Flow turbulent

Turbulent flow describes the situation in which fluid flows unpredictably with multiple eddy currents and is not parallel to the sides of the tube through which it is flowing. 

As flow is, by definition, unpredictable, there is no single equation that defines the rate of turbulent flow as there is with laminar flow. However, there is a number that can be calculated in order to identify whether fluid flow is likely to be laminar or turbulent and this is called Reynold s number (Re). 

If one were to calculate the units of all the variables in this equation, you would find that they all cancel each other out. As such, Reynold s number is dimensionless (it has no units) and it is simply taken that 

Given what we now know about laminar and turbulent flow, the main points to remember are that 

Turbulent Flow. Perhaps the best known heat-transfer correlation for fully developed turbulent flow is that owing to Dittus and Boelter.27 The mass transfer analogy based on the Dittus-Boelter correlation is  

It can be argued that any turbulent flow correlation should not be applied for Re 10,000. However, in current thin-channel ultrafiltration devices, the entrance geometry is such that fully developed turbulent flow occurs at much lower Reynold s numbers. Measurements of fluid velocity versus pressure drop show a definite transition from laminar to fully developed turbulent flow at Re = 2000. 

For flat rectangular channels where dh = 2b, Equation 20 becomes  

At small curvatures, the Dean number (De) governs the transport processes in coiled tubes and channels  

Turbulent flow is characterized by the presence of eddies, which means that the local flow velocity u generally differs from the time-average value u. The velocity fluctuates in a chaotic way and the average difference between u and equals zero. However, the root-mean-square average 

Local flow velocities depend on the distance scale x considered and, for a scale comparable to the size of an energy-bearing eddy, the velocity near that eddy is 

The velocity gradient in an eddy is given by u x)/(x) and it is seen to increase strongly with decreasing size. The eddies have a rather short lifetime, given by 

Kolmogorov considered droplet break-up in turbulent flow due to inertial forces see e.g. refs. 2, 19, 20. By combining eqn. (2.12) with the Bernoulli relation p H- = constant), local pressure fluctuations near energy-bearing eddies are given by 

In turbulent flow, the boundary conditions constant wall temperature and constant heat flux lead to approximately the same mean Nusselt numbers. Correlations in the far turbulent regime (Re 10 ) are noted here. The hydrodynamic entry length is approximately independent of Re, so that an approximation for fully turbulent flow after length x can be made for 

This expression can also be used for the thermal entrance region 40j. 

A widely used correlation in turbulent regime is the Dittus- Boelter correlation 115]  

A more complex but also more accurate correlation for the convective heat transfer in the transition regime is the Gnielinski correlation [14]  

The use of turbulent Nu correlations in the transition regime from laminar to turbulent flow must to be treated with caution. Heat transfer coefficient values will be overpredicted. An equation to calculate heat transfer rates in the transition region was proposed by Gnielinski [65]  

For turbulent flow through a randomly packed bed of monosized spheres of diameter x the equivalent equation is  

Based on extensive experimental data covering a wide range of size and shape of particles, Ergun (1952) suggested the following general equation for any flow 

In practice, the Ergun equation is often used to predict packed bed pressure gradient over the entire range of flow conditions. For simplicity, this practice is followed in the Worked Examples and Exercises in this chapter. 

Ergun also expressed flow through a packed bed in terms of a friction factor defined in Equation (6.13)  

Laminar and Turbulent Flow, Reynolds Number These terms refer to two distinct types of flow. In laminar flow, there are smooth streamlines and the fluid velocity components vary smoothly with position, and with time if the flow is unsteady. The flow described in reference to Fig. 6-1 is laminar. In turbulent flow, there are no smooth streamlines, and the velocity shows chaotic fluctuations in time and space. Velocities in turbulent flow may be reported as the sum of a time-averaged velocity and a velocity fluctuation from the average. For any given flow geometry, a dimensionless Reynolds number may be defined for a Newtonian fluid as Re = LV p/p where L is a characteristic length. Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow occurs. The geometry-dependent critical Reynolds number is determined experimentally. 

Macroscopic and Microscopic Balances Three postulates, regarded as laws of physics, are fundamental in fluid mechanics. These are conservation of mass, conservation of momentum, and conservation of energy. In addition, two other postulates, conservation of moment of momentum (angular momentum) and the entropy inequality (second law of thermodynamics) have occasional use. The conservation principles may be applied either to material systems or to control volumes in space. Most often, control volumes are used. The control volumes may be either of finite or differential size, resulting in either algebraic or differential conservation equations, respectively. These are often called macroscopic and microscopic balance equations. 

