Supersonic Mach Number Regimes Research Articles

Prediction of Base Pressure in a Suddenly Expanded Flow Process at Supersonic Mach Number Regimes using ANN and CFD

Sudden expansion of flow in supersonic flow regime has gained relevance in the recent pasts for a wide run of applications. A number of kinematic as well as geometric parameters have been significantly found to impact the base pressure created within the suddenly expanded stream. The current research intends to create a predictive model for base pressure that is established in the abruptly extended stream. The artificial neural network (ANN) approach is being utilized for this purpose. The database utilized for training the network was assembled utilizing computational fluid dynamics (CFD). This was done by the design of experiments based L27 Orthogonal array. The three input parameters were Mach number (M), nozzle pressure ratio (NPR) and area ratio (AR) and base pressure was the output parameter. The CFD numerical demonstrate was approved by an experimental test rig that developed results for base pressure, and used a nozzle and sudden extended axis-symmetric duct to do so. The ANN architecture comprised of three layers with eight neurons in the hidden layer. The algorithm for optimization was Levenberg-Marquardt. The ANN was able to successfully predict the base pressure with a regression coefficient R2 of less than 0.99 and RMSE=0.0032. The importance of input parameters influencing base pressure was estimated by using the ANN weight coefficients. Mach number obtained a relative importance of 47.16% claiming to be the most dominating factor.

Study of base pressure behavior in a suddenly expanded duct at supersonic Mach number regimes using statistical analysis

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

Base Pressure Behaviour in a Suddenly Expanded Duct at Supersonic Mach Number Regimes using Taguchi Design of Experiments

Abstract Experimental investigations are carried out to study the control of base pressure without and with the use of micro-jets through suddenly expanded axi-symmetric passage in the supersonic regime. Four micro jets having an orifice diameter of 1mm were located at 90° intervals. In the base area, active controls jets have been placed on a pitch of a circle diameter that is 1.3 times the exit diameter of the nozzle. The jets were dispensed abruptly into the axi-symmetric tube maintained at a cross-sectional area of 4.84 times the exit nozzle area. The variation of base pressure as a function of flow control parameters namely Mach number, nozzle pressure ratio (NPR) and length to diameter) ratio (L/D) are evaluated experimentally. This study also assesses the impact of flow control variables on base pressure for two cases viz. with control and without control respectively. An L 9 orthogonal array of Taguchi and the analysis of variance were employed to investigate the percentage of contribution of these parameters and their interactions affecting the base pressure. The correlations between the various factors affecting the base pressure were obtained by using multiple linear regression equations. Confirmation tests were conducted in order to test the developed linear regression equations for their practical significance. Both the regression models were found to be significant and reliable with a percentage deviation lying in the range of − 6.12% to 10.26% for base pressure without control and −13.92% to 6.58% for base pressure with control. Analysis of variance was also performed in order to determine the statistical significance of each parameter on the total variability of base pressure. The study concluded that Mach number is the most influential parameter affecting base pressure followed by NPR and L/D.

Study of Effect of Flow Parameters on Base Pressure in a Suddenly Expanded Duct at Supersonic Mach Number Regimes using CFD and Design of Experiments

Effectiveness of active control of micro jets has been examined by conducting experiments through an abruptly expanded axi-symmetric duct in a view to control base pressure. For this purpose, 1mm orifice diameter micro jets have been deployed at an interval of 900 along the exit diameter of the nozzle. The experiments have been conducted by considering three flow parameters at three levels. Mach number (M), length to diameter (L/D) ratio and area ratio (AR) are the three parameters used to conduct and analyze the flow experiments. Base pressure is considered to be the response variable. The experimentation has been carried out for two cases, i) without active control; ii) with active control. An L9 orthogonal array has been implemented to plan the experiments. It is observed that the control becomes effective for lower area ratios when compared to the higher ones. In addition to this, at high area ratios suction at the base decreases and hence base pressure continuous to diminish with increasing L/D until it reaches a value of L/D=6. The obtained experimental results are subjected to multiple linear regression analysis and Analysis of variance (ANOVA). The performances of the two linear regression models were tested for their prediction accuracy with the help of 15 random test cases. It is observed that, both linear regression models for base pressure without and with control are statistically adequate and capable of making accurate predictions. Furthermore, this work also concludes that, Mach number is the most significant factor affecting base pressure followed by area ratio and L/D ratio for both cases of experimentation. The obtained experimental results are further validated by CFD analysis and are found to be in good concurrence with each other.

