Delft University of T e c i i n o i o g y Ship Hydromechanics laboratory
Library Mekelweg 2 26282 CD Delft Phone: +31 (0)15 2786873 E-mail: p.w.deheer@tudelft.nl I S S N 1 8 1 3 - 8 5 3 5
December 2006
Vol. 3, No. 2
JOURNAL OF NAVAL ARCHITECTURE AND
MARINE ENGINEERING
An International Research Publication
'OPT-AAARINE-WARE' (OPTIMIZATION O F V E S S E L ' S PARAMETERS THROUGH SPREADSHEET MODEL)
Abhijit De and Ashish Jha 49-58
NUMERICAL SIMULATION O F ADVANCED ADSORPTION REFRIGERATION CHILLER WITH /VIASS R E C O V E R Y
M.Z.I Khan, S. Sultana, A. Akisawa and T. Kashiwagi 59-67
E F F E C T O F PRESSURE STRESS WORK AND VISCOUS DISSIPATION IN NATURAL CONVECTION F L O W ALONG A V E R T I C A L F L A T P L A T E WITH HEAT CONDUCTION
M.M. Alam, M.A. Alim and M. K. Chowdlniiy 69-76
STUDY O F MOLTEN SALT CORROSION O F S U P E R N L 7 5 USING THERMOGRAVIMETRIC TECHNIQUE
T.S. Sidhii, S Prakash and R.D. Agrawal 77-82
ournal of Naval Architecture and Marine Engineerins
December, 2006
}ittp://jnarne.8in.net
"OPTI-AAARINE-WARE"(OPTIMIZATION OF VESSEL'S
PARAMETERS THROUGH SPREADSHEET MODEL)
Abhijit De* and Ashisli Kumar^
'Research Scholar , Department of Marine Engineering, Jadavpur University, Kolkata:- 700032, India, Tel.:- 91-33¬ 23730312, E-mail: abhiiitde549l28@gmail.com
^Research Scholar, Department of Marine Engineering, Jadavpur University, Kolkata :- 700032, India, Tel.:- 91-9830582762, E-mail: ashishiha5615(a)anail.com
Abstract
77)6 objective of Ihis paper is to describe and evaluate a scheme of engineering-economic analysis for determining optimum ship's main dimensions and power requirement al basic design stage. We have divided Ihe optimization problem into five main parts, namely, Input, Equation, Constraint, Output and Objective Function. The constraints, which are the considerations to be fulfilled, become the director of Ihis process and a minimum and a maximum value are set on each constraint so as lo give Ihe working area of Ihe optimization. The outputs (decision variables) are optimized in favor of minimizing Ihe objective function. Microsoft Excel-Premium Solver Platform (a spreadsheet modeling lool is utilized lo model Ihe optimization problem). This paper is commenced by Ihe descriphon of Ihe general optimization problems, and is followed by Ihe model conslruclion of Ihe optimization. A case study on the determination of ship's main dimensions and ils power requirement is peiformed wilh the main objective to minimize Ihe Economic Cost of Transport (ECT). After simulating Ihe model and verijy'ing the residts, U is obserx'ed lhal the spreadsheet model yields considerably comparable results with Ihe main dimensions and power requirement dala of Ihe real operated ships (tanker). Il is also experienced lhal Ihis kind of optimization process needs no exhaustive efforts in producing programming codes, if the problem and the optimization model have been well defined.
Keywords: Optimization, design , Ship power requirement
N O M E N C L A T U R E
PSP Premium Solver Platform HFO Heavy Fuel Oil
ECT Economic Cost of Transport DO Diesel Oil
DWT Dead Weight Tonnage LO Lub Oil
NLP Non-Linear Programming ME Main Engine
GRG Generalized Reduced Gradient GE Generator
GUI Graphical User Interface SFOC Specific Fuel Oil Consumption
LP Linear Programming RFR Freight Rate
B/T Breadth by Draft Ratio ATC Annual Tons of Cargo
BHP Brake Horse Power L W L Length of Water Line
LPP Ship's length between L/B Length by Breadth Ratio
perpendiculars Ap Blade Area
DHP Delivered Horse Power Sim Simulation
T Draft LOC Lub Oil Consumption
1. Introduction
The problems in designing ship and marine machinery appear due to numerous considerations that must be taken into account. These conditions increase the capital cost and the complexity of the design option. Therefore, ship's design and its selected machinery must guarantee that the ship and its machinery w i l l operate with low level of failure, safely and efficiently, with high level of availability and will deliver an optimum rate of return on the capital being employed.
Abhijit De, Ashish Kumar/Journal of Naval Architecture and Marine Engineermg 3(2006) 49-58 Thoip and Armstrong (Thorp et al, 1982) utilized a comprehensive method to select the machineiy an-angement for a Panamax-size bulk carrier of 70,000 DWT. Their economic assessment was only focused on two alternatives o f slow speed diesel installation and medium speed diesel installation. Some parameters that were included in their study are also taken in our study. One o f the major differences with their study is that our study tackles the problem at the basic design process allowing the optimization process to determine the ship's main dimension and its machinery characteristics within the given constraints.
This paper proposes an alternative method for optimizing marine designs, particularly in determining ship's main dimension and its power requirement at basic design stage. Spreadsheet modeling is utilized and non-linear programming (NLP) can express our problem. The Generalized-reduced gradient (GRG) method can work in conjunction with the NLP problems. Basic diagrammatic concepts o f the optimization process and a case study are also given comprehensively
2. Premium Solver Platform and the basic optimization model
The determination of ship's main dimensions and its machinery power requirement encounters many constraints and considerations in its synthesized process (Sen, 1998). A number o f methods are available to solve the multi constraints and multi variables optimization problem such as those are summarized in (Rao, 1991).Fm-thermore, the optimization of ship's design can be defined as an attempt to resolve the conflicts of a design situation, i n such a way that the variables under the control of the decision-maker take their best possible value.
Generally, a classic multiple constrained optimization problems can be represented as follows.
X(ib)j<Xj<X(„b)j f o r j = 1,2,3,...,p
where X is a vector o f n variables and the function g^, ....,g„, all depend on X. lb and uh stand for low bound and upper bound respectively.
This paper employs the Microsoft Excel-PSP software (PSP) to deal with the above general expression o f optimization problem. PSP combines the ftinction of a graphical user interface (GIU), an algebraic modeling language and optimizers for linear, non-linear, and integer program. Each o f these ftmctions is integrated into the host spreadsheet program, which allows us to specify an objective function, constraints and other supporting features interactively. The PSP then makes the complete optimization model and produces the matrix form required by the optimizers. The optimizers itself employ the simplex (for LP model), the GRG (for NLP), and branch and bound methods to find an optimal solution and sensitivity information. For the LP problem, the focus of this model representation is the LP coefficient matrix. This is the Jacobian matrix o f partial derivatives o f the objective function and constraints with respect to the decision variables. In LP problems, the matrix entries are constant and need to be evaluated only once at the start ofthe optimization. On the other hand, in NLP problems, the Jacobian matrix entries are variable and must be recomputed at each new trial point.
Assuming linear model for a certain problem, the PSP uses a straightforward implementation of simplex method with bounded variables to find the optimal solution. For a NLP, the PSP uses the GRG method, as implemented in the GRG2 code (Ladson et al, 1978) &. (Ladson et al, 1992). GRG requires function values and the Jacobian matrix, which is not constant for NLP models. The PSP approximates the Jacobian matrix using finite difference method.
