CFD Analysis of Impeller Design for A Respirator

CFD Analysis of Impeller Design for A Respirator

CFD Analysis of Impeller Design for A Respirator

Suresh Pittala

School of Mechanical & Industrial Engineering, Hawassa University, P. O. Box 5, Hawassa, Ethiopia.

Abstract

Designing impellers for respirator are important for fluid flow analysis. A new model is designed and analyzed for fluid flow using computational fluid dynamics (CFD). To improve the efficiency of pump, CFD analysis is used in the pump industry. In the present model Acrylonitrile butadiene styrene (ABS) material is used to reduce noise and cutting down the cost. The number of impeller blades is proposed to increase from 6-8 to 20 to increase fluid velocity. Inlet blade angle is reduced to less than 40 degrees from greater than 45 degrees to increase efficiency and outlet fluid velocity. From the CFD analysis, the velocity and pressure in the outlet of the impeller is outlet flow conditions are used to calculate the efficiency by using the empirical relations. In the first case outlet angle is increased, and in the second case inlet angle is decreased and they are obtained from the CFD analysis. It causes

to improve efficiency.

KEY WORDS: Computational Fluid Dynamics (CFD) analysis, Impeller design, Respirator.

1. Introduction

   The powered air purifying respirator (PAPR) specifically designed to protect health care professionals from residual chemical/ biological/ radiological agents when they are performing first responder duties during homeland security or terrorist situations. Weighing less than six pounds, the system features a lightweight, chemical-resistant belt- mounted blower with two HC CBA/ RCA canisters. The canisters contain a pleated high-efficiency (P-100) filter to remove aerosols, radio nuclides, and solid particulates, as well as an impregnated, activated carbon bed to adsorb (filter out) gases and vapors. Experimental setup of PAPR is shown

   in fig.1.

   Fig.1. Experimental setup Powered Air Purifying Respirator (PAPR)

   Impellers are prevalent for much different application in the industrial or other sector. Nevertheless, their design and performance prediction process is still a difficult task mainly due to the great number of free geometric parameters, the effect of which cannot be directly evaluated. The significant cost and time of the trial and error process by manufacturing and testing of physical prototype reduces the profit margins of the impeller manufacturers. For this reason CFD analysis is currently used in hydrodynamic design for different impeller types. Impeller is a rotating part of a centrifugal compressor/pump that imparts kinetic

   energy to a fluid. Here under we introduced

   1. modeling laws and (2) Vibration and noise [1, 2].

      1. Modeling Laws The modeling laws includes both the affinity law and model law. These two laws are stated below:

         1. Affinity Law for similar conditions of flow the capacity will vary directly with the ratio of speed and/or impeller diameter and the head with the square of this ratio at the point of best efficiency.

         2. Model Law two geometrically similar pumps working against the same head will have similar flow conditions if they run at speeds inversely proportional to their size, and in that case their capacity will vary with the square of their size.

      2. Vibration and noise Here we introduce mechanical noise source and methods for reducing noise.

         1. Mechanical noise source the two comely used mechanical noise sources are

            described as: (a) Common mechanical

            P V 2 P V

            1 1 Z1g 2 2 Z2 g

            sources that may produce noise include 2

            vibrating pump components or surfaces

            2 (1)

            because of the pressure vibration that are generating in the liquid or air. Example: Impeller or seal rubs, Vibrating pipe walls, unbalanced rotors. (b) In centrifugal

            V2 = 0; Z1 = Z2.

            The difference pressure equation is given by

            V 2 *

            machines, improper installation of couplings often causes mechanical

            vibration at twice pump steep.

            (P2 P1 ) 2

            Where

   2. 1. Methods for reducing noise the following are the comely used methods for reducing noise inside a mechanical operates. (a) Increase or decrease the pump speed to avoid system resonances of the mechanical system. (b) Decrease suction lift, increase air pressure. (c) Suction pipe should be straight.

         According to Bernoulli [3] the differential pressure equation is given by

         P1 =Initial pressure at the inlet of the impeller, in bar

         P2 = Final pressure at the outlet of the impeller, in bar

         = Density of air in kg/m3 V =Velocity of air in m/s

         It is well known [4, 5, 6] that three dimensional flow characteristic for an impeller of an axial turbo fan for improving the airflow rate and the static pressure. To consider an incompressible steady three-dimensional flow, the Reynolds (RANS) equations are used as

         the governing equations, and the standard k- turbulence model is chosen. The pitch angles of 44°, 54°, 59°, and 64° are implemented for the numerical model. The numerical results show that airflow rates of each pitch angle are 1,175 CMH, 1,270 CMH, 1,340CMH, and 800 CMH,

         respectively. The difference of the static pressure at impeller inlet and outlet are

         120 Pa, 214 Pa, 242 Pa, and 60Pa according to respective pitch angles. It means that the 59° of the impeller pitch angle is optimal to improve the airflow rate and the static pressure.

