scholarly journals On steady rotational high speed flows: the compressible Taylor–Culick profile

2006 ◽  
Vol 463 (2077) ◽  
pp. 131-162 ◽  
Author(s):  
Joseph Majdalani
Keyword(s):  
Mach Number ◽  
High Speed ◽  
Sonic Point ◽  
Rocket Motors ◽  
One Dimensional ◽  
Flow Models ◽  
Isentropic Flow ◽  
Aspect Ratios ◽  
Gas Compression ◽  
Solid Rocket

We consider the compressible flow analogue of the well-known Taylor–Culick profile. We first present the compressible Euler equations for steady, axisymmetric, isentropic flow assuming uniform injection of a calorically perfect gas in a porous chamber. We then apply the Rayleigh–Janzen expansion in powers of , where M w is the wall Mach number. We solve the ensuing equations to the order of and apply the results up to the sonic point in a nozzleless chamber. Area averaging is also performed to reconcile with one-dimensional theory. Our solution agrees with the existing theory to the extent that it faithfully captures the steepening of the Taylor–Culick profile with downstream movement. Based on the closed-form expressions that we obtain, the main flow attributes are quantified parametrically and compared to the existing incompressible and quasi-one-dimensional theories. Verification by computational fluid dynamics is also undertaken. Comparison with two turbulent flow models shows excellent agreement, particularly in retracing the streamwise evolution of the velocity. Regardless of the Mach number, we observe nearly identical trends in chambers that are rescaled by the (critical) sonic length, L s . Using a suitable transformation, we prove the attendant similarity and provide universal criteria that can be used to assess the relative importance of gas compression in solid rocket motors. Owing to sharper velocity gradients at the wall, we find that an incompressible model underestimates the skin friction along the wall and underpredicts the centreline speed by as much as 13% at the sonic point. In practice, such deviations become appreciable at high-injection rates or chamber aspect ratios.

A Theory for the High-Speed Flow of Gas-Solids Mixtures under Conditions of Equilibrium and Constant Fractional Lag

1969 ◽  
Vol 184 (3) ◽  
pp. 59-66 ◽  
Author(s):  
B. N. Cole ◽  
H. M. Bowers ◽  
F. R. Mobbs
Keyword(s):  
Mach Number ◽  
Speed Of Sound ◽  
Gas Dynamics ◽  
High Speed ◽  
Solid Particles ◽  
High Speed Flow ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Speed Flow ◽  
Constant Area

A theory is presented for the high-speed, one-dimensional flow of a gas-solids mixture, assuming constant fractional lags of temperature and velocity between the solid particles and the gas. A mixture speed of sound is is derived and used as the basis of a mixture Mach number. Expressions are deduced which are parallel to many well-known relationships in orthodox one-dimensional gas dynamics. The investigation covers frictionless flow in a variable area duct and flow with friction in a constant area duct. The effect of solids volume is also taken into account.

Numerical simulation of ignition transient in solid rocket motor: a revisit

2017 ◽  
Vol 89 (6) ◽  
pp. 936-945 ◽  
Author(s):  
Junaid Godil ◽  
Ali Kamran
Keyword(s):  
Flow Field ◽  
Motor Development ◽  
Solid Propellant ◽  
Research Effort ◽  
Solid Rocket Motor ◽  
Content Type ◽  
Rocket Motors ◽  
One Dimensional ◽  
Erosive Burning ◽  
Solid Rocket