Super-soliton dust-acoustic waves in four-component dusty plasma using non-extensive electrons and ions distributions

Based on Sagdeev pseudo-potential and phase-portrait, the dynamics of four-component dust plasma with non-extensively distributed electrons and ions are investigated. Three distinct types of nonlinear waves, namely, soliton, double layer, and super-soliton, have been found. The basic features of such waves are high sensitivity to Mach number, non-extensive parameter, and dust temperature ratio. It is found that the multi-component plasma is a necessary condition for super-soliton's existence, having a wider amplitude and a larger width than the regular soliton. Super-solitons may also exist when the Sagdeev pseudo-potential curves admit at least four extrema and two roots. In our multi-component plasma system, the super-solitons can be found by increasing the Mach number and the non-extensive parameter beyond those of double-layers. On the contrary, the super-soliton can be produced by decreasing the dust temperature ratio. The conditions of the onset of such nonlinear waves and its merging to regular solitons have been studied. This work shows that the obtained nonlinear waves are found to exist only in the super-sonic Mach number regime. The obtained results may be of wide relevance in the field of space plasma and may also be helpful to better understand the nonlinear fluctuations in the Auroral-zone of the Earth's magnetosphere.

Effect of excess superthermal hot electrons on finite amplitude ion-acoustic solitons and supersolitons in a magnetized auroral plasma

The effect of excess superthermal electrons is investigated on finite amplitude nonlinear ion-acoustic waves in a magnetized auroral plasma. The plasma model consists of a cold ion fluid, Boltzmann distribution of cool electrons, and kappa distributed hot electron species. The model predicts the evolution of negative potential solitons and supersolitons at subsonic Mach numbers region, whereas, in the case of Cairn's nonthermal distribution model for the hot electron species studied earlier, they can exist both in the subsonic and supersonic Mach number regimes. For the dayside auroral parameters, the model generates the super-acoustic electric field amplitude, speed, width, and pulse duration of about 18 mV/m, 25.4 km/s, 663 m, and 26 ms, respectively, which is in the range of the Viking spacecraft measurements.

Arbitrary amplitude ion acoustic solitary waves and double layers in a magnetized auroral plasma with q-nonextensive electrons

Using the Sagdeev pseudo-potential technique, further investigation on the effect of nonextensive hot electrons on finite amplitude nonlinear low-frequency electrostatic waves in a magnetized two-component plasma have been reported in detail. The plasma model consists of cold ions fluid and nonextensively distributed electrons. The existence domain for the nonlinear structures have been established analytically and numerically. Apart from the compressive and rarefactive soliton solutions that have been reported earlier, the present investigation shows that double layer structures can be obtained for certain values of nonextensive electrons in the supersonic Mach number regime. The present results may provide an explanation for the observed nonlinear structures in the auroral region of the Earth’s magnetosphere.

Ion acoustic solitons and supersolitons in a magnetized plasma with nonthermal hot electrons and Boltzmann cool electrons

Arbitrary amplitude, ion acoustic solitons, and supersolitons are studied in a magnetized plasma with two distinct groups of electrons at different temperatures. The plasma consists of a cold ion fluid, cool Boltzmann electrons, and nonthermal energetic hot electrons. Using the Sagdeev pseudo-potential technique, the effect of nonthermal hot electrons on soliton structures with other plasma parameters is studied. Our numerical computation shows that negative potential ion-acoustic solitons and double layers can exist both in the subsonic and supersonic Mach number regimes, unlike the case of an unmagnetized plasma where they can only exist in the supersonic Mach number regime. For the first time, it is reported here that in addition to solitions and double layers, the ion-acoustic supersoliton solutions are also obtained for certain range of parameters in a magnetized three-component plasma model. The results show good agreement with Viking satellite observations of the solitary structures with density depletions in the auroral region of the Earth's magnetosphere.

Effect of hot ion temperature on obliquely propagating ion-acoustic solitons and double layers in an auroral plasma

Properties of obliquely propagating ion-acoustic solitons and double layers in a magnetized auroral plasma composed of hot adiabatic ions and two types of, cool and hot Maxwellian electrons are studied using Sagdeev pseudo-potential technique and assuming the quasi-neutrality condition. The new and surprising result which emerges from the model is that in contrast to the case of cold ions where ion-acoustic solitons and double layers are found for subsonic Mach numbers only, the hot ions case allows these nonlinear structures to exist for both subsonic and supersonic Mach number regimes. The double layers exist at lower angle of propagation as hot ion temperature is increased. The soliton electric field amplitudes are increased but their width and pulse duration are decreased with the increase in hot ion temperature. For the auroral zone parameters, the maximum electric field amplitude, width, pulse duration and speed for the solitons come out to be in the range ∼ (0.3–15)mV/m, ∼ (195–455)m, (7–20)ms and (22–26)km/s, respectively. The results seem to be in agreement with the Viking satellite observations in the auroral zone.

