Little Little Fluid Dynamics
Here is another tutorial homework of mine from last semester that might be useful for beginners like me. I used ANSYS software for these elementary level designs.
Which design is better in terms of controlling the fluid dynamics, sharper one or smoother one?
Pipe 1
Pipe 2
Results:
Since the inlet and outlet diameters of both pipes are same and the path the fluid needs to travel same, it is expected that the pipe having a design that the flow rate does not change too much or having smoother change to have better conservation of energy, so lesser energy loss. Therefore, it is expected to be that the second pipe design is a better match with the theory and expectations.
As Bernoulli’s Equation states (in the case of inviscid flow, incompressible, steady flow along the same streamline), the energy is conserved and the total energy equals to kinetic, potential and pressure energy combined. If the flow does not change its potential energy (assumed to be no height change), the energy is transferred between kinetic and pressure energy (due to mass conservation, areas changing so the kinetic energy, meaning that the materials in equals to material out). That’s why the pressure in the same streamline of smaller diameter pipe is smaller, darker blue, (but the velocity is faster, more reddish), and its opposite in the pipe having bigger diameter (greater static pressure but smaller velocity).
The energy loss in the expansion area of the first pipe as shown in Figure 1b is bigger compared to the second pipe design as shown in the Figure 2b. Although, the velocity in the first design is higher compared to the second design after the expansion area (Figure 1c vs. Figure 2c), the pressure is more controlled and uniformly distributed (no turbulence like movements close to expansion area) in the second design after the expansion area (First design like flows might be life threatening in the real-life human applications). Energy is lost due to “recirculating zones”(flow is blocked in such areas) appears around sharp corners in the first design (red box) as shown in Figure 1b. Such energy loss is called minor energy loss, and in this case it is Borda-Carnot head loss, also known as expansion loss. In those areas, the particles collide and lose energy and the particles having higher energy lose more energy. So, to decrease energy loss, it is important to connect two pipes causing less recirculation areas by rounding off the sharper corners as in the case of design 2.
In these flows above, it is known that the flow is in the same streamline. It is also known that the diameters of the pipes are changing. Since the mass will be conserved, the velocity will change so the kinetic energy. When the kinetic energy changes, also known as dynamic pressure, and the potential energy is assumed to be constant, the static pressure energy will also change. When the area increases the static pressure increases (velocity decreases), when the area that fluid flows decreases the static pressure decreases (velocity increases so some part of it converted to kinetic energy). However, in the viscous flow (= in the reality), the pressure is continually lost across the tube/s (due to friction, resistance of the flow and so on). Whenever the velocity/diameter changes the energy loss occurs. The energy loss can be controlled over controlling the parameters like smoother pipe diameter change in the flow instead of sudden change in the diameter of the flows. If the velocity/diameter change happens suddenly (as in the case of the first pipe), (pressure so) energy could be lost due to additional shear interaction between the particles of the fluid or separation of the flow and mixing of the fluid (even if they are same fluid and along the same streamline, the pressure, kinetic and static, characteristics were not same). It is also possible to lose some energy due to unwanted turbulence in the flow (due to additional resistance in the flow). To prevent such energy loss, guide vanes (in turning points) or smoother transition of the fluid from different pipe diameters (along the same streamline) are used (as in the case of second design).
References:
· Chapter 4 — Minor Losses : https://web.engr.uky.edu/~acfd/me330-lctrs.pdf
· Chapter 3 Fluid Mechanics — Losses of energy in real fluids: https://doi.org/10.1016/B978-075065213-1/50003-9
· Chapter 5 Conservation of Momentum — Loss in a suddenly expanding pipe: https://vscht.cz/uchi/ped/hydroteplo/materialy/introduction.fluid.mech.pdf
