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THE COLLEGE OF AERONAUTICS
CRANFIELD
THE "TURBOCODE" SCHEME FOR THE PROGRAMMING
O F THERMODYNAMIC CYCLE CALCULATIONS ON AN
ELECTRONIC DIGITAL COMPUTER
by
CoA R E P O R T AERO 198 July 1967
THE COLLEGE O F AERONAUTICS CRANFIELD
T h e " T u r b o c o d e " Scheme for the P r o g r a m m i n g of T h e r m o d y n a m i c Cycle Calculations on an
E l e c t r o n i c Digital Com.puter
by
J . R , P a l m e r , M , A . , C . E n g . , A . F . R . A e . S .
SUMMARY
T h e " T u r b o c o d e " Scheme for p r o g r a m m i n g t h e r m o d y n a m i c cycle
c a l c u l a t i o n s on an e l e c t r o n i c c o m p u t e r is d e s c r i b e d in t e r m s of the F e r r a n t i " P e g a s u s " v e r s i o n . The s t r u c t u r e and g e n e r a l mode of operation of the s c h e m e i s d e s c r i b e d in the main body of the R e p o r t , while d e t a i l s of the m a j o r p r o g r a m s e g m e n t s and t h e i r s p e c i f i c a t i o n s , the method of p r o g r a m m i n g and the method of running a T u r b o c o d e p r o g r a m a r e given in A p p e n d i c e s .
2. B a s i c Concepts 1 2 . 1 R e q u i r e m e n t s 1 2 . 2 B r i c k s and Station V e c t o r s 2 2 . 3 B r i c k Data 4 2 . 4 Engine V e c t o r 4 2 . 5 O t h e r T y p e s of B r i c k 4
3 . The M a s t e r P r o g r a m and Codewords 5 4 . A s s e m b l y and Execution of P r o g r a m 7
5. Conclusions 9 Acknowledgements 9
R e f e r e n c e s 9
Appendix 1 Writing a T y p i c a l M a s t e r P r o g r a m 10 Appendix 2 N o t e s on F u n c t i o n s , Subroutines and B r i c k s 14
Appendix 3 Abbreviated B r i c k Specifications 27
Appendix 4 O p e r a t i n g I n s t r u c t i o n s 41 F i g u r e s 1 - 9
1
-1. Introduction
The operations involved in calculating the performance of a given thermo-dynamic cycle a r e of certain well-defined types, independent of the nature of the particular cycle investigated. Thus the application of an electronic digital computer to such calculations can be greatly facilitated by the provis-ion of a scheme whereby pre-programmed operatprovis-ions can be assembled to form a complete program for analysing the cycle.
This report describes such a scheme, known as "Turbocode", which has been developed for this purpose in the Department of Aircraft Propulsion of the College of Aeronautics, While the scheme described here was developed for use with a F e r r a n t i "Pegasus" computer, and so was written partly in the machine code and partly in the Autocode of that machine, its concepts and methods a r e readily applicable to other types of computer. An Algol 60 version is in the course of development, with particular reference to the College's I . C . T . 1905 computer, and this version will, subject to variations in hardware representation, be adaptable for any Algol-compatible machine with little extra effort. It is intended to supplement the present report with a report on the Algol version as soon as it has been fully developed and tested.
The scheme originated in "Scheme P " , developed for the English Electric "Deuce" computer by Bristol Siddeley Engines Ltd. (ref, 1), whose assistance in the early stages is gratefully acknowledged, but it has since been considerably extended in scope.
2. Basic Concepts 2.1 Requirements
If we consider the calculation of the design-point performance of a simple turbojet in t e r m s of a digital computer (see fig. 1), we find that portions of program are required capable of performing the following
functions:-(a) Data Input,
(b) Calculation of "unit p r o c e s s e s " under the following headings:-(1) Intake;
(2) Compressor; (3) Diffuser;
(4) Combustion Chamber; (5) Turbine;
(6) Jet Pipe; and (7) Propelling Nozzle.
(c) Calculation of "overall p r o c e s s e s " Involving linking the results of two or more unit
processes:-(1) Compressor and Turbine Power Balance;
(2) Compressor and Turbine Rotational Speed Balance;
and unchoked cases, respectively); and
(4) Calculation of Thrust, Specific Fuel Consumption, etc. (d) Results Output.
2.2 Bricks and Station Vectors
In order to make it possible to link the various unit processes in a more or less arbitrary order, it is essential that the corresponding program segments, known as Bricks from their Deuce origins, should follow as
closely as possible a standard format for data and results. Essentially, any process may be thought of as an operator which acts on a set of quantities defining the state of the gas at inlet to the process, thereby computing a corresponding set of quantities defining the state of the gas at outlet. These sets of quantities are known as Station Vectors, in the sense that a vector is an ordered set of numbers, and the unit processes are primarily concerned with evaluating such vectors at various reference planes or stations within the engine.
For air, or for the products of combustion of a given fuel in air, the gas state is completely defined by five quantities,
thus:-(1) fuel-air ratio;
(2) total or static pressure;
(3) total or static temperature, and
(4) and (5) any two of mass flow, velocity and flow area. (Note: If mass flow and area are specified, there are in general two possible velocities, one subsonic and the other supersonic, which are compatible with the given conditions, but the nature of the partic-ular process will usually determine which solution is applicable). Thus a minimal Station Vector would consist of just five elements. However, the particular set of five that is convenient or necessary is not the same in all contexts: consequently, a redundant system of eight elements has been adopted, as
follows:-(1) fuel-air ratio a (non-dimensional) (2) mass flow W (Ib/s)
(3) static pressure p (Ibf/in abs) 2 (4) total pressure P (Ibf/in abs) (5) static temperature t ( K) (6) total temperature T (°K) (7) velocity V (ft/s); and (8) flow area A (ft^),
Provided that sufficient information is given to define at least the
minimal five elements, then the remaining three can always be found by using the familiar
relations:-- 3
(A) the Perfect Gas Equation of State p = Rpt/144
where R = gas constant (ft Ibf/lb K) and p = density (lb/ft ); (B) the Continuity Equation
W = pAV;
(C) the Energy Equation H = h + V^/2g J
"c
where H = f (T,a) and h = f.(t,a) are the total and static enthalpies respectively (C.H.U./lb);
(D) the Isentropic Equation
where it = f (T,o) and ir = f (t,») are functions of the temperature-dependent entropy s (=/ —^—)(ft Ibf/lb K) given by
7r = exp -^=r- ; Bind
(E) the Mach Number Equation M = V/y g -yRt
where-y = f (t,a) is the specific heat ratio (non-dimensional)
It will be noticed that "exact" thermodynamics is implied, in the sense that the specific heat at constant p r e s s u r e , and the enthalpy, entropy function and specific heat ratio that depend on it, a r e functions of temperature and fuel-air ratio, but not of p r e s s u r e . (In particular, dissociation effects are not allowed for).
In practice it is not always necessary or possible to compute the whole of a Station Vector: thus If neither the velocity nor the flow area is known, it is not possible to find the static pressure and temperature from given total values, or vice v e r s a . To cater for this eventuality, we note that each of the eight Station Vector elements is essentially non-negative, and it is therefore convenient to denote any quantity which has not been calculated, or otherwise provided, by a suitable negative number. This is equivalent to a blcink or dash in a written table of values, and permits a simple test for the presence or absence of any particular quantity,
2.3 Brick Data
Although the program for each Brick will define the corresponding thermodynamic process in principle, and although the relevant Inlet Station Vector will define the gas state at inlet to the process, this information is rarely sufficient. One or more items of the Outlet Station Vector may be needed ( e . g . total temperature for a combustion chamber, or static pressure for a nozzle), but in addition certain items which are not part of any Station Vector may be required ( e . g . adiabatic efficiency, pressure ratio, or
pressure loss factor). Such information, qualitatively different from Station Vector material, is known as Brick Data : its nature and the order of
occurrence of the elements cannot be generalised, since it must depend on the particular sequence of Bricks required for any given problem. It is t h e r e -fore the responsibility of the Turbocode programmer to define the Brick Data list he requires in the course of coding his problem.
2.4 Engine Vector
Although the calculation of the Station Vectors throughout the cycle
constitutes the major means whereby successive processes are linked together, and although knowledge of these items is valuable in itself, the linking of processes and the calculation of the "end products" - thrust, specific fuel consumption, etc - requires the generation of intermediate or final results which, like Brick Data, are different in kind from Station Vector material, Such items a r e collectively known as the Engine Vector which, like the Brick Data, is different in nature and layout for each engine cycle, and must be defined by the Turbocode programmer. On occasion, an Engine Vector result generated by one Brick may be required as data by another, so that provision is made for Engine Vector elements to be used as either input or output for a Brick. F u r t h e r m o r e , it is sometimes necessary to add or otherwise man-ipulate Engine Vector (or indeed Brick Data) elements, and a Special Brick (Brick 22) is available for this purpose: typical applications would be the adding of main and bypass gross thrusts, or of main and reheat fuel flows.