The basic format o f the offered optimization process is given in Figure 1. There are five folders within the optimization, namely the INPUT folder, EQUATION folder, CONSTRAINT folder, OUTPUT folder and the OBJECTIVE FUNCTION. The INPUT folder consists of all the parameters that are used in the entire optimization process. For a complex problem, such parameters can be classified into several directories, which will make fault identification easier.
which minimize/maximize f(X)
Subject to constraints
g(ib)i<gi(X)<g(„b)i f o r i = 1,2,3,...,m and
Abhijit De, Ashish Kumar/Journal of Naval Architecliire and Marine Engineering 3(2006) 49-58 A l l basic calculations of the optimization are located in the EQUATION folder. The result of each equation is continuously updated, since the process in the CONSTRAINT folder and the OUTPUT folder always affect the variables employed in the EQUATION folder.
The CONSTRAINT folder contains all considerations that must be satisfied and becomes the director of the optimization process. A minimum and a maximum value are set on each constraint to give the working area of the optimization. The optimum values are located in the center of the form. The determination of the minimum and the maximum values depend on the characteristics of the constraints.
Eq. n = Ln(Eq. 3)
E Q U A T I O N S
Example:
Eq. 1 = C l x C 2 Eq. 2 = SQRT (C3) Eq. 3 = Eq. 1 xEq. 2
MIN V A L U E Example: Constr. 1 Constr. 2 Constr. 3 Constr.n Min Value M i n Value M i n Value Min Value C O N S T R A I N T S Example:
Constr. l = (Eq. I-Eq. 2 ) x X l Constr. 2 =Eq. 2 x (Eq 3 '>X2) Constr. 3 =Eq. n-Eq. 2~ X3 Constr. n = SQRT (Eq 1 xXn)
M A X V A L U E
Example:
Constr. 1 Max Value Constr. 2 Max Value Constr. 3 Max Value Constr. n Max Value
MIN V A L U E
Example:
Dec. Var 1 M i n Value Dec Var2 M i n Value Dec. Var3 M i n Value Dec. Var n M i n Value
O U T P U T S (DecisionVar) Example: Decision Variable 1 ( X I ) Decision Variable 2 (X2) Decision Variable 3 (X3) Decision Variable n (Xn) M A X V A L U E Example:
Dec. Var I Max Value Dec. Var 2 Max Value Dec. Var 3 Max Value Dec. Var n Max Value
O B J E C T I V E F U N C T I O N
Example: Minimize
X I + X2 + X3+ +Xn
Figure 1: Basic format o f the optimization process
Ahinjil De, Ashish Kwnar/Joiirnal of Naval Architecture and Marine Engineering 3(2006) 49-58
3. Case Study: Basic Design Optimization Process For Tanker With Specified
Throughput
3.1 Problem statement
At the basic design stage, it is required to design a numbers of series ships (tanlcer) delivering contract of a certain throughput, which have optimum main dimension and optimum specified power, ECT is utilized as the objective of the optimization problem. Port characteristics require such constraints, as the ship must not exceed 200m in length and 11m in draught. The conceptual problem is shown in Figure 2. Some economic data are employed during the optimization process, as shown in Table 1 (Refer Appendix)
PORT A
PORT B
What is the o p t i m u m basic design output, which minimizes the Economic Cost o f Transport ( E C T ) during the economic l i f e
cycle o f the ship and machinery?
O B J E C T I V E F U N C T I O N
INPUT
I Estimated annual throughput I Economic l i f e
machineiy and ship I Owner Equity
Steel, f u e l , lub. o i l , tax, interest rate, port service charge rate, and other basic costs Depreciation Period Etc.
CONSTRAINTS
I Expected Repl. Cost I Reliability Function I Average Cargo
Weight per ship I Total pumping cap. I Pump cap.
I %Rated B H P Req. 1 Req. Freight Rate Midship Coefficient Max allowable ship length at port Etc.
OUTPUT
I Number o f ships I Draught I B / T Ratio I L / B Ratio I B l o c k Coefficient I Service Speed I Propeller R p m I Port T i m e Per Trip I Number o f UnloadingPump/host I Etc.
3.2. Model structure
Figure 2: Problem statementTo simplify the optimization problem, the INPUT folder and the EQUATION folder are grouped into several directories. In this particular optimization, the INPUT folder covers: the ship data, machineiy data, and reliability data. Each directory represents collection of parameters that are used in the calculation process.
The EQUATION folder consists of several directories such as the ship coefficient, machinery, reliability, loading and unloading, fiiel, operating cost and the economic considerations. The CONSTRAfNT folder comprises of the "Opti-Marine-Ware"(Optimization of Vessel's Parameters Through Spreadsheet Model) 52
Abhijit De, Ashish Kiimai/Joiinml of Naval Arcliitecture and Marine Engineering 3(2006) 49-58 expected replacement cost, reliability index, unloading pump capacity, specific fuel oil consumption (SFOC) for Maine Engine (ME) and and the maximum allowable ship length in port. The OUTPUT folder yields the optimum preventive maintenance intei-val, block coefficient, optimum design draught, optimum, B/T ratio, and the number o f ships. These values are sought with the main objective to minimize the ECT of the ship. ECT, the objective for this particular optimization problem is composed by several variables, namely the required freight rate (RFR), the inventory cost of cargo and the annual tons of cargo carried (ATC) (Hunt et al ,1995).
The optimum value of RFR itself depends on the annual capital recovery o f the vessel cost, the annual operating cost, and the annual throughput (Gransberg et al, 1998). The sequence of this design process indicates strict relationship among each design consideration.
No. of opr. ShiD Ujiit Port Cost pnstant oyage per year Unit Insur Cost No. of opr. Ship 0 . of opr. Ship
\
Voyage per year Anr Annual LO Cost Annual DO CostFigure 3: Interdependency between variables
For instance, it might be not a simple work to relate the optimum number o f shore connection, which must be fitted on a tanker with the resulted RFR or outcomes o f the loan repayment scheme. However, it is believed that those variables somehow interconnect and affect each other. Hence, the basic naUire of ships and its machinery design optimization process would lie on the ability of the engineers to accommodate all of the design considerations and to provide adequate flexibility in altering the decision variables, while fulfilling the main objecdve of the optimization process.
Abhijit De, Ashish Kiimar/Jowiia! of Naval Architecture and Marine Engineering 3(2006) 49-58
M I N V A L U E S
OPTIMUM:
No. of Req, Ship, B/T ratio Draught, Cb, Vs, propeller rpm. Prop, Diameter, pitch ratio.
OUTPUT O B J E C T I V E F U N C T I O N Reduce gradient, set another Decision variable values CONSTRAINT M I N V A L U E Replacement Cost Reliability Cargo weight Pumping capacity SFOC LOC Cavitation Number BHP req, RFR Max Allowable Lpp I,/B Ratio M A X V A L U E Set starting value of decision variables
E Q U A T I O N
Resistance calculation Ship Coefficient Fuel consmpt. Calculation MARKOV Evaluation Voyage Calculation Lubrication oil Powering calculation Vessel cost estimation R,F,R calculation Time value of monev Operating cost Loan Renavment INPUT/ Machinery / / Adjustment / / Cargo / / Economic / / Voyage / / Ship / / Port / / data / / factor / / Load data / / data / / data /1 data / j data /
Figure: 4 Optimization Model Structure
Figure 4 shows the general structure of this optimization problem. The optimization process is commenced by setting the initial value of the decision variables. Using relevant basic parameters located in the INPUT folder, all basic calculations are executed in the EQUATION folder. The results are then exported to the CONSTRAINT folder to calculate all constraints accordingly.The optimization problem can be mapped as shown in Table 2 (Refer Appendix). The objective is to minimize f (X), which is the ECT while determining the optimum value of X I to X12 subject to constraint g l (X) to g l 6 (X) , (Refer Appendix Table 2). The basic ship design and ship resistance formulae are mainly taken form Clarke (1975), Oosterveld et al (\915, Harvald, (1983) & SNAME ( 1967) and the economic parameters and major assumptions related to cost calculation from Hunt et al , (1995) and Kiss (1992),
3.3. Further description of the directories
Abhijit De, Ashish Kiimar/Joiiriml of Naval Architecture and Marine Engineering 3(2006) 49-58 The INPUT folder consists of g i v g i parameters and grouped into several directories. The ship data directoiy talces the cargo density of 915 kg/m . Appendages factor, which influences the resistance calculation, is assumed to have value of 0.03. This directory also allocates the need to use a reduction gear for engine speed reduction. The machinery data directoiy allows the alternative of using either single main engine or multiple main engines. The model also provides flexibility in employing number of generator set. Their reliability model is assumed to be represented by Weibull distribution, and its related parameters (y,P,r|) must be defined accordingly. The Weibull analysis is then used to fmd the best period/interval to carry out the maintenance program. The unit cost of failure replacement and unit cost of preventive replacement is also assumed before the optimization process can be executed (Jardine, 1973) & (Rasmussen, 1990). The voyage data directoiy is one of the vital directories in the optimization model. Optional trip distance and number of intermediate port make the model flexible. The assumed outbound and inbound load factors allow the model to be more realistic.