         Also it is known that [7, 8] the turbo machinery flow is unsteady due to the relative motion between different components of the machine: for example the impeller blade passing in front of the stator vanes or in front of the tongue of the volute. Furthermore, in hydraulic machines the flow is fully turbulent and three-dimensional. Computing the entire

         real flow (unsteady and turbulent) through the whole pump requires a large computer memory and computational time even for the most performing computers [9]. Thus, a simplified simulation technique must be used in order to obtain useful results in a storage pump.

         A finite element based method has been developed [10] for computing fluid- induced forces on an impeller in a volute casing. Potential flow theory is used assuming irrigational, in viscid and incompressible flow. Both excitation forces and motion dependent forces are calculated. The numerical results are compared with experimental results obtained at the California Institute of Technology. In two-dimensional and three-dimensional simulations the calculated pump characteristics near the design point are about 20% higher than the experimental curve. This is caused by viscous losses that are not taken into

         account in our model. The magnitude of the excitation force is predicted well for optimum and high flow rates. At low flow rates the calculated force is too large which is probably related to inaccuracies in the calculated pressure.

2. COMPUTATIONAL FLUID DYNAMICS (CFD)

   1. Methods and Governing Equations

      CFD solvers are usually based

      on the finite volume method that includes

      approximations of the governing equations of fluid mechanics and the fluid region to be studied. The set of approximating equations are solved numerically for the flow field variables at each node.

      <Unsteady> + <Convention> =

      <Diffusion> + <Generation>

      Fig 2: General conversation

      To kep the details simple, we illustrate the fundamental ideas underlying CFD by applying them to the following simple first order differential equation [11]:

      the following steps: (a) Domain is

      du u

      0; 0 x 1;u 0 1

      1. discredited into a finite set of control volumes or cells. (b) General conservation or transport equation for mass, momentum, energy, etc., are discredited into algebraic equations which are shown in fig2. (c) All equations are solved to render flow field. (d) Governing differential equations become algebraic.

         (e) The collection of cells is called the grid or mesh. (f) System of equations is solved simultaneously to provide solutions.

         CFD applies numerical methods called discretization to develop

         dx m

         It first considers the case where m

         = 1 when the equation is linear. This later considers the case where m = 2 when the equation is nonlinear. This derives a discrete representation of the above equation with m = 1 on the following grid:

         This grid has four equally-spaced representation is termed first order

         grid points with x

         being the spacing

         accurate. Using (6) in (5) and excluding

         between successive points. Since the governing equation is valid at any grid

         point, we have

         higher-order terms in the Taylors series, we get the discrete equation as

         ui ui1 u 0

         x i

         (7)

         This method of deriving the

      2. discrete equation using Taylors series

         Here the subscript i represents the value at grid point xi . In order to get an expression for (du/dx) i in terms of u at the grid

         expansions is called the finite-difference method. However, most commercial CFD codes use the finite-volume or finite- element methods which are better suited

         points, we expand

         as

         ui1 in a Taylors series

      3. for modeling flow past complex geometries. For example, the fluent code uses the finite-volume method whereas

         ansys (software) uses the finite-element

         A simple rearrangement of (5) gives

         method.

3. CFD Procedure and Analysis

   The error in (du / dx)i

   , due to the

   Fluid flow analysis performed on the impeller, using ansys

   neglected terms in the Taylors series, is called the truncation error. Since the truncation error is O( x), this discrete

   CFX. Numerical results fully characterized the flow field, providing detailed flow information such as flow speed, flow

   angle, pressure, boundary layer development, losses. The flow field information from CFD simulation was then used to help elucidate the flow physics [12]. Impeller, blade geometry is shown in fig. 3 and fig. 4. Impeller design specification is shown in table 1.

   Fig.3. Impeller geometry front view and side view

   Fig.4. Blade geometry

   S. No.	Parameter	Size
   1.	Inlet diameter (Di)	22.67 mm
   2.	Outlet diameter(D0)	67.74 mm
   3.	Blade number	20
   4.	Inlet angle ()	38o
   5.	Outlet angle ()	820
   6.	Blade thickness (t)	2.5 mm
   7.	Shaft diameter (Ds)	6 mm

   Table1. Design specification of Impeller

   1. Meshing

      Turbo grid uses unstructured meshes in order to reduce the amount of time spent generating meshes, simplifying the geometry modeling and mesh generation process, model more complex geometries than can be handled with conventional, multi-block structured meshes, and let the mesh to be adapted to resolve the flow-field features. This flexibility allows picking mesh topologies that are best suited for particular application. The geometry is created by using Solid Works and the extruded geometry is meshed by Turbo Grid. Meshing of Single Blade and 20 blades Impeller is shown in fig. 6 and fig.7.Mesh

