A Note on the Estimation of Average Pressures from Instantaneous Velocities in Unsteady Flow

1967 ◽  
Vol 71 (678) ◽  
pp. 440-440
Author(s):  
C. J. Wood
Keyword(s):  
Unsteady Flow ◽  
Boundary Layers ◽  
Data Reduction ◽  
Bluff Body ◽  
Wake Vortex ◽  
Two Dimensional ◽  
Experimental Check ◽  
Velocity Measurements ◽  
Periodic Disturbance ◽  
Oncoming Stream

In a recent paper, the author described some experiments in which the average base pressure on a two-dimensional bluff body was estimated from a random sample of instantaneous velocity measurements taken in the irrotational flow outside the separating boundary layers at the trailing edge. Although the oncoming stream was steady, the flow near the model was subject to a periodic disturbance emanating from the wake vortex street. An experimental check showed that the pressure estimates obtained by using the steady Bernouilli equation were reasonably accurate. This note points out that the method of data reduction used in ref. 1 is not an approximation; it is exact.

Turbulent Flow Between Two Disks Contrarotating at Different Speeds

1996 ◽  
Vol 118 (2) ◽  
pp. 408-413 ◽  
Author(s):  
M. Kilic ◽  
X. Gan ◽  
J. M. Owen
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Unsteady Flow ◽  
Turbulent Flow ◽  
Boundary Layers ◽  
Axial Flow ◽  
Radial Component ◽  
Velocity Measurements ◽  
Type Flow ◽  
Radial Outflow

This paper describes a combined computational and experimental study of the turbulent flow between two contrarotating disks for −1 ≤ Γ ≤ 0 and Reφ ≈ 1.2 × 106, where Γ is the ratio of the speed of the slower disk to that of the faster one and Reφ is the rotational Reynolds number. The computations were conducted using an axisymmetric elliptic multigrid solver and a low-Reynolds-number k–ε turbulence model. Velocity measurements were made using LDA at nondimensional radius ratios of 0.6 ≤ x ≤ 0.85. For Γ = 0, the rotor–stator case, Batchelor-type flow occurs: There is radial outflow and inflow in boundary layers on the rotor and stator, respectively, between which is an inviscid rotating core of fluid where the radial component of velocity is zero and there is an axial flow from stator to rotor. For Γ = −1, antisymmetric contrarotating disks, Stewartson-type flow occurs with radial outflow in boundary layers on both disks and inflow in the viscid nonrotating core. At intermediate values of Γ, two cells separated by a streamline that stagnates on the slower disk are formed: Batchelor-type flow and Stewartson-type flow occur radially outward and inward, respectively, of the stagnation streamline. Agreement between the computed and measured velocities is mainly very good, and no evidence was found of nonaxisymmetric or unsteady flow.

Paper 29: Unsteady Flow Effects Downstream of an Annular Cascade of Self-Excited Blades

1969 ◽  
Vol 184 (7) ◽  
pp. 83-88
Author(s):  
V. G. Nabar
Keyword(s):  
Unsteady Flow ◽  
Boundary Layers ◽  
Large Concentration ◽  
Two Dimensional ◽  
Hot Wire ◽  
Dimensional Theory ◽  
Wall Boundary ◽  
Blade Tip ◽  
Flow Effects ◽  
Annular Cascade

This paper presents a two-dimensional theory for calculating streamwise perturbations in the flow downstream of a cascade of self-excited blades and gives details of hot-wire measurements of unsteadiness downstream of an annular cascade. The theoretical values show little variation from blade to blade, whereas the experiments exhibit a large concentration of perturbations near the hub and a comparatively smaller one near the tip. It is thought that periodic circulation is shed largely from the blade tip and root within the annulus wall boundary layers, in a manner similar to the shedding of steady circulation from the aeroplane wings.

Computation and Simulation of Wake-Generated Unsteady Pressure and Boundary Layers in Cascades: Part 1—Description of the Approach and Validation

1996 ◽  
Vol 118 (1) ◽  
pp. 96-108 ◽  
Author(s):  
S. Fan ◽  
B. Lakshminarayana
Keyword(s):  
Boundary Layer ◽  
Unsteady Flow ◽  
Flat Plate ◽  
Boundary Layers ◽  
Numerical Procedure ◽  
Computational Domain ◽  
Two Dimensional ◽  
Unsteady Pressure ◽  
Blade Row ◽  
Euler Solver

The unsteady pressure and boundary layers on a turbomachinery blade row arising from periodic wakes due to upstream blade rows are investigated in this paper. A time-accurate Euler solver has been developed using an explicit four-stage Runge–Kutta scheme. Two-dimensional unsteady nonreflecting boundary conditions are used at the inlet and the outlet of the computational domain. The unsteady Euler solver captures the wake propagation and the resulting unsteady pressure field, which is then used as the input for a two-dimensional unsteady boundary layer procedure to predict the unsteady response of blade boundary layers. The boundary layer code includes an advanced k–ε model developed for unsteady turbulent boundary layers. The present computational procedure has been validated against analytic solutions and experimental measurements. The validation cases include unsteady inviscid flows in a flat-plate cascade and a compressor exit guide vane (EGV) cascade, unsteady turbulent boundary layer on a flat plate subject to a traveling wave, unsteady transitional boundary layer due to wake passing, and unsteady flow at the midspan section of an axial compressor stator. The present numerical procedure is both efficient and accurate in predicting the unsteady flow physics resulting from wake/blade-row interaction, including wake-induced unsteady transition of blade boundary layers.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

Two-dimensional leaps in near-critical flow over isolated orography

2005 ◽  
Vol 461 (2064) ◽  
pp. 3747-3763 ◽  
Author(s):  
E.R Johnson ◽  
G.G Vilenski
Keyword(s):  
Unsteady Flow ◽  
Equations Of Motion ◽  
Fold Increase ◽  
Flow Speed ◽  
Two Dimensional ◽  
Subcritical Flow ◽  
One Dimensional ◽  
Petviashvili Equation ◽  
Lee Wave ◽  
Supercritical Flows

This paper describes steady two-dimensional disturbances forced on the interface of a two-layer fluid by flow over an isolated obstacle. The oncoming flow speed is close to the linear longwave speed and the layer densities, layer depths and obstacle height are chosen so that the equations of motion reduce to the forced two-dimensional Korteweg–de Vries equation with cubic nonlinearity, i.e. the forced extended Kadomtsev–Petviashvili equation. The distinctive feature noted here is the appearance in the far lee-wave wake behind obstacles in subcritical flow of a ‘table-top’ wave extending almost one-dimensionally for many obstacles widths across the flow. Numerical integrations show that the most important parameter determining whether this wave appears is the departure from criticality, with the wave appearing in slightly subcritical flows but being destroyed by two-dimensional effects behind even quite long ridges in even moderately subcritical flow. The wave appears after the flow has passed through a transition from subcritical to supercritical over the obstacle and its leading and trailing edges resemble dissipationless leaps standing in supercritical flow. Two-dimensional steady supercritical flows are related to one-dimensional unsteady flows with time in the unsteady flow associated with a slow cross-stream variable in the two-dimensional flows. Thus the wide cross-stream extent of the table-top wave appears to derive from the combination of its occurrence in a supercritical region embedded in the subcritical flow and the propagation without change of form of table-top waves in one-dimensional unsteady flow. The table-top wave here is associated with a resonant steepening of the transition above the obstacle and a consequent twelve-fold increase in drag. Remarkably, the table-top wave is generated equally strongly and extends laterally equally as far behind an axisymmetric obstacle as behind a ridge and so leads to subcritical flows differing significantly from linear predictions.

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