Purpose The capability to predict and evaluate the motor pressure during each phase by means of a numerical analysis can significantly increase the efficiency of the preliminary design process with a reduction of both the motor development and operational costs. This paper aims to perform numerical simulation to analyze the ignition transient in solid rocket motor by solving Euler equation coupled with some semi-empirical correlations. These relations take into account the main phenomena affecting the ignition transient. Coupling relationships include the heat transfer of the gas to the propellant and erosive burning rate relationship. Design/methodology/approach The current research effort divides motor into series of control volumes along the port axis, and the variation of port area, burning surface and burning rate along the port are taken into account. A set of governing equations are then solved using explicit, time-dependent, predictor-corrector finite difference method. The numerical model helps to capture and embed shock wave associated with igniter flow within the solution. Second-order artificial viscosity dampens out the numerical oscillations due to sharp gradient within the flow field. The developed computer code predicts the start-up characteristics of motor. The study also provides comparison of simulation results with in-house experimental motor. Findings Simulations are performed with and without erosive burning to demonstrate that the flow model is a good physical approximation of motor. Numerical results calculated by this model without erosive burning are not in good agreement with experimental results. This minor discrepancy has motivated the inclusion of erosive burning in numerical model. The simulated results are then compared with the experimental data for head-end and rear-end pressure. The agreement between simulation and experiment is remarkable. In summary, major finding of this study is that unsteady quasi-one-dimensional gas dynamic model can capture the flow field in the motor during ignition transient effectively. Research limitations/implications Unsteady quasi-one-dimensional gas dynamic model can capture the flow field in the motor during ignition transient effectively. However, in systems where two- and three-dimensional effects are pre-dominant, one would require to develop a more elaborate, multi-dimensional model which will allow for further understanding of the flow behavior and eventually lead to modeling of rocket motors with more complex geometries. Practical implications The close agreement between experimental and simulation results can be considered as forced to some degree, because the general mathematical model of erosive burning contains a free variable erosive burning exponent. However, in future, this variable can be established a priori by erosive burning tests. Originality/value The solid propellant ignition process consists of series of rapid events and must be completed in a fraction of a second. An understanding of the dynamics of ignition has become increasingly vital with the development of larger and more sophisticated solid propellant rocket motors. This research effort provides the simulation framework to predict and evaluate the motor pressure during each phase by means of a numerical analysis, thus significantly increasing the efficiency of the preliminary design process with a reduction of both the motor development and operational costs.

Energy partitioning in high speed impact of analogue solid rocket motors

1999 ◽  
Vol 103 (1029) ◽  
pp. 519-528
Author(s):  
W. P. Schonberg
Keyword(s):  
High Speed ◽  
Failure Modes ◽  
Rocket Motor ◽  
Solid Rocket Motor ◽  
Solid Rocket Motors ◽  
Rocket Motors ◽  
Response Characteristics ◽  
Fast Running ◽  
Solid Rocket ◽  
Full Scale Tests

Abstract Modelling the response of solid rocket motors to bullet and fragment impacts is a high priority among the military services from standpoints of both safety and mission effectiveness. Considerable effort is being devoted to characterising the bullet and fragment vulnerability of solid rocket motors, and to developing solid rocket motor case technologies for preventing or lessening the violent responses of rocket motors to these impact loadings. Because full-scale tests are costly, fast-running analytical methods are required to characterise the response of solid rocket motors to ballistic impact hazards. In this study, a theoretical first-principles-based model is developed to determine the partitioning of the kinetic energy of an impacting projectile among various solid rocket motor failure modes. Failure modes considered in the analyses include case perforation, case delamination, and fragmentation of the propellant simulant material. Energies involved in material fragmentation are calculated using a fragmentation scheme based on a procedure developed in a previous impact study utilising propellant simulant material. The model is found to be capable of predicting a variety of response characteristics for analogue solid rocket motors under high speed projectile impact that are consistent with observed response characteristics. Suggestions are made for improving the model and extending its applicability to a wider class of impact scenarios.

Quasi-One-Dimensional Modeling of Internal Ballistics and Axial Acoustics in Solid Rocket Motors

2016 ◽  
Vol 32 (4) ◽  
pp. 882-891
Author(s):  
V. Kalyana Chakravarthy ◽  
Arvind S. Iyer ◽  
Debasis Chakraborty
Keyword(s):  
Solid Rocket Motors ◽  
Rocket Motors ◽  
One Dimensional ◽  
Dimensional Modeling ◽  
Internal Ballistics ◽  
Solid Rocket

Damping of modal perturbations in solid rocket motors

2016 ◽  
Vol 120 (1231) ◽  
pp. 1425-1445 ◽  
Author(s):  
A.S. Iyer ◽  
V.K. Chakravarthy ◽  
S. Saha ◽  
D. Chakraborty
Keyword(s):  
Computational Fluid Dynamic ◽  
Fluid Dynamic ◽  
Sectional Area ◽  
Dynamic Simulations ◽  
Cross Sectional ◽  
Solid Rocket Motors ◽  
Rocket Motors ◽  
One Dimensional ◽  
Solid Rocket ◽  
High Length

ABSTRACTQuasi-one-dimensional (quasi-1D) tools developed for capturing flow and acoustic dynamics in non-segmented solid rocket motors are evaluated using multi-dimensional computational fluid dynamic simulations and used to characterise damping of modal perturbations. For motors with high length-to-diameter ratios (of the order of 10), remarkably accurate estimates of frequencies and damping rates of lower modes can be obtained using the the quasi-1D approximation. Various grain configurations are considered to study the effect of internal geometry on damping rates. Analysis shows that lower cross-sectional area at the nozzle entry plane is found to increase damping rates of all the modes. The flow-turning loss for a mode increases if the more mass addition due to combustion is added at pressure nodes. For the fundamental mode, this loss is, therefore, maximum if burning area is maximum at the centre. The insights from this study in addition to recommendations made by Blomshield(1)based on combustion considerations would be very helpful in realizing rocket motors free from combustion instability.

