1.1Background And Motivation
There is a vast engineering application of turbomachinery ranging from aircraft engines to steam turbines. Turbomachinery refers to a group of machines which rotate, such as fans, turbines, and pumps. These machines are divided into two groups: (1) those that extract energy (turbines) and those that add energy to the fluid (pumps). Turbomachinery is a common application in engineering where fluid machinery design is of interest, where the pump in this discussion gets the attention. Hydraulic machines like pumps transmit power by means of a working fluid. Pumps all have a common practice to increase the pressure of a fluid by converting its kinetic energy to pressure energy. Pumps are divided into Positive-displacement (PDPs) and dynamic pumps. Positive-displacement pumps force fluids by volume changes. A cavity opens, and the fluid is admitted through an inlet, trapped, and then squeezed through an outlet. Their great advantage is the delivery of any fluid regardless of its viscosity. On the other hand, dynamic pumps add momentum to the fluid by means of fast-moving blades or certain special designs. There is no closed volume, the fluid increases momentum while moving through open passages and its high velocity is converted to a pressure increase by exiting into a diffuser according to White . The most common application is the centrifugal pump, which basically consist of an impeller rotating within a spiral casing. Fluid enters the pump axially through a suction pipe (via the eye of the impeller); discharged radially from the impeller around the entire circumference into the casing. The casing 'collects' the fluid, which has kinetic energy, decelerates it to increase the pressure of fluid. Then the fluid is discharged throughout the delivery flange. Performance charts are used as a guideline to select a pump that would suit one's requirements. The optimal or rated and half rated speed for a 'family' of pumps (geometrically similar pumps having different sizes) is given in the chart. The charts give total head against flow rate with efficiency curves fitted in as well. Since the fluid flow inside a centrifugal pump is very complex, pumps are treated as 'black boxes', which is an approach concerned with the fluid immediately before entering and immediately after leaving the pump.
1.2.1 Principal operation
Centrifugal pumps have a rotating impeller that is immersed in the fluid. Fluid enters the pump near the axis of the impeller, and the rotating blades ‘sweeps’ the fluid out towards the ends of the blades at high pressure. The impeller also gives the fluid a relatively high velocity that can be converted into pressure in the diffuser. In high pressure pumps, a number of impellers may be used in series, and the diffusers following each impeller may contain guide vanes to gradually reduce the fluid velocity. For low pressure pumps, the diffuser is generally a spiral passage, known as a volute, with its cross-sectional area increasing gradually to reduce velocity efficiently. The impeller must be primed before it can begin operation – that is, it must be surrounded by the fluid when the pump is started .
1.2.2 Output parameters
The head rise across the pump (H), in meters (m), is given by Bernoulli as (1.1) where
is the pressure in Pascal’s (Pa)
is the density f the fluid in kg/m3
is the acceleration due to gravity in m/s2
is the flow velocity in m/s
is the height above a chosen datum in meters (m)
is the head supplied by the pump in meters (m)
is the head loss due to friction in meters (m);
1 and 2 refers to the inlet state and outlet state respectively
Usually and are about the same, is small and thus the net pump head equals the change in pressure head:...