Analysis of Flow Through Roots Blower Systems

Kinematic analysis of a Roots blower with involute flanks and circular root and tip sections is explained. The thermo-fluid model for the blower is described. Two mathematical models have been used to model the blower and its piping system. In the first model flow is assumed steady in the pipes,whereas in the second the unsteady flow in the pipes is taken into consideration. Leakage from the pressure side to the suction side of the blower is treated with a simple model. The change of volumetric efficiency at different operating conditions is given. It is possible to investigate the property variations with time at different parts of the blower system with the computer program written. Qualitative comparisons of the results with experimental ones are satisfactory. INTRODUCTION American engineer Roots developed this version of positive displacement machines and showed some examples in 1867. Since then,because of their inherent simplicity Roots machines become widely used in many industrial applications. The capacity of these machines can go up to 20.000 lit/s. Roots blowers may be used in two stages and their compression ratios can go up to 2.5. Their rotational speed range is 600 3000 rpm. Due to the displacement type of operation of the blower,pulsating flow takes place in the suction and delivery pipes. Various investigations have been carried out on Roots blowers. Their suitability as superchargers is investigated by Ryde [1]. The estimation of volumetric efficiency and leakage in Roots blower is an important factor which has been investigated by various researchers [2-7] . This investigation is on the modelling and solution of the flow through a Roots blower considering the unsteadiness of flow in all parts of a blower system. A computer program is developed for this purpose which could simulate Roots blower systems .. Only qualitative comparisons was made possible due to the lack of well documented test cases in the open literature during the time of investigation. 126 KINEMATICS OF ROOTS BLOWER The Roots blower is a positive displacement type compressor consisting two rotors rotating in opposite directions within a casing as shown in figure 1. The relative positions of the rotors are TRAPPED i\XKET 0/SCHA.Il'-E O,.EN/116Figure.!. Roots Blower Geometry maintained by a pair of gears in such a way that a fine clearance is present between rotors and casing. As the rotors rotate, the air is drawn into the space between the rotor and casing. Then, inlet air is trapped between the rotor and casing as the tip of the rotor passes the edge of the inlet opening. As the rotation continues the opposite tip of the rotor passes the edge of the outlet opening and the trapped air is pushed through the outlet opening. The space between the rotor and casing where gas is trapped is referred as "trapped pocket", whereas the space at su.ction and ,discharge sides of the blower are called "inlet tract"·and "outlet port" respectively. The backflow from the outlet port to the trapped pocket is an important factor in the operation of the machine. The general requirements of geometry are;that the machine should have a maximum possible displacement volume, no interference between the lopes to provide rotation,and split cylindrical form for easy machining. These requirements are met by a two lobe rotor of involute or cycloid flank profiles for single point of contact and no interference. In this investigation involute flank profile is chosen. The root and tip of the rotor is assumed to be in a circular form. Geometry of the Roots Blower For the geometry chosen, the machine can be described by 4 variables these are: 1. Pressure angle (~) 2. Distance between the centers 3. Rotor length (L) 4. Outlet and Suction opening dimensions. Figure 2 shows the detailes of the involute rotor flanks. The pitch circle diameter of the timing gears is equal to the distance between the .centers of the lobes. By definition, the locus of the center of curvature of involute curve is a circle, which is referred as base circle. The normal to the