scholarly journals Hysteresis in Supersonic Flow Past a Plane Cascade of Cylindrical Rods

2021 ◽  
Vol 56 (6) ◽  
pp. 886-896
Author(s):  
S. V. Guvernyuk ◽  
F. A. Maksimov
Keyword(s):  
Mach Number ◽  
Supersonic Flow ◽  
Stokes Equations ◽  
Aerodynamic Drag ◽  
Flow Regimes ◽  
Wake Flow ◽  
Computational Technique ◽  
Infinite Plane ◽  
Continuous Increase ◽  
Number Range

Abstract— The results of numerical simulation of the interaction of supersonic flow with a permeable screen in form of an infinite plane cascade (lattice) of circular cylinders are given. The interaction regime in which the shocks ahead of the cylinders are localized on the scale of the cascade step is considered. The multi-block computational technique in which the viscous boundary layers are resolved by means of local grids using the Navier–Stokes equations, while the effects of inteferrence between the shock-wave structures in supersonic wake are described within the framework of Euler’s equations. The action of shock waves induced by the neighboring elements of lattice to the near-wake region behind the intermediate elements can ambiguously affect the aerodynamic lattice performance as well as generate time-dependent phenomena in the wake. The flow regimes are classified depending on continuous increase and decrease in the free-stream supersonic air flow in the Mach number range from 2.4 to 4.2 with reference to the lattice of the 80% permeability. The sources of the hysteresis behavior of the lattice aerodynamic drag with respect to the Mach number and the mechanisms of the onset of self-oscillating wake flow regimes are discussed.

Simple Formulae for Supersonic Flow past a Cone

1975 ◽  
Vol 26 (1) ◽  
pp. 11-19 ◽  
Author(s):  
W H Hui
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Supersonic Flow ◽  
Surface Pressure ◽  
Simple Formula ◽  
Pressure Coefficient ◽  
Circular Cone ◽  
Number Range ◽  
Thin Shock Layer ◽  
Cone Vertex

SummaryThe problem of the supersonic flow with attached shock wave past a circular cone at zero angles of attack is treated, using the thin-shock-layer expansion. The solution is calculated to the fourth approximation. A simple formula is then derived for the surface pressure coefficient by the application of the parameter-straining technique and it is shown to be very accurate for the whole Mach number range for which the shock remains attached to the cone vertex.

Direct simulation of turbulent supersonic boundary layers by an extended temporal approach

2001 ◽  
Vol 429 ◽  
pp. 187-216 ◽  
Author(s):  
THIERRY MAEDER ◽  
NIKOLAUS A. ADAMS ◽  
LEONHARD KLEISER
Keyword(s):  
Numerical Simulation ◽  
Mach Number ◽  
Direct Numerical Simulation ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Mach Numbers

The present paper addresses the direct numerical simulation of turbulent zero-pressure-gradient boundary layers on a flat plate at Mach numbers 3, 4.5 and 6 with momentum-thickness Reynolds numbers of about 3000. Simulations are performed with an extended temporal direct numerical simulation (ETDNS) method. Assuming that the slow streamwise variation of the mean boundary layer is governed by parabolized Navier–Stokes equations, the equations solved locally in time with a temporal DNS are modified by a distributed forcing term so that the parabolized Navier–Stokes equations are recovered for the spatial average. The correct mean flow is obtained without a priori knowledge, the streamwise mean-flow evolution being approximated from its upstream history. ETDNS reduces the computational effort by up to two orders of magnitude compared to a fully spatial simulation.We present results for a constant wall temperature Tw chosen to be equal to its laminar adiabatic value, which is about 2.5 T∞, 4.4 T∞ and 7 T∞, respectively, where T∞ is the free-stream temperature for the three Mach numbers considered. The simulations are initialized with transition-simulation data or with re-scaled turbulent data at different parameters. We find that the ETDNS results closely match experimental mean-flow data. The van Driest transformed velocity profiles follow the incompressible law of the wall with small logarithmic regions.Of particular interest is the significance of compressibility effects in a Mach number range around the limit of M∞ ≃ 5, up to which Morkovin's hypothesis is believed to be valid. The results show that pressure dilatation and dilatational dissipation correlations are small throughout the considered Mach number range. On the other hand, correlations derived from Morkovin's hypothesis are not necessarily valid, as is shown for the strong Reynolds analogy.

