Design and Optimization of Thermal Systems Episode 1 Part 5 ppsx

Though simulation may be carried out with scale models and prototypes, the expense and effort involved gen-erally makes it impossible to use these for design because many different desig

involved in these steps are outlined in the following sections and some of the crucial elements, such as modeling, simulation, and optimization, are discussed

in greater detail in later chapters

2.3.1 P HYSICAL S YSTEM

The starting point of the quantitative design process is the physical system obtained from conceptual design This serves as the initial design that is mod-eled, simulated, and evaluated in the search for an acceptable design Therefore, the system must be well defined in terms of the following:

1 Overall geometry and configuration of the system

2 Different components or subsystems that constitute the system

3 Interaction between the various components

4 Given or fixed quantities in the system

5 Initial values of the design variables

A sketch may be used to represent the system configuration and the ous components that interact with each other Several of these were given in Chapter 1 For instance, Figure 1.8 presents the schematic for vapor compression and vapor absorption systems for refrigeration and air conditioning Similarly, Figure 1.10 gives the physical representations for several manufacturing thermal systems and Figure 1.12 gives those for electronic equipment cooling systems These sketches indicate the different components and subsystems that are part

vari-of the overall thermal system The physical characteristics vari-of these components and how they are linked with the others, particularly in terms of material, heat, and fluid flow, are also included

In several cases, particularly for thermodynamic systems, the behavior and characteristics of the system may be represented graphically State diagrams, which represent the equilibrium states through which a given material goes, are commonly used to indicate the thermodynamic cycle in many applications such

as those related to refrigeration, power plants, and internal combustion engines

Acceptable design

Design evaluation Simulation

Optimal design

Automation and control

FIGURE 2.14 Various steps involved in the design and optimization of a thermal system

and in the implementation of the design.

Similarly, changes in temperature, pressure, and velocity with location and time are used to indicate the basic nature of the process in many systems Such graphi-cal representations are largely qualitative and often idealized, thus modeling the physical system The actual numbers and other quantitative details are obtained through analytical and numerical calculations Figure 2.15 shows qualitatively the typical thermodynamic cycles for a power plant and for a four-stroke inter-nal combustion engine, indicating the various stages in the two processes An analysis of these systems would then yield the actual pressures and temperatures involved (Moran and Shapiro, 2000).

The physical system must also include information on the given and, thus, fixed quantities in the problem and on the initial values of the design variables Again, these may also be given in the form of sketches or graphs, as well as

in symbolic or mathematical forms Quantities that are often fixed are certain dimensions; materials and their characteristics; flow rates; and torque, pressure,

or force exerted Quantities that may be varied to obtain a satisfactory design are determined from the parameters that are not given, from operating conditions, and from the configuration of the system

Consider the glass fiber drawing system shown in Figure 1.10(c) The basic configuration of the system is sketched in this figure In addition, the dimensions

Entropy

Turbine Boiler

Heat transfer

Exhaust Ignition

Heat transfer

Power Compression

FIGURE 2.15 Thermodynamic cycles for (a) a Rankine engine with superheating of

steam for power generation, and (b) an internal combustion engine based on the stroke Otto cycle.

four-and material of the fiber are given quantities, with specified tolerance levels The draw speed of the fiber is a requirement in most cases for the desired productiv-ity The dimensions, material, and heating arrangement of the furnace could be taken as the design variables, although the given constraints will generally fix the domain of variation to fairly tight limits The tension exerted on the fiber is

to be determined for given operating conditions Therefore, the physical system

is specified in terms of these inputs Figure 2.16 shows a photograph of the actual

optical fiber drawing system, known as the draw tower The simple sketch shown

in Figure 1.10(c) is a schematic that gives the essential features of the system, which is much more complicated in actual practice due to power supply, control arrangement, feed mechanism, and other practical considerations

FIGURE 2.16 Draw tower for the manufacture of optical fibers (From Fiber Optic

Materials Research Program, Rutgers University, New Jersey.)

