Parabolic Nozzles Research Articles

Evaluation of generalized k-ω turbulence model in strong separated flow estimation of thrust optimized parabolic nozzle

One of the frequently reported defects of RANS-based turbulence models is overestimation of turbulent kinetic energy production in high speed separated flow problems, which causes significant prediction errors. The correct estimation of such flow in thrust optimized parabolic nozzles extremely depends upon the accurate prediction of the onset of flow separation. In this paper, firstly, the significant error of conventional RANS-based turbulence models is shown to predict the onset of flow separation in this type of nozzles. Then, the prediction accuracy is improved through the modification of the essential parameters of the generalized k-ω (GEKO) turbulence model. It was found that modifying the separation and mixing parameters of the GEKO model to realize the turbulent kinetic energy production resulted in the accurate prediction of onset of flow separation at the extensive range of nozzle pressure ratios. Using this modified model with new coefficients reduced the error of about 30% of the k-ω-sst model in estimating the onset of flow separation. Also, the nozzle pressure value at which the transition from free shock separation (FSS) to restricted shock separation (RSS) occurs is well predicted by this approach. After strengthening the turbulence model, the flow physics has been investigated with increasing and decreasing nozzle chamber pressure. The length of the separation shock and reflected shock waves which impose the presence of FSS or RSS patterns and transitional phenomena are discussed. Our new findings show that unlike the transition from FSS to RSS, the inverse transition from RSS to FSS did not depend on the length of the separation and reflective shocks.

Numerical investigation on thrust efficiency dropping phenomenon of annular expansion–deflection nozzles

The flow patterns in a large-expansion-ratio annular expansion–deflection (ED) nozzle are numerically investigated, focusing on the flow mechanisms underlying the sudden thrust efficiency (η) dropping phenomenon. The objective of the present work is to provide a physical understanding of the ED nozzle flow physics responsible for the nozzle performance variation. The simulations are performed by solving the Reynolds averaged Navier–Stokes equations in combination with the one-equation Spalart–Allmaras turbulence model. The Advection Upstream Splitting Method is used to discretize the convective fluxes, and the second-order central scheme is used to discretize the viscous fluxes. The present investigation demonstrates that two flow mechanisms exist, which can cause the sudden η dropping: one is supersonic flow impingement at the nozzle exit, and the other is the formation of the internal normal shock. The pintle arc radius downstream of the throat plays an important role in determining the size and redirection of the supersonic core flow region, thus influencing the overall nozzle performance. A large radius dimension gives a higher η value at the first rising stage, a large dropping nozzle pressure ratio (NPR), and a large mode transition NPR. Interestingly, a cap shock is proved possible in the current large-expansion-ratio ED nozzle, in which the near-shroud shock acts as the internal shock in the traditional thrust-optimized or parabolic nozzles.

Numerical investigation of second throat exhaust diffuser performance with thrust optimized parabolic nozzles

Free or restricted shock separation phenomena can occur inside a thrust optimized parabolic (TOP) nozzle during over-expanded operations. In the case of restricted shock separation, a cap shock pattern forms in the nozzle which leads to a substantial total pressure drop. This induces further related issues in the process of ground testing of such nozzles using a second throat exhaust diffuser (STED). In the present study, the flow physics in several TOP nozzles operating at over-expanded conditions is investigated numerically. At first, the strong effect of the initial expansion angle of a TOP nozzle on flow separation pattern and shock structure is demonstrated. Results reveal that for high initial expansion angles, restricted shock separation occurs even at low nozzle pressure ratios, while free shock separation takes place for small initial expansion angles at even high nozzle pressure ratios. Subsequently, the effect of separation patterns in TOP nozzles on the starting pressure of a STED is studied. Current results show that the presence of a restricted shock separation pattern leads to a considerable increment of the critical cross sectional area of the flow inside the diffuser. Therefore, the minimum starting pressure of the STED is increased up to 30% after the resizing of the second throat area to eliminate the flow choking inside it.

