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CHAPTER 2 Non-pulsatile and pulsatile internal flow The purpose of this chapter is to give a brief overview of the pulsatile internal flow in pipes since the flow in an exhaust system on an IC engine is highly pulsatile. The exhaust manifold, situated between the engine and the turbine, can be viewed as being made of straight and curved pipe sections. Therefore, the flow in bent pipe has also been considered. The frequency and the am- plitude of the pulsatile flow in the exhaust system will be determined by the numbers of cylinders of the engine and at which operation point the engine is working, i.e. the engine rotational speed and the throttle position. The ge- ometry of the exhaust manifold will also affect the flow into the turbine, since single and double bends will introduce secondary flow, junctions will disturb the flow and there are also pressure waves that will be reflected in the manifold. Therefore, a literature survey on the steady and unsteady flow in different pipe configurations has been conducted. 2.1. Flow in curved pipes There are many applications where flow in bent pipes can be found, for example pipe-lines, exhaust systems and the blood flow in arteries. One typical feature of the flow in bent pipes is the so called Dean vortices, which are a pair of counter- rotating vortices. When the flow enters the bend, the fluid is accelerated near the inner wall. Simultaneously, the fluid near the outer wall is decelerated due to the adverse pressure gradient. This induces a secondary flow in the transverse plane of the pipe. Further downstream, the centrifugal force induces a second flow in the central part of the cross section from the inner wall to the outer wall and forms the two counter-rotating vortices, see Figure 2.1. Sudo et al. (1998) investigated the steady turbulent flow in a circular- sectioned 90◦ bend. The curvature radius ratio, defined as the ratio between the radius of the bend and the pipe radius, was four and the flow was assumed to be turbulent. At the inlet to the bend, φ=0◦, the primary flow accelerates near the inner wall. At φ=30◦ the secondary flow starts to develops into a counter rotating pair of vortices. Between φ=75◦ and 90◦ the primary flow is greatly distorted and the turbulence intensity and Reynolds stresses increases. Downstream of the bend, the distribution of primary flow velocity gradually 3PDF Image | Numerical computations of the unsteady flow in a radial turbine
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