scholarly journals Critical Mach Numbers of Flow around Two-Dimensional and Axisymmetric Bodies

Aerodynamics ◽  
2021 ◽  
Author(s):  
Vladimir Frolov
Keyword(s):  
Mach Number ◽  
Cross Section ◽  
Flow Simulation ◽  
The Body ◽  
Two Dimensional ◽  
Critical Mach Number ◽  
Method Of Integral Relations ◽  
Viscosity Factor ◽  
Mach Numbers ◽  
Axisymmetric Bodies

The paper presents the calculated results obtained by the author for critical Mach numbers of the flow around two-dimensional and axisymmetric bodies. Although the previously proposed method was applied by the author for two media, air and water, this chapter is devoted only to air. The main goal of the work is to show the high accuracy of the method. For this purpose, the work presents numerous comparisons with the data of other authors. This method showed acceptable accuracy in comparison with the Dorodnitsyn method of integral relations and other methods. In the method under consideration, the parameters of the compressible flow are calculated from the parameters of the flow of an incompressible fluid up to the Mach number of the incoming flow equal to the critical Mach number. This method does not depend on the means determination parameters of the incompressible flow. The calculation in software Flow Simulation was shown that the viscosity factor does not affect the value critical Mach number. It was found that with an increase in the relative thickness of the body, the value of the critical Mach number decreases. It was also found that the value of the critical Mach number for the two-dimensional case is always less than for the axisymmetric case for bodies with the same cross-section.

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 The onset of unsteadiness of two-dimensional bodies falling or rising freely in a viscous fluid: a linear study

2011 ◽  
Vol 690 ◽  
pp. 173-202 ◽  
Author(s):  
Pauline Assemat ◽  
David Fabre ◽  
Jacques Magnaudet
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Strouhal Number ◽  
Cross Section ◽  
Vortex Shedding ◽  
The Body ◽  
Mode Switching ◽  
Two Dimensional ◽  
Body Dynamics ◽  
Mass Ratios

AbstractWe consider the transition between the steady vertical path and the oscillatory path of two-dimensional bodies moving under the effect of buoyancy in a viscous fluid. Linearization of the Navier–Stokes equations governing the flow past the body and of Newton’s equations governing the body dynamics leads to an eigenvalue problem, which is solved numerically. Three different body geometries are then examined in detail, namely a quasi-infinitely thin plate, a plate of rectangular cross-section with an aspect ratio of 8, and a rod with a square cross-section. Two kinds of eigenmodes are observed in the limit of large body-to-fluid mass ratios, namely ‘fluid’ modes identical to those found in the wake of a fixed body, which are responsible for the onset of vortex shedding, and four additional ‘aerodynamic’ modes associated with much longer time scales, which are also predicted using a quasi-static model introduced in a companion paper. The stability thresholds are computed and the nature of the corresponding eigenmodes is investigated throughout the whole possible range of mass ratios. For thin bodies such as a flat plate, the Reynolds number characterizing the threshold of the first instability and the associated Strouhal number are observed to be comparable with those of the corresponding fixed body. Other modes are found to become unstable at larger Reynolds numbers, and complicated branch crossings leading to mode switching are observed. On the other hand, for bluff bodies such as a square rod, two unstable modes are detected in the range of Reynolds number corresponding to wake destabilization. For large enough mass ratios, the leading mode is similar to the vortex shedding mode past a fixed body, while for smaller mass ratios it is of a different nature, with a Strouhal number about half that of the vortex shedding mode and a stronger coupling with the body dynamics.

Lift and drag in two-dimensional steady viscous and compressible flow

2015 ◽  
Vol 784 ◽  
pp. 304-341 ◽  
Author(s):  
L. Q. Liu ◽  
J. Y. Zhu ◽  
J. Z. Wu
Keyword(s):  
Mach Number ◽  
Viscous Flow ◽  
Compressible Flow ◽  
Velocity Component ◽  
Transverse Velocity ◽  
The Body ◽  
Far Field ◽  
Two Dimensional ◽  
Wide Range ◽  
Lift And Drag

This paper studies the lift and drag experienced by a body in a two-dimensional, viscous, compressible and steady flow. By a rigorous linear far-field theory and the Helmholtz decomposition of the velocity field, we prove that the classic lift formula $L=-{\it\rho}_{0}U{\it\Gamma}_{{\it\phi}}$, originally derived by Joukowski in 1906 for inviscid potential flow, and the drag formula $D={\it\rho}_{0}UQ_{{\it\psi}}$, derived for incompressible viscous flow by Filon in 1926, are universally true for the whole field of viscous compressible flow in a wide range of Mach number, from subsonic to supersonic flows. Here, ${\it\Gamma}_{{\it\phi}}$ and $Q_{{\it\psi}}$ denote the circulation of the longitudinal velocity component and the inflow of the transverse velocity component, respectively. We call this result the Joukowski–Filon theorem (J–F theorem for short). Thus, the steady lift and drag are always exactly determined by the values of ${\it\Gamma}_{{\it\phi}}$ and $Q_{{\it\psi}}$, no matter how complicated the near-field viscous flow surrounding the body might be. However, velocity potentials are not directly observable either experimentally or computationally, and hence neither are the J–F formulae. Thus, a testable version of the J–F formulae is also derived, which holds only in the linear far field. Due to their linear dependence on the vorticity, these formulae are also valid for statistically stationary flow, including time-averaged turbulent flow. Thus, a careful RANS (Reynolds-averaged Navier–Stokes) simulation is performed to examine the testable version of the J–F formulae for a typical airfoil flow with Reynolds number $Re=6.5\times 10^{6}$ and free Mach number $M\in [0.1,2.0]$. The results strongly support and enrich the J–F theorem. The computed Mach-number dependence of $L$ and $D$ and its underlying physics, as well as the physical implications of the theorem, are also addressed.

