Characteristic Length for Reynolds Number Calculation

mariyam_ali · January 13, 2025, 01:43

Hello everyone,
I hope this message finds you well. I'm currently working on the numerical simulation of fluid flow around a pair of elliptical cylinders arranged in tandem, with a gap between them, in a 2D setup. I've encountered a challenge regarding the appropriate characteristic length for calculating the Reynolds number in various configurations of the cylinders.

Here's a summary of the cases I'm analyzing:

Case 1: Both elliptical cylinders are placed vertically.
Case 2: The first cylinder is placed vertically, and the second horizontally.
Case 3: The first cylinder is placed horizontally, and the second vertically.
Case 4: Both cylinders are placed horizontally.
Given these configurations, I'm unsure about the most suitable characteristic length to use for each case in the Reynolds number calculation. Should I consider the major axis, minor axis, or some other dimension? Additionally, how should I account for the gap between the cylinders in these calculations?

I would greatly appreciate any insights or suggestions you might have to help clarify this aspect of the simulation.

Thank you for your time and assistance!

Best regards,
Mariyam Ali

Marc_462 · January 13, 2025, 03:07

The characteristic length in Reynolds number calculations is subjective. In cases involving elliptical cylinders, the appropriate choice between the major and minor axes depends on the ellipses' orientation and the dominant flow behavior.

When both cylinders are vertically or horizontally placed, using the minor axis as the characteristic length is suitable if the flow encounters the ellipses along this dimension. Conversely, when the major axis faces the flow, it becomes the preferred choice, as it represents the primary dimension resisting the flow.

For configurations where the first cylinder is vertical and the second horizontal, or vice versa, the interaction between the cylinders becomes more complex. In such cases, determining the characteristic length based on the projection of the ellipse in the flow direction may be the most appropriate approach.

This scenario is similar to airfoil simulations, where the characteristic length is typically the chord length. Even when considering two airfoils or a biplane configuration, the chord remains the relevant characteristic length, regardless of variations in the angle of attack. Similarly, for flow over an object, the characteristic length is typically defined as the height of the object facing the flow.

Regarding the gap between the cylinders, incorporating an effective length that accounts for the gap’s influence on the Reynolds number is a valid approach. In systems involving ducts or intakes, the diameter of the channel or duct becomes an essential parameter to consider.

In complex flow scenarios, particularly in turbulence, multiple characteristic lengths such as the integral scale, dissipation scale, or Taylor microscale may be employed for Reynolds number calculations. Each approach is valid, provided the chosen system is clearly defined to maintain meaningful and consistent interpretations.

I hope these insights will be valuable to your research.

Best regards,
Marc

mariyam_ali · January 13, 2025, 10:23

Thanks a lot, Marc! Your explanation is incredibly detailed and provides valuable insights into the complexities of choosing the appropriate characteristic length in Reynolds number calculations, especially for cases involving elliptical cylinders. The distinction between using the major and minor axes based on the orientation and flow direction is particularly helpful.

FMDenaro · January 13, 2025, 10:42

I would highlight that you have multiple choices for the velocity U and lenght L in the definition of the Re number, all defining a different value.
The real issue is when you work with the non dimensional form of the equations not when working with the dimensional one.
In the former case you want to use U and L that characterize the problem in such a way that you have not only non dimensional variables but normalized ones, that is they are O(1). That will help in checking the code.
If you use U and V that do not characterize your problem, the equations are still non dimensional but not normalized.

January 13, 2025, 01:43	Characteristic Length for Reynolds Number Calculation	#1
mariyam_ali New Member mariyam ali Join Date: Jan 2022 Posts: 8 Rep Power: 5	Hello everyone, I hope this message finds you well. I'm currently working on the numerical simulation of fluid flow around a pair of elliptical cylinders arranged in tandem, with a gap between them, in a 2D setup. I've encountered a challenge regarding the appropriate characteristic length for calculating the Reynolds number in various configurations of the cylinders. Here's a summary of the cases I'm analyzing: Case 1: Both elliptical cylinders are placed vertically. Case 2: The first cylinder is placed vertically, and the second horizontally. Case 3: The first cylinder is placed horizontally, and the second vertically. Case 4: Both cylinders are placed horizontally. Given these configurations, I'm unsure about the most suitable characteristic length to use for each case in the Reynolds number calculation. Should I consider the major axis, minor axis, or some other dimension? Additionally, how should I account for the gap between the cylinders in these calculations? I would greatly appreciate any insights or suggestions you might have to help clarify this aspect of the simulation. Thank you for your time and assistance! Best regards, Mariyam Ali

January 13, 2025, 03:07		#2
Marc_462 Member Marc Aragó Cebolla Join Date: Oct 2021 Location: Spain Posts: 40 Rep Power: 5	The characteristic length in Reynolds number calculations is subjective. In cases involving elliptical cylinders, the appropriate choice between the major and minor axes depends on the ellipses' orientation and the dominant flow behavior. When both cylinders are vertically or horizontally placed, using the minor axis as the characteristic length is suitable if the flow encounters the ellipses along this dimension. Conversely, when the major axis faces the flow, it becomes the preferred choice, as it represents the primary dimension resisting the flow. For configurations where the first cylinder is vertical and the second horizontal, or vice versa, the interaction between the cylinders becomes more complex. In such cases, determining the characteristic length based on the projection of the ellipse in the flow direction may be the most appropriate approach. This scenario is similar to airfoil simulations, where the characteristic length is typically the chord length. Even when considering two airfoils or a biplane configuration, the chord remains the relevant characteristic length, regardless of variations in the angle of attack. Similarly, for flow over an object, the characteristic length is typically defined as the height of the object facing the flow. Regarding the gap between the cylinders, incorporating an effective length that accounts for the gap’s influence on the Reynolds number is a valid approach. In systems involving ducts or intakes, the diameter of the channel or duct becomes an essential parameter to consider. In complex flow scenarios, particularly in turbulence, multiple characteristic lengths such as the integral scale, dissipation scale, or Taylor microscale may be employed for Reynolds number calculations. Each approach is valid, provided the chosen system is clearly defined to maintain meaningful and consistent interpretations. I hope these insights will be valuable to your research. Best regards, Marc FMDenaro likes this.

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January 13, 2025, 10:23		#3
mariyam_ali New Member mariyam ali Join Date: Jan 2022 Posts: 8 Rep Power: 5	Thanks a lot, Marc! Your explanation is incredibly detailed and provides valuable insights into the complexities of choosing the appropriate characteristic length in Reynolds number calculations, especially for cases involving elliptical cylinders. The distinction between using the major and minor axes based on the orientation and flow direction is particularly helpful.

January 13, 2025, 10:42		#4
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,961 Rep Power: 73	I would highlight that you have multiple choices for the velocity U and lenght L in the definition of the Re number, all defining a different value. The real issue is when you work with the non dimensional form of the equations not when working with the dimensional one. In the former case you want to use U and L that characterize the problem in such a way that you have not only non dimensional variables but normalized ones, that is they are O(1). That will help in checking the code. If you use U and V that do not characterize your problem, the equations are still non dimensional but not normalized.