A THEORETICAL MODEL TO PREDICT CAVITATION INCEPTION IN CENTRIFUGAL PUMPS

Transcription

1 HEFAT007 5 th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics Sun City, South Africa Paper number: AA A THEORETICAL MODEL TO PREDICT CAVITATION INCEPTION IN CENTRIFUGAL PUMPS Ahmed A. B. Al-Arabi Higher Institute of Engineering Hoon Libya Sobeih M. A. Selim Faculty of Engineering, Minoufiya Uniersity Shibin El-Kom Egypt ABSTRACT This paper presents a theoretical model for the prediction of the incipient of caitation in centrifugal pumps. The model includes the physical fluid parameters and the real working phenomena at off-design condition. The parameters considered in the model were flow rate ratio, pump rational speed, water temperature, thermodynamic properties of water, nuclei and gas content, relatie elocity and incidence angle. The thermodynamic effect had a more complex expression compared with other parameters. The present model has been tested against extensie earlier published experimental results in centrifugal pumps at wide operating conditions. The comparison of the predicted net positie suction head at inception with the published data showed a good agreement was achieed. This agreement means that the roles played by operating parameters, off-design phenomena and thermodynamic properties of water are consistent with the present model. The results obtained from the present model make it possible to explain why there is a difference between the real net positie suction head alues and the theoretical ones in the preious published models. Therefore, the present model could help the pump user and designer to estimate the incipient net positie suction head at arious conditions. INTRODUCTION Caitation behaiour is one of the most important aspects to be considered in designing and operating flow machines. Pump designers wish to know the conditions for the appearance of caitation in pumps and the extent of the resulting damage. This because the caitation erosion is most likely between the caitation inception condition and performance breakdown. Prediction of these items remains difficult because of the complexity of the phenomena and because seeral factors affecting caitation in a certain applications remains unknown, such as the air content handled by the pump. Commercially aailable pumps must be able to accommodate such uncertainties and operate satisfactory oer a range of application conditions. Pump designers and users hae been concerned with caitation primarily when pumping water. Most experimental data and guidelines were taken with and apply to water. Howeer, water has ery unusual physical properties affecting caitation. It was considerably higher latent heat of eaporation and surface tension than those of other liquids. Attempts hae been made for decades to empirically correlate the caitation performance of centrifugal pumps with theoretical basis for their design. Pearsall [] deeloped a design procedure that allows optimum or best caitation performance to be obtained for pumps. He stated that the most important parameters to obtain good caitation performance are the geometric factors such as impeller eye diameter, hub/tip ratio and blade angles. The design method was based on potential flow, linearised theory with added empirical loss factors. This method applies essentially to the design condition. Gongwer [] analysed a number of impellers and obtained an empirical basis of design. His equation was of the form of equation () Cm U () NPSE K + K From the measurements to be assigned the alues of K.4 and K Lewis [3] data agree closely with results of Gongwer. More reliance is placed on the so-called inception, that is the point where the performance first starts to be affected by caitation. For these Lewis quotes K.8 and K 0.3, which correspond closely with Gongwer[]. Grist [4] presented a theoretical method based on spherical caities by which the olumetric performance of a caitating centrifugal pump impeller at best efficiency flow rate was mathematically modeled and at beyond,

