Design Review #2 (Oct 29th 2014 - Dec 8th 2014)
1. Introduction
This design review will consist of our team’s calculations and engineering justifications for proposed full scale models. The report will also contain an update on the progress of our small scale testing. This small scale testing will be used to help our team decide the best configuration from the baffles in sound attenuation. We are confident that this testing along with our engineering design work will result in a design that will meet our design goals.
The engineering design analysis detailed throughout the rest of the report will include information about sound waves and how to best absorb them. In addition, you will find pressure drop calculations that will be critical in any sound attenuator design. Another key component of our research were the flow simulations shown below. These simulations helped us to see what may happen in full scale testing and how we can adjust our design to increase insertion loss.
The conclusion of the report will show what work is upcoming from our team and what we expect the schedule for next calendar year to look like. This will help us determine what needs to be done to complete the project successfully.
The engineering design analysis detailed throughout the rest of the report will include information about sound waves and how to best absorb them. In addition, you will find pressure drop calculations that will be critical in any sound attenuator design. Another key component of our research were the flow simulations shown below. These simulations helped us to see what may happen in full scale testing and how we can adjust our design to increase insertion loss.
The conclusion of the report will show what work is upcoming from our team and what we expect the schedule for next calendar year to look like. This will help us determine what needs to be done to complete the project successfully.
2. Scaled Testing Update
Our team is currently continuing the work that we had discussed with SPX at our first design review. We have most of the rectangular baffles ready for small scale testing. We are currently finalizing the specifics of the fabrication of the metal tube baffles. Since our last design meeting, we have finalized the meters that are necessary for our small scale testing. In order to save money, we have decided to rent the sound meter that is needed. This testing will be conducted and completed after the first of the year.
In order to meet the hard deadline in May, we must work concurrently with fabrication of full scale models. Because of this, we have detailed below some full scale metal tube baffles that we would like to begin fabrication on in the near future. This will allow our small scale testing to be completed around the same time the full scale tube baffles are fabricated. We will then use the results of our scaled testing and our engineering justifications to arrange the fabricated full scale baffles in a way that will meet design goals.
In order to meet the hard deadline in May, we must work concurrently with fabrication of full scale models. Because of this, we have detailed below some full scale metal tube baffles that we would like to begin fabrication on in the near future. This will allow our small scale testing to be completed around the same time the full scale tube baffles are fabricated. We will then use the results of our scaled testing and our engineering justifications to arrange the fabricated full scale baffles in a way that will meet design goals.
3. Proposed Design for Fabrication
Due to the research we have found on sound attenuation, we believe that our tubed baffle setup will be a viable option. The tubed baffles will be of perforated metal rolled around the insulation used in the current set-up. We would like to have these tubed baffles fabricated full- scaled, in order to meet the project completion deadline. Below is our engineering justification on why we think the tubed baffles will be an improvement to the current rectangular designs.
3.1. Engineering Justification
- Sound Reflection: The tubed baffles will reflect sound in more desirable directions than the rectangular baffles (See Figure). The front of the rectangular baffles reflect sound straight back into the atmosphere, whereas the tube baffles will deflect the sound into the other tubed attenuators. This deflection of sound waves into the other attenuators will increase the amount of sound being absorbed.
- Sound Absorption: The perforated metal used has a very high absorption coefficient, shown in the table below. Since the air will hit only perforated metal on the front of the tubed baffles, as opposed to the sheet metal on the rectangular baffles, more sound will be absorbed.
- Sound Propagation: The tubed baffle setup will allow the sound waves to interfere more frequently with the attenuators. The rectangular set-up limits the interference and “streamlines” the sound in between baffles.
3.2. Drawings For Fabrication
4. Pressure Drop Calculations
4.1. Tube Style Attenuators
A large part of our design analysis deals with the pressure drop across the sound attenuator. It is important because excessive pressure drop defeats the purpose of the attenuation design. For the tube style attenuators, we created an excel spreadsheet that calculated the pressure drop across the tubes. These calculations were calculated using equations taken from the Seventh Edition Fundamentals of Heat and Mass Transfer written by Theodore L. Bergman and Adrienne S. Lavine.
The process begins by first identifying the diameter of the tubes. Once the diameter has been selected, the next step is to decide the configuration of the tubes. The most important values are the number of tube rows, the distance between tubes, and the distance between rows of tubes. The last value that needs to be entered into the spreadsheet is the speed of the air going through the attenuators. This is dependent on the atmosphere or test set up used.
This point in the calculations is where the process changes for aligned and staggered tubes. I will first detail the aligned tube process. The first thing that must be done (after the inputs abovehave been determined) is to find the properties of the fluid (air) going through the attenuator. For the example calculations below a film temperature of 300 K was used as an assumption. The next step is to find the max speed of the air. For an aligned tube, the equation used is:
V (max) = V (∞)*(St/ (St-D))
Where St = distance between rows and D = diameter of tubes. Once this value has been calculated, the maximum Reynolds number can be found using the equation:
Re (max) = (V (max)*D)/ν
Where ν = kinematic viscosity of air at film temperature. Once these values are determined, graphs must be used to determine friction factor (ʄ) and correction factor (X). These variables are necessary to solve for pressure drop using the equation:
Δp = NL*X*((ρ*V(max)^2)/2)*ʄ
Where NL is the number of rows present of tubes.
