Improvements in the prediction of performance of ...

Improvements in the prediction of performance of centrifugal slurry pumps handling slurries B K Gandhi 1, S N Singh2 and V Seshadri2* IMechanical Engineering Department, SGSITS, Indore, India 2Department of Applied Mechanics, Indian Institute of Technology, New Delhi, India

Abstract: A methodology based on a loss analysis procedure has been presented to predict the performance of centrifugal slurry pumps handling solid-liquid mixtures. Various energy-head losses in the pump have been estimated using analytical models based on the pump geometry and the properties of suspended solids. The proposed methodology accounts for the constructional differences of the slurry pump as compared with the conventional pump. The predicted values of head over the operating range of flowrates of the pump have been found to be in reasonable agreement with the measurements made at various rotational speeds and solid concentrations. Keywords: centrifugal slurry pump, multi sized particulate, pump geometry, leakage loss, impeller slip loss, friction loss, performance

NOTATION a A b Cv Cw d dh Dw E f Frm g h !1h H

k1 characteristic local acceleration (m/s2) flow area at the impeller-volute (m2) impeller width (m) volume concentration of solids (fractional) weight concentration of solids (%) representative solid particle size (m) average hydraulic diameter for the flow passage (m) impeller eye diameter at the leakage flow path (m) a constant defined in reference [23] friction factor modified Froude number gravitational acceleration (m/s2) head loss due to flow phenomena (m of flowing fluid column) additional head loss due to flow of slurries (m of flowing fluid column) total head developed by the pump (m of water column, or mwc)

k2 L N Ns Q Qd r Re Rem S Sc U v* V Vw V'w W

The MS was received on 2 June 1999 and was accepted after revision for publication on 20 October 1999. *Corresponding author: Department of Applied Mechanics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India. A06499

@ IMechE 2000

Wo

z

volute area variation coefficient for linear variation of casing area with angle (m2/rad) flowrate coefficient = flowrate through impeller/2n (m3/s rad) length (m) revolution per minute (r/min) metric specific speed

=N

(r/min)

x Qg.5

(m3/h)IHo.75 (mwc) flowrate (m3/s) flowrate delivered (m3/h) impeller radius (m) Reynolds number modified particle Reynolds number specific gravity radial running clearance between impeller and casing (mm) impeller peripheral velocity (m/s) friction velocity (m/s) flow velocity (m/s) whirl component of absolute velocity of liquid at the impeller (m/s) corrected whirl velocity at the impeller (m/s) modified particle settling velocity for solid concentration and local acceleration (m/s) unhindered particle settling velocity (m/s) number of vanes in the impeller Proc Instn Mech

Engrs Vol 214 Part A

474

fJ K V (J

B K GANDHI, S N SINGH AND V SESHADRI

vane angle (deg) average surface roughness (m) kinematic viscosity (m2/s) slip factor

Subscripts

1 2 d dp f Imp 1 m mIX 0 s sh slip th vol

w

impeller eye impeller tip delivery design point friction ith casing element impeller leakage mixture of liquid-solid (slurry) mIxmg at volute tongue solid shut-off impeller slip theoretical volute water

1 INTRODUCTION Centrifugal slurry pumps are being used extensively for short and medium distance transportation of homogeneous and heterogeneous mixtures of solid materials by pipelines. The pump characteristics playa key role in the reliability of the transportation system. Evaluation of the pump performance experimentally [1-3] to establish its dependence on various properties of solid material and slurry is expensive and time consuming. Hence it is necessary to resort to the prediction tools available. The prediction models developed for conventional pumps are not applicable directly to slurry pumps as the latter differ in construction [4, S]. In the absence of any reliable prediction tool, the performance characteristics of slurry pumps are generally evaluated with clear water and then modified to include the effect of solid particles in terms of head and efficiency ratios [S,6]. Many investigators [1,7-13] have proposed correlations for estimation of these ratios, quantifying the dependence on various parameters such as solid concentration, pump geometry, flowrate and solid properties such as specific gravity, particle shape, size and size distribution. Most of these correlations are empirical in nature and have been developed on the basis of experimental data obtained near the best efficiency point (BEP) for a limited number of pumps. It is also seen that the efforts are mostly directed towards estimation of the head ratio as the value of the efficiency ratio is normally assumed to be the same as that of the head ratio. Proc Instn Mech Engrs Vol 214 Part A

Roco et al. [14] were the first to apply a loss analysis procedure for estimating the head-capacity characteristics of centrifugal pumps designed to handle solid-liquid mixtures. They classified the head losses into three categories, namely local, secondary flow and friction. The head developed was estimated by subtracting these losses from the theoretical head. Further, they also developed semi-empirical correlations to estimate the various head losses for clear liquid (water) and then incorporated the additional head losses for solid-liquid mixtures from the knowledge of the clear liquid losses and non-dimensional numbers characterized by the slurry properties and the pump specific speed. They have predicted the head-capacity characteristics of seven pumps having different geometries and specific speeds. They found the predictions to be reasonably accurate for handling silica sand up to 35 per cent concentration by volume. The pumps selected had a narrow running clearance between the impeller and the volute casing to minimize the effect of leakage of impeller discharge towards the suction side. However, many investigators [S, 6] since then have reported that this clearance is very large in slurry pumps so as to avoid choking and also to minimize erosion wear. These clearances cause additional energy losses due to leakage flow and are one of the main factors responsible for lower values of efficiency of these pumps [S, 6]. Gandhi et ai. [IS] have proposed an analytical procedure to estimate this leakage flow and also to estimate various head losses, namely impeller slip, mixing and friction. On the basis of the estimation of these losses, they have formulated a methodology for predicting the slurry pump performance for clear liquids. Their methodology calculates the losses from the knowledge of pump geometry and rotational speed and does not require the knowledge of experimentally determined coefficients which are frequently used in the existing loss analysis procedures for the conventional centrifugal pumps [16,17]. They have reported an accuracy of :f:3 per cent for predicting the clear water head- ~ / +-::Y )( / :