The relationship between a Brick and its associated Inlet and Outlet Station Vectors, Brick Data and Engine Vector is portrayed diagrammatically in fig. 2.
2.5 Other Types of Brick
The type of Brick described above is that most frequently needed, and indeed the requirements of the thermodynamic processes associated with such Bricks determines the whole pattern of the Turbocode Scheme. There is,
however, a need for various non-thermodynamic Bricks, covering such functions a s :
-(a) Station Vector Input (Brick 16); (b) Brick Data Input (Brick 15);
(c) Arithmetic on Engine Vector or Brick Data elements (Brick 22); (d) Station Vector Output (Brick 31); and
5
-Evidently the detailed Structure and use of such a Brick depends on its particular function, and so will be described later when the various available Bricks are dealt with.
3. The Master Program and Codewords
In terms of the concepts just defined, we see that in order to program a particular problem the user is provided with a set of Standard Bricks. These must be linked together by a suitable Master Program to form a coherent whole, and in the course of writing this the user must define the elements of Brick Data, and of the Engine Vector, and their order of
occurrence, and must then provide suitable Data Tapes giving Station Vector and Brick Data information to suit.
Since most Bricks follow a set pattern as regards their individual inputs and outputs, the Master Program can readily be formulated in terms of simple coded instructions, known as Codewords. The most general form of Codeword consists of seven elements, each consisting of an unsigned integer, separated from one another by commas, the whole Codeword being terminated by Carriage Return Line Feed (CRLF)
thus:-n, a, b, c, d, e, f CR LF
The elements of the Codeword are normally interpreted as follows:-n = Brick Number, i . e . the referefollows:-nce follows:-number of the Brick which
performs the required function. The system permits the use of Brick numbers in the range 0 to 63 inclusive, although by no means every number in this range has so far been allocated; a = Inlet Station Vector Number: the allocation of Station Vector
Numbers, within the range 0 to 23 inclusive, is largely under the u s e r ' s control, except that Station Vector 0 always refers to free stream (ambient) conditions, and that certain Bricks refer to more than one Outlet Station Vector, in which case all Outlet Station Vectors must be numbered in sequence, starting
with:-b = Outlet Station Vector Numwith:-ber;
c = F i r s t Brick Data Item Number: any further Brick Data Items must follow in sequence. The Brick Data list for the whole program starts at item 0, and there is provision for items numbered up to 63;
d = F i r s t Engine Vector Results Item Number: any further Engine Vector Results Items must follow in sequence. The Engine Vector list for the whole program starts at item 0, and there is provision for items numbered up to 31;
e = F i r s t Engine Vector Data Item Number: this permits reference to a previously calculated Engine Vector Item as data. Certain Bricks require more than one Engine Vector Data Item: since it is not always possible to arrange for these items to be computed or
s t o r e d in s t r i c t s e q u e n c e , a n o n - s t a n d a r d Codeword i n t e r p r e t a t i o n i s used in t h e s e c a s e s , whereby e l e m e n t s b e s i d e s e m a y be used to define additional i t e m s ( s e e , for e x a m p l e . B r i c k 33); and
f = J u m p Codeword N u m b e r . N o r m a l l y the Codewords a r e obeyed in the o r d e r in which they a r e w r i t t e n in the M a s t e r P r o g r a m .
O c c a s i o n a l l y , h o w e v e r , it i s n e c e s s a r y to m a k e a jump (conditional o r unconditional) to a Codeword o t h e r than the next in sequence: the n u m b e r of the Codeword c o n c e r n e d i s t h e r e f o r e written a s element f. F o r t h i s p u r p o s e the Codewords a r e n u m b e r e d in s e q u e n c e f r o m 0, although it m u s t be s t r e s s e d that t h e s e Codeword n u m b e r s (which m a y r a n g e up to 87) a r e not p a r t of the Codewords t h e m s e l v e s , and m u s t not a p p e a r on the M a s t e r P r o g r a m Tape a s punched.
In m a n y c a s e s , not e v e r y item of the Codeword i s needed, in which c a s e t h e c o r r e s p o n d i n g element is written a s z e r o . To allow a s compact a M a s t e r P r o g r a m a s p o s s i b l e , and to r e d u c e the r i s k of e r r o r s due to miscounting long s t r i n g s of z e r o s , it is p e r m i s s i b l e to omit any z e r o s , with t h e i r p r e c e d i n g c o m m a s , that m a y o c c u r at the r i g h t - h a n d end of the Codeword, F o r e x a m p l e
(1) n , 0, 0, 0, 0, 0, 0 C R L F m a y be written a s n CR L F
(2) n , a, b , 0, d, 0, 0 C R L F m a y be written a s n, a, b , 0, d C R L F but (3) n, a, b , 0, 0, 0, f C R L F must be written in full, unless f happens to be z e r o , i . e . u n l e s s the J u m p Codeword N u m b e r i s z e r o , in which c a s e n , a, b C R L F would suffice.
On the o t h e r hand, a few B r i c k s ( e . g . B r i c k s 27 and 34) r e q u i r e m o r e i t e m s to be specified than one Codeword can a c c o m m o d a t e . F o r t h i s p u r p o s e B r i c k 26 is provided: t h i s h a s the effect of introducing a f u r t h e r Codeword which can be used to augment the Codeword i m m e d i a t e l y following, for the benefit of the B r i c k c o r r e s p o n d i n g to t h i s second Codeword.
The M a s t e r P r o g r a m i s n o r m a l l y prefixed by the s t a n d a r d P e g a s u s d i r e c t i v e s D (to punch the Date and S e r i a l N u m b e r ) and N (to punch the p r o g r a m N a m e which follows it, t e r m i n a t e d by at l e a s t two b l a n k s ) . Next c o m e s t h e d i r e c t i v e J 2 0 0 . 0 , which c a l l s in the Codeword Input section of the T u r b o c o d e S c h e m e to r e a d the Codewords which then follow. The last item in the M a s t e r P r o g r a m i s the s e q u e n c e
(6) C R L F
w h e r e 0 is an unsigned i n t e g e r denoting the Codeword n u m b e r (usually 0) at which the M a s t e r P r o g r a m i s to s t a r t o p e r a t i n g once the B r i c k s have been r e a d i n . A t y p i c a l M a s t e r P r o g r a m i s d e s c r i b e d in Appendix 1.
7
-4. Assembly and Execution of Program
Although the user could copy the requisite Bricks onto the same tape as the Master Program, or could select and input the relevant Brick Tapes
manually, this is obviously tedious, inconvenient, and a potential source of e r r o r . Consequently the whole process has been made automatic, its action being best described by following the input and obey procedures for the Master Program, Bricks and Data. A few explanatory notes are added for the
benefit of those unfamiliar with the Pegasus computer, but this is not intended to be a full operator's guide, which is given in Appendix 4.
(a) The main Turbocode Scheme is input. This consists of five main
sections:-(i) the Codeword Input routine, which controls the reading and storage of Codewords;
(ii) the Assembly routine, which reads and stores the requisite Bricks;
(ill) the Codeword Obey routine, which interprets the codewords in the required sequence by calling up the relevant data, entering the corresponding Brick to perform the calculation, and storing the results;
(iv) a set of Subroutines which perform tasks common to a number of Bricks, such as: finding enthalpy change or isentropic pressure ratio for a given temperature change; finding outlet temperature for given inlet temperature and enthalpy change or isentropic pressure ratio; finding any one of mass flow, velocity or area from the other two; finding Mach Number from velocity, or vice versa; finding static conditions and area for given total conditions, mass flow and velocity; and finding static conditions and velocity (subsonic or supersonic as specified) for given total conditions, mass flow and area; and
(v) a number of Function routines, which calculate specific heat (Cp), enthalpy (h) and isentropic pressure ratio (TT) as functions of temperature and fuel-air ratio, and also combustion fuel-medium ratio as a function of inlet temperature and fuel-air ratio and of outlet temperature. These Functions are used by various Bricks and
Subroutines. The Functions and Subroutines are described in detail in Appendix 2.
(b) The Master Program is input. The directives D and N are read and obeyed by Initial Orders, as is the directive J 200.0 to transfer control to Codeword Input. The Codewords are then read, each being packed and stored as a single 39-bit word with suitable numbers of bits allocated to each of the seven elements of the Codeword. At the same time a list is built up of the Brick Numbers called for. When the terminal sequence "(0)" is read, the Entry Codeword Number is stored and control passes to the Assembly routine.
