- #1
Talal
- 7
- 4
Hello,
For a project I am working on, I am trying to design a 2D with parallel sinusoidal patterns. Imagine a 2D section of a pipe (two parallel surfaces with distance in between). Each surface is basically a sine function. Peak points meet with each other, as well as troughs. Liquid is intended to flow through the topography. The 2D section is solid. Using Sine function phase shift I can establish different amplitudes and wave lengths. My question is, given that I decided on a certain corrugation geometry, how can I measure the roughness of the pipe ? This 2D pattern (consisting of two parallel sine functions), will be 3D printed onto glass. I understand that I can modify and transform the sine wave and establish different amplitude lengths and heights. However, I couldn't figure how to measure the roughness between these plates. I have looked at Relative roughness and other definitions. However, I am not sure I want to apply these simple formulas to my case. I want to account for the entirety of the topography (top and bottom sine waves) and take inconsideration the whole shape and it's effect on roughness. The other formulas give averages.
Will your flow be laminar or turbulent? If turbulent, does the roughness fit on a Moody chart? What is the ratio of channel width in the "roughness direction" vs the perpendicular direction (which is presumably smoother?).
It is good that you recognize that relative roughness may not meet your needs, but you should compare standard methods to your experimental results first. If the standard methods work, then you are done. If not, you are in R&D territory, and need to develop a method. And everything is easier if the flow is laminar.
I haven't looked into whether the flow is laminar or turbulent. The working conditions are 2900 psi and flow rate of 40ml/h (flow rate is subject to change).
)
Please find the attached picture for further explanation. My aim is to co-relate a roughness magnitude with the length, height, spacing and number of amplitudes.
A lot depends on whether the flow is laminar or turbulent. That really needs to be calculated first. Even if it's only a rough estimate.
What is the purpose of this? Are you working with a gas, a Newtonian fluid, a non-Newtonian fluid? Are you trying to calculate a pressure drop, a heat transfer coefficient, or something else? Is the dimension perpendicular to the paper larger, smaller, or comparable to Hmin? Is dimension 2a larger, smaller, or comparable to Hmin?
I will be passing a Newtonian fluid. Unfortunately I can not give the main reason behind this experiment, I need to apply different roughness values by adjusting the magnitudes of length and height of the amplitudes. 2a is comparable to Hmin. I will upload a better picture tomorrow, since all of my work is saved in my office's PC. Regardless, 2a can be adjusted to equal Hmin. The distance between plates is subject to change in order to see how will that will effect the fluid. I did fluid mechanics in my undergrad, correct me if I am wrong, but the moody diagram helps establish the friction factor. That is something I will consider later in my project. However, like I previously mentioned, I am wanted to know if there an equation, or through the use of integration, that I can quantify roughness based on the topography of the pipe. Finally, the dimension prependicular to the paper is comparable to 2a.
Much of which is meaningless if the flow is laminar.
You have two rough and two smooth surfaces. Read through HDS5 Hydraulic Design of Highway Culverts (available online for free). They discuss how to deal with a similar problem. It may give you some ideas.
Thank you for the recommendation. Tomorrow I will share some of the documents that I have been looking into.
In 1938 Dr. Abbot of Unv. Michigan developed the Profilometer. A diamond sylus lab instrument to measure many parameters of Surface Texture.
Summary, there are Flaws, Lay, Waviness and Roughness on any machined surface. Look at ASNI /ASME B46.1 Standards for in depth details on parameters, calculations etc.
I think you want to qualify numerically the best surface parameter to fit your application relative to flow. There are over 110 parameters used , to date. Each parameter is calculated to describe one unique feature of the surface. Ra or Average Roughness is most popular parameter but tells nothing of the surface other than an average number. Two surfaces can have the same average number but vastly different reflectivity, lubrication adhesion, functionality. Rp counts the number of Peaks, Rv counts number of Valleys, Rtm is average of the Peaks to Valleys, etc...you get the idea.
Peak Count per inch may be a better parameter.
Trying to qualify a squiggly line calculated from many peak to valley excursions , numerically is a very tough job. People have been doing it for 79 years now.
The Profilometer product line was sold to Precision Devices..good website and source on this.
http://www.predev.com/
Been there done that.