2 breakdown in the net positie suction head generated head characteristic. The interaction of impeller geometry on the caity growth and collapse phenomenon was included in this analysis. Ardizzon and Paesi [5] presented a theoretical ealuation of the effect of the impeller entrance geometry and of the incidence angle on caitation inception in centrifugal pumps. His model based on the effect of the shape of the boundary layer surfaces and the flow pattern. Their model expressed the NPSHi as a function of caitation blade coefficient, meridional elocity at the suction side in the absence of pre-rotation, the shock losses at the inlet edge of the blade and the peripheral elocity at impeller inlet. The influence of incidence angle on caitation was shown as a function of the blade geometry. Schweiger and Kercan [6] conducted a theoretical study of the problem of the flow field and caitation condition in a pump at partial flows. They supposed that the flow conditions at part capacity are basically similar, regardless the geometrical shape of the centrifugal pump. Kutta-Toukowski theorem was used to simplify the conformal mapping. By means of this transformation the impeller with straight blades could be transformed into a circle around in which the flow conditions were known and mathematically analysed in details. Various methods hae been deised to analyse the thermodynamic effects. The methods for incipient caitation assume geometric similarity of the apour caity between fluids, allows ariation with temperature Stahl and Stepanoff[7], Salemann [8], Sparker [9], Ruggeri and Moore [0] and Zika []. Another method for incipient caitation was deried by a thermodynamic analysis, Jacobs []. While this methods seems quite reasonable, its theoretical results are in a gross numerical disagreement with experimental data. Numerical methods to design and to optimize pump hydraulics are used nowadays. Hirschi, et al., [3], Dupont P. [4], Dupont and Aellan [5], Hirschi, et al., [6], Brewer, et al., [7], Zgolli, R. and Azouz, H. [8]. Most of these numerical methods hae mainly focused on the efficiency and on the stability of head cure through a better control of recirculation and reduction of secondary flows. Neertheless, only few attempts to improe caitation in pumps using numerical approaches hae been done. NET POSITIVE SUCTION HEAD The net positie suction head (NPSH) can be estimated by applying Bernoulli, s equation between the pump inlet and a point immediately upstream of the blade, the NPSH will be, P P P P ΔC NPSH o o + + Loss g g g g + () ρ ρ Head losses are the sum iscous losses that appear between the pump inlet and just upstream of the blade leading edge and the incidence losses that appear when the flow angle at the impeller inlet differs from the ane angle β. The iscous loss may be expressed by (0.04 C /g) and the incidence losses or shock losses may be presented by (ΔC /g). In the presence of recirculation and when losses are taken into account the preious equation may be written in the following form, 3 BLADE CAVITATION NUMBER (σ b ) and SHOCK LOSS Caitation commences immediately downstream of the blade where the static pressure (P ) is minimum and the relatie elocity (W ) is maximum. Neglecting the loss between the leading edge of the blade and the point at which the caitation appears, the blade caitation number may be obtained from the experimental data. The blade caitation number is dependent upon the operating parameters such as flow rate ratio, rotational speed and water temperature. Al-Arabi A. A. B.[9] obtained an empirical relationship between the blade caitation number and these operating parameters from the extensie experimental results in a centrifugal pump at wide operating conditions. These empirical parameters are, for Q/Q opt 0.8 (4) forq/q opt > 0.8 (5) N max 3000 rpm and T max 363 K The predicted blade caitation number alues were compared with the experimental results obtained by Al-Arabi A. A. B.[9]. and good agreement was achieed. This comparison is shown in figure a, b, c and d. Al-Arabi A. A. B.[9] analysed a wide experimental data and obtained an empirical relationship for the shock losses in the form, C -.59 ln (Q/Q opt ) C ln (Q/Q opt ) 0.07 C ( Cm ) U ΔC NPSH (.04 + σ b ) + σ b + g g g (3) σ bi 0.56( Q/ Q opt ) ( N Nmax) ( T Tmax) σ bi 0.8( Q/ Q opt ) ( N Nmax) ( T Tmax) for (Q/Q opt <.0) (6) for (Q/Q opt >.0) (7)