(c) The Bricks Tape is now scanned. Each Brick is preceded by its Number, which is read and compared with the list of Bricks required that was built up during Codeword input. If the particular Brick is needed, it is read In and stored, the corresponding Brick Number being deleted from the list, and
the Brick Number and starting block number of the Brick are punched on the Output Tape, but otherwise the Brick is rejected. As soon as all Bricks (which are stored end-to-end in the order in which they are read) have been input, the computer comes to a stop order without attempting to read the rest of the Bricks Tape. The Bricks a r e punched in decreasing order of frequency of use, in order to keep scanning time to a minimum. If, however, some Brick is called for which is not on the tape, the computer will come to a stop order in a different register. The operator can then identify the missing Brick by reference to the list of Brick Numbers punched out and, if the
missing Brick is genuinely required and has not been called for by a punching e r r o r in the Codeword, can input a separate tape bearing this Brick. When the last Brick required has been input, its final block number is punched on the output tape, so that the operator can check that the available storage capacity has not been exceeded. (The last available block number is 858). Details of the various Bricks are given in Appendices 2 and 3.
(d) While the computer is stopped, the Data Tape is loaded, certain hands witches are set, and the computer restarted. Control now passes to Codeword Obey, which calls up the Entry Codeword (Number 0) specified by the sequence "(0)". The various elements of the Codeword are unpacked and
used to address the various data and results items, and to identify the Brick required, which is then obeyed. The input of data occurs under the control of either Brick 15 (Station Vectors) or Brick 16 (Brick Data), while the out-put of results is controlled by Brick 31 (Station Vectors) or Brick 32 (Engine Vector). As each Brick completes its task, control reverts to Codeword Obey which then calls up the next Codeword in sequence or, if a jump has occurred, the Codeword whose Number is element f of the Codeword just obeyed. This process continues until such time as the data is exhausted, denoted in standard Pegasus fashion by the directive Z on the Data Tape, when a stop order is obeyed, At this point another Data Tape can be loaded and the computer restarted, if desired.
Since various Bricks require to know whether or not particular Station Vector Items have been provided, either as data or as the result of previous calculation, it is essential to restore each Station Vector to its initial state (consisting of "blanks" - actually negative numbers, as described in 2.2 above - or values which have been read as data) after printing out the results for one data point, and before reading fresh data. Also, it is desirable that the amount of fresh data should be minimised, all data items being assumed to be the same as for the previous point unless explicitly altered. To meet these requirements, a second copy is kept of all Station Vectors, in which only the data items appear, and not items subsequently computed. This copying is carried out automatically by Brick 15 as soon as any alterations have been made to a Station Vector. The calculations for a particular data point normally end when the Engine Vector is printed out by Brick 32. As soon as printout has finished, all Station Vectors in use are reset by being overwritten by their second copies: the Master Program is then re-entered at the beginning via the Jump Codeword Number of the Codeword associated with Brick 32.
9
-5. Conclusions
The "Turbocode" Scheme for programming thermodynamic cycle
calculations on an electronic digital computer has been described specifically in terms of the Ferranti "Pegasus" version, though an Algol 60 version is in course of development. The structure and general mode of operation of the scheme is described in the main body of the Report, while Appendices describe in some detail the Functions, Subroutines, and Bricks ( i . e . major program segments) of which the Scheme is built up; they also give detailed information on the method of programming, the Brick specifications and the method of running a Turbocode program on the computer. Further information and copies of the various Program Tapes, may be obtained from the Department of Aircraft Propulsion of the College of Aeronautics.
Acknowledgement
The assistance and encouragement of Mr. B.V. Archer, formerly of the Department of Aircraft Propulsion, in the early stages of planning and programming the Turbocode Scheme is gratefully acknowledged.
References
(1) Bristol Siddeley Engines Ltd. - D . E . U . C . E . Programme No. 11017/1 Scheme P
(2) Fielding, D. and Topps, J . E . C . - Thermodynamic Data for the Calculation of Gas Turbine Performance - Aeronautical Research Council R. & M. 3099
Appendix 1 - Writing a Typical Master Program
This appendix describes the process whereby a Turbocode Master Program is planned and written.
The problem is to find the design-point performance of a single-shaft turbojet, without reheat, having a fixed area convergent propelling nozzle.
The first step is to draw a sketch of the engine (see Fig. 3), and to mark on it the various components and the Stations, numbered in sequence through the engine, at which Station Vectors are to be calculated. Using the list of Bricks available (see Appendix 3), we now write on the diagram the numbers of the Bricks required, aligning them with the stations, or between the pairs of stations, to which they refer. Input Brick numbers are written on the left, output Brick numbers on the right, and Bricks dealing with calculations performed after the Station Vectors have been found are also written on the right. The choice of Bricks and the order in which they occur are largely self-evident, but the following points should be
noted:-(1) The compressor is here defined by its design-point pressure ratio, which requires the use of Brick 2 : had the temperature rise been chosen. Brick 10 would have been used instead.
(2) The compressor work must be calculated, by use of Brick 3, after the compressor calculation has been performed, but before undertaking the turbine calculation (since compressor work is an input data item to the turbine Brick 4): it is therefore convenient to place Brick 3 immed-iately after Brick 2.
(3) Whether Brick 29 (in which the fundamental pressure loss is ignored) is used for the combustor, as here, or Brick 6, which calculates this loss, it is still necessary to allow for frictional pressure loss in the combustor. This is most conveniently done by using Brick 1 (also employed for the intake and jet pipe), which is placed before Brick 29. Since the fundamental loss is not calculated, a suitable allowance should be made for it in selecting the values of the parameters Xp and/or AP of Brick 1.
(4) Since the convergent nozzle Brick 8 assumes isentropic flow, any losses due to the nozzle (other than those taken account of by the discharge and thrust coefficients in Brick 8) are combined with those of the jet pipe in the appropriate use of Brick 1.
(5) Note that the output Bricks, 31 and 32, must occur in that order, since the latter r e s e t s the Station Vectors after output has finished and then jumps back to start a new calculation.
To facilitate the actual coding, printed Program Sheets A (for Code-words) and B (for listing Brick Data and Engine Vector items) are used, as shown in figs. 4a, 4b and 5. These are used as
follows:-(a) On Sheet A (figs 4a, 4b) fill in the Codeword Numbers, Brick Numbers and Inlet and Outlet Station Vectors by referring to fig. 3 .
11
Note that Codewords nos. 0-1 and 11-14 inclusive do not have Inlet and Outlet Station Vectors in the normal sense, so that elements a and b of these Codewords should be left blank at this stage.
(b) Using the Abbreviated Brick Specifications (see Appendix 3), list the various items of Brick Data, Engine Vector Results and Engine Vector Data opposite each Codeword.
(c) On Sheet B (fig. 5) fill in and number the Brick Data and Engine Vector items by copying them in order from Sheet A (the Engine Vector items being copied from the Engine Vector Results Column). (d) On Sheet A, fill in the numbers appropriate to the first Item for
each Codeword in the Brick Data and Engine Vector Results Columns, copying them from Sheet B. Also number each Engine Vector Data Item individually.
(e) The columns c, d, and e for the "standard form" Codewords ( i . e . Codewords nos. 2-10 inclusive) can now be filled in, remem-bering that it is not essential to fill in any right-hand side zeros. Note that the following right-hand side quantities, though significant, are zeros and so have not been filled in: Codeword 2 item a,
Codeword 3 item c. Codeword 5 item d and Codeword 8 item e. (f) Of the "non-standard form" Codewords, only nos. 11-14 require
further additions as shown, in accordance with the requirements of their specifications. It will be noticed that Codeword 13 instructs Brick 31 to print Station Vectors 0-7 inclusive, while Codeword 14 instructs Brick 32 to print Engine Vector items 0-6 inclusive, and then to reset Station Vectors 0-6 inclusive (see remarks below on Data Tape). Item f of Codeword 14 is a significant zero, since it is required to jump back to Codeword 0 to read new data, but is omitted in accordance with the usual convention.
(g) FÜ1 in the heading "D N SIMPLE TURBOJET TEST J200.0" and the ending "(0)" instructing the program to start operating at Codeword 0.
The Program Tape can be punched directly from Sheet(s) A, remember-ing that, apart from the headremember-ing and endremember-ing, only the items in the columns between double vertical lines are actually punched, each item being separated from its neighbours by commas, and each Codeword being terminated by
"Carriage Return, Line Feed" - as noted in the column headings. Figure 6 shows the Program Tape as punched.
In order the prepare the Data Tape, we note firstly that Brick 15 here precedes Brick 16, so that Station Vector Data must precede Brick Data, and secondly that each set of data in either category must be terminated by the characters "-1 CRLF". Figure 7 shows a Data Tape as punched. The following points should be noted:
(a) Each Station Vector item is a triad of signed numbers -viz: S.V. number. Item number, Item value - terminated by
CRLF. (see Specification of Brick 15). (b) The items given fall into three
groups:-(1) The minimum number of items ( a o . Wo, po, to and Vo) necessary to define S.V.O. (Brick 30 computes the rest). The Turbine Inlet Temperature T .