The process begins by first identifying the diameter of the tubes. Once the diameter has been selected, the next step is to decide the configuration of the tubes. The most important values are the number of tube rows, the distance between tubes, and the distance between rows of tubes. The last value that needs to be entered into the spreadsheet is the speed of the air going through the attenuators. This is dependent on the atmosphere or test set up used.
This point in the calculations is where the process changes for aligned and staggered tubes. I will first detail the aligned tube process. The first thing that must be done (after the inputs abovehave been determined) is to find the properties of the fluid (air) going through the attenuator. For the example calculations below a film temperature of 300 K was used as an assumption. The next step is to find the max speed of the air. For an aligned tube, the equation used is:
V (max) = V (∞)*(St/ (St-D))
Where St = distance between rows and D = diameter of tubes. Once this value has been calculated, the maximum Reynolds number can be found using the equation:
Re (max) = (V (max)*D)/ν
Where ν = kinematic viscosity of air at film temperature. Once these values are determined, graphs must be used to determine friction factor (ʄ) and correction factor (X). These variables are necessary to solve for pressure drop using the equation:
Δp = NL*X*((ρ*V(max)^2)/2)*ʄ
Where NL is the number of rows present of tubes.
The above graph shows the values needed to find ʄ and X. Once these values are found. It is a simple plug in to find the proper pressure drop.
Finding the pressure drop for staggered tubes is similar but with a few notable differences. The most important difference is when finding the V (max). In order to find V (max). You must first find St (distance between tubes) and Sd (distance diagonally between tubes). If St < Sd then you use the same equation as before:
V (max) = V (∞)*(St/ (St-D))
However, if Sd < St then you use the following equation to find V (max):
V (max) = V (∞)*(St/2 (Sd-D))
Once the value for V (max) is found, the same procedure as before is followed. The only difference is that the chart below is used for staggered tubes.
Finding the pressure drop for staggered tubes is similar but with a few notable differences. The most important difference is when finding the V (max). In order to find V (max). You must first find St (distance between tubes) and Sd (distance diagonally between tubes). If St < Sd then you use the same equation as before:
V (max) = V (∞)*(St/ (St-D))
However, if Sd < St then you use the following equation to find V (max):
V (max) = V (∞)*(St/2 (Sd-D))
Once the value for V (max) is found, the same procedure as before is followed. The only difference is that the chart below is used for staggered tubes.
4.2. Rectangular Style Attenuators
Calculating pressure drop for the rectangular style attenuators beings in a similar way to the tube style calculations. The first step is deciding all the input values (surface area, distance between baffles, etc.) and also the fluid properties. Once these values are found, you can begin the rectangular specific calculations.
The next step is to determine the hydraulic diameter. This can be found using the equation:
Dh = 4*Ac/P
Where Ac is the cross sectional area and P is the wetted perimeter. This hydraulic diameter will be used in the pressure drop equation we get to later. Once the hydraulic diameter is calculated, the Reynolds number must be found once again. The equation used for this is:
ReD = um*D/v
Where um is air velocity, D is diameter, and ν is kinematic viscosity. This number is also necessary to find future variables. After finding the Reynolds number, the surface roughness needs to be looked up.
The following is a small table of different surface roughness values for materials:
The next step is to determine the hydraulic diameter. This can be found using the equation:
Dh = 4*Ac/P
Where Ac is the cross sectional area and P is the wetted perimeter. This hydraulic diameter will be used in the pressure drop equation we get to later. Once the hydraulic diameter is calculated, the Reynolds number must be found once again. The equation used for this is:
ReD = um*D/v
Where um is air velocity, D is diameter, and ν is kinematic viscosity. This number is also necessary to find future variables. After finding the Reynolds number, the surface roughness needs to be looked up.
The following is a small table of different surface roughness values for materials:
Once the surface roughness is found the next step is to find the friction factor. This is done by using the following Moody Diagram:
Once friction factor is found, pressure drop can be directly calculated using:
Example Rectangular Baffle Calculation
5. Flow Simulations
In addition to the pressure drop calculations above, our group has also been working with flow simulations in SolidWorks. These simulations (detailed below) gave us an idea of the pressure loss across the attenuators from another source to verify the calculations above. This gives our group more assurance that our tube set ups will not affect the pressure loss too much. The following graphics and table will detail the setup we are currently working with.
We will be able to use this model to predict pressure drop for possible full scale designs we look at in the future.
6. Future Work
This section will detail a rough schedule of future work we will provide for SPX. The first step we can take when we return in January is to do the small scale testing with the design of experiments as detailed in our first design review. When this testing is complete, we will have experimental data and engineering analysis to use when making our full scale designs proposals. We will then present our possible full scale designs to SPX for review. Once reviewed, we will attempt to fabricate these designs for full scale testing. We will then perform testing and analysis to provide a design solution to the problem of sound attenuation.