The economic data directory, as shown in Table 1 is gathered from many different sources and plays a very important role within the optimization model. The annual adjustment factor provides more realistic calculadon of the operating cost.
The EQUATION folder is also divided into several directories. The coefficient and ship directory collects all equations for determining the main dimensions of the ship. Since such equations usually stand as empirical formula, then the interpolation process takes part when some values lie beyond the original range (Kiss, 1992). The determination of ship resistance and power prediction is earned out using Harvald power prediction method (Harvald Sv. A A , 1983). The propeller design and its cavitation prediction are based on the Wageningen B-series propellers (Clarke, 1975, Oostei-veld et al,1975, Hai-vald, 1983). The vessel cost director y allows us to perform a basic hull cost, outfit cost, machinery cost and estimated overhead cost (Hunt et al, 1995). The SFOC-Speed-Power directory estimates the optimum percentage of rated BHP to be used during the service condition. The reliability directory determines failure rate, reliability and unreliability of the main engine based on the given Weibull parameters. This directory also estimates the expected length of operating hours before failure cycle. The number of voyage per year, which strongly influences the ECT, is optimized in the trip per year directoiy. The Fuel and lubricating oil directory estimates the annual fuel and lubricating oil requirement. Since the model does not refer to any pardcular engine, the calculation is then made empirically. The operational cost directory determines the annual operational cost for all ships. Because the investment scheme also affects the value of the optimized ECT, the loan repayment directory and the time value of money directoiy are then allocated to give flexibility for detennining the prefeiTed investment scenario.
60000 50000 40000 '3000C 20000 10000 0 -1 LPP-DWr & LPP-T Verification / a ^ • a ^ A A A ~ ^Jmf^ • -w ^ A A o» • --?e a ° * • -A «twDt wm^T* 14 12 10 ^ 8
I
E 6 4 2 0 50 100 150 LPP (meters) 200 250 300• LPP-DWT Real • LPP-DWT Sim A L P P - T Real • L P P - T Sim
Figure 8: LPP-DWT & LPP-T Verification
Abhijit De, Ashish Kwnar/Joumal of Naval ArchilecUire and Marine Engineermg 3(2006) 49-58
3.5.
Results verification
To verify tire performance of tliis optimization program, comparison on BHP, DWT, and T (draught) has been made on several tanker data (obtained from different shipping companies). The comparisons are shown in Figure 8 and 9. Generally, it is observed that the results of the simulation vei-y closely conform to the real data.
At some points the optimization result drastically shifts to a new point. This is caused by any adjustment made to the optimization program, which is different from that of the previous one. For instance, i f the throughput is less than 300,000 ton, then we could set the maximum cargo carrying capacify of the constraint at the value of 25,000 ton. Once we increase the throughput, the optimization cannot produce optimum results, until we increase the maximum value of the cargo carrying capacity.
D W T - B H P & D W T - L P P V e r i f i c a t i o n 300 250 ? 200 150 % 100 50 0 ••if*?'-'"'-! - A ' 20000 4 0 0 0 0 60000 80000 D W T (ton) 100000 30000 25000 20000 15000 10000 5000 120000
D W T - L P P Real D W T - L P T Real D W T - L P P Real D W T - L P P S i m
Figure 9: DWT-BHP & DWT-LPP Verificarion
4. Conclusion
For basic design stage or feasibility shidy puiposes, this method could be employed before commencing any further design stage. The case study presented here shows how this optimization program can effectively and precisely become consistent with the real ship's design. Moreover the most challenging part of the optimization problem is to express the problem in mathematical expressions which can be executed by the PSP.
The ship main dimensions and its power requirement that are obtained through this method can be further traced down into a more detail analysis to design the machineiy system on board. Additional task can easily be added within the optimization program by inserting a new directory within the INPUT and the EQUATION folder. Associated constraints and expected output can be attached with the objective either to minimize or to maximize the objective function. This kind of optimization process can also be utilized to select marine machinery from a certain number of available alternatives or to detemine maintenance management scheme, as utilized by authors in reference (Artana K B et al, 2000, 2001)
Acknowledgement
The authors grateflilly acknowledge the cooperation of Retired Prof J.P.Kundu, Department of Naval Architecture and Ocean Engineering, IIT Kharagpur.
Abhijit De, Ashish Kumar/Journal of Naval Architecliire and Marine Engineering 3(2006) 49-58
References
Artana, K, B. and Ishida, K. (2001): Detennination of ship machinery performance and its maintenance management scheme using M A R K O V process analysis. Marine Technology I V , WIT Press: 379-389 based marine machinery selection: a sUidy case on main engine cooling system. Proceedings: Sixth International Symposium on Marine Engineering (ISME 2000), Tokyo. 2: 791-796
Clarke, A.C.F. (1975): Regression Analysis of Ship Data, International Shipbuilding Progress.22: 227- 249 Gransberg, D. and Basilotto, J.P. (1998): Cost engineering optimum seaport capacity, Joumal of Cost Engineering, 4
Harvald Sv. A.A. (1983): Resistance and Propulsion of Ships, John Wiley & Sons.
