Design and Optimization of Thermal Systems Episode 2 Part 4 doc

These steps analyze the design and ensure that the problem ment is satisfied.state-In this chapter, we will consider the synthesis of the different steps and stages that constitute the d

may be coupled with the modeling of fluid flow adjacent to the rod and other parts of the system to complete the model of a given system.4.43 Consider heat conduction in a two-dimensional, rectangular region of length 0.3 m and width 0.1 m The dimension in the direction normal

to this region may be taken as large The dimensionless temperature

is given as 1.0 at one of the longer sides and as 0.0 at the others Solve the governing Laplace equation by the SOR method and determine the optimum relaxation factor Discuss how, in actual practice, such a simulation may be linked with those for other parts of the system.4.44 Consider the fan and duct system given in Example 4.7 Vary the zero-flow pressure, given as 80 in the problem, and the zero-pressure flow rate, given as 15 here, by o20% Discuss the results obtained Are they consistent with the physical nature of the problem as represented by the equations?

4.45 Show the information-flow diagram for Problem 4.18 Also, draw the information-flow diagram for the simulation of Problem 4.35 Do not solve the equations; just explain what approach you will use

of a Thermal System:

A Synthesis of Different Design Steps

5.1 INTRODUCTION

In the preceding chapters, we discussed the main aspects involved in the design

of a thermal system An acceptable or satisfactory design must satisfy the given requirements for the system and must not violate the limitations or constraints imposed by the application, materials, safety, environmental effects, and other practical considerations At this stage, we are not concerned with the optimiza-tion of the system and are largely interested in obtaining a feasible design Though any design that meets the given requirements and constraints may be adequate for some applications, it is generally desirable to seek a domain of acceptable designs from which an appropriate design is selected on the basis of cost, ease of fabrica-tion, availability of materials, convenience in usage, etc

The various considerations that are involved in the development of an able design of a thermal system have been discussed in Chapter 2 These led to the following main steps:

accept-1 Formulation of the design problem

2 Conceptual design

3 Initial design

4 Modeling of the system

5 Simulation of the system

6 Evaluation of the design

7 Selection of an acceptable design

Optimization of the design follows the determination of a domain of able designs and is not included here Most of the other aspects, particularly prob-lem formulation, conceptual design, modeling, and simulation, were discussed

accept-in detail accept-in the precedaccept-ing chapters The first step accept-in the foregoaccept-ing list quantifies the design problem, and the second step provides the basic idea or concept to achieve the desired goals The remaining steps constitute what might be termed

as the detailed, quantitative design process, or simply the design process for

convenience These steps analyze the design and ensure that the problem ment is satisfied.

state-In this chapter, we will consider the synthesis of the different steps and stages that constitute the design effort in order to obtain an acceptable design Individual aspects, such as modeling and simulation of thermal systems, which were dis-cussed in detail earlier, will be considered as parts of the overall design strategy The main purpose of this chapter is to link the different aspects that are involved

in the design of a thermal system and to demonstrate the design procedure, ing with the problem formulation, proceeding through modeling and simulation, and ending with an acceptable design Examples are employed to illustrate this coupling

start-Several diverse thermal systems, ranging from those in materials processing

to those in energy and environmental systems, were considered in the previous chapters It has been shown that the basic concerns, modeling, simulation, and system characteristics, vary significantly from one class of systems to another For instance, lumped steady-state modeling is usually adequate for refrigeration and air-conditioning systems, leading to algebraic equations, whereas distributed time-dependent modeling is generally needed for manufacturing processes and electronic equipment cooling, resulting in partial differential equations Con-sequently, the simulation procedures vary with the type of system under con-sideration The design strategy itself may be affected by these considerations Therefore, examples of thermal systems from different application areas are con-sidered in this chapter and the corresponding design strategies presented The systems considered range from relatively simple ones to fairly complicated ones

in order to demonstrate the applicability of the basic ideas to the design of a wide variety of systems

Before proceeding to the complete design process for typical thermal tems, an aspect that needs more detailed consideration is that of initial design

sys-In many cases, the initial design is reached by considering the requirements and constraints of the problem and choosing the design variables, through approxi-mate analysis and estimates, so that these satisfy the given problem statement If different components are to be chosen and assembled for a thermal system, the choice of these components is guided by the requirements and constraints, so that the initial design is itself an acceptable design Though redesign is obviously needed in case the initial design is not acceptable, it is important to employ the best possible initial design so that it is either acceptable by itself or the number of redesigns needed to converge to an acceptable design is small

