MODELLING AND SIMULATION OF SEPARATION OF COWPEA AND IMPURITIES IN A PNEUMATIC CLEANER WITH COUNTER-FEED

Mathematical models were developed to study the displacements of cowpea and impurities particles and to predict cleaning efficiencies during separation in a vertical pneumatic cleaner. The predicted horizontal displacements were plotted against the vertical displacements at different angles of injection and air velocities. The plots showed that at a particular air velocity the amount of impurities that are removed from cowpea increased as the angle of injection increased. Experimental studies also confirm that cleaning efficiencies increased as the angle of injection increased at a particular air velocity. There was a high correlation between the predicted and experimental cleaning efficiency.


INTRODUCTION
Cowpea (vigna unguiculata), is an annual legume that is widely grown in West Africa, Southeast Asia, Latin America and the United States of America.West Africa accounts for the largest part of world cowpea production and Nigeria is the highest producer and consumer of cowpea in the world accounting for over 22% of the world production [1].It has been observed that freshly harvested and threshed cowpea in Nigeria contains between 27%-33% impurities, and this poses a threat to human consumption and large scale agricultural processing [2].This has necessitated the development of cleaning machines such as stationary vertical flow pneumatic cleaner which has proved effective in removing impurities from cowpea [3].
Pneumatic cleaning has many advantages that include flexibility, safety and low initial cost.There is however need to investigate the interaction of various parameters that influence aerodynamic separation of cowpeaimpurities mixture in a cowpea pneumatic cleaner.Such parameters include physical and aerodynamic properties of components of the mixture, angle of injection of cowpea-impurities mixture into the vertical air stream, air velocity, moisture content, and angle of injection of the air stream into the vertical tunnel [4].This will help to determine the combination of parameters that will produce optimum cleaning or separation.This investigation can be carried out by the development of mathematical models to simulate the separation process in the cleaner.
Different researchers have investigated the influence of different parameters that influence separation in a pneumatic system.Examples are the effect of tilt angle of air blower on the cleaning efficiency of a prototype pneumatic separator for cowpea [5] and a computer model to analyse the particle separation that occurs when grain and chaff are winnowed by being thrown or dropped in the wind [6].Adewumi's group [7] developed a two-dimensional mathematical model to predict particle trajectory when threshed cowpea materials were projected from a thresher into a horizontal air stream.The models were used to obtain displacement equations that were solved numerically to obtain a plot of the particle trajectory that was used as a guide for selecting the dimensions of a cross flow pneumatic classifiers for the grains.A two-dimensional equation to investigate grain and straw separation in a vertical and horizontal air stream had been developed in [4,8].It was concluded that for separation to be successful in a vertical air stream, the particles should fall into two well-separated bands while in horizontal air stream the particles can be separated into different fractions.
This work was carried out to develop mathematical models for investigating the separation of cowpea-impurities mixture in a vertical airflow and for predicting the cleaning efficiency.

MATHEMATICAL MODELLING
The equations of displacement of a particle from the point of injection into the air stream in a vertical flow cleaner was developed by determining the resultant of all forces acting on it in the horizontal and vertical directions [9].The acceleration component of the resultant force was then integrated twice to obtain the displacement equation.
where: x is horizontal displacement of particle, m; y is the vertical displacement of particle, m;  is direction of particle's motion measured from the horizontal, degree; is mass of particle, kg; is acceleration due to gravity, m/s 2 ; is the drag force, N; is time of flight, s.
The drag force is given by: where: is the drag coefficient of particle, dimensionless; is density of air, kg/m 3 ; is area of particle projected to the air stream, m 2 ; is velocity of particle relative to air, m/s.

METHODOLOGY
Equations ( 3) and (4) were solved numerically by MATHCAD using the physical and aerodynamic properties of cowpea (Ife 98-12 variety) and impurities namely chaffs (4 and 8 cm long), immature grains and insect infested grains [10].Experimental studies of cleaning efficiencies at different air velocities and angles of injection was carried out using a vertical pneumatic cleaner developed at the Department of Agricultural Engineering, Federal University of Agriculture Abeokuta using Ife 98-12 variety of cowpea.An empirical model for predicting cleaning efficiency from air velocity and angle of injection was then developed using Design Expert 8.The model is given by Cleaning Efficiency = -88.418x 1.974X 1 + 30.469X 2 -0.124X1X 2 -0.0106X 1 2 -1.427X 2 2  where: X 1 represented the air velocity in m/s; X 2 is the angle of injection in degrees.

RESULTS AND DISCUSSIONS
Plots of horizontal displacement against vertical displacement of cowpea (Ife 98-12 variety) and impurities particles injected at angles of injection of 15, 30, 45 and 60 o are shown in Figures 1 to 4.
These plots predict the effect of angle of injection on separation of impurities from cowpea.The plots show that at angle of injection of 15 o and with air velocity of 4 m/s only chaff-4 cm was lifted or blown away while the other heavier particles of sound grain, insect infested grain and chaff-8 cm fell into the air stream.With an angle of injection of 30 o , chaff-8 cm was also lifted or blown away along with chaff-4cm while sound grain and insectinfested grain fell into the air stream.With an angle of injection of 45 o , all the impurities namely chaff-4 cm, chaff-8cm and insect infested grain were lifted or blown away while only the sound grain to fall through the air stream.The case was the same when the angle of injection was increased to 60 o with the impurities being lifted farther away from the sound grain.The plots showed that the amount of impurities removed from the mixture at a particular air velocity increased as the angle of injection increased.Optimum lifting or separation of all impurities from sound grains occurred from angle of injection of 45 o upwards.This is similar to observation made by [11] that the efficiency of separation of foreign materials from grains in a cross-flow cleaner was high when the directional air stream was set at angles between 30 o and 60 o to the horizontal.Also [6] reported that when grain and chaff are winnowed by being thrown through or dropped in the wind, maximum separation is obtained when the mixture is thrown against the wind at an angle of about 140 o to the horizontal.This is a useful guide in the inclination of the hopper.
The experimental and predicted cleaning efficiencies are shown in Table 1.It was observed that at a particular air velocity, the experimental cleaning efficiency increased as the angle of injection increased from 15 to 60 o .This is in agreement with the prediction of the plots.The predicted cleaning efficiencies were correlated with
Figure 5).The high correlation coefficient of 0.98 obtained shows that the model predicted well the experimental values.

Table 1 .
Predicted and experimental cleaning efficiencies for Ife 98-12.The plots of horizontal displacement against vertical displacement of the cowpea and impurities particles predicted that the quantity of impurities removed from cowpea by a vertical pneumatic cleaner increased as the angle of injection increased.Optimum separation occurs from angle of injection of 45 o .2. The predicted cleaning efficiencies as the angle of injection increased from 15 to 60 o increased from 30.7 to 61.5%, 59.3% to 79.0% and 76.1 to 85.0%. 3. The cleaning efficiencies obtained experimentally at angles of injection of 15 to 60 o increased from 27.7% to 61.1%, 63.2% to 75.9% and 76.7% to 87.2%.The high coefficient of correlation between the predicted and experimental cleaning efficiency shows that the model predicted well the cleaning efficiency.