Velocities at planes 1, 2, 3, 5 and 6 - these are necessary if the corresponding areas and static pressures and temp-eratures are needed, but otherwise can be omitted. The velocities at planes 4 and 7 are not given, since these a r e computed by Bricks 29 and 8 respectively (see specifications). (c) Each Brick Data item is a pair of signed numbers - viz: Item
number. Item value - terminated by CRLF. (see specification of Brick 16).
(d) Only one set each of S.V. Data and Brick Data are here shown, so that only one point will be calculated, but any number of further sets could have followed, subject to the
following:-(1) S.V. Data must always precede Brick Data.
(2) Only these items which have changed from the previous point need be stated, all other quantities being automatically reset to their previous values.
(3) Nevertheless, something must always be provided for each of Bricks 15 and 16 to read: if no items have been changed, merely the terminating "-1 CRLF" suffices. (In the unlikely event of no change of item in either category - i . e . a
repetition of the previous point - two successive "-1 CRLF" ' s would be needed).
(4) In accordance with Standard Pegasus practice, the Data Tape ends with the directive "Z", which causes the computer to stop. It can be restarted when a fresh Data Tape has been loaded, if necessary.
(5) Name Sequences - i . e . the directive "N", followed by any sequence of characters not including two or more successive blanks, followed by at least two blanks - can be used freely. (e) Obviously the numbering of the various items must agree precisely
with the numbers allocated on the program sheets. It is not, however, essential for the items to be punched in the same order, though there is little reason not to do so.
(f) As noted earlier, the question of how many Station Vectors need resetting must be dealt with. Obviously one solution is to reset them all, but this is unnecessarily time-consuming, so the general rule is - reset only up to the last Station Vector for which one or more items are given on the Data Tape (in this case S.V.6) - see Data Tape (fig. 7) and Codeword 14(fig. 4b). Any higher-numbered Station Vectors must necessarily be recomputed afresh for each
(2) (3)
13
-point.
Finally, fig. 8a shows the output resulting from running this Master Program with the given Data. The following points may be
observed:-(a) Each "N" directive (including that on the Autocode master tape) causes the name following it to be punched.
(b) The " D " directive on the Master Program causes the Data and Serial Number to be punched.
(c) As each Brick is read in, its number and first block address in the main store is punched. After all Bricks have been read, the number of the last block used is punched.
(d) Since Brick 31 precedes Brick 32, the Station Vectors are punched before the Engine Vector.
(e) Fig. 8b shows a second section of output for the same program and data, for which Station Vector Output (apart from the printing of the S.V. nos. and areas for those S . V . ' s whose areas are known) has been inhibited by depressing handswitch 13 on the console.
Appendix 2 - Notes on Functions, Subroutines and Bricks
While it is not essential for the user to know the mode of operation of the Bricks, nor of the Subroutines and Functions on which most of them depend, in order to write and use Turbocode Master Programs successfully, it may be useful and instructive to describe briefly how these basic constit-uents of the scheme work. Not every Brick is described, since some are so essentially simple in conception that their specifications (see Appendix 3) can provide all the necessary information.
A. 2.1 Functions
A . 2 . 1 . 1 . Specific Heat
The specific heat of air at constant pressure i s , at moderate pressures and in the absence of dissociation, a function only of temperature. In the range 200 - 2000 K, the empirical Cp - temperature curve can be approx-imated to an adequate order of accuracy by a fourth-order polynomial in
4
X = —„„„ , where T is the temperature in K, thus:- C„ = E a.x
900 ^ PA . „ 1
•"• 1=0
Another similar polynomial gives the specific heat of the stoichiometric ^ ' i
products of combustion, thus:- C = E a.x ^S 1=0 '
Then for any fuel-air ratio a between zero and the stoichiometric value a 1 + «H
^, we have Cp = Cp^ + j - ^ . —j—§• (Cp - Cp^).
A simple routine known as SPHT, evaluates first Cp , then ^.(Cp -s
for given T, and finally Cp for given a,
Since the fuel assumed is the Standard Kerosine proposed by Topps, (ref. 2) which has the property that the molecular weight of its products of combustion is equal to that of air at all fuel-air ratios, its gas constant — (equal to the difference between the specific heats at constant pressure and at constant volume) is fixed at a value of 0,0685522 C . H . U . / l b . giving
•p
Cv = Cp - — and thence the specific heat ratio y = Cp/Cv. J
A . 2 . 1 . 2 . Enthalpy
Since the increment of enthalpy dh = CpdT, the enthalpy relative to a given datum is obtained by term-by-term integration of the specific heat polynomials, leading to
5 • 5 .
1 I I
h , = E b.x and h^ = E b, x , whence at fuel-air ratio a ^ 1=0 ^ S 1=0 '
15
-a 1 + Ola
h = h , + T-^ . 5- (h^ - h j . A 1 + a Og S A
T h e s e e x p r e s s i o n s a r e evaluated by a routine (Called ENTH) s i m i l a r to t h a t used for Cp, only the coefficients and the n u m b e r of t e r m s being
different.
A. 2 . 1 . 3 . I s e n t r o p i c P r e s s u r e Ratio
T h e i n c r e m e n t of t e m p e r a t u r e - d e p e n d e n t entropy i s given by ds = C p d T / T , so that the value of s ° r e l a t i v e to a given datum can be obtained by dividing the t e r m s of the specific heat polynomial by T and then i n t e g r a t i n g , giving
^ 4 . 4 ^
s^ = E c.x + c^ log T and s „ = E c.'x + c' log T , whence at f u e l - a i r
A i 5 ^ e S . . 1 5 ^ e
1=0 1=0 o o a 1 + a s / O o .
r a t i o a s = s . + . (s^ - s . ) . A 1 + a Og ' S A
In p r a c t i c e the t e m p e r a t u r e d e p e n d e n t entropy is used to r e l a t e t e m p -e r a t u r -e and p r -e s s u r -e chang-es a c r o s s i s -e n t r o p i c p r o c -e s s -e s , in a c c o r d a n c -e with the r e l a t i o n R , ^ 2 o o
J log^ P^ = ^2 • ^ •
P ^ J ( s ° - sO) J s ° J s ° o r - = exp = exp — ^ exp —
JB° so that it is useful to work in t e r m s of the function TT = exp —^ ,
^ 2 '^2
f r o m which ^r- = — . P h y s i c a l l y , TT i s the i s e n t r o p i c p r e s s u r e r a t i o n e c e s s a r y to r e a c h the given t e m p e r a t u r e from the r e f e r e n c e t e m p e r a t u r e (273.16 K).
T h e routine f o r evaluating TT (called P R E S ) , i s l a r g e l y the s a m e in p r i n c i p l e a s t h o s e for Cp and h, a p a r t from the evaluation of the l o g a r i t h m i c t e r m , and the final exponentiation.
A . 2 . 1 . 4 . Combustion F u e l - A i r Ratio
It m a y r e a d i l y be shown that if fuel is burnt at 100% efficiency in a m e d i u m (which is not, in g e n e r a l , p u r e a i r , but the p r o d u c t s of an e a r l i e r combustion at f u e l - a i r r a t i o a. ), causing a t e m p e r a t u r e r i s e from T^^^ to TQU^,
then the f u e l - m e d i u m r a t i o «„„+ ( i . e . m a s s of added fuel divided by m a s s of medium) is given by
a , = Ah, / E . C . V . out M
w h e r e Ah = i n c r e a s e in enthalpy of m e d i u m between T. and T ^ and M in out
E . C V . = Effective Calorific Value = True Calorific Value of fuel + inlet enthalpy of fuel + — X enthalpy of air at T^^^
s
- (1 + — ) X enthalpy of stoichiometric products at T +
8
Consequently the E . C . V . is a function of T ^ for a given fuel comp-osition and fuel temperature, and represents the gross calorific value less the heat necessary to raise the stoichiometric products through the temper-ature interval. The relevant routine (called FUEL) uses the ENTH function to evaluate Ah,,, and E . C . V .
M
It can be shown that the final fuel-air ratio is given by
Of. + a . (1 + a , ) .
in out in A . 2 . 2 Subroutines (S)
(a) Sl_ evaluates the change of enthalpy between two given temperatures at given fuel-air ratio by direct use of the ENTH function.
(b) S2^ is the inverse of SI, finding the outlet temperature for given values of inlet temperature, fuel-air ratio and enthalpy change. The ENTH function gives the inlet enthalpy, and thence the outlet enthalpy. The outlet temperature appropriate to this enthalpy value is found iteratively, the enthalpies corresponding to the various outlet temperature values being compared with the known value. The starting approximation is T = given h/Cp (T inlet) and the iteration formula is
T , = T - h(Tn) - given h Cp(Tn)
tNote: here and subsequently the notation Cp(T), h(T), etc, denotes that these quantities are functions of the bracketed argument.]
