Computational Analysis of the Transonic Flow Field of Two-Dimensional Minimum Length Nozzles

1991 ◽  
Vol 113 (3) ◽  
pp. 479-488 ◽  
Author(s):  
B. M. Argrow ◽  
G. Emanuel
Keyword(s):  
Supersonic Flow ◽  
Flow Field ◽  
Method Of Characteristics ◽  
Reynolds Numbers ◽  
Boundary Layer Separation ◽  
Minimum Length ◽  
Two Dimensional ◽  
Sonic Line ◽  
Inlet Geometry ◽  
Straight Sonic Line

The method of characteristics is used to generate supersonic wall contours for two-dimensional, straight sonic line (SSL) and curved sonic line (CSL) minimum length nozzles for exit Mach numbers of two, four and six. These contours are combined with subsonic inlets to determine the influence of the inlet geometry on the sonic-line shape, its location, and on the supersonic flow field. A modified version of the VNAP2 code is used to compute the inviscid and laminar flow fields for Reynolds numbers of 1,170, 11,700, and 23,400. Supersonic flow field phenomena, including boundary-layer separation and oblique shock waves, are observed to be a result of the inlet geometry. The sonic-line assumptions made for the SSL prove to be superior to those of the CSL.

Design and Verification of Minimum Length Nozzles with Specific/Variable Heat Ratio Based on Method of Characteristics

2016 ◽  
Vol 13 (06) ◽  
pp. 1650034 ◽  
Author(s):  
Lei Fu ◽  
Shuai Zhang ◽  
Yao Zheng
Keyword(s):  
Mach Number ◽  
Flow Field ◽  
Method Of Characteristics ◽  
Wave Theory ◽  
Minimum Length ◽  
Two Dimensional ◽  
Conservation Of Mass ◽  
Novel Technique ◽  
Field Uniformity ◽  
Exit Mach Number

Two-dimensional (2D) and axisymmetric minimum length nozzles (MLN) with constant and variable specific heat were strictly designed using the method of characteristics. Requirements for the exit Mach number and flow field uniformity were proposed for the nozzles design. In solutions to kernel zone flow field reported previously, violent vibrations of upper wall discrete points at the inlet were observed. Meanwhile, slight compressions could be observed in the flow field of axisymmetric nozzles designed by those methods. In this study, we proposed a novel technique in which the inlet grid is intensified to overcome the limitations mentioned above. Additionally, methods based on conservation of mass and eliminating wave theory were proposed to determine the contour of the nozzle’s upper wall. Inviscid numerical simulations by CFD revealed that the proposed nozzle could meet the requirements for exit Mach number and flow field uniformity in various situations, and axisymmetric nozzles designed from eliminating wave theory exhibited better flow field compared with those designed from conservation of mass.

Comparison of Minimum Length Nozzles

1988 ◽  
Vol 110 (3) ◽  
pp. 283-288 ◽  
Author(s):  
B. M. Argrow ◽  
G. Emanuel
Keyword(s):  
Inflection Point ◽  
Method Of Characteristics ◽  
Accurate Method ◽  
The Other ◽  
Minimum Length ◽  
Turn Angle ◽  
Sonic Line ◽  
The One ◽  
Axisymmetric Minimum Length Nozzle ◽  
Straight Sonic Line

A second-order accurate method-of-characteristics algorithm is used to determine the flow field and wall contour for a supersonic, axisymmetric, minimum length nozzle with a straight sonic line. Results are presented for this nozzle and compared with three other minimum length nozzle configurations. It is shown that the one investigated actually possesses the shortest length as well as the smallest initial wall turn angle at the throat. It also has an inflection point on the wall contour, in contrast to the other configurations.

Two-Dimensional Unsteady Viscous Flows

2017 ◽  
Author(s):  
Jian-Jun Shu
Keyword(s):  
Circular Cylinder ◽  
Flow Field ◽  
Hydrodynamic Force ◽  
Viscous Flows ◽  
Reynolds Numbers ◽  
Fundamental Solutions ◽  
Time Dependent ◽  
Two Dimensional ◽  
Low Reynolds Numbers ◽  
Rotational Motions

A number of new closed-form fundamental solutions for the two-dimensional generalized unsteady Oseen and Stokes flows associated with arbitrary time-dependent translational and rotational motions have been developed. As an example of application, the hydrodynamic force acting on a circular cylinder translating in an unsteady flow field at low Reynolds numbers is calculated using the new generalized fundamental solutions.

