Numerical and Experimental Study on the Pressure Distribution in a Volute of High-Speed Centrifugal Fan with Impeller- Volute interaction

This paper shows a numerical simulation in capturing the dynamic and static pressure effects inside a centrifugal fan due to the impeller-volute interaction. The fan used in this study is a single-stage machine with an unshrouded impeller and external volute. Three volute tongue designs were investigated. Volute C had a full tongue and did not allow any flow recirculation. Volute B had a reduced tongue length thereby opening the recirculation port. Finally the tongue of volute A had a rounded leading edge to make it less sensitive to off-design flow conditions. For the numerical simulation, the viscous Navier-Stokes equations are handled with unstructured grid and the relative reference frames technique is applied to take into account the impeller-volute interaction. The data obtained allow the analysis of the main phenomena existent in these fans, such as: pressure changes in the volute for different flow rates and the secondary flow generated in the volute due to the width change between the impeller and the volute. Numerical results are compared with the experimental pressure data measured in the volute and agreement is found show that at low flow rates ,the volute decelerates the airflow leading to an increase in pressure throw the volute. At these low flow rates separation or flow unsteadiness can occur from the underside of the tongue and the strength of the instability increased when the mass flow rate was reduced further. The pressure fluctuation for various mass flow rates is a non-periodical nature and it is manifest as the broad band components in higher level of random frequency (up to nearly 500 Hz).This investigation concentrates on the measurement of the flow characteristic in the volute casing and the volute tongue configuration.

S ubscri pt s 1 = Ent r y t o t he i m pel l er 2 = Ex i t from t he I i m pel l e r i = Im p el l er

INTRODUCTION
Flow in centrifugal machines produces a complex three-dimensional phenomenon involving turbulence, secondary flows, unsteadiness, etc. (Brennen, 1994) [1]. Moreover, the geometry is complex and asymmetric due to the volute shape. The relative movement between impeller and volute generates an unsteady interaction which affects not only the overall performance (flow structure, losses), but is also responsible for pressure fluctuations, Which are one of the most Important sources of vibration and hydraulic noise (Dong et al., 1997) [2] . impellers of centrifugal pumps with volute casings at operating in off-design conditions are subjected to some static radial thrust, due to the non-uniform distributions of pressure and moment flux around the impeller (Rolling et al., 1960) [3].
Some authors (Kaupert et al., 1999) [4] have measured the unsteady pressure field inside the impeller of a centrifugal pump using piezoresistive pressure transducers and a telemetry system. They found amplitudes particularly high at the trailing edge of the blades (pressure side) and relative values up to 35 percent of the pump head at off-design conditions. Another important contribution to the understanding of the unsteady pressure field in the near-tongue region of the volute has been reported by (Whitefield et al., 2000) [5]. They used Particle Tracking Velocimetry (PTV) complemented with pressure measurements to measure the velocity distribution vicinity of three volute tongues of centrifugal fan. It was found that separation eddy (swirling, reverse flow) exists down stream of the leading edge of the tongue and that the flow separation from the leading edge of the tongue was reduced by the design modifications. Parrondo et al. (2000) [6] presented an experimental study on the unsteady pressure centrifugal pump with spiral volute casing to measure and analyze the static pressure and the fluctuating pressure field existing in the volute. The results show that the static pressure around volute is uniform for the best efficiency point, but it exhibits either a maximum for lower flow rates or a minimum for higher flow rates . The pressure amplitude is small in the best efficiency region, and it increases fast in the region just behind the tongue for low and high flow rates.
Both experimental and numerical approaches have been reported and have contributed to the understanding of the highly complex flow interactions that occur in a centrifugal volute. Hagelstein et al. (2000) [7] studied the flow in a centrifugal compressor volute. The measurements were carried out at the diffuser exit. Several peripheral positions in the volute at the different levels of stage performance were located to carry on the measurements. The flow at the diffuser exit results in a forced vortextype secondary flow inside the volute with an increase of swirl velocity from the vortex center to the volute walls. The results were compared with those obtained using the numerical results and agreement is observed. CFD (computational fluid dynamic) has proven to be a very useful tool in the analysis of the flow inside volute casing, both in design and performance prediction. Much research has been carried out in the last years and used different techniques. Croba et al. (1996) [8] used relative reference frames technique to solve the unsteady flow in the casing while Blanco et al. (2000) [9] and Gonza`laz et al. (2002)[10] used sliding mesh technique, which has been applied to turbo machinery flow. However, due to the difficulties of the task, most of studies have been carried out with strong simplifications of the problem either in the geometry or in the flow characteristics. Research is slowly tending toward more complete simulations.
The purpose of the present simulation is to show a numerical study of a centrifugal fan for three tongue configurations and for different mass flow rates taking into account the complex geometry and the turbulence of the flow. It has been done with the commercial software package, FLUENT 5.3. This code uses the finite volume method and the Navier-Stokes equations with the ability to handle unstructured grid, including relative reference frames and making unsteady calculations with moving meshes.