5.2 INITIAL DESIGN

The search for an initial design follows the formulation of the problem and the conceptual design It is thus the first step in the quantitative design procedure The analysis of the system, through modeling and simulation, and evaluation

of the design for its acceptability are based on the initial design The initial, starting design affects the convergence of the iterative design process and often

even influences the final acceptable or optimal design obtained Therefore, the development of an initial design is a critical step in the design procedure, and considerable care and effort must be exerted to obtain a design that is acceptable

or as close as possible to an acceptable design

Ideally, the design variables should be selected so that the initial design isfies the given requirements and constraints Unfortunately, this is usually not possible for thermal systems because analysis only yields the outputs on system behavior for given inputs, rather than solve the inverse problem of yielding the inputs needed for a desired behavior If the outputs and inputs were connected by simple relationships that could be inverted to obtain the inputs for required out-puts, the problem would be considerably simplified However, thermal systems usually involve complexities arising from nonlinear mechanisms, partial differ-ential equations, coupled phenomena, and other complications, as discussed in Chapter 1 This makes it very difficult to solve the inverse problem in order to select the design variables, in an initial design, to satisfy all the requirements and constraints Consequently, iteration is generally necessary to obtain a satisfac-tory design

sat-Several approaches may be adopted in the selection or development of the initial design The approach that is appropriate for a given problem is a function

of the nature of the thermal system under consideration, information available on previous design work, and the scope of the design effort Some of the commonly used methods for obtaining an initial design are

1 Selection of components to meet given requirements and constraints

2 Use of existing systems

3 Selection from a library of previous designs

4 Use of current engineering practice and expert knowledge of the cation

appli-Selection of Components

In general, a combination of all the approaches given above is used to come up with the best initial design for practical thermal systems However, each of these may also independently yield the desired starting point for iterative design Selec-tion of components is particularly valuable in thermodynamic systems, such as refrigeration, air conditioning, and heating systems, where the design of the over-all system generally involves selecting the different components to meet the given requirements or specifications An example of this is the air-cycle refrigeration system, based on the reverse Brayton cycle and shown in Figure 5.1, which is commonly used aboard jet aircrafts to cool the cabin The turbine, the compres-sor, and the heat exchanger may be selected based on the desired temperature and pressure in the cabin, along with the thermal load, to obtain an initial design

An analysis of the thermodynamic cycle shown yields the appropriate cations of the components for an ideal cycle or for a real one with given isentropic efficiencies (Reynolds and Perkins, 1977; Howell and Buckius, 1992) For an ideal

specifi-Work Turbine

Compre-ssor

P H

3 2a

1

4a

Heat exchanger

Heat exchanger

Heat rejected (a)

Compressor Actual

2a 2s

Turbine

Actual

Entropy (b) Heat input

FIGURE 5.1 The hardware and the thermodynamic cycle, with real, nonideal compressor

and turbine, for the Brayton cycle.

cycle, the efficiency H, which is the ratio of the work done to the energy input into the system, is given by the expression

P P

H L

(5.1)

where G is the ratio of the specific heat at constant pressure Cp to that at constant

volume C v , and P H , P L are the high and low pressures in the system, respectively The corresponding temperatures can be calculated for isentropic processes and then for a real, nonideal system using the efficiencies Any constraints on pres-sures or temperatures given in the problem can be taken care of by a proper choice

of these components A given range of desired efficiency for satisfactory systems may also be taken as a requirement Therefore, the initial design itself satisfies the problem statement and is an acceptable design This design may be modeled and simulated to study the system behavior under different operating conditions

to ensure satisfactory performance in practical use Example 5.1 and Example 5.2 discuss this approach for thermodynamic systems

Existing Systems

The development of an initial design based on existing systems for applications similar to the one under consideration is a very useful technique Unless a com-pletely new concept is being considered for the given application, systems that perform similar, though different, tasks are usually available and in use For instance, if a forced-air furnace is being designed for continuous heat treatment of silicon wafers as a step in the manufacture of semiconductor devices, as shown in Figure 5.2, similar systems that are being used for other processes, such as baking

of circuit boards and curing of plastic components, may be employed to obtain initial estimates of the heater characteristics, wall material and dimensions, con-veyor design, interior dimensions, etc This provides the starting point for the iterative design-redesign process, which varies the relevant design variables to arrive at an acceptable design

Conveyor

Heaters Silicon wafers

FIGURE 5.2 A thermal system for the heat treatment of silicon wafers in the manufacture

of electronic circuitry.