(c) S2a is a modification of S2 to find the temperature corresponding to a given absolute enthalpy and fuel-air ratio.
(d) S4 evaluates the isentropic pressure ratio between two given temperatures at given fuel-air ratio by direct use of the PRES function.
(e) S5^ is the inverse of S4, finding the outlet temperature for given values of inlet temperature, fuel-air ratio and isentropic pressure ratio. The PRES function gives the inlet value of TT, and thence the outlet value. The outlet temperature appropriate to this w value is found iteratively, the ir values corresponding to the various out-let temperature values being compared with the known value. The starting approximation ^^ ^ ^ 273.16 (given IT) ^ / " ^ ^ P ^"^ "^^^^
17
-(f) S7, S14 and SI 5 solve the continuity equation W = 144pAV/Rt to find V, A o r W r e s p e c t i v e l y for given values of the o t h e r two q u a n t i t i e s , and of p and t .
(g) S8 and S9 solve the Mach N u m b e r equation M = Y/Jg^y (t)Rt for M o r V r e s p e c t i v e l y for given v a l u e s of the o t h e r of t h e s e q u a n t i t i e s and of t , using the SPHT function to find Cp and thence
7-(h) S l l finds the c r i t i c a l ( i . e . sonic) v a l u e s of p , t, V and A, given a, W, P and T . T h i s involves i t e r a t i n g on t to find v a l u e s of V = y 2 g ^ J t h ( T ) - h(t)} and of sonic velocity a = Jg^yïtyRt which a r e equal. The s t a r t i n g approximation is tg = T - 0 . 0 1 K,
y' -4
n ^^ and the i t e r a t i o n f o r m u l a is t . = t +
n+l ' n g JCp(t ){7(t ) + 1] • ^ n n
(i) SI 2 and SI 7 find p , t , and V ( s u p e r s o n i c and subsonic r e s p e c t i v e l y ) for given a, W, P , T and A. A p r e l i m i n a r y u s e of S l l e n s u r e s that the given a r e a i s not l e s s than the c r i t i c a l a r e a ( o t h e r w i s e a solution is i m p o s s i b l e ) . The value of t is then found i t e r a t i v e l y to give a calculated a r e a equal to the given v a l u e , using the r e l a t i o n s
p = P7r(t)/7r(T).
V = y 2 g c J f h ( T ) h(t)} and A = WRt/144pV. The s t a r t i n g a p p r o x -imation i s t = 200°K (SI2) o r t = T - 0.01°K (S17), and the
o o i t e r a t i o n f o r m u l a i s
1 - given A/A(tn) t . = t
""' " JCp(tn){-/^
(j) 316^ finds p , t and A for given a, W, P , T and V. The s t a t l c -t o - -t o -t a l en-thalpy change is v2/2o. J , and S2 is used -to find -t from
sc
t h i s , enabling p = P7r(t)/n^(T) to be found. S14 then d e t e r m i n e s A. A . 2 . 3 B r i c k s (B)
A. 2 . 3 . 1 Input (B15 and B16)
Input of Data i s controlled by B15 and B16, whose specifications give all n e c e s s a r y information.
A. 2 . 3 . 2 Ouput (B31 and B32)
Output of R e s u l t s i s controlled by B31 and B32, whose specifications give a l l n e c e s s a r y information.
A. 2. 3 . 3 . O t h e r N o n - T h e r m o d y n a m i c B r i c k s (B22 and B26) (a) B22 p e r m i t s a r i t h m e t i c manipulation of B r i c k D a t a , Station V e c t o r and Engine V e c t o r i t e m s , a s d e s c r i b e d in its specification.
(b) B26 i s effectively a dummy b r i c k whose p u r p o s e i s to provide an e x t r a codeword to extend the information contained in the codeword i m m e d i a t e l y following it. T h i s i s useful for c e r t a i n B r i c k s which r e q u i r e unusually l a r g e a m o u n t s of d a t a , from r a n d o m l y d i s t r i b u t e d p a r t s of the s t o r e . F o r f u r t h e r information s e e specifications of B26, B27 and B34.
A. 2. 3 . 4 . Duct F l o w , Mixing, e t c . (Bl , B 5 , B 9 ,B24 and B30)
(a) B l allows for r e l a t i v e o r absolute changes of m a s s flow a n d / o r t o t a l p r e s s u r e in adiabatic flow, such a s o c c u r in i n t a k e s , jet p i p e s , combustion c h a m b e r dlffusers and i n t e r -c o m p r e s s o r d u -c t s . Conditions at the inlet and outlet Station V e c t o r s (suffices a and b , r e s p e c t i v e l y ) a r e r e l a t e d by the equations: Orb = a a Tb = Ta Wb = X>,,Wa - AW W Pb = XpPa - AP w h e r e X ^ , AW, X p a n d A P a r e given a s B r i c k D a t a , If Vj, is specified, SI6 finds p ^ , tb and Ab, while if Ab i s specified, SI7 finds pb, tb and Vb ( s u b s o n i c ) .
(b) B5 d e a l s with the f r i c t i o n l e s s p a r a l l e l mixing of flows a and b , leading to the mixed flow (b + 1). T h e m a s s flow, a r e a , f u e l - a i r r a t i o and t o t a l t e m p e r a t u r e a r e found by s i m p l e c o n s e r v a t i o n equations: Wb+1 = Wa + Wb Ab+1 = Aa + Ab b ( T b , i ) = Wah(Ta) . W^MTb) Wb+1 = W a a a WjjOb b+1 i + ö a l+Ob
19
-Fb+1 '^"^ ~- Wb+1 - Fb+1
S2a i s then used to find Tb+l from «b+l ^^^ h ( T b + i ) . To find the velocity, s t a t i c p r e s s u r e and s t a t i c t e m p e r a t u r e , the m o m e n t u m c o n s e r v a t i o n equation m u s t be s a t i s f i e d , v i z :
-(^O^^fl^^ + I44pb^i A b , i ) = ( ^ + 1 4 4 p a A a ) + ( ^ + 144pbAb).
BC B e 6 C
T h i s i s a c c o m p l i s h e d by i t e r a t i o n on Vjj^j^: s i n c e 2
h(tjj^^) = h(Tb+l) - Vb+i / 2 g c J , S2a can be used to find %+i and the above m o m e n t u m equation to find Pb+1 • S7 then finds ^ b + 1 ' which i s substituted for the p r e v i o u s value if they do not a g r e e sufficiently c l o s e l y . F i n a l l y ,
Pb+i = Pb+1 'r(Tb+i)/»r (tb+l) i s c a l c u l a t e d .
(c) B9 d e a l s with adiabatic t o t a l p r e s s u r e l o s s in a p a r a l l e l duct in t e r m s of a t o t a l p r e s s u r e l o s s coefficient
P - Ph
•5^ ^ , given a s B r i c k D a t a , a, W. T and A a r e unchanged ^ a " Pa
a c r o s s t h e duct, and pb, tb and Vb (subsonic) a r e found by S I 7 . (d) B24 m e r e l y computes intake m o m e n t u m d r a g Xp = WoVo/gp. (e) B30 i s designed to " f i l l - i n " m i s s i n g i t e m s in a Station Vector if sufficient i t e m s a r e available t o define i t . Specific-a l l y , Specific-a Specific-and e i t h e r P Specific-and T o r p Specific-and t m u s t be given, t o g e t h e r with any two of W, V and A. The calculation i s effected by using a p p r o p r i a t e s u b r o u t i n e s among S2, S4, S7, S14, SI 5, S16 and S I 7 . T h i s B r i c k i s p a r t i c u l a r l y useful for finding f r e e s t r e a m conditions.
A . 2 . 3 . 5 . C o m p r e s s o r (B2, B 3 , BIO and B12)
(a) B2 c a l c u l a t e s outlet conditions from an adiabatic c o m p r e s -sion p r o c e s s for which the inlet Station Vector and the total p r e s s u r e r a t i o P b / P a and the polytropic efficiency rvjol (Brick Data i t e m s ) a r e given, the r e l e v a n t equations b e i n g ;
% = Wb = Pb = = " a = Wa = P a X P b / P a
Tb is found using S5 at the equivalent isentropic pressure ratio (Pb/Pa) ^ ° The remaining elements of the outlet Station Vector are calculated by SI 6 or SI 7 according as Vb or Ab is given.
(b) B3 determines the work done in an adiabatic process AH = Wbh(Tb) - Wah(Ta)
(c) BIO is similar to B2, but with the total temperature rise ATab given instead of the total pressure ratio. Consequ-ently Tb = Ta + ATab- S4 calculates the isentropic total
pressure ratio P b ' / P a , whence the true ratio Pb/Pa = (Pb'/Pa) ï'^ In other respects the calculation proceeds as in B2.
