## Design and CFD Analysis of a CPU fan to determine mass flow rate at different speed

Design and CFD Analysis of a CPU fan to determine mass flow rate at different speed

Problem statement:

To validate a cfd code to perform a cfd flow analysis of a typical axial fan using sliding mesh method and to validate the results using affinity laws or fan laws.

Axial fan:

Axial fans are commonly used devices to induce a flow of fluid whose inlet and outlet is equivalently parallel to the shaft of the fans.

Axial fans are generally preferred for cooling and exhaust purposes majorly because of low pressure head and considerable higher flow rate.

The axial fans when operated induces a lower pressure gradient which induces the flow unlike centrifugal fans.

Abstract:

Fans used in cooling systems of computer peripherals are required to remove the heat produced by the hardware effectively. The design of blade profiles has to be done so as to improve its efficiency and flow rate. In this case study, a typical 3D model of the fan is subjected to transient case analysis using mesh motion and the flow rate is determined for each case with varying speed using ANSYS fluent solver. The results obtained from the solver are post-processed so as to obtain the graphical representation for comparison. Fig 1; The solid model of the domain. Fig 2: The dimensions of the fan.

1. GENERAL STEPS FOLLOWED IN CURRENT SIMULATION PROCESS

Pre processing The solid model is imported into the design modeler and rotating and stationary domains are created. ANSYS meshing module is used to create the Mathematical mesh for analysis and subsequently named selections are also assigned.

Processing – In this stage the mathematical model is solved for the various boundary conditions with a transient case solver and the solution data is saved in .cdat format so that it’s compatible to be opened in a post processor.

Post processing – In post processing stage, the results are loaded and post processed to view the differences.

2. PRE -PROCESSING:

Modelling of static and rotating domain using Space Claim:

The rotating domain is modelled using Spaceclaim modeller. The outer enclosure has a cylidrical cavity where the rotating domain containing the solid cavity of the fan is present. So that there is a sliding mesh motion between the stationary and rotating domain. Fig 3: The dimensions of the rotating domain.

Dimension of the rotating domain with a dia of 63.02 mm. and a clearance of 2.5 mm radially and 5 mm axially on either sides. Fig 4: The dimensions of the outer enclosure. Fig 5: The assemblage of full computational domain.

2.1  Meshing of the computational Domain:

Meshing:

Meshing for the domain is carried out using ANSYS meshing module. Mesh refinement is done using sizing options. The mesh options used are as follows

Mesh priority : CFD Fluent

Element size : 8 mm.

Growth rate : 1.2

Avg. element quality : .83329

No. of nodes : 41613

No. of elements : 216297 Fig 6: The cut section view of the mathematical mesh model. Fig 7: Non conformal mesh method in-between the stationary and rotating domain.

Body sizing options to capture proximity settings is used to improve element quality around the fan blades in the rotating domain. Fig 8: Element quality table for the mathematical mesh.

3. SOLVING THE MATHEMATICAL MODEL USING ANSYS FLUENT MODEL:

CASE 1 : when the same impeller of constant diameter is made to run at different angular velocities(R.P.M.)

Setting up the solver using ANSYS fluent module.

After successfully importing the module from ANSYS meshing module, the solution type is set to transient.

CFD model used was realizable K-e model with enhanced wall functions.

Fluid used : Air

Boundary conditions used :

Pressure inlet and outlet with gauge pressure equal to 0 Pa.

Symmetry conditions for side walls.

Setting up zone motion:

The rotating domain is selected and mesh motion is enabled.

The centre of axis is : ( 0 , 0 , 0 )

The rotation vector for axis is : ( 1 ,0 ,0 )

The speed of rotation is given as per the requirement.

Type of initialisation: Hybrid initialisation

SLIDING MESH METHOD:

In sliding mesh method, the computational domain is divided into a static and rotating domain such that the boundary conditions for rotating devices need not be defined explicitly.

This method in ANSYS Fluent can be used to effectively model both translational and rotational domain.

The mesh settings hugely depend on the time step value. Hence it is recommended to use a minimal value of time step until the solution moves towards steady solution, hence this method is computationally expensive.

Solution and convergence:

Time step size: 0.05 seconds since the mesh is not very refined, a moderate time-step would produce good results. Although the solution was begun with a lower timestep of 0.005 seconds.

Convergence criteria

It is assumed if the mass flow rate remains fairly constant, along with reducing values of the residual plot, convergence is attained. Fig 9: typical residual plot for the simulation.

In the solver, Report files and plots were created in order to study the time dependent nature of mass flow rate through a plane that coincides with the face of the rotating domain. Fig 10: The mass flow rate Report plot for 1500 R.P.M. Angular velocity.

The data file for each and every time step is stored in .cdat format so that it can be later loaded up in ANSYS CFD Post.

