A method for predicting Mach stem height in steady flows

2021 ◽  
pp. 095441002110015
Author(s):  
Song-Guk Choe
Keyword(s):  
Analytical Model ◽  
Slip Line ◽  
Flow Region ◽  
Rocket Engines ◽  
Steady Flows ◽  
Mach Stem ◽  
Stem Height ◽  
Mach Numbers ◽  
Relative Errors ◽  
Cfd Method

The prediction of Mach stem height can be important in the design of supersonic intake in supersonic and hypersonic flows. It is also important because of the progress in aircraft and rocket engines. An analytical method of predicting the Mach stem height is necessary in theoretical field of shock reflection and is the basis of the comparable computational fluid dynamics (CFD) method. A method for predicting the Mach stem height in steady flows is performed based on the earlier models. In this article, an analytical model for predicting the Mach stem height is improved based on two main assumptions: one is the calculation of the triple point deflection angle when the Mach stem is an oblique shock and the other is about the shape of the free part of the slip line. Under these assumptions, the relations predicting of Mach stem height in two-dimensional steady flow are derived based on the advanced averaging method of the subsonic flow region. The Mach stem heights are decided solely for the incoming flow Mach numbers and the wedge angles by the improved analytical model. As a result, the Mach stem heights by the model of this article are found to agree well with experimental results at lower Mach numbers, but there are relative errors at higher Mach numbers. The convexity of the slip line is also considered.

An analytical model for asymmetric Mach reflection configuration in steady flows

2019 ◽  
Vol 863 ◽  
pp. 242-268
Author(s):  
Shobhan Roy ◽  
Rajesh Gopalapillai
Keyword(s):  
Analytical Model ◽  
Mach Reflection ◽  
Wedge Angle ◽  
Steady Flows ◽  
Mach Stem ◽  
Stem Height ◽  
Von Neumann ◽  
Reflection Configuration ◽  
Symmetric Reflection ◽  
Subsonic Region

An analytical model is presented for the configuration of Mach reflection (MR) due to the interaction of two-dimensional steady supersonic flow over asymmetric wedges. The present asymmetric MR model is an extension of an earlier model for the symmetric MR configuration. The overall Mach reflection (oMR) in the asymmetric wedge configuration is analysed as a combination of upper and lower half-domains of symmetric reflection configurations. Suitable assumptions are made to close the combined set of equations. The subsonic pocket downstream of the Mach stem is taken to be oriented along an average inclination, based on the streamline deflections by the Mach stem at the triple points. This assumption is found to give satisfactory results for all types of oMR configurations. The oMR configuration is predicted for all types of reflections such as direct Mach reflection (DiMR), stationary Mach reflection (StMR) and inverse Mach reflection (InMR). The reflection configuration and Mach stem shape given by the model for various sets of wedge angles, especially those giving rise to InMR, have been predicted and validated with the available numerical and experimental data. The von Neumann criterion for oMR is accurately predicted by this model. The asymmetric Mach stem profile is well captured. The variation of Mach stem height with wedge angle is also analysed and it is found that simplification of an asymmetric MR to a symmetric MR leads to over-prediction of the Mach stem height and hence the extent of the subsonic region.

A parametric study of Mach reflection in steady flows

1997 ◽  
Vol 341 ◽  
pp. 101-125 ◽  
Author(s):  
H. LI ◽  
G. BEN-DOR
Keyword(s):  
Present Model ◽  
Mach Reflection ◽  
Incident Shock ◽  
Incident Shock Wave ◽  
Incoming Flow ◽  
Steady Flows ◽  
Mach Stem ◽  
Stem Height ◽  
Von Neumann ◽  
Set Up

The flow fields associated with Mach reflection wave configurations in steady flows are analysed, and an analytical model for predicting the wave configurations is proposed. It is found that provided the flow field is free of far-field downstream influences, the Mach stem heights are solely determined by the set-up geometry for given incoming-flow Mach numbers. It is shown that the point at which the Mach stem height equals zero is exactly at the von Neumann transition. For some parameters, the flow becomes choked before the Mach stem height approaches zero. It is suggested that the existence of a Mach reflection not only depends on the strength and the orientation of the incident shock wave, as prevails in von Neumann's three-shock theory, but also on the set-up geometry to which the Mach reflection wave configuration is attached. The parameter domain, beyond which the flow gets choked and hence a Mach reflection cannot be established, is calculated. Predictions based on the present model are found to agree well both with experimental and numerical results.

A study of the asymmetric shock reflection configurations in steady flows

2017 ◽  
Vol 825 ◽  
pp. 1-15 ◽  
Author(s):  
Yuan Tao ◽  
Weidong Liu ◽  
Xiaoqiang Fan ◽  
Bin Xiong ◽  
Jiangfei Yu ◽  
...  
Keyword(s):  
Analytical Model ◽  
Mach Reflection ◽  
Shock Reflection ◽  
Horizontal Distance ◽  
Steady Flows ◽  
Two Dimensional ◽  
Mach Stem ◽  
Stream Tube ◽  
Triple Points ◽  
Asymmetric Shock