Hunt, C E . and Butman, B.S. (1995): Marine Engineering Economics and Cost Analysis, Cornell Maritime Jardine A.K.S. (1973): Maintenance, Replacement and Reliability, Pitman Publishing
Kiss RK (1992): Ship Design and Construction, The Society of Naval Aixhitects and Marine Engineers, New York
Lasdon, L.S., Waren, A.D. Jain, A. and Ratner, M (1978): Design and testing of a generalized reduced gradient code for nonlinear programming, A C M Transactions on Mathematical Software, 4: 34-49
Lasdon, L.S. and Smith, S. (1992): Solving large sparse nonlinear programs using GRG, ORSA Joumal on Computing, 4: 2-15
Oosterveld, M.W.C. and Oossanen, P.V. (1975): Further Computer-Analyzed Data of the Wageningen B- Screw Series, Intemational Shipbuilding Progress, 22: 251-261
Thoi-p, I . and Armstrong, G. (1982): The Economic Selection of Main and Auxiliary Machinery, Transaction O f ImarE. 951:2-7
Rao, S.S. (1991): Optimization Theory and Applicadon, 2nd edition, Willey Eastem Limited, New Delhi
Appendix
Table 1 : Economic data input*
Economic life of machineiy Years 20.00
Loan repayment period Years 20.00
Interest rate % 0.10
Rate of return on equity % 0.12
Economic life of ship Years 20.00
Ship depreciation period Years 15.00
Machinery depreciation period Years 15.00
Tax rate % 0.30
Annual inflation rate % 0.01
Average fuel price (HFO/DO) US$/lb. 0.08
Average crew cost per month US$/month 1,250.00
Source: mainly obtained from Reference (Hunt et al ,1995)
Table 2: Optimization statement
Find
X, Min value < Time (t) independent variable < Max. value
x . Min value < Number of ships < Max. value
X3 Min value < Draught < Max. value
x_, M i n value < B/T ratio < Max. value
X5 M i n value < Block coefficient < Max. value
X6 M i n value < Service speed < Max. value
X7 Min value < Propeller rpm < Max. value
Xg Min value < Diameter propeller < Max. value
x . M i n value < Pitch ratio < Max. value
XlO M i n value < Time required for preventive replacement < Max. value
Abhijil De, Ashish Kiimar/Joiirnal of Naval Architecture and Marine Engineering 3(2006) 49-58 X l 1 M i n value < Port time per trip (loading)
Xi2 M i n value < Number o f unloading pump/host Which minimizes: Economie Cost o f Transport (ECT) (f(X))
Max. value Max. value RFR Total cost Annual port cost ƒ (unit cost, grt, voyage per year, no. of operated ship)
Annual insurance cost ƒ (voyage per year, weight o f cargo, unit insurance, no. of ship) Annual overhead cost ƒ (constant, no. o f ship)
Annual crew cost/(unit o f crew cost, no. o f crew, no. of ship) Annual expected replacement cost ƒ (reliability, no. of ship) Annual m/r cost ƒ (reliability, no. o f ship)
Annual diy docking expenses ƒ (constant, no. of ship) Annual administration cost ƒ (constant, no. o f ship)
Owner equity Constant
Throughput Given
Cargo cost unit Constant
Number of voyage Operating dayy(docking days, unscheduled maintenance days, time at port) Turn round time
Interest rate Constant Subject to
gi(X) Min value < Exptd. replacement cost,y(ReliabiUty index,Cost of fail. rep,Cost of Prev. rep)<Max. value g2(X) Min value < Reliability function,^(failure distribution parameters) <Max. value g3(X) Min value < Ave. cargo wt./ship,y(throughput,No. of ship, voy./ year,Load factor) <Max. value g4(X) Min value < Total pumping capacity,y(Pump capacity. No. of req. pump) <Max. value g5(X) Min value < Pump capacity/(Cargo weight. Port time, Cargo density) <Max. value g6(X) Min value < SFOC for full load MEy(DHP, engine rpm) <Max. value g7(X) Min value < SFOC for full load GEy(DHP, diesel generator rpm) <Max. value g8(X) Min value < Cavitation noy(TI-IP,Projected Blade Area(Ap),dyn. press, at tip radius) <_Max. value g9(X) Min value < Local cavitation no./press, at the screw centerline, dyn.press. at dp radius) <Max. value gio(X) Min value < %Rated BHP requirement/min resulted SFOC at feasible region) <Max. value gll(X) Min value < Required freight rate/Ann.Vessel cost,total opr.Cost, throughput) <Max. value gl2(X) Min value < Midship coefficient/Displacement, Breadth, Draught, Lpp) <Max. value
gl3(X) Min value < L/B ratio/Lpp/Breadth) <Max. value
gl4(X) Min value < Max allowable ship length at port/Vol.Displ,Breadth,Draught,Block coef) <Max. value
gl5(X) Min value < Length of water line (LWL) ƒ (LOA) <Max. value
g.6(X) Min value < Length between perpendicular (LPP) f (LWL) <Max. value
ournal of Naval Architecture and Marine Engineerins
December, 2006 littp://jname. 8m. net
NUMERICAL SIMULATION OF ADVANCED ADSORPTION
REFRIGERATION CHILLER WITH AAASS RECOVERY
M.Z.I. Khan^ S. Sultana^ A. Akisawa', T. Kashiwagi*
'Graduate School of Bio-Applications and Systems Engineering, Tokyo University of A. & T., 2-24-16, Naka-machi, Koganei-shi, Tokyo 184-8588, Japan
^Department ofMathematics, Stamford University, Dhaka, Bangladesh
Abstract
777/5 paper investigates tlie tiiermodynamic fi-ameworlc of a tliree-bed advanced adsorption cliiller, wiiere tlie mass recoveiy scheme has been utilized such that the peiformances of this chiller conld be improved and a CFCfree-based sorption chiller driven by the low-grade waste heat or any renewable energy source can be developed for the next generation of refrigeration. Silica gel-water is chosen as adsorbent-refrigerant pair. The three-bed adsorption chiller comprises with three sorption elements (SEs), one evaporator and one condenser. The configurahon of SEI and SE2 are identical, but the configuration of SE3 is taken as half of SEI or SE2. Mass recoveiy process occurs between SE3 with either SEJ or SE2 and no mass recoveiy benveen SEJ and SE2 occurs. Tlie mathematical model shown herein is solved numerically. In the present numerical solution, the heat source temperature variation is taken from 50 to WC along with coolant inlet temperature at 30°C and the chilled water inlet temperature at J4''C. A cycle simulation computer program is constructed to analyze the influence of operating conditions (hot and cooling
water temperature) on COP (coefficient of performance), SCP (specific cooling power), rj (chiller efficiency) and chilled water oidlet temperature.
Keywords: Adsorption; COP; SCP; Mass recovery; Silica gel-water
N O M E N C L A T U R E
A area (m^) Subscripts
Cp specific heat (J kg"' K ' ' ) ads adsorber, adsorption Dso pre-exponential constant (m^s'') cond condenser
E. activation energy (Jkg'') chill chilled water L latent heat o f vaporization (J kg"') cw cooling water
lit mass flow rate (kg s"') des desorber, desorption Ps saturated vapor pressure (Pa) eva evaporator
q
»
q
concentration ( kg / kg) hex heat exchanger q
»
q concentration equilibrium (kg / kg) hw hot water Qs, isosteric heat of adsorption (J kg"') in inlet R gas constant (Jkg"'K"') out outlet Rp average radius o f a particle (m) s silica gel
T temperahire (K) se sorption element
t time (s) w water
U heat transfer coefficient (W m"^K"') wv water vapor W weight (kg)
\. Introduction
Since the Montreal Protocol called for a ban on the use o f CFCs, there have been increased research efforts over the last twenty years on the development o f refrigeration technologies which address the environmental concems of ozone layer depletion and global warming. The sorption cooling system is environment-friendly compared with traditional CFC systems as it employs safe and non-polluting refrigerants. The most common thermally-driven sorption cooling system is the gas-liquid absorption system ( L i B r - H 2 0 , H 2 0 - N H 3 ) which offers numerous advantages in specific applications. However, such a system possesses certain limitations in operating conditions shidied by Douss et al. (1989) and Stitou et al. (2000). Thus, adsorption systems have attracted increased research interests as an altemative cooling solution. However, the main limitation in the commercial application o f adsorption systems is its rather low coefficient of performance. In order to improve 1813-8535 © A N A M E Publication. A l l rights reserved
M.Z.I. Khan, S. Sidtana, A. Akisawa, T. Kasbiwagi/Joiimal of Naval Architecture and Marine Engiiieerhi 3(2006) 59-67 the performance of such coohng systems, several advanced cycles have been proposed such as the continuous cycle by Cacciola et al. (1995), cascading cycle by Douss et al. (1989) and Stitou et al. (2000), forced convection cycle by Critoph (1998) and thermal wave cycle by Miles (1989). Wang et al. (2002) incorporated heat and mass recovery processes into the continuous cycle to improve its thermal performance. However, the resulting COP is still rather low being below 1.0. Recently, Leong and L i u (2004) modeled a combined heat and mass recovery adsorption cycle employing a compact zeolite adsorbed bed and obtained COP values which are slightly better than those of Wang et al. (2002). Douss and Meunier (1989) proposed a cascading cycle with a higher COP of
1.06. Stitou et al. (2000) analyzed different cascading cycles which coupled solid-gas reactions with the liquid-gas absorption process. The COP can be increased by more than 30% compared with double-effect absorption cycles. In cascading cycles, different condenser and evaporators are employed for different pairs. The system configuration and operation are inherently more complex compared with continuous cycles. The forced convection and thermal wave cycles are both capable of achieving high COP values. However, for actual engineering application, the operating conditions of these systems are difficult to control. Meunier (1986) studied the system performance of cascading cycle in which an active/methanol cycle is used topped by zeolite/water cycle. To improve the COP value, Shelton et al. (1990) proposed thennal wave regenerative adsorption heat pump. To improve the cooling power. Pons and Poyelle (1999) studied the influence of mass recovery process in conventional two beds adsorption cycle. Later, Wang (2001) investigated the perfonnances of vapor (mass) recovery cycle with activated carbon-methanol as adsorbent/adsorbate pair and demonstrated that the mass recovery cycle is effective for the low regenerating temperature.