On the Pressure Distribution Round Certain Aerofoils of High Aspect Ratio

1926 ◽  
Vol 30 (182) ◽  
pp. 129-141
Author(s):  
D. M. Wrinch
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
High Aspect Ratio ◽  
Special Interest ◽  
Cylindrical Body ◽  
The Body ◽  
The Other ◽  
Two Dimensional ◽  
Reasonable Accuracy ◽  
Lifting Force

The development of aerodynamical research into the usefulness of wing profiles of various types for aerofoils of high aspect ratio lends special interest to new results in two-dimensional hydrodynamics relating to the motion of a perfect fluid in the presence of a cylindrical body, especially in the case when the curve of cross-section of the body possesses only a smali amount of camber and is cusped at one end and rounded at the other.The possibility of formulating a theory which represents with reasonable accuracy the actual motions of aerofoils of high aspect ratio in a stream of air, when the air it taken to be inviscid, depends, of course, essentially in the first place on finding motions in which there is a force on the body at right angles to the direction of streaming. No theory which omits to produce this lifting force can give an account of the actual motions of aerofoils which is even approximately satisfactory.

On the entry problem for a compressible liquid

1966 ◽  
Vol 25 (3) ◽  
pp. 577-587 ◽  
Author(s):  
H. G. Pinsent
Keyword(s):  
Free Surface ◽  
Mach Number ◽  
Compressible Liquid ◽  
The Body ◽  
Gravitational Effects ◽  
Inviscid Liquid ◽  
Mach Numbers

The problem considered is the entry of a thin symmetric wedge impinging normally on the free surface of a compressible inviscid liquid, gravitational effects being neglected. Since the body is thin, the problem is a linear one, and its solution is possible for the whole range of Mach numbers of the body's motion in the liquid. It is shown that the free-surface elevations are lowered considerably as the Mach number increases, and that the presence of the free surface acts so as to lower the pressure differences arising from compressibility.

scholarly journals Subsonic potential flow past a circle and the transonic controversy

1983 ◽  
Vol 24 (3) ◽  
pp. 243-261 ◽  
Author(s):  
M. D. Van Dyke ◽  
A. J. Guttmann
Keyword(s):  
Mach Number ◽  
Circular Cylinder ◽  
Potential Flow ◽  
Maximum Velocity ◽  
Two Dimensional ◽  
Number Series ◽  
Critical Mach Number ◽  
Potential Flows ◽  
Two Dimensional Flow ◽  
Continuous Range

AbstractThe Mach-number series expansion of the potential function for the two-dimensional flow of an inviscid, compressible, perfect, diatomic gas past a circular cylinder is obtained to 29 terms. Analysis of this expansion allows the critical Mach number, at which flow first becomes locally sonic, to be estimated as M* = 0.39823780 ± 0.00000001. Analysis also permits the following estimate of the radius of convergence of the series for the maximum velocity to be made: Mc = 0.402667605 ± 0.00000005, though we have been unable to determine the nature of the singularity of M = Mc. Since Mc exceeds M* by some 1.1%, it follows that this particular “airfoil” can possess a continuous range of shock-free potential flows above the critical Mach number. This result hopefully resolves a 70-year old controversy.

Aerodynamic analysis and design of Busemann biplane: towards efficient supersonic flight

2011 ◽  
Vol 226 (2) ◽  
pp. 217-238 ◽  
Author(s):  
D Maruyama ◽  
K Kusunose ◽  
K Matsushima ◽  
K Nakahashi
Keyword(s):  
Mach Number ◽  
Design Method ◽  
Three Dimensional ◽  
Aerodynamic Characteristics ◽  
Aerodynamic Performance ◽  
The Body ◽  
Analysis And Design ◽  
Expansion Waves ◽  
Mach Numbers ◽  
Inverse Design Method

Aiming to realize a low-drag supersonic transport, Busemann biplane concept was adopted in this study. Two- and three-dimensional (2D and 3D) biplanes were analysed and designed to improve their aerodynamic performance using computational fluid dynamics. It was confirmed that 3D biplane wings have better aerodynamic-performance areas than 2D biplane airfoils. A winglet is also useful for improvement of their aerodynamic performance. Aerodynamic characteristics of these biplanes at their off-design conditions were also analysed. In 3D wings, a flow choking and its attendant hysteresis as starting problems, which arise when the biplanes accelerate from low Mach numbers, disappear at lower Mach numbers than those in 2D airfoils. It was confirmed that hinged slats and flaps are effective to settle these issues. Finally, interference effects of a body with the biplanes were investigated. When the biplane wings are affected by the expansion waves from the body, their aerodynamic performance at the design Mach number and the starting Mach number are better and lower than those of their isolated wings, respectively. A 3D biplane wing obtained by an inverse-design method was applied to the body. The wing of this wing–body configuration achieves higher aerodynamic performance than the 2D flat-plate airfoil at sufficient lift conditions, which is the almost identical performance of 2D biplane airfoils.