3 At the design condition Q/Q opt and incidence angle is zero, then ΔC 0. The meridional elocity at the inlet of the blade with recirculation was obtained from Selim et al [0] as follow, Cm 3.(Q/Q opt )+0.65 (8.a) Cm / Cm 0.69 (Q/Q opt ) -.7 (8.b) Also the relatie recirculating elocity can be obtained from Selim et al [0] and is gien by, W.86 (Q/Q opt )+5.88 (9.a) W 6.05 (Q/Q opt ) (N) 0.03 (9.b) 4 THERMODYNAMIC EFFECT The boiling of liquid in the process of caitation is a thermal process and is dependent on the liquid properties such as the pressure, temperature, latent heat of aporization, and specific heat. Therefore when pumping hot water and other liquids the required NPSH will be changed, and caitation inception will be delayed by the thermodynamic effect. The thermodynamic effect can be understood through the equation of caitation coefficient (σ c ) which is gien by, P P σ c (0) ρ c The caity pressure is gien by, P c P + P g - ΔP () Substituting equation () into equation (0) and rearranging, the caitation coefficient this leads to, The deriatie of ΔP can be obtained as follows: w σ P P P Δ g P + () c ρ w ρ w ρ w ΔP P ( T ) P ( TR ) (3) For equilibrium condition, Q L Q V, then V L ρ L C p ΔT V ρ L (4) The local reduction in temperature difference ΔT can be expressed in terms of the local pressure drop ΔP as: dt Δ T Δ P dp (5) The Clausius Clapegron equation can now be used to approximate the slop of the apour pressure temperature cure as: dt dp T ( V V ) T ( ρ ρ ) L l L (6) For conditions remote or far from the critical point ρ L >> ρ and hence, dt T (7) dp L.ρ Consider the caity as sphere bubble, the olume of the apour is gien by V (8) V π R π R N n 3 3 The olume of the liquid layer surrounding the caity is gien by (9) The liquid layer thickness (δ) is a function of the thermal diffusiity of the liquid (D), and the aporization time (t) gien by, (0) It is stated by Preece [] that for R >> R o Rayleigh gies, At time (t) the bubble radius is gien by, R Since R is independent of time, and therefore R >> R o it follows that R R t () Substituting R from equation () into equation (), the bubble radius is gien by, Therefore, from the preious equations the alue of ΔP is gien by, l ρ ρ 4 S R N 3 n 3. R o ρ ΔP ( ) L (4) ρ L C p T 3D It must be known that the number of nuclei is a function of flow rate ratio and water temperature, then l / 3 ( 4πR N δ ) V L 4πR. δ n δ R R 4 3 R o S ρ. R L ( D.t ) S ρ. o L R o t o dt R t 4 ρ T ρ L L. ρ () (3)

4 N Q C Q opt n. Therefore ΔP is gien by, (5) (6) (7) Where, F, n and m are determined experimentally 4. Variation of Latent Heat with Temperature ( T ) Substitute equation (5) into ΔP equation yields 4 S 3 t Nn n R o Q P 3 ρ ( L) Δ C m L C p T Q opt 3D ρ ρ Δ P F ρ L [ L] C A change of state from liquid to apour at constant temperature also requires the input of energy, called the (latent heat of aporization). The latent heat of eaporation is the energy required to oercome the molecular forces of attraction between the particles of a liquid, and bring them to the apour state, where such attractions are minimal. The ariation of latent heat with water temperature is sited in steam tables at arious water temperatures and may expressed in an empirical form as follows, L ( T ) (8) The empirical relationship of (ρ /ρ L ) with temperature was found from steam tables and it has the following form; ρ / ρ L ( T ) ( 9) The ariation of specific heat with water temperature was found to be ery small which can be considered constant with temperature. 5 EFFECT OF TEMPERATURE ON THE GAS PRESSURE P T The gas pressure has a noticeable effect on the caitation inception where gas content playing a major effect during caitation condition. The gas pressure is a function of thermal conductiity, Henry s constant and gas contents. Each is subjected to temperature change. The form of the gas pressure equation can be written as, n Q Q opt m P gas K. K h (α + α ) (30) The ariation of Henry s constant with water temperature was obtained by Ueberfeld J., et. al [] and Washington Uniersity Courses [3]. Henry s law constant was found to be aried with temperature according to the following relationship, K h (T) (3) In a practical case where the quantity of each gas dissoled in water is less than the maximum amount possible at standard pressure, then gas is not released as the pressure is lowered until a pressure is reached where the quantity of gas present becomes the maximum possible amount which can be dissoled at this pressure. When this critical pressure is reached, gas is released and aeration of a caity would be expected in caitation experiments. The ariation of dissoled gases content (α) with temperature has been found according to information obtained from Omega Engineering Inc., [4]. The results may be fitted by, α ( T ) (3) The ariation of free gas contents (α ) has been found from the experimental results and it is expressed in the form,.05 Q α (33) Q opt It can be seen that (α ) is affected by the flow rate ratio only, while the effect of temperature was found to be ery small and can be neglected. Accordingly, the preious results can be summarised to obtain P g by the following equation, P gas K [( T )[( T ) + (450.4 (Q/Q opt ).05 )] (34) Therefore the change in ΔP due to thermodynamic effect is gien by, ΔP F [ T ] [ T ] [/C p ] [T -n ] [Q/Q opt ] m (35) 6 EQUATION FOR PREDICTING NPSHi The equations deeloped in preious sections are used to deelop an equation for predicting