In this study, silica gel-water has been selected as the adsorbent-adsorbate pair because of the low regeneration temperaUire of silica gel and the high latent heat of vaporization of water. Additionally, this working pair is non-toxic and environment friendly. In the present study, a novel strategy of mass recovery cycle is proposed to improve the cooling effect. In the new strategy, mass recovery process occurs between SE3 with either SEI or SE2 and no mass recoveiy between SEI and SE2 occurs. The present strategy is completely different from the conventional mass recovery cycle as there is no heating and cooling process during mass recoveiy process in conventional mass recovery cycle. In the present strategy additional heating and cooling accelerated the desorption/adsoi-ption process; thus the system provides the better cooling output.
2. Working Principle of the Mass Recovery Chiller
The schematic diagram and time allocation of the proposed three-bed mass recovery chiller are shown in Fig. 1 and Table 1, respectively. The three-bed mass recoveiy chiller comprises with three sorption elements (SEs) (adsorber/desorber heat exchangers), a condenser, an evaporator, and metalic tubes for hot, cooling and chilled water flows as shown in Fig. 1. The design criteria of the three-bed mass recovery chiller are almost similar to that of the three-bed chiller without mass recovery which is proposed and devoloped by Saha et al. (2003) and (2006). However, in the proposed design, it needs extra piping, which connects two beds during mass recoveiy. The configeration of SE3 in the three-bed chiller with mass recovery is taken as half size of SEI or SE2 where SEI and SE2 are taken same. Operational strategy of the proposed chiller is shown in Table 1. In proposed design, mass recoveiy process occurs between SE3 with either SEI or SE2 and no mass recovery between SEI and SE2 occurs. To complete a f u l l cycle for the proposed system, the chiller needs 10 modes, namely A , B , C, D, E, F, G, H, I and J as can be seen from Table 1.
Vapor refrigerant •^Closed V I X Opened V: valve Evaporator Capillary Tube Qev. Chilled water
Fig. 1: Schematic of three bed chiller with mass recovery
M.Z.I. Khan, S. Sultana, A. Akisawa, T. Kashiwagi/Joiiriial of Naval Architecture and Marine Engineerin 3(2006) 59-67 In mode A , SEI and SE3 work as desorber. The desorption-condensation process takes place at condenser pressure {Feed)- The desorber ( SEI, SE3) is heated up to temperaUire (Tdef) by heat input Q^es, provided by the driving heat source. The resulting refrigerant is cooled down by temperaUire {Tco„d) in the condenser by the cooling water, which removes condensation heat, SE2 works as adsorber in mode A. In the adsoiption-evaporation process, refrigerant (water) in evaporator is evaporated at evaporation temperature, T„a, and seized heat, g^va from chilled water. The evaporated vapor is adsorbed by adsorbent (silica gel), at which cooling water removes the adsorption heat, Q^.
Table 1: Operational strategy of three bed chiller with mass recoveiy
Mode B is the pre-cooling process for SE3. In pre-cooling process, SE3 is isolated from evaporator, condensed or any other beds. Cooling water is supphed to the bed for short time (30s) in this period. SEI works as desorber and SE2 works as adsorber in mode B also.
Mode C is the adsorption process for SE3, SE2 and desorption process for SEI.
In mode D, SE3 (at the end position of adsorption-evaporation process) and SEI (at the end position of desoiption-condensation process) are connected with each other continuing cooling water and hot water, respectively that can be classified as two-bed mass recovery process. This time SE3 is isolated from evaporator and SEI is isolated from condensed. Here mass recovery occurs only bed to bed. In this mode SE2 works as adsorber. When the concentration levels of both beds SE3 and SEI reach in nearly equilibrium levels, then warm up process will start, called mode E (pre-heating or pre-cooling).
In mode E, SE2 and SE3 are heated up by hot water, and SEI is cooled down by cooling water. When the pressure of SE2 and SE3 are nearly equal to the pressure of condenser then SE2 and SE3 are connected to condenser. When the pressure of SEI is neariy equal to the pressure of evaporator then SEI is connected to evaporator.
In mode F, SE2 and SE3 work as desorber and SEI works as adsorber.
Mode G is the pre-cooling process for SE3. In this mode, SE2 works as desorber and SEI works as adsorber. Mode H is the adsorption-evaporation process for SEI and SE3. SE2 works as desorber in this mode.
In mode I , SE3 (at the end position of adsoiption-evaporation process) and SE2 (at the end position of desoiption-condensation process) are connected with each other continuing cooling water and hot water, respectively that can be classified as two-bed mass recovery process. When the concentration levels of both beds SE3 and SE2 reach in neariy equilibrium levels, then warm up process will start, called mode J (pre-heating or pre-cooling). SEI works as adsorber in this mode.
Mode J is the pre-heating/ pre-cooling process for all bed. In this period, SEI and SE3 are heated up by hot water, SE2 is cooled down by cooling water. Mode J is the last process for all sorption elements (SEs), after this mode, all soiption elements will retum to its initial position (Mode A). That's why to complete one cycle, it needs 10 modes.
M.Z.I. Khan, S. Stihana, A. Akisawa, T. Kashiwagi/Joiiriial of Naval Architecture and Marine Engineerin 3(2006) 59-67
3. Mathematical Formulation
3.1 Energy balance for the adsorber/desorber heat exchanger
Adsoiption and desoiption lieat balances are described by identical equations, where heat transfer fluid (water) temperature temi Ti„md. Tout denotes cooling water upon adsorption and hot water upon desorption. 7),ev denotes reactor bed temperaUire. The adsorbent bed temperature, pressure and concentration are assumed to be uniform throughout the adsorbent bed. The heat transfer and energy balance equations for the adsorbent bed can be described as follows:
T = T
w,out hex
Thex) exp
U hex ^ hex
(1)^ { ( w , ( C p , + Cp,, q) + ( W ^ , , Cp,, + Wn,,, CpA,)T,,, }= W^Q, ^
dt
5
W,Cp,,{y(T,,, - T , , J
+ ( 1 -
y ) ( T , , , - T , , J } ^ +
iii,,CpjT,,,i„
- T , , , „ , J
dt
(2),where, 5 is either 0 or 1 depending whether the adsorbent bed is working as desorber or adsorber and y is either 1 or 0 depending on whether the bed is connected with evaporator or another bed. Equation (1) expresses the importance o f heat transfer parameters, namely heat transfer area and heat transfer coefficient [/;,£,.. The left hand side o f the adsorber/desorber energy balance equations (Eq. 2) provides the amount o f sensible heat required to cool or heat the silica-gel (s), the water (w) contents in bed as well as metallic (hex) parts o f the heat exchanger during adsorption or desoiption. This term accounts for the input/output o f sensible heat required by the batched-cycle operation. The first term on the right hand side o f Eq. (2) represents the release o f adsorption heat or the input o f desorption heat, while the second and third terms represent for the sensible heat o f the adsorbed vapor. The last teim on the right hand side of Eq. (2) indicates the total amount of heat released to the cooling water upon adsorption or provided by the hot water for desorption. Equation (2) does not account for extemal heat losses to the environment as all the beds are well insulated.