4. CFD POST PROCESSING OF RESULT USING ANSYS CFD POST:

The initial state of the solution is loaded up in Post processor software. The velocity and pressure at upstream and downastream of the fan are taken as the surface averaged value from the post processor. The parameters such as thrust, power and efficiency are calculated from Slip stream theory. Fig 11. The streamline plot for 1500 R.P.M.  flow starting from inlet zone. Fig 12. The velocity contour plotted on a plane paralell to the axis of fan. Fig 13. The Pressure contour with user defined range for pressure value. Fig 14. The vector plot for 1500 R.P.M.

Slipstream theory:

The slipstream theory is based on Bernoulli’s principle and continuity equation. The assumption made is the propeller is a section plane and has negligible thickness. The upstream and downstream values of the propeller and termed with suffixes 1 and 2 respectively. The values of velocities calculated from the parallel faces of the rotating domain are termed as c1 and c2 respectively.

Let D be the diameter of the fan.

Area of flow considered A = π/4*D2    m2

Mass flow rate is given by m0 = ρ*A*C    Kg/s

Thrust F = A*(P2 – P­1) = 0.5* ρ*A*(C22 – C12)  N

From Bernoulli’s principle,

The pressure gradient can be calculated as follows

P2 – P1 = 0.5*ρ*(C22 – C12)  Pa

As there is no heat transfer during the whole process, the total change in stagnation enthalpy is

Δh0 = 0.5*(C22 – C12)  J/Kg since the change in specific enthalpy is negligible

The Ideal power requirement Wi = m0* Δh0  Watts.

The actual power requirement  Wa = Thrust*Cu Watts.

Efficiency of fan η    = Actual Power / Ideal Power

= 0.5*ρ*A*(C22 – C12)*C1 / ρ*A*C*0.5*(C22 – C12

= C1/C

C is the mean flow velocity given by m0 = ρAC where, m0 is the mass flow rate.

The cross section area of rotating domain is A = π/4 * (0.06302)2  m2

Where, diameter = 63.02 mm or 0.06302 m.

The values of c1 and c2 are tabulated from the post processor.

Applying Bernoulli’s principle, we get pressure difference.

P2 – P1 = .5*ρ*(C22 – C12)  in pascals.

Ρ = 1.225 Kg/m3.

 S.no 1 2 3 4 5 6 Angular velocity (N) RPM 250 500 750 1000 1250 1500 Mass flow rate (m0) Kg/s 0.00038 0.00085 0.00125 0.0015 0.0019 0.0024 Mean velocity (C) m/s 0.099449 0.222452 0.327135 0.392562 0.497245 0.6281 Upstream velocity (c1) m/s 0.0725503 0.174402 0.272568 0.359127 0.439903 0.502935 Downstream velocity (c2) m/s 0.121885 0.244046 0.35832 0.450038 0.606823 0.733266 Pressure difference (H) Pa 0.00587535 0.017849 0.033136 0.045056 0.107016 0.174404 Actual power (P) Watts 1.33e-06 9.71e-06 2.82e-05 5.05e-05 0.000147 0.000274 Efficiency (η) % 72.9522 78.3998 83.3197 91.4828 88.4679 80.0072

Table 1: The parametrs calculated using Slip stream theory.

The data obtained from the post processor is plotted using Microsoft Excel spreadsheet software.

4.1 Graphical representation of the tabulated data: Fig 15. Mass flow rate Vs. R.P.M. value for different speeds. Fig 16. Pressure difference Vs. R.P.M. value for different speeds. Fig 17. Actual Power Vs. R.P.M. value for different speeds. Fig 18. Efficiency Vs. R.P.M. value for different speeds.

4.2 Validation of results using AFFINITY LAWS:

Fan laws or Affinity laws:

The fan law is also called by Affinity law or pump law. These laws are used to bring out the proportionality between various parameters in fans, pumps such as the shaft speed, Discharge, Pressure head.

The main advantage of Affinity laws is it’s not only applicable to fans and blowers, but also to complicated turbo-machinery. These concepts are abundantly used in heating ventilation and air-conditioning (HVAC) and also in hydraulics.

The affinity laws are formulated from Buckingham’s π theorem. The formulation from the theorem states that “For a Dynamically similar blades having different diameters running at different speeds, by knowing the rate of discharge or pressure head for one system, the same can be found out for any other system given that dynamic similarity is maintained.

4.2.1 Law 1: Flow is proportional to Angular speed

(Q1/Q2) = (N1/N2)

The graph between the angular velocity and flow rate is linear and when plotted is a straight line.

Verification of Flow rate:

Q1  = N1/N2*Q2 = 250/500*0.00085 = 0.000425 Kg/s.

Error percentage = (0.0000425 – 0.00038)/0.00038 = 11.84 %

Q3  = N3/N4*Q4 = 750/1000*0.0015 = 0.001125

Error Percentage = (0.00125 – 0.001125)/0.00125 = 10%

4.2.2 Law 2: Pressure gradient is proportional to the square of Angular speed

(H1/H2) = (N1/N2)2

H5 = (N5/N2)2 * H2 = (1250/500)2 * 0.017849 = 0.11155625 Pa.

