser-ejector configurations, which consisted of two different area ratio nozzles and two duct sizes which gave duct-to-nozzle area ratios of 73.06 and 20.40, were used in this investigation. The nozzle for configuration 1 was an 18-deg, half-angle conical nozzle with an area ratio of 18.00, and the nozzle for configuration 2 was a 7.58-deg, half-angle conical nozzle with an area ratio of 10.76. The stagnation conditions for the driving fluids ranged in pressure from 51 to 866 psia and temperature from 450 to 516 R. The cell-to-driving fluid pressure ratios (Pc/Pt) for the different driving fluids were dependent on the ratio of specific heats, gamma. An increase in gamma resulting from a decrease in temperture, such as for hydrogen, produced a decrease in Pc/Pt. A decrease in gamma resulting from the change from a single-phase to a two-phase fluid (condensation), such as for air, nitrogen, and argon, caused the Pc/Pt ratios to increase.

: Charts and tables are presented for determining approximate values of the initial turning angles and the boundary shapes of jets exhausting to low ambient temperatures. The tables have been compiled to facilitate calculations pertaining to jet flow for various ratios of specific heats from 1.10 to 1.667 and Mach numbers from 1.0000 to 100.00. The ratios p/p sub t and A/A at the nozzle throat and the Prandtl-Meyer angle are given for each Mach number and ratio of specific heats.

A numerical solution of the Kirchhoff equation for the propagation constant of longitudinal sound waves in infinitely long cylindrical tubes has been obtained. The solution, which avoids the wide-tube approximations, shows that the percentage errors in the von Helmholtz-Kirchhoff tube velocity correction and tube absorption are both roughly equal to the percentage the velocity correction is of the free-space velocity. The error in the von Helmholtz-Kirchhoff equations can be plotted as a function of fD/a, pD/ηa, and γ. (f is the sound frequency, D the tube diameter, a the free-space velocity, p the gas pressure, η the viscosity, and γ the ratio of specific heats.) Recent absorption measurements in Ar are in agreement with values calculated numerically, but measured velocities indicate the need for considering molecular slip at the tube wall. Thermal relaxation is introduced into Kirchhoff's basic equation by using the Eucken relation k/coη − (9γ −5)/4 and considering γ to be the ratio of complex relaxing specific heats. Viscothermal and relaxation effects are found to be additive only if the frequency is near the cutoff frequency for the first unsymmetric mode and the f/p values do not extend to the megacycle/second atmospheres range.

Nomenclature A = area CD = drag coefficient CL = lift coefficient Cp = pressure coefficient CV = jet velocity ratio Cμ = blowing coefficient (jet momentum ratio) c = chord DLG = flap deflection, lap and gap f = jet orifice diameter L = lift M = Mach number n = number of jets p = static pressure p0 = total pressure q = freestream dynamic pressure S = wing reference area V = speed x/c = nondimensional distance measured in a chordwise sense α = angle of attack, or jet skew angle β = jet pitch angle γ = ratio of specific heats = flap deflection λ = jet orifice spacing ρ = density

In suddenly expanded flows, due to the abrupt expansion of the flow from a nozzle into an enlarged duct, the pressure reduces in the base region of the enlarged duct which increases the base drag. The techniques used to increase the base pressure are namely passive control technique and active control technique. In passive control technique the geometrical modifications are employed by providing splitter plates, ribs, cavities etc. while in active control technique the secondary control jets are provided in the base region of an enlarged duct to increase base pressure up to atmospheric pressure. The air blowing pressure from secondary control jets should be optimum. This paper presents the computational fluid dynamic (CFD) analysis to optimize blowing pressure ratio i.e. the ratio of inlet pressure of control jets to the atmospheric pressure, to increase base pressure up to atmospheric pressure in the base region of an enlarged duct. In the present study, CFD analysis was carried out for different air blowing pressure ratios to optimize it. Flow and geometry parameters considered for the analysis are Mach number, area ratio, nozzle pressure ratio and blowing pressure ratio. Mach numbers considered for analysis are 1.5, 2.0 and 2.5. Area ratios and nozzle pressure ratios considered for analysis are 2, 5 and 8. The CFD analysis is done for different combinations of Mach numbers, area ratios, and the nozzle pressure ratios by varying blowing pressure ratio from 2 to 8 in step of 1. Based on analysis results anyone can select optimum value of blowing pressure ratio at a given Mach number, area ratio and nozzle pressure ratio to increase base pressure nearly up to atmospheric pressure.