(d) B12 is similar to BIO, the work input AH being given instead of the total temperature r i s e . The enthalpy rise is AH/Wa, from which S2 finds T^. The rest of the calculation is as in BIO.
A. 2. 3.6 Turbine (B4 and B27)
(a) B4 calculates outlet conditions from an adiabatic turbine for which the inlet Station Vector, work output (consisting of a portion AH required to drive a compressor - an Engine Vector Item - and a portion 6H required to drive auxiliaries and other loads, and to make good losses - a Brick Data Item) - and adiabatic efficiency Had ^^^ given. The equations are:
"b = «a Wb = Wa
Ahab = - (AH + 6H)/Wa. whence T^, from S2. S2 is also used to find the isentropic outlet temperature Tb associated with the isentropic enthalpy drop Ahab/lad' ^^'^ ^^ is then used to find Pb/Pa- The remaining items are then found in a similar manner to those for a compressor (see B2 above). For use in subsequent off-design calculations
- Ahab/Ta is computed as an Engine Vector quantity. (b) B27 deals with two adiabatic turbines in series in a turboprop engine, with provision for the cases of a two-spool engine with power offtake from the L . P . turbine (type 1) and for a free-turbine type (type 2). Station Vectors a, b, (b+1) denote H . P . inlet, L . P . inlet and L . P . outlet respectively. Besides the inlet Station Vector, the outlet static pressure and velocity must be specified. Then we
have: 21 have:
-S5
% = "b+1 = *^a Wb = Wb+i = Wa
finds the i s e n t r o p i c outlet s t a t i c t e m p e r a t u r e tJ . , from which SI finds t h e a s s o c i a t e d t o t a l - t o s t a t i c enthalpy drop { h ( T J - h ( t | ^ i ) i . N o w i h ( T j ^ ^ ^ ) - h ( t t , ^ i ) l = v J + i / 2 g ^ J . and t h i s quantity is a s s u m e d to be unaffected by t u r b i n e l o s s e s , enabling t h e i s e n t r o p i c t o t a l - t o - t o t a l enthalpy d r o p [h(Ta)-h(Tb+i)i to be found, and t h e n c e , by multiplication by the o v e r a l l adiabatic efficiency, the actual d r o p . U s e of S2 and S4 d e t e r m i n e s the v a l u e s of T^j^_j and P b + l . and S16 then finds P b + i . tb+l ^^'^ -^b+1
T h e conditions at plane b , and the quantity - A h a b / T a a r e now computed in the s a m e way a s in B4. We then find
the L . P . t u r b i n e g r o s s work output AHj, j^+x = Wb{h(Ta)-h(Tb+l)-6hab]: s u b t r a c t i n g from t h i s the c o m p r e s s o r and a u x i l i a r y p o w e r s
AH and ÓHT p (both z e r o in the c a s e of type 2) gives the net work output A H ^ p net, from which the L . P . power follows from S H P L P = A H i , p net X J / 5 5 0 . F i n a l l y ,
-Ahb^b+l/'^b ~ " ^ ^ b b + l / W b T b is calculated a s an Engine Vector i t e m .
A . 2 . 3 . 7 Combustion C h a m b e r (B6, B29 and B39)
(a) B6 c a l c u l a t e s the outlet f u e l - a i r r a t i o and fundamental t o t a l p r e s s u r e l o s s for f r i c t i o n l e s s c o n s t a n t a r e a " c o n s t a n t p r e s s u r e " heat addition up to a specified outlet t o t a l t e m p e r -a t u r e Tjj. Thus Ab = A-a, -and or out i s found using the F U E L function, leading to Wb = Wa(l + a out), ob = a a + (1 + aa)a out and the fuel flow (Engine Vector item) F = 3600 a out
Wa/rjb-A check i s now m a d e to e n s u r e that the t e r m p e r a t u r e r i s e demanded does not exceed the t h e r m a l choking l i m i t . The outlet s t a t i c t e m p e r a t u r e tj^* c o r r e s p o n d i n g to choking is found i t e r a t i v e l y a s follows; from a s t a r t i n g value tb = T a , the SPHT function finds Cp(tb ), whence -y^tb ). By m o m e n t u m c o n s e r v a t i o n , pb* = (pa + WaVa/144gcAa)/[-y(tb*) + 1^, and S7 then finds Vb* and S9 finds Mb*. If Mb* is not equal to unity, a new value of tb is found from the i t e r a t i o n formula
If the value of tb e x c e e d s 2000°K (the upper limit of the t h e r m o d y n a m i c d a t a ) , t h e r m a l choking cannot o c c u r , and t h e r e i s no f u r t h e r i t e r a t i o n .
Once tjj* (being l e s s than 2000°K) h a s been found, S2 * * *2
finds T^j from t^ and Vb l2g^J: if the value of Tj^ r e q u i r e d e x c e e d s T, , a symbol denoting " t h e r m a l choking" i s p r i n t e d , and exit o c c u r s to the J u m p Codeword. In the a b s e n c e of choking, the a c t u a l outlet conditions a r e found by i t e r a t i o n on Vb: using a s t a r t i n g value of 1000 f t / s , S2 c a l c u l a t e s
2
tb f r o m Tb and Vb / 2 g J , and m o m e n t u m c o n s e r v a t i o n gives WaVa WbVb
pb = pa + 7~rr~T~ - —~~ ;— and a calculated velocity Vb' 144g^A^ 144gcAb
i s then found by S7. If t h e s e v a l u e s of Vb do not a g r e e , the l a t e r value r e p l a c e s the e a r l i e r and t h e c y c l e i s r e p e a t e d . F i n a l l y , S4 i s used to find P, .
(b) B29 i s a s i m p l e r a l t e r n a t i v e to B6 ignoring the fundam-ental t o t a l p r e s s u r e l o s s . Consequently no question of t h e r m a l choking a r i s e s , and Pj^ is taken a s equal to Pa- S17 then finds the v a l u e s of pb, tb and
Vb-(c) B39 was w r i t t e n for a s p e c i a l application, and i s not likely to be much u s e d . It is the equivalent of B29 for constant volume h e a t i n g , the p r i n c i p a l difference being that the s t a n d a r d equation for t h e outlet f u e l - m e d i u m r a t i o a out = A h j ^ / E . C . V .
[Ah]yi - R(Tb - T a ) / J \ i s modified to a out
l^E.C.V. + R T b / J i A . 2 . 3 . 8 Heat E x c h a n g e r (B37 and B38)
T h e c a l c u l a t i o n of an a i r - t o - a i r heat exchanger i s p e r f o r m e d jointly by B37(cold side) and B38(hot s i d e ) . The Station V e c t o r s a r e a and (a+1) for the cold s i d e , and b and (b+1) for the hot s i d e .
(a) B37 . We have a^^^^^ = «a, Wa+i = Wa, Aa+1 = Aa and Pg^^j^ = Xp Pa - ^ P Q (analogously to B l ) . Now initially the hot s i d e inlet t e m p e r a t u r e Tj^ i s unknown, so for the f i r s t i t e r a t i o n we take T^ = Ta+x = Ta- On subsequent i t e r a t i o n s we have h(Ta+x) " h(Ta) = nthlh(Tb) - h(T^)J, w h e r e rjth i s the t h e r m a l r a t i o ( B r i c k Data i t e m ) , and from t h i s quantity and T a S2 c a l c u l a t e s T ^ ^ ^ .
23
-(b) B 3 8 . We have ab+x= «b- Wb+i = Wb,Ab+x = Aa and Pb+1 = A.pjj Pb - A P H - On e n t e r i n g the B r i c k , Tb will have been calculated by an e a r l i e r b r i c k (usually B4) and in g e n e r a l will not a g r e e with the value most r e c e n t l y used by B 3 7 . Consequently exit o c c u r s to the J u m p Codeword c o r r e s p o n d i n g to B37, which p r o c e e d s to r e c a l c u l a t e using the new v a l u e of T ^ .
When the values of T. a g r e e , the i t e r a t i o n c e a s e s , and we find h(Tb) - h(Tb+l) = ^ ^ h(Ta+l) - HTa.)\, which S2 u s e s with Tb to find T b + l - F i n a l l y , S17 c a l c u l a t e s pb+1, tb+l and Vb+1.