3.2 Energy balance for the evaporator
In the present analysis, it is assumed that the tube bank surface is able to hold a certain maximum amount o f condensate and the condensate would fiow into the evaporator easily. The heat transfer and energy balance equations for evaporator can be expressed as:
"^ehilhoul
c h i l l . i nTeva) exp
TT A
eva eva
chill Cp,chill )
( 3 )dt
f w ,
C
w ,
eva,hex
^p,eva)Teva } " TWg C
(T,^^
j
T,
xdq
des
dt
+ lTlchillCp,chill (T,
chill,in
'chill,out
f
(4),
where the subscripts chill and eva indicate chilled water and evaporator respectively. The left hand side of Eq. (4) represents the sensible heat required by the liquid refrigerant (iv) and the metal o f heat exchanger Uibes in the evaporator. On the right hand side, the first term gives the latent heat o f evaporation (E) for the amount of refrigerant adsorbed (dq^Jdt), the second term shows the sensible heat required to cool down the incoming condensate from the condensation temperature r„,„/ to evaporation temperaUire T;,,» , and the last term represents the total amount of heat given away by the chilled water.
3.3 Energy balance for the condenser
The heat transfer and energy balance equations for condenser can be expressed as:
cond,out
cond + (Te
'cond
)exp
^ cond ^ cond
^cw^pw
(5)
M.Z.I. Khan, S. Sultana, A. Akisawa, T. Kashiwagi/Joiinial of Naval Architecliire and Marine Engineerin 3(2006) 59-67
^^^if^cw,w^pw'^^^conddiex^p,cond)^cond. ~ ^^s
~ ^s^p,wi'^des ~ '^cond ) + ^cw^pw^cwjn ~ '^cw,out)
(6), _ r 1
I "^cw'~^pwy-cwdn
where the subscripts cw and cond indicate cooling water and condenser, respectively. The left hand side of Eq. (6) represents the sensible heat required by the metallic parts of heat exchanger tubes due to the temperature variations in the condenser. On the right hand side, the first term gives the latent heat of vaporization (L) for the amount of refrigerant desorbed (dqjjdt), the second term shows the amount of sensible heat requirement to cool down the incoming vapor from the desorber at temperahire Tj^s to condenser at temperature Tco„d, and the last term represents the total amount of heat released to the cooling water.
3.4 Mass balance
Mass and heat balances are based on the assumption that both the temperature and the amount of refrigerant adsorbed are uniform in the adsorbent beds. Since the temperatures in an adsorption cycle are unsteady state, the energy balance equations (Eqs. 2, 4, 6) must account for sensible heat input and/or output during cycle period. The mass balance for the refrigerant can be expressed by neglecting the gas phase as:
'^^g'"."' _ _^r ('^Ides-coud ^ '^leva-ads ^
dt \ dt dt
d (7),where, subscripts des-cond and eva-ads stand for the vapor flow from desorber to condenser and evaporator to adsorber, respectively.
3
.5
Adsorption rate
The adsorption rate is expressed as
dq ,
r * \— = k,apX{q -q) (8), where, the overall mass transfer coefficient
{k,ap)
for adsoiption is given by:k,a^={l5D^)l{R^f (9).
The adsorption rate is considered to be controlled by surface diffusion inside a gel particle and surface diffiisivity (D,) is expressed by Sakoda and Suzuki (1984) as a fiinction of temperature by:
Z 3 , = D , „ x e x p [ - ( £ J / ( i ? r ) ] (10)
and q is the amount adsorbed in equilibrium with pressure Pj(r„,) and is chosen from a concise analytical expression of experimental data by the following form:
q'' = k[P,{T^„)IP^{T^)\'" (11),
where P/J,,,) and P,{T,) are the saUiration vapor pressure at temperatures 7,,, (water vapor) and T, (silica gel), respectively; the parameters k and n are taken as constants. Chihara and Suzuki (1983) obtained experimental values for k and n for the silica gel-water pair as the constants k = 0.346 kglkg and n =\.6,k denotes the limiting amount adsorbed at P,(T„)I P/TJ = 1. As the Eq. (11) describes the physical phenomenon of adsorpdon, the water vapor and the adsorbent temperahires are not equivalent. The refrigerant temperahire in the vapor phase is defined by the temperatures of the evaporator (during adsorption) or condenser (in desorption); the adsorbent temperature is determined by the heat transfer fluid (hot or cooling water) temperaUire. Only for refrigerants in the adsorbed phase are the temperatures of refrigerant and adsorbent taken as equivalent.
Brunauer (1945) states that i f a plot of log q' against log (P/TJ/ P/TJ) gives a straight line, the adsorption data obey the Freundlich equation. The slope of the straight line then gives l/n, and intercept gives log k. For a specific case of carbon monoxide adsorption on coconut charcoal, Branauer (1945) mentions that both k and n decrease with increasing temperature. In fact, the value of l/n would approach the limiting value of unity when the temperaUire increases enough for the amount adsorbed (q*) to become very small.
By comparing Freundlich equation plots to experimental data obtained from the literatiire of Hubard (1954) and from the manufactiirer, NACC (1992), the authors obtained good agreement only in a relatively naiTow pressure and temperahire range for constant values of k and l/n. This led them to adapt the Freundlich equation to the manufacUirer's experimental data NACC (1992) for a more precise fit in this shidy, based on the work of Saha et al. (1995):
M.Z.I. Khan, S. Sultana, A. Akisawa, T. Kashiwagi/Joiiriial of Naval Architecture and Marine Engineerin 3(2006) 59-67
q* = A(TJ.[P,iTJ/PXT^)f'''' (12), where,
A(TJ = A0 + Al.T^+A2.Tj' +A1,.T^ .40 = -6.5314 A 1 = 0.72452E-01 /( 2 =-0.2395 lE-03 3 = 0.25493E-06 B{TJ = B0 + Bl.T^+B2. T]- + 53. 5 0 = -15.587 5 1 =0.15915 5 2 = -0.50612E-03 5 3 = 0.53290E-06.
The numerical values of AO ~ AT, and 50 ~ 53 are determined by the least-square fits o f experimental data. The other values adapted in simulation are presented in Tables 2 and 3.
The saturation vapor pressure and temperature are correlated by Antoine's equation, which can be written as:
3820 ^
18.3
(13).r - 4 6 . l j ^ '
= 133.32 X exp
Table 2 Baseline Parameters
Values Adopted in Simulation Symb
ol
Value Unit Symbol Value Unit Abed 1.45 m R 4.62E+2 J / k g . K Aeva 0.665 m Ro 0.35E-3 m A ^con c 0.998 m Uads 1380 W / m l K 924 J / k g . K Udes 1540 W / m l K c 4.18E+3 J / k g . K Ueva 3550 W / m l K Cp.chiU 4.20E+3 J / kg. K Ucond 4070 W / m l K
r 386 J / kg. K Ws 14 kg Cp.Al 905 J / k g . K Wkhex 12.67 kg 2 . 5 4 E ^ m V s Wfte. 5.33 kg Ea 2.33E-H3 J / k g w 5 kg L 2.50E-H6 J / k g w eva.w 25 kg Qs, 2.80E+6 J / k g
Table 3: Standard operating condition
Hot water Cooling water Chilled water Time Temperature
(°C)
5 0 - 9 0 30 14 Total cycle time = 900s, Mass
recovery time = 160s, Pre heating/cooling time = 30s.
Flow rate (kg/s) 0.4 0.4(ads)+0.34(cond) O.U
Total cycle time = 900s, Mass recovery time = 160s, Pre heating/cooling time = 30s.
3.6 Measurement of system performance
The performance o f a three-bed adsoiption chiller with mass recoveiy is mainly characterized by specific coohng power (SCP) which is defined as cooling capacity per kg silica gel, coefficient o f performance (COP), waste heat recovery efficiency, r| and can be measured by the following equations:
t,..