5 NPSH at incipient caitation taken into account the arious operating parameters and the phenomena occurring at off design conditions in addition to the thermodynamic parameters of the water. The thermodynamic effect has a more complex expression compared with other parameters and for this reason its calculation seems more difficult. The expression of the predicting NPSH at caitation inception is obtained by combining the forgoing results This expression is gien by, NPSHi (.04 + σ b,i ) ( Cm / g ) + (σ bi U / g ) + ( ΔC / g ) - σ g + σ (36) NNPSHi [.04 + (0.8 (Q x 0.67 ) (N/N max ) (T/T max ) -. ] [( [0.69 Q X -.7 * ( Qx )] / g) + [(0.8 Q x 0.67 (N/N max ) (T/T max ) -. U / g ] + ( [-.59 (Log Q x ) 0.047] / g ) 0.703K[ T 4.34 ][( T 6.66 ) + (450.4[ Q ].05 X ] ρw F[ T ][ T ρw 0.33 ][ ][ T C p n ][ Q X ] m + (Q opt /Q)>0.8 (37) Where, Qx is the ratio. Equation (37) gies the NPSH i as a function of flow condition (flow rate ratio, rotational speed, water temperature), water thermodynamic properties and off-design phenomena (recirculation flow). 7 COMPARISON OF THEORETICAL NPSHi WITH THE EXPERIMENTAL RESULTS The predicted NPSH i alues were compared with the experimental results obtained by Al-Arabi A. A. B.[9], where the impeller has (N s 0.3, Z 6, β.5º and β 8º). These trends correspond well with the present model. Figure a,b,c and d shows the ariation of measured and calculated NPSH i with flow rate ratio at arious rotational speeds and arious water temperatures. A good agreement is in fact found between the measured NPSH i and the calculated NPSH i at wide range of flow rate ratios, pump rotational speed and water temperature. Figure 3 shows a comparison between the calculated NPSH i and all experimental data conducted by -Arabi A. A. B.[9] at arious operating conditions. This figure illustrates a good agreement between theoretical and experimental results with a correlation coefficient of The present model has been tested against arious published results as shown in figures 4 to. Figure 4 shows the comparison of the calculated NPSH i with experimental NPSH i found by Ardizzon and Paesi [5]. The comparison has been carried out for three different impellers A,B and C. Figure 5 shows the comparison of the prsesnt model with experimental results obtained by Hosien [6], and ery good agreement was achieed. Figures 6 to 8 show the comparisons between the calculated NPSH i and the experimental results published by Chalaby [7], and Pearsall [8] and good agreement was achieed oer wide range of flow rate ratio. Figures 9 and 0 show the comparison between the model and the published results obtained by El-Kadi [9] and Prasad [30] taken into account the ariation of NPSH i with water temperature. The comparison was carried out at flow rate ratio (Q/Q opt 0.8), and good agreement has been obtained. Figure shows the comparison between the present model and the published results obtained by Sebestyen et., at. [3], taken into account the ariation of NPSH i with pump rotational speed. Unfortunately the comparison could not been carried with some published results due to the absence of some important data in the published papers. This agreement between the present model and wide published experimental results means that the roles played by operating parameters, offdesign phenomena and thermodynamic properties of water are consistent with the present analysis. Howeer, the analysis presented in this paper are only a step towards better understanding the factors controlling the incipient caitation and gie an example how the way of modeling caitation inception should be. Neertheless, there still remains much to be understood. The results obtained from the