2.3.2 M ODELING

The modeling of the physical system, obtained from the conceptual design and from the formulation of the design problem, is an extremely important step in the design and optimization of the system Because most practical thermal systems are fairly complex, it is necessary to focus on the dominant aspects of the system, neglecting relatively small effects, in order to simplify the given problem and make it possible to investigate its characteristics and behavior for a variety of conditions Idealization and approximation of the processes that govern the sys-tem are also used to simplify the analysis The basic conservation principles and properties of the materials involved are also important elements in modeling of thermal systems The next chapter is devoted to modeling of thermal systems and only a brief outline is given here as an introduction to this process

Both analytical and experimental procedures are employed to model the tem Because experimentation usually involves much greater time, effort, and cost, as compared to analysis, experimental methods are used sparingly and only for the validation of the analytical results or when the inputs needed for design are not easily obtainable by analysis Modeling of the thermal system yields a set

sys-of algebraic, differential, or integral equations, which govern the behavior sys-of the actual system These may be written as

F i (x1, x2, x3,z , x n) 0 for i  1, 2, 3, z , n (2.7)

where x i and F i represent, respectively, the physical variables and the equations that govern the problem In most cases, numerical methods are necessary to solve these equations, particularly the nonlinear ordinary and partial differential equations often encountered in thermal systems Discretized equations are then derived based on numerical techniques such as the finite difference and finite element methods for implementation on the computer, giving rise to a numerical model for the process or system The analytical and/or numerical results obtained must be validated, preferably by comparisons with available experimental data,

to ensure that the model is an accurate and valid representation of the cal system The results obtained from experimental and numerical methods are frequently represented in terms of simple algebraic equations by means of curve fitting These equations can then be used to characterize the system behavior and

physi-to optimize its performance

Modeling of the thermal system also allows one to determine the conditions under which the results from an experimental scale model can be used to predict the behavior of an actual physical system This involves dimensionless parameters that must be kept the same between the two for obtaining similar distributions of flow, forces, heat transfer rates, and so on Using the basic principles of dimen-sional analysis, the governing dimensionless groups are determined for a given thermal process or system This also simplifies the experiment by reducing the number of parameters that need to be varied to characterize a given process, since most thermal systems are governed by a much smaller number of dimensionless groups as compared to the total number of physical variables in the problem

As a result of the various simplifications and approximations, the given lem is brought to a stage where it may be solved analytically or numerically Mod-eling not only simplifies the problem, but also eliminates relatively minor effects that only serve to confuse the main issues It also provides a better understand-ing of the underlying mechanisms and thus allows a satisfactory inclusion of the experimental results into the overall model Material property data and empirical results, available on the characteristics of devices and components that comprise the system, are also incorporated into the model.

prob-Modeling is generally first applied to individual components, parts, or systems that make up the thermal system under consideration Using the vari-ous experimental and analytical methods for modeling, separate models are thus developed for the constituents of the system These individual models, or sub-models, are then brought together or assembled in order to take into account the interaction between the various parts of the system The different submodels are linked to each other through boundary conditions and the flow of mass, momen-tum, and energy between these When these individual models are coupled with each other, the overall model for the thermal system is obtained This model is subjected to a range of conditions to study the behavior of the system and thus obtain a satisfactory or optimal design

sub-Consider the simple power plant system sketched in Figure 2.17 The various subsystems, such as the boiler, condenser, turbine, and pump, are first considered individually and the corresponding models developed After all these individual models, or submodels, have been developed, they must be brought together to yield the model for the complete thermal system, as shown schematically in Figure 2.18 In this particular example, the models of the individual subsys-tems are coupled through the fluid flow and the energy transport Thus, the outlet from the boiler is the inlet to the turbine, whose outlet is the inlet to the condenser Using such conditions, the different parts of the system are linked to each other through a central control unit This then yields the model of the power plant Additional subsystems such as the superheater, feedwater heater, and cooling tower may also be brought in for practical and more complicated systems Similar considerations apply in the development of models for other thermal systems