      S. No.	Parameter	Classical model	New model	Benefits of New model
      1.	Inlet angle	550	380	Flow increment
      2.	Outlet angle	750	820	Flow increment
      3.	Number of blades	6	20	Flow increment
      4.	Material	Steel	ABS (C8H8)	Cost reduction
      5.	Outlet velocity	26.22 m/s	35.46 m/s	Outlet velocity increment

      S. No.	Parameter	Classical model	New model	Benefits of New model
      1.	Inlet angle	550	380	Flow increment
      2.	Outlet angle	750	820	Flow increment
      3.	Number of blades	6	20	Flow increment
      4.	Material	Steel	ABS (C8H8)	Cost reduction
      5.	Outlet velocity	26.22 m/s	35.46 m/s	Outlet velocity increment

      statistics and comparison between Classical model and new model is shown in tab.2 and tab3

      Fig.6. Meshing of Single Blade

      Fig.7. 20 blades Impeller

      S. No.	Mesh measure	Value
      1.	Minimum face angle	26.2748
      2.	Maximum face angle	153.725
      3.	Maximum element	382,072
      4.	Minimum volume	1,74683e- 012 [inches]
      5.	Maximum edge	1970.8

      Table.2. Mesh Statistics

      Table.3. Comparison between Classical model and new model

   2. CFX Preprocessor

      In the present work, the effect of inflow/outflow boundary conditions on the impeller is studied. Two types of inflow/outflow conditions are considered, static inflow with extrapolated outflow boundary condition 1(BC1), and dynamic inflow boundary condition 2 (BC2) that accounts for upstream influence in the subsonic flow. For the current problem air as ideal gas has been chosen these have the following properties. The values of fluid are shown in tab.4.

      Molar mass	28.96 kg/ kmol
      Density	1.024 kg/m³

      Tab.4. Values of fluid

      3.2.1 Wall Boundary Conditions

      No-slip conditions were prescribed on the impeller blade surface surface. Zero Neumann boundary condition was imposed for pressure at the walls.

      3.3 CFX Postprocessor

      In this we can view the results such as contours, vectors and streamlines. In the results velocity contour, total pressure and pressure contours are shown.

4. Static pressure contours at 10000 rpm, 8000 rpm, 6000 rpm, 4000 rpm, and 2000 rpm at 70 % are shown in the following figures 8a, 8b, 8c, 8d and 8e:

   Fig.8a. 10000 rpm

   Fig.8b. 8000 rpm

   Fig.8c. 6000 rpm

   Fig.8d. 4000 rpm

   Fig.8e: 2000 rpm

   As Sean in the figures the pressure distribution will vary as the speed of the impeller changes. From fig 8a the pressure at inlet is as compared to the pressure at outlet in 10000 rpm case but in the 2000 rpm case the pressure at inlet is

   low and the pressure at outlet is high that means the exit velocity in 2000 rpm is low as compared to 10000 rpm.

   Total Pressure contours at 10000 rpm, 8000 rpm, 6000 rpm, 4000 rpm, and 2000 rpm at 70 % are shown in the fooling figures 9a, 9b, 9c, 9d and 9e:

   Fig.9a. 10000 rpm

   Fig.9b. 8000 rpm

   Fig.9c. 6000 rpm

   component are shown in Figs for 10000 rpm, 8000 rpm, 6000 rpm, 4000 rpm and 2000 rpm respectively. The figures X axis represents axial chord and Y axis represents velocity in m/s. the figures represents flow variations in 10000 rpm , 8000 rpm , 6000 rpm , 4000 rpm and 2000

   rpm at contours 20% , 50%, 70% span wise.

   1. Mean span wise pressure profiles

      Mean contours of span wise pressure component are shown in Figs for 10000 rpm , 8000 rpm, 6000 rpm, 4000 rpm and 2000 rpm respectively. The figures X axis represents axial chord and Y axis represents pressure in Pa. the figures represents flow variations in 10000 rpm , 8000 rpm , 6000 rpm , 4000

      rpm and 2000 rpm at contours 20% , 50%, 70% span wise. Static pressure contours at 20%, 50% and 70% at 8000 rpm and10000 rpm is shown in fig.10a and fig.10b.