S p e c i f i c C o o l i n g P o w e r - r h , , , j j [ C ^ , j ( T c h i i i , i n ~ T g y i i gm ) d t M ^ c h i l l ' - ^ w J V ^ c h i l l , i n
0
here, Ws.cuiier stands for the total mass of silica gel in the chiller. Coefficient o f performance (COP) =
s,cliiller * ^ cycle
m chill 'cyclo
1(
T,
c h i l l j i n ' chill.oul ril hoi l ( T h o t , i n ^ hol,out )d.M.Z.I. Khan, S. Sultana, A. Akisawa, T. Kashiwagi/Joumal of Naval Architecture and Marine Engineerin 3(2006) 59-67 and the Waste Heat Recovery Efficiency, t| =
4. Calculation Procedure
In the present analysis, a cycle simulation computer program is developed to predict the performance o f the three-bed chiller with mass recovery. The above mentioned set o f coupled equations is solved by finite difference approximation with a time step o f one second. The results taken in the study are from the cyclic steady state conditions. A real chiller starts its operation from the unbalance conditions; however, it reaches in balance condition after few cycles. Therefore, an iteration technique is employed in the solution procedure to f i x the initial conditions for the cyclic steady state. In the beginning o f the solution process, the initial conditions are assumed; however, those are adjusted for the cyclic steady conditions by the iteration process.
When two beds are connected with each other, the vapor pressure is unknown, which are essential for the calculation o f adsorption/desorption rate inside the adsorbent beds. In this state, vapor pressure is assumed initially and the amounts of vapor adsorbed/desorbed by the beds are calculated. Conceptually, the desorbed vapor from one reactor bed (SEI) should be equal to the amount of adsorbed vapor by the other reactor bed (SE3). I f these amounts are not equal then vapor pressure are adjusted for next iteration. Once the satisfactory convergence criterion is achieved, then process goes for the next time step. The output results have almost no dependency on the assumed initial conditions. The convergence factor is taken as 10"^ for all parameters.
5. Results and Discussion
In order to clarify the performance of mass recovery cycle, cycle simulation runs are performed. Since our main interest is to utilize the low grade waste heat as the driving source, the investigation was conducted for hot water between 50 and 90°C. The base line parameters and standard operating conditions for the chiller operation are listed in Table 2 and Table 3, respectively. The effect of operating temperature (hot and cooling water) is calculated by the simulation runs.
5.1 Effect of driving heat source temperature on SCP and COP
Figure 2 shows heat source temperaUire variation on SCF (specific cooling power), ft is seen that SCP for three-bed mass recovery chiller increases with the increase o f heat source temperature. This is because the amount o f refrigerant circulated increases, due to increased refrigerant desorption with higher driving source temperature. Another reason is that, in the proposed cycle, SEI and SE2 connect with SE3 one by one during mass recovery, which accelerates cooling effect. In Fig. 3, COP is depicted with the variation o f driving heat source temperaUire. It is seen that COP o f the proposed cycle is also increased with the increase of heat source temperaUire as we observed for SCR It is already stated that the SCP is improved due to the mass recovery process. The mass recovery process generates more desorption heat and that is transfeiTed from the desorber through desorbed vapor. So, in the low heat source temperahire (65-80°C), proposed chiller gives better performance. 120 0.6 0.2 20 0 0 45 55 65 75 85 95 45 55 65 75 85 95 Heat Source Temperature [°C]
Fig.2 The effect o f heat source temperature on specific cooling power.
Heat Source Temperature [°CI Fig. 3 The effect of heat source lenperalure on
COP.
M.Z.I. Khan, S. Suhana, A. Akisawa, T. Kashiwagi/Joiimal of Naval Architecture and Marine Engineerin 3(2006) 59-67
45 55 65 75 85 95 45 55 65 75 85 95 Heat Source Temperature [°C] Heat Source Tenperature f C ]
Fig, 4 The effect of heat source tenperature on waste Fig- 5 The effect o f heat source temperature on heat recovery efficiency. Chilled water outlet temperature.
5.2 Effect of driving lieat source temperature on chiller efficiency, ti
Figure 4 presents tiie waste lieat recovery efficiency, r|, as a function of heat source temperahire. For three-bed proposed cycle employing mass recovery scheme with heating/cooling, r| rises from 0.03 to 0.046 as hot water inlet temperature is increased from 50 to 65°C with a cooling source 30°C. This is because improvement o f cooling capacity o f the proposed chiller in this range. It is also observed that r| is boosted by about 25% than that of conventional cycle demonstrated in Khan et al. (2005).
5.3 Effect of driving heat source temperature on chilled water outlet temperature
The effect o f heat source temperature on average chilled water outlet temperahire is depicted in Fig. 5. The chilled water temperahire level needs to be considered according to demand side requirement. Mass flow rate o f chilled water can control the outlet temperature of chilled water. From Fig. 5, it is seen that the cyclic average chilled water outlet temperahire of the proposed cycle decreases with the increase o f the driving heat source temperature. Low chilled water outlet temperature is expected from real machine.
18 22 26 30 34 38 42 i g 22 26 30 34 38 42 Cooling Source Temperature [°C] Cooling Source Temperature [°C]
Fig.6 The effect o f cooling source tenperature on pig. 7 The effect o f cooling source temperature on
specific cooling power. qqP
5.4 Effect of coohng source temperature on SCP and COP
Figure 6 and 7 show the effect o f cooling water inlet temperatures on SCP and COP, respectively. In the present simulation, cooling water mass flow rate into adsorber is taken as 0.4 kg/s, while for the condenser the coolant mass flow rate is taken as 0.34 kg/s. The SCP increases steadily as the cooling water inlet temperature is lowered from 40 to 20°C. This is due to the fact that lower adsoiption temperatures resuh in larger amounts o f refrigerant being adsorbed and desorbed during each cycle. The simulated COP values also increase with lower cooling water inlet temperature. For the three bed chiller the COP value reaches 0.62 with 70°C driving source temperature in combination with a coolant inlet temperature o f 20°C.
6. Conclusions
A novel three-bed mass recovery chiller with silica gel as adsorbent and water as adsorbate is proposed and the performances are evaluated by numerical technique. For the utilization of the demand, multi-bed mass recovery Numerical Simulalion of Advanced Adsorption Refrigeration Chiller with Mass Recoveiy 66
M.Z.I. Khan, S. Sidtana, A. Akisawa, T. Kashiwagi/Joiinial of Naval Architecture and Marine Engineerin 3(2006) 59-67 cycle is presented and the effects of operating conditions are investigated. The following concluding remarks can be drawn from the present analysis:
(i) The main feahire of the proposed chiller is the ability to be driven by relatively low temperahire heat source. The chiller can utilize the fluctuated heat source temperature between 50 and 90°C to produce effective cooling along with a coolant inlet at 30°C.
(ii) In the cycle simulation study, hot and cooing water temperatures are the most influential parameters. SCP increases with the increase of hot water temperature and opposite tendency for cooling water temperahire. Highest COP value is obtained for hot water temperature variation from 65 to 78°C. (iii) In the low heat source temperature, COP improves significantly.
(iv) Waste heat recovery efficiency, r| rises from 0.03 to 0.046 as hot water inlet temperature is increased from 50 to 65°C with cooling source at 30°C.
( v ) Delivered outlet chilled water temperature of the proposed cycle decreases with the increase of driving heat source temperature.
References
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[Journal of Naval Architecture and Marine Ensineerins
December, 2006
littp://jname.8m.net
E F F E C T O F PRESSURE STRESS WORK AND VISCOUS DISSIPATION
IN NATURAL CONVECTION FLOW ALONG A VERTICAL F L A T
PLATE WITH HEAT CONDUCTION
Md. M. A I a m \ M . A. Alim^ and Md. M . K . Chowdhury^
'Department ofMathematics, Dhaka University o f Engineering and Technology, Gazipur-1700, Bangladesh.