Focusing effects in two-dimensional, supersonic flow

1949 ◽  
Vol 242 (844) ◽  
pp. 153-171 ◽  
Keyword(s):  
Method Of Characteristics ◽  
Inverse Transformation ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Geometrical Method ◽  
Independent Variables ◽  
Flow Problems ◽  
Sonic Line ◽  
Hodograph Transformation ◽  
Line Patterns

The steady, supersonic, irrotational, isentropic, two-dimensional, shock-free flow of a perfect gas is investigated by a new, geometrical, method based on the use of characteristic co-ordinates. Some of the results apply also to more general problems of compressible flow involving two independent variables (§1). The method is applied in particular to the treatment of the non-linear, non-analytic features. The variation in magnitude of discontinuities of the velocity gradient is determined as a function of the Mach number in § 4. The reflexion at the sonic line of such discontinuities is treated in § 7. The isingularities of the field of flow are discussed in §§ 5 to 5.4; Craggs’s (1948) results are extended to the case when the velocity components are not analytic functions of position, and to the case in which both the hodograph transformation and the inverse transformation are singular.. Examples are given of singularities that occur in familiar flow problems, but have not hitherto been described (§§ 5.3, 5.4). Some properties are established of the geometry in the large of Mach line patterns; these properties are useful for the prediction of limit lines (§ 5.2). The problem of the start of an oblique shockwave in the middle of the flow is briefly reviewed in §6. In the appendix it is shown that the conventional method of characteristics for the numerical treat­ ment of two-dimensional, isentropic, irrotational, steady, supersonic flows must be modified near a branch line if a loss of accuracy is to be avoided.

Axially-symmetrical supersonic flow near the centre of an expansion

1950 ◽  
Vol 2 (2) ◽  
pp. 127-142 ◽  
Author(s):  
N.H. Johannesen ◽  
R.E. Meyer
Keyword(s):  
Approximate Solution ◽  
Supersonic Flow ◽  
Conventional Method ◽  
Velocity Gradient ◽  
Method Of Characteristics ◽  
Simple Wave ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Initial Curvature ◽  
Boundary Wall

SummaryWhen a uniform, two-dimensional supersonic flow expands suddenly round a corner in a wall it forms a pattern known as a Prandtl-Meyer expansion or centred simple wave. If the flow is two-dimensional but not initially uniform, or if it is axially-symmetrical, the expansion is still centred, but is not a simple wave. An approximate solution is given in this paper for the isentropic, irrotational, steady two-dimensional or axially-symmetrical flow of a perfect gas in the neighbourhood of the centre of such an expansion. The solution is designed to replace the conventional method of characteristics in such a region.The main application is to a jet issuing from a nozzle that discharges into a container with a pressure lower than that in the nozzle; in particular, a formula is derived for the initial curvature, at the lip of the nozzle, of the boundary of the jet. The solution also applies to the flow near an edge in a boundary wall, and a formula is derived for the velocity gradient on the wall immediately downstream of the edge.

Simulation of a 2D Channel Flow Around a Square Obstacle with Lattice-Boltzmann (BGK) Automata

1998 ◽  
Vol 09 (08) ◽  
pp. 1129-1141 ◽  
Author(s):  
J. Bernsdorf ◽  
Th. Zeiser ◽  
G. Brenner ◽  
F. Durst
Keyword(s):  
Flow Field ◽  
Lattice Boltzmann ◽  
Incompressible Flows ◽  
Focal Point ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Blockage Ratio ◽  
Two Dimensional ◽  
Viscous Incompressible Flows ◽  
Turbulent Flow Field

Results for time-dependent, viscous, incompressible flows were investigated using the lattice-Boltzmann (BGK) automata. The decay of a synthetic turbulent flow field and the time evolution of an initial vortex were simulated for validation purposes. The focal point was the investigation of the instationary flow around a square obstacle in a two-dimensional channel for a range of Reynolds numbers between 80 and 300 and a blockage ratio of 0.125. The Strouhal number was measured for this case and found to be in the range of data given in the literature.