MODEL DESCRIPTION AND COMPUTATIONAL METHOD
Although predictions on the unsteady flow field are always valuable, numerical simulation of centrifugal fans is not easy due to the usual CFD difficulties: turbulence modeling, flow separation, boundary layer (Lakshminarayana, 1991), etc. Beside that, there are also specific problems, as:  Extremely complex geometry: a great number of cells is needed and, due to skew ness, usually unstructured grids give better convergence than structured ones.
 Energy transfer is generated mainly by the centrifugal force in the impeller. A cascade simulation is not valid and these force source terms must be included in the equations of the moving zone.
 The interaction between impeller and volute requires an unsteady solution process. In addition, the blade position with respect to the volute tongue must be taken into account.

Fan, Geometry and Grid:
Geometrical discrimination of the centrifugal fan is made for the numeric treatment, and computational grid is generated using the FLUENT preprocessor Gambit. In a pre-step, the walls limiting the airflow space are separated to form the volute and some more auxiliary edges needed for forming inner faces for impeller are constructed in Gambit. This is helpful since the complete grid is built up as block-structured.


Unstructured triangular cells are used to define the impeller zone and volute zone. Once the geometry is defined, the model is ready to be simulated. A view of the generated grid for three cases can be seen in Figure (1) while detail of surface between impeller and volute defines the grid interfaces (interior) needed for the relative rotation of the impeller. The moving reference frame technique provided by FLUENT allows relative motion of the impeller grid with respect to the volute during simulation. Grid faces do not need to be aligned on both sides. The impeller and volute grid for three cases is shown in Table (1).

Al-Raf i d ai n E n gin eeri n g
Vol .20 No. 5 O ctob er 2012 72 The CFD approach allows for simplifications of the problem by considering : -A fixed topology of the rotating wheel -Centrifugal and Carioles forces in the wheel region -The air as incompressible -Turbulence as fully modeled The steady state solution is obtained by solving Navier -Stokes equations with the implicit module of the CFD system, including the centrifugal force source in the impeller and the unsteady terms: with bold characters denoting vector quantities and the operator is the velocity vector,  is the shear stress tensor and p is the pressure.
In the proposed CFD approach, two domains are considered, one is in the laboratory reference frame, and the other is calculated according to a rotating reference frame, i.e. centrifugal and Coriolis forces are added to Eq. (2): Where x is the nodal coordinate vector; Xo is the center of rotation;  is the angular velocity vector (that is, the angular velocity of the rotating frame). The above equations are solved using the finite element technique.
The turbulence behavior of the flow is simulated with the standard k- model.
Turbulent intensity is not measured it is estimated to 5%. The pressure velocity couplings are calculated through the SIMPLE algorithm. Second order, upwind discretization have been used for convection terms and central difference schemes for diffusion terms.

Boundary Conditions:
The modeled boundary conditions are considered with more physical meaning for turbo machinery flow simulations, that is, total pressure at the inlet and a variable static pressure proportional to the kinetic energy at the outlet. The flow rate is changed by modifying the static pressure to kinetic energy ratio at the outlet condition, which simulates different closing positions of a valve. Some tests are carried out using a fixed flow rate at the inlet. Although it provides a better stability and faster convergence, this condition is found to be less physically correct, because the pressure obtained are quite different to the measured ones.