Laminar Free Convection Over Two-Dimensional and Axisymmetric Bodies of Arbitrary Contour

1974 ◽  
Vol 96 (4) ◽  
pp. 435-442 ◽  
Author(s):  
F. N. Lin ◽  
B. T. Chao
Keyword(s):  
Free Convection ◽  
Experimental Information ◽  
The Body ◽  
Two Dimensional ◽  
Universal Functions ◽  
Body Contour ◽  
Convection Boundary ◽  
Smooth Objects ◽  
Elliptical Cylinders ◽  
Axisymmetric Bodies

A rapid computation procedure is described for the prediction of heat transfer in laminar free convection boundary layers, either two-dimensional or axisymmetrical, over isothermal smooth objects with fairly arbitrary shape. The analysis employs suitable coordinate transformation which makes it possible to express the solutions of the governing conservation equations in terms of a sequence of universal functions that depend on the fluid Prandtl number and a configuration function. The latter is completely determined by the body contour and its orientation relative to the body force that generates the motion. Several of the leading universal functions have been evaluated and tabulated. The theory was applied to a number of body configurations and the results compared well with published analytical and/or experimental information. Some new results are also obtained for the local Nusselt number over horizontal elliptical cylinders and ellipsoids or revolution.

Design and validation of a two-dimensional variable geometry inlet

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Huacheng Yuan ◽  
Yunfei Wang ◽  
Jun Liu ◽  
Zhengxu Hua
Keyword(s):  
Mach Number ◽  
Wind Tunnel ◽  
Three Dimensional ◽  
Aerodynamic Performance ◽  
Back Pressure ◽  
Variable Geometry ◽  
Two Dimensional ◽  
Validation Experiment ◽  
Mach Numbers ◽  
Dimensional Variable

Abstract The design of a two-dimensional variable geometry inlet which applied to a tandem type turbine-based combined cycle (TBCC) propulsion system was investigated in the present paper through three-dimensional simulations and wind tunnel tests. The operation Mach number range was between 0 and 3. A multi-ramp geometry scheme was adopted to achieve acceptable performance at different inflow Mach number. The first ramp angle was fixed whilst the angles of the second and the third ramps were variable at different inflow Mach numbers. The Mach numbers at throat region were maintained between 1.3 and 1.5 at different inflow Mach numbers according to this variable geometry scheme. A fixed geometry rectangular-to-circular shape diffuser was adopted to improve aerodynamic performance of the inlet. Three-dimensional numerical simulations were carried out between Ma1.5 and Ma3.0. The results indicated that good aerodynamic performance can be achieved at different inflow speed. At the design point, total pressure recovery of the inlet was 0.66 at critical condition. Wind tunnel validation experiment tests were conducted at Ma2.0, showing the movement of terminal shock wave from downstream to upstream as the back pressure increased. The inlet operated at supercritical, critical and subsonic conditions at different back pressure.

Influence of Wind on the Aerodynamic Resistance for a Case of the Arrangement of the Equipment on Locomotive Bodywork LE 060EA

2015 ◽  
Vol 809-810 ◽  
pp. 1151-1156
Author(s):  
Sorin Arsene
Keyword(s):  
Comparative Analysis ◽  
Cross Section ◽  
Power Supply ◽  
Aerodynamic Resistance ◽  
Flow Simulation ◽  
The Body ◽  
Electric Locomotive ◽  
Aerodynamic Forces ◽  
Cross Section Area ◽  
Section Area

In the case of electric railway vehicles of surface, the equipments which allow power supply are placed on their bodywork. The mode to dispose these equipments contributes to increase the resistance to motion of the vehicle due to the variation cross-section area. Gusts of wind that occurs during the movement of vehicles lead to increased aerodynamic forces. As a model analyzed, we considered the situation determined by the dispose of the equipments supply on the body of electric locomotive type LE 060 EA of 5100 kW, when such a vehicle is travelling with the first post station in the driving direction. The equipment’s components of supply were modeled geometric at scale 1: 1 in 3D. The obtained assembly was imported in an air flow simulation program to determine the aerodynamic resistances. To observe which is the influence of the gusts wind regarding the resistance to moving we considered five point values for wind speed: 5m / s, 10m / s, 15m / s, 20m / s and 25m / s. With results of the simulations we performed a comparative analysis.

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