The nature of turbulent flow

In turbulent flow there is a complex interconnected series of circulating or eddy currents in the fluid, generally increasing in scale and intensity with increase of distance from any boundary surface. If, for steady-state turbulent flow, the velocity is measured at any fixed point in the fluid, both its magnitude and direction will be found to vary in a random manner with time. This is because a random velocity component, attributable to the circulation of the fluid in the eddies, is superimposed on the steady state mean velocity. No net motion arises from the eddies and therefore their time average in any direction must be zero. The instantaneous magnitude and direction of velocity at any point is therefore the vector sum of the steady and fluctuating components. 

If the magnitude of the fluctuating velocity component is the same in each of the Three principal directions, the flow is termed isotropic. If they are different the flow is said to be anisotropic. Thus, if the root mean square values of the random velocity components 

There are two principal characteristics of turbulence. One is the scale which is a measure of the mean size of the eddies, and the other is the intensity which is a function 

The intensity of turbulence I is defined as the ratio of the mean value of the fluctuating component of velocity to the steady state velocity. For flow in the A-direction parallel to a surface this may be written as  

For isotropic turbulence, from equation 12.15, this becomes  

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The basic nature of the turbulent exchange process is not yet well enough known to allow accurate prediction of behavior without recourse to experiment. Correlation of the growing body of experimental knowledge in this field, however, offers the possibility of evaluating time-averaged point values of thermal and material transport for many conditions of industrial interest. It is the purpose of this discussion to present some of the more elementary considerations of the nature of turbulent flow with particular emphasis upon thermal and material transport. 

To understand atmospheric dispersion, therefore, it is necessary to understand the nature of turbulent flows and the structure of the atmosphere near the Earth s surface. Turbulent flows exhibit apparently random fluctuations in local velocity and pressure (Mathieu and Scott 2000). These fluctuations appear over a wide range of length and time scales. Reynolds (1895) drew an analogy between the behavior of the velocity in a turbulent flow and the velocity of the individual molecules in a gas, leading to the definition of the instantaneous velocity at a point as having a mean and a fluctuating component ... 

In turbulent flow the fluid has a chaotic pattern as shown by the Reynolds experiment. Because of the nature of turbulent flow, the velocity will actually fluctuate (see Figure 3-1). It is possible to time-smooth these fluctuations such that... 

Reynolds (Rl) suggested that the natures of turbulent momentum and thermal transport were similar. K rm n (K2) extended this analysis and defined eddy conductivity in the following way for steady, uniform, two-dimensional flow ... 

The complexities of turbulent flow are outside the province of this book. However, there are two further properties of laminar convective flow that are relevant to understanding the electrochemical situation. The first is easily understood by considering an excellent illustration of it—river flow. It is a matter of common observation that rivers (which flow convectively as a result of being pushed by gravity) move at maximum rale in the middle. At the river bank there is hardly any flow at all. This observation can be transferred to the flow of liquid through a pipe. The flow reaches a maximum velocity in the center. The liquid actually in contact with the walls of the pipe does not flow at all. The stationary layer is a few micrometers in thickness, about 1 % of the thickness of the diffusion layer set up by natural convection in an unstirred solution when an electrode reaction in steady state is occurring. 

NATURE OF TURBULENCE. Because of its importance in many branches of engineering, turbulent flow has been extensively investigated in recent years, and a large literature has accumulated on this subject. Refined methods of measurement have been used to follow in detail the actual velocity fluctuations of the eddies during turbulent flow, and the results of such measurements have shed much qualitative and quantitative light on the nature of turbulence. 

Due to chaotic nature, the turbulent flow is high dimensional in nature. Therefore, the implementation of turbulent flow control schemes for practical applications is chaUenging. However, the form and structures in a turbulent flow can be diagnosed and control of turbulent flow is realizable by suitable actuation. It is difflcult to specify the requirement of an ideal actuator for turbulent flow control. The ideal characteristics of an actuator for turbulent flow control can be described based on the following guidelines. 

I. Nature of turbulence. Since turbulent flow is important in many areas of engineering, the nature of turbulence has been extensively investigated. Measurements of the velocity fluctuations of the eddies in turbulent flow luve helped explain turbulence. 

Convection is influenced by the fluid flow adjacent to the solid surface. To appreciate the mechanics of this mode of heat transfer, the nature of the fluid flow in relation to the particular flow process must be known. Consideration of the flow structure created by the passage of a turbulent fluid over a smooth solid surface shows (see Fig. 4.24)... 

The probability density function of u is shown for four points in Fig. 11.16, two points in the wall jet and two points in the boundary layer close to the floor. For the points in the wall jet (Fig. 11.16<2) the probability (unction shows a preferred value of u showing that the flow has a well-defined mean velocity and that the velocity is fluctuating around this mean value. Close to the floor near the separation at x/H = I (Fig. 11.16f ) it is hard to find any preferred value of u, which shows that the flow is irregular and unstable with no well-defined mean velocity and large turbulent intensity. From Figs. 11.15 and 11.16 we can see that LES gives us information about the nature of the turbulent fluctuations that can be important for thermal comfort. This type of information is not available from traditional CFD using models. 

In industrial ventilation the majority of air velocity measurements are related to different means of controlling indoor conditions, like prediction of thermal comfort contaminant dispersion analysis adjustment of supply airflow patterns, and testing of local exhausts, air curtains, and other devices. In all these applications the nature of the flow is highly turbulent and the velocity has a wide range, from O.l m in the occupied zone to 5-15 m s" in supply jets and up to 30-40 m s in air curtain devices. Furthermore, the flow velocity and direction as well as air temperature often have significant variations in time, which make measurement difficult. 

Transitional flow The nature of flow in the zone between laminar and turbulent flow. 

In forced convection, circulating currents are produced by an external agency such as an agitator in a reaction vessel or as a result of turbulent flow in a pipe. In general, the magnitude of the circulation in forced convection is greater, and higher rates of heat transfer are obtained than in natural convection. 

It may be noted that no assumptions have been made concerning the nature of the flow within the boundary layer and therefore this relation is applicable to both the streamline and the turbulent regions. The relation between ux and y is derived for streamline and turbulent flow over a plane surface and the integral in equation 11.9 is evaluated. 

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