Comparison of Micro-Pressure Wave Radiated Out of Tunnel Exit between Slab Track and Ballast Track

2011 ◽  
Vol 90-93 ◽  
pp. 2183-2187 ◽  
Author(s):  
Feng Geng ◽  
Qian Zhang
Keyword(s):  
Pressure Wave ◽  
High Speed ◽  
High Speed Train ◽  
Tunnel Length ◽  
One Dimensional ◽  
Isentropic Flow ◽  
Calculation Process ◽  
Ballast Track ◽  
Reduction Effect ◽  
The One

Based on the one-dimensional unsteady compressible non-isentropic flow theory, micro-pressure wave radiated out of tunnel exit generated by a high-speed train entering a tunnel was investigated. In calculation process, the track roadbed and tunnel length were considered. The results, which were qualitatively and quantitatively analyzed, show that the ballast track has reduction effect of micro-pressure wave in long tunnel.

On the rotational compressible Taylor flow in injection-driven porous chambers

2008 ◽  
Vol 603 ◽  
pp. 391-411 ◽  
Author(s):  
BRIAN A. MAICKE ◽  
JOSEPH MAJDALANI
Keyword(s):  
Two Dimensional ◽  
Dimensional Approach ◽  
Dimensional Theory ◽  
Rocket Motors ◽  
One Dimensional ◽  
Flow Equations ◽  
Isentropic Flow ◽  
Experimental Approaches ◽  
Turbulent Models ◽  
Explicit Criteria

This work considers the compressible flow field established in a rectangular porous channel. Our treatment is based on a Rayleigh–Janzen perturbation applied to the inviscid steady two-dimensional isentropic flow equations. Closed-form expressions are then derived for the main properties of interest. Our analytical results are verified via numerical simulation, with laminar and turbulent models, and with available experimental data. They are also compared to existing one-dimensional theory and to a previous numerical pseudo-one-dimensional approach. Our analysis captures the steepening of the velocity profiles that has been reported in several studies using either computational or experimental approaches. Finally, explicit criteria are presented to quantify the effects of compressibility in two-dimensional injection-driven chambers such as those used to model slab rocket motors.

Study on Shaped Charge Jet Initiation of Solid Rocket Motors

2019 ◽  
Author(s):  
Hao CUI ◽  
Rui GUO ◽  
Pu SONG ◽  
Jinsheng XU ◽  
Xiaohui GU ◽  
...  
Keyword(s):  
High Speed ◽  
Shaped Charge ◽  
Solid Rocket Motors ◽  
Rocket Motors ◽  
Jet Impact ◽  
Solid Rocket ◽  
Battlefield Environment ◽  
Shaped Charge Jet ◽  
The Impact ◽  
Jet Initiation

Abstract In order to study the mechanism of initiation of solid rocket motors under the impact of shaped charge jets, a shaped charge jet initiation test was experimentally studied to evaluate the safety of the motor under attack in the battlefield environment. The ex-perimental results indicated that the motor had a detonation reaction under the shaped charge jet impact. The response of the mo-tor was recorded by a high-speed camera. In addition, the mechanism of initiation of the propellant charge was evaluated using by numerical simulations. Pressure-time and reaction-time curves of propellants were analyzed in this paper.

The Effect from Hole Area on Pressure Waves Produced by a High-Speed Train through Tunnel with Perforated Wall

2011 ◽  
Vol 94-96 ◽  
pp. 1733-1736
Author(s):  
Yuan Gui Mei ◽  
Yong Xing Jia
Keyword(s):  
Numerical Method ◽  
Pressure Wave ◽  
High Speed ◽  
Method Of Characteristics ◽  
Pressure Waves ◽  
High Speed Train ◽  
One Dimensional ◽  
Isentropic Flow ◽  
Perforated Wall ◽  
Hole Area

The perforated wall has great effect on pressure waves produced by high-speed train through a tunnel. In this paper the effect is investigated numerically by the method of characteristics based on one-dimensional unsteady compressible non-isentropic flow theory. The numerical method is validated by experimental results of Netherlands NLR. The effect from hole area in perforated wall is investigated principally and the results shows that the pressure wave is alleviated remarkably in tunnel with perforated wall.

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