Exploring Laminar-to-Turbulent Transition
Josh Allen
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08/03/2020
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UCARE research presentation in the subject of Fluid Dynamics
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- [00:00:00.217]Hello, my name is Josh Allen and I am an undergraduate student in Mechanical
- [00:00:04.911]Engineering. Today I will be exploring laminar-to-turbulent transition for fluid flow in a channel.
- [00:00:11.918]The transition from laminar flow to turbulent flow has been studied for over 130 years
- [00:00:17.050]but a concrete process to predict it has not been found. The potential impact of flow control for
- [00:00:23.478]laminar to turbulent transition in engineering applications is very great. Recent studies show
- [00:00:28.750]that friction loss in a pipeline can be reduced by as much as 95% when turbulent flow returns to
- [00:00:34.679]laminar flow. This is the ultimate goal of the research, push flow that has become turbulent
- [00:00:39.581]back to laminar. Flow control technologies that reduce friction loss by 1% could save up to 2
- [00:00:45.929]billion dollars annually. Since much of the world’s energy comes from liquid or gas sources
- [00:00:51.731]there is a great need of research in the field of transportation of fluids.
- [00:00:57.765]My research focuses on examining the effects of a fluid transitioning from laminar to
- [00:01:02.668]turbulent flow in a channel. The axes for channel are aligned so that x is in the streamwise
- [00:01:07.817]direction, y is the wall normal, and z is in the spanwise direction. The navier-stokes equation is a
- [00:01:13.810]partial differential equation that describes the flow of an incompressible fluid. The solution of
- [00:01:19.391]the navier-stokes equation is the velocity of the fluid in channel flow. In order to solve the
- [00:01:24.844]navier-stokes equation direct numerical simulation or DNS is used. Disturbances in channel flow
- [00:01:31.005]can cause the flow to transition from laminar to turbulent flow. These disturbances in the fluid
- [00:01:36.220]can be reduced by increasing the Reynolds number. Reynolds number can be characterized by
- [00:01:40.672]four parameters: density, speed of the fluid flow, length, and dynamic viscosity of the fluid. The
- [00:01:47.242]results obtained from simulations using DNS will provide the best parameters for fluid flow through a channel.
- [00:01:55.014]Simulations using DNS were run though the Holland Computing Center. The data
- [00:01:59.764]acquired after the simulations were finished was used to analyze the flow through a channel for
- [00:02:04.862]certain parameters. In order to better organize and understand the data Matlab was used to
- [00:02:09.612]sort and create different visuals such as the figure 1. Each simulation was run for 20000 time
- [00:02:15.012]steps at an interval of 1 and with specific conditions and parameters. A total of 10 different
- [00:02:20.289]initial conditions were used and the simulations were run at an interval of 5000 Reynolds
- [00:02:25.482]number from 5000 to 50000 Reynolds number for each initial condition. Figure 1 depicts the
- [00:02:31.830]wall shear stress vs time for the first initial condition. Initially all flow is laminar for all Reynolds
- [00:02:38.662]numbers of all the initial conditions, however, the laminar flow for each is not the same value.
- [00:02:44.462]All values of shear stress are around 2 but they fluctuate by plus or minus .1. Then as the time
- [00:02:52.474]increases a spike in shear stress forms for certain Reynolds numbers. The spike is a large change
- [00:02:58.820]in shear stress and indicates the transition from laminar to turbulent flow.
- [00:03:05.304]The transition from laminar to turbulent flow cannot be predicted using regular
- [00:03:09.154]mathematic means. Figure 2 shows the time when flow transitioned from laminar flow to
- [00:03:14.353]turbulent flow for each initial condition and at each Reynolds number. Also, the average
- [00:03:19.662]transition time is shown on the figure. At a Reynolds number of 5000 none of the initial
- [00:03:24.441]conditions transitioned from laminar to turbulence in the 20000 time steps. However, as
- [00:03:30.089]Reynolds number increases some initial conditions begin to transition but others do not.
- [00:03:37.482]Figure 8 shows the values of wall shear stress for the seventh initial condition. For the
- [00:03:42.138]seventh initial condition the flow transitioned for all Reynolds numbers except 5000, whereas
- [00:03:47.392]the flow only transitioned for 4 Reynolds numbers for the first initial condition. Shear stress is
- [00:03:52.722]also known as skin friction. When the flow is laminar there is no skin friction from the fluid flow,
- [00:03:58.228]but when there is a transition to turbulence there is a large spike in skin friction. As the
- [00:04:02.826]Reynolds number increases the fluid speed increases which increases the skin friction.
- [00:04:10.592]Figure 12 is a plot of the difference among the average value of shear stress of laminar
- [00:04:15.152]flow and the spike value of flow as it transitioned. The graph shows an upward trend as the
- [00:04:20.829]Reynolds number increases and the difference between the spike and average laminar value increases.
- [00:04:27.677]Figure 13 shows the difference in shear stress of the average turbulent value and the
- [00:04:32.507]spike value. This graph does not have any solid trends because turbulence is a chaotic and random process.
- [00:04:40.559]Another indicator of transition from laminar to turbulent flow is energy, just as shear
- [00:04:46.096]stress was. The flow begins laminar at a value of 1 and then as the time step increases the flow
- [00:04:52.857]transitions from laminar to turbulent.
- [00:04:58.927]Figure 15 depicts the difference in energy for all 10 initial conditions between the
- [00:05:03.974]average laminar value and the spike in energy. As Reynolds number begins to increase the
- [00:05:09.185]energy of the fluid flow is also increasing.
- [00:05:14.740]Figure 21 shows the energy vs time for the seventh initial condition. This plot has 9
- [00:05:20.384]Reynolds numbers that reach turbulence, only 5000 does not.
- [00:05:27.103]Figure 25 shows the energy difference from the spike value and the average value of
- [00:05:31.748]turbulence. Since turbulence is chaotic process there are many different values of energy at the
- [00:05:38.135]same Reynolds number, however, there seems to be a slight trend; as Reynolds number
- [00:05:43.551]increases the difference in energy decreases.
- [00:05:48.830]Thank you for watching my presentation, funding for this research was provided by
- [00:05:52.840]UCARE and simulations for the research were done with Holland Computing Center.
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