Low frequency solitons and double layers in a magnetized plasma with two temperature electrons

Finite amplitude non-linear ion-acoustic solitary waves and double layers are studied in a magnetized plasma with cold ions fluid and two distinct groups of Boltzmann electrons, using the Sagdeev pseudo-potential technique. The conditions under which the solitary waves and double layers can exist are found both analytically and numerically. We have shown the existence of negative potential solitary waves and double layers for subsonic Mach numbers, whereas in the unmagnetized plasma they can only in the supersonic Mach number regime. For the plasma parameters in the auroral region, the electric field amplitude of the solitary structures comes out to be 49 mV/m which is in agreement of the Viking observations in this region.

Turbulence Model Studies to Investigate the Aerodynamic Performance of a NASA Dual Control Missile at Supersonic Mach Numbers

This paper contains an investigation of the ability of some of the current turbulence models to predict viscous effects in supersonic Mach number regimes. In most cases, these turbulence models have been derived and validated in traditional subsonic to transonic Mach number regimes and their application to supersonic and hypersonic regimes is assumed valid without a proper recourse to understanding the wider implications of the viscous flow field at high Mach numbers. In such flow regimes, such characteristics as the strong shock interactions with control surfaces and evolving vortices present in the flow, or other large entropy gradient effects brought about by the forebody or other fin surfaces, produce non-trivial challenges for the turbulence models. This study was aimed at interrogating the strength of the turbulence models to model such physics. The Applied Vehicle Technology Panel Group 082 of the Research Technology Organisation selected a dual control NASA missile to investigate the capabilities of Computational Fluid Dynamics (CFD) to predict the flow field and performance characteristics of complex-shaped projectiles at high Mach numbers. There are two types of difficulties that are encountered when computing such problems. The first type are geometry based, and are related to the shape of the nose and forebody, number and types of strakes or forward control mechanisms, fin geometry deployment, and shape and design of the cowls and intakes. The second type of difficulty deals with flow complexities such as the heat transfer (M > 4) implications; the vortices shed from the forebody and other control surfaces; the interaction of these vortices with the body structures, the free stream, and with each other; the base flow interaction with the free stream; the boundary-layer development; and, in the case of supersonic flows, the shock boundary-layer interactions. Air-breathing missiles with intakes or missiles with jet-controlled guidance systems add to the flow complexities. Various turbulence models employed in current CFD codes are tested for their ability to address these viscous issues.

Investigation of Crossflow Shocks on Delta Wings in Supersonic Flow

In the study described, a finite difference approach to solving the rotational Euler equations, explicitly fitting shocks as a boundary, is applied to a variety of geometrical shapes in the lower supersonic Mach number regime. It is shown how special techniques based on the physics of the flow can be used to circumvent a variety of numerical difficulties encountered with the conical flow problem that are primarily associated with the initial value characteristics of the hyperbolic scheme, causing embedded shock-induced entropy and crossflow layers to develop on the body surface. UMEROUS investigations over the past several decades have dealt with the problem of supersonic flow over thin wings. Many of the earlier methods used linearized potential flow theory and slender body assumptions to obtain solutions. The failure of linearized potential flow solutions for flows where significant supersonic crossflow regions exist is fairly well known (e.g., Refs. 1-3). More recently, nonlinear methods, such as the method of characteristi cs4 and the method of lines, 5 were developed which were adequate at small angles of attack and simple, but not very thin, cross- sectional shapes. Nevertheless, these nonlinear methods did not broach the topic of crossflow embedded shocks which occur on thin bodies, even at relatively small angles of attack. Under certain geometric and flow conditions, a large ex- pansion occurs around the leading edge, causing an embedded region of supersonic crossflow to occur on the leeward side of the body. Since the supersonic region has no advance warning of the symmetry plane crossflow stagnation condition, an embedded shock forms, causing the crossflow to become subsonic and capable of satisfying this boundary condition. A shock-capturing finite-difference approach was developed and applied to complex shapes with embedded shocks in the high supersonic to hypersonic Mach number regime.6'7 This shock-capturing approach uses the con- servation form of the Euler governing equations in order to resolve the embedded shocks with a minimal amount of numerical instability. In contrast to the aforementioned nonlinear methods in- tegrating the rotational form of Euler equations, a technique was developed to integrate the irrotational equations for supersonic conical flow. A relaxation method was applied to the conical full potential flow equation in Ref. 3 that relied heavily on numerical transonic techniques. Numerical solutions were computed successfully for circular/elliptic cones and thin winglike cross sections from low to high in- cidence at freestream Mach numbers between 1.2 and 3. This method captures the shocks over a few mesh points, ap- parently without numerical instabilities. Using the nonlinear