OPTIMIZATION OF THERMAL SYSTEM: PROCEDURE AND REVIEW
1
Prof. M J Zinzuvadia,
2Prof. P. M. Agrawal,
3Er. Nishith Patel
1,2Asso. Professor, Mechanical Engineering Department, B V M Engineering College, V V Nagar ( Gujarat )
3Technical Director, Cipriani Harrison Valves Corp., V. U. Nagar.
Email: [email protected] ABSRACT:
Many types of thermal systems are used in process industries, power generation, refrigeration and air conditioning. These systems are made up of components like pump, compressors, heat exchanger and duct. For given application, many workable systems can be designed and if there exists additional requirement, design is optimized.
In this paper, all the steps of design procedure are discussed. Then frequently used optimization methods are enlisted and they are outlined with the help of corresponding, published design work.
INTRODUCTION:
Many practical applications of mechanical engineering require energy transfer and fluid flow through different devices like pump, compressor, engine and heat exchanger. These devices together make the thermal system. When thermal system is designed to perform required function, it is known as Workable system. But when we have some additional requirements also, designer optimizes the design by considering suitable criterion and appropriate optimization method. The thermal system thus obtained will be the optimum thermal system.
LITERATURE REVIEW AND PROCEDURE:
Different areas of thermal engineering like power generation, refrigeration, air conditioning and heating incorporate many types of thermal systems.
Design of these thermal systems requires technical expertise in corresponding areas and expert’s designing effort gives workable design. In practice, there will be many solutions for given practical problem and hence many workable systems. But recent advances consider optimization of thermal system by using like cost, size or weight of the system [1].
For optimizing a thermal system, as a preliminary step, system simulation is carried out by modeling components of the system mathematically. System simulation becomes mathematical statement for optimization and it can predict performance of the system when input condition is given. Then suitable criterion for optimization is decided by considering economics of the system and with the help of appropriate optimization method, optimum thermal system is obtained. As a first step of design procedure, equations are developed to represent performance characteristic of components of thermal system.
These equations are useful for system simulation and for developing mathematical statement for optimization.
Equation development is divided in two categories, namely, equation fitting and modeling of thermal equipment. Equation fitting is purely a number processing operation. Here experimental or catalog data of component is used. Most useful method for this purpose is Polynomial representation [2]. When number of data points available is same as the degree of polynomial (n) plus 1, polynomial represents those data points exactly. As an example, the pressure rise developed by centrifugal pump is function of two variables, namely speed and flowrate. Polynomial representation can be used for such situations also.
When many data points are available, calculation of coefficients in polynomial representation becomes difficult. In such situations, from available data points, best fit is obtaining with the help of method of least squares.
Modeling of thermal equipments uses some physical laws for equation development. Heat exchangers, distillation separators and turbomachines appear almost universally in thermal systems and they have physical explanations for their performance. Hence the knowledge of the
13-14 May 2011 B.V.M. Engineering College, V.V.Nagar,Gujarat,India
National Conference on Recent Trends in Engineering & Technology
physical relationship will be useful for developing equations. For modeling heat exchangers its effectiveness is an useful tool and performance of turbomachines can often be expressed in terms of dimensionless groups [3].
Thermal system is collection of components whose performance parameters are interrelated. Equations developed for performance of all components of thermal system, along with energy and mass balances form a set of simultaneous equations [4]. Solution of these simultaneous equations, many of which may be non-linear also, is simulation of thermal system in mathematical sense [5]. Simulation of thermal system thus obtained is useful to obtain the operating variables of the system at part load and over load condition, in addition to optimization of thermal system.
Generally successive substitution or Newton–Raphson method is used for system simulation. Method of successive substitution is straight -forward technique and easy to program.
Sometimes this method may give very slow convergence, which is considered as the disadvantage of this method. While Newton–
Raphson technique, a bit more complex, is a powerful technique.