Mass Balance Applied to the control volume, the principle of conservation of mass may be written as (Whitaker, Introduction to Fluid Mechanics, Prentice-Hall, Englewood Cliffs, N.J., 1968, Krieger, Huntington, N.Y., 1981) 

This equation is also known as the continuity equation. 

6-4 Fixed control volume with one inlet and one outlet. 

On occasion, turbulent flow is encountered with dilute polymer solutions. As with the turbulent flow of Newtonian fluids, pressure drops are conveniently handled in terms of the Fanning friction factor 

Equations 16.36 and 16.37 apply to all fluids in both laminar and turbulent flow. 

The next question is. How do you define a Reynolds nmnber for a fluid that has a variable viscosity Metmer and Reed ° proposed that the known relation between friction factor and Reynolds number for the laminar flow of Newtonian fluids be applied to the laminar flow of non-Newtonians as well  

Since (16.38) has been defined to apply to all fluids in laminar flow, it may now be used to obtain a generalized Reynolds number— applicable to all fluids in both laminar and turbulent flow— by combining it with (16.37)  

Actually, Metzner and Reed used an alternative formulation. Since the shear stress at the tube wall is a unique function of the apparent shear rate for laminar flow in cylindrical tubes, the power law may be written at the tube wall with the aid of (16.24) as 

As previously noted, if the Reynolds number in the tube is larger than about 2000, the flow will no longer be laminar. Because fluid elements in contact with a stationary solid boundary are also stationary (i.e., the fluid sticks to the wall), the velocity increases from zero at the boundary to a maximum value at some distance from the boundary. For uniform flow in a symmetrical duct, the maximum velocity occurs at the centerline of the duct. The region of flow over which the velocity varies with the distance from the boundary is called the boundary layer and is illustrated in Fig. 6-3. 

Because the fluid velocity at the boundary is zero, there will always be a region adjacent to the wall that is laminar. This is called the laminar sub- 

The velocity field in turbulent flow can be described by a local mean (or time-average) velocity, upon which is superimposed a time-dependent fluctuating component or eddy. Even in one-dimensional flow, in which the overall average velocity has only one directional component (as illustrated in Fig. 6-3), the turbulent eddies have a three-dimensional structure. Thus, for the flow illustrated in Fig. 6-3, the local velocity components are 

The time-average velocity (u) obviously has zero components in the y and z directions, but the eddy velocity components are nonzero in all three directions. The time-average velocity is defined as 

The average in Eq. (6-16a) is taken over a time T that is long compared to the period of the eddy fluctuation. 

Laminar Flow Reynolds numbers less than 2,100 Transition Flow Reynolds numbers between 2,100 and 10,000 Turbulent Flow Reynolds numbers greater than 10,000 

Turbulent Flow For engineering purposes, semi-empirical equations are generally used to describe heat transfer in turbulent flow. These correlations adequately predict heat transfer in this region. (Nomenclature is presented in Chapter 44.) 

For short tube lengths, the equation above should be corrected to reflect entrance effects as given below  

Due to the viscosity of polymer melts (and most solutions), laminar flow is all that you would expect to see (recall that viscosity is in the denominator of the Reynolds number (Re) and that large Re is required for turbulent flow). However, turbulent flow can be encountered in dilute polymer solutions. As with the turbulent flow of Newtonian fluids, pressure drops are conveniently handled in terms of the Fanning friction factor  

The Reynolds analogy, which links the heat and mass transfer coefficients to the friction factor, according to 

According to Chilton and Colburn [3.10], [3.11] the effect of the Prandtl number on the heat transfer can be described by the empirical statement 

3 Convective heat and mass transfer. Single phase flow 

A better analytically based equation which is valid over a wide range of Prandtl or Schmidt numbers is obtained if we presume a turbulent parallel flow, i.e. a steady-state turbulent flow with vanishing pressure gradient, and velocity, temperature and concentration profiles which are only dependent on the coordinate y normal to the wall. Then, as follows from (3.134) to (3.139), 

The total values for the shear stress, heat and diffusional fluxes are independent of the coordinate normal to the wall and therefore equal to the values at the wall. In the laminar sublayer we have 

Alternatively, the explicit equation for the friction factor derived by Swamee and Jain (Equation 2.13) can be solved for the absolute roughness. 

