Unsteady transonic flows in two-dimensional channels

1972 ◽  
Vol 52 (3) ◽  
pp. 437-449 ◽  
Author(s):  
T. C. Adamson
Keyword(s):  
Inviscid Flow ◽  
Time Varying ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Flow Disturbance ◽  
Specific Heats ◽  
Isentropic Flow ◽  
Perturbation Potential ◽  
Temporal Flow ◽  
Nozzle Flows

A two-dimensional, unsteady, transonic, irrotational, inviscid flow of a perfect gas with constant specific heats is considered. The analysis involves perturbations from a uniform sonic isentropic flow. The governing perturbation potential equations are derived for various orders of the ratio of the characteristic time associated with a temporal flow disturbance to the time taken by a sonic disturbance to traverse the transonicregime. The case where this ratio is large compared to one is studied in detail. A similarity solution involving an arbitrary function of time is found and it is shown that this solution corresponds to unsteady chimel flows with either stationary or time-varying wall shapes. Numerical computations are presented showing the temporal changes in flow structure as a disturbance dies out exponentially for the following typical nozzle flows: simple accelerating (Meyer) flow and flow with supersonic pockets (Taylor and limiting Taylor flow).

Unsteady transonic flows with shock waves in two-dimensional channels

1973 ◽  
Vol 60 (2) ◽  
pp. 363-382 ◽  
Author(s):  
T. C. Adamson ◽  
G. K. Richey
Keyword(s):  
Shock Waves ◽  
Stationary Solutions ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Specific Heats ◽  
Isentropic Flow ◽  
Flow Disturbances ◽  
Shock Position ◽  
Temporal Flow ◽  
Transonic Region

A two-dimensional unsteady transonic flow of a perfect gas with constant specific heats is considered, solutions being found in the form of perturbations from a uniform, sonic, isentropic flow. Longitudinal viscous stress terms are retained so that shock waves can be included. The case where the characteristic time of a temporal flow disturbance is large compared with the time taken by a sonic disturbance to traverse the transonic regime is studied. A similarity solution involving an arbitrary function of time is employed, such that the channel walls are in general not stationary. Solutions are presented for thick (shock fills transonic region) and thin (shock tends to a discontinuity) shock waves for both decelerating and accelerating channel flows. For the thin-shock case, both numerical and asymptotic solutions are given. Flow pictures illustrating variations in shock position and structure as well as velocity distributions are shown for exponentially decreasing and for harmonic temporal flow disturbances.

scholarly journals Some nozzle flows found by the hodograph method

1959 ◽  
Vol 1 (1) ◽  
pp. 80-94 ◽  
Author(s):  
T. M. Cherry
Keyword(s):  
Exact Solutions ◽  
Two Dimensions ◽  
Nozzle Design ◽  
Perfect Gas ◽  
Field Equations ◽  
Rigid Boundary ◽  
Hodograph Method ◽  
Isentropic Flow ◽  
Fixed Boundaries ◽  
Nozzle Flows

For investigating the steady irrotational isentropic flow of a perfect gas in two dimensions, the hodograph method is to determine in the first instance the position coordinates x, y and the stream function ψ as functions of velocity compoments, conveniently taken as q (the speed) and θ (direction angle). Inversion then gives ψ, q, θ as functions of x, y. The method has the great advantage that its field equations are linear, so that it is practicable to obtain exact solutions, and from any two solutions an infinity of others are obtainable by superposition. For problems of flow past fixed boundaries the linearity of the field equations is usually offset by non-linearity in the boundary conditions, but this objection does not arise in problems of transsonic nozzle design, where the rigid boundary is the end-point of the investigation.

Solutions for supersonic rotational flow around a corner using a new co-ordinate system

1968 ◽  
Vol 34 (4) ◽  
pp. 735-758 ◽  
Author(s):  
T. C. Adamson
Keyword(s):  
Similarity Solution ◽  
Inviscid Flow ◽  
Numerical Results ◽  
Rotational Flow ◽  
Incoming Flow ◽  
Two Dimensional ◽  
Governing Equations ◽  
Perfect Gas ◽  
Convex Corner

A co-ordinate system consisting of the left-running characteristics (α = const.) and the streamlines (ϕ = const.) is used. The governing equations are derived in terms of α and ϕ for a two-dimensional steady supersonic rotational inviscid flow of a perfect gas. The equations are applied to the problem of an initially parallel supersonic rotational flow which expands around a convex corner. The velocity of the incoming flow at the wall is considered to be either supersonic (case 1) or sonic (case 2). For each case, solutions uniformly valid in the region near the leading characteristic and in the region near the corner, are found for the Mach angle and flow deflexion angle in terms of their values on the leading characteristic and at the corner. In case 2, a transonic similarity solution is found and composite solutions are constructed for each region. Comparisons are made with existing exact numerical results.