Thank you guys for you replies. Your recommended readings are interesting. I got my hands on a copy of ''Handbook of Surface Metrology". Looks promising. I kindly ask that the admins keep this thread live for one more week. I need to do some serious reading, after which I would like to return here and present m findings and any questions I might have. Thank you again guys for your efforts.
Hey guys. This past weekend I still have been investigating the shape factor on surface roughness. Just to clarify, this image describes what I initially aimed to achieve; a sinusoidal corrugation with varying geometrical parameters. I came across a paper titled "A generalized mechanical model for suture interfaces of arbitrary geometry". The paper provided useful information such as geometrical description of surfaces and the inclusion of shape factor, Beta, to describe surface topography. However, it focused on the effects of surface geometry on mechanical properties. Please have a read through it. The paper encompasses my goals, which is to vary a geometric parameter and measure another parameter. In the case of the paper, it did so for stiffness and toughness. I need the same for roughness.
In addition to my previous post. I do not mind going with triangular waves and quantify roughness in terms of apex angle change.
Here is the paper
If you look at a Moody chart, roughness is parameterized as epsilon / D. Your roughness can easily be parameterized the same way. Your surface can be completely characterized by sinusoidal, frequency, amplitude, perpendicular to flow. You also need to characterize the fact that two walls are smooth. Since you are defining the surface topography as sinusoidal, attempting to use statistical parameters derived for a wide range of surface topography will cause loss of information.
All of which is meaningless if the flow is laminar.
My only grudge against using relative roughness (epsilon / D) is because I tend to use triangular waves. Both waves (sinusoidal and triangular) would have the same relative roughness. In other words, I need something to consider the shape factor. I am more than willing to ignore sinusoidal waves in favour of triangular waves since at least I can manipulate the apex angle. This way, I can ignore the shape factor. Still, I need to measure roughness based on apex angle. Any idea ?
Hello guys. Thank you for all the support you guys provided me with. This is an amazing platform for knowledge seekers. I will be definitely staying. Aside from that, I would like to give an update on my situation as well as close the lid on my case.
After reviewing several sources including BS (British Standards) I came to the following conclusions. There are several ways to calculating roughness, most famous being Ra (arithmetic average), which is an amplitude function. Several roughness mathematical models consider different functions such as (spacing and slope in addition to amplitude). All these models apply both Waviness and Profile. However, the cut off length is the governing factor. Depending on the cut off length you would be looking at roughness or waviness or profile. This cut-off value is 0.8mm for British standards. Furthermore, one might consider using more than one roughness measurement since different shapes and materials can have similar theoretical roughness values. As such, the most reliable way to measure roughness is through measuring devices.
Based on what I have mentioned, can you guys answer me the following. Assuming the cut-off length of 0.8mm, does that mean any topography with dimensions below 0.8mm will be considered as roughness'? Would you recommend that I go ahead with measuring the roughness for my pattern using different mathematical models? In other words, the roughness of my pattern would be described with different mathematical models in order to further distinguish between patterns that might have similar values for set mathematical models.
the reason Doctor Abbott decided on the cut off width of 0.030" as a Roughness Sampling Length was because in 1932, the typical pocket scale ( the machinists little metal 6 inch ruler) had 1/32" divisions on it. At the time, this was the smallest practical measurement used. So everything smaller than 0.030" ( 0.8mm) was roughness, and everything longer LENGTH was waviness. This has been carried forward as an arbitrary means of dividing Roughness and Waviness.
The electrical response of the instrument is Roughness Cutoff Width (RWC).
All metrology instruments have many RCW values but the bench mark is 0.030". A minimum of 5 RWC are used to evaluate a surface. Sample length and RCW get swapped around and this does get confusing.
Hello,
hope you are keeping well during these tough and uncertain times. My project developed during this time and I need your advice with measuring the drag due to friction and due to form with the same channel geometry. Please find the attached image. The unit is in micron. I have n number of corrugations and length L. The channel width is 200 (y-axis) and the depth is 40 microns (depth going towards the page z-axis). Flow is in the x-direction. Flow is Laminar and the fluid is distilled water.
I have measured the delta P for the channel and I can measure the total Drag coefficient Cd = 2a deltaP/(roh)U^2...however, since I have corrugations on both sides of the channel the equation becomes 4a deltaP/ (roh)U^2. Assuming the equation does measure the total Cd and I don't have to multiply it by n (number of corrugations), how can I separate the drag force into drag due to form and drag due to friction with my channel design?