ANALYSIS OF NUMERICAL RESULTS.
The possibilities of the numerical simulation in the study of the flow inside a fan are wider than the experimental ones. In particular, results corresponding to the pressure distributions inside the impeller and near-tongue region and the flow in the volute are presented, and the unsteady calculation combined with the moving reference frame technique has proved to be a good tool to investigate the impellervolute interaction.

Static Pressure inside the Fan:
The st at i c pr ess ure di st ri but i on on t he i m pel l er and fa n casi n g on t h e mid-pl ane for t hree cases (A, B, C ) for vari ous m ass fl ow rat es are shown i n Fi gure . (4 ) . t he st at i c pressure ri se t hrough t he fan i s cl earl y seen i n this fi gure, as ar e t he radi al pr essure gra di ent s.
The s t at i c pr essu re has a m i ni m um val ue at t he i m pel l er e ye , and around t he i m pel l er at t he angul ar posi t i on ab out (Ø=95°) for c as e A and (Ø=40°) for cas es B and C . Thi s i s because t he t ongue confi gurat i on affect s t he vol ut e are a (vol ut e pressure ) whe re vol ut e pressure act s back on t he i m pel l er. The st at i c pressure i nc reas es as t he an gul ar posi t i on around t he vol ut e i ncreas es ex cept at posi t i on Ø=60° for cas e C .
In cases B a nd C , t he hi gher p ressu res can b e observ ed upst ream of t he l eadi ng ed ge of t he vol ut e t ongu e (st a gnat i on poi nt ). Al so, i t can be s een t hat t he pr essur e di s t ri but i on over t he su ct i on pressur e si de of t he bl ad es i s cl earl y appr eci at ed, and t he st at i c pressure i ncre ases as t he m ass fl ow decre as es . The resulting distributions, shown in Figure (3), characterize the dynamic behavior of the impeller-volute interactions on the mid-plane of the fan for three cases for different flow rates. From this figure, it can be seen that the dynamic pressure in the impeller increases as the radius ratio (radial gradients) increases, and the dynamic pressure magnitude is greater on the pressure side of the blade channel than on the suction side. On the suction side, a greater amount of disorder seems to exist which, could be caused by a localized recirculation zones formation in the impeller channels. The dynamic pressure within a fan impeller grows in magnitude as the mass flow rate is further departed from the lower flow rate region (0.0091kg/s , and non flow), and as the trailing edge (r/ri= 1) of a blade is approached.
At nominal flow rate (i.e. m˙=0.03046 kg/s), the dynamic pressure in the fan is large since the volute pressure distribution is small and uniform. At lower flow rate, the volute static pressure distribution rises; this manifests itself in the impeller as a dropping dynamic pressure after the blade passage rotates past a tongue (downstream of the tongue location about (Ø=90°) for case A and about (Ø=60°) for case B and C). Therefore, it can be seen how the tongue has no dynamic effect on flow rates near the nominal one, whereas it affects quite severely the dynamic pressure for off-design conditions. The unsteady pressure field in the volute caused by the impeller rotation (i.e., jet-wake flow), is mostly steady in the impeller frame. Also, in this figure it can be observed that, the dynamic pressure has a maximum value in case

Vol u te d esi gn s an d measu re men t L ocati on
The col l ect i ng vol ut e whi ch i s part of t he cent ri fugal fan, i t i s a ful l y i nt egrat ed part of t he case and i t s cover.
Three vol ut e t ongue des i gns are i nvest i gat ed. In t ype A, t he l eadi ng edge of t he t ongue i s rounded, i n t ype B, t he t ongue i s cut back, al l owi ng for fl ow reci rcul at i on. Fi nal l y, t ype C , where a ful l t ongue i s used, i t i s al m os t i m possi bl e for t he ai r t o reci rcul at e ar The det ai l s of t he gap bet ween t he vol ut e t ongue and t he i m pel l er for t hree vol ut e t ongue confi gurat i on are shown i n Tabl e (2) and Fi gure (6).The m eas urem ent s for t he present s t udy are carri ed out on t he frontwal l of t he fan casi ng. S everal m eas urem ent t aps are arranged on t hi s wal l , as shown i n Fi gure (2). Thes e t aps are di st ri but ed on radi al and angul ar posi t i ons, as fol l ows ; 1. Ei ght t aps are arranged al ong a radi al pat h at angul ar posi t i on of 60° on the shroud.