2.3.3 S IMULATION

Simulation is the process of subjecting the model for a given thermal system to various inputs, such as operating conditions, to determine how it behaves and thus predict the characteristics of the actual physical system Though simulation may be carried out with scale models and prototypes, the expense and effort involved gen-erally makes it impossible to use these for design because many different designs and operating conditions need to be considered and evaluated Prototype testing is largely used before going into production, after the system design has been com-pleted Therefore, simulation with mathematical models is particularly valuable in the design process because it provides information on the behavior of the given system under a range of conditions without actually constructing a prototype

FIGURE 2.17 The physical system corresponding to the thermodynamic cycle shown in

Figure 2.15(a) (Adapted from Howell and Buckius, 1992.)

Turbine Pump

The mathematical models derived for thermal systems are generally mented on digital computers because of the complex nature of the governing equations, complicated boundary conditions, and complicated geometrical con-figurations that are usually encountered The presence of several coupled sub-models representing different components of the system and the incorporation of material properties, experimental data, and other empirical information further complicate the model The resulting numerical model is then subjected to differ-ent values of the design variables, over the ranges determined by the constraints Both the hardware and the operating conditions are varied to study the system

imple-characteristics This process is known as numerical simulation and is an

impor-tant step in the design and optimization process Only a brief outline of numerical simulation is given here, with a detailed discussion of the various procedures, types, and considerations, along with examples, given in Chapter 4

An important question that must be answered in any numerical simulation is how closely or accurately it represents the actual, real-world, system This involves ascertaining the validity of the various approximations made during modeling, as well as estimating the accuracy of the numerical algorithm Certainly, if experimen-tal data from a prototype are available, a comparison between these and the results from the simulation could be used to determine the validity and accuracy of the latter However, such experimental data are rarely available, at least not during the design process Consequently, the first step is to consider the simulation results in terms of the physical nature of the system and to ascertain that the observed trends agree with the expected behavior of the real system Numerical parameters chosen

by the designer or engineer, such as grid size, time step, computational domain, and so on, are then varied to ensure that the results are independent of these Some-times, simpler or similar systems for which experimental results are available may

be simulated to validate the model For instance, if a new system for plastic tion molding is being developed, the simulation scheme may be applied to an earlier version for which experimental data are available Comparisons between the simu-lation results and experimental data could then be used to estimate the accuracy of the simulation Therefore, considerable effort is directed at obtaining an accurate one-to-one correspondence between the model and the actual system

injec-All these measures are relatively approximate indicators, which generally fice for the study and evaluation of the different designs obtained After the final design is approved and a prototype is fabricated, more detailed results are obtained for the validation and improvement of the model and the simulation In fact, results obtained over the years from systems on the market are also used to modify and improve the models and the simulation for the design and optimization of these systems in the future

suf-Simulation is mainly used to determine the behavior of the thermal system

so that the design can be evaluated for satisfactory performance It also provides inputs for optimization Though there are many strategies that can be used for simulating thermal systems, as discussed in Chapter 4, a common approach is to fix the hardware and vary the operating conditions over the desired ranges The

hardware is then changed to consider a different design and the process repeated The simulation of the system is carried out with different design variables until an acceptable design or a range of acceptable designs is obtained.

An Example

Suppose a simple counterflow heat exchanger, as shown in Figure 2.19(a), is to be

designed The design variables are the two outer diameters D1 and D2 of the inner

and outer tubes, respectively; the two wall thicknesses t1 and t2; and the length

L of the heat exchanger The operating conditions are the inlet temperatures T 1,i,

T 2,i and the mass flow rates m m1, 2of the two corresponding fluid streams Let

us assume that a mathematical and numerical model has been developed for this system, allowing the calculation of the heat transfer rates and temperature dis-tributions in the two fluid streams, as sketched in Figure 2.19(b) Let us take the

heat transfer rate Q and the outlet temperature T 2,o of the outer fluid stream as the outputs from the model and the remaining variables as inputs Then these

FIGURE 2.19 (a) A counterflow heat exchanger, and (b) typical temperature distributions

in the two fluid streams.