Library of Previous Designs

Any industry involved with the design of systems and equipment would generally develop many successful designs over a period of time for a variety of applica-tions and design specifications Even for the design of a particular system, several designs are usually generated during the process to obtain the best or optimal design Consequently, a library of previous successful designs can be built up for future use Note that these designs may not have been translated into actual physi-cal systems and may have remained as possible designs for the given application Such a library provides a very useful source of information for the selection of an initial design For instance, an effort on the design of heat exchangers would give rise to many designs that may not be chosen for fabrication because they were not the optimum or because they did not meet the requirements for a given applica-tion However, for different design specifications, some of the earlier designs that were discarded might be satisfactory Similarly, the design of an air compressor may yield many designs that are discarded because the pressure or the flow rate

is too low However, if this information is retained, it can be used for selecting

an initial design for some other applications Therefore, considerable effort is saved in the development of the initial design if such a library of earlier designs, along with their specifications, is available As soon as a new design problem is initiated, the library may be employed to obtain a design with outputs as close as possible to the given requirements For instance, if the total rate of heat transfer desired from the heat exchanger is given, a design that gives the closest heat trans-fer rate is chosen from the design library This approach is particularly suitable for equipment, such as heat exchangers, heat pumps, boilers, and refrigerators

Expert Knowledge

The last approach for developing an initial design is based on information able on the particular application and corresponding types of thermal systems, along with current engineering practice Such an approach is very hard to quan-tify because the available information is often vague and may not have a solid

avail-analytical foundation This is what is often termed as expert knowledge, i.e., the

information obtained from an expert in the area Several ideas developed over the years form the basis for such knowledge and play a major role in determining what is feasible Information from earlier problems and attempts to resolve them

is also part of this knowledge Many aspects in thermal systems are very cult to analyze or measure, such as contact thermal resistance between surfaces, radiative properties of surfaces, surface roughness, fouling in heat exchangers, and losses due to friction Similarly, random processes such as demand for power, changes in environmental conditions, and fluctuations in operating conditions are not easy to ascertain In all such circumstances, current engineering practice and available information on the given application are used to come up with the initial design These aspects are considered in greater detail in terms of knowledge-based design methodology in Chapter 11

diffi-Example 5.1

A refrigeration system is to be designed to maintain the temperature in a storage facility in the range of –15 to –5nC, while the outside temperature varies from 15 to 22nC The total thermal load on the storage unit is given as 20 kW Obtain an initial design for a vapor compression cooling system.

Solution

Since the lowest temperature in the storage facility is –15nC, the evaporator must operate at a temperature lower than this value Let us select the evaporator tem- perature as –25nC Similarly, the ambient temperature can be as high as 22nC Therefore, the condenser temperature must be higher than this value to reject energy

to the environment Let us take the temperature at which the condenser operates

as 30nC The total thermal load is 20 kW, which is 20/3.517  5.69 tons Therefore, the refrigeration system must be capable of providing this cooling rate Since addi- tional energy transfer may occur to the system and also for safe operation, let us design the system for 7.5 tons, which gives a safety factor of 7.5/5.69  1.32.

We must now choose the refrigerant Because of environmental concerns with chlorofluorocarbons and because of the relatively large refrigeration system needed here, let us choose ammonia as the refrigerant The various parts of the system are shown in Figure 1.8(a) All these parts, except the compressor, usually have high efficiencies and may be assumed to be ideal The compressor efficiency could range from 60 to 80% Let us take this value as 65% The thermodynamic cycle in terms of a temperature-entropy plot is shown in Figure 5.3 The fluid entering the

Entropy, s

Evaporator

Throttling valve

Condenser 30°C

Saturated vapor –25

–25

188.7 30 151.5

3 2a 1

3

2s Compressor 2a

FIGURE 5.3 Thermodynamic cycle for the vapor compression refrigeration system

con-sidered in Example 5.1, along with the calculated conditions at various states.

throttling value is assumed to be saturated liquid and that leaving the evaporator

is assumed to be saturated vapor These conditions are commonly employed in vapor compression refrigeration systems The nonideal behavior of the compressor

is seen in terms of an increase in entropy during compression.