The correction of wind tunnel nozzles for two-dimensional, supersonic flow

1950 ◽  
Vol 2 (3) ◽  
pp. 195-208 ◽  
Author(s):  
R. E. Meyer ◽  
M. Holt
Keyword(s):  
Wind Tunnel ◽  
Uniform Flow ◽  
Pressure Measurements ◽  
Two Dimensional ◽  
Simple Test ◽  
Perfect Gas ◽  
Isentropic Flow ◽  
Two Dimensional Flow ◽  
Stream Direction ◽  
Flow Stream

SummaryThe paper is concerned with the two-dimensional, steady, irrotational, isentropic flow of a perfect gas in a wind tunnel nozzle which is found to produce a flow in the test rhombus deviating slightly from the desired uniform flow.The minimum corrections are derived that must be applied to the liners in order to produce a uniform flow in the test rhombus. If the uncorrected nozzle produces a flow of uniform direction, measurement of the pressure on the axis, in the test rhombus, suffices to determine these corrections (Section 5). If not, further pressure measurements are required (Section 6). A simple test is indicated for checking whether the flow stream direction is uniform (Section 6).The method cannot be used to correct for deviations from a two-dimensional flow.

scholarly journals Doppler spectrum of microwave SAR signals from two-dimensional time-varying sea surface

2016 ◽  
Vol 30 (10) ◽  
pp. 1265-1276 ◽  
Author(s):  
Yunhua Wang ◽  
Yanmin Zhang ◽  
Huimin Li ◽  
Ge Chen
Keyword(s):  
Sea Surface ◽  
Doppler Spectrum ◽  
Time Varying ◽  
Two Dimensional

A Viscous-Inviscid Interaction Procedure—Part 1: Method for Computing Two-Dimensional Incompressible Separated Channel Flows

1986 ◽  
Vol 108 (1) ◽  
pp. 64-70 ◽  
Author(s):  
O. K. Kwon ◽  
R. H. Pletcher
Keyword(s):  
Experimental Data ◽  
Finite Difference ◽  
Turbulent Flows ◽  
Inviscid Flow ◽  
Companion Paper ◽  
Separated Flows ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Interaction Scheme ◽  
Laminar And Turbulent Flows

A viscous-inviscid interaction scheme has been developed for computing steady incompressible laminar and turbulent flows in two-dimensional duct expansions. The viscous flow solutions are obtained by solving the boundary-layer equations inversely in a coupled manner by a finite-difference scheme; the inviscid flow is computed by numerically solving the Laplace equation for streamfunction using an ADI finite-difference procedure. The viscous and inviscid solutions are matched iteratively along displacement surfaces. Details of the procedure are presented in the present paper (Part 1), along with example applications to separated flows. The results compare favorably with experimental data. Applications to turbulent flows over a rearward-facing step are described in a companion paper (Part 2).

Study of Vaneless Diffuser Rotating Stall Based on Two-Dimensional Inviscid Flow Analysis

1996 ◽  
Vol 118 (1) ◽  
pp. 123-127 ◽  
Author(s):  
Yoshinobu Tsujimoto ◽  
Yoshiki Yoshida ◽  
Yasumasa Mori
Keyword(s):  
Propagation Velocity ◽  
Flow Instability ◽  
Present Report ◽  
Inviscid Flow ◽  
Rotating Stall ◽  
Critical Flow ◽  
Two Dimensional ◽  
Vaneless Diffuser ◽  
Flow Angle ◽  
Pressure Disturbance

Rotating stalls in vaneless diffusers are studied from the viewpoint that they are basically two-dimensional inviscid flow instability under the boundary conditions of vanishing velocity disturbance at the diffuser inlet and of vanishing pressure disturbance at the diffuser outlet. The linear analysis in the present report shows that the critical flow angle and the propagation velocity are functions of only the diffuser radius ratio. It is shown that the present analysis can reproduce most of the general characteristics observed in experiments: critical flow angle, propagation velocity, velocity, and pressure disturbance fields. It is shown that the vanishing velocity disturbance at the diffuser inlet is caused by the nature of impellers as a “resistance” and an “inertial resistance,” which is generally strong enough to suppress the velocity disturbance at the diffuser inlet. This explains the general experimental observations that vaneless diffuser rotating stalls are not largely affected by the impeller.

Time-Varying Channel Estimation Using Two-Dimensional Channel Orthogonalization and Superimposed Training

2012 ◽  
Vol 60 (8) ◽  
pp. 4439-4443 ◽  
Author(s):  
Roberto Carrasco-Alvarez ◽  
R. Parra-Michel ◽  
Aldo G. Orozco-Lugo ◽  
Jitendra K. Tugnait
Keyword(s):  
Channel Estimation ◽  
Time Varying ◽  
Two Dimensional ◽  
Superimposed Training ◽  
Time Varying Channel
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