Development of Two-Dimensional Wakes Within Curved Channels: Theoretical Framework and Experimental Investigation

1996 ◽  
Vol 118 (3) ◽  
pp. 506-518 ◽  
Author(s):  
M. T. Schobeiri ◽  
J. John ◽  
K. Pappu
Keyword(s):  
Coordinate System ◽  
Equations Of Motion ◽  
Wake Flow ◽  
Turbulent Shear ◽  
Curvature Radius ◽  
Two Dimensional ◽  
Mean Velocity ◽  
General Validity ◽  
Turbulent Shear Stress ◽  
Curved Channels

The development of a wake flow downstream of a cylindrical rod within a curved channel under zero streamwise pressure gradient is theoretically and experimentally investigated. The measured asymmetric wake quantities such as the mean velocity and turbulent fluctuations in longitudinal and lateral directions as well as the turbulent shear stress are transformed from the probe coordinate system into the curvilinear wake eigen-coordinate system. For the transformed non-dimensionalized velocity defect and the turbulent quantities, affine profiles are observed throughout the flow regime. Based on these observations and using the transformed equations of motion and continuity, a theoretical frame work is established that generally describes the two-dimensional curvilinear wake flow. The theory also describes the straight wake as a special case, for which the curvature radius approaches infinity. The comparison of the theory with the experimental data pertaining to the curvilinear and straight wakes demonstrate the general validity of the theory.

scholarly journals Development of Two-Dimensional Wakes Within Curved Channels, Theoretical Framework and Experimental Investigation

1994 ◽  
Author(s):  
M. T. Schobeiri ◽  
J. John ◽  
K. Pappu
Keyword(s):  
Coordinate System ◽  
Equations Of Motion ◽  
Wake Flow ◽  
Turbulent Shear ◽  
Curvature Radius ◽  
Two Dimensional ◽  
Mean Velocity ◽  
General Validity ◽  
Turbulent Shear Stress ◽  
Curved Channels

The development of a wake flow downstream of a cylindrical rod within a curved channel under zero streamwise pressure gradient is theoretically and experimentally investigated. The measured asymmetric wake quantities such as the mean velocity and turbulent fluctuations in longitudinal and lateral directions as well as the turbulent shear stress are transformed from the probe coordinate system into the curvilinear wake eigen-coordinate system. For the transformed non-dimensionalized velocity defect and the turbulent quantities, affine profiles are observed throughout the flow regime. Based on these observations and using the transformed equations of motion and continuity, a theoretical frame work is established that generally describes the two-dimensional curvilinear wake flow. The theory also describes the straight wake as a special case, for which the curvature radius approaches infinity. The comparison of the theory with the experimental data pertaining to the curvilinear and straight wakes demonstrate the general validity of the theory.

scholarly journals On the Development of Two-Dimensional Wakes within Curved Channels: Experimental and Theoretical Investigation

1994 ◽  
Vol 1 (1) ◽  
pp. 19-35
Author(s):  
M. T. Schobeiri ◽  
K. Pappu ◽  
J. John
Keyword(s):  
Coordinate System ◽  
Equations Of Motion ◽  
Wake Flow ◽  
Turbulent Shear ◽  
Curvature Radius ◽  
Two Dimensional ◽  
Mean Velocity ◽  
General Validity ◽  
Turbulent Shear Stress ◽  
Curved Channels

The development of a wake flow downstream of a cylindrical rod within a curved channel under zero streamwise pressure gradient is theoretically and experimentally investigated. The measured asymmetric wake quantities such as the mean velocity and turbulent fluctuations in longitudinal and lateral directions as well as the turbulent shear stress are transformed from the probe coordinate system into the curvilinear wake eigen-coordinate system. For the transformed nondimensionalized velocity defect and the turbulent quantities, affine profiles are observed throughout the flow regime. Based on these observations and using the transformed equations of motion and continuity, a theoretical framework is established that generally describes the two-dimensional curvilinear wake flow. The theory also describes the straight wake as a special case, for which the curvature radius approaches infinity. To demonstrate the general validity of theory, experimental results pertaining to curved wake as well as straight wake flows are compared with the developed theory.

Theoretical and Experimental Study of Development of Two-Dimensional Steady and Unsteady Wakes Within Curved Channels

1995 ◽  
Vol 117 (4) ◽  
pp. 593-598 ◽  
Author(s):  
M. T. Schobeiri ◽  
K. Pappu ◽  
J. John
Keyword(s):  
Equations Of Motion ◽  
Theory Development ◽  
Detailed Comparison ◽  
Wake Flow ◽  
Turbulent Shear ◽  
Two Dimensional ◽  
Curved Channel ◽  
Mean Velocity ◽  
Wake Flows ◽  
Unsteady Wake

Development of steady and periodic unsteady wake flows downstream of stationary and rotating cylindrical rods within a curved channel under zero longitudinal pressure gradient is theoretically and experimentally investigated. Wake quantities such as the mean velocity and turbulent fluctuations in longitudinal and lateral directions, as well as the turbulent shear stress, are measured. For the nondimensionalized velocity defect, affine profiles are observed throughout the flow regime. Based on these observations and using the transformed equations of motion and continuity, a theoretical frame work is established that generally describes the two-dimensional curvilinear wake flow. To confirm the theory, development of steady and periodic unsteady wakes in the above curved channel are experimentally investigated. The detailed comparison between the measurement and the theory indicates that the complex steady and unsteady wake flows are very well predicted.

