LESSON-11 APPLICATION OF STUDY FLOW ENERGY EQUATION (SFEE)

 APPLICATION OF STEADY FLOW ENERGY EQUATION (SFEE) IN STEADY FLOW ENGINEERING DEVICES

The application of steady flow energy equation can be used to study the performance of many engineering devices that undergo thermodynamic processes, as these devices closely satisfy the conditions for steady flow processes.

For example, the engineering devises like boiler, turbine, condenser/heat exchanger, feed water pump, cooling tower, and stack of steam power plant (Fig. 11.1) run nonstop for many months before these are shut for maintenance. Therefore these engineering devises must run under steady state conditions and can be analyzed as steady flow devices by applying steady flow energy equation.

   

Fig. 11.1. Steam power plant

 There are a number of steady flow engineering devices. However, some common steady flow engineering devices are discussed below.

11.1. Boiler:

It is used to generate steam (Fig. 11.2). The boiler is characterized by the following features:  

(a) Velocity change between inlet and exit point is not appreciable and may be neglected             (b) Elevation change between inlet and exit point may also be neglected:           Zi = Ze   ( c) There is no shaft work,              The steady flow energy equation is          ………….(11.1) By applying the features of steam boiler, the above equation reduces to    q = (he - hi) = + ve    so   he > hi

Fig. 11.2. Boiler

11.2. Nozzle and diffusers: Nozzle :  A flow passage of reducing cross-sectional area to increase velocity by reducing pressure (Figure 11.3). Diffusers: A flow passage of increasing cross-sectional area to reduce velocity by increasing pressure (Figure 11.3). Examples: Jet engines, rockets, spacecraft, garden hoses. The nozzle and diffusers are characterized by the following features: The steady flow process equation is  By applying the features of nozzles and diffusers, the above equation reduces to,            In the case of nozzles,  Ce > Ci    so    hi > he In the case of diffusers, Ce < Ci    so    hi < he

Fig. 11.3. Nozzle and diffuser

11.3. Turbines:  A device to produce shaft work from a flow of gas through a set of blades attached to a freely rotating shaft (Figure 11.4).  Uses: Turbine engines, power generation The turbine is characterized by the following features: Usually  ,  or estimated heat losses,  and ΔK.E small compared with Δh ,

Fig. 11.4. Turbine

 The steady flow energy equation is

By applying the features of turbine, the above equation reduces to,            

    =  + ve    so h_i > h_e

11.4. Compressors, Pumps and Fans: Compressor: A device where shaft work input is used to raise the pressure of a gas passing through it (Figure 11.5).  Pump: Similar to a compressor but handles liquids.  Fan: This moves air usually with slight pressure rise. The Compressors, Pumps and Fans are characterized by the following features: Usually   unless intentionally cooled,    and ΔK.E small for compressors, For the steady state steady flow process

Fig. 11.5. Compressor

By applying the features of compressors/ pumps/fans, the above equation reduces to,            

        so   h_i < h_e

NOTE: For Reciprocating compressor 

11.5. Mixing Chambers: Combining two or more streams at different conditions, to produce a (usually) single mixed stream (Figure 11.6). The mixing chamber is characterized by the following features: Usually    Mass Balance:         or

Fig. 11.6. Mixing chamber

Energy Balance:

By applying the features of mixing chamber, the above equation reduces to,            

 

or   

11.6. Heat Exchangers: Devices that transfer energy between moving fluid streams (usually not mixed) at different temperatures as shown in Fig. 11.7. Uses:  Condenser, evaporator

Fig. 11.7. Heat exchanger

11.6.1.  Taking Control volume as whole heat exchanger, as shown in Fig. 11.8    The heat exchanger is characterized by the following features:   Energy Balance:    By applying features of heat exchanger, the above equation reduces to,        or

Fig. 11.8. Heat exchanger.

11.6.2. Taking Control volume around Fluid A, as shown in Fig. 11.9     The heat exchanger is characterized by the following features: Energy Balance: By applying features of heat exchanger, the above equation reduces to,

Fig. 11.9. Heat exchanger.

 or     

      (steady flow)

  or   

or