In this paper the asymmetric shock reflection configurations in two-dimensional steady flows have been studied theoretically. For an overall Mach reflection, it is found that the horizontal distance between both triple points in the Mach stem is related to the angles of two slip streams. Based on the features of the converging stream tube, several assumptions are put forward to perform better the wave configurations near the slip streams. Therefore, we present an analytical model here to describe the asymmetric overall Mach reflection configurations which agrees well with the computational and experimental results.

scholarly journals FLOW SIMULATION OVER REENTRY CAPSULE AT SUPERSONIC AND HYPERSONIC SPEEDS. THE COMPARE BETWEEN TWO REENTRY CAPSULES. PART 1

2020 ◽  
pp. 45-51
Author(s):  
Pavel Timofeev ◽  
◽  
Vladimir Panchenko ◽  
Sergey Kharchyk ◽  
◽  
...  
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Flow Direction ◽  
Numerical Algorithms ◽  
Flow Simulation ◽  
Ansys Fluent ◽  
Forward Shock ◽  
Hypersonic Speeds ◽  
Mach Numbers ◽  
Cfd Method

This study presents flow simulation over the reentry capsule at supersonic and hypersonic speeds. Numerical algorithms solve for the CFD method, which is produced using help ANSYS Fluent 19.2. The using GPU core to get a solution faster. The main purpose – flow simulation and numerical analysis reentry capsule; understand the behavior of supersonic and hypersonic flow and its effect on the reentry capsule; compare temperature results for the range Mach numbers equals 2–6. This study showed results on velocity counters, on temperature counters and vector of velocity for range Mach numbers equals 2–6. This study demonstrates the importance of understanding the effects of shock waves and illustrates how the shock wave changes as the Mach number increases. For every solves, the mesh had adapted for pressure gradient and velocity gradient to get the exact solution. As a result of the obtained solution, it is found that a curved shock wave appears in front of the reentry capsule. The central part of which is a forward shock. An angular expansion process is observed, which is a modified picture of the Prandtl- Mayer flow that occurs in a supersonic flow near the sharp edge of the expanding region. It is revealed that with an increase in the Mach number, the shock wave approaches the bottom of the reentry capsule, and there is also a slope of the shock to the flow direction, with an increase in the Mach number. The relevance and significance of this problem for the design of new and modernization of old reentry capsules.

scholarly journals A Coupled, Semi-Numerical Model for Thermal Analysis of Medium Frequency Transformer

Energies ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 328 ◽  
Author(s):  
Haonan Tian ◽  
Zhongbao Wei ◽  
Sriram Vaisambhayana ◽  
Madasamy Thevar ◽  
Anshuman Tripathi ◽  
...  
Keyword(s):  
Numerical Model ◽  
Analytical Model ◽  
Electromagnetic Analysis ◽  
Medium Frequency ◽  
Fluid Analysis ◽  
Fluid Behavior ◽  
Proposed Model ◽  
Computational Fluid Dynamics Cfd ◽  
Cfd Method ◽  
Thermal Fluid Analysis

Medium-frequency (MF) transformer has gained much popularity in power conversion systems. Temperature control is a paramount concern, as the unexpected high temperature declines the safety and life expectancy of transformer. The scrutiny of losses and thermal-fluid behavior are thereby critical for the design of MF transformers. This paper proposes a coupled, semi-numerical model for electromagnetic and thermal-fluid analysis of MF oil natural air natural (ONAN) transformer. An analytical model that is based on spatial distribution of flux density and AC factor is exploited to calculate the system losses, while the thermal-hydraulic behavior is modelled numerically leveraging the computational fluid dynamics (CFD) method. A close-loop iterative framework is formulated by coupling the analytical model-based electromagnetic analysis and CFD-based thermal-fluid analysis to address the temperature dependence. Experiments are performed on two transformer prototypes with different conductor types and physical geometries for validation purpose. Results suggest that the proposed model can accurately model the AC effects, losses, and the temperature rises at different system components. The proposed model is computationally more efficient than the full numerical method but it reserves accurate thermal-hydraulic characterization, thus it is promising for engineering utilization.

scholarly journals Neural network-based analytical model to predict the shear strength of steel girders with a trapezoidal corrugated web

2021 ◽  
Author(s):  
Miguel Abambres ◽  
He J
Keyword(s):  
Neural Network ◽  
Shear Strength ◽  
Analytical Model ◽  
Analytical Models ◽  
Steel Girders ◽  
Concentrated Load ◽  
Corrugated Web ◽  
Input Variables ◽  
Artificial Neural Network Ann ◽  
Relative Errors

<p>Corrugated webs are used to increase the shear stability of steel webs of beam-like members and to eliminate the need of transverse stiffeners. Previously developed formulas for predicting the shear strength of trapezoidal corrugated steel webs, along with the corresponding theory, are summarized. An artificial neural network (ANN)-based model is proposed to estimate the shear strength of steel girders with a trapezoidal corrugated web, and under a concentrated load. 210 test results from previous published research were collected into a database according to relevant test specimen parameters in order to feed the simulated ANNs. Seven (geometrical and material) parameters were identified as input variables and the ultimate shear stress at failure was considered the output variable. The proposed ANN-based analytical model yielded maximum and mean relative errors of 0.0% for the 210 points from the database. Moreover, still based on those points, it was illustrated that the ANN-based model clearly outperforms the other existing analytical models, which yield mean errors larger than 13%.</p>

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