Talal
That is easy. buy a metrology instrument that measures form error or profile ( specifically Waviness) and measures Surface Roughness (Ra) so you can separate Waviness and Roughness. These have been on the market since 1950.
Hello Mike,
I wish to measure the drag coefficient and skin friction instead of roughness using theoretical analysis. Is stokes law the only way?
There are over 110 parameters of Roughness identified by various industrial standards organizations world wide. What you call skin friction could be identified as Surface Roughness (Ra) what you call drag could be one of the other parameters like Peak Count per inch, Rt, Rtm or some other parameter. Good luck as I am sure what you are looking for has already been measured by these parameters. These parameters were created to fix a unique surface problem in manufacturing - example - sheet metal on automobiles would rust on the show room floor in the 1970s when the " gas shortage" hit the economy. Auto makers rolled thinner and thinner car bodies to save weight. This caused increase in Peak Count per inch of sheet metal. The Peaks stuck out past the paint thickness and caused rust. Only after a parameter that measured Peaks per inch was created were the stel mills able to control the surface of the sheet metal rolled.
the parameter is there for you to find. good luck!
It sounds like you want to predict pressure loss vs flow rate through rectangular channels of varying geometry. Drag coefficient does not apply to flow through channels. A relevant parameter is hydraulic diameter (search the term). Since you have laminar flow, the pressure drop is probably mostly skin friction. I am not aware of any published method for calculating pressure drop in your situation. If I wanted to develop such a method, here is how I would do it:
Start by making a set of straight channels. One 200##\mu## wide, one 70##\mu## wide, and one at the mean channel width one of your channels. Then I would measure the pressure drop vs flow for those three channels and several actual channels. I would compare the measured pressure drops to that of the three straight channels.
I would calculate hydraulic diameter and Reynolds number for all channels three ways - at the maximum width, minimum width, and average width. Then I would use those numbers in a Moody Chart to see how well they predict actual pressure drop.
correct me please, all drag and friction analysis relies on area consideration..
as in surface
now you are into my "area" surface irregularies to micro inch
For a project I am working on, I am trying to design a 2D with parallel sinusoidal patterns. Imagine a 2D section of a pipe (two parallel surfaces with distance in between). Each surface is basically a sine function. Peak points meet with each other, as well as troughs. Liquid is intended to flow through the topography. The 2D section is solid. Using Sine function phase shift I can establish different amplitudes and wave lengths. My question is, given that I decided on a certain corrugation geometry, how can I measure the roughness of the pipe ? This 2D pattern (consisting of two parallel sine functions), will be 3D printed onto glass. I understand that I can modify and transform the sine wave and establish different amplitude lengths and heights. However, I couldn't figure how to measure the roughness between these plates. I have looked at Relative roughness and other definitions. However, I am not sure I want to apply these simple formulas to my case. I want to account for the entirety of the topography (top and bottom sine waves) and take inconsideration the whole shape and it's effect on roughness. The other formulas give averages.
Will your flow be laminar or turbulent? If turbulent, does the roughness fit on a Moody chart? What is the ratio of channel width in the "roughness direction" vs the perpendicular direction (which is presumably smoother?).
It is good that you recognize that relative roughness may not meet your needs, but you should compare standard methods to your experimental results first. If the standard methods work, then you are done. If not, you are in R&D territory, and need to develop a method. And everything is easier if the flow is laminar.
I haven't looked into whether the flow is laminar or turbulent. The working conditions are 2900 psi and flow rate of 40ml/h (flow rate is subject to change).
Please find the attached picture for further explanation. My aim is to co-relate a roughness magnitude with the length, height, spacing and number of amplitudes.
A lot depends on whether the flow is laminar or turbulent. That really needs to be calculated first. Even if it's only a rough estimate.
What is the purpose of this? Are you working with a gas, a Newtonian fluid, a non-Newtonian fluid? Are you trying to calculate a pressure drop, a heat transfer coefficient, or something else? Is the dimension perpendicular to the paper larger, smaller, or comparable to Hmin? Is dimension 2a larger, smaller, or comparable to Hmin?