Basic to thermal system optimization is the decision regarding which criterion is to be optimized. Minimum cost is probably the most common criterion. The achievement of minimum first cost is important but minimization of total cost during the life of equipment, which includes operating cost also, should not be overlooked.
In designing a workable system, arbitrarily certain parameters are assumed and individual components are selected around these assumptions.
But when optimization is an integral part of the design, the parameters are kept free to float and until combination of parameters optimizes the design [6]. The suitable method of optimization optimizes design within the concept means it can’t suggest new concept.
Calculus methods, Search methods, Dynamic programming, Geometric programming and linear programming are frequently used optimization methods. The basis of optimization by calculus is, to use derivatives to indicate the optimum. The method of Lagrange multipliers
performs an optimization where equality constraints exist and function is differentiable.
In search methods of optimization number of combinations of values of independent variables is examined and conclusions are drawn from the magnitude of the objective function at these combinations. The method of exhaustive search, where the objective function is calculated at all possible combinations, is an inefficient method.
Search methods, when applied to continuous functions, the exact optimum can only be approached, not reached, by a finite number of trials. On the other hand, when function exists only at specific values of the parameters, search methods are often superior to calculus methods.
Search methods are useful for single variable and multivariable- unconstrained and constrained optimization. N. Mc Closkey [7] has used Steepest – descent search for designing insulated steel tank for storing ammonia. In this problem, total cost comprises of vessel cost, insulation cost and recondesation cost and author has found out operating temperature of storage tank such that total cost becomes minimum.
Another method of optimization is Dynamic programming and it gives optimum function as result, rather than an optimum state point. This method is suitable for those problems, where desired result is path, e. g. the best route of a gas pipeline. A series of ultra filters is employed to separate protein and lactose from by-product of cheese manufacture. Klinkowski [8] shows that operating cost of a stage is function of inlet and outlet protein concentration and dynamic programming can be used to calculate concentration at each stage for minimum total cost.
This method can also be used to find pressure drop in sections of multi-branch duct.
Polynomial representations appear frequently in thermal systems. Here Geometric programming is applicable as it optimizes a function that consists of a sum of polynomials. In first stage of solution, this method gives optimum value of the function.
When objective function and constraints both are linear combinations of the variables, Linear programming is used for optimization. This is a well-developed method, useful in solving
13-14 May 2011 B.V.M. Engineering College, V.V.Nagar,Gujarat,India
National Conference on Recent Trends in Engineering & Technology
practical problems related to fuel consumption, efficiency and cost of the thermal system.
DISCUSSION AND CONCLUSION:
Following points can be concluded about Optimization of thermal systems:
1. Optimum thermal system should be preferred over Workable system, because Optimum thermal system is designed with focus on a suitable criterion.
2. Design of optimum thermal system, requires additional effort, so the decision about the optimization should be justified.
3. The thermal system is optimized by a step by step procedure, but within the step many options will be present.
Experienced designer can select the correct option.
4. Accuracy of collected data and correct description of criterion of design are important for optimization of thermal system.
REFRENCES:
[1] Stoecker W. F., “Design of Thermal Systems”, Third edition, McGraw- Hill Company.
[2] Wambsganss M. W. Jr., “Curve fitting with Polynomials”, Mach. Des., vol. 35, no. 10, p.167 [3] Olson Reuben M., Essentials of Engineering Fluid Mechanics, Fourth edition, Harper & Row Publishers, N. Y., pp.489-495
[4] ASHRAE, “Procedure for Simulating the performance of components and systems for Energy calculations”, New York, 1975.
[5] Stoecker W. F., “ A Generalized Program for Steady state Simulation”, ASHRAE Trans., vol. 77, pt I, pp. 140-148, 1971
[6] Fox R. L., Optimization Methods for Engineering Design, Addition- Wesly, 1971 [7] McCloskey N., “ Storage facilities associated with Ammonia pipeline”, ASME pap. 69, 1969.
[8] Klinkowski P. R., “Ultrafilteration: An emerging Unit Operation”, Chem. Eng., vol.85, no.
11, pp164- 173, 1978