      Fig.9d. 4000 rpm

      Fig.9e. 2000 rpm

      200

      S tatic p ressu re(P a)

      S tatic p ressu re(P a)

      -300

      -800

      -1300

      -1800

      -2300

      S tatic P ressu re vs Axial ch o rd @ 10000 R P M

      0 0.	1 0.	2 0.	3 0.	4 0.	5 0.	6 0.	7 0.	8 0.	9 1

      Axial_ C h o rd

      Profiles of span wise velocity

      S tatic pressure 20 static pressure 50 static pressure 70

      Fig.10a Static pressure contours at 20%, 50% and 70% at10000 rpm

      200

      T o tal p ressu re(P

      T o tal p ressu re(P

      150

      100

      50

      0

      – 50

      0 0 .	1 0 .	2 0 .	3 0 .	4 0 .	5 0 .	6 0 .	7 0 .	8 0 .	9 1

      0 0 .	1 0 .	2 0 .	3 0 .	4 0 .	5 0 .	6 0 .	7 0 .	8 0 .	9 1

      T o tal P ressu re vs Axial ch o rd @ 10000 R P M

      static p ressu re vs axial ch o rd @ 8000 R P M

      0 0 .	1 0 .	2 0 .	3 0 .	4 0 .	5 0 .	6 0 .	7 0 .	8 0 .	9 1

      0 0 .	1 0 .	2 0 .	3 0 .	4 0 .	5 0 .	6 0 .	7 0 .	8 0 .	9 1

      200

      – 100

      Axial_ ch o rd

      0

      S tatic p ressu re (P a)

      S tatic p ressu re (P a)

      -2 0 0

      -4 0 0

      -6 0 0

      -8 0 0

      -1 0 0 0

      total pressure 20 total pressure 50 total pressure 70

      Fig.11. 20%, 50% and 70% at 10000

      rpm

      -1 2 0 0

      -1 4 0 0

      Axial_ ch o rd

      300.000

      250.000

      Head Vs Discharge

      s tatic pres s ure 20 s tatic pres s ure 50 s tatic pres s ure 70

      Discharge (lt/

      Discharge (lt/

      200.000

      Fig.10b Static pressure contours at 20%, 50% and 70% at 8000 rpm.

      1. Mean Span wise total pressure

         150.000

         100.000

         50.000

         0.000

         0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00

         Head (Pa)

         profiles

         Mean contours of span wise

         Series1

         Fig.12: Head vs Discharge

         The graph shows head vs discharge-

         total pressure component are shown in Figs for 10000 rpm , 8000 rpm, 6000 rpm, 4000 rpm and 2000 rpm respectively. The figures X axis represents axial chord and Y axis represents total pressure in Pa. the figures represents flow variations in 10000 rpm , 8000 rpm , 6000 rpm , 4000

         rpm and 2000 rpm at contours 20% , 50%, 70% span wise at outlet. Total pressure profile 20%, 50% and 70% at 10000 rpm and head vs discharge is shown in fig.11 and fig. 12.

         axis represents head in Pa and Y-axis represents discharge in m3 /s. The above graph shows there is no formation of surge and stall.

      2. RPM vs Mass flow rate

      The graph shows at different rpms (10000, 8000, 6000, 4000 and 2000) the

      behavior of fluid flow at outlet. If the rpm increases the flow at outlet will also increases. From the figure X-axis represents rpm and Y-axis represents mass flow rate in kg/s. Rpm vs Mass flow rate

      (10000, 8000, 6000, 4000 and 2000 rpm)

      is shown in fig.13.

      R P M v s M ass Flow R ate

      				rpm vs m ass flo w ra te

      				rpm vs m ass flo w ra te

      0 .0 0 0 7

      0 .0 0 0 6

      M ass F lo w R ate

      M ass F lo w R ate

      0 .0 0 0 5

      0 .0 0 0 4

      0 .0 0 0 3

      0 .0 0 0 2

      0 .0 0 0 1

      0

      2000 3000 4000 5000 6000 7000 8000 9000 10000

      R P M

      Fig.13. Rpm vs Mass flow rate (10000, 8000, 6000, 4000 and 2000 rpm)

5. Analysis was carried out for CFD cases for RPM of 10000, 8000, 6000, 4000 and 2000. It has been observed that all the cases are free from surge and stall. Velocity obtained from the CFD predictions of 35.46 m/s is achieved at outlet for the 10000 rpm case. There is no formation of wake in any of the cases. It has been observed that velocity of the fluid is directly proportional to impellers RPM.Correlation has been derived between Head and Discharge. Correlation has been derived between RPM and Mass flow rate.

   Future work should involve advancing the solution further in time for

   dynamic inflow or outflow boundary condition; and all the present simulations may be performed on a finer grid. Grid refinement may be done in order to obtain accurate results in both span wise as well as pitch wise direction.

6. Acknowledgements

   My profound thanks are due to the referee for his valuable and constructive comments and to Dr. Koya Purnachandra Rao for his stimulating discussions.

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