Comparison with Experimental Data
The results of the numerical simulation were recorded for the same locations considered in the experiments. The static pressure distributions around the volute for three cases (A, B, C) for three mass flow rates are compared in Figure (8). Agreement between the numerical and experimental data is good, although the numerical result is obtained for a complete revolution of the impeller and the experimental is an instantaneous measurement. Fi gu re .8 : Co mp ari son of th e stati c p ressu re arou n d th e vol u te f or th ree c ases Some differences have arisen in the comparison between the numerical and experimental static pressure in the volute of the tested centrifugal fan, especially near tongue region. Also, from this comparison it can be concluded that, the accuracy of the prediction of the circumferential pressure distribution is better at lower flow rate, which leads to the assumption that the intensity of the dynamic pressure is a source of inaccuracy in the calculation.

Di s cu ssi on of Resu l ts
The s t at i c pressure and pres s ure fl uct uat i ons at di fferent poi nt s on t he cent ri fugal fan casi ng are det erm i ned by wat er m onom et er or by t he out put of t he pressure t ransducer. The m ass fl ow rat e val ues whi ch are used i n t he res ent st udy cover t he val ues, nearl y nonfl ow , 0.0091 kg/ s, 0.0168 kg/ s , 0.023 kg/ s, 0.03046 kg/ s . These val ues are chos en arbi t rari l y but t he m ax i m um val ue of t he m ass fl ow rat e (0.03046 kg/ s) i s l i m i t ed by t he cont rol val ve and fan desi gn.

3.1O veral l Perf orman ce an d S tati c Pressu re Measu remen ts
Fi gure ( 9) show t he di fference bet ween t he perform ance m ap of t he fan for t he t hree cases ( A , B , and C ) , whi ch i s l arger at l ower m ass fl ow rat e , but t hes e di fferences di sappear as fl ow rat e i s i ncreased . At t he l ow fl ow rat es, cases A and B provi de an i m proved pressu re com pared wi t h t hat for case C .

Pressure Fluctuation measurements
Fi gure ( 11)  fl uct uat i on at posi t i on Ø = 240 o for t he t hree cases i s hi gher at radi us rat i o r/r I = 0.727, and case C has hi gher pressure fl uct uat i on t han cases ( A and B ) .Thi s fi gure al so shows t hat at radi us rat i o hi gher t han (r/ r I >1), t he pres s ure fl uct uat i on i s nearl y const ant CONCLUSIONS 1. The impellervolute interaction in the centrifugal fan is successfully predicted by a numerical model using finite volume commercial code. The qualitative numerical data analysis shows that the main flow phenomena are adequately simulated: static and dynamic pressure variation around the volute and impeller, changes with flow rate . 2. Agreement between the numerical and experimental static pressure data in the volute is fairly good; some differences have arisen, especially near tongue region and at higher flow rate. 3. The unsteady calculation combined with the moving reference frame technique has proved to be a good tool to investigate the impellervolute interaction. 4. The pressure fluctuation for various mass flow rates is non-periodical nature, as the mass flow rate is reduced, the pressure fluctuation amplitude increases. 5. The higher level of random frequency of pressure fluctuation for various mass flow rates is manifested as the broad band components (from 0 Hz to about 500 Hz). 6. The pressure fluctuation strength value around the volute for three cases (A,B and C) is maximum at Ø = 30 0 and is nearly constant at other position toward the volute exit. 7. The maximum pressure fluctuation in the radial direction for various flow rates and three cases is observed at radius ratio before the trailing edge of blades of the impeller (from r/ri = 0.727 to r/ri = 0.909).