A new method to quickly generate hypersonic waverider forebody configurations has been developed. The new method is an extension of the analysis method and power law method.and is called “Osculating analysis Method”. In this new method the constraint of creating only one attached wave shock in the forebody design by analysis or power law method is removed. More than one attached forebody shock waves can be created in the new method. For the purpose to integrate with ramjet or scramjet, a hypersonic forebody integrated with inlet was designed. The design objective is that the hypersonic forebody has three attached shock waves in the design flight condition. To better understand the forebody performance, three dimensional flow field calculation of the design waverider forebody (designed by osculating analysis method) integrated with hypersonic inlet and two comparative reference waverider forebodies(designed by analysis method and power law method, respectively) integrated with hypersonic inlet in the design and off design conditions were conducted. The computational results show that the performance of design waverider with three attached shock wave is great better than that of two comparative reference waveriders. Compared with two comparative reference models, the flow coefficient is increased by 10.38%, 8.2%; the recovery coefficient of total pressure is increased by 9.38%, 7%, respectively; the uniformity coefficient of inlet exit is increased by 8.8%,6.2%. Three waverider forebodies integrated with hypersonic inlet show better perforemance in high Mach number and attack angle than that in low mach number and negative attack angle. CFD predictions show that the design mach number of waverider forebody should be great than the real flight mach number and the design attack angle should be less than that of real flight condition. Test of the design waverider forebody integrated with hypersonic inlet was performed at a 500-mm-diameter hypersonic tunnel. Experimental results were obtained for a range of conditions, including the on-design Mach number and off-design Mach number. The experimental results were greatly agreed with those of simulation predictions. Vapor screen results for the model indicate three attached (or very nearly attached, within the limits of observation) shock waves along the entire leading edge. Simulation predictions generally agree with the measured pressure distribution.

An experimental demonstration was carried out in a ballistic range at high Mach numbers with the low specific heat ratio gas hydrofluorocarbon HFC-134a to observe the unstable bow-shock wave generated in front of supersonic blunt objects. The shadowgraph images obtained from the experiments showed instability characteristics, in which the disturbances grow and flow downstream and the wake flow appears wavy because of the shock oscillation. Moreover, the influence of the body shape and specific heat ratio on the instability was investigated for various experimental conditions. Furthermore, the observed features, such as wave structure and disturbance amplitude, were captured by numerical simulations, and it was demonstrated that computational fluid dynamics could effectively simulate the physical instability. In addition, it was deduced that the shock instability is induced by sound emissions from the edge of the object. This inference supports the dependence of the instability on the specific heat ratio and Mach number because the shock stand-off distance is affected by these parameters and limits the sound wave propagation.

An active noise control work in jets from contoured and conical supersonic axisymmetric nozzles (henceforth contoured and conical jets, respectively) with plasma actuators is conducted. The Mach 1.65 contoured nozzle is designed by using the method of characteristics for shock-free jet. The Mach 1.65 conical nozzle has converging and diverging conical sections with a sharp throat. Eight actuators, distributed uniformly around the nozzle exit, are used and the jet is forced with azimuthal modes of 0-3, and ±4 and at forcing Strouhal numbers ranging from 0.18 to 4.0. Far-field acoustic is measured by a linear microphone array covering polar angles from 25 to 80q relative to the jet axis. At a far-field polar angle of 30q, more noise reduction is observed at a higher azimuthal mode of 3 or ±4 in both jets. The maximum reduction in overall sound pressure level is 1.5 and 2.6 dB for the contoured and conical jets, respectively. At a polar angle of 80q (near sideline), the reduction in noise level is negligible. In the conical jet, there is a competition for energy between the naturally-occurring structures and those generated by forcing, similar to the process taking place in forcing an imperfectly-expanded supersonic jet. At moderate forcing Strouhal numbers, the structures generated by forcing prevail and thus the naturally-occurring structures are suppressed or weakened. This seems to be responsible for the reduced or suppressed screech tones in the conical jet.

In the present work for a quasi-one-dimensional isentropic compressible flow model, an empirical equation of the Mach number is constructed as a function of the stagnation pressure ratio for an analytical equation that algebraic procedures cannot invert. The Excel 2019 Solver tool was applied to calibrate the coefficients and exponents of the empirical equation during its construction for the Mach number range from 1 to 10 and 1 to 5. A specific heat ratio from 1.1 to 1.67 and the generalized reduced gradient iterative method were used to minimize the sum of squared error, which was set as the objective function. The results show that for Mach 1 to 10, an error of less than 0.063% is obtained, and for Mach 1 to 5, an error of less than 0.00988% is obtained. It is concluded that the empirical equation obtained is a mathematical model that reproduces the trajectories of the inverted curves of the analytical equation studied.

The quasi-one-dimensional method for the dual-mode scramjet (DMR) of the hypersonic RBCC powered vehicle was simplified in most of open researches. Furthermore, these simplified method can not fully capture the processes of wall heat transfer, changes in the boundary layer and the ratio of specific heat and the transonic flow in the reacting flow. Addressing this problem, we establish the models for processing core flow area, transonic flow and pre-combustion shock train (PCST) based on the governing equations for quasi-one-dimensional flow and certain assumptions. Thus the quasi-one-dimensional model of dual-mode scramjet engine that incorporates the changes in wall heat transfer and in the ratio of specific heat is built. Then, the reliability and accuracy of the model are assessed qualitatively and quantitatively by experiment and CFD numerical simulation. There is a high agreement between the theoretical calculations and the results of experimental data and CFD numerical simulation. This work expands the application scope and increases the reliability of quasi-one-dimensional model of dual-mode scramjet engine in RBCC engine. The results shed new light on the preliminary performance assessment and engineering application of dual-mode scramjet engine.