Posted: May 9th, 2022

Flow of Compressible Fluid

Flow of Compressible Fluid

Introduction to CFD
Computational Fluid Dynamics (CFD) is used in simulating the motion in the fluid. It is used in the analysis the problems that are associated with turbulent flows, compressible and incompressible fluids. The CFD modeling allows the simulation in compressible and incompressible flow and hence providing a robust and accurate way of solving problems. The concept of CFD can be applied in airplanes, car spoilers, injectors among others.
CFD Methodology
The process of CFD analysis is analysed in 5 steps as shown below

Figure 1: A detailed flow chart of CFD analysis (Rahmati, 2018)
The analysis of CFD in ANSYS CFX is conducted in a mesh model pipe by applying appropriate boundary conditions. The velocity fluid is set at inlet velocity of 53.4 m/s while the outlet is defined through zero relative pressure. The walls are defined using No-slip wall boundary conditions.
Results

Picture 2. Simulation graph from CFD software

Results Discussion
The main objective is to study the numerical results and compare with the experimental results and accuracy of the results that were obtained. The three tests that were carried out were solved using the inlet velocities 53.4 m/s, 49.7 m/s and 45.3 m/s which were obtained from experimental results. The pressure contour plot was obtained. The pressure in the domain is calculated with respect to relative pressure when the relative pressure is applied to zero. There is zero pressure at outlet in the contour plot and maximum pressure at inlet with respect to flow inlet velocity. The streamline plot is also obtained. There is an increase in velocity from zero at wall to the maximum at centre. The reason is due to No-slip wall boundary condition where due to viscosity it will stick on the wall thereby the velocity of fluid on the wall will be zero.

Figure 2. Pressure Contour at inlet velocity 53.4 m/s

Figure 3. Velocity streamline plot (53.4 m/s)