^Department o f Mathematics, Bangladesh University o f Engineering and Technology, Dhaka-1000, Bangladesh. Email: maalim(ft!math.buet.ac.bd
Abstract
tins paper, tlie effect of viscous dissipation and pressure stress work on free convection flow along a vertical flat plate has been investigaled. Heat conduction due to wall thickness b is considered in this investigation. With a goal to attain similarity solutions of the problem posed, the developed equations are made dimensionless by using suitable transformations. The non-dimensional equations are then transformed into non-linear equations by introducing a non-similarit}> transformation. The resulting non-linear similar equations together with their corresponding boundaiy conditions based on conduction and convection are solved numerically hy using the finite difference method along with Newton's linearization approximation. Numerical resuils for the details of the velocit)' profiles, temperature profdes, skin friction coefficients and the surface temperature distributions are shown both on graphs and tabular form for differenl values of Ihe parameters entering into the problem.
Keywords: Free convection, viscous dissipation, pressure vvork and conduction.
N O M E N C L A T U R E
b Plate thickness T Fluid asymptotic temperamre
Cp Specific heat ïï,v Velocity components along x, y directions
d ll,V
respectively.
Dimensionless velocity components
f Dimensionless stream function x,y Cartesian coordinates
g Acceleration due to gravity x,y Dimensionless Cartesian coordinates
L
Reference length, V ^ ' ^ 1S^'^ Greek Symbol
1 Length o f the plate li Co-efficient o f thennal expansion
N Viscous dissipation parameter W Stream function
P Coupling parameter,
p = {!c^lkXblL)d"'
Fluid and solid thermal conductivities
Pr Prandtl number n Dimensionless similarity variable
T Temperamre p Density o f t h e f l u i d
n Temperamre at outer surface o f the plate
Solid temperamre
e Dimensionless temperamre
M M. Alam, M. A. Alim, M. K. Chowdhmy/Journal of Naval Architecture and Marine Engineering 3(2006) 69-76 1. Introduction
Free convection f l o w is often encountered i n cooling o f nuclear reactors or in the study o f the structure o f stars and planets. The study o f temperaUire and heat transfer is o f great importance to the engineers because o f its almost universal occurrence in many branches o f science and engineering. Although heat transfer analysis is most important for the proper sizing o f fuel elements in the nuclear reactors cores to prevent bumout. The viscous dissipation effect plays an important role in namral convection i n various devices w h i c h are subjected to large deceleration or which operate at high rotational speeds and also in strong gravitational field processes on large scales (on large planets) and in geological processes. The discussion and analysis o f namral convection flows, pressure and viscous stress work effects are generally ignored but here we have considered the effects o f viscous dissipation and pressure work on a namral convection flow along a vertical flat plate with heat conduction. The influence and importance o f viscous stress work effects i n laminar flows have been examined by Gebhart (1962) and Gebhart and MoUendorf (1969). I n both o f the investigations special flows over semi-infinite flat surfaces parallel to the direction o f body force were considered. Gebhart (1962) considered flows generated by the plate surface temperamres, which vary as powers o f ^ (the distance along the plate surface f r o m the leading edge), and MoUendorf (1969) considered flows generated by plate surface temperahires, which vary exponentially i n ^. Zakemllah (1972) has been investigated the viscous dissipation and pressure work effects in axisymmetric namral convection flows. Ackroyd (1974) smdied the stress work effects i n laminar flat plate namral convection flow. Takhar and Soundalgekar (1980) have smdied the effects o f viscous and Joule heating on the problem posed by Sparrow and Cess (1961), using the series expansion method o f Gebhart (1962). Joshi and Gebhail (1981) have shown that the effect o f pressure stress work and viscous dissipation i n some namral convecfion flows. Pozzi and Lupo (1988) smdied the coupling o f conduction w i t h laminar namral convection along a flat plate. Miyamoto et al. (1980) has been investigated the effect o f axial heat conduction in a vertical flat plate on free convection heat transfer.
In the present work, we have investigated the viscous dissipation and pressure work effect on the skin friction and the surface temperamre distribution i n the entire region f r o m leading edge to down stream o f a viscous incompressible flow along a semi-infinite vertical flat plate. The entire thermo-fluid dynamic field resulting f r o m the coupling o f namral convection along and conduction inside the heated plate has been considered. The transformed non similar boundary layer equations goveming the flow together w i t h the boundary conditions based on conduction and convection were solved numerically using the Keller box (implicit finite difference) method, Cebeci and Bradshaw (1984) along w i t h Newton's linearization approximation method in the entire region. We have smdied the effect o f the Prandtl number Pr, the viscous dissipation parameter N and pressure w o r k parameter e on the velocity and temperamre profiles as well as on the skin friction and surface temperamre.
2. Governing Equations of tlie Flow
Steady two dimensional laminar free convection boundaiy layer flow o f a viscous incompressible fluid along one side o f a semi-infinite vertical flat plate o f thickness ' è ' insulated on the edges with temperature Tt, The flow configuration and the coordinates system are shown i n Fig. 1. The mathematical statement o f the basic conservation laws o f mass, momenmm and energy for the steady viscous incompressible flow are:
y.q=0 (1) p{q.V)q = -yP + juV'q-¥F (2)
pCp{q.V)T-{q.V)P = V.{icVT) + M^ (3)
Where q = { l l , v ) , it and V are the velocity components along the X and y - axes respectively, F is the body force per unit volume which is defined as -pg, T is the temperamre o f the fluid i n the boundary layer, g is the acceleration due to gravity, K is the thermal conductivity and Cp is the specific heat at constant pressure and p is the viscosity o f the fluid. I n the energy equation the viscous dissipation and pressure work terms are included. A f t e r introducing Boussinesq approximation,p = p^ [l-fi{T-T_^)] the basic equations (1) to (3) become:
517 dV
M M. Alam, M. A. Alm, M. K. Clwwdhiiiy/Joiirnal of Naval Architecture and Marine Engineering 3(2006) 69-76 _dÏÏ _dïi d^ÏÏ ^ N Upper surface T=Tb Lower ^ surface Ni/' / A |<— interface ll g O ^ , y
Fig.1: Pliysical conflguration and coordinates system
u ~ + v = - + ( )^ -h—
dx dy pc dy^ c dy pC dx (6)
(7) The appropriate boundary conditions to be satisfied by the above equations are
ïi = v = Q at y = 0
IT ^ 0 , T ^ T „ as J 7 ^ 0 0
The temperamre and the heat flux are considered continuous at the interface for the coupled conditions and at the interface we must have
Ic dZ„ dT
kj- dy dy' (8)
Where k, and /c/are the thermal conductivity o f the solid and the fluid respectively. The temperamre To i n the solid as given by Pozzi and Lupo (1988) is
7 ; „ = r ( x , o ) - { r , - r ( j , o ) } ^
b (9)
Where T(x ,0) is the unknown temperamre at the interface to be determined f r o m the solutions o f t h e equations. We observe that the equations (4) - (6) together w i t h the boundary conditions (8) - (9) are non-linear partial differential equations, which have been solved numerically and are described i n the following sections.
3. Transformation of the Governing Equations
Equations (4)-(6) may now be non-dimensionalized by using the following dimensionless dependent and independent variables: X T — TT, yr~ .2/3 d V , 0 = — - , 1 = , r f = / ? ( r , - r j T , - T . g (10) L L L
As this namral convection problem is o f parabolic namre the characteristic length, L has been defined i n terms o f v and g, which are the intrinsic properties o f the system. The reference length along the ' j ' direction has been modified by a factor d" in order to eliminate this quantity f r o m the dimensionless equations and the boundary conditions. Using the above relations (10) the non-dimensional f o r m o f the goveming equations are:
