Flows, laminar, turbulent

In the forced convection heat transfer, the heat-transfer coefficient, hy mainly depends on the fluid velocity because the contribution from natural convection is negligibly small. The dependence of the heat-transfer coefficient, hy on fluid velocity, IT, which has been observed empirically (1—3), for laminar flow inside tubes, is h V1//3 for turbulent flow inside tubes, h V3//4 and for flow outside tubes, h V2/73. Flow may be classified as laminar or turbulent. Laminar flow is generally characterized by low velocities and turbulent flow by high velocities. It is customary to use the Reynolds number, Rtf, to identify whether a flow is laminar or turbulent. 

Lim, H. K., Chan, K. W., Sisenwine, S., and Scatina, J. A. (2001). Simultaneous screen for microsomal stability and metabolite profile by direct injection turbulent-laminar flow LC-LC and automated tandem mass spectrometry. Anal. Chem. 73 2140-2146. 

FHow in a tube can be laminar or turbulent, depending on the flow conditions Ruid flow is streamlined and thus laminar at low velocities, but turns turbulent as the velocity is increased beyond a critical value. Transition from laminar lo turbulent flow does not occur suddenly rather, it occurs over some range of velocity where the flow fluctuates between laminar and turbulent flows before it becomes fully turbulent. Most pipe flows encountered in practice are turbulent. Laminar flow is encountered when highly viscous fluids such as oils flow in small diameter tubes or narrow passages. 

Lim,H.K. Chan, K.W. Sisenwine, S. Scatina, J.A. Simultaneous Screen for Microsomal Stability and Metabolite Profile by Direct Injection Turbulent-laminar Flow LC-LC and Automated Tandem Mass Spectrometry, Anal. Chem. 73(9), 2140-2146 (2001). 

Fluid flow is generally categorized into two flow regimes laminar and turbulent. Laminar flow is characterized by smooth and constant fluid motion, whereas turbulent flow is characterized by vortices and flow fluctuations. Physically, the two regimes differ in terms of the relative importance of viscous and inertial forces. The relative importance of these two types of forces for a given flow condition, or to what extent the fluid is laminar, is measured by the Reynolds number Re) ... 

Fluids move (the flow variable) due to a difference in pressure (the effort variable). The rate of flow is limited by the resistance located in the flow path. The amount of this resistance depends on whether the flow is laminar or turbulent. Laminar flow is smooth, and flow occurs in streamlines. There is little mixing between layers of fluid motion in laminar flow (Figure 2.9.1). 

It is useful to analyze some simple modes of flow in Newtonian fluids. As indicated at the start of this chapter, the analogy between Newton s Law and Hooke s Law can be used to solve some problems of viscous flow. To do this, one assumes the flow is laminar and not turbulent. Laminar flow usually occurs at small flow rates. For simplicity, it will be assumed that the liquid is incompressible and that no slip occurs at the interface between the fluid and its container. 

Steady flow in straight, rigid pipes is characterized by only one dimensionless parameter, the Reynolds number. It was shown by Osborne Reynolds that for Re < 2000, incidental disturbances in the flow field are damped out and the flow remains stable and laminar. For Re > 2000, brief bursts of fluctuations appear in the velocity separated by periods of laminar flow. As Re increases, the duration and intensity of these bursts increases until they merge together into full turbulence. Laminar flow may be achieved with Re as large as 20,000 or greater in extremely smooth pipes, but it is unstable to flow disturbances and rapidly becomes turbulent if perturbed. 

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. 

A low Reynolds number indicates laminar flow and a paraboHc velocity profile of the type shown in Figure la. In this case, the velocity of flow in the center of the conduit is much greater than that near the wall. If the operating Reynolds number is increased, a transition point is reached (somewhere over Re = 2000) where the flow becomes turbulent and the velocity profile more evenly distributed over the interior of the conduit as shown in Figure lb. This tendency to a uniform fluid velocity profile continues as the pipe Reynolds number is increased further into the turbulent region. 

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 phenomena are quite complex even for pipe flow. Efforts to predict the onset of instabiHty have been made using linear stabiHty theory. The analysis predicts that laminar flow in pipes is stable at all values of the Reynolds number. In practice, the laminar—turbulent transition is found to occur at a Reynolds number of about 2000, although by careful design of the pipe inlet it can be postponed to as high as 40,000. It appears that linear stabiHty analysis is not appHcable in this situation. 

The shear stress is hnear with radius. This result is quite general, applying to any axisymmetric fuUy developed flow, laminar or turbulent. If the relationship between the shear stress and the velocity gradient is known, equation 50 can be used to obtain the relationship between velocity and pressure drop. Thus, for laminar flow of a Newtonian fluid, one obtains ... 

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 ... 

For laminar flow a = 0.5. For fully developed turbulent flowO.88 < a < 0.98, but can be taken to be unity with Httle error. 

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.

For laminar flow (Re < 2000), generally found only in circuits handling heavy oils or other viscous fluids, / = 16/Re. For turbulent flow, the friction factor is dependent on the relative roughness of the pipe and on the Reynolds number. An approximation of the Fanning friction factor for turbulent flow in smooth pipes, reasonably good up to Re = 150,000, is given by / = (0.079)/(4i e ). 

Flow in tubular reactors can be laminar, as with viscous fluids in small-diameter tubes, and greatly deviate from ideal plug-flow behavior, or turbulent, as with gases, and consequently closer to the ideal (Fig. 2). Turbulent flow generally is preferred to laminar flow, because mixing and heat transfer... 

Eddy diffusion as a transport mechanism dominates turbulent flow at a planar electrode ia a duct. Close to the electrode, however, transport is by diffusion across a laminar sublayer. Because this sublayer is much thinner than the layer under laminar flow, higher mass-transfer rates under turbulent conditions result. Assuming an essentially constant reactant concentration, the limiting current under turbulent flow is expected to be iadependent of distance ia the direction of electrolyte flow. 

M ass Transfer. Exhaust gas catalytic treatment depends on the efficient contact of the exhaust gas and the catalyst. During the initial seconds after start of the engine, hot gases from the exhaust valve of the engine pass through the exhaust manifold and encounter the catalytic converter. Turbulent flow conditions (Reynolds numbers above 2000) exist in response to the exhaust stroke of each cylinder (about 6 to 25 times per second) times the number of cylinders. However, laminar flow conditions are reached a short (- 0.6 cm) distance after entering the cell passages of the honeycomb (5,49—52). 

For turbulent flow of a fluid past a solid, it has long been known that, in the immediate neighborhood of the surface, there exists a relatively quiet zone of fluid, commonly called the Him. As one approaches the wall from the body of the flowing fluid, the flow tends to become less turbulent and develops into laminar flow immediately adjacent to the wall. The film consists of that portion of the flow which is essentially in laminar motion (the laminar sublayer) and through which heat is transferred by molecular conduction. The resistance of the laminar layer to heat flow will vaiy according to its thickness and can range from 95 percent of the total resistance for some fluids to about I percent for other fluids (liquid metals). The turbulent core and the buffer layer between the laminar sublayer and turbulent core each offer a resistance to beat transfer which is a function of the turbulence and the thermal properties of the flowing fluid. The relative temperature difference across each of the layers is dependent upon their resistance to heat flow. 

Limiting Nusselt numbers for laminar flow in annuli have been calculated by Dwyer [Nucl. Set. Eng., 17, 336 (1963)]. In addition, theoretical analyses of laminar-flow heat transfer in concentric and eccentric annuh have been published by Reynolds, Lundberg, and McCuen [Jnt. J. Heat Ma.s.s Tran.sfer, 6, 483, 495 (1963)]. Lee fnt. J. Heat Ma.s.s Tran.sfer, 11,509 (1968)] presented an analysis of turbulent heat transfer in entrance regions of concentric annuh. Fully developed local Nusselt numbers were generally attained within a region of 30 equivalent diameters for 0.1 < Np < 30, lO < < 2 X 10, 1.01 <... 

Immersed Bodies When flow occurs over immersed bodies such that the boundaiy layer is completely laminar over the whole body, laminar flow is said to exist even though the flow in the mainstream is turbulent. The following reladonships are apphcable to single bodies immersed in an infinite flmd and are not valid for a.s.semhlage.s of bodies. 

No simple equation exists for accomplishing a smooth mathematical transition from laminar flow to turbulent flow. Of the relationships proposed, Hausen s equation [Z. Ver Dtsch. Ing. Beih. Veifahrenstech., No. 

Equation (5-62) predicts the point of maximiim velocity for laminar flow in annuli and is only an approximate equation for turbulent flow. Brighton and Jones [Am. Soc. Mech. Eng. Basic Eng., 86, 835 (1964)] and Macagno and McDoiigall [Am. Inst. Chem. Eng. J., 12, 437 (1966)] give more accurate equations for predicting the point of maximum velocity for turbulent flow. 

Laminar and Turbulent Flow, Reynolds Number These terms refer to two distinct types of flow. In laminar flow, there are smooth streamlines and the fuiid 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 = LU p/ I 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. 

Here, h is the enthalpy per unit mass, h = u + p/. The shaft work per unit of mass flowing through the control volume is 6W5 = W, /m. Similarly, is the heat input rate per unit of mass. The fac tor Ot is the ratio of the cross-sectional area average of the cube of the velocity to the cube of the average velocity. For a uniform velocity profile, Ot = 1. In turbulent flow, Ot is usually assumed to equal unity in turbulent pipe flow, it is typically about 1.07. For laminar flow in a circiilar pipe with a parabohc velocity profile, Ot = 2. 

Laminar and Turbulent Flow Below a critical Reynolds number of about 2,100, the flow is laminar over the range 2,100 < Re < 5,000 there is a transition to turbulent flow. For laminar flow, the Hagen-Poiseuille equation... 

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