For ammonia, the various pressures may be determined from available tables or charts (Van Wylen et al., 1994) Therefore, the pressure at the inlet to the compres- sor is 151.5 kPa The pressure at the entrance to the throttling valve is 1167.1 kPa, which is also the pressure at the exit of the compressor The temperatures at the evaporator exit and valve entrance are –25nC and 30nC, respectively The enthalpy

at the compressor exit is obtained from

H  h h

s a

2 1

2 1

 0.65

where H is the compressor efficiency and the various states are shown in Figure 5.3

The entropy is constant between the states 2s and 1 Using this condition, the enthalpy h 2s is obtained as 1733 kJ/kg Therefore, with h1 1430.9 kJ/kg, h 2a is

obtained from the preceding equation as h 2a 1895.7 kJ/kg This also gives the temperature at the compressor exit as 188.7nC The coefficient of performance (COP) is obtained as

COP  Heat removedEnergy input  h h



m  26 38

1088 49

 24.24 r 10 kg/s  87.25 kg/hr Therefore, an initial design for the refrigeration system is obtained It is seen that several design decisions had to be made during this process Clearly, different values

of the design variables could have been chosen, leading to a different initial design This implies that the design obtained is not unique In addition, because each part was chosen to satisfy the given problem statement, the initial design itself is an acceptable design The fluid chosen is ammonia and the system capacity is 7.5 tons The inlet and outlet conditions for each system part are obtained in terms of the inlet temperature and pressure, as given in Figure 5.3 The mass flow rate of the refrigerant is 87.25 kg/h Thus, these items may be procured based on the given specifications Because the items available in the market may have somewhat different specifications, the design may be adjusted to use available items, rather than have these custom made, in order

to reduce costs However, the system should be analyzed again if these items are changed to ensure that it meets the given requirements and constraints.

Example 5.2

A remote town in Asia is interested in developing a 20 MW power plant, using the burning of waste material for heat input and a local river for heat rejection It is found that temperatures as high as 350nC can be attained by this heat source, and typical temperatures in the river in the summer are around 30nC Obtain a simple initial design for such a power plant.

Solution

A Rankine cycle, such as the one shown in Figure 2.15, may be chosen without superheating the steam to simplify the system This system has been analyzed extensively, as given in most textbooks on thermodynamics, and can be designed based on available information (see Moran and Shapiro, 2000) Water is chosen as the working fluid, again because of available property data, common use in typi- cal power plants, and easy access to water at this location Due to the temperature ranges given, the boiler temperature is taken as 300nC to ensure heating and boil- ing with energy input at 350nC The condenser temperature is taken as 40nC to allow heat rejection to the river water, which is at 30nC Then the initial tempera- ture cycle of the proposed power plant may be drawn, as shown in Figure 5.4 The various states are given, with the idealized states indicated by subscript s, as in the previous example.

Now, we can proceed to first model the system and then analyze the dynamic cycle All the components are taken as lumped, in order to simplify the model and because interest lies mainly in the energy transport and not in the detailed information for each component The process is approximated as steady, which would apply for a steady operation of the power plant and not for the start-

thermo-up and shutdown stages or for power surges The transient effects, which erably complicate the analysis, may be considered later for designing the control system Thus, the analysis with steady lumped components will lead to coupled algebraic equations, which can be solved to obtain the power delivered, water flow rate needed, heat input, and other desired quantities.

4s

2s 2 40°C

Pump

FIGURE 5.4 Thermodynamic cycle for the power plant design considered in Example 5.2.

Considering first the ideal cycle with isentropic turbine and pump, the steam tables are used to obtain properties at the relevant temperatures We find that, for

saturated steam, the enthalpy h1 2749 kJ/kg and entropy s1 5.7045 kJ/kg, which

is equal to s 2s for an ideal turbine Then the quality x 2s is obtained as

Similarly, for saturated liquid, h3 167.57 kJ/kg, s3 s 4s 0.5725 kJ/kg The

enthalpy h 4s is obtained by using the ideal pump work per unit mass, v3(p4 – p3 ),

where v3 is the specific volume at state 3 and the p’s are the pressures Thus,

h 4s  h3 v3 (p4 – p3 )  167.57 1.0078 r 10 r (8.581 – 0.007384) r 10 3

 167.57 8.64  176.21 kJ/kg

where the pressures are in MPa and 10 3 is used to obtain the work in kJ/kg Then, the work done, or power output, for the ideal case is given by

Wm W ( Turbine ideal, W Pump ideal, ) m h [( 1 h2s)) (h4s h3 )]

where m is the mass flow rate of water/steam It is calculated for the ideal cycle as

 47.45 MW The overall thermal efficiency is 20/67.45  0.2965, or 29.65%.

Thus, an acceptable initial design of the thermal system is obtained by choosing components and thermodynamic states based on given constraints and require- ments The efficiencies of the turbine and the pump can be adjusted if better information is available As in Example 5.1, the design is not unique and several acceptable designs can be developed The various components, such as the turbine,