6 present model make it possible to explain why there is a difference between the real NPSH i and the theoretical ones in the published models. Some deiated points hae been appeared in the results. This deiation may be attributed to the experimental error in readings due to the presence of air and high angle of attack at ery low flow rate ratio. The program shows that the local pressure drop ΔP is influenced considerably by the temperatures, where both constants m and n hae two different alues equal to and 30.3, respectiely at T 50, while at T > 50 these constants are equal to and 7.4 respectiely. This difference in constants may be attributed to seeral parameters which are affected by temperature such the gas content, the surface tension, the number and olume of the bubbles and also the time required for growth of the bubbles. 9 CONCLUSION The predicted model of NPSH i presented herein deiates from earlier attempts in the following points: (a) It includes many parameters controlling the caitation inception such as flow rate ratio, rotational speed and water temperature. (b) It considers the effect of off-design phenomena on the meridional elocity, relatie elocity and incidence angle. (c) It includes the thermodynamic properties of the water (d) It considers the role played by the nuclei in the caitation inception. For the present models the predicted dependence of the NPSH i on the flow rate ratio, rotational speed and water temperature agree well with a wide earlier experimental published data. The analysis presented herein showed that the caitation inception is ery complex and therefore seeral simplifying assumptions hae been made according to the physics of the processes as currently understood. This is reflected in the deriation of the relationships. Therefore, the present model represents an addition to knowledge in this aspect, which could help the pump user and designer to estimate the NPSH i at arious operating conditions. NOMENCLATURE Cm Meridional elocity in non-recirculation condition Cm Meridional elocity in recirculation condition C P Specific heat d,d Inlet and outlet impeller diameters b Blade thickness D Thermal diffusiity of the liquid g Acceleration due to graity K Thermal conductiity K h Henry s constant L Latent heat N Pump rotational speed N n Number of nuclei N s Specific speed NPSH Net positie suction head NPSH i Inception of net positie suction head NPSE Net positie suction head P o Local static pressure P atm Atmospheric pressure. P c Caity pressure Pg Gas pressure P ms Local static pressure at the inlet of the pump. P Vapor pressure Q/Q opt Pump flow rate ratio. R Caity radius S Surface tension constant T R Temperature at caity layer T Temperature away from the caity surface t Vaporization time U Peripheral elocity V L / V Ratio liquid olume to apour olume W Relatie elocity at inlet of the pump in non-recirculation condition W Relatie elocity at inlet of the pump in recirculation condition Z Number of blades. Greek symbols β, β Blade inlet and outlet angles ρ Density of water ρ / ρ l The ratio of apour density to liquid density γ Specific weight of water σ bi Blade caitation inception number σ b Blade caitation number λ a Constant 0.04 ΔC Shock losses P Local cooling effect ΔT Local reduction in temperature Difference δ Liquid layer thickness α Dissoled gas content Free gas content α

