CONTROLS
CONTROLS
General Input
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Inlet Diameter | min: 0.001, max: 600
Inlet Type | Types: Re-entrant, Sharp Edged, Slightly Rounded, Well Rounded
Fluid Density | min: 300, max: 1300
Dynamic Viscosity | min: 0.0000088, max: 10
Mass Flow Rate | min: 0.001, max:1 000 000
Elevation | min: 10, max: 1000
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Roughness | min: 0, max: 1
Length | min: 1, max: 1 000 000
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Pump Input | min: 1, max: 1 000 000
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Turbine Output | min: 1, max: 1 000 000
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Kinetic Energy Correction Factor | min: 1, max: 2
Diameter Ratio Squared | min: 0.01 max: 0.99
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Length | min: 1, max: 1 000 000
Kinetic Energy Correction Factor | min: 1, max: 2
Diameter Ratio (Sudden Contraction)| min: 0.01, max: 0.99
Angle (Gradual Contraction)| Angles: 30, 45, 60
INFORMATION
The purpose of Hydraulic Grade Lines and Energy Grade Lines are to graphically show the mechanical energy of a streamline using heights. These heights are calculated using the Bernoulli Equation where each term is divided by gravity to get the heads. \[ \frac{P}{\rho g} + \frac{V^2}{2g} + z = H \]
Bernoulli Equation (divided by gravity)
Each term is named as follows:| \(P\) | Pressure(Pa) |
| \(\rho\) | Fluid Density(kg/m3) |
| \(V\) | Velocity of Fluid(m/s) |
| \(z\) | Elevation(m) |
| \(g\) | Acceleration due to gravity(9.81m/s2) |
| \(H\) | Bernoulli Head(m) |
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Pressure Head
Pressure Head is the height a column of fluid must be to produce an equivalent static pressure. \[\frac{P}{\rho g}\]
Pressure Head
Velocity Head| \(P\) | Pressure(Pa) |
| \(\rho\) | Fluid Density(kg/m3) |
| \(g\) | Acceleration due to gravity(9.81m/s2) |
Velocity Head is the height the fluid must start at to reach the same velocity during frictionless freefall. \[\frac{V^2}{2g}\]
Velocity Head
Elevation Head| \(V\) | Velocity of the Fluid(m/s) |
| \(g\) | Acceleration due to gravity(m/s2) |
Elevation Head displays the potential energy of the fluid.
\[z\]
Elevation Head
| \(z\) | Elevation(m) |
Hydraulic Grade Lines are found using a piezometer to measure static pressure at several points along the pipe system. The following expression is used to convert the measured static pressure into head.
\[HGL = \frac{P}{\rho g} + z \]
Hydraulic Grade Line \((HGL)\)
Energy Grade Lines are found using a Pitot tube to measure dynamic and static pressures at several points along the pipe system. The following expression is used to convert the measured static and dynamic pressure into head.| \(P\) | Pressure(Pa) |
| \(\rho\) | Fluid Density(kg/m3) |
| \(g\) | Acceleration due to gravity(9.81m/s2) |
| \(z\) | Elevation(m) |
\[EGL = \frac{P}{\rho g} + \frac{V^2}{2g} + z\]
Energy Grade Line \((EGL)\)
Notice that the difference differ by the \(\frac{V^2}{2g}\) term which is called the dynamic head or velocity head. It is also important to note that the difference between HGL and EGL will increase if the fluid's velocity increases or will decrease if the fluid's velocity decreases because they differ by the dynamic head.| \(P\) | Pressure(Pa) |
| \(\rho\) | Fluid Density(kg/m3) |
| \(g\) | Acceleration due to gravity(9.81m/s2) |
| \(V\) | Fluid Velocity(m/s) |
| \(z\) | Elevation(m) |
Stationary Bodies such as reservoirs have the head at their surface because the Velocity is 0m/s and Pressure is at atmospheric pressure. Therefore, stationary bodies only have elevation as effective head. This also means that EGL is equal to HGL on stationary bodies. The elevation of these stationary bodies is often measured from the centerline of a pipe system well below the surface of the body.
The simulation focuses on providing a visual representation of Hydraulic and Energy Grade Lines in a turbulent system. The calculations present in the simulation utilize the Bernoulli Energy Equation, which includes the changes in mechanical energy caused by pumps, turbines, and head loss. \[ \frac{P_1}{\rho_1 g} + \alpha_1\frac{V^2_1}{2g} + z_1 + h_{pump, u} = \frac{P_2}{\rho_2 g} + \alpha_2\frac{V^2_2}{2g} + z_2 + h_{turbine, e} + h_L \]
Bernoulli Energy Equation
The simulation simplifies the effects of pumps and turbines to a single value. The component will either be specified as an addition or a removal of mechanical energy to the overall system. The efficiencies of the pump and turbines are assumed to be 100%.| \(P\) | Pressure(Pa) |
| \(\rho\) | Fluid Density(kg/m3) |
| \(g\) | Acceleration due to gravity(9.81m/s2) |
| \(V\) | Fluid Velocity(m/s) |
| \(z\) | Elevation(m) |
| \(\alpha\) | Energy Correction Factor |
| \(h_{pump,u}\) | Mechanical Energy provided in head(m) |
| \(h_{turbine,e}\) | Mechanical Energy removed in head(m) |
| \(h_L\) | Head Loss(m) |
Kinetic Energy Correction Factor (alpha) is given as a correction to a definition within Bernoulli’s Equation. It is typically given as 1.05 for turbulent flows and 2 for laminar flow. In elementary analysis of turbulent flow systems, this value is often ignored.
