A proper framework for studying noise from jets with non-compact sources

A quantitative assessment of the acoustic source field produced by a laboratory-scale heated jet with a gas dynamic Mach number of 1.55 and an acoustic Mach number of 2.41 is performed using arrays of microphones that are traversed across the axial and radial plane of the jet's acoustic field. The nozzle contour comprises a method of characteristics shape so that shock-related noise is minimal and the dominant sound production mechanism is from Mach waves. The spatial topography of the overall sound pressure level is shown to be dominated by a distinct lobe residing on the principal acoustic emission path, which is expected from flows of this kind with supersonic convective acoustic Mach numbers. The sound field is then analysed on a per-frequency basis in order to identify the location, strength, convection velocity and propagation angle of the various axially distributed noise sources. The analysis reveals a collection of unique data-informed polar patterns of the sound intensity for each frequency. It is shown how these polar patterns can be propagated to any point in the far field with extreme accuracy using the inverse square law. Doing so allows one to gauge the kinds of errors that are encountered using a nozzle-centred source to calculate sound pressure spectrum levels and acoustic power. It is proposed that the measurement strategy described here be used for situations where measurements are being used to compare different facilities, for extrapolating measurements to different geometric scales, for model validation or for developing noise control strategies.

Dual-Bell Nozzle Design

The dual-bell nozzle is an altitude adaptive nozzle concept that offers two operation modes. In the framework of the German Research Foundation Special Research Field SFB TRR40, the last twelve years have been dedicated to study the dual-bell nozzle characteristics, both experimentally and numerically. The obtained understanding on nozzle contour and inflection design, transition behavior and transition prediction enabled various follow-ups like a wind tunnel study on the dual-bell wake flow, a shock generator study on a film cooled wall inflection or, in higher scale, the hot firing test of a thrust chamber featuring a film cooled dual-bell nozzle. A parametrical system study revealed the influence of the nozzle geometry on the flow behavior and the resulting launcher performance increase.

On Construction of the External Frankl Nozzle Contour Using Quadratic Curvature

The aim of the article is to develop a method, an algorithm, and appropriate software for constructing the external contour of the Frankl nozzle in the supersonic part using S-shape curves. The method is based on the problem of constructing a curve with the natural parameterization. The curve passes through two given points with the given inclination angles of the tangents and provides the given inclination angle of the tangent at the point with the given abscissa [4]. To control the inflection point of the S-shaped curve, the inclination angle of the tangent at a point with the known abscissa is used. In the case, when the curvature is given by a quadratic function, the system of five nonlinear equations is formulated, among which three equations are integral. The system has five unknown variables – three coefficients of the quadratic function, the total length of the curve and the length of the curve to the point with a known abscissa. The lemma on the relation between solutions of the original and the scalable systems, in which the coordinates of the points are multiplied by the same value, is proved. Due to this lemma, it becomes possible, using the obtained solution of the well-scalable system, to find easily the corresponding solution of a bad-scalable (singular) system. To find a solution to the system, we suggest to use the modification of the r-algorithm [5] solving special problem on minimization of the nonsmooth function (the sum of the modules of the residuals of the system), under controlling of the constraints on unknown lengths, in order to guarantee their feasible values. The algorithm is implemented using the multistart method and the ralgb5a octave function [6]. It finds the best local minimum of nonsmooth function by starting the modification of the r-algorithm from a given number of starting points. The algorithm uses an analytical computation of generalized gradients of the objective function and the trapezoid rule to calculate the integrals. The computational experiment was carried out to design the fragment of supersonic part in the external contour of a Frankl-type nozzle. The efficiency of the algorithm, developed for constructing S-shape curves, is shown.

New Contour Design Method for Rocket Nozzle of Large Area Ratio

A rocket engine for space propulsion usually has a nozzle of a large exit area ratio. The nozzle efficiency is greatly affected by the nozzle contour. This paper analysed the effect of the constant capacity ratio in Rao’s method through the design process of an apogee engine. The calculation results show that increasing the heat capacity ratio can produce an expansion contour of smaller expansion angle and exit area ratio. A simple modification of Rao’s method based on thermally perfect gas assumption was made and verified to be more effective. The expansion contour designed by this method has much thinner expansion section and higher performance. For the space engine, a new extension contour type for the end section of the nozzle is proposed. The extension curve bent outward with increasing expansion angle increases the vacuum specific impulse obviously.

Characterisation of Mach number 1.5 and 2 Nozzle Jets using Computational Techniques

In this paper a supersonic nozzle was designed using the MOC method and the nozzle contour has been created. The computational model was developed to model the characteristics of the jet of Mach number 1.5 & Mach number 2 nozzles. The computational model was created with compressible flow field properties in order to get the most accurate result. The pressure inlet and outlet boundary conditions have been applied with viscous flow solver. In order to get the shock flow visualization and high-speed jet characteristics the exit has been extended to 5D vertical and 15D horizontal and the virtual atmosphere has been created. For both models, the CAA (computation acoustical analysis) carried out using flows, Williams and Hawkings acoustic solver to get far-field noise radiation. The experimental technique and future works were discussed. The Jet characteristics of two nozzles were examined and noise sources have been compared.

Characteristics Analysis of Dual Bell Nozzle using Computational Fluid Dynamics

Space exploration and space tourism have now become a raging competition among the developed nations. For this reason, different types of advanced rocket nozzles with prospective privileges are introduced. Altitude adaptive dual bell nozzle will soon replace the conventional nozzles for the first stage rocket launcher. Indeed, this nozzle has auto adaption capability based on altitude. The major feature of a dual bell nozzle is the two bell-shaped contours separated by an inflection point. This nozzle has left rooms for researchers to test different flight conditions and transition characteristics. In this paper, a dual bell nozzle contour has been developed in MATLAB and analysed for different thermodynamic parameters. ANSYS Fluent is used in analysing flow through the nozzle. Shadowgraph imaging technique is used for measuring density gradient and compared it with fluent results. The simulations were performed by using the k-epsilon turbulence model.

Design of an arc-based thrust-optimized nozzle contour

A total of ten arc-based nozzle contours have been numerically compared to an existing thrust-optimized design. Verification and validation of the numerical model was achieved using published experimental data and the resulting numerical uncertainty of the model relative to thrust was less than 0.10%. Analysis of the arc-based nozzles indicated that the contour angles had the greatest effect on thrust. Optimization of the contour angles suggested that an increase in thrust coefficient of 0.25% could be achieved compared to the existing thrust-optimized nozzle. The result shows that an arc-based design method may be used to produce an equivalent thrust-optimized nozzle.

Supersonic Nozzle Optimization Design with Spline Curves Fitting the Nozzle Profiles

Supersonic nozzle contour optimization design was applied to 0.6m×0.6m continuous transonic wind tunnel to improve flow quality in the test section. The Mach number root mean square deviation with the design value was chosen as optimization target. And the CFD results were verified with experimental results. Cubic spline curves with the optimal interpolating point distribution scheme were used to fit the nozzle contour. Efficient global optimization based on the Gaussian process surrogate model was used to reduce the times of evaluation. Results indicate that, the optimization framework can generate a supersonic nozzle contour with better flow quality and more accurate Mach number and that the optimal Mach number root mean square deviation is 0.001.