7 REFRENCES [] Pearsall I. S., Design of pump impeller for optimum caitation performance, Proc. Inst. Mech. Engrs, Vol. 87, July 973, pp [] Gongwer, G. A., A theory of caitation flow in centrifugal pumps impellers, Treans. Am. Soc. Mech. Engrs.,V63, 94, pp [3] Lewis W. P., The design of centrifugal pump impellers for optimum caitation performance, Lnstn Engrs. Aust. Elect. Mech. Eng. Trans. EM6, (), 964, pp [4] Grist E., The olumetric performance of caitating centrifugal pumps- Part : Theoretical analysis and method of prediction, ImechE Journal of Institute of Mechanical Engineers, Vol. 00, No. A3, 986, pp , London. [5] Adrizzon G. and Paise G., Theoretical ealuation of the effects of the impeller entrance geometry and of the incident angle on caitation inception in centrifugal pumps, ImechE Journal of Institute of Mechanical Engineers, Vol. 09, 995, pp [6] Schweiger F. and kercan V., Flow and caitation in centrifugal pumps at partial loads, Mechanical Journal, Noember- December, No. -, 979, pp. -. [7] Stahl H. A. and Stepanoff A. J., Thermodynamic aspects of caitation in centrifugal pumps, Annual Meeting Chicago, III. Noember 3-8, of Tur. American Society of Mechanical Engineers. Manuscript at ASME Headquarters, 956, Paper No. 55-A-30. [8] Salemann V., 958, "Caitation and NPSH requirements of arious liquids", ASME, paper no. 58-pA8, December. [9] Spraker W. A., The effects of fluid properties on caitation in centrifugal pumps, Trans. ASME, J. Eng. Pwr., 965, pp [0] Ruggri R. S. and Moor R. D., Method of predicting of pump caitation performance for arious liquid temperature and rotatie speed, Technical note NASA D-59, Washington, D. C., June 969. [] Jacobs, R. B., Prediction of symptoms of caitation, Journal of Research of the National Bureau of Standards Engineering and Instrumentation, Vol. 65C, No. 3, July 96, pp [3] Hirschi R., Dupont Ph., Aellan F., Fare J. N., Guelich J. F., and Parkinson E., Centrifugal pump performance drop due to leading edge caitation: Numerical prediction compared with model rests, ASME Journal of Fluid Engineering, Vol.0, December 998, pp [4] Dupont P., Numerical prediction of caitation in pumps, Swiss Fedral Institute of Technology of Lausanne (EPFL), 000, pp.(59-65), winterthur, Switzerland. [5] Dupont P., and Aellan, F., Numerical computation of leading edge caity, CAVITATION 9, Vol. 6, 99, pp , Portaland, Oregon, ASME, Summer annual meeting. [6] Hirschi R., Dupont P., Aellan, F. Fare J. N., Guelich J. F., and Parkinson E., Centrifugal pump performance drop due to leading edge caitation: Numerical prediction compared with model rests, ASME Journal of Fluid Engineering, Vol. 0, December 998, pp [7] Brewer H., James C., Burgreen G. W., and Burg C. O. E., A design method for inestigating caitation delay, The 8 th International Conference on Numerical Ship Hydraulic, September 003, -5, Busan Korea. [8] Zgoli, R., and Azouz H., Numerical approach to the prediction of caitation in pumps, Fifth International Symposium on Caitation (CAV003), Osaka-Japan, Noember -4, 003. [9] Al-Arabi A. A. B., Caitation inception in centrifugal pumps, Ph.D. Thesis, Menoufiya Uniersity, Noember 005, Egypt. [0] Selim S. M. A., El-Kadi M. A., El- Mayit M. M. and Al-Arabi A. A. B., Recirculating flow in the suction side of the centrifugal pump, Engineering Journal, Helwan Uniersity, Faculty of Engineering Matria-Ciro, Vol. 98, April 005, pp. 4-39, Egypt. [] Preece C. M., Treatise on materials