Part 1
Introduction and Theory
Fluid flows from region of high potential to areas of low potential. The flow of the fluid is dependent on the viscosity. Viscosity is closely related to the density of the fluid. Viscosity increases with increase in the density of the fluid. Fluids are classified depending on areas in which they are applicable. The ability to compress the liquid can be directly classified as compressible and non-compressible. Compressible fluids can be compressed under high pressures and the particles can easily change in the position.
The compressible flow of the fluid is based on the Reynold number of the fluid that flows in a particular speed. Reynold number is dimensionless and therefore it is considered as a ratio. Reynolds number gives the relationship between the fluid inertial forces and viscous forces. Theoretically the Reynolds number of lamina flow does not exceed 2100 value and transient flow the Reynolds number is between 2100 and 4000 by value. In turbulent flow the Reynolds number does not exceed 400 by value (Lam & Liu, 1999 p.58).
In carrying out the experiment, numerical analysis is carried out for the purposes of finding the solutions to some of the questions. Numerical analysis can be carried out with the help of the software that guides in the whole process. The speed of flow of fluid becomes high leading to compressible flow. High speed results in choking features such as the choking phenomenon and sometimes the formation of shock waves. Compressible flow is commonly applicable in engineering especially aerospace engineering (Ghrist, 2007 p.37). The parameters that guides the experiment includes the mass flow rate, Reynolds number and Friction factor
Mass flow rate m at the nozzle entry
m=A_ρ V_0,where A=Inlet zozzle area=0.0009078 m^2,ρ=density of air=1.2 kg/m^3 ,V_0=velocity of air at the nozzle
Reynolds number,Re=ρV_piped d/u V_(pipe )
Viscosity of air,μ=1.8×〖10〗^(-5) kg/m s
Friction Factor
Friction factor is calculated using Darcy^’ s equation.f=2∆p.d/(ρV_(〖pipe〗^2 ))
Objectives
To investigate the relationship between friction factor and Reynolds number for flow through smooth pipes
To investigate whether the flow is laminar or turbulent and compare the friction factors with those from Moody diagram.
Methodology
In the first step, the pipe section was attached to the measuring nozzle and the intake connection by the use of union nuts. The connection was done by considering the longer end (abatement section) for the inlet which was connected to the measuring nozzle. The pressure measurement point was connected to the differential manometers as:
34mm dia pipe : Measuring range 0-25 mbar
24mm and 16mmpipe : Measuring range 0-200 mbar.
The pressure measurement point was connected to the point for measuring nozzle to the negative connection of the velocity display.
In the next step, the compressor was switched on and set to the desired speed. The velocity V0 was recorded from the nozzle and the pressure loss Δp in the data sheet. The new velocity was set and the measurement was repeated. In the last step, the pipe and the procedure was repeated to the two other remaining pipes.
Results
The table was completed and two curves were plotted. The curve of Δp Vs. m for all the three pipes on the same graph and the graph of f vs Re. The frictional factors were compared with the factors from Moody’s chart and the observations were recorded. The results were later discussed.
Pipe Vo AP m Vpipe d/μ Re f h
Diameter m/s mbar kg/s M/s metre of
air
34 mm 17.6 1.8 0.019173 21.10871 1888.889 47846.4 0.000228916 0.153061
Measuring 21.2 2.3 0.023094 25.4264 1888.889 57633.16 0.000201598 0.195578
range 24.9 3 0.027125 29.86402 1888.889 67691.78 0.000190613 0.255102
0-25 mbar 28.6 3.9 0.031156 34.30165 1888.889 77750.4 0.000187829 0.331633
31.5 4.5 0.034315 37.77979 1888.889 85634.18 0.000178657 0.382653
33.9 5 0.036929 40.65825 1888.889 92158.69 0.000171396 0.42517
37 5.7 0.040306 44.37626 1888.889 100586.2 0.000164022 0.484694
40 6.7 0.043574 47.97433 1888.889 108741.8 0.000164962 0.569728
41.4 7.6 0.0451 49.65343 1888.889 112547.8 0.00017468 0.646259
44.9 8.2 0.048912 53.85119 1888.889 122062.7 0.000160233 0.697279
24 mm 22.3 0.8 0.024293 53.67712 1333.333 85883.39 1.11064E-05 0.068027
Measuring 26.1 4.2 0.028432 62.82389 1333.333 100518.2 4.25657E-05 0.357143
range 29.5 7.6 0.032136 71.00785 1333.333 113612.6 6.02922E-05 0.646259
0-200 mbar 31.1 9.9 0.033879 74.85912 1333.333 119774.6 7.06652E-05 0.841837
34.4 13.8 0.037474 82.80237 1333.333 132483.8 8.05107E-05 1.173469
36.9 16.8 0.040197 88.81998 1333.333 142112 8.5182E-05 1.428571
38.7 20 0.042158 93.15266 1333.333 149044.3 9.21933E-05 1.70068
39.4 21.7 0.042921 94.8376 1333.333 151740.2 9.6507E-05 1.845238
39.5 22 0.04303 95.0783 1333.333 152125.3 9.73464E-05 1.870748
16 mm 15.2 25.8 0.016558 82.32094 888.8889 87809 0.000101524 2.193878
Measuring 17.5 40 0.019064 94.77739 888.8889 101095.9 0.000118746 3.401361
range 22.2 70.5 0.024184 120.2319 888.8889 128247.4 0.000130052 5.994898
0-200 mbar 23.2 86.2 0.025273 125.6477 888.8889 134024.3 0.000145602 7.329932
19.3 52.1 0.021025 104.5259 888.8889 111494.3 0.000127162 4.430272
23.8 95.8 0.025927 128.8973 888.8889 137490.4 0.000153761 8.146259
23.9 96.5 0.026036 129.4388 888.8889 138068.1 0.000153591 8.205782
23.3 87.8 0.025382 126.1893 888.8889 134602 0.000147034 7.465986
21.5 66.9 0.023421 116.4408 888.8889 124203.5 0.000131578 5.688776