Fluid-Structure Interaction for Flutter Predictions in Transonic and Supersonic Flows

2011 ◽  
Author(s):  
Zhi Yang ◽  
Xiang Zhao ◽  
Sijun Zhang ◽  
Chien-Pin Chen
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Structural Response ◽  
Supersonic Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Solver ◽  
Compressible Turbulent Flow ◽  
Transonic And Supersonic Flows

This paper describes a numerical methodology coupling Euler/Navier-Stokes equations and structural modal equations for predicting flutter in transonic and supersonic flows. This coupling between Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) is achieved through a Multi-Disciplinary Computing Environment (MDICE), which allows several computer codes or ‘modules’ to communicate in a highly efficient fashion. The present approach offers the advantage of utilizing well-established single-disciplinary codes in a multi-disciplinary framework. The flow solver is density-based for modeling compressible, turbulent flow problems using structured and/or unstructured grids. A modal approach is employed for the structural response. Two benchmark cases are employed to validate the present method. Flutter predictions in subsonic flows for an AGARD 445.6 wing at different Mach numbers (0.499 to 1.141) are presented and compared with experimental data. Supersonic plate flutter with Mach number range between 1.8 and 3.2 is studied and the critical Mach number is computed, our results are in a good agreement with the analytical solutions.

Auto and Cross Correlation Measurements in a Turbine Cascade Using a Digital Correlator

1982 ◽  
Author(s):  
P. J. Bryanston-Cross ◽  
J. J. Camus
Keyword(s):  
Mach Number ◽  
High Speed ◽  
Cross Correlation ◽  
Turbine Blades ◽  
Image Plane ◽  
Strongly Correlated ◽  
Trailing Edge ◽  
Number Range ◽  
Cross Correlations ◽  
Digital Correlator

A simple technique has been developed which samples the dynamic image plane information of a schlieren system using a digital correlator. Measurements have been made in the passages and in the wakes of transonic turbine blades in a linear cascade. The wind tunnel runs continuously and has independently variable Reynolds and Mach number. As expected, strongly correlated vortices were found in the wake and trailing edge region at 50 KHz. Although these are strongly coherent we show that there is only limited cross-correlation from wake to wake over a Mach no. range M = 0.5 to 1.25 and variation of Reynolds number from 3 × 105 to 106. The trailing edge fluctuation cross correlations were extended both upstream and downstream and preliminary measurements indicate that this technique can be used to obtain information on wake velocity. The vortex frequency has also been measured over the same Mach number range for two different cascades. The results have been compared with high speed schlieren photographs.

Spin-up from rest of a compressible fluid in a rapidly rotating cylinder

1992 ◽  
Vol 237 ◽  
pp. 413-434 ◽  
Author(s):  
Jae Min Hyun ◽  
Jun Sang Park
Keyword(s):  
Mach Number ◽  
Compressible Fluid ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Axial Direction ◽  
Ekman Layer ◽  
Infinite Cylinder ◽  
Full Time ◽  
Viscous Effects ◽  
Initial State

Spin-up flows of a compressible gas in a finite, closed cylinder from an initial state of rest are studied, The flow is characterized by small reference Ekman numbers, and the peripheral Mach number is O(1). Comprehensive numerical solutions have been obtained for the full, time-dependent compressible Navier-Stokes equations. The details of the flow, temperature, and density evolution are described. In the early phase of spin-up, owing to the thermoacoustic disturbances caused by the compressible Rayleigh effect, the flows are oscillatory, and this oscillatory behaviour is pronounced at higher Mach numbers. The principal dynamical role of the Ekman layer is dominant over moderate times of orders of the homogeneous spin-up timescales. Owing to the density stratification in the radial direction, the Ekman layer is thicker in the central region of the interior. The interior azimuthal flows are mainly uniform in the axial direction. As the Mach number increases, the rate of spin-up in the interior becomes slower, and the propagating shear front is more diffusive. Explicit comparisons with the results for an infinite cylinder are made to ascertain the contributions of the endwall disks. In contrast to the usual incompressible spin-up from rest, the viscous effects are relatively more important for the case of a compressible fluid.