Water is flowing in a 10-m horizontal smooth pipe at 4 m/s and 25°C. The density of water is 1000 kg/m and the viscosity of water is 0.001 kg/m s. The pipe is Schedule 40, 1 in. nominal diameter (2.66 cm ID). Water inlet pressure is 2 atm. Calculate pressure drop in the pipe using hand calculations and compare the results with those obtained using Hysys, PRO/ii, and Aspen software. 

Reynolds number is calculated to determine the flow regime  

Since Reynolds number is greater than 4000, the flow is turbulent. The relative roughness of the smooth pipe is 

The calculated friction factor f= 0.0176. Then the pressure drop 

---

In situations where a low concentration of suspended solids needs to be separated from a liquid, then cross-flow filtration can be used. The most common design uses a porous tube. The suspension is passed through the tube at high velocity and is concentrated as the liquid flows through the porous medium. The turbulent flow prevents the formation of a filter cake, and the solids are removed as a more concentrated slurry. 

CO2 corrosion often occurs at points where there is turbulent flow, such as In production tubing, piping and separators. The problem can be reduced it there is little or no water present. The initial rates of corrosion are generally independent of the type of carbon steel, and chrome alloy steels or duplex stainless steels (chrome and nickel alloy) are required to reduce the rate of corrosion. 

The first term (AQ) is the pressure drop due to laminar flow, and the FQ term is the pressure drop due to turbulent flow. The A and F factors can be determined by well testing, or from the fluid and reservoir properties, if known. 

If these assumptions are satisfied then the ideas developed earlier about the mean free path can be used to provide qualitative but useful estimates of the transport properties of a dilute gas. While many varied and complicated processes can take place in fluid systems, such as turbulent flow, pattern fonnation, and so on, the principles on which these flows are analysed are remarkably simple. The description of both simple and complicated flows m fluids is based on five hydrodynamic equations, die Navier-Stokes equations. These equations, in trim, are based upon the mechanical laws of conservation of particles, momentum and energy in a fluid, together with a set of phenomenological equations, such as Fourier s law of themial conduction and Newton s law of fluid friction. When these phenomenological laws are used in combination with the conservation equations, one obtains the Navier-Stokes equations. Our goal here is to derive the phenomenological laws from elementary mean free path considerations, and to obtain estimates of the associated transport coefficients. Flere we will consider themial conduction and viscous flow as examples. 

Most ion-molecule techniques study reactivity at pressures below 1000 Pa however, several techniques now exist for studying reactions above this pressure range. These include time-resolved, atmospheric-pressure, mass spectrometry optical spectroscopy in a pulsed discharge ion-mobility spectrometry [108] and the turbulent flow reactor [109]. 

The time-to-distance transfonnation requires fast mixing and a known flow profile, ideally a turbulent flow with a well-defined homogeneous composition perpendicular to the direction of flow ( plug-flow ), as indicated by tire shaded area in figure B2.5.1. More complicated profiles may require numerical transfomiations. 

To avoid imposition of unrealistic exit boundary conditions in flow models Taylor et al. (1985) developed a method called traction boundary conditions . In this method starting from an initial guess, outflow condition is updated in an iterative procedure which ensures its consistency with the flow regime immediately upstream. This method is successfully applied to solve a number of turbulent flow problems. 

Petera,. 1. and Nassehi, V., 1993. Flow modelling using isoparametric Hermite elements. In Taylor C. (ed.), Numerical Methods in Laminar and Turbulent Flow, Vol. VIII, Part 2, Pineridge Press, Swansea. 

The first form of aerosol modifier is a spray chamber. It is designed to produce turbulent flow in the argon carrier gas and to give time for the larger droplets to coalesce by collision. The result of coalescence, gravity, and turbulence is to deposit the larger droplets onto the walls of the spray chamber, from where the deposited liquid drains away. Since this liquid is all analyte solution, clearly some sample is wasted. Thus when sensitivity of analysis is an issue, it may be necessary to recycle this drained-off liquid back through the nebulizer. 