Flow Characteristics of Parabolic Nozzle by Changing the Shape of Nozzle Exit

This paper deals with parabolic nozzles which can be used in aerospace applications. Parabolic nozzles are mechanical devices which produces mechanical energy by converting the thermal and pressure energy produced as a result of combustion. This project aims at providing the flow characteristics of parabolic nozzle by changing the shape of the exit area. The analyses were further extended by changing the pressure values. The analysis processes were carried out using Computational Fluid Dynamics software ANSYS CFX.

Effect of nozzle geometry on critical-subcritical flow transitions

The geometry of converging-diverging nozzles affects the conditions at which critical-subcritical flow transition occurs. The objective of this work is to develop guidelines to identify the optimum nozzle geometry that maximizes critical pressure ratio while minimizing pressure drop across the nozzle. Experiments were conducted in a facility with 1.5 in. ID PVC pipelines and a 30 ft. long lateral pipeline section. In total, 27 different nozzle geometries were tested, divided into two groups – conical and parabolic nozzles. Nozzles from the ASTAR, Deich, LJ and Moby Dick nozzle groups showed improved performance compared to other nozzle groups. It was determined that a smaller diverging angle and absence of an elongated throat resulted in a higher critical pressure ratio. Length of converging and diverging sections of nozzles did not have as much of an impact on nozzle performance as the throat diameter and shape of converging and diverging sections.

Experimental and Computational Exploration of Underexpanded Jets from Conical, Bell and Double Parabolic Nozzles

The flow structure of the jet emanating from supersonic nozzle with different profiles at underexpanded condition were investigated systematically. Experiments were carried out on conical, bell and double parabolic nozzle at Nozzle Pressure Ratios (NPR) of 4.5, 5 and 5.5. For the sake of comparison, the divergent length was the same for all the nozzles. Numerical simulations were also conducted in a two dimensional computational domain taking a density-based solver with RANS equations and SST k-ω turbulence model. The experimental and numerical results matched well all NPRs. The shock cell length, potential core length and supersonic core length at different NPRs were determined from experiments and compared to numerical predictions. These values are also compared to the predicted values based on the equations previously developed by researchers. It is observed that there is not much influence in nozzle profiles in the shock cell length, potential core length and supersonic core length.

Design of a double parabolic supersonic nozzle and performance evaluation by experimental and numerical methods

Purpose The purpose of this paper is to design a double parabolic nozzle and to compare the performance with conventional nozzle designs. Design/methodology/approach The throat diameter and divergent length for Conical, Bell and Double Parabolic nozzles were kept same for the sake of comparison. The double parabolic nozzle has been designed in such a way that the maximum slope of the divergent curve is taken as one-third of the Prandtl Meyer (PM) angle. The studies were carried out at Nozzle Pressure Ratio (NPR) of 5 and also at design conditions (NPR = 3.7). Experimental measurements were carried out for all the three nozzle configurations and the performance parameters compared. Numerical simulations were also carried out in a two-dimensional computational domain incorporating density-based solver with RANS equations and SST k-ω turbulence model. Findings The numerical predictions were found to be in reasonable agreement with the measured experimental values. An enhancement in thrust was observed for double parabolic nozzle when compared with that of conical and bell nozzles. Research limitations/implications Even though the present numerical simulations were capable of predicting shock cell parameters reasonably well, shock oscillations were not captured. Practical implications The double parabolic nozzle design has enormous practical importance as a small increase in thrust can result in a significant gain in pay load. Social implications The thrust developed by the double parabolic nozzle is seen to be on the higher side than that of conventional nozzles with better fuel economy. Originality/value The overall performance of the double parabolic nozzle is better than conical and bell nozzles for the same throat diameter and length.