Control of trailing-edge separation by tangential blowing inside the bubble

2004 ◽  
Vol 108 (1086) ◽  
pp. 419-425 ◽  
Author(s):  
P. R. Viswanath ◽  
K. T. Madhavan
Keyword(s):  
Separation Bubble ◽  
Effective Means ◽  
Separated Flow ◽  
Wake Flow ◽  
Turbulent Shear ◽  
Trailing Edge ◽  
Mean Velocity ◽  
Turbulent Shear Stress ◽  
Edge Separation ◽  
Tangential Blowing

Abstract Experiments have been performed investigating the effectiveness of steady tangential blowing, with the blowing slot located downstream of separation (but inside the separation bubble) to control a trailing-edge separated flow at low speeds. Trailing-edge separation was induced on a two-dimensional aerofoil-like body and the shear layer closure occurred in the near-wake. Measurements made consisted of model surface pressures and mean velocity, turbulent shear stress and kinetic energy profiles in the separated zone using a two-component LDV system. It is explicitly demonstrated that the novel concept of tangential blowing inside the bubble can be an effective means of control for trailing-edge separated flows as well. Blowing mass and momentum requirements for the suppression of wall and wake flow reversals have been estimated.

Conditional Sampling in a Transitional Boundary Layer Under High Freestream Turbulence Conditions

2003 ◽  
Vol 125 (1) ◽  
pp. 28-37 ◽  
Author(s):  
Ralph J. Volino ◽  
Michael P. Schultz ◽  
Christopher M. Pratt
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Streamwise Velocity ◽  
Turbulent Shear ◽  
Conditional Sampling ◽  
Freestream Turbulence ◽  
Mean Velocity ◽  
Transitional Boundary Layer ◽  
Turbulent Shear Stress ◽  
Order Of Magnitude

Conditional sampling has been performed on data from a transitional boundary layer subject to high (initially 9%) freestream turbulence and strong (K=ν/U∞2dU∞/dx as high as 9×10−6) acceleration. Methods for separating the turbulent and nonturbulent zone data based on the instantaneous streamwise velocity and the turbulent shear stress were tested and found to agree. Mean velocity profiles were clearly different in the turbulent and nonturbulent zones, and skin friction coefficients were as much as 70% higher in the turbulent zone. The streamwise fluctuating velocity, in contrast, was only about 10% higher in the turbulent zone. Turbulent shear stress differed by an order of magnitude, and eddy viscosity was three to four times higher in the turbulent zone. Eddy transport in the nonturbulent zone was still significant, however, and the nonturbulent zone did not behave like a laminar boundary layer. Within each of the two zones there was considerable self-similarity from the beginning to the end of transition. This may prove useful for future modeling efforts.

scholarly journals Compressible mixing layer in shock-induced separation

2019 ◽  
Vol 863 ◽  
pp. 620-643 ◽  
Author(s):  
P. Dupont ◽  
S. Piponniau ◽  
J. P. Dussauge
Keyword(s):  
Turbulent Transport ◽  
Mixing Layer ◽  
Spreading Rate ◽  
Turbulent Shear ◽  
Free Shear Layer ◽  
Mean Velocity ◽  
Entrainment Velocity ◽  
Spatial Growth ◽  
Turbulent Shear Stress ◽  
High Mach

Unsteadiness in separated shock–boundary layer interactions have been previously analysed in order to propose a scenario of entrainment–discharge as the origin of unsteadiness. It was assumed that the fluid in the separated zone is entrained by the free shear layer formed at its edge, and that this layer follows the properties of the canonical mixing layer. This last point is addressed by reanalysing the velocity measurements in an oblique shock reflection at a nominal Mach number of 2.3 and for two cases of flow deviation ($8^{\circ }$ and $9.5^{\circ }$). The rate of spatial growth of this layer is evaluated from the spatial growth of the turbulent stress profiles. Moreover, the entrainment velocity at the edge of the layer is determined from the mean velocity profiles. It is shown that the values of turbulent shear stress, spreading rate and entrainment velocity are consistent, and that they follow the classical laws for turbulent transport in compressible shear layers. Moreover, the measurements suggest that the vertical normal stress is sensitive to compressibility, so that the anisotropy of turbulence is affected by high Mach numbers. Dimensional considerations proposed by Brown & Roshko (J. Fluid Mech., vol. 64, 1974, 775–781) are reformulated to explain this observed trend.