(a)

(b) Distance

2 1

quantities may be given in terms of the design variables and the operating tions, for given fluids, as

condi-Q  F (D1, D2, L, t1, t2, m m1, 2, T 1,i , T 2,i) (2.8)

T 2,o  G (D1, D2, L, t1, t2, m m1, 2, T 1,i , T 2,i) (2.9)Simple analytical expressions may be derived if the overall heat transfer coefficient is taken as a known constant (Incropera and Dewitt, 2001) The diameters and the length may be chosen so that the constraints due to size or space limitations are not violated Tube diameter and thickness choices may be restricted to those available from the manufacturer to reduce costs The length

L and diameter D1 initially may be held constant while different values of D2are considered Then L and D2 may be kept fixed, while D1 is varied, and so on Each combination of these three design variables represents a different system design that is subjected to different flow rates and temperatures, which repre-sent the operating conditions, to study the behavior of the system in terms of outlet temperatures and overall rate of heat transfer Thus, the model is used

to consider many different designs and operating conditions in order to obtain the inputs for evaluating the design as well as for optimizing the system Many different design possibilities can be considered easily once the model and sim-ulation scheme have been developed Numerical simulation is, therefore, the appropriate approach even for such a simple system Additional considerations arise in practical heat exchangers, such as different tube materials, ambient heat loss, insulation, and so on, making numerical simulation a very important element in the design process Further consideration of heat exchangers is given

in Chapter 5

The operating conditions for a particular system design are usually varied over wide ranges Certainly, the ranges expected in practice are covered during simulation But it is all right to get carried away and consider values far beyond the expected domain because these results will indicate the versatility of the system and how it would perform if the operating conditions exceeded the ranges for which the system is designed Conditions beyond those employed

for the design are often known as off-design conditions and simulation at these

conditions provides valuable information on the operation of the system and

on the model, particularly on its range of applicability This also relates to the safety of the system because operating temperature, pressure, speed, and

so on, may exceed the design conditions due to a malfunction in the system

or operator error Simulation would indicate if the system would be damaged under these conditions and how its performance would be affected In the fore-going heat exchanger example, simulation would yield the heat transfer rate and the outlet temperatures of the two fluids for different designs, given by the

tube diameters D1 and D2 and the length L, and for different operating

condi-tions, including off-design, given by the flow rates m1and m2and the inlet

temperatures T and T

2.3.4 E VALUATION : A CCEPTABLE D ESIGN

The next step in the design process is the evaluation of the various designs obtained for determining if any of them are acceptable for the given design problem As discussed earlier, an acceptable design is one that satisfies the given requirements for the system without violating the given constraints Therefore, the results from the simulation of the system are considered in terms of the problem statement

to determine if a particular design is acceptable Safety, environmental, tory, and financial constraints are also considered If the design is not satisfactory because it violates the constraints or does not meet the requirements, a different design is chosen, simulated, and evaluated This process is continued until an acceptable design is obtained If none of the designs chosen over the given ranges

regula-of the design variables is found to be satisfactory, we may terminate the process

or go back to the conceptual design stage and seek other alternatives

If the design under consideration is found to meet all the requirements and constraints, an acceptable or workable design is obtained and the design speci-fications are noted If we are only interested in obtaining a workable design for the given thermal system, the design process may be terminated at this stage However, in almost all practical cases, there are many possible solutions to the given design problem and the acceptable design obtained is, by no means, unique Therefore, it is more useful to seek additional satisfactory designs by continuing the simulation with different values of the design variables This effort would generally lead to a domain of acceptable or workable designs From this domain, the best design may be chosen based on a given criterion such as minimum cost