Sound Produced by Large Area-Ratio Nozzles During Fixed and Transient Operations

Analysis of the acoustic signature produced by truncated ideal contour and thrust-optimized parabolic nozzles is conducted during both fixed and transient (startup) operations. The truncated ideal contour nozzle experiences free-shock separation flow, whereas the thrust-optimized parabolic nozzle experiences both free-shock separation and restricted-shock separation flow states during startup. This study provides a direct comparison of the acoustic signature produced during free-shock separation and restricted-shock separation flow states while operating under identical nozzle pressure ratios. During a transient episode, the continuous wavelet transform is used to compare the acoustic signatures produced by the nozzles. The truncated ideal contour nozzle demonstrates a gradual increase in broadband frequency energy with increasing nozzle pressure ratio and with broadband shock noise appearing at higher nozzle pressure ratios. The thrust-optimized parabolic nozzle, however, displays a much larger sensitivity to the nozzle pressure ratio. In particular, the free-shock separation to restricted-shock separation transition, which occurs around nozzle pressure ratio 24.4, is weakly revealed in the acoustic signature along sideline angles to the nozzle. At nozzle pressure ratio 13, the acoustic signal observed at shallow angles to the nozzle decreases abruptly across a broad range of frequencies. The latter phenomenon is attributed to the formation of an open-ended subsonic core surrounded by a supersonic annular flow in the thrust-optimized parabolic nozzle during free-shock separation operations of the nozzle, which does not occur in the truncated ideal contour nozzle.

Numerical Simulation of Separated Cold Gas Nozzle Flows

A numerical method for the simulation of separated cold gas nozzle flows is presented and applied to six subscale nozzles. The nozzles considered were a truncated ideal nozzle, two thrust-optimized parabolic nozzles, and three dual bell nozzles. For the thrust-optimized parabolic contours, the occurrence of free and restricted shock separation and the cap shock pattern are discussed. Comparisons with experimental data are provided. Shortcomings of the numerical method are pointed out.

Appearance of Restricted Shock Separation in Rocket Nozzles

Uncontrolled flow separation in nozzles of rocket engines is not desired because it can lead to dangerous lateral forces. Different origins for side loads were identified in the past. Meanwhile, it is proven that in thrust-optimized or parabolic nozzles, a major side load occurs as a result of the transition of separation pattern from free shock separation to restricted shock separation and vice versa. Reasons for the transition between the separation patterns are discussed, and the cap-shock pattern, which is identified to be the cause of this transition, is closely analyzed. It turns out that this pattern can be interpreted as an inverse Mach reflection of the internal shock at the nozzle axis. To prove the transition effect as main side-load driver, a subscale test campaign has been performed. Two different nozzle contours, a thrust-optimized and a truncated ideal nozzle with equal performance data, were tested. Highest side loads were measured in the thrust-optimized nozzle, when the separation pattern changes from free to restricted shock separation. Side loads measured in the truncated ideal nozzle were only about one-third as high as in the thrust-optimized nozzle.

Pulsed laser propulsion

Abstract : A fluid mechanical model is developed to assess the performance in both finite background pressure and vacuum environments of a rocket that is propelled by the absorption of radiant energy from a remotely stationed, repetitively pulsed laser. The model describes the gaseous propellant flow within a conical nozzle that is subjected to a series of point energy depositions at the apex of the cone. An equivalence between conical and parabolic nozzles is discussed for finite background pressure operation. The model predicts laser parameters necessary to achieve high specific impulses, i. e., 600 to 1000 sec. Scaling laws for high thrust - high specific impulse rocket systems are discussed.

Experimental and theoretical modeling of laser propulsion

Some schemes of laser propulsive systems are discussed. The question concerned with a body acceleration due to series of air blast waves generated by laser sparks is studied. For this purpose the numerical solutions of gasdynamic equations are found under appropriate initial conditions corresponding to the real ones. Radiative losses and spatial effects at the nozzle exit are taken into account. Theoretical results presented as coupling coefficients (equivalent to reciprocal thrust cost realizing under periodical pulse laser operation) are compared with the experiment. Using conical and parabolic nozzles irradiated by pulsed CO 2 laser the thrust cost about 2000 W/N is achieved which is close to the minimum possible one for the air blast wave-nozzle wall interaction. The main characteristics of laser propulsive jet are presented. Experimental results on recoil momentum transfered to solids under their evaporation by the pulsed CO 2-laser are presented as well. The question of plasma shielding effects on the momentum transfer under the vapour optical breakdown conditions is touched on.