8 [] Zika V.T., Thermodynamics of incipient caitation in centrifugal pumps, ASME Journal of Fluid Engineering, December 984, pp science and technology, Bell laboratories, lnc. Murray Hill, New Jersey Vol. 6, 979. [] Ueberfeld J., Zbinden, H., Gisin, N., and Pellaux J., Determination of Henry s constant using a photoacoustic sensor, J. Chem. Thermodynamics, Vol. 33, 00, pp [3] Washington Uniersity Courses, Volatility of aqueous solutes: Henry s Low constant, EnH 55 Winter, 004. [4] Omega Engineering Inc., The fundamental technical dissoled oxygen conductiity and resistiity, 004, USA and Canada. [5] Adrizzon G. and Paise G., Theoretical ealuation of the effects of the impeller entrance geometry and of the incident angle on caitation inception in centrifugal pumps, ImechE Journal of Institute of Mechanical Engineers, Vol. 09, 995, pp ] Hosien M. A. E., Caitation inception in centrifugal pumps, M.Sc.Thesis, Menoufia Uniersity, 986, Egypt. [7] Chalaby. A. A. and Thew M.T., Caitation in a small centrifugal pump: Effect of some ariations in impeller geometry and comparison of water with water-antifreeze mixtures, Proceedings of IAHR Symposium, 98, pp.-5, Amsterdam. [8] El-kadi M. A., Caitating in centrifugal pumps handling hot water, Eng. Res. Journal, Helwan Uni., October Vol.77, 00, p.p [9] Prasad R., Temperature effect on the caitation performance of centrifugal pumps, Proceeding of the Fifth Conference on Fluid Machinery, 975, Budapest. [30] Sebestyen Gy. And Szabo A., Qualificatie inestigation of caitation in pumps, Proceeding of the Eighth Conference on Fluid Machinery, 987, Budapest T 40 C Theoretical N 500 rpm N 800 rpm N 00 rpm N 600 rpm N 800 rpm N 3000 rpm T 0 C Theoretical N 500 rpm N 800 rpm N 00 rpm N 600 rpm N 800 rpm N 3000 rpm bi 0.60 bi (a) (b)

9 T 60 C Theoretical N 500 rpm N 800 rpm N 00 rpm N 600 rpm N 800 rpm N 3000 rpm T 80 C N 600 rpm bi bi N 800 rpm N 3000 rpm Theoretical ( c ) ( d ) Figure (a, b, c and d ) Variation of blade caitation inception number with flow rate ratio at different rotational speed and water temperatures N 800 rpm T 0 C N 600 rpm T 60 C N 900 rpm T 80 C N 900 T 0 C N 700 T 60 C N 800 T 90 C ( a ) ( b )

10 N 3000 T 0 C N 800 T 50 C 0.00 N 900 N 3000 T 70 C T 90 C 0.00 N 600 N 700 T 70 C T 90 C ( c ) ( d ) Figure ( a, b, c and d ) Variation of NPSH with flow rate ratio at different rotational speed and water temperatures.00 Theoretical NPSHi ( m ) Impeller A Impeller B Impeller C Ardizzon and Paesi results (995) Experimental Fig. 3 Comparison of calculated NPSH i with experimental NPSH i at arious operating conditions Fig. 4 Comparison of the present model with experimental results of Ardizzon and Paesi (995)

11 Hosien results (986) 6.50 Inhibited water Chalaby and Thew results (98) Fig. 5 Comparison of the present model with experimental results of Hosien M. (986) Fig. 6 Comparison of the present model with experimental results of Chalaby and Thew (98) /50 water-antifreeze mixture Chalaby and Thew results (98) Pearsall results (973) Fig. 7 Comparison of the present model with experimental results of Chalaby and Thew (98) Fig. 8 Comparison of the present model with experimental results of Pearsall (973)

12 Prasad results (975) El-Kadi results (00) Water temperature ( C) Fig. 9 Comparison of the present model with experimental results of El-Kadi (00) Water temperature ( C) Fig. 0 Comparison of the present model with experimental results of Prasad (975).05 Sebestyen et. al. (987) N (rpm) Fig. Comparison of the present model with experimental results of Sebestyen et., al. (987)