Area=0.00090857
Area=0.00045254
Area=0.00020129

Figure 1: Graph of Ap vs mass

Figure 2: Graph of f vs Re
Analysis and Discussion
The area of each pipe was calculated and using in finding other parameters. The diameter of each pipe was considered when finding other parameters. The results indicated the different values and variation of the values in three of the pipes obtained. The next step involved plotting of the values and carrying out the analysis by considering the shapes of the graphs.
The experimental frictional factor is obtained from the data that was obtained after conducting the experiment. On the other hand, frictional factor can also be obtained from the Moody chart. The Moody chart can be used in predicting the frictional factor by basing on the Reynold number and the relative friction of the surface.
The graphs that were plotted were from different values that were obtained from the experiment. The pipe used in the experiment was not smooth and therefore the internal walls might have frictional forces. The frictional force in the pipe caused additional pressure drop thereby resulting in an increase in the frictional number.
In conducting the analysis, the flow of air inside the smooth pipe was turbulent. The relationship is derived from the calculations. The calculation from experimental results revealed that the Reynolds number was above 4000 value and therefore it was categorized as turbulent flow. The flow inside the pipe was turbulent.
On considering the effect of the mass flow rate which caused the change in pressure across the pipe, the graph was plotted using the values that were obtained from the experiment. The graph showed that the mass flow rate is directly proportional to the change in pressure that is developed inside the pipe. The relationship implies that the increase in the mass flow rate of air in the pipe results in the corresponding increase in the pressure difference in the pipe and vice versa.
In analysing the effect of Reynolds number on the frictional factor, the graph was plotted using the values obtained from the experiment. From the graph, Reynolds number and frictional number are directly proportional. This implies that an increase in the Reynolds number of the amount of air inside the pipe results in the corresponding increase in the frictional factor. On the other hand the decrease in Reynolds number of the air in the pipe results into the decrease in the frictional factor. The relationship shows that the factors are directly proportional to each other.
Part 2: Pressure Distribution in the Bend
Introduction
Pressure distribution through the bend has been widely applicable in engineering. Investigation through the bend is important in improving the performance and minimizes some of the losses that might occur (Crawford et al, 2007 p.77). The flow through the bend is also dependent on the Reynolds number and the radius of curvature of the bend. The flow is normally controlled by centrifugal force that acts on the fluid. Pressure losses normally take place at the bend and it is always caused by friction and momentum exchanges which eventually results in the change of direction flow. The factors that determines the flow at the bend includes the great angle, the curvature ratio and Reynolds Number. The flow through the bend is applicable in increasing the performance and minimizing the losses (Dutta and Nandi, 2016 p.23).
Objective
The objective of the experiment is to determine the pressure distribution in a bend at a fan speed of 300000/min.
Methodology
A complete instrument was set up. The union nuts were used to attach to the bend and then measuring nozzle to the intake connection. The pressure measurement point was connected for the measuring nozzle to the negative connection of the velocity display. The next step involved switching on the fan and adjusting it to the speed to 30000/min. The manometer bar was connected in the sequence of 0…25 to the pressure measurements from points p1 to p6. The pressures were recorded starting from p1 to p 6.

Figure 3: Bend angle values
Results
The measured pressure levels were listed in the table below.
Table 2. Pressure levels in Inner and Outer band
Negative Pressure in mbar, Speed 30000/min
Outer bend Inner bend
0 45 90 0 45 90
p1 p2 p3 p4 p5 p6
13.9 9.8 12.5 19.6 25.4 20

Analysis and Discussion
There is the lower pressure level on the inner surface of the bend than the outer surface. The difference is caused by the centrifugal forces that come about by the circular movement of the fluid. Along the bend, there is a pressure loss. The loss of pressure is dependent on the radius of curvature. Increase in the radius of curvature results into increase in losses as a result of friction on the wall. The decreases in the radius of curvature results led to higher losses as a result of separation. The flow of the fluid along the bend is guided by a number of parameters which includes Reynold’s number, the radius of curvature and centrifugal force. The use of bend pipes is commonly applied in the nuclear reactor system. Friction in the fluid is one of the factors that could cause the variation in the results that were obtained. Friction is as a result of the walls of the pipe used in the experiment which was rough.

References
Crawford, N.M., Cunningham, G. and Spence, S.W.T., 2007. An experimental investigation into the pressure drop for turbulent flow in 90 elbow bends. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 221(2), pp.77-88.
Dutta, P. and Nandi, N., 2016. Effect of bend curvature on velocity & pressure distribution from straight to a 90 pipe bend-A Numerical Study. REST Journal on Emerging trends in Modelling and Manufacturing, 2(4).
Lam, C.Y. and Liu, C.Y., 1999. An Experimental facility for compressible flow. INTERNATIONAL JOURNAL OF ENGINEERING EDUCATION, 15(1), pp.58-63.
Ghrist, R., Serre, D., ma Mère, À., Schochet, S., Seregin, G., Gallagher, I., Saint-Raymond, L., Sell, G.R., Málek, J., Rajagopal, K.R. and Pileckas, K., 2007. Handbook of Mathematical Fluid Dynamics. Elsevier, 4, pp.1-37.

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