I will be passing a Newtonian fluid. Unfortunately I can not give the main reason behind this experiment, I need to apply different roughness values by adjusting the magnitudes of length and height of the amplitudes. 2a is comparable to Hmin. I will upload a better picture tomorrow, since all of my work is saved in my office's PC. Regardless, 2a can be adjusted to equal Hmin. The distance between plates is subject to change in order to see how will that will effect the fluid. I did fluid mechanics in my undergrad, correct me if I am wrong, but the moody diagram helps establish the friction factor. That is something I will consider later in my project. However, like I previously mentioned, I am wanted to know if there an equation, or through the use of integration, that I can quantify roughness based on the topography of the pipe. Finally, the dimension prependicular to the paper is comparable to 2a.
Much of which is meaningless if the flow is laminar.
You have two rough and two smooth surfaces. Read through HDS5 Hydraulic Design of Highway Culverts (available online for free). They discuss how to deal with a similar problem. It may give you some ideas.
Thank you for the recommendation. Tomorrow I will share some of the documents that I have been looking into.
In 1938 Dr. Abbot of Unv. Michigan developed the Profilometer. A diamond sylus lab instrument to measure many parameters of Surface Texture.
Summary, there are Flaws, Lay, Waviness and Roughness on any machined surface. Look at ASNI /ASME B46.1 Standards for in depth details on parameters, calculations etc.
I think you want to qualify numerically the best surface parameter to fit your application relative to flow. There are over 110 parameters used , to date. Each parameter is calculated to describe one unique feature of the surface. Ra or Average Roughness is most popular parameter but tells nothing of the surface other than an average number. Two surfaces can have the same average number but vastly different reflectivity, lubrication adhesion, functionality. Rp counts the number of Peaks, Rv counts number of Valleys, Rtm is average of the Peaks to Valleys, etc...you get the idea.
Peak Count per inch may be a better parameter.
Trying to qualify a squiggly line calculated from many peak to valley excursions , numerically is a very tough job. People have been doing it for 79 years now.
The Profilometer product line was sold to Precision Devices..good website and source on this.
http://www.predev.com/
Been there done that.
Thank you guys for you replies. Your recommended readings are interesting. I got my hands on a copy of ''Handbook of Surface Metrology". Looks promising. I kindly ask that the admins keep this thread live for one more week. I need to do some serious reading, after which I would like to return here and present m findings and any questions I might have. Thank you again guys for your efforts.
Hey guys. This past weekend I still have been investigating the shape factor on surface roughness. Just to clarify, this image describes what I initially aimed to achieve; a sinusoidal corrugation with varying geometrical parameters. I came across a paper titled "A generalized mechanical model for suture interfaces of arbitrary geometry". The paper provided useful information such as geometrical description of surfaces and the inclusion of shape factor, Beta, to describe surface topography. However, it focused on the effects of surface geometry on mechanical properties. Please have a read through it. The paper encompasses my goals, which is to vary a geometric parameter and measure another parameter. In the case of the paper, it did so for stiffness and toughness. I need the same for roughness.
In addition to my previous post. I do not mind going with triangular waves and quantify roughness in terms of apex angle change.
Here is the paper
If you look at a Moody chart, roughness is parameterized as epsilon / D. Your roughness can easily be parameterized the same way. Your surface can be completely characterized by sinusoidal, frequency, amplitude, perpendicular to flow. You also need to characterize the fact that two walls are smooth. Since you are defining the surface topography as sinusoidal, attempting to use statistical parameters derived for a wide range of surface topography will cause loss of information.
All of which is meaningless if the flow is laminar.
My only grudge against using relative roughness (epsilon / D) is because I tend to use triangular waves. Both waves (sinusoidal and triangular) would have the same relative roughness. In other words, I need something to consider the shape factor. I am more than willing to ignore sinusoidal waves in favour of triangular waves since at least I can manipulate the apex angle. This way, I can ignore the shape factor. Still, I need to measure roughness based on apex angle. Any idea ?
Hello guys. Thank you for all the support you guys provided me with. This is an amazing platform for knowledge seekers. I will be definitely staying. Aside from that, I would like to give an update on my situation as well as close the lid on my case.