Two-dimensional simulation of unsteady heat transfer from a circular cylinder in crossflow

2007 ◽  
Vol 570 ◽  
pp. 177-215 ◽  
Author(s):  
SALEM BOUHAIRIE ◽  
VINCENT H. CHU
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Circular Cylinder ◽  
Reynolds Numbers ◽  
Boundary Layer Separation ◽  
Length Scale ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Transfer Rates ◽  
Two Dimensional Model

The heat transfer from the surface of a circular cylinder into a crossflow has been computed using a two-dimensional model, for a range of Reynolds numbers from Re=200 to 15550. The boundary-layer separation, the local and overall heat-transfer rates, the eddy- and flare-detachment frequencies and the width of the flares were determined from the numerical simulations. In this range of Reynolds numbers, the heat-transfer process is unsteady and is characterized by a viscous length scale that is inversely proportional to the square root of the Reynolds number. To ensure uniform numerical accuracy for all Reynolds numbers, the dimensions of the computational mesh were selected in proportion to this viscous length scale. The small scales were resolved by at least three nodes within the boundary layers. The frequency of the heat flares increases, and the width of each flare decreases, with the Reynolds number, in proportion to the viscous time and length scales. Despite the presence of three-dimensional structures for the range of Reynolds numbers considered, the two-dimensional model captures the unsteady processes and produced results that were consistent with the available experimental data. It correctly simulated the overall, the front-stagnation and the back-to-total heat-transfer rates.

Supersonic Nozzle Design

1946 ◽  
Vol 13 (4) ◽  
pp. A265-A270 ◽  
Author(s):  
A. E. Puckett
Keyword(s):  
Flow Field ◽  
Method Of Characteristics ◽  
Supersonic Nozzle ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Nozzle Design ◽  
Small Areas ◽  
Engineering Problems ◽  
Two Dimensional Flow ◽  
Flow Changes

Abstract A two-dimensional flow field in which the velocity is everywhere supersonic can always be represented approximately by a number of small adjacent quadrilateral flow fields in each of which the velocity and pressure are constant. These quadrilaterals must be separated by lines representing waves in the flow; changes in velocity and pressure through any wave can be computed. By increasing the number of small areas into which the complete flow field is divided, the accuracy of this approximate solutions may be increased without limit. This constitutes the “method of characteristics” solution, which has been known for many years. This method may be applied to the graphical computation of flow in a supersonic nozzle, with the particular aim of producing uniform supersonic flow at the end of the nozzle. It is pointed out that such a computation is essentially simple and rapid, and its essential features are presented in a form which, it is hoped, may be easily applied to engineering problems.

Investigation of Scramjet Inlet Flow Using a Flux-Splitting Solver

2010 ◽  
Author(s):  
D. M. Holian ◽  
R. R. Mankbadi
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Boundary Layer Separation ◽  
Navier Stokes ◽  
Shock Interactions ◽  
Flux Splitting ◽  
Operation Conditions ◽  
Inlet Geometry ◽  
Proper Operation ◽  
Good Agreement

A detailed analysis is carried out on a rectangular scramjet inlet to analyze the flow field. The focus is on examining boundary layer separation and shock interactions to ensure proper operation of the inlet. We developed herein a flux-splitting Navier Stokes solver to be used for optimizing the inlet geometry and operation conditions. The results seem to be in good agreement with that of FLUENT CFD software and explain the experimental results of Haberle (2008).

The development of weak waves in the steady two-dimensional flow of a gas with vibrational relaxation past a thin wedge

1975 ◽  
Vol 69 (1) ◽  
pp. 109-128 ◽  
Author(s):  
R. P. Hornby ◽  
N. H. Johannesen
Keyword(s):  
Supersonic Flow ◽  
Shock Tube ◽  
Small Angle ◽  
Vibrational Relaxation ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
Two Dimensional ◽  
Wave Decay ◽  
Two Dimensional Flow ◽  
Thin Wedge

The method of characteristics is used to calculate the supersonic flow past a wedge of small angle with non-equilibrium effects. The wave decay and development distances are presented in a concise similarity form which permits accurate extrapolation to very weak waves. The numerical solutions are compared with shock-tube flows of CO2 and N2O.

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