On the correlation between aerodynamic drag and wake flow for a generic high-speed train

2021 ◽  
Vol 215 ◽  
pp. 104698
Author(s):  
Xiao-Bai Li ◽  
Xi-Feng Liang ◽  
Zhe Wang ◽  
Xiao-Hui Xiong ◽  
Guang Chen ◽  
...  
Keyword(s):  
High Speed ◽  
Aerodynamic Drag ◽  
Wake Flow ◽  
High Speed Train

Computational study of unsteady gas flow in the combustion chamber of a ramjet engine with heat transfer

2021 ◽  
pp. 50-61
Author(s):  
Надежда Петровна Скибина
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Supersonic Flow ◽  
Combustion Chamber ◽  
Gas Flow ◽  
Stokes Equations ◽  
Heat Conducting ◽  
Measuring Device ◽  
Ramjet Engine ◽  
Mach Numbers

Проведено численное исследование нестационарного турбулентного сверхзвукового течения в камере сгорания прямоточного воздушно-реактивного двигателя. Описана методика экспериментального измерения температуры на стенке осесимметричного канала в камере сгорания двигателя. Математическое моделирование обтекания исследуемой модели двигателя проводилось для скоростей набегающего потока M = 5 ... 7. Начальные и граничные условия задачи соответствовали реальному аэродинамическому эксперименту. Проанализированы результаты численного расчета. Рассмотрено изменение распределения температуры вдоль стенки канала с течением времени. Проведена оценка согласованности полученных экспериментальных данных с результатами математического моделирования. Purpose. The aim of this study is a numerical simulation of unsteady supersonic gas flow in a working path of ramjet engine under conditions identical to aerodynamic tests. Free stream velocity corresponding to Mach numbers M=5 ... 7 are considered. Methodology. Presented study addresses the methods of physical and numerical simulation. The probing device for thermometric that allows to recording the temperature values along the wall of internal duct was proposed. To describe the motion of a viscous heat-conducting gas the unsteady Reynolds averaged Navier - Stokes equations are considered. The flow turbulence is accounted by the modified SST model. The problem was solved in ANSYS Fluent using finite-volume method. The initial and boundary conditions for unsteady calculation are set according to conditions of real aerodynamic tests. The coupled heat transfer for supersonic flow and elements of ramjet engine model are realized by setting of thermophysical properties of materials. The reliability testing of numerical simulation has been made to compare the results of calculations and the data of thermometric experimental tests. Findings. Numerical simulation of aerodynamic tests for ramjet engine was carried out. The agreement between the results of numerical calculations and experimental measurements for the velocity in the channel under consideration was obtained; the error was shown to be 2%. The temperature values were obtained in the area of contact of the supersonic flow with the surface of the measuring device for the external incident flow velocities for Mach numbers M = 5 ... 7. The process of heating the material in the channel that simulated the section of the engine combustion chamber was analyzed. The temperature distribution was studied depending on the position of the material layer under consideration relative to the contact zone with the flow. Value. In the course of the work, the fields of flow around the model of a ramjet engine were obtained, including the region of supersonic flow in the inner part of axisymmetric channel. The analysis of the temperature fields showed that to improve the quality of the results, it is necessary to take into account the depth of the calorimetric sensor. The obtained results will be used to estimate the time of interaction of the supersonic flow with the fuel surface required to reach the combustion temperature.

scholarly journals Implicit MAC scheme for compressible Navier–Stokes equations: low Mach asymptotic error estimates

2020 ◽  
Author(s):  
David Maltese ◽  
Antonín Novotný
Keyword(s):  
Mach Number ◽  
Initial Data ◽  
Error Estimate ◽  
Strong Solution ◽  
Stokes Equations ◽  
Main Tool ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Mach Number ◽  
Mac Scheme

Abstract We investigate the error between any discrete solution of the implicit marker-and-cell (MAC) numerical scheme for compressible Navier–Stokes equations in the low Mach number regime and an exact strong solution of the incompressible Navier–Stokes equations. The main tool is the relative energy method suggested on the continuous level in Feireisl et al. (2012, Relative entropies, suitable weak solutions, and weak–strong uniqueness for the compressible Navier–Stokes system. J. Math. Fluid Mech., 14, 717–730). Our approach highlights the fact that numerical and mathematical analyses are not two separate fields of mathematics. The result is achieved essentially by exploiting in detail the synergy of analytical and numerical methods. We get an unconditional error estimate in terms of explicitly determined positive powers of the space–time discretization parameters and Mach number in the case of well-prepared initial data and in terms of the boundedness of the error if the initial data are ill prepared. The multiplicative constant in the error estimate depends on a suitable norm of the strong solution but it is independent of the numerical solution itself (and of course, on the discretization parameters and the Mach number). This is the first proof that the MAC scheme is unconditionally and uniformly asymptotically stable in the low Mach number regime.

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