After reviewing several sources including BS (British Standards) I came to the following conclusions. There are several ways to calculating roughness, most famous being Ra (arithmetic average), which is an amplitude function. Several roughness mathematical models consider different functions such as (spacing and slope in addition to amplitude). All these models apply both Waviness and Profile. However, the cut off length is the governing factor. Depending on the cut off length you would be looking at roughness or waviness or profile. This cut-off value is 0.8mm for British standards. Furthermore, one might consider using more than one roughness measurement since different shapes and materials can have similar theoretical roughness values. As such, the most reliable way to measure roughness is through measuring devices.
Based on what I have mentioned, can you guys answer me the following. Assuming the cut-off length of 0.8mm, does that mean any topography with dimensions below 0.8mm will be considered as roughness'? Would you recommend that I go ahead with measuring the roughness for my pattern using different mathematical models? In other words, the roughness of my pattern would be described with different mathematical models in order to further distinguish between patterns that might have similar values for set mathematical models.
the reason Doctor Abbott decided on the cut off width of 0.030" as a Roughness Sampling Length was because in 1932, the typical pocket scale ( the machinists little metal 6 inch ruler) had 1/32" divisions on it. At the time, this was the smallest practical measurement used. So everything smaller than 0.030" ( 0.8mm) was roughness, and everything longer LENGTH was waviness. This has been carried forward as an arbitrary means of dividing Roughness and Waviness.
The electrical response of the instrument is Roughness Cutoff Width (RWC).
All metrology instruments have many RCW values but the bench mark is 0.030". A minimum of 5 RWC are used to evaluate a surface. Sample length and RCW get swapped around and this does get confusing.
Hello,
hope you are keeping well during these tough and uncertain times. My project developed during this time and I need your advice with measuring the drag due to friction and due to form with the same channel geometry. Please find the attached image. The unit is in micron. I have n number of corrugations and length L. The channel width is 200 (y-axis) and the depth is 40 microns (depth going towards the page z-axis). Flow is in the x-direction. Flow is Laminar and the fluid is distilled water.
I have measured the delta P for the channel and I can measure the total Drag coefficient Cd = 2a deltaP/(roh)U^2...however, since I have corrugations on both sides of the channel the equation becomes 4a deltaP/ (roh)U^2. Assuming the equation does measure the total Cd and I don't have to multiply it by n (number of corrugations), how can I separate the drag force into drag due to form and drag due to friction with my channel design?
Talal
That is easy. buy a metrology instrument that measures form error or profile ( specifically Waviness) and measures Surface Roughness (Ra) so you can separate Waviness and Roughness. These have been on the market since 1950.
Hello Mike,
I wish to measure the drag coefficient and skin friction instead of roughness using theoretical analysis. Is stokes law the only way?
There are over 110 parameters of Roughness identified by various industrial standards organizations world wide. What you call skin friction could be identified as Surface Roughness (Ra) what you call drag could be one of the other parameters like Peak Count per inch, Rt, Rtm or some other parameter. Good luck as I am sure what you are looking for has already been measured by these parameters. These parameters were created to fix a unique surface problem in manufacturing - example - sheet metal on automobiles would rust on the show room floor in the 1970s when the " gas shortage" hit the economy. Auto makers rolled thinner and thinner car bodies to save weight. This caused increase in Peak Count per inch of sheet metal. The Peaks stuck out past the paint thickness and caused rust. Only after a parameter that measured Peaks per inch was created were the stel mills able to control the surface of the sheet metal rolled.
the parameter is there for you to find. good luck!
It sounds like you want to predict pressure loss vs flow rate through rectangular channels of varying geometry. Drag coefficient does not apply to flow through channels. A relevant parameter is hydraulic diameter (search the term). Since you have laminar flow, the pressure drop is probably mostly skin friction. I am not aware of any published method for calculating pressure drop in your situation. If I wanted to develop such a method, here is how I would do it:
Start by making a set of straight channels. One 200##\mu## wide, one 70##\mu## wide, and one at the mean channel width one of your channels. Then I would measure the pressure drop vs flow for those three channels and several actual channels. I would compare the measured pressure drops to that of the three straight channels.
I would calculate hydraulic diameter and Reynolds number for all channels three ways - at the maximum width, minimum width, and average width. Then I would use those numbers in a Moody Chart to see how well they predict actual pressure drop.
correct me please, all drag and friction analysis relies on area consideration..
as in surface
now you are into my "area" surface irregularies to micro inch