Turbulence Measurements in a Straight Walled Two Dimensional Diffuser

1986 ◽  
Author(s):  
A. Mobarak ◽  
M. A. Fouad ◽  
M. A. Metwally
Keyword(s):  
Cross Sections ◽  
Turbulence Intensity ◽  
Turbulent Shear ◽  
Maximum Pressure ◽  
Probe Type ◽  
Two Dimensional ◽  
Turbulent Shear Stress ◽  
Diffuser Flow ◽  
Attached Flow ◽  
Velocity Turbulence

Turbulent flow field of a straight walled two dimensional diffuser Is experimentally studied using a hot wire anemometer (X-probe type). The diffuser flow Is tested at the optimum angle corresponding to maximum pressure recovery and consequently at conditions of attached flow. Diffuser side walls are made of different materials to study the effect of wall roughness. Measurements of static pressure, flow velocity, turbulence intensity and turbulent shear stress are carried out at six cross-sections distributed along the axial length of the diffuser. At each cross-section measurements were taken at nine planes distributed along the diffuser width between the parallel walls. Variations of boundary layer displacement thicknesses are studied through their relations to turbulence intensity. The present detailed experimental results are intended as an input to a turbulence model for prediction of diffuser flow.

scholarly journals Two-dimensional fluid motion referred to a network of orthogonal curves

1949 ◽  
Vol 196 (1045) ◽  
pp. 301-310 ◽  
Keyword(s):  
Coordinate System ◽  
Gaussian Curvature ◽  
Large Scale ◽  
Equations Of Motion ◽  
Fluid Motion ◽  
Parameter Family ◽  
Two Dimensional ◽  
Gradient Wind

A theory already developed is applied to the case of two-dimensional motion parallel at each point of space to some member, Ʃ, of a one-parameter family of surfaces, the coordinate-system being a network of orthogonal curves drawn on Ʃ. The geodesic curvatures of the orthogonal curves and their relationship to the Gaussian curvature of Ʃ are worked out.The equations of motion and of continuity are expressed in terms of the geodesic curvatures. Meyer’s aerodynamical equations are derived as particular cases when the network is fixed in space and the surfaces are all planes. A formula for a large-scale gradient wind is also obtained as an example of the use of a moving network drawn on a sphere.

Development of a Two-Dimensional Turbulent Wake in a Curved Channel With a Positive Streamwise Pressure Gradient

1996 ◽  
Vol 118 (2) ◽  
pp. 292-299 ◽  
Author(s):  
J. John ◽  
M. T. Schobeiri
Keyword(s):  
Pressure Gradient ◽  
Reynolds Stress ◽  
Gaussian Function ◽  
Two Dimensional ◽  
Curved Channel ◽  
Mean Velocity ◽  
Velocity Defect ◽  
Curved Channels ◽  
Stress Components ◽  
Streamwise Pressure Gradient

The development of turbomachinery wake flows is greatly influenced by streamline curvature and streamwise pressure gradient. This paper is part of a comprehensive experimental and theoretical study on the development of the steady and periodic unsteady turbulent wakes in curved channels at different streamwise pressure gradients. This paper reports on the experimental investigation of the two-dimensional wake behind a stationary circular cylinder in a curved channel at positive streamwise pressure gradient. Measurements of mean velocity and Reynolds stress components are carried out using a X-hot-film probe. The measured quantities obtained in probe coordinates are transformed to a curvilinear coordinate system along the wake center line and are presented in similarity coordinates. The results show strong asymmetry in velocity and Reynolds stress components. The Reynolds stress components have higher values at the inner half of the wake than at the outer half of the wake. However, the mean velocity defect profiles in similarity coordinates are almost symmetric and follow the same Gaussian function for the straight wake data. A comparison with the wake development in a curved channel at zero streamwise pressure gradient suggests the decay rate of velocity defect is slower and the growth of wake width is faster for a positive streamwise pressure gradient.

The calculation of three-dimensional turbulent boundary layers in incompressible flow

1969 ◽  
Vol 37 (4) ◽  
pp. 625-642 ◽  
Author(s):  
J. F. Nash
Keyword(s):  
Shear Stress ◽  
Incompressible Flow ◽  
Energy Equation ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Turbulent Energy ◽  
Two Dimensions ◽  
Turbulent Shear ◽  
Developable Surface ◽  
Turbulent Shear Stress

A method is described for calculating the development of a three-dimensional turbulent boundary layer, over a flat or developable surface, in incompressible flow. The method involves the numerical integration of the equations of motion by an explicit finite-difference method. The shear stress is determined by a parallel integration of the turbulent energy equation modified by the inclusion of empirical functions of a form which has proved successful in two dimensions, and the additional assumption is made that the turbulent shear stress acts in the direction of the rate of strain of the mean motion. The treatment of the turbulent energy equation follows closely the work of Bradshaw, Ferriss & Atwell (1967) in two dimensions.Comparison with experiment is found to be substantially more difficult than in two dimensions. Particular difficulty is encountered in translating the recorded details of the experiment into boundary conditions for the calculation. The comparisons submitted here give some indication that the method as a whole performs satisfactorily, but they do not provide a definitive assessment of the validity of the basic assumptions. A plea is made for an experiment to supply data in a suitable form for making a more careful assessment of methods of this type.

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