A . 2 . 3 . 9 P r o p e l l i n g Nozzle (B8, B23 and B25)
(a) B8 d e a l s with the design point calculation of a s i m p l e convergent nozzle in i s e n t r o p i c flow, for which the inlet Station Vector and the outlet s t a t i c p r e s s u r e (equal to the f r e e s t r e a m value Po) a r e given. Then orb = o^a. Wb = Wa, Pb = P a and T^ = Ta- It i s initially a s s u m e d that the nozzle is unchoked, so that S5 c a l c u l a t e s tjj from Tb and P o / P b - SI then finds the a s s o c i a t e d enthalpy drop Ahb, frona
I
which V]3 = .^^g^JAh^ . S8 then c a l c u l a t e s Mb: if t h i s i s not g r e a t e r than unity, the nozzle i s indeed unchoked, pb = Po. and S14 c a l c u l a t e s the t h e o r e t i c a l a r e a A b ' . Then the t r u e a r e a Ab = A b ' / C j ) , w h e r e Cjy i s the d i s c h a r g e coefficient ( B r i c k Data I t e m ) , the t h e o r e t i c a l g r o s s t h r u s t X Q = WbVb/gc. and the t r u e g r o s s t h r u s t X Q = X Q C-p, where C T is the t h r u s t coefficient (Brick Data Item), a r e c a l c u l a t e d .
If, h o w e v e r , M^, i s found to exceed unity (on the now fallacious a s s u m p t i o n that pb = P Q ) . the nozzle is choked, and it i s n e c e s s a r y to i t e r a t e on tb to find the exit conditions. F r o m a s t a r t i n g value tb = T b / 1 . 1 2 5 , SI finds the t o t a l t o -s t a t i c enthalpy d r o p Ahjj, whence Vb =j2g^Ah^, and S8 c a l c u l a t e s Mj^. If Mb i s not equal to unity, the i t e r a t i o n formula tbjj^j = t b ^ X Mb^ ' is used to find a new value of t b . When the c o r r e c t value of tb h a s been found, SI6 finds pb and A b ' . The r e s t of the calculation p r o c e e d s a s for the
unchoked case, except that now
X Q ' = WbVb/gc + 144Ab(pb "
Po)-(b) B23 correspondingly deals with the design point calc-ulation of a convergent-divergent nozzle in isentropic flow. Station Vectors a, b and (b+1) refer to inlet, throat and exit respectively. The calculation of exit conditions, and of X Q (for a given value of Pb+1 - Po^ proceeds exactly as for the unchoked convergent nozzle of B8, except that Mb+i is not constrained to be subsonic. If Mb+i is found to be not greater than unity, the nozzle is in fact convergent, and exit from the Brick occurs at this point after printing an appro-priate symbol denoting "convergent nozzle".
Otherwise throat conditions are calculated by the method adopted In B8 for the choked case.
(c) B25 calculates the off-design behaviour of a convergent-divergent nozzle, assuming that either (i) Ab/Ab+i (Brick Data item) or (ii) Ab+l (Station Vector item) is fixed at a known value. Since the alternative possibilities a r e rather involved, it may be helpful to refer to Fig. 9 in reading this description.
It is first assumed that the nozzle is choked, and the throat conditions are calculated by the method of B8 (choked case)(point A, fig. 9). Since this gives a value for A^, the value of A.^+1 = Ab 7 Axj/A]3^_j^ can be found in case (1). In case (ii), it is necessary to check that the given value of Ab+l is not less than Ab, otherwise A.\^^-i is too small for the given flow: if this should be so, a symbol is printed to denote "Ab+l < Aj^" and exit occurs to the Jump Codeword.
The next stage i.. to calculate the exit conditions appro-priate to the known value of Ab+l for subsonic Vb+i (Point B). Thus ob+l = o-a, Wb+i = Wa, Pb+l = Pa and Tb+x = Ta, and S17 finds Pb+1. tb+x and Vi^+x. In case (ii), if this value of Pb+l is less than po, the nozzle cannot accommodate the flow with the given a r e a , so a symbol denoting "Pb+i < Po" ^^
printed and exit occurs to the Jump Codeword. In case (i) with Pb+l ^ Po' *^^ nozzle is in fact unchoked ( i . e . the actual
operating point is above Point B in fig. 9) and we recalculate with PXJ+X ~ Po' using S5 to find tb+i and SI to find Ahb+i,
25
-whence Vb+i = J 2g„J Ahj^^x and calculating A^^j from SI4 (Point C). Then Aj^ = Ab+l X Ab/Ab+l and SI 7 recalculates p^, tjr, and Vb (subsonic)(Point D).
If, however, the subsonic value of Pb+1 is not l e s s than p , this last phase of the calculation is repeated for the known value of Ab+l for supersonic Vj^^x ( i - e . using S12 instead of S17)(Point E). We now assume a normal shock at the exit plane, whose outlet conditions a r e given by Station Vector (b+2). Then ob+2 = a^, W^+g = Wa. Tb+2 = Ta and Ab+2 = Ab+l. We iterate on Vb+2 to find exit conditions
consistent with momentum conservation in the same way as for B6 (Point F ) . K the resulting value of Pb+2 ^ PQ ( i - e . if the actual operating point is below Point F in fig. 9), there is no shock in the divergence, and the calculation is complete.
The remaining possibility (that Pb+2 ^ Po) implies that there is indeed a shock in the divergence (though not n e c e s s -arily at exit), so that Pb+l "" PQ- SI2 is therefore used to find Pb+l • *b+l and Vb+x (supersonic) consistent with the known value of Ab+l.
In all c a s e s , the calculation concludes by evaluating X Q ' = g^ -I- 144 Ab+l (Pb+1 - Po) and X Q = X Q ' C p .
A. 2.3.10 Various Bricks for Completing the calculation (B33, B34, B35 and B36
(a) B33 is very brief, since it merely calculates the net thrust and specific fuel consumption of a turbojet from the equations
Xj^ = X Q - Xp and s . f . c . = F/Xj^.
(b) B35 is used in simplified turbojet off-design calculations to find the turbine inlet t e m p e r a t u r e . F o r previously calculated or given values of compressor work AH, auxiliary work öH, turbine m a s s flow W^, and turbine enthalpy drop ratio -Ahab/Ta (assumed constant at the design-point value), the brick calculates
Ahab = (AH + 6H)/Wb and Ta = - Ahab r " Ahab/Ta- If this
value does not agree with the value previously used (by the combust-ion brick), the new value of Ta replaces the previous one and a Jump Exit occurs to the codeword corresponding to the combustion brick.
(e) B36 is used in simplified turbojet off-design calculations to find the inlet air m a s s flow, assuming the propelling nozzle (of given throat area Aa, which is a Brick Data item) to be choked. If the value of A calculated by the nozzle brick does
a
not agree with the given value, the previously used value of WQ is scaled according to the equation
new WQ = old WQX given Aa/calculated Aa
and a Jump Exit occurs to the Codeword appropriate to the Brick in which WQ is first used.
(d) B34 finds the off-design bypass ratio for a turbofan (bypass) engine in which the bypass and turbine exhaust
s t r e a m s mix. Station Vectors a, b, (b+1) denote bypass duct exit, ( L . P . ) turbine inlet and turbine outlet (before actual mixing occurs) respectively. It is necessary for Vb+x to be specified.
Since mixing requires that Pb+x " Pa' conditions at plane (b+1) a r e found for a known p r e s s u r e ratio P b + l / P b ' i" the same manner as for B27. F o r given auxiliary work öH, the "free" output of the turbme is AH = ^^+i Ahb^b+1 ' "^*^' Now at an e a r l i e r stage in the calculation, the proportions ^a. ^b of the fan m a s s flow (such that X^ + X]-, = 1) passing through the gas generator and bypass duct respectively will have been calculated or specified. Then if AH is the work input to the fan, power balance between fan and turbine r e q u i r e s that the value of Xj^ be scaled according to the equation.
Xbn+l = Xbn X AH/AHj^^^ leading to the new value Xa^+l = 1 - ^h^+x •
If either of X^, X^ falls outside the range 0 to 1, it is impossible to obtain a solution (because the turbine exit p r e s s u r e is below the fan exit p r e s s u r e even at zero bypass ratio), so a symbol denoting "no solution" is printed and a Jump Exit o c c u r s .