Error percentage = 4.243 %

4.2.3 Law 3: Power is proportional to the cube of shaft speed

(P1/P3) = (N1/N3)3

Verification of theoretical power:

P6 = (N6/N3)3 * P3  = (500/1000)3 * 2.82E-05 = 2.256E-4

Error percentage = 17.66%

Inference:

The simulation has been carried out to determine the characteristics of the fan when operated in different angular velocities.

It has been theoretically and analytically seen that when operated in the range of maximum efficiency range, the obtained results are very closer to ideal solution indicated by reduced error percentage.

The curves are used to identify the working range and capacity of each fan so that they can be used in the specific applications.

5. CASE 2: When the Angular speed is constant with varying Diameter ratio:

When the Angular speed is held constant:

In this case the model of the fan along with the Enclosure is scaled up and by factor of 1.5, 2, 2.5 and the corresponding parameters such as Mass flow rate, Pressure gradient, Efficiency are found out for each given cases.The simulation is carried out with a constant velocity of 500 R.P.M.

The initial size of the model used is considered as Scale 1 and the model is scaled accordingly to ratio 1.5, 2 and 2.5 respectively using Solid modelling package. Fig 19. Dimensions for Diameter ratio 1.5. Fig 20. Dimensions for Diameter ratio 2. Fig 21. Dimensions for Diameter ratio 2.5.

5.1 Meshing

The mesh settings for this case was carried out in a similar fashion as of the first case.

Global mesh size was increased proportionally from the first case in the factor of 1.5, 2 and 2.5 respectively.

Proximity capture is enabled for edges with no. of cells across faces set to 1.

 Diameter ratio 1.5 2 2.5 No. of nodes 36469 39555 39808 No. of elements 186779 202423 204368 Minimum quality 22% 14% 13%

Table 2: Mesh parameters comparison for all the conditions.

The mesh size was scaled accordingly in order to maintain a cell count of 200K in order to make the simulation easier to run for the given hardware specifications. A grid independency test was carried out in order to look for the converged results for the original unscaled model at 1250 R.P.M. The results for different mesh sizes from 15 mm. is shown in the following graph. Fig 22. Grid Independency test for Diameter ratio 1 with angular velocity 1250 R.P.M.

5.2 Solver:

Realizable K-e model with enhanced wall treatment is used. Sliding mesh method is employed for The rotating domain.

The same equations used in section 4 were used to extract data from post processor and Slip stream theory is used to calculate power, efficiency for all cases.

5.3 Results from calcuation:

The results from the calculation is tabulated using function calculator in cfd post and tabulated as follows.

 S.no 1 2 3 4 Diameter Ratio 1 1.5 2 2.5 Mass flow rate (Kg/s) 0.00085 0.0029 0.00675 0.0129 Area of cross section (m^2) 0.00311922 0.005928 0.0115645 0.0185465 Downstream velocity (m/s) c2 0.174402 0.259949 0.368193 0.452238 Upstream velocity(m/s) c1 0.244046 0.437232 0.541179 0.643723 Mean velocity (m/s) C 0.222452 0.399349 0.476475 0.567795 Pressure Gradient (Pa) 0.017849 0.075704 0.096352 0.128539 Actual Power (Watts) 9.71e-06 0.000167 0.00041 0.00108 Efficiency (%) 78.4 65.093 77.274 79.64

Table 3: The parameters tabulated for various diameter ratio.

5.4 Graphs and comparison:

The results obtained for original model and scaled models with constant Angular velocity are compared by plotting the obtained data. The Diameter ratio is plotted on the x-axis for all graphs. Fig 23. Mass flow rate Vs. Diameter ratio. Fig 24. Pressure gradient Vs. Diameter ratio. Fig 25. Actual power required Vs. Diameter ratio. Fig 26. Efficiency Vs. Diameter ratio.

It can be noted from Fig 26, 25, 24 and 23 that the cases actually do not match with the correlations of affinity laws. It is because the model of the fan is only scaled up but it cannot be surely stated that dimensional similarity is maintained.

INFERENCES FROM AFFINITY LAWS:

• Comparison of results is best suited if the efficiency of the two models are fairly the same even if the dynamic similarity is maintained.
• Assumes that pump efficiency is always constant. Which is not true in all cases. This leads to errors in calculation if a real case system is studied.
• When this law is applied to flow components with constant diameter (case 1), then the results from affinity law relations can be accurately correlated to experimental or numerical data.
• If the model of the fan is scaled up accordingly, keeping the speed constant, the errors in the result may increase drastically.

6.RESULTS AND DISCUSSIONS:

From the results and inferences from Affinity laws, it can be ssen that the maximum error percentage obtained in CASE 1 was 17% when numerical results were compared. This is because of the fact that affinity laws can be only used for very low R.P.M. ranges and when the efficiency is constant, which is not possible in our case.

From the numerical simulation it was found that for the first case where the diameter is constant, the trends for the graph were closer to values predicted using affinity laws. But for the second case, since dimensional similarity and constant efficiency cannot be maintained, the results does not conform to affinity laws.

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