Head Loss (hL) represents the total frictional losses associated with the fluid flow along the pipe system. These frictional losses are proportional the velocity of the fluid flowing through the pipes. Head Loss is split into major and minor loss.\[h_{L,total} = h_{L,major} + h_{L,minor}\] Major loss is characterized by the summation of frictional losses in long straight pipe systems. Minor losses are associated with pipe fittings, valves, other various non-straight components in a pipe system. These components disrupt the smooth flow of the fluid and induce flow separation and mixing. This is represented as: \[h_{L,total} = h_{L,major} + h_{L,minor} = \sum_{i} f_i \frac{L_i}{D_i}\frac{V_i^2}{2g} + \sum_{j} K_{L, j} \frac{V_j^2}{2g}\]
Total Head Loss
The friction factor (f) for turbulent flow is solved implicitly using the Colebrook-White Equation given as:
\[\frac{1}{\sqrt{f}} = -2.0\mathrm{log}\left(\frac{\frac{\epsilon}{D}}{3.7} + \frac{2.51}{Re\sqrt{f}}\right)\]
| \(h_{L,total}\) | Total Head Loss(m) |
| \(f\) | Darcy-Weisbach friction factor |
| \(L\) | Length of pipe component(m) |
| \(D\) | Diameter of Pipe Component(m) |
| \(V\) | Fluid Velocity(m/s) |
| \(g\) | Acceleration due to gravity(9.81m/s2) |
| \(K_L\) | Minor Loss Coefficient |
| \(i\) | # of frictional components |
| \(j\) | # of minor loss components |
Darcy-Weisbach Friction Factor Equation
The equation is solved using an computation-heavy iterative method.| \(f\) | Darcy-Weisbach friction factor |
| \(\epsilon\) | Roughness(m) |
| \(D\) | Pipe Diameter(m) |
| \(Re\) | Reynolds Number |
Minor loss (kL) has been found empirically and tabulated for many components of a pipe system.
REFERENCES
Y. A. Çengel and J. M. Cimbala, Fluid Mechanics: Fundamentals and Applications, 3rd ed. New York, NY, USA: McGraw-Hill, 2014.Engineering ToolBox, (2004). Steel Pipes and Maximum Water Flow Capacity. Accessed Mar. 29, 2021. [Online]. Available: https://www.engineeringtoolbox.com/steel-pipes-flow-capacities-d_640.html
B. Setiawan. "Pelton Turbine Blade". Pelton Turbine Blade | 3D CAD Model Library | GrabCAD. Accessed Apr. 6, 2021. [Online]. Available: https://grabcad.com/library/pelton-turbine-blade-4
VERKÍS HF. "NESJAVELLIR HOT WATER MAIN." Nesjavellir hot water main | Projects | www.verkis.com. Accessed Apr. 7, 2021. [Online]. Available: https://www.verkis.com/projects/utilities/water-supply-systems/nr/982
P. M. Ligrani, "A Study of Dean Vortex Development and Structure in a Curved Rectangular Channel with Aspect Ratio of 40 at Dean Numbers up to 430," Naval Postgraduate School Monterey, Monterey, CA, United States, July 1, 1994. Accessed Mar. 25, 2021 [Online]. Available: https://ntrs.nasa.gov/citations/19950005258
Md. M. Hoque, Md. M. Alam, "Effects of Dean Number and Curvature on Fluid Flow through a Curved Pipe with Magnetic Field," Procedia Eng., vol. 56, pp. 245-253, 2013. Accessed: Mar. 19, 2021, doi: 10.1016/j.proeng.2013.03.114. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1877705813004682
M. M. Noor, A. P. Wandel, T. Yusaf, "ANALYSIS OF RECIRCULATION ZONE AND IGNITION POSITION OF NON-PREMIXED BLUFF-BODY FOR BIOGAS MILD COMBUSTION," IJAME, vol. 8, pp. 1176-1186, Jul.-Dec., 2013. Accessed: Mar. 25, 2021, doi: 10.15282/ijame.8.2013.8.0096. [Online]. Available: http://ijame.ump.edu.my/images/Volume_8/8_Noor%20et%20al.pdf
A. Guessab, C. Mansour, T. Baki, "Combustion of Methane and Biogas Fuels in Gas Turbine Can-type Combustor Model," JAFM, vol. 9, no. 5, pp. 2229-2238, Jul., 2016. Accessed: Mar. 17, 2021, doi: 10.18869/acadpub.jafm.68.236.24289. [Online]. Available: https://www.researchgate.net/publication/307966931_Combustion_of_Methane_and_Biogas_Fuels_in_Gas_Turbine_Can-type_Combustor_Model