Otherwise, the Engine Vector items bypass ratio Xa/Xb and turbine enthalpy drop ratio Ahb,b+1/Tb a r e c a l c -ulated, all gas generator m a s s flows and a r e a s a r e scaled in the ratio Xbjj^_x/Xbj^, as is the main fuel flow, while the bypass duct m a s s flow, area and fuel flow (if any) a r e scaled in the ratio
Xan+l/Xan 27 Xan+l/Xan -Appendix 3 - A b b r e v i a t e d B r i c k Specifications L i s t of B r i c k s A v a i l a b l e B r i c k T i t l e 1 T r a n s f o r m a t i o n of M a s s F l o w and T o t a l P r e s s u r e 2 C o m p r e s s i o n (given T o t a l P r e s s u r e Ratio) 3 Work Done 4 Single T u r b i n e 5 F r i c t i o n l e s s C o n s t a n t - A r e a Mixing 6 C o n s t a n t P r e s s u r e C o m b u s t i o n with F u n d a m e n t a l P r e s s u r e L o s s 8 C o n v e r g e n t N o z z l e 9 C o n s t a n t - A r e a Duct T o t a l P r e s s u r e L o s s 10 C o m p r e s s i o n (given T o t a l T e m p e r a t u r e R i s e ) 12 C o m p r e s s i o n (given Work Input)
15 Station V e c t o r Input 16 B r i c k Data Input
22 A r i t h m e t i c on E n g i n e V e c t o r , Station V e c t o r s and B r i c k Data 23 O p t i m u m C o v e r g e n t - D i v e r g e n t N o z z l e
24 Intake M o m e n t u m D r a g
25 Off-Design C o n v e r g e n t - D i v e r g e n t N o z z l e
26 S u p p l e m e n t a r y C o d e w o r d (for u s e with B r i c k s 27 and 34) 27 Two T u r b i n e s in s e r i e s
29 C o n s t a n t P r e s s u r e C o m b u s t i o n without F u n d a m e n t a l P r e s s u r e L o s s 30 C o m p l e t i n g Station V e c t o r
31 Station V e c t o r Output
32 E n g i n e V e c t o r Output and Station V e c t o r R e s e t 33 T u r b o j e t Net T h r u s t and Specific F u e l C o n s u m p t i o n 34 D e t e r m i n a t i o n of Off-Design B y p a s s R a t i o
35 D e t e r m i n a t i o n of T u r b o j e t Off-Design T u r b i n e Inlet T e m p e r a t u r e 36 D e t e r m i n a t i o n of Off-Design Intake M a s s F l o w
37 A i r - t o - A i r Heat E x c h a n g e r (Cold Side) 38 A i r - t o - A i r Heat E x c h a n g e r (Hot Side) 39 C o n s t a n t V o l u m e C o m b u s t i o n
Brick 1 : Transformation of Mass Flow and Total P r e s s u r e
Description: Given Sa, either Vb or Aj, (optional) and the factors X , A ^ , Xp, and A^, calculates S (or part of it) using the equations
% = «a Wb P b T b = ^w ^a = ^P Pa = Ta - AW - A P
P. , tv and A, or V. a r e calculated from continuity if Vjj or A^j given. F o r m of Codeword: 1, a, b, c
S.V. : a^. Wa, P a , T^ Vb or A-^ (optional)
2 B . D . : X (dimensionless), A^f (Ib/s), Xp (dimensionless), Ap (Ibf/in ) E . V . Data : nil
E . V . Results : nil
Brick 2 : Compression (given Total P r e s s u r e Ratio)
Description: Given Sa, either V- or Aj^ (optional), ^ul^a. ^^'^ "^pol' calculates Sb (or part of it).
F o r m of Codeword: 2, a, b, c S.V. : a^. Wa. Pa- Ta
Vjj or Ajj (optional)
B . D . : P b / P a (dimensionless), Hpol (dimensionless: given as a fraction, not as a percentage)
E . V . Data : nil E . V . Results : nil Brick 3: Work Done
29 -Form of Codeword: 3, a, b , 0, d S.V. : a a , Wa. Ta. a b , Tb B . D . : nil E . V . Data : nil E . V . Results : AH(CHU/s) Brick 4 : Single Turbine
Description: Given Sa, either Vb or A^ (optional), compressor work AH. auxiliary work öH. and rjad. calculates S, (or part of it) and -Ah/Ta-F o r m of Codeword: 4, a, b, c, d, e
S.V. : a^. Wa. Pa, T^ Vjj o r A^ (optional)
B . D . : 6H(CHU/s), 17 ad (dimensionless: given as a fraction, not as a percentage).
E . V . Data : AH(CHU/s)
E . V . Results : -Ah/Ta(CHU/lb°K)
Brick 5 : Frictionless Constant-Area Mixing
Description: Given Sa and Sb, calculates Sb+l assuming frictionless constant-a r e constant-a mixing.
Form of Codeword: 5, a, b
S.V. : « ^ . W^, Pa. Ta, Va. A^ " b ' ^^b' Pb' Tb- Vb. Ajj B . D . : nil
E . V . Data : nil E . V . Results : nil
Remarks : In allocating S.V. N o s . , it is Important to number those of one of the inlet s t r e a m s (Sb) and of the mixture (Sb+l) consecutively.
Brick 6 : Constant P r e s s u r e Combustion with Fundamental P r e s s u r e Loss Description: Given Sa. T{j and combustion efficiency rjb. calculates Sb. fuel
flow F and thermal choking temperature Tb . If given T^ exceeds Tb . latter is printed on a new line and Jump Exit o c c u r s .
F o r m of Codeword: 6. a, b, c, d, 0, f S.V. : Oa. Wa. Pa, Ta- Va. Aa. T^
B . D . : rib (dimensionless - given as a decimal fraction, not as a percentage) E . V . Data : nil
E . V . Results : F(lb/h) Brick 8 : Convergent Nozzle
Description: Given Sa, PQ (ambient), discharge coefficient C Q and thrust
coefficient Crp, calculates Sj^ and gross thrust X Q , assuming an isentropic convergent nozzle, F o r m of Codeword : 8, a, b , c, d S.V. : PQ, a a . Wa. P a . Ta B . D . : Cjj, C-p (both dimensionless) E . V . Data : nil E . V . Results : X Q (Ibf)
Brick 9 : Constant-Area Duct Total P r e s s u r e Loss
Description: Given Sa and p r e s s u r e loss factor AP/(Pa - Pa). calculates Sjj. F o r m of Codeword: 9, a, b, c
S.V. : a^, p^, P^ B . D . : A P / ( P ^ - p^) E . V . Data : nil E . V . Results : nü
Brick 10 : Compression (given Total Temperature Rise)
31
-Sjj (or part of it).
F o r m of Codeword: 10, a, b , c S.V. : aa, W^, P a . T
Vjj or A^j (optional)
B . D . : ATab(deg C), n nol (dlïnensionless: given as a decimal fraction, not as a percentage)
E . V . Data : nü E . V . Results : nil
Brick 12 : Compression (given Work Input)
Description: Given S . either Vj^ or Aj^ (optional). AH and I p o i , calculates Sb (or part of it)
F o r m of Codeword: 12, a, b, c, 0, e S.V. : a a . W^. P ^ . Ta
Vjj or A, (optional)
B . D . : n Dol (dimensionless: given as a decimal fraction, not a s a percentage) E . V . Data : AH (CHU/lb)
E . V . Results : nil
Brick 15 : Station Vector Input
Description: Reads S.V. items from data tape on Reader A and stores them, also making a duplicate copy for subsequent resetting by Brick 32. Missing items in any S.V. automatically set equal to a small negative number, to enable parts of bricks concerned with calculating p, t, V and A to be bypassed if essential data is not provided.
Each item consists of three signed n u m b e r s :
-(1) Integer denoting S . V . n o . , terminated by Sp (or CRLF); (2) Integer denoting item no. within S.V. ( a = 0 , W = l , p = 2,
P = 3, t = 4, T= 5, V = 6, A = 7), terminated by Sp (or CRLF); (3) Number denoting value to which item is to be set, terminated by
Sp (or CRLF). List of items is terminated by "-1 C R L F " . F o r m of Codeword: 15
Ë . D . : nil E . V . Date : nil E . V . Results : nil
Remarks : Since starting S.V. values a r e reset at the end of each cycle, for Second and subsequent cycles it is necessary to punch only those items which a r e to be changed. If no alterations a r e required, only the terminal " - C R L F " is needed.
Brick 16 : Brick Data Input
Description: Reads B . D . items from data tape on Reader A and stores them. Each item punched as two signed numbers, each terminated by Sp or CRLF, of which first is B . D . Item No. and second its value. List of items is terminated by "-1 CRLF" F o r m of Codeword : 16 S.V. : nil B . D . : nil E . V . Data : nil E . V . Results : nU
Remarks: B . D . items are r a r e l y over-written by any brick ( exceptions being given in the appropriate specifications); thus for second and subsequent cycles it is usually necessary to punch only such items as a r e to be altered. If no alterations a r e required, only the terminal "-1 CRLF" is needed.
Brick 22 : Arithmetic on Engine Vector, Station Vectors and Brick Data Description: This Brick is provided to make possible simple arithmetic
oper-ations on Engine Vector Items, and also t r a n s f e r s of items between the Engine Vector and a Station Vector or Brick Data. Element c denotes the operation required, and elements a, b and d the operands, in accord-ance with the following
scheme:-c = 0: E.V.j^ X E.V.13 to E . V . ^ c = 1: E . V . a / E . V - b to E.V.^j c = 2: E . V . ^ + E.V.ij to E . V . ^ c = 3: E . V , ^ - E . V . j j to E.V.^j c = 4: - E . V . a to E . V . j j c = 5: B . D . ^ to E . V . ^
