Introduction to Turbulence AEEM Why study turbulent flows?

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Introduction to Turbulence AEEM 7063-003 Dr. Peter J. Disimile UC-FEST Department of Aerospace Engineering Peter.disimile@uc.

1 Introduction to Turbulence AEEM Dr. Peter J. Disimile UC-FEST Department of Aerospace Engineering Intro to Turbulence: C1A Why 1 Most flows encountered in engineering and nature are turbulent. Turbulence is responsible for intense mixing which brings fluid particles with different momentum levels into close contact and thus enhances momentum transfer. Turbulence allows for the transport of mass, momentum, and energy to other regions of flow much more rapidly than molecular diffusion, greatly enhancing the transfer of mass, momentum, and heat. As a result, turbulent flow is associated with much higher values of friction, heat transfer, and mass transfer coefficients Intro to Turbulence: C1A Why 2 1

Yet a turbulent boundary layer is thicker than a laminar bl for the same free-stream

2 Flat plate: velocity gradient at the wall, and thus the wall shear stress, is much larger for turbulent flow than a laminar. Yet a turbulent boundary layer is thicker than a laminar bl for the same free-stream velocity. du dy Intro to Turbulence: C1A Why 3 Turbulent friction is also larger in confined duct flow The Moody Diagram Intro to Turbulence: C1A Why 4 2

attached to the body longer and produces a smaller wake Intro to Turbulence: C1A Why 5 Most of the drag is due

3 It has been observed that sometimes an increase of speed can actually produce a decrease in drag. Laminar Boundary Layer: separates earlier on body and produces a bigger wake Turbulent Boundary Layer: stays attached to the body longer and produces a smaller wake Intro to Turbulence: C1A Why 5 Most of the drag is due to skin friction, very small wake. Most of the drag is due to pressure drop, i.e., large wake. Intro to Turbulence: C1A Why 6 3

Note: Components of pressure drag (P) and skin-friction drag (V) for laminar and turbulent flows past an

4 Frictional forces in a turbulent flow are > a laminar flow, but pressure forces tend to be reduced enough such that total drag goes down! Note: Components of pressure drag (P) and skin-friction drag (V) for laminar and turbulent flows past an non-streamlined body at high Re #. Intro to Turbulence: C1A Why 7 adverse pressure gradient Laminar bl Turbulent bl Separation IDEAL FLOW LAMINAR FLOW TURBULENT FLOW Intro to Turbulence: C1A Why 8 4

Note: 1- BL becomes turbulent on roughened sphere earlier than for smooth sphere. 2- Turbulent BL s are better at mixing high momentum outer flow with BL flow.

Re = 30,000 (with trip wire turbulent separation) Trip From Van Dyke; Album of Fluid Motion Parabolic Press, 1982; Original photographs by Werle, ONERA, 1980 Re= 15,000 (laminar separation)

5 Note: 1- BL becomes turbulent on roughened sphere earlier than for smooth sphere. 2- Turbulent BL s are better at mixing high momentum outer flow with BL flow. 3- Energized by the outer flow the turbulent BL separates further back on the sphere, resulting in a smaller wake and less drag (1/5 th as much at optimum speeds). Re = 30,000 (with trip wire turbulent separation) Trip From Van Dyke; Album of Fluid Motion Parabolic Press, 1982; Original photographs by Werle, ONERA, 1980 Re= 15,000 (laminar separation) Smooth Intro to Turbulence: C1A Why 9 Turbulence ranges from annoying bumpiness to severe jolts which cause structural damage and/or injuries. Sudden changes in air movement cause an aircraft to potentially pitch, yaw and roll. Intro to Turbulence: C1A Why 10 5

$Turbulence produces variations in the local temperature which impacts the density and therefore the index of refraction.$ $Turbulence produced by wind passing over the telescope dome produces variations in the index of refraction, shown below.$

6 Causes of Turbulence Convective currents Called convective turbulence Obstructions to wind flow Sometimes referred to as mechanical turbulence Kelvin Helmholtz clouds visual indicators of high level turbulence SHEAR ZONE Wind shear Intro to Turbulence: C1A Why 11 One application where turbulent flows have a large impact is related to seeing into the sky. Turbulence produces variations in the local temperature which impacts the density and therefore the index of refraction. Turbulence produced by wind passing over the telescope dome produces variations in the index of refraction, shown below. This area of research is referred to as Aero-optics. Wind Top view Side view Computational fluid dynamics simulation (D. de Young) Intro to Turbulence: C1A Why 12 6

motions made up of fluctuations which are

allowed to exist in light of dissipative

7 Where are turbulent flows found? Most flows encountered in engineering and nature are turbulent. Intro to Turbulence: C1A Why 13 What are turbulent flows? Turbulent flows are unsteady rotational motions made up of fluctuations which are random in space and time. These motions (i.e., vortical motions) come in all sizes, from the largest motion limited by the flow field itself down to the smallest scale, which is allowed to exist in light of dissipative processes. Animation 3.22: Numerical simulation of a Kelvin-Helmholtz instability [Wikipedia] Intro to Turbulence: C1A Why 14 7

flow goes through transition and becomes turbulent.

As the velocity is increased (i.e., the Re is increased) the flow transitions to a turbulent flow (Figure b).

8 How do flows become turbulent? Steady laminar flows become unstable at high Reynold's numbers and can no longer maintain a organized or ordered flow. Instability to small disturbances is an initial step in the process whereby a laminar flow goes through transition and becomes turbulent. Intro to Turbulence: C1A Why 15 How do flows become turbulent? Steady laminar flow of water exiting a tube (Figure a). As the velocity is increased (i.e., the Re is increased) the flow transitions to a turbulent flow (Figure b). Figure c represents the same flow conditions as (b) but with a short camera exposure to capture individual eddies. (Figure a) (Figure b) (Figure c) Intro to Turbulence: C1A Why 16 8

9 How does one study turbulence? Due to the random nature of turbulent flows, some apsect of statistical methods are usually employed in their analysis. Unfortunately, much of the information which may be relevant to understanding turbulence is lost when statistical averaging is employed. If the flows are completely random and disorganized as in the case of homogeneous or isotropic turbulence, the smearing caused by averaging is not a concern. But in most turbulent flows, there is a deterministic (e.g., periodic or coherent) component which plays the dominant role. Therefore, statistical averaging techniques are inadequate and one must turn to conditional sampling methods in an attempt to uncover the existence of repetitive flow patterns. Intro to Turbulence: C1A Why 17 How does one study turbulence? Note: Turbulence is not a feature of the fluid, but of the flow field. Recall Reynold's (Re) number is the ratio of inertia forces to viscous forces. Velocity Re Ud Length scale viscosity Therefore if the Re is large, the dynamics of the flow are not controlled by molecular processes. Since the equations of motion are non-linear, each flow state has certain unique characteristics which are associated with its initial and boundary conditions. No general solution for the Navier-Stokes (NS) equations is known, therefore, no general solution to turbulence is available. Intro to Turbulence: C1A Why 18 9

10 Fundamental Turbulent Flows Wall bounded shear layers flows, i.e., the boundary layer. Three basic turbulent free shear flows are: i) a jet entering a domain with stagnant fluid, ii) a mixing layer, and iii) the wake behind objects such as cylinders. Such flows are often used as test cases to validate the ability of CFD software to accurately predict turbulent flows. jet mixing layer wake Intro to Turbulence: C1A Why 19 Intro to Turbulence: C1A Why 20 10

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