Depending on the type of nebulizer used and its efficiency, there may be initially a significant proportion of large droplets in the aerosol. Heavier than the very fine droplets, the larger droplets are affected by gravity and by turbulent flow in the argon sweep gas, which cause them to deposit onto the walls of the transfer tube. 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

Deutsch-Anderson equation assumes no reentrainment from collector well mixed turbulent flow, turbulent eddies small compared to precipitator dimensions... 

Most flow meters are designed and caHbrated for use on turbulent flow, by far the more common fluid condition. Measurements of laminar flow rates may be seriously in error unless the meter selected is insensitive to velocity profile or is specifically caHbrated for the condition of use. 

The transition from laminar to turbulent flow occurs at Reynolds numbers varying from ca 2000 for n > 1 to ca 5000 for n = 0.2. In the laminar region the Fanning friction factor (Fig. 2) is identical to that for Newtonian fluids. In the turbulent region the friction factor drops significantly with decreasing values of producing a family of curves. 

As of this writing, the only practical approach to solving turbulent flow problems is to use statistically averaged equations governing mean flow quantities. These equations, which are usually referred to as the Reynolds equations of motion, are derived by Reynold s decomposition of the Navier-Stokes equations (18). The randomly changing variables are represented by a time mean and a fluctuating part ... 

In general, V For laminar Newtonian flow the radial velocity profile is paraboHc and /5 = 3/4. For fully developed turbulent flow the radial... 

Averaging the velocity using equation 50 yields the weU-known Hagen-Poiseuille equation (see eq. 32) for laminar flow of Newtonian fluids in tubes. The momentum balance can also be used to describe the pressure changes at a sudden expansion in turbulent flow (Fig. 21b). The control surface 2 is taken to be sufficiently far downstream that the flow is uniform but sufficiently close to surface 3 that wall shear is negligible. The additional important assumption is made that the pressure is uniform on surface 3. The conservation equations are then applied as follows ... 

In the forced convection heat transfer, the heat-transfer coefficient, mainly depends on the fluid velocity because the contribution from natural convection is negligibly small. The dependence of the heat-transfer coefficient, on fluid velocity, which has been observed empirically (1—3), for laminar flow inside tubes, is h for turbulent flow inside tubes, h and for flow outside tubes, h. Flow may be classified as laminar or... 

Reynolds Number. The Reynolds number, Ke, is named after Osborne Reynolds, who studied the flow of fluids, and in particular the transition from laminar to turbulent flow conditions. This transition was found to depend on flow velocity, viscosity, density, tube diameter, and tube length. Using a nondimensional group, defined as p NDJp, the transition from laminar to turbulent flow for any internal flow takes place at a value of approximately 2100. Hence, the dimensionless Reynolds number is commonly used to describe whether a flow is laminar or turbulent. Thus... 

Friction Coefficient. In the design of a heat exchanger, the pumping requirement is an important consideration. For a fully developed laminar flow, the pressure drop inside a tube is inversely proportional to the fourth power of the inside tube diameter. For a turbulent flow, the pressure drop is inversely proportional to D where n Hes between 4.8 and 5. In general, the internal tube diameter, plays the most important role in the deterrnination of the pumping requirement. It can be calculated using the Darcy friction coefficient,, defined as... 

The convective heat-transfer coefficient and friction factor for laminar flow in noncircular ducts can be calculated from empirically or analytically determined Nusselt numbers, as given in Table 5. For turbulent flow, the circular duct data with the use of the hydrauhc diameter, defined in equation 10, may be used. 

Fig. 5. Moody diagram for Darcy friction factor (13) (-----), smooth flow (----), whoUy turbulent flow ( ), laminar flow.

The minimum velocity requited to maintain fully developed turbulent flow, assumed to occur at Reynolds number (R ) of 8000, is inside a 16-mm inner diameter tube. The physical property contribution to the heat-transfer coefficient inside and outside the tubes are based on the following correlations (39) ... 

The predetonation distance (the distance the decomposition flame travels before it becomes a detonation) depends primarily on the pressure and pipe diameter when acetylene in a long pipe is ignited by a thermal, nonshock source. Figure 2 shows reported experimental data for quiescent, room temperature acetylene in closed, horizontal pipes substantially longer than the predetonation distance (44,46,52,56,58,64,66,67). The predetonation distance may be much less if the gas is in turbulent flow or if the ignition source is a high explosive charge. 

---