1 Acceptable design obtained Terminate iteration, communicate design

2 Acceptable design obtained Continue iteration to cover the given ranges of the design variables

3 Acceptable design not obtained Continue iteration with different design variables

4 Acceptable design not obtained over ranges of design variables nate iteration

Termi-The first and the third conditions are the ones shown in Figure 2.13 Termi-The second one yields a region of acceptable designs from which a suitable or optimal design may be developed, as mentioned previously The last condition indicates that a satisfactory design is not obtained over the given ranges of the design variables If additional conceptual designs are available, the design process may be reapplied

to a different conceptual design; otherwise a solution to the given design problem

is not obtained All these possibilities, along with others, do arise in actual practice

because there are cases where an acceptable design is not achieved with the given requirements and constraints In such cases, some of the requirements may be relaxed in order to obtain an acceptable design.

Considering again the simple counterflow heat exchanger discussed in the preceding section, the requirements and constraints may be written as

Constraints: (D1)min < D1 < D2 2 D2 < (D2)max L < L max (2.11)

Fixed Quantities: m2  ( m2)oo Δ m2 T 2,i  (T 2,i)o o ΔT 2,i (2.13)

where the subscript o refers to specified values and min and max refer to the

minimum and maximum allowable values, respectively The minimum and maximum values are based on space limitations, manufacturing, and other con-siderations Specified tolerance levels or variations in the values are also given Obviously, different requirements and constraints may be given for different applications Here, the fluid stream 2 is taken as fixed, while fluid stream 1 is varied Clearly, the tube material is another important consideration that may

be include in the problem Thus, the simulation of the system may be carried out for different designs and for different operating parameters, with the previous equations as the requirements and constraints All the quantities are varied over the permissible ranges

If the numerical simulation is carried out with different designs, obtained by varying the design variables over the given ranges, and if all acceptable designs are collected, a region over which the design is satisfactory is obtained This region may be represented mathematically in terms of the design variables as

domain of acceptable designs, may be sketched as shown in Figure 2.20 for a

particular value of D1 Similar regions may be shown for other values of D1, as

well as for D1 and L as the two variables, with D2 as given Such graphical resentations are obviously difficult to obtain or use for a large number of design variables However, this could be done easily on the computer The main idea here is that a number of acceptable designs may be obtained on the basis of simu-lation The selection for the best or optimal design may then be carried out from this region of acceptable designs

rep-2.3.5 O PTIMAL D ESIGN

It is rare that the design process would be terminated as soon as an acceptable design is obtained Only when the cost of optimization is decided as too high would the design activity stop after an acceptable design is obtained With grow-ing competition in the world today, it has become necessary to reduce costs while improving product quality Therefore, working with the first acceptable design obtained is no longer adequate At the very least, several possible designs must

be considered and the best chosen from among these, as measured in terms of an appropriate quantity such as cost, efficiency, or product characteristics Optimiza-tion refers to a systematic approach to minimize or maximize a chosen quantity or function The optimization process is obviously applied to acceptable designs so that the given requirements and constraints are satisfied Then the design finally obtained is an optimal one, not just an acceptable one Much of the latter portion

of this book is devoted to optimization of thermal systems and only a brief duction to the subject is given here to indicate its importance and position in the design process

intro-Optimization is of particular importance in thermal systems because of the strong dependence of cost and output on system design Usually, the optimal design is not easily determined from available simulation or acceptable design results A fairly elaborate effort has to be exerted in most cases to obtain the optimal design Since simulation is generally an involved and time-consuming process for most practical thermal systems, special techniques that reduce the number of designs to be simulated are of interest In addition, there are often very large differences between the performance of optimized and nonoptimized sys-tems in terms of energy consumption, product quality, overall thermal efficiency, and total costs

Optimization of a thermal system can be carried out in terms of the design hardware or the operating conditions The latter is particularly valuable because

FIGURE 2.20 Domain of acceptable designs, along with the given constraints, for a heat

exchanger.